Levell I Book 5

SchweserNotes'" for the CFA· Exam2014 Fixed Income, Derivatives, andAlternative Investments

rz-: I{ A P LAN SCHOOL OF PROFESSIONAL\!.) AND CONTINUING EDUCATION

BOOK 5 - FIXED INCOME, DERIVATIVES,AND ALTERNATIVE INVESTMENTS

Reading Anignmenu and L:aming Outcome Statemcnu 3

Study Seuion IS - Fixed Income: Buic COnccpu ..........•.......•...............•.....•......•... 9

Study Senion 16 - FIXed Income: An..lysu of Risk 79

Self-Test - Fixed Income Investments 137

Study Seuion 17 - Derivatives ..........•...................................•......•..............•.....• 142

Study Session 18 - Alternative Investments ..................................................•..... 230

Sdf-Tcst - Derivatives and Alternative Investments ......................................•..... 255

Formulu 258

IDdex ..•................•........................................................•.......................•.....•...... 260

020 13 Kaplan, Inc. ~1

SCHWESERNOTES'" 2014 CFA LEVEL I BOOK 5: FIXED INCOME.DERIVATIVES. AND ALTERNATNE INVESTMENTS

02013 Kaplan. Inc. All rights reserved.

Published in 2013 by Kaplan. Inc.

Printed in the United Sl2tes of America.

ISBN: 978-1-4277-4909-3/1-4277-4909-4PPN: 3200-4010

If.bi. book docs no, haY<,he hologram with the K.tplan Seln...:l<rlogo on .he bock <OY<r.i,,..,.discribured without permission of Kaplan Scbwcsu, a Division of Kaplan. Ine., and is in direct viola~ionof global copyright 1.1"". Your wi.aD« in PUl'Juinc potcntill v1olaron of this Jaw i. ,rcltly apprttiltcd.

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Ccn&in material, contained within this text arc the copyrightnl property of CFA Institute. Thefollowing i•• he (Opyrigb. disdo.u", for these ... ccriah, ·Cop>ori&h', 2013. CFAI•• ti.ucc. Reproducedand «publi.hed hom 2014 Leunin, Outeome S.. teme.... Le",II. II. and III '1uc"ion. from CFA'"Procnm M.. criaI •• CFA Inni""e S,udard. of Pcof... io.a1 Conduce. and CFAIn.tiallc. GlobalInvcltmCftt Performance Standards with permission (rom CfA In'titute. All Risht, Ra~d.·nne materials Play not be eopied without written permission from the author. The unauthorizedduplication of thel< note. i. a .,jol.. ion or global copyright law, and the CFA In"i,ul< Code of Ethic••Your 1"litanCe in punuins potential violator, of thi' law iJ ~atly appr«iatcd.

Disclaimer: The Sch~scr NotCi should be used in conjunction with the original Radin" as act forthby CFA In"i"'te in their 201. CFALc..11 Study Guide. The infOrmacioncon.ained in these Notelcovers topics contained in the reaclings referenced by CFA Institute and is betieeed to be accurate.Howcw:r. their acc:uncy c.a.nftOt be guuant~ nor i. any warra.nty COIIYCyt"d as to your ultimate examJuccns. The authors of the referenced rndin,p have not endorsed or 'PO~lOmi the" Notn.

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READING ASSIGNMENTS ANDLEARNING OUTCOME STATEMENTS

TINfollDwinl mau,i,,/ is a uvi~w 0111NFix~d Income, De,ilNJliwl. and Alumaliv~lnw,tmtnr, p,inripus tksip~d 10aJJ,t1S th</<aminl outeom« staumtnts Itt forth '"CF-AImtinur.

STUDY SESSION 15I

Reading Assignments

Eqlliry and Fix<d Incem«, CFA Program Level I 2014 Curriculum. Volume 5 (CFAInstitute, 2013)

52. Fixed-Income Securities: Defining Elements53. Fixed-Income Markets: Issuance, Trading, and Funding54. Introduction to Fixed-Income Valuation

page 9page 27page 41

STUDY SESSION 16Reading AssignmentsEqlliry and Fixed lncom<, CFA Program Level 12014 Curriculum, Volume 5 (CFAInstitute, 2013)

55. Understanding Fixed-Income Risk and Return56. Fundamentals of Credit Analysis

page 79page 108

STUDY SESSION 17

Reading AssignmentsD<,ivaliws andAlt<matiw lnvntmtnts. CFA Program Level 12014 Curriculum.Volume 6 (CFA Institute, 2013)

57. Derivative Markets and Instruments58. Forward Markets and Contracts59. Furures Markets and Contracts60. Option Markets and Contracts61. Swap Markets and Contracu62. Risk Management Applications of Option Strategies

page 142page 149page 165page 178page 206page 220

STUDY SESSION 18

Reading Assignment>Dtrivatiws and Alttrnativ~ Investments; CFA Program Level I 2014 Curriculum.Volume 6 (CFA Instirute, 2013)

63. Introduction to Alternative Investments page 230

02013 Kaplan, Inc.

Book 5 - FIXtd incom e, [krivalivc:s, and A1.. rnative InV<SlmonuIUadins Auignmonu ",d L<amiJlg OutCOme S.... men ..

LEARNING OUTCOME STATEMENTS (LOS)

Tb« CF-AInstitutt uarning OuttrJm, Stattm,nlJ a" lisua b,u,w. 7Mu a" Ttptattt/ in ttlchtDpicTtvi,w; hlJWlv,r, th, IJrtitT mal haw bun ,""ng,a in IJrti" to gtt a bttttr fit with thi

jllJW ef th, r,vi.w.

STUDY SESSION 15

Tbe topical cow"'g' corrtlplJn4s with thi following CF-AInstitutt assign.a r,aJing:52. FiJa:d-lncome Securities: Defining Elements

The candidate should be able to:a. describe the basic features of a fixcd-income security. (page 9)b. describe functions of a bond indenture. (page 11)c. comparc affirmative and negative covenanrs and identify examples of each.

(page 11)d. describe how legal. regulatoty. and tax considerations affect the issuancc and

trading of fixed-income securities. (page 12)e. describe how cash flows of fixed-income securities arc structured. (page 15)f. describe contingency provisions ,.frecting the timing andlor nature of cash flows

of fixed-income securities and identify whether such provisions benefit theborrower or the lender. (page 19)

The tDpi,al tlJvt"'g' (()rr'SplJn4swith the following CF-AInstitute assign.a r,aJing:53. Fixed-Income Masla:u: Issuance. Trading. and Funding

The candidate should be able to:a. describe classifications of global fixed-income markets. (page 27)b. describe the usc of interbank offered rates as reference rates in floating-rate debt.

(page 28)c. describe mechanisms available for issuing bonds in primary markets. (page 29)d. describe secondary markeu for bonds. (page 30)e. describe securities issued by sovereign governments. non-sovereign governments.

governmcnt agencies. and supranational entities. (page 30)f. describe types of debt issued by corporations. (page 32)g. describe short-term funding alternatives available to banks. (page 34)h. describe repurchase agreements (repos) and their importance to investors who

borrow shon term. (page 34)

Tbe tlJPual (()vt"'~ corr.spDnJs with thi following CF-AInstitute assignea mlaing:S4. Introduction to Flxed-Inccme Valuation

The candidate should be able to:a. calculate a bond's price given a market discount rate. (page 41)b. identify the relationships among a bond's price. coupon rate. maturity. and

market discount rate (yield-to-maturity). (page 43)c. define spot rates and calculate the price of a bond using spot rates. (page 45)d. describe and calculate the flat price. acerued interest. and the full price of a

bond. (page 46)e. describe matrix pricing. (page 48)f. calculate and interpret yield measures for fixed-rate bonds. floating-rate narcs.

and moncy market instruments. (page 50)g. define and compare the spot curve. yield curve on coupon bonds. par curve. and

forward curvc. (page 57)

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Book 5 - F",«i Income, Derivadves, and A1,trnati, .. InvesunenuRndlng As.igDmtnu ""d uaming Ou,comt S,a'trutnu

h. define forward rates and calculate spot rates from forward rates. forward ratesfrom spot rates. and the price of a bond using forward rates. (page 59)

i. compare, calculate. and interprer yield spread measures. (page 63)

STUDY SESSION 16I

TJu topic,," "',,"4ge cormponJs with tINflllDwing CFA Institut« 4Ssigntd ,..ading:55. Undentanding Fixed-Income Risk and Return

The candidate should be able to:a. calculate and interpret the sources of return from investing in a fixal-rate bond.

(page 79)b. define. calculate. and interpret Macaulay. modifial. and effective durations.

(page 85)c. explain why effectiVl:duration is the most appropriate measure of interest rate

risk for bonds with embedded options. (page 89)d. explain how a bond's maturity, coupon, embedded options. and yield level affect

its interest rate risk, (page 90)e. calculate the duration of a portfolio and explain the limitations of portfolio

duration. (page 90)f. calculate and interpret the moncy duration of a bond and price value of a basis

point (PVBP). (page 91)g. calculate and interpret approximate convexity and distinguish between approxi-

mate and effective convexity. (page 93)h. estimate the percentage price change of a bond for a specified change in yield,

giVl:n the bond's approximate duration and convexity. (page 95)I. describe how the term structure of yield volatility affects the interest rate risk of

a bond. (page 96)j. describe the relationships among a bond's holding period return, its duration,

and the investment horizon. (page 96)k. explain how changes in credit spread and liquid affect yield-to-maturity of a

bond and how duration and convexity can be used to estimate the price effect ofthe changes. (page 98)

The topical co~"agt cormponJs with lINflllDwing CFA 11IItitutt 4Ssigntd Ttading:56. Fundament:als of Cn:dit Analysis

The candidate should be able to:a. describe credit risk and credit-related risks affecting corporate bonds. (page 108)b. describe seniority rankings of corporate debt and explain the potential violation

of the priority of claims in a bankruptcy proceeding, (page 109)c. distinguish between corporate issuer credit ratings and issue credit ratings and

describe the rating agency practice of "notching". (page I 10)d. explain risks in relying on ratings from credit rating agencies. (page 111)e. explain the components of traditional credit an:alysis. (page 112)f. calculate and interpret financial ratios used in credit analysis. (page 114)g. evaluate the credit qu:ality of a corporate bond issuer and a bond of that issuer,

given kcy financi:al ratios of the issuer and the industry. (page I )8)h. describe factors that inAuence the level and volatility of yield spreads. (page 120)i. calculate the return impact of spread changes. (page 120),. Explain special considerations when cv:a.Iuatingthe credit of high yield,

sovereign, and municipal debt issuers and issues. (page 123)

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Book 5 - FIXtd Income, [kriwlives, and A1ternaliv< Inv<Slm<nuIUadins Auignm.nu ",d Uaming OUlCOmeS.... m.nu

STUDY SESSION 17

The tIIpicIII CIlIIt'"gt CII"t1plln4s with tht following CF-AImtitutt IISligntd ,,"ding:57. Derivative Marltet. and Instrument.

The candidate should be able to:a. define a derivative. and distinguish between exchange-traded and over-the-

counter derivatives. (page 142)b. contrast forward commitments with contingent claims. (page 142)c. define forward contracu, futures contracts, options (caUs and puu), swaps, and

credit derivatives, and compare their basic characteristics. (page 143)d. describe purposes of, and controversies related to, derivative markets. (page 144)e. explain arbitrage and the role it plays in determining priccs and promoting

market efficiency. (page 144)

The tilpiCIIICIlIIt"'gt ((I"tJPIln4s with the following CF-AInuisute IISsigned ,,"ding:58. r'Orwani Markell and Contraet.

The candidate should be able to:a. explain delivery/settlement and default risk for both long and short positions in

a forward contract. (page 149)b. describe the procedures for settling a forward contract at expiration, and how

tcrmination prior to expiration can affi:et credit risk. (page 150)c. distinguish betwccn a dealer and an end user of a forward contract. (page 151)d. describe characteristics of equiry forward contracts and forward contracu on

%cro-coupon and coupon bonds. (page 152)e. describe characteristics of the Eurodollar time deposit market, and define

UBOR and Euribor. (page 154)f. describe forward rate agreements (FRAI) and calculate the gain floss on a FRA.

(page 155)g. calculate and interpret the payoff of a FRA and explain each of the component

terms of the payoff formula. (page 155)h. describe characteristics of currency forward contracts. (page 157)

The tIIpielll ((I1It"'gt ((I"tSpllnas with the following CF-AInstitute tlSligned ,,"ding:59. Futurcs Marlten and Contracts

The candidate should be able to:a. describe the characteristics of futures contracts, (page 165)b. compare futures contracts and forward contracts, (page 165)c. distinguish between margin in the securities markets and margin in the futures

markeu, and explain the role of initial margin, maintenance margin, variationmargin, and settlement in futures trading, (page 166)

d. describe price limiu and the process of marking to market, and calculate andinterpret the margin balance, given the previous day's balance and the change inthe futures price. (page IG8)

e. describe how a futures contract can bc terminated at or prior to expiration.(page 170)

f. describe characteristics of the foUowing rypes of futures contrac ts : Treasury bill,Eurodollar, Treasury bond. stock index, and c·urrency. (page 171)

Pagc6 02013 Kaplan. Inc.

Book5 - F",«i Income. Derivadves,and A1ternadv. InvesunenuRnding Aslipmonu and uaming Outcomo S,*,o,uonu

Tbe topic.1 col!n.g~ co"ttponds with tM fllu,wing CFA lnstitut« iUsit;Mduuing:60. Option Marktts and Contracts

The candidate should be able to:a. describe call and put options. (page 178)b. distinguish between European and American options. (page 179)c. define the concept of moneyncss of an option. (page 180)d. compare exchange-traded options and over-the-counter options. (page 181)e. identify the types of options in terms of the underlying instruments. (page 181)f. compare interest rate options with forward rate agreements (FRAs). (page 182)g. define interest rat. caps.lloors. and collars. (page 183)h. calculate and Interpret option payoffs and explain how interest rat. options

differ from other types of options. (page 185)I. define intrinsic value and time value. and explain their relationship. (page 186)j. determine the minimum and maximum values of European options and

American options. (page 189)k. calculate and interpret the lowest prices of Europcan and American calls and

puts based on the rules for minimum valu es and lower bounds. (pag. 190)I. explain how option prices arc affected by the exercise price and the time to

expiration. (page 194)m.• xplain put-call parity for European options. and explain how put-call parity is

related to arbitrage and the construction of synthetic options. (page 195)n. explain how cash lIows on the underlying asset afTcct put-call parity and the

lower bounds of option prices. (pagc 197)o. determine the directional effi:ct of an interest rate change or volatility change on

an option's price. (page 198)

Tbe topic.1 COl!fflIg~cormponds with tM fllu,wing CFA Instituu iUsigntd rtuing:61. Swap Markets and Contraets

The candidate should be able to:a. describe characteristics of swap contracts and aplain how swaps are terminated.

(page 207)b. describe. calculate. and interpret the payments of currency swaps. plain vanilla

ineerese rate swaps. and equity swaps. (page 208)

The topic.1 col!n.g~ co"ttponds with tb« fllu,wing CFA Instituu iUsigntd rtuing:62. Risk Management Applications of Option Strategies

The candidate should be able to:a. determine the value at expiration. the profit. maximum profit. maximum loss.

breakeven underlying price at expiration. and payoff graph of the strategiesof buying and selling calls and puts and determine the potential outcomes forinvestors using these strategies. (page 220)

b. determine the value at expiration. profit. maximum profit. maximum loss.breakeven underlying price at expiration. and payoff graph of a coveredcall strategy and a protective put strategy. and explain the risk managementapplication of each strategy. (page 224)

02013 Kaplan. Inc.

Book 5 - FIXtd Income, [krivalivcs, and A11<tnauvt Invesr meetsIUadins Auignmonu IUIdUamiAg OUlcomo Slalomonu

STUDY SESSION 18

The topiclII CDUtrllgtCD"t1pDn4s with 1M follDwing cr~ImtilUft IISligntd ,,"ding:63. Introduction to Alternative Investments

The candidate should be able to:a. compare alternative investments with traditional investments. (page 230)b. describe categories of alternative investments. (page 230)c. describe potential benefits of alternative investments in the context of portfolio

management. (page 231)d. describe hedge funds. private equity. real estate. commodities. and other

alternative investments. including. as applicable. strategies, sub-categories.potential benefits and risks. fcc structures, and due diligence. (page: 232)

e. describe issues in valuing. and calculating returns on. hedge funds. privateequity, real estate, and commodities. (page 232)

f. describe. calculate. and interpret management and incentive fees and net-of-feesreturns to hedge funds. (page 244)

g. describe risk management of alternative investments, (page 246)

Pagt 8 02013 Kaplan. Inc.

The followiJag is a rn-icwofthe fixed Income BalK Concepu principlel dc-signed to .ddrns the lcuniogoutcome lutemenu Jet fOM by CFA Institute. TfUl topic il 1.110covered in.:

FIXED-INCOME SECURITIES: DEFININGELEMENTS

S.udy S••• ion 15

ExA.\I Focus

Here your focus should be on leaming the basic characteristics of debt securities and asmuch of the bond terminology as you can remember, Key items art: the coupon structureof bonds and options embedded in bonds: call options. put options, and conversion (tocommon stock) options.

BOND PRICES, YIELDS, AND RATINCS

There are two important points about fixed-income securities that we wiU developfurther along in the Fixed Income study sessions but may be helpful as you read thistopic review.

• The most common type of fixed-income security is a bond that promises to makea series of interest payments in fixed amounts and to repay the principal amountat maturity. When market interest rates (i.e., yields on bonds) inc",lu, the valueof such bonds aurtlUts because the present value of a bond's promised cash flowsdecreases when a higher discount rate is used.

• Bonds arc rated based on their relative probability of default (failure to makepromised payments). Because investors prefer bonds with lower probability ofdefault, bonds with lower credit quality must offer investors higher yields tocompensate for the grt:ater probability of default. Other things equal, a decrease ina bond', rating (an increased probability of default) will decrease the price of thebond, thus increasing its yield.

LOS 52.a: Describe the basic features of a fixed-income security.

CFA~ Prt1f.'llmCurriculum, Volume 5, pagt 300

The features of a fixed-income security include specification of:

• The issuer of the bond.• The maturity date of the bond.• The par value (principal value to be:repaid).• Coupon rate and fre:que:ney.• Currency in which payments will be:made.

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Study Sessioo 15Cros$-~ft~oce to CFA lrutiwte Assigntd ~adin8 '52 - Ftstd-loCODltSecuritits: Dtfioiog Eltmtnu

Issuers of Bonds

There are several types of entities that issue bends when they borrow money. including:

• Corporations_ Often corporate bonds arc divided into those issued by financialcompanies and those issued by nonfinancial companies.

• Sovereign national go..,mmenu_ A prime example is U.S. Treasury bonds, butmany countries issue sovereign bonds.

• Nonsovneign gcm:rnmenu. Issued by gcm:rnment entities that arc not nationalgovern menu. such as the state of California or the ciry of Toronto.

• Quasi-govcrnmcot entities. Not a direct obligation of a country's government orcentral bank. An example is the Federal National Mongage Association (Fannie Mac).

• Supranational entities. Issued by organizations that operate globally such as theWorld Bank. the European Investment Bank. and the International Monetary Fund(IMF).

Bond Maturity

The maturiry date of a bond is the date on which the principal is to be repaid. Once abond has been issued. the time remaining until maturiry is referred to as the term tomaturiry or tenor of a bond.

When bonds arc issued, their terms to maturity range from one day to 30 years or more.Both Disney and Coca-Cola have issued bonds with original maturities of100 years. Bonds that have no maturity date arc called perpetual bonds. They makeperiodic interest payments but do not promise to repay the principal amount.

Bonds with original maturities of one year or less arc referred to as money marketsecurities. Bonds with original maturities of more than one year arc referred to as apicalmarket securities.

Par Value

The par value of a bond is the principal amount that will be repaid at maturity. The parvaluc is also referred to as the fi/(~ velu«; mil"'"" vllllI~. mJnnptilJn 1IIt11l~.or principalvllllI~ of a bond. Bonds can have a par value of any amount. and their prices arc quotedas a percentagc of par. A bond with a par value of $1.000 quoted at 98 is selling for$980.

A bond that is selling for more than its par value is said to be trading at a premium topar; a bond that is selling at less than its par value is said to be trading at a discount topar; and a bond that is selling for cxaedy its par value is said to be trading at par.

Coupon Payments

The coupon rate on a bond is the annual percentage of its par value that will be paid tobondholders. Some bends make coupon interest payments annually. while others makesemiannual. quarterly, or monthly payments. A $1.000 par value semiannual-pay bond

J>.gc:10 02013 Kaplan. Ine,

Study Session ISCrou-Rd'erenc< 10 CFA Institule Assigned ReadUlg 'S2 - Fixed-Income Securities: Defining Elements

with a 5% coupon would pay 2.5% of $1,000, or $25, cnty six months. A bond with afixed coupon rate is called a plain vanilla bond or a conventional bond.

Some bonds pay no interest prior to maturity and arc called zero-coupon bonds or purediscount bond s, Pur« JiStDU1l' refers to the fact that these bonds are sold at a discountto their par value and the interest is aU paid at maturity when bondholders receive thepar value. A 10-ycar, $1,000, zero-coupon bond yielding 7% would sell at about $500initially and pay $1,000 at maturity. We discuss various other coupon structures later inIhis topic review.

Currencies

Bonds arc issued in many currencies. Sometimes borrowcrs from countries withvolatile currencies issue bonds denominated in euros or U.S. dollars to make themmore snrscdve to a wide range investors. A dual-currency bond makes coupon interestpayments in one currency and the principal repayment at maturity in another currency.A currency option bond gives bondholdcrs a choice of which of two currcncics thcywould like to receive their payments in.

LOS 52.b: Describe functions of a bond indenture.

LOS 52.c: Compare affirmative and negative covenants and identify examplesof each.

CFA® Program Currjrulum, Vo/Umt 5, pag~ 306

The legal conuact between the bond issuer (borrower) and bondholders (lenders) iscalled a trust deed, and in the United States and Canada, it is also often referred to asthe bond indenture. The indenture defines the obligations of and restrictions on theborrower and forms the basis for all future transactions between the bondholder and theissuer,

The provisions in the bond indenture arc known as (ollt1la1lts and include both 1ltgari",rollt1la1lts (prohibitions on the borrower) and ajJirmariv~ (ollt1la1ltJ (actions the borrowcrpromises to perform).

Negativt: covenants includc restrictions on assct sales (thc company can't sell assetsthat have been pledged as collateral), negative pledge of collateral (the company can'tclaim that the same assets back several debt issues simultaneously), and restrictionson additional bcrrowings (the company can't borrow additional money unless certainfinancial conditions arc mer),

Negativc covcnants serve to protect the interests of bondholders and prevent the issuingfirm from taking actions that would increase the risk of default. At the same time, thecovenants must not be so restrictive that thcy prevent the firm from taking advantagc ofopportunities that arise or responding appropriately to changing business circumstances.

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Study Se";"n 15Cross-lUft",nce to CFA I",titult Assi&ned lUading '52 - Fu.td·incomt Securities: Dtfining Eltmtnu

Affirmatiw: covenants do not typieally restrict the operating decisions of the issuer.Common affirmative covenants are to make timely interest and principal payments tobondholders. to insure and maintain assets. and to comply with applicable laws andregulations.

LOS 52.d: Describe how legal, regulatory, and tax considerations affect theissuance and trading of fixed·income securities.

CF.A® Prognzm Curr;<IIlum. VDlumt 5. pagt 314

Bonds are subject to diEkrent legal and regulatory requirements depending on wherethey are issued and traded. Bonds issued by a firm domiciled in a country and alsotraded in that country's currency are referred to as domestie bonds. Bonds issued bya firm incorporated in a foreign country that trade on the national bond market ofanother country in that country's currency arc referred to as foreign bonds. Examplesinclude bonds issued by foreign firms that trade in China and arc denominated in yuan.which are called pll""" bomb, and bonds issued by firms incorporated outside the UnitedStates that trade in the United States and are denominated in U.S. dolws, which arecalled YAnktt bonds.

Eurobonds arc issued outside the jurisdiction of anyone country and denominated ina currency diEkrent feom the currency of the countries in which they arc sold. They aresubject to less regulation than domestic bonds in most jurisdictions and were initiallyintroduced to avoid U.S. regulations. Eurobonds should not be confused with bondsdenominated in euros or thought to originate in Europe, although thcy can be both.Eurobonds got the "euro" name because they were first introduced in Europe. and mostarc still traded by firms in European capitals. A bond issued by a Chinese firm that isdenominated in yen and traded in markets outside Japan ·...ould fit the definition of aEurobond. Eurobonds that trade in the national bond market of a country other thanthe country that issues the currency the bond is denominated in, and in the Eurobondmarket. arc referred to as global bonds.

Eurobonds arc referred to by the currency they arc denominated in. Eurodollar bonds arcdenominated in U.S. dollars, and eutoyen bonds arc denominated in yen. The majorityof Eurobonds are issued in bearer form. Ownership of bearer bonds is evidenced simplyby possessing the bonds, whereas ownership of registered bonds is recorded. Bearerbonds may be more attractive than registered bonds to those seeking to avoid taxes.

Other legal and regulatory issues addressed in a trust deed include:

o Legal information about the entity issuing the bond.o Any assets (collateral) pledged to support repayment of the bond.o Any additional features that increase the probability of repayment (credit

enhancemenu).o Covenants describing any actions the firm must take and any actions the firm is

prohibited from taking.

Page 12 02013 KapIan.llIC.

Study S.uion 15Cross-Rd'ereDC< 10 CFA Institute Asai~ ReadUlg'52 - Fixed-IncomeSecurilies: Defining ElemeDts

Issuing Entitie»

Bonds arc issued by several types of1egal entities, and bondholders must be awareof which entity h.., actually promised to make the interest and principal payments.Sovereign bonds arc most often issued by the treasury of the issuing country,

Corporate bonds may be issued by a well-known corporation such as Microsoft, by asubsidiary of a company, or by a holding company that is the overall owner of severalopeming companies. Bondholders must pay attention to the specific entity issuing thebonds because the credit quality can differ among related entities.

Sometimes an entity is created solely for the purpose of owning specific assets andissuing bonds to provide the funds to purchase the assets, These entities are referred tovariously as special purpose entities (SPEs), special purpose vchicles (SPYs), or specialpurpose companies (SPCS) in different countries. Bonds issued by these entities arccalled securitized bonds. As an example, a firm could seU loans it h.., made to customersto an Spy that issues bonds to purchase the loans. The interest and principal paymentson the loans arc then wed 10 make the interest and principal payments on the bond s,

Often, an Spy can issue bonds at a lower interest rate than bonds issued by theoriginating corporation. This is because the assets supporting the bonds are ownedby the SPY and are used to make the payments to holders of the securitized bondseven if the company itself runs into financial trouble. For this reason, Spy s arc calledba.a.luuptcy remote vehicles or entities.

Sou,al of&pllymm,

Sovereign bonds arc typically repaid by the laX receipts of the issuing country. Bondsissued by nonsovercign government entities arc repaid by either general taxes, revenuesof a specific projecl (e.g., an airport), or by special taXes or fees dedicated to bondrepayment (e.g., a water district or sewer district).

Corporate bonds are generally repaid from cash generated by the firm's operations. Asnoted previowly, securitized bonds arc repaid from the cash Rows of the financial assetsowned by the Spy.

(A/Ia'vaL IIntl CrrJi, E,,""ntnnmfs

Unsecured bonds represent a claim to the overall assets and cash Rows of the issuer.Secured bonds are backed by a claim to specific assets of a corporation, which reducestheir risk of default and, consequently, the yield that investors require on the bonds.Assets pledged to support a bond issue (or any loan) arc referred to as collateral.

Because they arc backed by collateral, secured bonds arc It,,;or to unsecured bonds.Among unsecured bonds, twO different issues may have different priority in the eventof bankruptcy or liquidation of the issuing entity. The claim of senior unsecured debt isbelow (after) that of secured debt but ahead of luborJi"IIua, or junior, debt.

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Sometimes secured debt is referred to by the type of collateral pledged. Equipment trustcertificates are debt securities backed by equipment such as railroad cars and oil drillingrigs. Collateral trust bonds arc backed by financial assets, such as stocka and (other)bonds. Be aware that while the term debentures rc&:rs to unsecured debt in the UnitedStates and elsewhere, in Great Britain and some other countries the term refers to bondscollateralized by specific asscu.

The most common type of securitized bond is a mortgage-backed security (MBS). Theunderlying assets arc a pool of mortgages, and the interest and principal payments fromthe morrgagcs are used to pay the interest and principal on the MBS.

In some countries, especially European countries, financial companies issue coveredbonds. Covered bonds are similar to asset-backed securities, but the underlying assets(the cover pool), although segregated, remain on the balance sheet of the issuingcorporation [i.e., no SPY is created). Special legislation protects the assets in the coverpool in the event of firm insolvency (they are bankruptcy remere). In contrast to anSpy structure, covered bonds also provide recourse to the issuing firm that must replaceor augment non-performing assets in the cover pool so that it always provides for thepayment of the covered bond's promised interest and principal payments.

Credit enha.neement can be either internal (built into the srrucrure of a bond issue)or external (provided by a third party). One method of internal credit enhanccmentis olltrro/Jarmzliurion. in which the collateral pledged has a value greater than the parvalue of the debt is.sued. A second method of internal credit enhancement is t"WS

spm"', in which the yield on the financial assets supporting the debt is greater thanthe yield promised on the bonds issued. This gives some protection if the yield on thefinancial assets is less than anticipated. If the assets perform as anticipated. the execsscash Row from the collateral can be used to retire (payoff the principal on) some of theoutstanding bonds.

A third method of internal credit enhancement is to divide a bond issue into rranchtl(French for dices) with different seniority of claims. Any losses due to poor performanceof the assets supporting a securitized bond are first absorbed by the bonds with thelowest seniority. then the bonds with the next-lowest priority of c1ainu. The most seniortranches in this structure can receive v<:ryhigh credit ratings because the probability isvety low that losses will be so large th ..t they cannot be ..bsorbcd by the subordinatedtranchcs. The subordinated tranches must have higher yields to eompensue investors forthe additional risk of dd:"u1t. This is .sometimes referred to as wartrfoll structure becauseavailable funds first go to the most senior tranche of bonds. then to the next-highestpriority bonds. and so forth.

External credit enhancements include surety bonds, bank guarantees. and letters ofcredit from financial institutions. Surrty bonth arc issued by insurance companies andarc a promise to make up any shortfall in the cash available to service the debt. BtlnftfUArantttl serve the same function. A lttt" of credit is • promise to lend money to theissuing entity if it docs not have enough cash to maltc the promised payments on thecovered debt. While all three of these external credit enhancements increase the creditquality of debt issues and decrease rheir yields, deterioration of the credit quality of theguarantor will also reduce the credit quality of the covered issue.

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Study Seuion 15Cross,Reference 10 eM butilule Assigned Reading '52 - Fixed-Income Securilies: DefiniDg Elen.enlS

Taxation of Bond Income

Mon often, the interest income paid to bondholders is taXed as ordinary income atthe same rate as wage and salary income. The interest income from bonds issued bymunicipal governments in the United Statcs. however, is most often exempt fromnational income tax and often from any Slate income taX in the Slate of issue.

When a bondholder sells a coupon bond prior to maturity, it may be at a gain or a lossrelative to iu purchase price. Such gains and losses arc considered capital gains income(rather than ordinary taxable income). Capital gains arc of len taXed at a lower rate thanordinary income.Capital gains on the sale of an asset that has been owned for more thansome minimum amount of time may be classified as Iong-ttrm capital gains and taxed atan even lower rate.

Pure-discount bonds and other bonds sold at significant discounts to par when issuedarc termed original issue discount (010) bonds. Because the gains ever an 010 bond'stenor as the price moves towards par value arc really interest income, these bonds cangenerate a tax liabiliry even when no cash interest payment has been made. In manytax jurisdictions. a portion of the discount from par at issuance is treated as taxableinterest income each year.This tax treatment also allows that the tax basis of the 010bonds is increased each ycar by the amount of interest income recognized, so there is noadditional capital gains tax Iiabiliry at maturiry.

Some tax jurisdictions provide a symmetric treatment for bonds issued at a premium topar. aUowing part of the premium to be used to reduce the taxable portion of couponinterest payments.

LOS 52.e: Describe how cash flows of fixed-income securities are structured,

CFA® Program Curriculum. ~/ume 5. paKt 319

A rypical bond has a bullet structure. Periodic interest payments (coupon paymenu)are made over the life of the bond. and the principal value is paid with the final imeresepayment at maturiry. The interest paymenu are referred to as the bond's coupons. Whenthe final payment includes a lump sum in addition to the final period's interest. it isreferred to as a baUoon paymeDt.

Consider a S1.000 face value 5-yar bond with an annual coupon rate of 5%. Witha bullet structure. the bond', promised payments at the end of each year would be: asfollows.

/ 2 3 5PMTPrincipal Remaining

S50$1,000

$50SI,OOO

S50SI,OOO

S50si.eoo

SI,050SO

A loan structure in whieh the periodic paymenu include both interest and somerepayment of principal (the amount borrowed] is called an amortizing loan. If abond (loan) is fully amortizing, this means the principal is fully paid off when thelast periodic payment is made. TypicaUy, automobile loans and home loans arc fully

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amortizing loans. If the 5-ycar. 5% bond in the previous table had a fully amortizingstructure rather than a bullet structure. the payments and remaining principal balanceat each year-end would be as foUows (final payment reflects rounding of previouspayments).

I 2 3 5PMT

Principal~maiojns$230.97$819.03

5230.97S629.01

S23O.97

S429.49

S230.97

5219.99

$230.98

SO

A bond can also be structured to be partially amortizing so that there is a baUoonpayment at bond maturity. JUStas with a bullet structure. However. unlike a bulletstructure. the final payment includes just the remaining unamortized principal amountrather than the full principal amount. In the following table. the final payment includes5200 to repay the temaining principal outstanding.

~'" I 2 3 5PMT

Principal~maining5194.78

$855.22

S194.78

$703.20

SI94.78S543.58

$194.78

$375.98

S394.78

$0

Sinking fund provisions provide for the repayment of principal through a series ofpayments over the life of the issue. For example. a 20-year issue with a face amount of5300 miUion may require that the issuer retire $20 million of the principal every yearbeginning in the sixth year.

Details of sinking fund provisions vary. There may be a period during which no sinkingfund redemptions arc made. The amount of bonds redeemed aceording to the sinkingfund provision could decline each year or increase each year, Some bond indenmresallow the company to redeem twice the amount required by the sinking fund provision.which is called a ,ullbli"l aptia" or an flU.kratt' si"ki"l fo,,'.The price at which bonds are redeemed under a sinking fund provision is typicaUypar but can be different from par. If the market price is 1= than the sinking fundredemption price. the issuer can satisfy the sinking fund provision by buying bonds inthe open market with a par value equal to the amount of bonds that must be redeemed,This would be the case if interest rates had risen since issuance so that the bonds weretrading below the sinking fund redemption price.

Sinking fund provisions offer both advantages and disadvantages to bondholders. On theplus side. bonds with a sinking fund provision have less credit risk because the periodicredemptions reduce the total amount of principal to be repaid at maturity. The presenceof a sinking fund. however. can be a disadvantage to bondholders when interest ratesfall.

This disadvantage to bondholders can be seen by considering the case where interestrares have fallen since bond issuance, so the bonds arc trading at a price above thesinking fund redemption price. In this case, the bond trustee will select outstandingbonds for redemption randomly. A bondholder would suffer a loss if her bonds wereselected to be redeemed at a price below the current market price. This mearu the bonds

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Study Session ISCtoss-Rd'ereoc< 10 eM Institule Assigned Rea<llilg 'S2 - Fixed-Income Securilies: Defining E1emeolS

have more reinvatment ,ill,because bondholders who have their bonds redeemed canonly reinvest the funds at the new, lower yield (assuming they buy bonds of similar risk).

P,oftsso,i Not«: The tonapt of reinuestment ,islt is dernloped mor« in sllbuqllmttopic re~iews. It cen be definul as the IInu,tllinty llbout the inures' to be ellm,d

~ on cltShfolll1 from II bond that are Ttin~ested in otht, debt securities. In tht CIIStof~ II bond with IIsinltingfond. tht grtllter probllbility of ,tetiving tht p,ind",1

rtpll,mmt prior to mllturity increeses the ",pteud cltShfolll1 during the bond"lift lind, thtrefl,e, the unu,tllinty llbout interest incam« on rtin~etttd fonds.

There ate several coupon structures besides a Jixed-coupon structure, and we summarizethe most important ones here.

Floating-Rate Notes

Some bonds pay periodic Interest that depends on a current market rate of interest.These bonds arc called ftoating-rate notes (FRN) or Aoarers. The market rate of interestis called the reference rate, and an FRN promises to pay the reference rate plus someinterest margin. This added margin is typically expressed in basis points, which archundredths of 1%. A 120 basis point margin is equivalent to 1.2%.

As an example, consider a Aoating-rate note that pays the London Interbank Offi:r Rate(UBOR) plus a margin of 0.75% (75 basis points) annually. If I-year UBOR is 2.3% atthe beginning of the year, the bond will pay 2.3% + 0.75% • 3.05% of its par value atthe end of the year. The new I-year rate at that time will determine the rate of interestpaid at the end of the next year. Most Aoaters pay quarterly and arc based on a quarterly(90-day) reference rate. A variable-rate note is one for which the margin above thereference rate is not fixed.

A Aoating-rate note may have a cap, which benefits the issuer by placing a limit onhow high the coupon rate can rise. Often, FRNs with caps also have a Aoor, whichbenefits the bondholder by placing a minimum on the coupon rate (regardless of howlow the reference rate fails). An inverse Aoatct has a coupon rate that increases when thereference rate decreases and decreases when the reference rate inereascs.

OTHER COUPON STRUCTURES

Step-up coupon bonds arc structured so that the coupon tate increases over timeaccording to a predetermined schedule. Typically, step-up coupon bonds have a clIlIftllturt that allow> the firm to redeem the bond issue at a set pricc at each step-up date.If the new highcr coupon rate is greatcr than what the market yield would be at the callprice, the firm will call the bonds and retire them. This means if market yields rise, abondholder may, in tum, get a higher coupon rate because the bonds arc ICIS likely to becalled on the step-up dare,

Yields could increase because an issuer's credit rating has fallen, in which case the higherstep-up coupon rate simply compensates investors for grca'cr credit risk. Aside from this,

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we can view step-up coupon bonds as having some protection against increases in marketinterest rates to the extent they arc: offset by increases in bond coupon rates,

A credit-linked coupon bond carries a provision stating that the coupon rate will go upby a certain amount if the credit rating of the issuer &lIs and go down if the credit ratingof the issuer improves. While this offers some protection against a credit downgrade ofthe issuer. the higher required coupon payments may make the financial situation of theissuer worse and possibly increase the probability of default.

A payment-in-kind (PIIC) bond allows the issuer to make the coupon paymcots byincreasing the principal amount of the outstanding bonds. eSKntiaily paying bondinterest with more bonds. Firms that issue PIK bonds typically do so because theyanticipate that film cash Aows may be less than required to service the debt. oftenbecause of high levels of debt financing (leverage). These bonds typically have higheryields because of a lower perceived credit quality from cash Aow shortf.alls or simplybecause of the high leverage of the issuing firm.

With a deferred coupon bond, also called a split coupon bond. regular couponpayments do not begin until a period of time after issuance. These are issued by firmsthu anticipate cash Aows will increase in the future to allow them to make couponinterest payments.

Deferred coupon bonds mo.ybe appropriatc financing for 0. firm financing 0. largcproject tho.t will not be completed and generuing revenue for some period of time utefbond issuance. Deferred coupon bonds may offer bondholders tax advo.nt:tges in somejurisdictions. Zero-coupon bonds can be considered a type of deferred coupon bond.

An index-linked bond has coupon po.ymenls andlor 0. principal value that is based on 0.

commodity index, an equity index, or some other published index number. loBation-linked bonds (also called linkers) arc the most common type of index-linked bonds.Their paymenu are based on the change in an inAo.tion index. such u the ConsumerPrice Index (CPI) in the United States. Indexed bonds that will not pay less than theiroriginal pu value at m:tlurity. even when the index has decreased. are termed principalprotected bonds.

The different structures of inAation-indexed bonds include:

• Indexed-annuity bonds. Fully amortizing bonds with the periodic po.yments directlyadjusted for inRuion or deAation.

• Indexed zero-coupon bonds. The payment ae maturity is adjusted for inAacion.• Interest-indexed bonds. The coupon rate is adjusted for inAation while the principal

value remains unchanged.• Capital-indexed bonds. This i. the most common structure, An example is U.S.

Treuuty InAacion Protected Securities (TIPS). The coupon rate remains constant,and the principal value of the bonds is Increased by the rate of inAacion (ordecreased by deRation).

To better understand the structure of capital-indexed bonds, consider a bond with. puvalue of $1.000 at issuance. a 3% annual coupon rate paid semiannu:Uly. and 0. provisionthat the principal value will be adjusted for inAacion (or deAacion). If six months uterissuance the reponed inAation has been 1% over the period. the principal value of the

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bonds is increased by 1% from SI,OOO to $1,010, and the six-month coupon of 1.5% iscalculated as 1.5% of the new (adjwted) principal value ofSI,010 (i.e., 1.010 x 1.5%.SI5.15).

With this structure we can view the coupon rate of 3% as a real rate of interest.Unexpected inRation will not decrease the purchasing power of the coupon interestpayments. and the principal value paid at maturity will have approximatcly the samepurchasing power as the S1,000 par value did at bond issuance.

Equity-linked notes (ETN) arc traded debt securities, typically with no periodic interestpayments. for which the payment at maturity is based on an equity index. The paymentmay be less than or more than the amount invested, depending on the change in thespecified index over the life of the ETN.

LOS 52.f. Describe contingency provisions affecting the timing and/or natureof cash Bows of fixed-income securities and identify whether such provisionsbenefit the borrower or the lender.

CFA* PrDl'"m Curriculum. Yo/141M5. pllg~ 331

A contingency provision in a contract describes an action that may be taken if anevent (the contingency) actuaUy oceurs. Contingency provisions in bond indenturesare referred to as embedded options, embedded in the sense that they arc an integralpart of the bond contract and arc not a separate security. Some embedded options areexercisable at the option of the issuer of the bond and, therefore, arc valuable to theissuer; others arc exercisable at the option of the purchaser of the bond and. thus. havevalue to the bondholder.

Bonds that do not have contingency provisions are referred to as straight or option-mebonds.

A eall option gives the il1~'the right to redeem all or pa" of a bond issue at a specificprice (call price) if they choose to. !u an example of a call provision, consider a 6% 20-year bond issued at par on June 1,2012, for which the indenture includes the followingCil/l sd1tduk:

• The bonds can be redeemed by the issuer at 102% of par after June 1,2017.• The bonds can be redeemed by the issuer at 101% of par after June I, 2020.• The bonds can be redeemed by the issuer at 100% of par after June I, 2022.

For the 5-ycar period from the issue date until June 2017. the bond is not callable. Wesay the bond has five years of <111/proft<tiDn, or that the bond is <111/profttwJ forfive years. This 5-ycar period is also referred to as a "'clrout ptrioJ. a cushion. or adifrrmmt ~,ioJ.

June I, 2017, is referred to as the fint <111/""ft, and the <111/p,i<~ is 102 (102% of parvalue) between that date and June 2020. The amount by which the aU price is above paris referred to as the <110prrmium. The call premium at the fim call date in this exampleis 2%, or S20 per S1,000 bond. The call price declines to 101 (101 % of par) after

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Jun~ I, 2020. Aft~r, Jun~ 1, 2022, the bond is callable at par, and that date is referred toas the jim PA' eAUdate,

For a bond that is currently callable, the call price puts an up~r limit on the value ofthe bond ill the market,

A call option has value to the issu~r because it gives the issuer the right to redeem thebend and issue a new bond {borrow} if the market yield on the bond declines, Thiscould occur eieher because interest rates in genersl have decreased or because the creditquality of the bond has increased (default risk has decreased].

Consider a situation where the market yield on the previously discussed 6% 20-ycubond has declined from 6% at issuance to 4% on June 1, 2017 (the 6cst call date). Ifthe bond did not have a call option. it would trade at approximately $1,224. With a callprice of 102. the issuer can redeem the bonds at 51,020 each and borrow that amountat the current market yield of 4%, reducing the annual interest paym~nt from $60 ~rbond to 540.80.

~ p",ftsso,i Now This is AntJ1ol""' So"jinAndnlA hom, mortlAg' whtn mortgAge~ ratesfoil in ortl" to "tlu" th, monthly pAym,ntr.

The issuer will only choose to exercise the call option when it is to their advantag~ todo so. That is, they can reduce their interest ~xp~ns~ by calling the bond and issuingnew bonds at a lower yield. Bond buyers arc disadvantaged by the call provision andhave more reinvestment risk because their bonds will only be called (redeemed prior tomaturity) when the proceeds can be reinvested only at a lower yield. For this reason, acallable bond mwt off~r a high~r yield (sell at a lower pried than an otherwise identicalnoncallable bend, The differ~lIce in price between a caUable bond and an otherwiseidentical noncallable bond is equal to the value of the call option to the issuer,

There an: three sryln of rxercis« for callable bonds:

1. Am~riean style-th~ bonds can be called anytim~ aft~r the 6cst call date,

2. European stylc-th~ bonds can only be called on the call date specified.

3. Bermuda srylc-th~ bonds can be called on specified dates aft~r the 6rst call date.ofeen on coupon payment dates.

Note that these an: only styl~ names and an: not indicative of where the bonds areissued.

To avoid the higher interest rates required on callable bonds but still pr=~ the optionto redeem bonds early when corporate or operating events require it. issuers introducedbonds with make-whole caU provisions. With a make-whole bond. the call price is not6x~d but includes a lump-sum paym~nt based on the pr~s~nt value of the futun: couponsthe bcndholder wiU not receive if the bond is called ~arly.

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With a make-whole call provision, the calculated call price is unlikely to be Iower thanthe market value of the bond. Therefore the issu« is unlikdy to call the bond aceptwhen corporate circumstances, such as an acquisition or «structuring. require it. Themake-whole provision does not put an upper limit on bond value. when interest ratesfall as does a «gular <all provision. The make-whole provision actuaUy penal ius theissuer for calling the bond. The net effect is that Ihe bond can be called if necessary, butit can also be issued at a lower yidd than a bond with a traditional call provision.

Putable Bonds

A put option gives the bondholJ" the right to sell the bond back to the issuing companyat a prespecified price, rypically par_ Bondholders are likely to exercise such a put optionwhen the fair value of the bond is less than the put price because interest rata have riscnor the credit qualiry of the issuer has fallen. Exercise styles used arc similar to those weenumerated for callable bonds.

Unlike a call option, a put option has value to the bondholder because the choice ofwhether to exercise the option is the bondholder's. For this reason, a putable bond willsdl at a higher price (offer a lower yidd) compared to an otherwise identical option-frcebond.

Convertible Bonds

Convertible bonds, rypically issued with maturities of 5-10 years, give bondholders theoption to exchange the bond for a specific number of shares of thc issuing corporation'scommon stock. This gives bondholders the opportuniry to profit from increases in thevalue of the common shares. Regardless of the price of the common shares, the value ofa convertible bond will be at least equal to its bond value without the conversion option.Because the conversion option is valuable to bondholders, convertible bonds can beissued with lower yields compared to otherwisc identical straight bonds.

Esscntially, the owner of a convertible bond has the downside protection (compared toequiry shares) of a bond, but at a reduced yield, and the upside opportuniry of equiryshares. For this reason convertible bonds are often referred to as a hybriti w:urity, partdebt and part equity.

To issuers, the advantages of issuing convertible bonds are a lower yidd (interest cost)compared to straight bonds and the fact that debt financing is converted to equiryfinancing when the bonds arc converted to common shares. Some terms related toconvertible bonds arc:

• Conversion price. The price per share at which thc bond (at its par valuc) may beconverted to common stock.

• Conversion ratio. Equal to the par valuc of the bond divided by the conversionprice. If a bond with a $1,000 par value has a conversion price of S40, its (onlltnionratio is (1,000/40 • ) 25 shares per bond.

• Conversion value. This is the market valuc of the shares that would be receivedupon conversion. A bond with a conversion ratio of 25 shares when the currentmarket price of a common share is $50 would have a conversion value of25 )( 50 •SI,250.

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Even if the share price increases to a level where the conversion value is significantlyabove the bond's par value, bondholders might not convert the bonds to common stockuntil thoy must because the interest yield on the bonds is higher than the dividend yieldon the common shares received through conversion. For this reason, many convertiblebonds have a call provision. Because the call price will be less than the conversion valueof the shares, by exercising their call provision, the issuers can force bondholders toexercise their convenion option when the conversion value is significantly above the parvalue of the bonds.

Warranu

An alternative way to give bondholders an opporrunity for additional returns whenthe firm's common shares increase in value is to include warrant. with straight bondswhen they arc issued. Warrants give their holden the right to buy the firm's commonshares at a given price over a given period of time. As an example, warrants that givetheir holden the right to buy shares for 540 will provide profits if the common sharesincrease in value above $40 prior to expiration of the warrants. For a young firm, .. suingdebt can be difficult because the downside (probability of firm failure) is significant,and the upside is limited to the promised debt payments. Including warrants, whicharc sometimes referred to as a "sweetener," makn the debt more attractive to investorsbecause it adds potential upside profits if the common sharcs increase in value.

Contingent Convertible Bonds

Contingent convertible bonds (referred to as ·CoCos") arc bonds that convert from debtto common equity automatically if a specific event occurs. This type of bond has beenissued by some European banks. Banks must maintain specific levels of equity financing.If a bank's equity falls below the required level, thoy must somehow raise more equityfinancing to comply with regulations. CoCos arc often suucrured so tbat if the bank'sequity capital falls below a given level, thoy arc automatically converted to commonstock. This has the effect of decreasing the bank's debt liabilities and increasing its equitycapital at the same time, which helps the bank to meet its minimum equity requirement.

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Study Session ISCtoss-Rd'em>c< to eM Institute Assigned IUadUIg 'S2 - Fixed-Inconv Securities: Oefin;"g E1ftUeau

KEy CONCEPTS

LOS 52.aBasic features of a fixed income security include the issuer, maturity date, par value,coupon rate, coupon frequency, and currency.• Issuers include corporations, governments, quasi-government entities, and

supranational entities.• Bonds with original maturities of one year or less are money marker securities.

Bonds with original maturities of more than one year are capital marltct securities.• Par value is the principal amount that wiU be repaid to bondholders at maturity.

Bonds are trading at a premium if their market price is greater than par value ortrading at a discount if their price is less than pu value.

• Coupon rate is the percentage of par value that is paid annually as interest. Couponfrequency may be annual, semiannual, quanerly, or monthly. Zero-coupon bondspay no coupon interest and arc pure discount securities.

• Bonds may be issued in a single currency, dual currencies (one currency for interestand another for prineipal), or with a bondholder's choice of currency.

LOS 52.bA bond indenture or trust deed is a contract between a bond issuer and the bondholders,which defines the bond's features and the issuer's obligations. An indenture specifics theentity issuing the bond, the source of funds for repayment, assets pledged as collateral,credit enhancements, and any covenants with which the issuer must comply.

LOS 52.cCovenants are provisions of a bond indenture that protect the bondholders' interests.Negative covenants arc restrictions on a hond issuer's operating decisions, such asprohibiting the issuer from issuing additional debt or selling the assets pledged ascollateral, Affirmative covenants are administrative actions the issuer must perform, suchas making the interest and principal payments on time.

LOS 52.dLegal and regulatory matters that affect fixed income securities include the places wherethcy arc issued and traded, the issuing entities, source. of repayment, and collateral andcredit enhancements.• Domestic bonds trade in the issuer's home country and currency. Foreign bonds

arc from foreign issuers but denominated in the currency of the country wherethey trade. Eurobonds arc issued outside the jurisdiction of any single country anddenominated in a currency other than that of the counuies in which they trade.

• Issuing entities may be a government or agency; a corporation, holding company, orsubsidiary; or a special purpose entity.

• The source of repayment for sovereign bonds is the country's taxing authority. Fornon-sovereign government bonds, the sources may be taxing authority or revenuesfrom a project. Corporate bonds are repaid with funds from the firm's operations.Securitized bonds arc repaid with cash Rows from a pool of financial assets.

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• Bonds arc secured if they arc backed by specific collateral or unsecured if theyrepresent an overall claim against the issuer's cash Rows and asseU.

• Credit enhancement may be internal (overeollateralization, excess spread, rraneheswith different priority of claims) or external (surety bonds, bank guarantees, lettersof credit).

Interest income is typically taxed at the same rate as ordinary income, while gains orlosses from selling a bond are rased at the capiral gains tax rate. However, the increasein value toward par of original issue discount bonds is considered interest income. Inthe United Srates, interest income from municipal bonds is usually tax-exempt at thenationallcvcl and in the issuer's state.

LOS 52.eA bond with a bullet structure pays coupon interest periodically and repays the entireprincipal value at marurity.

A bond with an amonizing structure repays pan of its principal at each payment date. Afully amonizing structure makes equal payments throughout the bond's life. A partiallyamortizing structure has a balloon payment at maturity, which repays the remainingprincipal as a lump sum.

A sinking fund provision requires the issuer to retire a ponion of a bond issue atspecified times during the bonds' life.

Floating-rate notes have coupon rates that adjust based on a reference rate such asUBOR.

Other coupon structures include step-up coupon notes, credit-linked coupon bonds,payment-in-kind bonds, deferred coupon bonds, index-linked bonds, and equity-linkednotes,

LOS52.fEmbedded options benefit the party who has the right to exercise them. Call optionsbenefit the issuer, while put options and conversion options benefit the bondholder.

Call options allow the issuer to redeem bonds at a specified call price,

Put options allow the bondholder to sell bonds back to the issuer at a specified put price.

Conversion options allow the bondholder to exchange bonds for a specified number ofshares of the issuer's common stock.

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Study Session ISCtoss-Rd'ereoc< to eM institute Assigned ReadUlg '52 - Fixed-Income Securities: Defining ElemeolS

CONCEPT CHECKERS

1. A bond's indenture:A. contains its covenants.B. is the same as a debenture.C. relates only to its interest and principal payments.

2. A dual-currency bond pays eoupon interest in a currency:A. of the bondholder's ehoice.B. other than the home currency of the issuer,C. other than the currency in which it repays principal.

3. Which of the following bond covenants is mott IUCVrtlU/y described as anaffirmative covenant? The bond issuer must not:A. violate laws or regulations.B. scll assets pledged as collateral.C. issue more debt with the same or higher seniority.

4. An investor buys a pure-discount bond, holds it to maturity, and receives itspar value. For taX purposes, the increase in the bond's value is mDst li"tly to betreated as:A. a capital gain.B. interest inc.ome.C. tax-exempt income.

5. A 10-year bond pays no interest for thrcc years. then pays $229.25, followedby payments of$35 semiannually for seven years, and an additional $1,000 atmaturity. This bond is a:A. step-up bond.B. zero-coupon bond.C. deferred-coupon bond.

6. Which of the following statements is most IICCVrtltt with regard to Aoating-rateissues that have caps and Aoors?A. A cap is an advantage 10 the bondholder, while a Aoor is an advantage to the

issuer.B. A Aoor is an advantage to the bondholder. while a cap is an advantage to the

issuer.C. A Aoor is an advantage to both the issuer and the bondholder, while a cap is

a disadvantage to both the issuer and the bondholder.

7. Which of the following most IIccvr"ttly describes the maximum price for acurrently callable bond?A. Its par value.B. The call price.C. The present value of its par value.

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ANSWERS - CONCEPT CHECKERS

1. A An indenture is the conn ... berween 1M company .nd its bondholde ... nd conla.ins 1Mbond's covenants.

2. C Dual-currency bonds pay coupon interest in one currency and principal in. differentcurreney. These currenci .. m.y or may not include the hom. currency of the issuer. Acurreney option bond allows the bondholder 10cboos •• currency in which 10 be paid.

3. A R.quiring the issu.r 10 comply witb a111.w. lnd regul.tions is an example of an2ffitmati~ covenant, Negative covenanrs arc rtStliCIioru on actions a bond issuer can"k e, Examples include preventing an issuer from ••Uing ...... that have been pledged ..ccllateral or from issuing additional debt with an equal or higMr pfiority of claim •.

4. B Tax authorities Iypically trcal the Increase in value of a pure-discoum bond low.rd paras inter ... income to the bondholder. In many jurisdictions thi. inleresl income i. laxedperiodically during 1M life of Ih. bond even though the bondholder does nOI receive anycash until maturity.

5. C This patre rn describes • deferred-coupen bond. The fi..1 p.ymenl of $229.25 is thevalue of th e acerued coupon p.ym.nts for lb. first three years.

6. B A cap is a maximum on rhe coupon rate and iJ advanlageow to the issuer. A floor is aminimum on th. coupon ral •• nd is. therefore •• dvantageous to the bondholder.

7. B Wh.never the price of the bond incr ...... bove the strike price stipulated on the calloption. it will be optimal for th. issu.r to call rhe bond. Theeretlcally, the price of.curr<ntly callable bond should never rise above ilS call pric e.

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Thc following is • rn-icw of the Fixed Income Bask Concepu principlcs designed to .ddrns the lcarniogouccome ltaccmenu Jet forth by CFA InStitute. TfUl topic il .flo covercG in.:

FIXED- INCOME MARKETS: ISSUANCE,TRADING, AND FUNDING

S[udy S••• ion 15

ExA.\I Focus

This topic review introduces many terms and ddinitioru. Focus on differcntlYP"sof issuers. mtun:s of the various debt security structures. and why diffen:nt sourcesof funds have different interest costs. Understand weU the differences between fixed-rate and floating-rate debt and how rates arc determined on floating-rue debt and forrepurchase agr«ments.

LOS 53.a: Describe classifications of global fixed-income markets.

CFA* Progrrzm Cumru/um. VII/um. 5. ptltr 348

Global bond markets can be classified by several bond characteristics, including typeof issuer. credit quality. maturity. coupon. currency. geography. indexing. and taXablestatus.

1Ype of imler. Common classifications arc government and government related bonds.corporate bonds. and structured finance (securitized bonds). Corporate bonds arc oftenfurther classified as issues from financial corporations and issues from nonfinancialcorporations. The largest issuers by total value of bonds ouutanding in global marketsarc financial corporations and governments.

CwJi, 'futility. Standard & Poor's (S&P). Moody·s. and Fitch all provide credit ratingson bonds. For S&P and Fitch. the highest bond ratings arc MA. M. A.and BBB.and arc considered ;nunmun' grrzJe bonJs.The equivalent ratings by Moody's arc Alathrough Baa3. Bonds BB~ or lower (Bat or lower) arc termed high-yield. speculative,or "junk" bonds. Some institutions arc prohibited from investing in bonds ofless thaninvestment grade.

Or;ti""[ mtlturi,i,s. Securities with original maturities of on. ycar or loss arc classifiedas money marlu:t securities. Examples include U.S. Treasury bills. commercial paper(issued by corporations). and negotiable certificates of deposit. or CDs (issued by banks).Securities with original maturities greater than one ycar arc referred to as capital marketsecurities.

Coup"n strurture. Bonds arc classified as either floating-rate or fixed-rate bonds,depending on whether their coupon interest payments arc stated in the bond indentureor depcnd on the level of a shore-term market reftrmct Ttlft determined over the lifeof the bond. Purchasing floating-ratc debe is attractive to some institutions that have

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variable-rates sources of funds (liabilities), such as banks. This allows these institutionsto avoid the balance sheet effects of interest rate increases that would increase the cost offunds but leave the interest income at a fixed rate. The value of fixed-rate bonds (assets}held would fall in the value, while the value of their liabilities would be much lessaffected.

Currtncy delUlminlltion. A bond's price and returns arc determined by the interest ratesin the bond's currency, The majority of bonds issued arc denominated in either U.S.dollars or euros.

GeofFllp"'. Bonds may be classified by the markets in which they arc issued. Recall thediscussion in the previous topic review of domestic (or national) bond markets, foreignbonds, and eurobonds, and the differences among them. Bond markets may also beclassified as developed markets or emerging markets. Emerging markets arc counuieswhose capital markets arc less well-cstablished than those in developed markets.Emerging market bonds arc typially viewed as riskier than developed market bonds andtherefore, havc higher yields.

Intkxing_ As discussed previowly, the cash Rows on some bonds arc based on an index(indes-linked bonds). Bonds with cash Rows determined by inRation rates arc referredto as inRation-indexed or inAation-linked bonds. InRation-linked bonds arc issuedprimarily by governments but also by some corporations of high credit quality.

TIIX stlltus. In variow countries, some issuers may issue bonds that arc exempt fromincome taxes. In the United States, these bonds an be issued by municipalities and arccalled municipal bonds, or munis. Tax exempt bonds are sold with lower yields thantaxable bonds of similar risk and maturity, to reReet the impact of taxes on the after-taxyield of taxable bonds.

LOS 53.b: Describe the usc of interbank offered ratcs as reference rates infloating-ratc debt.

CF-A®Progrttm Curriru/um, VII/umt 5, PIIgt 352

The most widely used reference rate for Rooting-rate bonds is the London InterbankOffer Rate (UBOR), although other reference rates, such as Euribor, arc also used. Liborrates arc published daily for several currencies and for maturities of one day (overnightrates) to one year. Thus, there is no single "UBOR rate" but rather a set of rates, such as·30-day U.S. dollar UBOR· or "90-day Swiss franc UBOR."

The rates arc based on expected rates for unsecured loans from one bank to anotherin the interbank money marla:t. An average is calculated from a survey of 18 banks'expected borrowing rates in the interbank market, mer excluding the highest and lowestquotes.

For Roating-rate bonds, the reference rate mwt match the frequency with which thecoupon rate on the bond is reset. For example, a bond denominated in euros with acoupon rate that is reset twice each year might use 6-month euro UBOR or 6-monthEuribor as a reference rate.

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LOS 53.c: Describe mechanisms available for issuing bonds in primarymarkets.

Sales of newly issued bonds arc referred to as primary market transactions. Newly issuedbonds can be regiseered with securities regulators for sale to the public. a public offering,or sold only to qualified investors. a private placement,

A public offering of bonds in the primary market is typically done with the help of aninvestment bank. The investment bank has expertise in the various steps of a publicoffering. including:

• Determining funding needs.• Structuring the debt security.• Creating the bond indenture.• Naming a bond trustee (a trust company or bank trust department).• Registering the issue with securities regulators.• Assessing demand and pricing the bonds given market conditions.• Selling the bonds.

Bonds can be sold through an underwritten offering or a best effons offering. Inan underwritten oft'cring. the entire bond issue is purchased from the issuing firm bythe investment bank. termed the underwriter in this case. While smaller bond issuesmay be sold by a single investment bank, for larger issues. the kad .",dnwriur headsa syndicate of investment banks who collectively establish the pricing of the issue andare responsible for selling the bonds to dealers. who in turn sell them to investors. Thesyndicate takes the risk that the bonds will not all be sold.

A new bond issue is publicized and dealers indicate their interest in buying the bonds.which provides information about appropriate pricing. Some bonds are traded on a wlNnissurd basis in what is called the grey market. Such trading prior to the offering date ofthe bonds provides additional information about the demand for and market clearingprice (yield) for the new bond issue.

In a bm t/forts offering, the investment banks sell the bonds on a commission basis.Unlike an underwritten offering. the investment banks do not commit to purchase thewhole issue (i.e .• underwrite the issue).

Some bonds. especially government bonds. are sold through an auction.

~ PrDftnDri NDU: &,all that a,tttiDn prDudum wtrt n:p/4intd in dttail in tIN~ Stud] Smi.n rovtring mirrot'Dn.mirs.

U.s. Treasury securities arc sold through single price auctions with the majority ofpurchases made by primary dealers that participate in purchases and sales of bonds withthe Federal Reserve Bank of New York to facilitate the open market operations of theFed. Individuals can purchase U.S. Trcasury securities through the periodic auetions aswell. but are a small part of the total.

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In a shelf registration, a hand issue is registered with securities regulators in its aggregatcvalue with a master prospccrus. Bonds can then he issued over time when the issuerneeds to raise funds. Because individual ofTcrings under a shdf rcgistration require Iessdisclosure than a separate rcgistration of a hand issue, only finaneaUy sound companicsarc grant<d this option. In some countries, hands registered under a shelf registrarioncan he sold only to qualified investors.

LOS 53_d: Describe secondary markets for bonds.

S<coodary markets refer to the trading of prcviously issued bonds. While somegovernment bonds and corporate bonds arc traded on exchanges, the great majorityof bond trading in the secondary market is made in the dealer, or ever-the-counter,market. Dealers post bid (purchase) prices and ask or offer (selling) prices for varioushand issues. The difference between the bid and ask prices is the dealer's spread. Theaverage spread is often between 10 and 12 basis points but varies across individual bondsaccording to their Iiquidiry and may be more than 50 basis points for an iOiquid issue. I

Bond trades arc cleared through a clearing system, just as equities trades arc. Settlement(the exchange of hands for cash) typieally occurs on the third trading day after the tradedate (T + 3) for corporate bonds, on the next trading day after the trade date (T + 1)for government bonds, and on the day of the trade (cash settlement) for some moncymarket securities.

LOS 53.e: Describe securities issued by sovereign governments, non-sovereigngovernments, government agencies, and supranational entities.

Sovereign Bonds

National govcrnments or their treasuries issue bonds backed by the wing power of thegovcrnment that arc referred to as SDWrtign bDnas. Bonds issued in the currency of theissuing government carry high credit ratings and arc considered to be essentially free ofdefault risk. Both a sovereign's ability to collect taxes and its ability to print the currencysupport these high credit ratings.

Sovereign nations also issue bonds denominated in currencies different from their own.Credit ratings are often higher for a sovereign's local currency bonds than for cxample,iu euro or U.S. dollar-denominated bonds. This is bccawe the national governmentcannot print the developed market currency and the developed market currency valueof local currency tax collections is dependent on the exchange rate between the two

currencies.

Fixed Income Marke.. : Issuance,Trading. and Funding. Choudhry, M.; Mann, S.; andWhitmer, L.; in CFA Program 2014 Lev .. I Curriculum, Volume 5 (CFA Institute, 2013).

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Trading is most active and prices most informative for the most recently issuedgovernment securities of a panieulat maturity. These issues are referred to as on-the-runbonds and also as benchmark bonds because the yields of other bonds are determinedrelative to the "benchmark" yields of sovereign bonds of similar maturities.

Sovereign governments issue fixed-rate, Roating-tate, and inRation-indexed bonds.

Nonsovereign Government Bonds

Nonsovereign government bonds are issued by states, provinces, counties. and sometimesby entities created to fund and provide services such as for the construction of hospitals,airports, and other municipal services. Paymenu on the bonds may be supported by therevenues of a speci6e project. from general tax revenues. or from special taxes or fcesdedicated to the repayment of project debt.

Nonsovereign bonds arc typically of high credit quality, but sovereign bonds typicallytrade with lower yields (higher prices) because their credit risk is perceived to be lessthan that of nonsovereign bonds.

~ PrOfiUOTjNo": ~ will allmin~ the ,,,Jjt f{WlUIJ OfJOV~Tdgnlind nontow"ign~ gowrnmmt bonds in OUTtopic ,.view Df·Funummt4ls DfC"Jjt A1III/y>iJ.·

Agency Bonds

Ageney or quasi-government bonds arc issued by entities created by notionalgovernments for specific purposes such as 6nancing small businesses or providingmortgage 6nancing. In the United States. bonds are issued by government-sponsoredenterprises (GSEs), such as the Federal National Mortgage Association and the TennesseeValley Authority.

Some quasi-government bonds are backed by the national government, which gives themhigh credit quality. Even those not backed by the national government typically havehigh credit quality although their yields are marginally higher than those of sovereignbonds.

Supranational Bonds

Supranational bonds are issued by supranational agencies. also known as multiill"TIlI4gmri~J. Examples arc the World Bank, the IMF, and the Asian Development Bank.Bonds issued by supranational agencies typicalJy have high credit quality and can be veryliquid. especially large issues of well-known entities.

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Study Sessioo 15Cros s-~f_oce to CFA I",titute Asaigned Reading '53 - Fu.ed·locome Marw: wuan«. Trading. and Fundiog

LOS 53.f: Describe types of debt issued by corporations.

CFA® ProfTtlm Curriculum. VIIlumt 5. pllgt 373

Bank Debt

Most corporations lUnd their businesses to some extent with bank loans. These aretypically UBOR·based. variable-rate loans. When the loan involves only one bank. itis referred to as a bilatenlloan. In contrast, when a loan is funded by several banks. itis referred to as a syndicated loan and the group of banks is the syndicate. There is asecondary market in syndicated loan interests that are also securitized, creating bondsthat arc: sold to investots.

Commercial Paper

For larger creditworthy corporation s, funding costs can be reduced by issuing short-term debt securities referred to as commercial paper. For these firms. the interest costof commercial papcr is less than the intcrest on a bank loan. Commcrcial paper yieldsmore than short-term soverelgn debt became it has. on average. more credit ruk and lessliquidity.

Firms USecommercial paper to fund working capital and as a temporary source of fundsprior to usuing longer-term debt. Debt that is tempol1lry until permanent financing canbe secured is referred to as bridge financing.

Commercial paper is a short-term, unsecured debt instrument. In the United States,commercial paper is issued with maturities of270 days or less. because debt securitieswith maturities of 270 da)"S or less are exempt from SEC rcgistration. Eurocommercialpaper (ECP) is issued in several ccunnies with maturities as long as 364 days.Commereial paper is issued with maturities as short as one day (overnight paper). withmost issues maturing in about 90 days.

Commercial paper is often reissued or ro/kJ DVtT when it matures. The risk that acompany will not be able to sell new commercial paper to replace maturing paper istermed roUDUfT risk, The twO important circumstances in which a company will facerollover diffieulties arc (I) there: is a dcrerioration in a eompani. actual or perceivedability to repay the debt at maturity. which will significantly increase the required yieldon the paper or lead to less-than-full subscription to a new issue, and (2) significantsystemic financial distress, as was experienced in the 2008 financial crisis. that may"fre=" debt markets so that very little commercial paper can be sold at all.

In order to gcr an acceptable credit I1Iting from the ratings services on their commercialpaper. corporations maintain backup lines of credit with banks. These are sometimesreferred to as li'luiJiry mhanummt or bllcltup li'luitliry lines. The bank agrees to providethe funds when the paper matures. if needed. except in the case of a mllttrilli ""verstchanl' (i.e .• when the company's financial situation has deteriorated significantly).

Similar to U.S. Tsbills, commercial paper in the United States is typically issued as apure discount security. making a singlc payment equal to the face value at maturity.

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Prices arc quoted as a pe=ntagc discount from fa", value. In contrast, ECP rates arcquoted as an IlJd-(Jn,i~IJ, that is, the percentage interest paid at maturity in addition tothe par value of the commercial paper.

Pr./nso,~ No": &cllllfrom QUllntiutilJl! Mtrhods rhllr a lBO-day T-bill'luowJ~ a' a JjICDun,,i~1J 0/296 fl' ,h~IBO-Ja, ptritul isp,iuJ a' $9BOpa $1,000 fau~ INllu~.The tfficrilJl! IBO-Ja, return is 1,000 19BO- 1 .2.04196. Fo, ECP ",i,h

II 1BO..Jay.aJJ-(Jn ,itld 0/296. ,h~ tffictiv~ return is limply 296.

Corporate BODds

In the previous topic review, we discussed several featurcs of corporate bonds. Corporatebonds arc issued with various coupon structures and with both fixed-rate and 1I0ating-rate coupon paymenu. They may be secured by collateral or unsecured and may havecall, put, or conversion previsions.

Wc also discussed a sinking fund provision as a way to reduce the credit risk of a bondby redeeming part of the bond issue periodically over a bond's life. An alternative to asinking fund provision is to issue a serial bond issue. With a serial bond issue, bonds arcissued with several maturity dates so that a portion of the issue is redeemed periodically.An important difference between a serial bond issue and an issue with a sinking fundis that with a serial bond issue, investors know at issuance when specific bonds will beredeemed. A bond issue that docs not have a serial maturity structure is said to have aterm maturity structure with all the bonds maturing on the same date.

In general, corporate bonds arc referred to as short-term if they are issued withmaturities of up to 5 years, medium-term when issued with maturities from 5 to 12years, and long-term when maturities exceed 12 years.

Corporations issue debt securities called medium-term notes (MTNs), which are notnecessarily medium-term in maturity. MTNs arc issued in various maturities, rangingfrom nine months to periods as long as 100 years. Issuers provide ma,u,i" rrzng~1(e.g.,18 months to twO yean) for MTNs they wish to sell and provide yield quotes forthose ranges. Investors interested in purchasing the notes make an offer to the iuuer'sagent, specifying the face value and an exact maturity within one of the ranges offered.The agent then confirms the issuer's willingness to sell those MTNs and effc:cu thetransaction.

MTNs can have fixed- or 1I0ating-rate coupons. but longer-maturity MTNs arc typicallyfixed-rate bonds. The notes issued can be combined with derivative instruments to createthe special features that an investor requires. The combination of the derivative andnotes is called a ltruCtuTtJ SfCuri".

Most MTNs. other than long-term MTNs. arc issued by financial corporations andmost buyers arc financial institutions. MTNs can be structured to meet an institution'sspecifications, While custom bond issues have less liquidity, they provide slightly higheryields compared to an issuer's publicly traded bonds.

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Study Soulon 15Cro,s-~f_Dce to CFA InatiNtc As$i£ned Reading '53 - Fu.ed-Jncome Marw: ~. Trading, aDd FundiDg

LOS 53-g: Describe short-term funding alternatives available to banks,

CFA® Pnpm Curriculum. VDlumt5. pagt 381

Customer deposits (retail deposits) arc a short-term funding source for banks, Checkingaccounts provide transactions services and immediate availability of funds but typicallypay no interest, Money market mutual funds and savings accounts provide less liquidityor less transactions services, or both, and pay periodic interest,

In addition to funds from retail accounts, banks offer ineerest-bearing certificates ofdeposit (CDs) that mature on specific dates and arc offered in a range of short-termmaturities, Nonnegotiable CDs cannot be sold and withdrawal of funds often incurs asignificant penalry,

Negotiable certificatel of depolit can be sold. At the wholesale level, large denomination(typically more than S I million) negotiable CDs arc an important funding source forbanks. They typically have maturities of one year or less and an: traded in domestic bondmarkets as well as in the Eurobond market.

Another 10Ura: of short-term funding for banks is to borrow excess reserves from otherbanks in the central bank fund, market. Banks in most countries must maintain aportion of their funds as reserves on deposit with the central bank, At any point in time,some banks may have more than the required amount of reserves on deposit. whileothers require more reserve deposits. In the market for central bank funds. banks withCXCA:SI reserves lend them to other banks for periods of one day (overnight funds) andfor longer periods up to a year (term funds). Central bank fund. rates refer to rates forthese transactions. which arc Strongly in8uenced by the dfect of the central bank's openmarket operations on the money supply and availability of short-term funds,

In the United States. the central bank funds rate is called the Fed funds rate and this ratein8uenecs the interest rates of many short-term debt securities.

Other than reserves on deposit with the central bank, funds that are loaned by onebank to another arc referred to as interbank funds. Interbank funds arc loaned betwecnbanks for periods of one day to a year. The se loans an: un secured and. as with many debtmarkets, liquidity may decrease severely during times of systemic financial distress.

LOS 53.h: Describe repurchase agreements (repos) and their importance toinvestors who borrow short term.

A repurchase (repo) agreement is an arrangement by which one party sells a security toa eounterparty with a commitment to buy it back at a later date at a specified (higher)price. The "I""hllSt Incr is greater than the selling price and accounts for the interestcharged by the buyer. who is. in effect. lending funds to the seller with the security ascollateral. The interest rate implied by the two prices is called the Ttl" retr, which is theannualized percentage difference between the twO prices. A repurchase agreement forone day is called an IIutmight Ttpo and an agreement covering a longer period is called a

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term up o. The interest COStof a repo is customarily less than the rate on bank loans orother short-term borrowing.

As an example, consider a firm that enters into a repo agreement to sell a 4%, 12-ycarbond with a par value of $1 million and a market value of $970,000 for $940,000 andto repurchase it 90 days later (the rcpo date) for $947,050.

The implicit interest rate for the 90-day loan period is 947,050 1940,000 - I .0.75%and the up. rflU would be expressed as the equivalent annual rate.

The percentage difference between the market value and the amount loaned is called thercpo margin or the haircut. In our example, it is 940,0001970,000 - 1 = -3.1%. Thismargin protects the lender in the event that the value of the security decreases over theterm of the repo agreement.

The rcpo rate is:

• Higher, the longer the repo term.• Lower, the higher the credit quality of the collateral security.• Lower when the collateral security is delivered to the lender.• Higher when the interest rates for alternative sources of funds arc: higher.

The repo margin is in8uenced by similar factors. The repo margin i.,

• Higher, the longer the repo term.• Lower, the higher the credit quality of the collateral security.• Lower, the higher the credit quality of the borrower.• Lower when the collateral security is in high demand or low supply.

The reason the supply and demand conditions for the collateral security affects pricing isthat some lenders want to own a specific bond or type of bond as collateral. For a bondthat is high demand, lenders must compete for bonds by offering lower repo lendingraees,

Viewed from the standpoint of a bond dealer. a reverse repo agreement refers to takingthe opposite side of a repurchase transaction, lending funds by buying the collateralsecurity rather than selling the eellaeeral securiry to borrow funds.

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KEY CONCEPTS

LOS 53 .aGlobal bond markets an be classified by:• Type of issuer: Government (and governmenr-related), corporate (fin>.ncial>.nd

nonfinancial), securitized.• Credit quality: Investment grade, non investment grade.• Original maturity: Money market (one yeu or leu), capital m..rket (more than one

year).• Coupon: Fixed rate, Aoating rate.• Currency and geographY' Domestic. foreign, global, eurobond markets; developed,

emerging markets.• Otber clu,ilications: Indexing. taxable status.

LOS 53.bInterbank lending rates, such as London Interbank Offered Rate (UBOR). arefrequently used u reference rotes for Aoating.rote debt. An appropriate reference rotcis one that matches a floating. rotc note's curreney and frequency of rate resets, such as6·month U.S. dollar LIBOR for a semiannual floating-rotc note issued in U.S. doUars.

LOS 53.cBonds may be issued in the primary market tllCOUgha public offering or a privateplacement.

A public offering using an investment bank may be underwritten. with the investmentbank or syndicate purchuing the entire issue and sclling the bonds to dealers: or on abest-cfforts buis. in which the investment bank sells the bonds on commission. Publicofferings may also take place through auctions. which is the method commonly used toissue government debt.

A private placement is the sale of an entire issue to a qualified investor or group ofinvestors. which are typically large institutions.

LOS 53.dBonds that have been issued previously trade in secondary markets, While some bondstrade on exchanges, most are traded in dealer markets. Spreads between bid and askprices arc narrower for liquid issues and wider for Jess liquid issues.

Trade settlement is typicolly three days uter a trade for corporate bonds. one day after atrade for government bonds. and same-day settlement for money marker instruments.

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LOS 53_eSovereign bonds arc issued by national governments and backed by their taxing po....er,Sovereign bonds may be denominated in the local currency or a foreign currency.

Nonsovercign government bonds are issued by governments below the narional level,such as provinces or cities. and may be backed by taxing authority or revenues from aspecific project.

Agency or quasi-government bonds arc issued by government sponsored entities and maybe explicitly or implicidy backed by the government.

Supranational bonds arc issued by multilateral agencies that operate across nationalborders.

LOS 53.fDebt issued by corporations indudes bank debt, commercial paper, corporate bonds,and medium-term notes.

Bank debt includes bilateral loans from a single bank and syndicated loans from multiplcbanks.

Commercial paper is a moncy market instrument issued by corporations of high creditquality.

Corporate bonds may have a term maturity structure (all bonds in an issue mature at thesame timc) or a serial maturity structure (bonds in an issue mature on a predeterminedschedule) and may have a sinking fund provision.

Medium-term notes are eorporate issues that can be structured to meet the requirementsof investors.

LOS 53.gShort-term funding alternatives available to banks include:• Customer deposits, induding checking accounts, savings accounts, and moncy

market mutual funds.• Negotiable CDs. which may be sold in the wholesalc market.• Ccntnl bank funds market. Banks may buy or sell excess reserves deposited with

their central bank.• Interbank funds_ Banks make unsecured loans to one another for periods up to a

year.

LOS 53.hA repurchase agtcemcnt is a form of short-term collateralized borrowing in which oneparty sells a security to another party and agrees to buy it back at a predetermined futuredate and price, The repo rare is the implicit ineerese rate of a repurchase agreement. Therepo margin. or haircut. is the difference between thc amount borrowed and the value ofthe security.

Repurchase agreements arc an important source of short-term financing for bonddealers. If a bond dealer is lending funds instead of borrowing. the agreement is known.. a reverse repo.

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Study St!Sioo 15Cross-~fmoce to CFA hutitute Assigned Reading '53 - Fu.ed·locomt Marktu: Issuanct, Trading. and Fuodiog

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CONCEPT CHECKERS

I. An analyst who describes a fixed-income securiry as being a structured financeinstrument is classifying the security by:A. credit quality,B. type of issuer.C. taxable status.

2. L1BOR rates arc determined:A. by countries' central banks.B. by money market regulators.C. in the interbank lending market.

3. In which type of primary market transaction does an investment bank sell bondson a commission basis?A. Single-price auction.B. Best·dforts offi:ring.C. Underwritten offering.

4. Secondary market bond transactions molt lilttl] take place:A. in dealer markets.B. in brokered markets.C. on organized exchanges.

5. Sovereign bonds arc described as on-the-run whcn they:A. arc the most recent issue in a specific maturity,B. have increased substantially in price since they ....ere issued.C. receive greater-than-expected demand from auction bidders.

6. An investor who buys €IOO,OOO face value of newly issued eurocommercialpaper and holds it to maturity is molt liltily to pay:A. less than €IOO,OOO and receive €IOO,OOO at maturi!),.B. €IOO,OOO and receive more than €IOO,OOO at maturity,C. less than €IOO,OOO and receive more than €IOO,OOO at maturity,

7. With which of the foUowing features of a corporate bond issue docs an investormost lilr~1yfacc the risk of redemption prior to maturi!),?A. Serial bonds.B. Sinking fund.C. Term maturity structure.

8. Smith Bank lends Johnson Bank excess reserves on deposit with the central bankfor a period of three months. Is this transaction said to occur in the interbankmarket?A. Yes.B. No, because the interbank market refers to loans for more than one year.e. No, because the interbank market docs not include reserves at the central

bank.

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Study Seuion 15Cross-Ref.rtn« 10 CFA Inslitutt Assigned Reading 153 - Fixtd-Incom. Mwu: Issuance,Trading. and Funding

9. In a repurchase agreement, the percentage difference between the repurchaseprice and the amount borrowed is most lIuurlluly described as the:A. haircut.B. repo rate.C. repo margin.

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Study SHsion 15eross-lUfertDct to CFA lrutilUtt Assign.d Reading '53 - Fu.ed-In<OMe Markw: h~. Tradift&, &ad Funding

ANSWERS - CONCEPT CHECKERS

1. B Fixed-income seceor classifications by typc of issuer include governm.nt. corporat e, andstructured 6nance instruments.

2. C UBOR rates are determined in th. marl,", for interbank lending,

3. B In a best-effons offering. an inveStment bank or banks do not underwrite (i.e., purcha~all of) a bond issue. but rather sell the bond. on a commirnon basis. Bond. sold byauction art offered directly to buyers by the issuer. typicaUy a government.

4_ A Th •• econd.I)' marker for bond. is primarily a dealer markot in which deal ... po.t bidand ask prices.

5. A Sovereign bond. are described as ."-,h..,,ln or bmchmllrltwhen thoy reprtsont the mostrecent issue in a specific maturity.

6. B Unlike comm ercial pap.r issued in tho IJnitod State •• which is typically a pure discountsecurity •• urocommercial paper pay. add-on interest. An investor who buys nowly issu.deuroccmmereial paper lends tho issuer the face value and reeeives tho face value plusinterese at maturiry.

7. B With a sinking fund. the issuer must redeem part of the issue prior to maturity. but thespecifie bonds to be redeemed arc not known. Serial bond. are issued with a schedule ofmaturities and each bond has a known maturity dat e. In an issue with a term maturitystructure, all the bonds are scheduled to mature on the same dat e.

8. C The interbank market refers to shen-rerm borrowing and lending among banks of fund.other tha.n those on deposit at a central bank. Loans of reserve. on dopo';t with a centralbank are said to occur in the central bank fund. n,arket.

9. B The repo rat. i. the percentage diff.r.nce berw een the repurchase price and tho amountborrowed. The repe margin or haircut is the perccn<a&<diff ere nee between the amountborrowed and the value of the collateral.

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Thc following is a rn-icwofthe fixed Income Basic Concepu principlcs designed to a.ddrns the lcuniogoutcome luc:cmenu Jet fOM by CFA InstiNte. TfUs topic is aflo CO\ocrrd in.:

INTRODUCTION TO FIXED-INCOMEVALUATION

S.udy Session 15

EXA.", Focus

The concepts introduced here are very important lOr understanding the factors thatdetermine the value of debt securities and various yield measures. The relationshipsbetween yield to maturity, spot rates, and forward rates are core material and come up inmany contexts throughout the CFA curriculum. Yield spread measures also have manyapplications. Note that while five of the required learning outcomes have the commandword ·calculate" in them, a good understanding of thc underlying concepts is just asimportant for exam success on this material.

LOS 54.a: Calculate a bond's price given a market discount rate.

CFAGiI Program Curriculum, VDlumL5, pagt 398

Calculating the Value of an Annual Coupon Bond

The value of a coupon bond can be calculated by summing the present values of all ofthe bond's promised cash flows. The market discount rate appropriate for discountinga bond's cash flows is called the bond's yield-to-maturity (YTM). If we know a bond'syield-to-maturity, we can calculate its value, and if we know its value (market price), wecan calculate its yield-to-maturity.

Consider a newly issued 10-year, $1,000 par value, 10% coupon, annual-pay bond. Thecoupon payments will be $100 at the end of each year the $1,000 par value will be paidat the end of year 10. First, let's value this bond assuming the appropriate discount rateis 10%. The present value of the bond's cash flows discounted at 10% is:

100 100 100 100 1,100-+-2 +-, +········+-9+-w = 1,0001.1 1.1 1.1 1.1 1.1

The calculator solution is:

N ~ 10; PMT a 100; FV a 1,000; JIY a 10; CPT -+ PV~ -1,000

where:N a number of yearsPMT s the annual coupon paymentIN • the annual discount rateFV ~ the par value or selling price at the end of an assumed holding period

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Sludy &slioo ISCroS$-~ft~Dce 10 CFA lrutitutt AnigMd Rtading'54 -Introduction to FlXtd-IDCIOmtValuation

ProftssoTi Now Talu "ott of II couple ofpoi"ts hue. The discou"t ret« is ."taed ItS

II whole "umba in pert."t. /0. "ot 0./0. The /0 coup." pllyments .fS/OO ellchliTet""m cllreofi" the N. /0 lind PMT. /00 mtrie«; The pri"cip"l "P"1ment

~ is in the FV. /.000 entry. wtly. "ott that the PV is "eglltillt; it will be the~ opposite lip to the tip .fPMT lI"d F'I. The cllkulator isjust ·thi"lti"g· thllt to

reuiw thr P"l"'mts 1IT11/ furure IIl1lw (to OW" the bond). you must plly tb«prtumvillue of the bond totIay (fou must buy the bo"d). Thllti wbJ the PV IImou"t is"Il"tive; it is II cllsh outjlDw to II bond bUJ".

Now let's value that same bond with a discount tate of 8%:

100 100 100 100 1,100-+--2 +--3 + +--, +--10 =1,134.201.08 1.08 1.08 1.08 1.08

The calculator solution is:

N. 10; PMT. 100; FV. 1,000; uy. 8; CPT -+ PV. -1,134.20

If the market discount tate for this bond were 8%, ir would sell at a premium of$ 134.20 above its par value. When bond yidds decrease, the ptesent value of a bond'spayments, its market value, increases.

If we discount the bond's cash lIows at 12%, the prescnt value of the bond is:

100 100 100 100 1,100-+ --2 +--) + +--, +-1-0 = 887.001.12 1.12 1.12 1.12 1.12

The calculator solution is:

N = 10; PMT = 100; FV = 1,000; IIY = 12; CPT -+ PV= -887

If the market discount tate for this bond were 12%, it would sell at a discount ofSI13to its par value. Whe" b."d ;yit/Js i"cnlUt, the prese"t villue of II bond's pa,mt"ts, itsmllrltet IIl1lue,,ucrelUtS.

Proftssori Note: Iti WfJnh noting hrrr thllt II296 ,ucrellSe in ,ieM-to-maruri"~ inculISn the bo"di ""Iue by more thlln II296 increllSt in ,ieM ,ucrellSn the bo"di~ villue. This il/"strlltn thllt the bo"di price-yield relatio"Ihip is CD""ex.lISwe will

explai" i" more ,utili! in II later topic mnrw.

Calcularing the value of a bond with semiannual coupon paymenu. Let'S calculate thevalue of the same bond with semiannual payments.

Rather than SIOO per year. the security will pay $50 every six months. With an annualYTM of 8%, we need to discount the coupon payments at 4% per period which resultsin a present value of:

50 50 50 50 1,050- +--2 +--) + +-1-9+---"20 = 1,135.901.04 1.04 1.04 1.04 1.04

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Study Se..ion 15Cross-lUfertnce to CFA Institute Assigned Reading '54 -Introduction to Fiud-Incomt Valuation

The calculator solution is:

N. 20; PMT. 50; FV. 1,000; IN. 4; CPT .....PV. -1,135.90

The value of a zero-coupon bond is simply the present value of the maturity payment.With a discount rate of 3% per period, a 5-period zero-coupon bond with a par value ofS 1,000 has a value of:

1,000 = $862.611.035

LOS 54.b: Identify the relationships among a bond's price, coupon rate,maturity, and market discount rate (yield-to-mararity).

cr~GIIProgrllm OImC1llum. Volum. 5, pal' 403

So far we have wed a bond's cash flows and an assumed yield-to-maturity in order tocalculate the value of the bond. Given a bond's price in the market, we can calculate itsyield-eo-maturity because it's a one-to-one relationship between the rwo. We can ...y thatthe ITM is the discount rate that makes the present value of a bond's cash flows equalto its price. For a 5-ycar, annual pay 7% bond that is priced in the market at $1,020.78,thc ITM will satisfy the following equation:

70 + 70 + 70 + 70 + 1,0701+ YrM (1+ YrMt (1 + YrM)3 (I + YrM)· (I + YrM)5

1,020.78

We can calculate the YrM (discount rate) that satisfies this equality as:

N = 5; PMT = 70; FV= 1,000; PV= -1,020.78; CPT -+ IN = 6.5%

By convention, the YrM on a semiannual coupon bond is expressed as two timesthe semiannual discount rate. For a 5-y~r, semiannual pay 7% coupon bond. we cancalculate the semiannual discount rate as YrM/2 and thcn double it to get the YrMexpressed as an annual yield.

35 + 35 + 35 + ... + 35 .... 1,035

1+ YrM2 {1+ YrMZ)2 {1+ YrM2)3 (1+ YrM2)9 . {I+ YrM2tO

= 1,020.78

N = 10; PMT = 35; FV = 1,000; PV = -1,020.78; CPT -+ IN = 3.253%

The YrM is 3.253 x 2 • 6.506%.

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Study S""OIl 15CtoSs-Rtft~Doe to eFA INtitult Assigned Reading '5~ - intrOduction to Fized-Ieceme Valuation

We can summarize the relationships between price and yield as follows:

I. At a point in time. a decrease (increase) in a bond', YTM will increase (decrease) itsprice.

2. If a bond', coupon rate is greater than its YTM. its price will be at a premium to parvalue. If a bond', coupon rate is less than its YTM. its price will be at a discount topar value.

3. The percentage decrease in value when the YTM increases by a given amount issmaller than the increase in value when the YTM decreases by the same amount (theprice-yield relationship is convex).

4. Other things equal. the price of a bond with a lower coupon rate is more sensitive toa change in yield than i, the price of a bond with a higher coupon rate.

5. Other things equal. the price of a bond with a longer maturity is more sensitive to achange in yield than is the price of a bond with a shorter maturity.

Figure I illustrate, the convex relationship between a bond', price and its yield-to-marurity:

Figure 1: Market Yield vs. Bond Value for an 8% Coupon Bond

BondValue

Premium IPar Value •• ~~.~~~•••••••••••••••

'- ~ MarkelYield

··················I··················

Olscoun, '0 I.. ,

6% 7% 8% 9% 10%

Relationship Between Price and Maturity

Prior to maturity, a bond can be selling at a significant discount or premium to parvalue. However. regardless of its required yield, the price will converge to par value asmarurity approaches. Consider a bond with S1.000 par value and a 3·year life: paying6% semiannual coupons. Thc bond values corresponding to required yields of 3%. 6%,and 12% as the bond approaches maturity arc presented in Figure 2.

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Study Session 15eross.Refe_ce to CFA Institute Assigoocl Reading '54 - Introduction to Flsed-Inceme v.Ju.tion

Fi!!!re 2: Bond Values and the P.ss.se of Time

TIme ItJMil/~rity (in YTM·396 YTM.696 YTM.1296

til")

3.0 SI,085.46 SI,OOO.OO S852.48

2.5 1,071.74 1,000.00 873.63

2.0 1,057.82 1,000.00 896.05

1.5 1,043.68 1,000.00 919.81

1.0 1,029.34 1,000.00 945.00

0.5 1,014.78 1,000.00 971.69

0.0 1,000.00 1,000.00 1,000.00

The change in value .... cciated with the passage of time for me three bonds representedin Figure 2 is presented graphically in Figure 3. This convergence: to par value atmaturity is known as the constant-yield price trajectory because it shows how the bond'sprice: would change .s time passes if its yicld-eo-maturiry remained consrant.

Figure 3: Premium, Par, and Discount Bonds

Dondv.luc (S)

A premiunl bond (e.g., 2 6% bond mding at

1,085.4581 __ -!Y..!r'::M~o:f:3%::)~"-~__ ~

A discount bond k.g., • 6% bond t .. ding ..ITM of 12%) "-

852.480L----_:=----~

A par ,.. lue bond (c.& .• a 6% bond ".ding 2t

ITM of6%) '-............................................................. ~i1.000.00

'- Time

LOS 54.c: Define spot rates and calculate the price of a bond using spot rates,

cr-A® Progrllm Wlrri<ulum, Volume 5. pllg< 407

The yield-to-maturity is calculated as if me discount rate for every bond cash flow is thesame, In reality, discount rates depend on the time period in which the bond paymentwill be made. Spot rates arc the market discount rates for a single payment to bereceived in the future. The discount rates for uro-coupon bonds arc spot rates and wesometimes refer to spot rates as zero-coupon '"tel or simply zero rattl.

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Study Stuion 1SCross-lUft"'Dce to eFA IrutilU~ Assi3ntd lUading '54 - InlNduction to FlUd-IDCIOm.Valuation

In order to price a bond with spot rates, we sum the pre~nt values of the bond'spaym~nts, each discounted at th~ spot rate for the number of periods before it will bepaid. The general equation for calculating a bond's value using spot rates (Sj) is:

CPN, CPN2 CPNx +FVx1+S, + (I +S2)2 + + (I +SN)N PV

&ample: Valuing_ bond usinglpot rata

Given the: following spot rates, calc:ulaa: th~ valu~ of a 3-)'.,.t, S'III annual-c:ouponbond.

Spot ratesI-year: 3%2-year: 4%3-year: S%

Answer:

SO + SO + I,OSO -48.54 -r- 46.23+907.03=$1,001.801.03 (1.04)2 (I.OS)'

This price, calculated using spot rates, is sometimes called the nO-lIrbitrllgt prict of abond because if a bond is priced differ.ntly. there will be a profit opportunity fromarbitrage among bonds.

Because tho bond value is slightly greater than its par value, we: know its YTM is slightlyless than its coupon rate of 5%. Using the price of 1,001.80, we can calculate the YTMfor this bond as:

N = 3; PMT = 50; FV = 1,000; PV = -1,001.80; CPT -+ I1Y=4.93%

LOS 54.d: Describe and calculate the flat price, accrued interest, and the fullprice of a bond.

CT-A" Prognzm Currir:uium, v"iumt 5, pllgt 409

The coupon bond values we have calculated so far arc calculated one period before thenext coupon payment will be made. For most bond trades, the settlement date, which iswhen cash is exchanged for the bond, will fall between coupon payment dates, As tim.passes (and future coupon payment dates get closer), tho value of the bond will increase.

Consider a bond with a 5% coupon that has a 5% yield-to-maturity, Just aft.r eachcoupon is paid, the bond value will be its par value. As time passes and the futurepayment dates get closer, the bond', value will increase. The rate of iner ... e in thebond's value is equal to tho bond's YTM so that the value of this bond between eouponpayment dates is par x (1+ YTM)tff, where t is the number of day. from the last couponpayment date until the date the bond trade will settle, and T is the number of days

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Study Session 15Cross-lUftrtftce to CFA " .. titutt Assigned Reading '54 -Introduction 10 Fixtd·lncomt Valuation

between the last coupon payment and the next. We refer to this as the full price (alsocallcd the ;nllD;u pr;<t) of the bond.

Let's work an example for a specific bond:

&ample: CaIculatinS the fuD price of a bond

A 5% bond malccs coupon payments on June 15 and Dca:mbcr 15 and is tradios witha YfM of 4'111.The boDd is purcbuc:d and will acttIe on Ausuat 21 when then: willbe four coupons remaining until maturity. Calculate the full price of the bond usingactual days.

St'p I: Calculate the value of the bond on the last coupon date (coupons arcsemiannual, 10 we usc 4/2 • 2% for the periodic discount rate):

N. 4; PMT. 25; FV. 1,000; IIY .2; CPT _ py. -1,019.04

Sttp 2: Adjust for the number of days since the last coupon payment:

Days bctwa:n June 15 and December 15 • 183 days.Days between June 15 and settlement on Ausuat 21 • 67 days.Full price. 1,019.04 x (1.02)G7111J• 1,026.46.

The accrued interest since the last payment date can be calculated as the eouponpayment times the portion of thc coupon period that has passed between the last couponpayment date and the settlement date of the transaction. For the bond in the previousexam pic, the accrued interest on the settlement date of Augwt 21 is:

$25 (67/183) • 59.15

The full pricc (invoice price) minus the accrued interest i. referred to as the aat price ofthe bond.

full price. flat price + accrued interest

So for the bond in our example, the flat price .. 1,026.46 - 9.15 .. 1,017.31.

The flat price of the bond is also referred to as the bond's clean price, and the full priceis referred to as the dirty price.

Note that the calculation of accrued interest does not discount the accrued interest to itspresent value so that the value of the bond on its last payment date 0,019.04) plus theaccrued interest of 59.15 is greatcrthan the full price of the bond, 1,019.04 + 9.15 =

1.028.19> 1,026.46.

So far, in calculating accrued interest, we used the actual number of days betweencoupon payments and the actual number of days between the last coupon date and thesettlement date. This actual/actual method is used most often with government bonds.

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Sludy S...ion 15CroSs-~f'~Dce 10 CFAInstilule Assigntd ~ading '54 - Inuoduaion 10 FlXtd·IDCIOm.Valuation

The 30/360 method i. most often used for corporate bonds. This method assumes thatthere are 30 days in each monm and 360 days in a year.

To calculate the accrued interest through the Augwt 21 settlement date on me bond inour example (Ihat has coupon payment dates on June IS and December IS). we wouldcalculate 2 x 30 • 60 days between June IS and August IS and men add the 6 days fromAugwt 15 to August 21 to gel 66 days. Assuming 30 days per month. mere arc 180 daysbetween coupon dates.

The accrued interest on the bond using the 30/360 method is 25 x 66 1 180 • 59.166,slightly more man the accrued interest of S9.1 5 calculated using the actuallactualmethod.

LOS 54.e: Describe matrix pricing.

cr-A® Prol"'m Curriculum, v,,/umt 5.pllgt 412

Mattix pricing is a method of estimating the required yield-to-rnaturity (or price) ofbonds mat are currently nOI traded or infrequently traded. The procedure is to UK

the YfMs of traded bonds that have credit quality very close 10 that of a nontradedor infrequently traded bond and arc similar in maturity and coupon. to estimate therequired YfM.

Ezample: Pricing an iUiquid bond

Rob Phelps, CFA. is estimating me ".Iue of a nonlradcd 4%. annual-pay. BB ratedbond that hu 6ve years remaining unlil maNril,.. He hu obtained the foDowingyields-to-maturity on similar corporate bonds:

BB rated. 4-year annual-pay. 5% coupon bond: YfM .4.738%BB rated, 6-year annual-pay, 4% coupon bond: YfM • 5.232%BB rated, 6-year annual-pay, 6% coupon bond: YfM • 5.284%

Estimate the value of the nontradcd bond.

AIl_r.S~p1: Take me average YfM of the 6-year bonds, (5.232 + 5.284) 12 • 5.258%.S~p2: Average the YfM of me 4-year bond wim me II_gl 6-year bond yield,

(4.738 + 5.258) I 2 • 4.998%.SrlP 3: Price me nontraded bond with a YfM of 4.998%.

N.5; PMT. 40; FV- 1,000; IIY -4.998; CPT ... PV- -956.79

The estimated value is 5956.79 per S1,000 par ".Iuc.

In using me averages in me preceding example. we have used a simple form of linear;nttrpDlarion. Because the maturity of the nontraded bond is 6ve years, we UK rhe simpleaverage of the YfMs for me 4-year and 6-year bonds.

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Study Swion 15Cross-lUfertftce to CFA Institute Assigned Reading '54 -Introduction to Fixed-Income Valuation

Consider a case where we are estimating the value of a 5-year, 5% annual-pay couponbond and have the YTMs of otherwise very similar bonds with 4-year and 7-yearmaturities, 4_738% and 5.336%, respectively. In this case. we estimate the YTM on the5-year bond as the yield on the 4-ycar bond, plus one-third of the difference betweenthe YTM of the 4-year bond and the YTM of the 7-year bond. Note that the difll:renccin maturity between the 4-year bond and the 5-ycar bond is one year and the differencebetween the maturities of the 4-y= and 7-year bonds is three years.

The calculatlon is:

(5-4)4.738%+ (7 -4) (5.336%-4.738%)

1= 4.738% + -(0.598%) = 4.937%3

N • 5; PMT • 50; FV • 1,000; IIY • 4.937; CPT ... PV. -1,002.73

A variation of matrix pricing used for pricing new bond issues focuses on the spreadsbetween bond yields and the yields of a benchmark bond of similar maturity that isessentially default risk free. Often the yield. on Treasury bond. are used as benchmarkyields for U.S. dollar-denominated corporate bonds. When estimating the YTM forthe new issue bond. the appropriate spread to the yield of a Treasury bond of the samematurity is estimated and added to the yield of the benchmark issue.

&ample: Eadmating the 'pn:ad for a IICW 6-yar, A rated band inuc

Consider the following market yield"

S-year. U.S. Treasury bond. YTM 1.48%S-ycar. A rated corporale bond, YTM 2.64%

7-year. Treasury bond, YTM 2.1 S%7-ycar. A rated corporale bond, YTM 3.55%

6-ycar Trc:uury band, YTM 1.74%

Eslimate the ~uired yield on a newly issued 6-year, A rated corporate bond

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Study St.slon 15Cro'$-~f_Dce to eFA lrutitute Auigntd ~adin8 '54 - Inttoduction to Fwd-IDCIOm. Valuation

Spread on the 7-ycar corporate bond is 3.55 - 2.15 = 1.40'l6.

Answer:

1. Calculate me spreads to the benchmark (Treasury) yields.

Spread on me 5-ycar corporate bond is 2.64 - 1.48 • 1.16%.

2. Calculate me ava-age spread because me 6-year bond is the midpoint of 6ve andSC\'Cnyears.

Average spread. (1.16 + 1.40) I 2 • 1.28~.

3. Add the average spread to me YrM of me 6-year Treasury (benchmark) bond.

1.74 + 1.28 • 3.02%, which is our estimate of me YrM on the newly issued6-year. A rated bond.

LOS 54.f: Calculate and interpret yield measures for fixed-rate bonds, floating-rate notes. and money market insuuments.

Yield Measures for Fixed-Rate Bonds

We have previously covered me coupon rate and yield-to-maturity for fixed-rate bonds.The effective yield for a bond depends on how many coupon payments are made eachyear and is simply the compound return. How frequendy coupon payments are made isreferred to as the periodicity of the annual rate.

An annual-pay bond with an 8% YrM has an effective yield of 8%.

A semiannual-pay bond (periodicity of two) with an 8% YTM has a yield of 4% """tysix months and an effective yield of \.042 - 1 = 8.16%.

A quarterly-pay bond (periodicity of four) with an 8% yield-to-maturity has a yield of2% every three months and an effective yield of 1.024 - 1 c 8.24%.

~ Projtsso,i Net«: This fll14ws tIN mtthotl Msrribttl in Quantitativt Mtthotls for~ raku14rinl tht tffirnw annual yit/J liwn a stautl annual rrI" anti tIN numbtr of

rompounJinl ptriotls P" }far.

Most bonds in the United State. make semiannual coupon payments (periodicity oftwo), and yields (YTMs) are quoted on a semiannual bond basis, which i•• imply twotimes the semiannual discount rate. It may be necessary to adjust the quoted yield on a

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Study Session 15Cross.lUferenCIO to CFA Institute Assigatd Reading '54 -Introduction to Fixtd·lncomt Valuation

bond to make it comparable with the yield on a bond with a different periodicity. This isillustrated in the following example.

Example: Adjusting yicIcU for periodicity

An Atlas Corporation bond is quoted with a YTM of "'16 on a semiannual bond bois.What yields should be used to compatt it with a quarterly-pay bond and an annual-pay bond!

Answer:

The 6m thins to note is that 4'16on a semiannual bond basis is an dttctiw: yield of2'16per 6-month period.

To compact: this with the yield on an annual-pay bond. which is an efkctive aDnualyield, we need to calculate the efFectiw: annual yield on the semiannual coupon bond.which is 1.022 - 1 • ".04'16.

For the annual YTM on the quarterly-pay bond. we need to calculate the dfectiw:qumerly yield and multiply by four. The quancrly yield (yield per quarter) that isequivalent to a yield of2'16 per six months is 1.02~ - I .0.995'16. The quoted annualrate for the equivalent yidd on a qumerly bond basis is 4 x 0.995 • 3.98'16.

Note that we haw: shown that the dfcctiw: annual yields III: the same for:

o An annual coupon bond with a yield of 4.04'16 on an annual basis (periodicity ofone).

o A semiannual coupon bond with a yidd of 4.0'16 on a semiannual basis(periodicity of two).

o A quara:rly coupon bond with a yield of 3.98'16 on quarterly basi, (periodicity offour).

Bond yields calculated using the stated coupon payment dates arc referred to asfollowing the street convention. Because some coupon datcs will fallon weekendsand holidays. coupon payments will actually be made the ncxt business day. The yieldcalculated using these actual coupon payment datcs is referred to as the true yield.Some coupon payments will be made later when holidays and weekends arc taken intoaccount. so true yields will be slightly lower than street convention yields. if only by afew basis points.

When calculating spreads between government bond yields and the yield on a corporatebond. the corporate bond yield is often restated to its yield on actual/actual basis tomatch the day count convention used on gove.rnment bonds (rather than the 30/360 daycount convention used for calculating corporate bond yields).

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Cun"nt yidd is simple to caleulare but offi,rs limited information. This measure looksat just one source: of return: a bDndi annual inltTNI iMDme-it does not consider capitalgains/lo$SCsor reinvestment income. The formula for the current yidd is:

. Id annual ash coupon paymentcurrent )"Ie cbond price:

&ample: Computios current yidd

Consider a 20-ynr, SI,OOOpar .... ue, 6% u",ia""IUII-,., bond that is cur",ndytrading at a Aat priee of $802.07_ Cakulate the curr.:nt yield.

The .""l1li' cash coupon payments total:

annual o:uh coupon payment. par .... ue x mtro coupon rate.S1,000 x 0.06 • S60

Because tK bond is trading at S802.07, the curtent yield is:

current yidd = 80~07 0.0748, or 7.48%.

Note that current yield is based on .""IUII coupon inte"," so that it is the same for asemiannual-pay and aMual-pay bond with the same coupon rate and price.

The current yidd does not account for gains or losses as the bond's price moves towardits par value over time. A bond's simple yidd takes a discount or premium into accountby assuming that any discount or premium declines evenly over the remaining )'t:arsto maturity. The sum of the annual coupon payment plus (minus) the straight-lineamortization of a discount (premium) is divided by the Aat price to get the simple yield.

For a callable bond, an investor's yidd will depend on whether and when the bond iscalled. The yidd-to-ca11 an be calculated for each possible call date and price. Thelowest of yield-to-maturity and the various yields-to-call is termed the yield-to-worst.The following example illustrates these calculations.

&ample: Y'scld-to-calland yidd-t e-_rst

Consider a 10-ynr,scmiannual-pay 6% bond trading at 102 on January I, 2014. Thebond is callable acconling to the following schedule:

Callable at 102 on or after January I, 2019.Callable at 100 on or after January I, 2022.

Calculate the bond's YTM, yicld-ta-6m call, yicld-ta-6m par call, and yield-ta-worst.

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Answer:

The :prlJ-tll-"",,,,,i,, on th~ bond i. calcu1al~ as:

N. 20; PMT. 30; FV. 1.000; PV. -1.020; CPT-IIY. 2.867%

2 x 2.867 • 5.734% • YTM

To calculal~ th~ yirlJ-_-fim ~.U._ calculacc the yield-to-maturity using th~ numb~rof s~miannual periods until th~ fine call dat~ (10) for Nand th~ call pri« (1.020) forFV:

N. 10; PMT. 30; FV. 1.020; pv. -1.020; CPT_ IIY. 2.941%

2 x 2.941 • 5.882% • yield-to-fin! call

To calculate th~ yirlJ-_-fi"t ,., r.n (second call dat~). we calcu1ar~ th~ yield-to-maturity using the numMr of Kmiannual periods until eM finl par call dare (16) forNand tbe call pri« (1.000) for FV:

N. 16; PMT. 30; FV. 1.000; pv. -1.020; CPT-IIY. 2.M3%

2 x 2.843 • 5.686% • yield-to-fin! par ~a11

The lowest yi~ld. 5.686%. is realized if the bond is caII~ at par on January 1. 2022. soth~ ,ielJ- m is 5.686%.

The cption-adjusted yield is calculated by adding the value of the call option to thebond', current 8at pria:. The value of a callable bond is equal to the value of the bondif it did not have the call option. minw the value of the call option (because the IssuerDWns the call option}.

The option-adjusted yield will be less than the yield-to-maturity for a callable bondbecause callable bonds have high~r yields to compensate bondholders for the issu~r'scall option. The option-adjusted yield can be used to eompar~ the yields of bonds withvariow embedded options 10 each other and to similar option-free bonds.

Floating-Rate Note Yields

The valu~s of 80ating rate nota (FRNs) are more stable than those of fix~d-rat~ debtof similar maturity because the coupon interest rates are reset periodically based on areference rate, Recall that the coupon rate on a 80ating-rat~ note is the reference rateplw or minw a margin based on the credit risk of the bond relative to the credit riskof the reference rate instrument, The coupon rate for the nat period is set using tbe

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current reference rate for the reset period. and the payment at the end of the period isbased on this rate. For this reason, wc say that interest is paid in errmr«.

If an FRN is issued by a company that ha.s more (less) credit risk than the banks quotingUBOR, a margin is added to (subtracted from) UBOR, the reference rare. The liquidityof an FRN and irs taX treatment can also affect the margin.

We call the margin used to calculate the bond coupon payments the quoted marginand the call the margin required to return the FRN to its par value the required margin(also called the discount margin). When the credit quality of an FRN is unchanged. thequoted margin is equal to the required margin and the FRN returns to its par value ateach reset dare when the next coupon payment is reset to the current market rate (plusor minus the appropriate margin).

If the credit quality of the issuer decreases. the quoted margin will be less than therequired margin and the FRN will sell at a discount to its par value. If credit quality hasimproved. the quoted margin will be greater than the required margin and the FRN willsell at a premium to irs par value.

A somewhat simplified way of calculating the value of an FRN on a reset date is to usethe current reference rate plus the quoted margin to estimate the future cash flows forthe FRN and to discount these future cash flows at the reference rate plus the required(discount) margin. The following example illustrates this method. There are morecomplex models that produce better estimates of value.

Eumple: Priein, a S_tins-rate note on a reset date

A semiannual $1.000 par value FRN ha.s rwo yean to maturity. the refi:n:nce tate is1SO-clayUBOR, and the quoted margin is 60 ha.sis poinrs. 1SO-clayUBOR today (.coupon payment IUIdrc:sct date) is 3% and the required (discount) margin is S6 buispoints. Calculate the value of the FRN.

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In a simplified pricing model. all future coupon payments are based on the rcft:renccrate on rcsc:t date and then discounted using this reference rate and the requitedmargin.

Note that both UBOR and the margins are quoted on an annual basis and must bedivided by two 10 Ft the coupon rate for the FRN because it pays two coupons eachyear.

Coupon rate. (I80-day UBOR + quoted margin) 12 • (3.00% + 0.60%) 12 •1.80%.

Coupon payments. 1.80'K1x 1.000 • S18 every six months for two yean.

The appropriate discount rate is (I80-day UBOR + discount margin) 12. (3.00% +0.86%) 12 • 1.93%.

N .4: PMT. 18: IIY. 1.93: FV. 1.000: CPT- PV. -995.04

The estimated value of the FR.'" today can then be calculated as:

Because the discount margin is greater than the quoted margin. the FRN will trade at• discount.

Yields for Money Market Instruments

Recall that yields on money market securities can be stated as a discount from face valueor as add-on yields. and can be based on a 360-day or 365-day basis. U.S. Treaswy billsare quoted as annualized discounts from face value based on a 360-day year. LlBOR andbank CD rates are quoted as add-on yields. We need to be able to:

• Calculate the actual payment on a money market security given its yield andknowledge of how the yield was calculated.

• Compare the yields on fWO securities that are quoted on different yield bases.

Both discount basis and add-on yields in the money market are quoted as simpleannual interest. The following example illustrates the required caleulations and quoteconventions.

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Example: MODey market yiclclsI. A SI.000 90-dayT-bill is priced with an annualized discount of 1.2'16.Calculate

its market pric:c and ill annualized add-on yield based on a 365-day ~ar.

2. A SI million negotiable CD with 120 days to maturity is quoted with an add-onyield of 1.4'16based on a 365-day year. Calculate the payment at maturity for thisCD and its bond equivalent yield.

3. A bank deposit for 100 days is quoted with an add·on yield of 1.5'16based on a360-day year. Calculate the bond equivalc:nt yield and the yield on a semiannualbond basis.

An'_r:

I. The diKount from (ac:cvalue is 1.2'lf1x 90 I 360 x 1.000 • $3 so the current pric:cis 1.000 - 3 • S997.

The equivalent add-on yield for 90 days is 3 I 997 • 0.3009'16. The annualizcdadd-on yield based on a 365-day year is 365 I 90 x 0.3009 • 1.2203'16. This add-on yield based on a 365-day year is tc~rred to as the bond cqui .... ent yield for amoney market security.

2. The add-on interest for the 120-day period is 120 I 365 x 1.4'16 • 0.4603'16.

At maturity. the CD will pay SI million x (1 + 0.004603) • SI.004.603.

The quoted yield on the CD is the bond equivalent yield because it is an add-onyield annualized based on a 365-day year.

3. Because tbe yield of 1.5'16is an annualized effective yield wculatcd based on a360-day year. the bond equivalent yield. which is based on a 36S-day year. is:

(365 I 360) x 1.5'16 • 1.5208'16

We may want to compare the yield on a money market .ccurity to the YTM ofa semiannual-pay bond. The method is to convert the money market .ecurity·.holding period return to an effective semiannual yield. and then double it.

Because the yield of 1.5'16is wculated as the add-on yield for 100 day. times100 I 360. the l00-day holding period tcturn i. 1.5'16x 100 I 360 • 0.4167'16.The effi:ctive annual yield is 1.004167""'100 -1 • 1.5294'16. the equivalentsemiannual yield is 1.015294~ - 1 .0.7618'16. and the annual yield on asemiannual bond basis it 2 x 0.7618'16. 1.5236'16.

Because tbe periodicity of the money market security. 365 I 100. is greater thanthe periodicity of 2 for a semiannual-pay bond. the simple annual rate for themoney marltc:t security. 1.5'16. is less than the yield on a semiannual bond basi••which bas a periodicity of2.

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Study Session 15Cross-lUferenc:e to CFA Institute Assigned Readillg '54 -Introduction to Fixed·lncome Valuation

LOS 54.g: Define and compare the spot curve, yield curve on coupon bonds,par curve, and forward curve.

CFAII Progrrzm o."ictlb.m, Volumt 5, pagt 429

A yield curve shows yields by matwity. Yield curves ate constructed for yields of varioustypes and it's very importa.nt to understand exacdy which yield is being shown. Theterm structure of interest rates refers to the yields at diffi:t<nt maturities (terms) fOr likesecurities or interest rates. The yields on U.S. Treaswy coupon bonds by maturity can befound at I7tasury.pV, and several yield curves arc available at BlHmbtrg.com.

The spot rate yield curve (spot curve) fOrU.S. Treasuty bonds is also referred to as theU'D curw (for zero-coupon) or strip ctI,vt (because zero-coupon U.S. Treasury bondssre also called SlTippt" Trtlllurin). Recall that spot rates arc the appropriate yields, andtherefore appropriate discount rates, for single payments to be made in the future.Yields on zero-coupon government bonds arc spot rates. Earlier in this topic review, wccalculated the value of a bond by discounting each separate payment by the spot ratecorresponding to the time until the payment will be received. Spot rates arc usuallyquoted on a semiannual bond basis, so they arc directly comparable to YTMs quored forcoupon government bonds.

A yield curve for coupon boods shows the YTMs for coupon bonds at variousmaturities. Yields arc calculated for several maturities and yields for bonds withmaturities between these ate estimated by linear interpolation. Figure 4 shows a yieldcurve for coupon Treasuty bonds constructed from yields on l-month, 3·month.6-month, l-year, 2-ycar. 3-ycar. 5-year. 7-year. to-year, 20 year. and 30-y= maturities.Yields arc expressed on a semiannual bond basis.

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Figure 4: U.S. Trcaswy Yield Curve u of August 1, 2013

4.0

1.5

•~

••

••L.o. .....

2.5

2.0

1.0

0.0E - - ••• ~ k ~ k ~_ .Ii -E ~;::;;to

1 me""h 0.02 S,_ IA93 m.""h 0.04 7y= 2.156mcmth 0.08 10y= 2.741 )"Qr 0.13 ZOy= 3.482 )'Of 0.35 JOy= 3.773ynr 0.65

Souto:: http://,, ...w.t.reISury.p/I'ClOUl'CC''<I:nu:r

A par bond yield curve, or JNlT l1<TW, is not calculated from yields on actual bonds butis constructed from the spOt curve. The yields reflect the coupon rate that a hypotheticalbond at each maturity would need to have to be priced at par. Alternatively, they can beviewed u the YTM of a par bond at each maturity.

Consider a 3-year annual-pay bond and spot rates for one, two, and three years of SI' S2'and S,. The following equation can be used to calculate the coupon rate necessary forthe bond to be trading at par.

PMT + PMT ..L PMT +100 100

I+SI (I+S2r· (I+S3)'

With SpOt rates of 1%, 2%. and 3%, a 3·ycar annual par bond will have a payment thatwill satisfy:

PMT PMT PMT +100-- + + 100. so the payment is 2.96 and the par bond coupon1.01 (1.02)2 (1.03)3

rate is 2.96%.

Forward rates arc yields for future periods. The rate of interest on a I-year loan thatwould be made twO years from now is a forward rate. A forward yield curve shows thefuture rates for bonds or money market securities for the same maturities for annualperiods in the future. Typically, the forward curve would show the yields of I-yearsecurities for each future year, quoted on a semiannual bond buis.

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LOS 54.h: Define forward rates and calculate spot rates from forward rates,forward rates from spot rates, and the price of a bond using forward rates.

cr~~Progrrrmo."i",/"m. WI/umt 5. pal' 432

A forward rate is a borrowing/lending rare for a loan to be made at some future date.The noration used must identify both the length of the lendinglborrowing period andwhen in the future the money will be loaned/borrowed. Thus. Iyly is the rate for aI-year loan one year from now; 2y IY is the rare for a I-year loan to be made two yearsfrom now; 3y2y is the 2·year forward rate three years frem now; and so on.

The Relationship Between Short-Term Perward Rates and Spot Rates

The idea here is that bo"owinffo' th," JtllTlllt th. 3-J.II, lpot rete, 0' borrowinffo, one-Jta, p"ioM in thrtt SlI«tuillt ~Ilts. lho"k/ hll". tht sam« tolt. The Si arc the current sporrare. for i periods.

This relation is illustrated as (1 + S,)'. (I + SI)(1 + lyly)(1 + 2yly). Thus. S,.[(1 + SI)(I + lyly)(1 + 2yly)) II) - 1. which is the geometric mean return we covered inQuantirarive Merhod s,

&ample: Computing spot rates from forward ratcs

If the current I-year spot rate is 216. the I-year forward rate one year from IDday(11IJ) is 3'1&.and the I-year forward rate two yean from today (2yIJ) is 4%. what isthe 3-year spot rate!

S, • [(1.02)(1.03)(1.04»11' - 1 .2.997%

Answer:

This can be interpreted to mean that a dollar compounded at 2.997% for three yeanwould produce the same ending value as a dollar that earns compound interest of 2%the lint year, 3% the nat year. and 4% for the third year.

ProftJJO,i Nort: You can ft1 II lit? fO"" IlppTD",·mationof tht 3.,.", spot Ttl" with~ tht simple avtTllft of tht flrwa,d _N. In tht p"vious OCIImp/t.we Cllkuulttd~ 2.99796 lind th. limplt 1I11t'IIftof tht thre« IInnUilI'1Itt1is:

2+3+4 3%.3

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Forward Rates Given Spot Rates

We can use the same relationships we use to calculate spot rates from forward rates tocalculate forward rates from spOt rates.

Our basic relation between forward rates and SpOtrates (for two periods) is:

This again tells us that an invc:stment has the same expected yield (borrowing has thesame expected cost) whether we invest (borrow) for two periods at the 2-period spotrate, 52' or for one period at the current I-year rate. 51' and for the next period at theforward rate. Iyly. Givc:n two of these rates. we can solve for the other.

&ample: Computins a forward rate from spot rates

The 2-period spot tate. 52' is 8%. and the I-period spot tate, 51' is 4%. Calculate theforward tate for one period. one period from now. 1,1,.

The following 6gure illustrates the problem.

Finding a Forward Rate2-ycar bond (5, • 8.0%)

H-------------~.l~1-)"", bond (.odor)

(S, • 4.ClCIO%)I-)nl bUIUJ

(u". )'",If h,,", ,,,dA)·)(J),ly 1)

o 2

From our original equality, (I + 52)2• (1 + 5,)(1 + 1,ly), _ can get

(1+52)2 1=(I+lyly)(1+51)

Or, because we know that both choices have the same payoff in two years:

(1.08)2 = (1.04)(1 + lyly)

(1+1 1 )= (1.08)2Y y (1.04)

lyly = (1.08r -1 = 1.1664 -1 = 12.154%(1.04) 1.04

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In ome:r words. in_tors an: willing to accc:pt 4.0% on me: I-year bond today (whe:nmey could get 8.0% on the 2-year bond today) only because mey can get 12.154%on a I-year bond one: year from today. This future rate: that can be: lockc:d in today is aforward rate.

Similarly. 'M: can back omer forward rates out of me:spot rates_ We:know that:

(I + S,)'. (I + SI)(I + lyly)(I + 2yly)

And mat:

(I + S2)} • (1 + SI)(1 + Iyly). 10 we: can write: (1 + 5,)'. (1 + 52)2(1 + 2yly)

This lut e:quation says chat investing for mrc:c:yean at the: 3-year spot rate shouldproduce: me: same: e:nding value: u imrc:sting for two years at me: 2-year spot rate. andmen for a mird year at 2]1,. me: I-year forward rate. two years from now.

Solving for the: forward rate, 2]1" we: get:

(1+5 )33 -1=2yly

(1+52)2

Example: Forward rates &om spot rates

ut's extend the previow examplc: to three periods. The current I-year spot rate is4.0%, me current 2-year spot tate: is 8.0%, and the eureent 3-year spot tate is 12.0%.Calculate me: I-year forward rates one: and two yean from now.

Annn:r:

We:know the: following rc:lation must hold:

We:can we: it to 10M: for me: I-year forward rate:one: year from now:(1 08)2

(1.08)2 =(1.04)(1+1yly),101yly= (- ) -1=12.154'11>1.04

We:also know that me: relations:

(I + S,>'. (1 + SI)(1 + lyly) (I + 2yly)

and, c:qujyaJe:ntly (I + 53)3 • (I + 5})2(1 + 2yly) must hold.

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Study S... ion 15CroSs-~f'~Dce to CFA lostiNt. Assi&ntd ~ading '54 - Inttoduction to FllItd·IDCIOm.Valuation

Substituting values for S, and S2' "'"1: have:

(1.12)3. (1.08)2 " (1 .2yly)

so that the I-year forward rate two years from now is:

2 1 = (1.12>' -1 =20.45'111Y Y (l.08~

We can check our results by calculating:

S,. [(1.04)(1.12154)(1.2045»)11'-1. 12.00'IfI

This may aD seem a bit complican:d. but the basic relation. that borrowing forsucccssi~ periods at I-period rates should ha~ the same cost as borrowing atmultiperiod spot rares. can be summed up as:

(1 .52)2. (1 .5.)(1 • lyly) for two periods. and (1 • SJ' • (1 • S2)2(1 .2yly)for three periods.

Pro!tsso,'s Notr: Simple IIl1UagtJalsoKive Jecmt approximations fl, calculatingfl,warti ,aus from lpot mtes; In tht p1tuJing tXllmplt. wt haJ spot 'lltn 0/496 fl, on«~II' IInJ 896fl, two ~a1'1. Two ,ta1'1 lit 896 is 1696. so if tht

~ fi1'1t-,tll' ,au is 496. tht stconJ-,tll' 'aU is ck1St1D16 - 4 ; 1296 (actUilIis~ 12.154). Givtn II2-~1I' spot TtlU0/896 IInJ II3-~a, spot TtlU0/1296. wt CDUiJ

approximau tht 1-~II' flrwllrti ntufrom time tU/IDto time thrrt lIS (3" 12)-(2" 8) • 20. Thllt mllJ be ciDst tnough (actllill is 20.45) tllamrw, a multipk-cboicr qurstion IInJ. in lin, ClISt.StrWf lISa gooJ chtclt to maltt SUft tht tXJUt rete,ou calculau is Ttllsonabk.

We can also calculate implied forward rates for loans for more than one period. Givenspot rates of: l-year - 5%. 2-yar - 6%. 3-year - 7'111.and 4-year. 8%. we can calculate2,2,.

The implied forward rate on a 2-year loan two years from now, 2,2,. is:• 1/

2 (1.08') 2-1= -- -1=10.04%.1.062

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Study Session 15c.o... lUftrtftce to CFA IDStitutt Assigned Reading '54 -Introduction to Fixtd·lncomt Valuation

Proftllo,i Now Tbe app,n;mJttion wo,ks fl, multi-p.riod fl,ward ,am as w.IL

The dijfrrtnct bttwttn flu, ).an at 896 (= 3296) and two).a,s at 696 (= 1296)o is 2096. BuallS. that dijfrrtnct isfo, two ,.a,s. wt dillid. by two to ttt an annual

rat« of 1096. (4 x 8 - 6 x 2) = 10. whirh is ",ry ,/4St to thr e.xact solution of2

10.0496.

Valuing a Bond Using Forward Rates

EDmple: Computius a boud nlac UliuS forward ratcs

The cur",nt I-year rate. SI' il 4%. me I-year forward rate forlendiog from time. 1to time. 2 i. lyly. 5%. aad the I-year forward rate for lendiag from time. 2 totime. 3 is 2y Iy • 6%. Value a 3-year annual-pay bond with a 5% coupon and a parvalue of SI.OOO.

Answer:

bond vaIuc. ~ + 50 + 1.050 =I + ~ (I +S,)(I + Iyly) (I + S, )(1 + lyly)(1 + 2y1y)

50 50 + 1.050 -$1000981.04 + (1.04}(1.05) (1.04)(1.05}(1.06)- • .

Profrnt1,i Notr: /fyou thinlt this loolts II [jnk lilt. IIl1luinga bond using spot ,atts,as wt did fo, a,bitrag.jr re ""luation. you art correct. The du(ount [atton a"G 'lJuiUllknt to spot rat« du(o""t [atton.

If wt hilI/( a Stmillnnuill (oupon bond. th. ,al",lIItion mtthoJs art tht same, butw. woulJ UStth. stmUtnnual dis",unt rate ,"th" than th. annUilliud ,art andth. numbt, Ofpt,ioJs wouIJ b. tht numb" of StmiannUilI ptrioJs.

LOS 54.i: Compare, calculate, and interpret yield spread measures.

CFA* Prog,am UI"i",lum. v.,["mt 5. patt 436

A yield spread is the differenc:c between the yidds of two different bonds. Yield spreadsare rypically quoted in basis points.

A yield spread relative to a benchmark bond is known as a benchmark spread, Forexample, if. 5-year corporate bond has a yield of 6.25% and its benchmark, the 5-ye.rTreasury note, has a yield of 3.50%, the corporate bond has a benchmark spread of625 - 350 • 275 basis points.

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For fixed-<:oupon bonds, on-the-run government bond yields for the same or nearestmarurityare frequendy used as benchmarlu. The benchmark may change during abond's life. For a 5-ycar corporate bond. when issued, the benchmark spread is statedrelative to a 5-ycar government bond yield, but two yean later (when it has threeyears remaining to maturity) its benchmark spread will be stated relative to a 3-yeargovernment bond yield. A yield spread over a government bond is also known as aG-.pread.

An alternative to using government bond yields as bcnchmarlu is to usc rates for interestrate swaps in the same currency and with the same tenor as a bond. Yield spreads relativeto swap rates are known as interpolated spreads or I-spreads. l-spreads are frcquendystated for bonds denominated in euros.

~ Pro/tssoTi Note: FOOTbonds with tenon that do not match an on-t'" Tim~ lowrnment b.nd. ,Md spreads ma, b~ qUllUdwlatillt to an ·int.rpolaud

lowrnm~nt b.ntI ,Md. • Thes« aw stiD G-spreads.

As we noted in an earlier topic review, floating-rate securities typically usc UBOR as abenchmatk rate.

Yield spreads are useful for analyzing the factors that affect a bond's yield. If acorporate bond's yield increases from 6.25% to 6.50%, this may have been causedby factors that affect all bond yidds (macroeconomic factors) or by firm-specific orindustty-specific (microcconomic) factors. If a bond's yield increases but its yieldspread remains the same, the yield on its benchmark must have abo increased, whichsuggests macroeconomic factors caused bond yields in general to increase. However, ifthe yield spread increases. this suggests the increase in the bond's yield was caused bymicroeconomic facton such as credit risk or the issue's liquidity.

PrD/tssori Netr: R.caDfrom our discussion ofth. Fish" ./foer in Economics that~ an interot rtlU is compoud oft'" real rislt-frn rete, th. apuud inflation rete,~ anti a Tisltpwmium. ~ can thinlt of macrouonomic factors as thos~that 4ftct th~

real TisltfTU Tau anti apuud inflation. anti microtconomic factors as thos~ thataff«t th~ Crtdit and liquidity risltpremium.

Zero-Volatility and Option-Adjusted Spreads

A disadvantage of G.spreads and I-spreads is that thcy arc theoretically correct only ifthe .pot yield curve is flat so that yields are approximately the same across maturities.Normally. however, the spot yield curve is upward-sloping (i.e., longer-term yields arehigher than shorter-term yields).

A method for deriving a bond's yield spread to a benchmark spot yield curve thataccounts for the shape of the yield curve is to add an equal amount to each benchmarkspot rate and value the bond with those rates. When we find an amount which, whenadded to the benchmark spot rates, produces a value equal to the market price of the

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Study Seuion 15Cro ... lUfertftce to CFA Institute Assigned Reading '54 -Introduction to Fiud·lncome Valuation

bond. we have the appropriate yield curve spread. A yield spread calculated this way isknown as a u:ro·volatility spread or Z-spread.

Example: Zero-volatility spread

1-.2-. and 3-)'Qr spot ratc:l 00 Treasuries an: 4%. 8.167%. and 12.3n%. respectively.Consid.,r a 3-)'Qr, 9% annual coupon corpora.., bond trading at 89.464.The YTMis 13.50%, and the: TIM of a )-year Treasury is 12%. Compu.., the G-sprc:ad and theZ.sprcad of the: corpora.., bond.

G-sprcad • YTM._. - YTMr-..,. • 13.50 - 12.00 • 1.50%.

The G-.pread is:

To compu.., the Z-spread, set the present value of the bond's ash Sows equal to today'smarlcc:tpriee. Discount ca:h c:ash 80w at the appropriate :r.c:ro-couponbond spotra.., phu a fixed spread ZS. SoI-vc for ZS in the following equation and you ha-vcthez.sprcad:

89.<164 • 9 + 9 + 109 =>(1.04 + ZS)I (1.08167 + ZS)2 (1.I23n + zsy

ZS = 1.67% or 167 basis poina

Noc.. that this spread is found by uial-and-enor. In other wonls, pick a oumber ·ZS,·plug it imo the right-hand side of the equation, and see if the result equals 89.464. Ifthe right-hand side equals the left, then you have found the Z.spread. If not, adjust·ZS· in the appropriate direction and recalculate.

An optioo-adjwted spread (OAS) is used for bond. with embedded options. Looselyspeaking. the option-adjusted spread takes the option yield component out of theZ-spread measure; the OAS is the spread to the Treasury spot rate curve that the bondwould have if it were option-free.

If we calculate an OAS for a callable bond, it will be less than the bond's Z-spread. Thedifference is the extra yield required to compensate bondholders for the call option. Thatextra yield is the option value. Thus, we can write:

option value = Z-spread - OAS

OAS = Z-spread - option value

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Sludy S... lon 15Cro",-~ft~Dce 10 CFA Institute Assigntd ~ading'54 -Introduction to Fwd-IDCIOmt Valuation

KEY CONCEPTS

LOS 54.aThe price of a bond is the praent value of in future cash RoW$,discounted at the bond'syidd-to-maturity.

For an annual-coupon bond with N yean to maturity:

price = coupon + coupon + ...+ coupon + princ:ipal(I+ YrM) (1+ ITM)2 (1+ IT.M)~

For a semiannual-coupon bond with N years to maturity:

. _ coupon coupon coupon + principal

pnce- (1+ ~M)+ (1+~r+ ...+ (1+ ~rX2LOS 54.bA bond's price and ITM are inversely related. An increase in ITM decreases the priceand a decrease in ITM increases the price.

A bond wiU be priced at a discount to par value if its coupon rate is less than ilS ITM,and at a premium to par value jf its coupon rate is greater than its ITM.

Prices arc more sensitive to changes in ITM for bonds with lower coupon rata andlonger maturities, and less sensitive to changa in YTM for bonds with higher couponrata and shorter maturities.

A bond's price moves toward par value as time pass es and maturity approaches.

LOS 54.cSpot rates arc market discount rates for single paymenlS to be made in the future.

LOS 54.dThe full price of a bond includes interest accrued between coupon dates. The aat priceof a bond is the full price minus accrued interest.

Accrued interest for a bond transaction is calculated as the coupon payment times theportion of the coupon period from the previous payment date to the settlement date.

Methods for determining the period of accrued interest include actual days (typicallyused for government bonds) or 30-day months and 360-day years (typically used forcorporate bonds).

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Study Session 15Cro •••lUfertftce to CFA Institute AIIigntd Reading '54 -Introduction to Fixed·lncome Valuation

LOS 54.eMatrix pricing is a meehod used to estimate the yield-to-maturity for bonds tbat are nottraded or infrequently traded. The yield is estimated based on the yields of traded bondswith the same credit quality. If these traded bonds have different maturities than thebond being valued, linear interpolation is used to estimate the subject bond's yield.

LOS 54.fThe effective yield of a bond depends on its periodicity, or annual frequency of couponpayments. For an annual-pay bond tbe effective yield is equal to the yield-to-maturity.For bonds with grcater periodicity, the effective yield is greater than the yield-to-maturity.

A YTM quoted on a semiannual bond basis is two times the semiannual discount rate.

Bond yields that follow street convention use the stated coupon payment dates. A trueyield accounts for mupon payments that are delayed by weekends or holidays and maybe slightly lower than a meet convention yield.

Current yield is the ratio of a bond's annual eoupon payments to its price. Simple yieldadjusts current yield by using straight-line amortization of any discount or premium.

For a callable bond, a yield-to-call may be calculated using each of its call dates andprices. The lowest of these yields and YTM is a callable bond's yield-tc-werst,

Floating rate notes have a quotta margin relative to a reference rate, typically UBOR.The quoted margin is positive for issuers with more credit risk than the banks thatquote L1BOR and may be negative for issuers that have less credit risk than loans tothese banks. The uqui,.a mllrgin on a Roating rate note may be greater than the quotedmargin if credit quality has decreased, or less than the quoted margin if credit qualityhas increased.

For moncy market instruments, yields may be quoted on a discount basis or an add-onbasis, and may use 360-<lay or 365·day years. A bond-equivalent yield is an add-on yieldbased on a 365·day year.

LOS 54.gA yield curve shows the term structure of interest rates by displaying yields acrossdifferent maturities.

The spot curve is a yield curve for single payments in the future, such as zero-couponbonds or stripped Treasury bonds.

The par curve shows the coupon rates for bonds of various maturities that would resultin bond prices equal to their par values.

A forward curve is a yield curve composed of forward rates, such as l.year rates availableat each year over a IUture period.

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Study Session ISCroSs-~ft~Dce to CFA Instiwtt Assij;ntd ~ading '54 - Introduction to FIJItd·IDCIOmtValuation

LOS 54.hForward rates arc current lending/borrowing rates for short-term loans to be made infuture periods.

A SpOt rate for a maturity of N periods is the geometric mean of forward rates over theN periods. The same relation can be used to solve for a forward rate given spot rates fortwO different periods.

To value a bond using forward rates, discount the cash Bows at times I through N by theproduct of one plus each forward rate for periods I to N, and sum them.

For a 3-year annual-pay bond:

. coupon coupon ODupon+ principalpnce= (I+~) + (I+S.)(I+lyly) + (I+S.)(I+lyly)(1+2yly)

LOS 54.iA yield spread is the difference between a bond's yield and a benchmark yield oryield curve. If the benchmark is a government bond yield, the spread is known as agovernment spread or C.spread. If the benchmark is a swap rate, the spread is known asan interpolated spread or I.spread.

A zero-volatility spread or Z-spread is the percent spread that must be added to each spotrate on the benchmark yield curve to makc the present value of a bond equal to its price.

An option-adjusted spread or OAS is used for bonds with embedded options. For acallable bond, the OAS is equal to the Z-spread minus the call option value in basispoints.

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Study Seuion 15Cross.lUftrenc:eto CFA Institutt Assigned Reading '54 -Introduction to Fiucf.lncomt Valuation

CONCEPT CHECKERS

L A 20-year, 10% annual-pay bond has a par value ofSI,OOO. What is the price ofthe bond if it has a yield-to-maturity of 15%?A. $685.14.B. $687.03.C. $828.39.

2. An analyst observes a 5-year, 10% semiannual-pay bond. The face amount is£ 1,000. The analyst believes that the yield-to-maturity on a semiannual bondbasis should be 15%. Based on this yield estimate, the price of this bond wouldbe:A. £828.40.B. £1,189.53.C. £1,193.04.

3. An analyst observes a 20'year, 8% option-free bond with semiannual coupons.The required yield-to-marurity on a semiannual bond basis was 8%, butsuddenly it decreased to 7.25%. As a result, the price of this bond:A. increased.B. decreased.C. stayed the same.

4. A SI,OOO, 5%, 20-year annual-pay bond has a TIM of6,5%. If the TIMremains unchanged, how much will the bond value increase over the next threeyears?A. $13.62.B. $13.78.C. $13.96.

5. A market rate of discount for a single payment to be made in the future is a:A. spot rate.B. simple yield.C. forward rate.

6. If spot rates are 3.2% for one year, 3.4% for two years, and 3.5% for three years,the price of a $100,000 face value, 3-year, annual-pay bond with a coupon rateof 4% is dorm to:A. $101,420.B. $101,790.C. S 108,230.

7. An investor paid a full price of $1,059.04 each for 100 bonds. The purchase wasbetween coupon dates, and accrued interest was $23,54 per bond. What is eachbond's Rat prie.:?A. $1,000.00.B. $1,035.50.C. $1,082.58.

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Study Session ISCroS$-~ft~Dce to eFA lrutitu~ Anigntd ~ading '54 - Introduction to FIJItd-IDCIOmtValuation

8. Cathy Moran, CFA, U estimating a value for an infre<juendy traded bond with 6yean to maturity, an annual coupon of 7%, and a single-B credit rating. Moranobtains yields-to-maturity for more liquid bonds with the same credit rating:• 5% coupon, 8 years to maturity, yielding 7.20%.• 6.5% coupon, 5 years to maturity, yielding 6,40%.

The infrequently traded bond is most lilt~1ytrading at:A. par value.B. a discount to par value.C. a premium to par value.

9.

~70

Based on semiannual compounding, what would the TIM be on a 15-year, zero-coupon, $1,000 par value bond that's currendy uading at $331.40?A. 3.750%.B. 5.151%.C. 7.500%.

10. An analyst observes a Widget & Co. 7.125%, 4-year, semiannual-pay bondtrading at 102.347% of par (where par is SI.OOO). The bond is callable at 101 intwo years. What is the bond's yield-to-call!A. 3.167%.B. 5.664%.C. 6.334%.

II. A Aoating-rate note has a quoted margin of +50 basis points and a requiredmargin of +75 basis points. On its next reset date, the price of the note will be:A. equal to par value.B. less than par value.C. greater than par value.

12. Which of the following money market yields is a bond-equivalent yield?A. Add-on yield based on a 365-day year.B. Discount yield based on a 360-day year.C. Discount yield based on a 365-day year.

13. Which of the following yield curves is lees« lilt~1yto consist of observed yields inthe market?A. Forward yield curve.B. Par bond yield curve.C. Coupon bond yield curve.

The 4-year spot rate is 9,45%, and the 3-year spot rate is 9.85%. What i. theI-ycar forward rate three years from today?A. 8.258%.B. 9.850%.C. 11.059%.

14.

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Study Session 15Cross.lUferenc:e to CFA Institute Assigned Read;"g '54 -Introduction to Fixed·lncome Valuation

15. Given tho followingspot and forwald rates:• Current l-year spOtrat. is 5.5%.• One.yar forward rat. on. year from today is 7.63%.• One-year forward rat. rwo yean from today is 12.18%.• On.·year forward rat. three yean from today is 15.5%.

The value of a 4·y.ar, 10% annual-pay, $1,000 par value bond is cloltSt to:A. $996.B. $1,009.C. $1,086.

16. A corporat. bond is quoted at a spread of ~235 bas.. points over an interpolated12·y<arU.S. Treasury bond yidd. This spread .. a(n}:A. G-spr<ad.B. J-spread.C. Z-sprcad.

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Study Session 1~CroS$-~ft~Dce to CFA lrutitutt Anigntd ~ading 154 - Introduction to Fwd-lnCIOmt Valu.ation

CHALLENGE PROBLEMS

I. What is the yield on a semiannual bond basis of an annual-pay 7% coupon bondpriced at par?

2. What is the equivalent annual-pay YTM fer a 7% coupon semiannual-pay bond?

3. The yield-to-marurity on a quoted on a semiannual bond basis on 6-month.I-year. and 18-month T-biUs arc 2.80%.3.20%. and 4.02%. respectively. A1.5"year. 4% Treasury note is selling at par. If a 1.5-ycar semiannual-paycorporate bond with a 7% coupon is selling for 102.395. what is the spread overthe Treasury note fer this bond? Is the zero-volatility spread (in basis points)127. 130. or 133?

4. Assume the following spot rates arc quoted on a semiannual basis.

~." iii SpOIlIiIlnM.Nlrity

0.5 4.0%

1.0 4.4%

1.5 5.0%

2.0 5.4%

A. What is the 6-month forward rate one year from now?

B. What is the I-ycar forward rate one ycar from now?

C. What is the value of a 2-year. 4.5% coupon. semiannual-pay bond?

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Study Session 15Cross·lUferenc:e to CFA Institute Assigned Readiftg '54 -Introduction to Fixed·lncome Valuation

5. Assume the current 6-month rate is 3.5% and the 6-month forward rates (all ona semiannual bond basis) arc those in me following table.

Ptriot/s FTflmNIIW

FDr""""!lit",

2

3

4

3.8%

4.0%

4.4%

4.8%

A. Calculate the corresponding spot rates.

B. What is the value of a 1.5 year, 4% semiannual-pay bond based on spotrates?

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Sludy Session 15Cros$-~fe"'Dce 10 CFA Institule Assigned ~ading '54 - Inuoduction 10 F"uted-IDCIOmeValuation

CONCEPT CHECKERS - ANSWERS

I. B N. 20. IN • 15; FV • 1.000; PMT • 100. CPT --+ PV. -5687.03.

2. AN. 10. IN. 7.5. FV. 1.000; PMT. 50; CPT --+ PV • -5828.'10.

3. A The price-yield ",lationship is inverse. If the required yidd dec .... es, rhe bond', pricewiU increase, and vice: versa.

-I. A With 20 years 10 maturity, the value of the bond with an annual-pay yield of 6.5%is N • 20. PMT. 50. FV. 1.000. IN • 6.5. CPT - PV • -83~.72. With N • 17.CPT -+ PV • -848.3~. so Ihe value will increase S 13.62.

5. A A 'POI rate i, a diseount rare for a single fUlu", paymenl. Simple yield i, a measure of abond's yield Ihal accounts for coupon interest and assumes slraighl-Iine amortizalion of2 discount or premiurn. A forward rate: i.s an interest rate for a fututt period, such as a3-monlh raec six monw from loday.

bond value. 4.000 + 4.000 + 104.000 = SI01.419.281.032 (1.034)2 (1.035)3

6. A

7. B The full price includes accrued inrerest, while ehe 8at price dOOJnOI. Therefore. ehe 8at(or clean) price is 1.059.04 - 23.54. SI.035.50.

8. C Csing linear interpolatien, the yield on a bond with six years 10 maluri!), should be6040% • (1/3)(7.20% - 6.'10%) .6.67%. A bond with a 7% coupon and a yield of6.67% is al a premium 10 par value,

9. C N. 30; FV • 1.000; PMT. 0; PV. -331.40; CPT -+ IN. 3.750 x 2 • 7.500%.I

A1lernari"dy. (1.000)30-- -1 x2 = 7.5%331.4

10. C N. -I; FV. 1.010; PMT. 35.625; PV. -1.023.'17; CPT - IN. 3.167 x 2.6.334%.

II. B If the required margin is g""let Ihan Ihe quored martin. ehe eredit qualilY of the issuehu decreased and the price on the reser dare will be I... than par value.

12. A An add-on yield bued on a 365-day year is a bend-equivalent yield.

13. B Par bond yield curves are based on the Iheorelical yields thaI would cause bonds aleach malurilY 10 be priced al par. Coupon bond yields and forward interest rares tan beobserved directly from marker uansactions.

14. A (1.0?45)4. (1.0985)' x (J .3yly)

(1.0945)43yly = 3 -I = 8.258%

(1.0985)

Approximale forward rate. 4(9,45%) - 3(9.85%) • 8.25%.

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Study Session 1SCro$S.lUfermce to CFA l",tituto AsUgned Reading '54 - Introduction to Fixed·lncome Valuation

15. B Bond value.

100 100 100 1.100-- + + + -:----,-:---:-:---:-.,....-~1.055 (1.055)(1.0763) (1.055)(1.0763)(1.1218) (1.055)(1.0763)(1.1218)(1.155)~ 1,009.03

16. A G ••preads are quoted relative to an actual or interpolated government bond yield.)"preado are quoted r.l"i,,,, '0 swap ra .... Z·spreado are caleulaeed based on the ,hap. ofthe benchmark yield curve.

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Study &ssion 15CroS$-lUfe~Dce to CFA hutiwu Anigned Reading '54 - Introduction to F'llIed-lnCIOmeValuation

CHALLENGE PROBLEMS - ANSWERS

1. stmiannual bond baJis ITM • 2 x semiannual discount late

semiannual discounr rate • (1.07)112- 1 .0.344.3,44%

semiannual bond baJis ITM • 2 x 3,44% • 6.88%

(007)'2. annual-payITM. I+~ - 1 .0.0712.7.12%

3. Compute the YTM on the corporate bond:

N. 1.5 x 2 • 3; PV. -102.395; PMT. 7 12.3.5; FV. 100; CPT -- IN. 2.6588 x2.5.32%

G-.pread • ITMBond - ITMT ...... '1 • 5.32% - 4.0% • 1.32%, or 132 bp

Solve for the uro-volatility ,p~ by selling the present value of the bond', cash Bowsequal to the bond's price, discounting tach cash flow by the Treasury .pot rate plus afixed Z-spread.102,4_ 3.5 + 3.5 + 103.5

....0.028 + ZS ( 0.032 + ZS)2 ( 0.0402 + ZS)'I. I.... 1+=="':"";;::;2 . 2 - 2

Substituting each of the choices into this equation gives th. following bond values:

Z-SP",U' &nJV61w

127 bp 102,4821

l30bp 102.4387

133 bp 102.3953

A Z-sprtad of 133 bp produces a value dosest to the bond's price.

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Study Session 15Cross.lUf.rmce to CFA l",u.ul. Assigned Reading '54 -Introduction '0 Fiucl-Income Valuation

12m6m ~ 0.03103x2 ~0.OG21~ 6.21%

B. Iyly here refers 10 the I-yea: rare, on. yea, from ,od.y, •• pressed on a semiannua) bondbasis.

!r!r~2

NOI. Ihal the approximation 2 • 5.4 - 4.4 .6.4 works very well her. and is quite a billess work.

C. Dlscount each of lhe bond', cash flows (as a percenr of par) by the appropriale SpOIral.:

bo d I _ 2.25 + 2.25 + 2.25 + 102.25nva"·0040 1 , •I+T (1+ 0.~4] (1+ O'iO] (1+ 0.~54]

_ 2.25 + 2.25 + 2.25 + 102.25_ 98.361.02 1.0445 1.0769 1.1125

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S.udy Session 15CroS$-~ft~Dce.O eFA l",tilUto Anigned ~ading'54 -Inuoduction to HlItd-IDCIOmtValu.ation

5. A. (I+¥f -(I+¥](I+ 6~m]_[I+ 0.~35][1+0.~38]_1.0368

~ ~ 1.0368'12-I ~ 0.01822

SI.O. 0.0182 x2 • 0.036Ji ·3.6Ji%

(I+¥ r a(I+~ )(1+ 6m26m)(1+ 12~6m)

= (I +0.~35)( 1+0.~38)(1+O.~O)= 1.0576

~ -1.0576'" -I - 0.01882

SI.S • 0.0188x 2 .0.0376.3.76%

(1+S~.r =(1+ ~' ][1+6~6m][1+12~ ][1+18~6m]

~[I+ 0.~35][1+0.~38][1+O.~O][I+o.~4]~1.080?

S,.• =I 080?".-I =0.01%2 .

S2.0. 0.01%x 2 • 0.0392• 3.92%

2 + 2 + 102 -100.35B. 1+0.~35 (1+0.0;6-4]' (1+0.0;76]'

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The following is • rnicw of the Fixed Income: Anal)"i. of Risk principl •• dcsigned 10 add.... theleaming outcome statements let forth by CFA Iftllitutc. Thi.1 topic i. alto cOl'eM in:

UNDERSTANDING FIXED-INCOME RISKAND RETURN

S.udy S.s.ion 16

ExA.\I Focus

"Risk" in the title of this topic review refers primarily to risk arising from uncereainryabout future interese rates, Measurement of eredit risk is addressed in the followingtopic review, That said, there is a significant amount of testable material covered in thisreview, Calculations required by the learning outcomes include the sources of bondreturns, three duration measures, mon~ duration, the price value of a basis point, andapproximat~ convaity. You must also be able to eseimate a bond's price change for agiven change in yield based on irs duration and convexity. Important conceprs includehow bond characteristics affect interest rate risk, factOts that affect a bond's reinvestmentrisk, and the interaction among price risk, reinvesrmene risk, and the investmenthorizon.

LOS 55.a: Calculate and interpret the sources of return from investing in afixed-rate bond.

There are three sour= of retu.rns from investing in a fixed-rate bond:

1. Coupon and principal paymenrs.

2. Interest earned on coupon paymenrs that arc reinvested over the investor's holdingperiod for the bond.

3. Any capital gain or loss if the bond is sold prior to maturity.

We will assume that a bond makes all of its promised coupon and principal paym~nrs ontime (i.e., we are not addressing credit risk). Additionally, we assume that the internt ret«tll,ntJ on ,,;nvttftJ coupon plll"'tntf U fht SIImt lIS fht YTM on m. bona. There are fiveresults to gain from the analysis presented here.

Given the above assumptions:

). An investor who holds a fixed-rate bond to maturity will cam an annuali:r.c:drate ofreturn equal to the YTM of the bond when purchased.

2. An investor who sells a bond prior to maturity will earn a rate of return equal to theYTM at purchase if the YTM at sale has not changed sinee purchase.

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Study Session 16Cross-lUfmDC>e to CFA IrutilUte~ed Reading '55 - UndenWlding F'lXtd·lncomt Risk and IUtum

3. If the market YTM for the bond, our assumed reinvestment rate. increases(decreases) after the bond is purchased but before the first coupon date. a buy·and.hold investor's realized return wiD be higher (lower) than the YTM of the bondwhen purchased.

4. If the market YTM for the bond. our assumed reinvestment rate. incrtaJts after thebond is purchased but before the first coupon date. a bond investor will carn a rateof return that is lower than the YTM at bond purchase if the bond is held for a shortperiod.

5. If the market YTM for the bond. our assumed reinvestment rate. tUCrttUts after thebond is purchased but before the first coupon date. a bond investor will cam a rateof rerurn that is lower than the YTM at bond purchase if the bond is held for a longperiod.

We will present mathematical examples to demonstrate each of these results as _n usome intuition as to why these results must hold.

A bond investor's annuallzed holding period rate of rerum is calculated as thecompound annual return earned from the bond over the investorS holding period. Thisis the compound rate of return that. based on the purchase price of the bond, wouldprovide an amount at the time of the sale or marurity of the bond equal to the sum ofcoupon payments, sale or maturity value. and interest earned on reinvested coupons.

We will illustrate this calculation (and the first result listed carlier) with a 6% annual-paythree-year bond purchased at a YTM of7% and held to maturity.

With an annual YTM of7% the bond's purchase price is S973.76,

N = 3; IIY = 7; PMT = 60; FV = 1,000; CPT -> PV = -973.76

At marurity. the investor will have received coupon income and reinvestment incomeequal to the future value of an annuity of three $60 coupon payments calculated with aninterest rate equal to the bond's YTM. This amount is

60(1.07)2 + 60(1.07) + 60 • S192.89

N • 3; IIY. 7; PV. 0; PMT • 60; CPT -+ FV. -192.89

We can easily calculate the amount earned from reinvestment of the coupons as

192.89 - 3(60). $12.89

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Adding the maturity value of $1,000 to $192.89, we can calculate the investor's tate ofI

return over the three-year holding period as (1,192.89)3 -1 = 7% and demonsttate that973.76

$973.76 invested at a compound annual tate of7% would return $1,192.89 after threeyears.

We can calculate an investor's tate of return on the same bond purchased at a YfM of 5%.

Price at purchase:

N .3; IfY • 5; FV. 1,000; PMT • 60; CPT .....PV. -1027.23

Coupons and reinvestment income:

60(1.05)2 + 60(1.05) + 60. S189.15 or

N. 3; IfY. 5; PV. 0; PMT. 60; CPT .....FV. -189.15

Holding period return:

I

(1,189.15)3 -1=5%1,027.23

With these examples, we have demonstrated our first result: that for a fixed-rate bondthat docs not default and has a reinvestment rate equal to the YTM, an investor whoholds the bond until maturity will earn a tate of return equal to the YfM at purchase,regardless of whether the bond is purchased at a discount or a premium.

The intuition is straightforward. If the bond is sdling at a discount, the YTM isgreater than the coupon rate because together, the amonization of the disceunt and thehigher assumed reinvestment rare on coupon income increase the bond's return. For abond purchased at a premium, the YTM is less than the coupon rate because both theamortization of the premium and the reduction in interest earned on reinvestment of iucash flows decrease the bond's return.

Now let's examine the second result: that an investor who sells a bond prior to matwitywill earn a tate of return equal to the YTM as long as the YTM has not changed sincepurchase, For such an investor, we call the time the bond will be held the investor'sinvestment horizon. The value of a bond that is sold at a discount or premium topar will move to the par value of the bond by the maturity date, At data between thepurchase and the sale, the value of a bond at the same YTM as when it was purchasedis its carrying value and refleces the amortization of the discount or premium since thebond was purchased.

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P,o/m'IT's Not«: G.rrying V4lu~ is IIp,ift IIlong II bonJ's COnlt.Tlt·yitld p,ice~ trlljectory. ~ IIppli~J this cOTlerptin Finllnci.1 Rrpo"ing 111111Anillysis whm "'"11IIIIIIII" ulttl th~ tff«tiv~ interest ,at~ mtthoJ to (lIk ..lat~ th. (a'rying val... 0/a bona

Ii.bili".

Capital gains or losses at the time a bond is sold arc measured relative to this carryingvalue so bonds hdd to maturity have no capital gain or loss and bonds sold prior tomaturity at the same YfM as at purchase will havc no capital gain or loss.

Using the 6% three-year bond from our earlier examples, we can demonsuate this for aninvestor with a two·year holding period (investment horizon).

When the bond is purchased at a YfM of7% (for S973.76), we have:

Price at sale (at end of year 2, ITM • 7%):

1,060 I 1.07 ~ 990.65 or

N = 1; UY = 7; FV = 1,000; PMT = 60; CPT .... PV = -990.65

which is the carrying value of the bond.

Coupon interest and reinvestment income for rwo years:

60(1.07).60. S124.20 or

N = 2; UY = 7; PV = 0; PMT = 60; CPT -+ FV = -124.20

Investor's annual compound rare of return over the two-year holding period is:

I

(124.20+990.65)2 -1 = 7%

973.76

This result can be demonstrated for the cue where the bond is purchased at a ITM of5% (51,027.23) as wdl:

Price at sale (at end of year 2, ITM = 5%):

1.060 I 1.05 • 1,009.52 or

N. 1; I1Y. 5; FV. 1,000; PMT. 60; CPT .... pv. -1,009.52

which is the carrying value of the bond.

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Coupon interest and reinvestment income for two yean:

60(1.05) • 60 • 123.00 or

N • 2; IfY • 5; PV. 0; PMT. 60; CPT -. FV. -123.00

Investor's annual compound rate of return over the two-year holding period is:

1

(123.00 +1,009.52]2 -1 = 5%

1,027_23

For a bond investor with an investment horizon less than the bond's term to maturity,the annual holding period return will be equal to the TIM at purchase (under ourassumptions), if the bond is sold at that TIM. The intuition here u that if a bond willhave a rate of return equal to its TIM at maturity, which w~ showed, if we sell some ofthe remaining value of the bond discounted at that TIM, we will have earned that TIMup to the date of sale.

Now Ids examine our third result: that if rates rise (fall) before the first coupon date, aninvestor who holds a bond to maturity will earn a rate of return greater (less) than theTIM at purchase.

Based on our previous result that an investor who holds a bond to maturity will earn arate of return equal to the TIM at purchase if the reinvestment rate is also equal to theTIM at purchase, the intuition of the third result is straightforward. If the TIM, whichis also the reinvestment rate for the bond, increases (decreases) after purchase, the returnfrom coupon payments and reinvestment income will increase (decrease) as a result andincrease (decrease) the investor's rate of return on the bond above (below) its TIM atpurchase. The following calculations demonstrate these results for the three-year 6%bond in our previous examples.

For a three-year 6% bond purchased at par (YfM of 6%), first assume that the TIMand reinvestment rate increases to 7% after purchase but before the first couponpaym~nt date. The bond's annualized holding period return is calculated as:

Coupons and reinvestment interest:

60(1.07)2.60(1.07) .60.5192.89

N; 3; IfY; 7; PV; 0; PMT; 60; CPT -. FV; -192.89

Investor's annual compound holding period return:

1

(1,192.89]3 -1 = 6.06%1,000

which is greater than the 6% TIM at purchase.

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If the YTM decreases to 5% after purchase but before the first coupon date, we have thefollowing.

Coupons and reinvestment interest:

60(1.05)2 ~ 60(1.05) ~ 60.5189.15

N. 3: IIY. 5: PV. 0: PMT. 60: CPT --+ FV. -189.15

Investor's annual compound holding period return:1

(1,189.15)3 -1 = 5.94%1,000

which is leIS than the 6% TIM at purchase.

Note that in both cases, the investor's rate of return is between the YTM at purchase andthe assumed reinvestment rate (the new TIM).

We now turn OUtattention to the fourth and fifth results concerning the drecu of thelength of an investor's holding period on the rate of return for a bond that experiencesan increase or decrease in iu TIM before the first coupon date.

We have already demonstrated that when the TIM increases (decreases) after purchasebut before the first coupon date, an investor who holds the bond to maturity will earna rate of return greater (less) than the YTM at purchase. Now, we examine the rate ofreturn earned by an investor with an investment horizon (expected holding period) lessthan the term to maturity under the same circumstances.

Consider a three-year 6% bond purchased at par by an investor with a one-yearinvestment horizon. If the YTM increases from 6% to 7% after purchase and the bond issold after one year, the rate of return can be calculated as follows.

Bond price just after first coupon has been paid with YTM • 7%:

N a 2: IIY: 7: FV a 1,000: PMT a 60: CPT --+ PV: -981.92

There is no reinvestment income and only one coupon of 560 received so the holdingperiod rate of return is simply:

(981.92+60)_1 = 4.19%1,000

which is less than the TIM at purchase.

If the YTM i(masts to 5% after purchase and the bond is sold at the end of one year,the investor's rate of return can be calculated as follows.

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Bond price jusr after firsr coupon has been paid with YTM = 5%:

N • 2; IfY • 5; FV. 1,000; PMT • 60; CPT ..... PV. -1,018_59

And the holding period rate of return is simply:

(1,018.59+60)_1 = 7.86%

1,000which is greater than the YTM at purchase.

The intuition of this result is based on the idea of a trade-off' berwccn I1W'kct price risk(the uncercainty about price due to uncertainty about market YTM) and reinvestmentrisk (uncercainty about the tocal of coupon payments and reinvestment income on thosepayments due to the uncertainty about future reinvestment rates).

Previously, we showed that for a bond hdd to maturity, the investor's rate of returnincreased with an increase in the bond's YTM and decreased with a decrease in thebond's YTM. For an investor who intends to hold a bond to maturity, there is nointerest rate risk as we have defined it, Assuming no default, the bond's value atmaturity is its par value regardless of interest rate changes so that the investor has onlyreinvestment risk. Her realized return will increase when interest earned on reinvestedcash flows increases, and decrease when the reinvestment rate decreases.

For an investor with a short investment horizon, interest rate risk increases andreinvestment risk decreases. For the investor with a one-year investment horizon, therewas no reinvestment risk because the bond was sold before any interest on couponpayments was earned. The investor had only market price risk so an increase in yielddecreased the rate of return over the one-year holding period because the sale price islower. Conversely, a decrease in yield increased the one-year bolding period return tomore than the YTM at purchase because the sale price is higher.

To summarize:

sbort investment horizon: market price risk> reinvestment risk

long investment horizon: reinvestment risk> market price risk

LOS 55.b: Define, calculate, and interpret Macaulay, modified, and effectivedurations,

CFA* Progmm Curriculum, Volumt 5, pagr 477

Macaulay Duration

Duration is used as a measure of a bond's interest rate risk or sensitivity of a bond's foUprice to a change in its yield. The measure was first introduced by Frederick Macaulayand his formulation is referred to as Macaulay duration.

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A bond', (annual) Macaulay duration is calculated as the weighted average of thenumber of years until each of the bond's promised cash flows is to be paid, where theweights are the present values of cach cash flow as a percentage of the bond's full value.

Consider a newly issued four.ycar 5% annual-pay bond trading at par. The presentvalues of each of the bond's promised payments, discounted at 5%, and their weights inthe calculation of Macaulay duration, are shown in the following table.

CI : 50C2·50C,.50C. = 1,050

PYI : 50/1.05PY2 • 50/1.052

PY, • 501 1.05'PY4 = 1,050 1 1.054

: 47.62.45.35.43.19

= 86l.ai1,000.00

WI: 47.62/1,000W2·45.351I,OOOW,.47.62/I,OOOW4 = 863.84/1,000

: 0.04762.0.04535.0.04319= 0,86384

1.000

Note that the present values of all the promised cash flows sum to 1,000 (the full valueof the bond) and the weights sum to 1. While we have used a bond priced at par in thisexample, the calculation method i. the same with different yields and different bondprices, although the calculated weights would be different.

Now that we have the weights, and because we know the time until each promisedpayment is to be made, we can calculate the Macaulay duration for this bond as:

0.04762(1) + 0.04535(2) + 0.04319(3) + 0.86384(4) • 3.72325 years

The Macaulay duration of a semiannual-pay bond can be calculated in the same way:as a weighted average of the number of umianmllli ptriodl until the cash flows are to bereceival. In this case, the result is the number of semiannual periods rather than years.

Because of the improved measures of interest rate risk described below, we say thatMacaulay duration is the ...-eighted-average time to the receipt of principal and interestpayments, rather than our best estimate of interest rate sensitivity. Between coupondates, the Macaulay duration of a coupon bond decreases with the passage of time andthen goes back up significandy at each coupon payment date.

Modified Duration

Modified duration (ModOur) is calculated as Macaulay duration (MaeOur) divided byone plus the bond's yield to maturity. For the bond in our earlier example, we have:

ModOur = 3.72325 1 1.05 = 3.546

Modified duration provides an approximate percentage change in a bond's price for a 1%change in yield to maturity. The price change for a given change in yield to maturity canbe calculated as:

approximate percentage change in bond price. -Mod Our K l!.TIM

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Study Session 16Crou-Reft~ to CFA Institutt Assi3ntd Reading 155 _ Undtntanding Fiud-Incom. Risk and Return

Based on a ModDur of 3.546. tho price of tho bond should fall by approximatdy3.546 x 0.1 % • 0.3546% in respons. to a 0.1% inct esse in YTM. The resulting pri ee•stimate of $996.454 is very close to tho value of tho bond calculated direuly wing aYTM of 5.1 %. which is $996.462.

For an annual-pay bond. the general form of modified duration is:

ModDur • MacDur 1 (1 • YTM)

For a semiannual-pay bond with a YTM quoted on a semiannual bond basis:

ModDurSEMI • MacDurS£'\lIl (1 + YTM 12)

This modified duration can b. annuali zed (from semiannual periods to annual per iods)by dividing by two. and then used as the approximat. chang. in priee for a 1% chang.in a bonds YTM.

Approximate Modified Duration

We can approximate modified duration directly using bond values for an increase inYTM and for a decrease in YTM of tho sam. size.

In Figure 1 we illustrate this method. The calculation of approximate modified durationis based on a given chang. in YTM. V_is tho pri ce of tho bond if YTM is aurtaud byt.YTM and V_ is tho price of the bond if the YTM is incrtilStdby t.YTM. Note that V_> V•. Because of the convexiryof the price-yield relationship, the pri ce increase (to V).for a given deer ease in yield. is larger than the price decrease (to V.).

Ap. odified durati V_-V+prOXImate m c:u URban =2xVOXt.YTM

The formula uses tho averag. of the magnitud<S of the price inerca se and tho pricedecrease. which is why V__ V. (in the numerator) is divided by 2 (in the denominator).

YO' the eur rent price of tho bond. is in tho denominator to convert this average pricechange to a percentage. and the t. YTM term is in tho denominator to scale the durationmeasure to a 1% change in yidd by convention. Note that the t. YTM term in thedenominator must be entered as a decimal (rather than in a whole percentage) toproperly scale the duration estimate.

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Figure 1: Appropriate Modified Durarien

I'ricc

v_Approximate slope of tangen! 6ne

./.. .v : -: .

Mtu.II'ri",,-yidd curve

Tangent lint

'-----'----'--_._-------yI'M- -6YfM 6YTM

Eumple: Calculating approadmatc modi6ed duration

For a 2O-~, 4% annual-pay bond currcndy trading at par, calcularc the approximatemodified duration bued on a change in yield of 25 buls points.

The . od'~ d d . . ""l,O;;::~;..;;.~74~-....:966~.7~6appzoxtmate m me urabOa IS -r-2xl,OOOxO.0025

13.60 , and the

The price of the boad at a yield of 4% • 0.25% is:

N. 20; IIV. 4.25%; FV. 1,000; PMT. 40; CPT - pv. -966.76

The price of the bond at a yield of 4% - 0.25% is:

N • 20; IIV. 3.75%; FV. 1,000; PMT. 40; CPT - pv. -1034.74

approximate change in price for a 1% change in ITM is 13.6%.

Note that modified duration is a lin~arnrimau of the relation between a bond's priceand ITM. whereas the actual rdation is convex, not linear. This means that the modifiedduration measure provides good estimates of bond priccs for small changes in yield. butincreasingly poor estimates for larger changes in yield as the effect of the curvature of theprice-yield curve is more pronounced.

Effective Duration

So far. all of our duration measures han been calculated using the ITM and prices ofstraight (option-free) bonds. This is straightforward because both the future cash flows

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and their timing arc known with certainty. This is not the case with bonds that haveembedded options, such as a callable bond or a mortgage-backed bond.

We say mortgage-backed bonds have ap"f"lymtnt option, which is similar to a calloption on a corporate bond. The borrowers (people who take out mortgages) typicallyhave the option to payoff the principal value of their loans, in whole or in part, atany time. These prepayments accelerate when interest rates fall significandy becauseborrowers can refinance their home loans at a lower rate and payoff the remainingprincipal owed on an existing loan.

Thus, the pricing of bonds with embedded put, call, or prepayment options begins withthe benchmark yield curve, not simply the current TIM of the bond. The appropriatemeasure of interest rate sensitivity for these bonds is clfccUn: duration.

The calculation of effective duration is the same as the calculation of approximatemodified duration with the change in TIM, fiy, replaced by ficurve, the change inthe benchmark yield curve wed with a bond pricing model to generate V- and V +, Thefonnula for calculating effective duration is:

Effi:aive duration = __V_-_-_V_t.l.-_2 x Vo x ficurve

Another difference between calculating effective duration and the methods we havediscussed so far is that the effi:cts of changes in benchmark yields and changes in theyield spread for credit and liquidity risk arc separated. Modified duration makes nodistinction between changes in the benchmark yield and changes in the spread. Effectivcduration reBects only the sensitivity of the bond's value to changes in the benchmarkyield curve. Changes in the credit spread arc sometimes addressed with a separate "creditduration" measure.

Finally, note that unlike modified duration, effective duration does not necessarilyprovide better estimates of bond prices for smaller changes in yield. It may be thc casethat larger changes in yield produce more predictable prepayments or calls than smallchanges.

LOS 55.c: Explain why effective duration is the most appropriate measure ofinterest rate risk Corbonds with embedded options.

CF-A®Program eu"irulum, Volumt 5. pal' 485

For bonds with embedded options, the future cash Rows depend not only on futureinterest rates but also on the path that interest rates take over time (did they fall to a newlevel or rise to that level?). We mwt usc effective duration to estimate the interest raterisk of these bonds. The effective duration measure mwt also be based on bond pricc:sfrom a pricing modd. The fact that bonds with embedded options have uncertain futurecash Bows means that our present value calculations for bond value based on TIMcannot be used.

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LOS 55.d: Explain how a bond's maturity, coupon, embedded options, andyield level affect its interest rate risk.

CFA® Prol"'m Curriculum, Vo/umt 5.paft 488

Other things equal, an inutase in a bond's matu,ity will (usually) increase its interest raterisk. The present values of payments made further in the furure arc more sensitive tochanges in the discount rate used to calculate prescnt value than arc the present values ofpayments made sooner.

We must say ·usually· because there arc instances where an increase in a discountcoupon bond's maturity will dec rene its Macaulay duration. For a discount bond,duration 6rst increases with longer maturity and then decreases over a range of relativelylong marurities until it approaches the duration of a perpetuity, which is (1 + YTM) IITM.

Other things equal, an inutase in tht coupon Mtt of a bond will decrease its interest raterisk. For a given marurity and ITM, the duration of a zero coupon bond will be greaterthan that of a coupon bond. Increasing the coupon rate means more of a bond's valuewill be from payments received sooner so that the value of the bond will be less sensitiveto changes in yield.

Other things equal. an inutase (dumut) in II bond's YTM will decrease (increase) itsinterest rate risk. To understand this. we can look to the convexity of the price-yieldcurve and usc its slope as our proxy for interest rate risk. At lower yields, the price-yieldcurve has a steeper slope indicating that price is more sensitive to a given change inyield.

Addinf titht, IIput 0' II tall p,oviJion will decrease a suaight bond's interest rate risk asmeasured by effective duration. With a call provision, the value of the call increases asyields fall. so a decrease in yield will have less effect on the price of the bond. which isthe price of a straight bond minus the value of the call option held by the issuer. Witha put option. the bondholder's option to sell the bond back to the issuer at a set pricereduces the negative impact of yield increases on price.

LOS 55.e: Calculate the duration of a portfolio and explain the limitations ofportfolio duration.

CT-A® Program Cu"iev/um. VO/umt 5. PIIft 494

There arc rwo approaches to estimating the duration of a portfolio. The 6rst is tocalculate the weighted average number of periods until the portfolio's cash Rows willbe received. The second approach is to take a weighted average of the durations of theindividual bonds in the portfolio.

The 6rst approach is theoretically correct but not often used in practice. The yieldmeasure for calculating portfolio duration with this approach is the eash Row yield, theIRR of the bond portfolio. This is inconsistent with duration capruring the relationshipbetween ITM and price. This approach will not work for a portfolio that contains

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bonds with embedded options because me nuure cash Bows are not known withcertainty and depend on interest rate movements.

The second approach is typically used in practice. Using me durations of individualportfolio bonds makes it possible to calculate the duration for a portfolio that containsbonds with embedded options by using their effective durations. The weights for mecalculation of portfolio duration under thi> approach are simply me full price of eachbond as a proportion of me total portfolio value (using full prices). These proportions oftotal portfolio value arc multiplied by me corresponding bond durations to get portfolioduration.

portfolio duration. WI 01 + W2 02 + ". + W,/\ ON

where:Wi • full price of bond i divided by me tocal value of me portfolioOJ = the duration of bond iN • the number of bonds in me portfolio

One Iimication of this approach is that for portfolio duration to "make sense" theYTM of every bond in me portfolio must change by me same amount. Only with thisassumption of a parallel shift in me yield curve is portfolio duration calculated with thisapproach consistent with me idea of me percentage change in portfolio value per 1%change in YTM.

We can think of me second approach as a practical approximation of the theoreticallycorrect duration mat me first approach describes. This approximation is less accuratewhen mere is greater variation in yields among portfolio bonds. but is me same as theportfolio duration under me first approach when me yield curve is Aat.

LOS 55.f: Calculate and interpret the money duration of a bond and pricevalue of a basis point (PVBP).

The money duration of a bond position (also called "ollar "urarion) i>expressed incurrency units.

money duration. annual modified duration )( full price of bond position

Money duration is sometimes expressed as money duration per 100 of bond par value.

money duration per 100 units of par value = annual modified duration )( full bondprice per 100 of par value

Multiplying me money duration of a bond times a given change in YTM (as a decimal)will provide me change in bond value for that change in YTM.

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Eumple: MoDey duratioD

1. Calculate the money duration on a coupon date of a $2 miDion par value bondthat hu a modified duralion of7.42 and a full price of 101.32. c:xpn:ac:d for thewhole bond and per SI00 of face value.

2. What wiD be the implCl on the value of the bond of a 25 buis poinlS inac:uc: initsYTM~

Answ=1. 11M: money duration for the bond is modi6ed duration times the full value of the

bond:

7.42" S2.000.000 x 1.0132 = SI5.035.888

7.42 " 101.32 • $751.79

11M: money duration per S 100 of par value is:

Or. SI5.035.888 x ($2.000.000 I SI00). $751.79

2. SI5.035.888 x 0.0025 • $37.589.72

11M: bond value decreases by $37.589.72.

The price value of a basi, point (PVBP) is the money change in the full price of abond when its YTM changes by one basis point. or 0.01%. We can calculate the PVBPdirealy for a bond by calculating the average of the decrease in the full value of a bondwhen its TIM increases by one basis point and the increase in the full value of the bondwhen its TIM decreases by one basis point.

Eumple: Calculating the prio: value of a buis poiDt

A newly issued. 20-year.6% annual-pay Srraighl bond is priced ac 101.39. Calculatethe price value of a buis point for this bond assumiDg it has a par value of $ 1 million.

N • 20; PV. -101.39: PMT. 6; FV. 100: CPT .....IIY. 5.88

First ,..., nced 10 6nd the YTM of the bond:

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I1Y. 5.89; CPT _PV. -101.273 (V-)

N_ we need the values for tbe bond with TIM. of 5.89 and 5.87.

I1Y. 5.87; CPT _PV. -101.507 (V.)

PVBP(per $100 of par value). (101.507 -101.273) 12.0.117

For the S1 million par value bond. each 1 buh point change in the yield to malUrirywill change the bond's price by 0.117 x $1 million x 0.01 • $1.170.

LOS 55.g: Calculate and interpret approximate convexity and distinguishbetween approximate and effective convexity.

CFA* PYogrrzmCu"irulum, Volume 5, pagr 498

Earlier we explained thaI modified duration is a linear approximation of the relationshipbetween yield and price and that. became of the convc:x.iryof the true price-yieldrelation, duration-based estimates of bond's full price for a given change in TIM will beincreasingly different from actual prices, This is illustrated in Figure 2. Duration-basedprice estimates for a decrease and for an increase in YfM arc shown as Est.- and Est .•.

Figun: 2: Price-Yield Curve for an Oprlcn-Pree, 8%, 20·Ycar Bond

Price (% nfr,r)

for ..n 0plioo-rrtt bood.he'rn""ykM 1.'''''" i"cun\n; I(lW,UJ Il\corigin.

110.67Est.-

100.0090.79 ......... : ....... j ....~.. ---------~-------!-------

7% 8% 9%

Estimates of the price impact of a change in yield based only on modified duration canbe improved by introducing a second term based on the bond's convcxiry. Convexiry isa measure of the curvature of the price- yield relation. The more curved it is, the greaterthe convcxiry adjustment to a duration-based estimate of the change in price for a givenchange in TIM.

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A bond's convexity can be estimated as:

approximate convexity = Y_+Y+-2Yo(6YfM)2yo

where:the variables arc the same as those we used in calculating approximate modi6edduration

Effective convexity, like effective duration, must be used for bonds with embeddedoptions.

The calculation of effective convexity is the same as the calculation of approximateconvexity, except that thc change in thc yield cur,", rather than a change in the bond'sTIM, is used.

approximate effective convexity = Y_+ Y+-2Yo(6curvci Yo

A bond's convexity is increased or decreased by the same bond characteristics that aifc<:tduration. A longer maturity, a lower coupon rate, or a lower yield to maturity wiU allincrease convexity; and vice versa. For two bonds with equal duration, the one with cashRows that are more disperscd ov.. r timc will have thc greater convexity.

While the convexity of any option-free bond is positive, the convexity of a callable bondcan be negative at low yields. This is because at low yields the call option becomes morevaluablc and the call price puts an cffcctive limit on increases in bond value as shown inFigure 3.For a bond with negative convexity, the price increase from a decrease in TIMis s"",Ulr than the price decrease from an increase in TIM.

Figurc 3: Price-Yield Function of a Callable vs. an Option.Free Bond

Price (% of I'a,)

102

oplion-ffe'e bond

1 :call o~tion :

....~~.'~.::J 1.. .....···..r :callable bond

'----------~---------- YieldN~ga.h'\'Con,,\,xi.y y' !'<ni.i..:Con"~il)'

A putable bond also bas less convexity. In Figure <4 we illustrate the price-yield relationfor a putable bond. At higher yields, the put becomes more valuable so that the value ofthe putahle bond falls less than that of an option-free bond as yield increases.

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Study Session 16C-s-Reft~ ro CFA Insurult Assiptd Reading 155 - Undmr.ancUng Fiud-lnC'Om. Risk and Rerum

Figun: 4: Comparing the Price-Yield Curves (or Option-Free and Putable BondsPrice:

value or the pllt option

option-free bond'---------------------- Vide!

LOS 55.h: Estimate the percentage price change of a bond for a specifiedchange in yield, given the bond's approximate duration and convexity.

CFA® Progrllm Curriculum, Volume 5, pill' 498

By taking account of both a bond's duration (first-order effeas) and convexity (second-order effects), we can improve an estimate of the effects of a change in yield on a bond',value, especially for larger changes in yield.

change in full bond price. -annual modified duration(A YfM)

~ ~ annual convexity(A YfM)2

&ample: Eatimating price cJwagcs with duration ucl convaity

Consider an 8% bond with a full price of 5908 and a YTM of 9%. Eatimate thepcrcentase change in the full price of the bond (or a 30 basis point increase in YfMassuming the bond's duration is 9.42 and iu convexity is 68_33.

The duration effecr is -9.42 " 0.003 • 0.02826 • -2.826%.

The conl'CXity effect u0.5 " 68.33 " 0.0032 • 0.000307 • 0.0307%.

The expected change in bond price is (-0.02826 + 0.000307) • -2_7953%_

Note that the convexity adjustment to the price change is the same for both an increaseand a decrease in yield. As illustrated in Figure 5, the duration-only based estimate ofthe increase in price resulting from a decrease in yield is too low for a bond with positiveconvexity, and is improved by a positive adjustment for convexity. The duration-onlybased estimate of the decrease in price resulting from an increase in yield is larger thanthe actual decrease, so it's also improved by a positive adjustment for convexity.

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Study S... ion 16Cross-lUfmDClO to CFA InatiNt. Asoi£ned Reading '55 - UndentaAding F"tXtd·lncom. Risk andlUtutD

Figure 5: Duration-Based Price Estimates vs. Actual Bond Prices

Price

SI.OOO.oo$')<)3.53

~ Prices h ..sed nn durationJrt und~r~s.tin\:tldof JC1ual price's.

ssoaco$82804 1 ••••••••••••• ~•• ······:·····Stsk~$822.47 ."."".,,"1"""":.,,"" Aelu:oJ price. yield curve. .

:: Price esom aies based:: on a dur.ation 0{9.42

L- ~.__ ~_-'- )-r~1

8% 9% 10%

LOS 55.i: Describe bow the term structure of yield volatility affects the interestrate risk of a bond.

CFA® Propm Curriculum. Volumt 5. palt 507

The term structure of yield YOlatility refers ro the relation between the volatility ofbond yields and their times to maturity. We have seen that the sensitivity of a bond'sprice with respect to a gilltn change in yield depends on its duration and convexity. Froman investor's point of view, it'. the volatility of a bond's price that;' of concern, Thevolatility of a bond's price hu two components: the sensitivity of the bond's price to agiven change in yield and the volatility of the bond's yield.

In calculating duration and convexity, we implicidy assumed that the yield curve shiftedin a parallel manner. In practice, this is often not the cue. For example, changes inmonetary policy may have more of an effect on short-term interest rates than on longer.term rates.

It could be the cue that a shorter-term bond hu more price volatility than a longer-termbond with a greater duration because of the greater yield volatility of the shorter-termyield.

LOS 55.j: Describe the relationships among a bond's holding period return, itsduration, and the investment horizon.

CFA® Propm Curriculum. Volumt 5. palt 508

Macaulay duration hu an interesting application in matching a bond to an invcstor'sinvestment horizon. When the investment horizon and the bond'. Macaulay duration arematched, a parallel shift in the yield curve prior to the first coupon payment will not (orwill minimally) affeet the investor's horizon return.

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Earlier, wc illustrated the effect of a change in yield that occurs prior to the firstcoupon payment. Our resulu showcd that for an investor with a short investmenthorizon (anticipated holding period), the market price risk of the bond ourweighs iureinvestment risk. Because of this, an increase in yield prior to the first coupon datewas shown to reduce the horizon yield for a short investment horizon and increase thehorizon yield for a longer-term investment horizon. For a longer investment horizon, theincrease in reinvestment income from the yield increase was greater than the decrease inthe sale price of the bond.

For a decrease in yield, an investor with a short investment horizon will have a capitalgain and only a small decrease in reinvestment income. An investor with a long horizonwill be more affected by the decrease in reinvestment income and will have a horizonreturn that is less than the bond's original yield.

When the investment horizon just matches the Macaulay duration, the effect of a changein ITM on the sale price of a bond and on reinvestment income just offset each other.We can say that for such an investment, market price risk and reinvestment risk offsetcach other. The following example illustrates this result.

Enmple: IDvcatmcnt horizon yidds

Consider an eight-year, 8.5% bond priced at 89.52 to yield 10.5% to muurity. TheMacaulay duration of tbe bond is 6. We can cah;ulate the horizon yield for horizonsof 3 yan, 6 years. and 10 years. assuming tbe YTM falls to 9.5% prior to the fintcoupon date.

1(96.16 + 28.00) 189.52111) - 1 • 11.520%

Bond price:

N. 5; PMT. 8.5: FV. 100; IN. 9.5; CPT - pv. 96.16

Coupons and interest on reinvested coupons:

N .3;PMT• 8.5; PV• 0: IN• 9.5: CPT - FV.28.00

Horizon murn:

Bond prier:

N. 2; PMT. 8.5: FV. 100; IN. 9.5; CPT - PV. 98.25

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Coupons and interest on n:invCltcd coupons:

N • 6; PMT. 8.5; pv. 0; 1IY. 9.5; CPT _, FV. 64.76

Horizon murn:

(98,25 + 64.76) /89,52) 1/6 - 1 • 10,505%

HNI flI ",.",riry. 81#."Maturity value • ) 00

Coupons and interest on n:invCltcd coupons:

N • 8; PMT • 8.5; PV • 0; IfY • 9.5; CPT _, FV • 95,46

Horizon mum:

((l00 + 95.46) /89.52) 111- 1 • 10.253%

For an invatment horizon equal to the bond', Macaulay duration of 6, the horizonreturn is equal 10 the original YTM of 10.5%. For a abotlCr thrcc.)'\:ar investmenthorizon, the price increase from a tcducUon in the YTM to 9,5% dominaccs thedccrcuc in reinvcstment income so the horizon return, 11.520%, is Felter than theoriginal YTM, For an invator who holds the bond to maturity, there is no price effectand the decrease in reinvesuncnt income reduces the horizon return to 10.253%, lessthan the original YTM,

The difference between a bond's Macaulay duration and the bondholder's investmenthorizon is referred to as a duration gap. A positive duration gap (Macaulay durationgreater than the investment horizon) exposes the investor to market price risk fromincreasing interest rates. A negative duration gap (Macaulay duration less than theinvestment horizon) exposes the investor to reinvestment risk from decreasing interestrates.

LOS 55,k: Explain how changes in credit spread and liquid affect yield-to-maturity of a bond and how duration and convexity can be used to estimate theprice e.ffect of the changes.

CFA® Program CUTri<ulum,Volumt 5, palt 513

The benchmark yield curve's interest rates have two componenu; the real rate ofreturn and expected inllation. A bond's spread to the benchmark curve also has twocomponenu, a premium for credit risk and a premium for lack of liquidity relative tothe benchmark securities.

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Because we arc Ireating the yields associated with each component as additive, a givenincrease or decrease in any of these components of yield will increase or decrease thebond's YTM by the same amount.

With a direct relationship between a bond's yield spread to the benchmark yield curveand its YTM, we can estimate the impact on a bond's value of a change in spread usingthe formula we inuoduced earlier for the price effects of a given change in YTM.

%t. bond value: -duration(t.sprcad) ~ ~ convcxiry(t.sprcad)2

Example: Price dli:ct of spread changes

Consider a bond that is valued at $180,000 that bas a duration of8 and a convairyof 22. The bond's spread to the benchmark cum: incn:ucs by 25 basis poino due to acn:dit downgrade. What is the approximate change in the bond's market valud

With t.sprnd • 0.0025 we have:

Annn:r:

(-8 x 0.0025) ~ (0.5 x 22 x 0.00252) • -1.99% and the bond's value will fall byapproximately 1.99% x 180,000 • 53,588.

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Study s....on 16Cross-lUfmoC>e to CFA lrutitule Assi£ntd lUading '55 - Undtrttanding F"txtd·lnc:om~ Risk andlUturo

KEY CONCEPTS

LOS 55.aSources of return from a bond investment indude:• Coupon and principal paymenu.• Reinvestment of coupon paymenu.• Capital gain or loss if bond is sold before maturity.

Changes in yidd to maturity produce market price risk (uncertainty about a bond'sprice) and reinvestment risk (uncertainty about income from reinvesting couponpayments). An increase (a decrease) in TIM decreases (increases) a bond's price butincreases (dccrcascs) its reinvestmcnt incomc.

LOS 55.bMacaulay duration is the weighted average number of coupon periods until a bond'sscheduled cash Bows.

Modified duration is a linear estimate of the percentage change in a bond's price: thatwould result from a 1% change in iu TIM,

v -VApproximate modificd duration = - ±

2VoAYfM

Effective duration is a lincar estimate of the percentage change in a bond's price thatwould result from a I% change in the benchmark yield curve.

v -vEffective duration = ~ +

2Y. curve

LOS 55.eEffective duration is the appropriate mcasurc of interest rate risk for bonds withembedded options because changes in interest rates may change their future cash Bows.Pricing models arc wed to determine the prices that would result from a given sizcchange in the benchmark yield curve.

LOS 55.dHolding other faClors constant:• Duration increases when maturity increases.• Duration decreases when the coupon rate increases.• Duration decreases when TIM increases.

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LOS 55.cThere are twO methods for calculating portfolio duration:• Calculate the weighted average number of periods unti.1cash flows will be received

using the portfolio's IRR (its cash flow yield). This method is better theoretically butcannot be used for bonds with options.

• Calculate the weighted average of durations of bends in the portfolio (the methodmost often wed). Portfolio duration is the percentage change in portfolio value for aI% change in yield. only for parallel shifts of the yield curve.

LOS 55.fMoney duration is stated in currency units and is sometimes expressed per 100 of bondvalue.

money duration a annual modified duration x full price of bond position

money duration per 100 units of par value =

annual modified duration x fuJI bond price per 100 of par value

The price value of a basis point is the change in the value of a bond. expressed incurrency units. for a change in YTM of one basis point, or 0.01%.

PVBP. [(V_ - VJ 121 x par value x 0.01

LOS 55.gConvexity refers to the curvature of a bond's price-yield relationship.

. . V_+V+-2Voapproxunate convexity = 2

(6YrM) Vo

Effective convexity is appropriate for bonds with embedded options:

approximate effective convexity = V_+V+-2Vo(6curvc)2 Vo

LOS 55.hGiven values for approximate annual modified duration and approximate annualconvexity. the percentage change in the full price of a bond can be estimated as:

%6 full bond price. -annual modified duration(6 ITM) + ~ annualconvexity(6 ITM)2

LOS 55.iThe term structure of yield volatility refeu to the relationship between maturity andyield volatility. Short-term yielcU may be more volatile than long-term yields.1u a result.a short-term bond may have more price volatility than a longer-term bond with a higherduration.

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LOS 55.jOver a short investment horizon, a change in YTM affects market price more than itaffects reinvestment income.

Over a long investment horizon, a change in YTM affects reinvestment income morethan it affi:Cts market price.

Macaulay duration may be interpreted as the investment horizon for which a bond'smarket price risk and reinvestment risk just offset each other.

duration gap. Macaulay duration - investment horizon

LOS 55.kA bond's yield spread to the benchmark curve includes a premium for credit risk and apremium for iIIiquidiry.

Given values for duration and convexiry, the effect on the value of a bond from a givenchange in its yield spread (~sprcad) can be estimated as:

-duration(~sprcad) .. ~ convcxiry(~sprcad)2

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CONCEPT CHECKERS

I. The largest component of returns for a 7-ynr zero-coupon bond yidding 8%and hdd to maturity is:A. capital gains.B. interest income.C. reinvestment income.

2. An investor buys a buys a 10-year bond with a 6.5% annual coupon and aYTM of 6%. Before the first coupon payment is made, the YTM for the bonddecreases to 5.5%. Assuming coupon payments are reinvested at the YTM, theinvenor', return when the bond is held to maturity is:A. less than 6.0%.B. equal to 6.0%.C. greater than 6.0%.

3. A 14% annual-pay coupon bond has six yean to maturity. The bond is currentlytrading at par. Using a 25 basis point change in yield, the approximate modifiedduration of the bond is dosesr to:A. 0.392.B. 3.888.C. 3.970.

4. Assuming coupon interest is reinvested at a bond's YTM, what is the interestponion of an 18-year, S1,000 par, 5% annual coupon bond's return if it ispurchased at par and held to maturity?A. $576.95B. $1,406.62.C. $1,476.95.

5. Effi,ctive duration is more appropriate than modified duration for estimatinginterest rate risk for bonds with embedded options because these bonds:A. tend to have great<r credit risk than opeion-free bonds.B. exhibit high convexity that makes modified duration less accurate.C. have uncertain cash Rows that depend on the path of interest rate changes.

6. Which of the following three bonds (similar except for yield and maturity) hasthe least Macaulay duration? A bond with:A. 5% yidd and 10-year maturity.B. 5% yield and 20-year marurity.C. 6% yidd and 10-year marurity.

7. Portfolio duration has limited usefulne .. as a measure of interest rate risk for aponfolio because it:A. assumes yield changes uniformly across all maturities.B. cannot be applied if the ponfolio includes bond. with embedded options.C. is accurate only if the ponfolio's internal rate of return is equal to its cash

Row yield.

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8.

9.

The current prier of a $1,000, seven-year, 5.5% semiannual coupon bond isSI,029.23. The bond's price value of a basis point is c/DSlS' to:A. SO.05.B. SO.60.C. S5.74.

Why is the duration of callable bond less than that of an otherwise identicaloption-free bond? The value of the call option:A. increases when YfM increases,B. decreases when YfM increases.C. decreases when bond price increases.

10. Which of the following measures is lowest for a callable bond?A. Macaulay duration.B. Effective duration.C. Modified duration.

II. The modified duration of a bond is 7.87. The approximate percentage change inprice using duration only for a yield decrease of 110 basis points is clout, to:A. -8.657%.B.• 7.155%.C. .8.657%.

12. A bond has a eonvexity of 114.6. The convexity effect, if the yield decreases by110 basis points, is e/Dlm to:A. -1.673%.B.• 0.693%.C.• 1.673%.

13. Assume a bond has an effective duration of 10.5 and a convexity of 97.3. Usingboth of these measures, the estimated perG<ntage change in price for this bond,in response to a decline in yield of 200 basis points, is doust to:A. 19.05%.B. 22.95%.C. 24.89%.

14. An investor with an investment horizon of six years buys a bond with a modifiedduration of 6.0. This investment has:A. no duration gap.B. a positive duration gap.C. a negative duration gap.

Which of the following most aceum,," describes the relationship betweenliquidity and yield spreads relative to benchmark goveromcnt bond rates? Allelse being equal, bonds with:A. less liquidity have lower yield spreads.B. greater liquidity have higher yield spreads.C. less liquidity have higher yield spreads.

15.

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Study Session 16Croos-Reft~ to CFAIn$litutt Assiptd Rnding 155 - Undemanding Fiud-Incom. Riskand Relurn

16. An investor buys a 15-ycar, £800,000, zero-coupon bond with an annual YTMof 7.3%. If she sells the bond after 3 years for £346.333 she will have:A. a capital gain.B. a capital loss.C. neither a capital gain nor loss.

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ANSWERS - CONCEPT CHECKERS

1. B The increase in value or a zero..coupon bond over its lire is Interest income. J\ zero ..coupon bond. has 00 reinvestment risk over its Hre. A bond held to maturity has no,,"pital gain or loss.

2. A The decrease in the YrM to 5.5% will decrease the reinvenm.nt income over th.Hr. orthe bond so that the invesror will earn less than 6%. the YrM at purch sse,

3. B V_. 100.979

N • 6; PMT • 14.00; FV. 100; IN. 13.15; CPT - PV • -100.979

V, • 99.014

IN. 14.25; CPT _ PV. -99.035

VO. 100.000

I!>.y. 0.0025

Approximat. modified duration. V_ - V ~ IOO.?79-99.03S _ 3.8882V.I!>.YrM 2(JOO)(O.OO2S)

4. B The interest portion or a bond's return is the sum or the coupon payments and int«tstearned feem r.invening eeupon paym.nu over the holding period,

N • 18; PMT • 50; PV • 0; IN • 5%; CPT _ FV • -1,406.62

5. C Because bonds with embedded options have ca.sh Rows thar a~ uncertain and depend onru(we intercst rates, cfi"ecdvt'durailon must be used.

6. C Other things equal, Macaulay duration is less when yield is high.r and when marurityis shorter, The bond with the highest yield and shorte .. maturity must have th.lowutMacaulay duration.

1. A Portfolio duration u limited as a measun: or interest rat. risk because it assumes parallelshirts in the yield curve: that is. the discount rate at each maturity changes by the sam.amount. Portrolio duration can be calculated using .ff.Clive durations or bonds withembedded option s. By d.finition. a portfolio's internal tat. or return i. equal to iu cashOowyidd.

8. B PVBP • initial price - price ir yield u changed by I basis point. First. we need tocalculate the yield so we can calcula te the price or the bond with a I basu point changein yield. Using a financial calculator: PV. -1.029.23: FV. 1,000: PMT. 21.5 • (0.055• 1.000) 12: N .14 .2 • 7 years: CPT - IIY. 2.49998, multiplied by 2 • 4.99995.or 5.00%. Next, com pure the price or the bond at a yield or 5.00% + 0.01 %, or5.01%. Using thecalculator: FV. 1.000: PMT. 21.5: N. 14: IIY. 2.505 (5.01 (2);CPT - PV. 51.028.63. Finally. PVBP. 51,029.23 - 51,028.63. SO.60.

9. B When the YrM or a callable bond ralls, the increase in price is ltss than ror an option.rree bond because both bond price and the value or the call option incr ease. Callablebond value • straight bond value - call option valu e.

10. B The int.rat rat e sensitivity or a bond with an embedded call option will be Iess thanthat or an opticn-f ree bond. Effective duration takes the .ffect or the call option intoaecount and wiU, thererore. be le.. than Macaulay or modified duration.

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I I. C -7.87 x (-1.10%) .8.657%

12. B convuiry.«ccr. tl2 x convexity x (.o.YTM)2. (0.5)(I1~.6){O.01l)2• 0.00693 • 0.693%

13. C Tow estimated price change. (dural ion elTecl • conveJUry tITeel)

11-10.5 x H)'02)) • 197.3 x (-0.02)211 x 100 • 21.0%. 3.S9%. 2~.S9%

14. B Duration gap is Macaulay duralion minus Ihe inveStmenl horizon. Because medifiedduration equals Macaulay duralion I (I • YTM), Macaulay duration;' gr<altr thanmodified duration for any YTM grraler than ze ro. Therefore, this bond has a Macaulayduration grral« Ihan six years and Ihe investmem has a positive duration gap.

15. C The Its. Iiquidiry a bond has, the higher its yidd sprrad rel.. ive 10 its benchmark. Thisis because inveSlors require a higher yitld 10 compensate them for giving up Uquidiry.

16. A The price of the bond afltr three ytars Ihal will gtnerale neither a capital gain nor acapilalloss is Iht price if Ihe YTM remains al 7.3%. Afler Ihree years, ehe presenr valueof the bond is SOO,OOOI 1.073'2.343,473.57, 10 she will h",~ a eapiw gain rel.. ive tothe bond's carrying value.

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Th. roll""';og ia • rni... or the F... d Inco",.: Analysis or Ri.k principles d."gned to add.... thekunins outcome ltatemenu Kt (OM by CfA IMtiNk. Th.il topic i. allO cowrcd in:

FUNDAMENTALS OF CREDIT ANALYSIS

Study &..Ion 16

ExAM Focus

This topic rcvicw introduces credit analysis, primarily for corporue bonds. butconsiderations for credit analysis of high yield, sovereign, and municipal bonds are alsocovered. Focus on credit ratings, credit spreads, and the impact on return when ratingsand spreads change.

LOS 56.a: Describe credit risk and credit-related risks affecting corporatebonds.

cr-A® Program Curri(ulum, v"IU7M 5, pllg~ 530

Credit risk is the risk associated with losscs stemming from the failure of a borrower tomake timely and full payments of interest or principal. Credit risk has two components:Jtfoult rislt and um uwrity.

• Default risk is the probability that a borrower (bond issuer) fails to pay interest orrepay principal when due.

• Loss sCVI:rity,or «lIS givm tkfoult. refers to the value a bond investor willlosc if theissuer defaults. Loss severity can be stated as a monetary amount or as a percentageof a bond's value (principal and unpaid interest).

The expected loss is equal to the default risk multiplied by the loss scverity. Expectedloss can likewise be stated u a monetary value or as a percentage of a bond's value.

The rccovery rate is the percentage of a bond's value an investor will receive if the issuerdefaults. Loss severity as a percentage is equal to one minw the recovery rate.

Bonds with credit risk trade at higher yields than bonds thought to be free of credit risk.The diffcrence in yield between a credit-risky bond and a credit-risk-free bond of similarmarurity is called in yield spread. For example, if a 5-year corporate bond is rrading at aspread of .250 basis points to Treasuries and the yield on 5-yar Treasury notes is 4.0%,the yield on the corporate bond is 4.0% • 2.5% • 6.5%.

Bond price. arc inversely related to spreads; a wider spread implies a lower bondprice and a narrower spread implies a higher price. The sizc of the spread reRects the

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creditworthiness of the issuer and the liquidity of the market for its bonds. Spread risk isthe possibility that a bond's spread will widen due to one or both of these factors.

• Credit migration risk or downgrade risk is the possibility that spreads will increasebecause the issuer has become less creditworthy. As we will sec later in this topicreview, credit rating agencies assign ratings to bonds and issuers, and may upgrade ordowngrade these ratings over time.

• Market liquidity risk is the risk of receiving less than market value when sellinga bond and is reRected in the size of the bid-ask spreads. Market liquidity risk isgreater for the bonds of less creditworthy issuers and for the bonds of smaller issuerswith relatively linle publicly uaded debt.

LOS 56.b: Describe seniority rankings of corporate debt and explain thepotential violation of the priority of claims in a bankruptcy proceeding.

Each category of debt from the same issuer is ranked according to a priority of claims inthe event of a default. A bond's priority of claims to the issuer's assets and cash Rows isreferred to as its senioriry ranking.

Debt can be either secured debt or unsecured debt. Secured debt is backed by collateral,while unsecured debt or a~bmturrs represent a general claim to the issuer's assets andcash Rows. Secured debt has higher prioriry of claims than unsecured debt.

Secured debt can be further distinguished asjim lim or jim mortgllg~(where a specificasset is pledged), unior suur~a, or junior suu"a debt. Unsecured debt is further dividedinto s~nior,junior, and subordinllua gradations. The highest rank of unsecured debt issenior unsecured. Subordinated debt ranks below other unsecured debt.

The general seniority rankings for debt repayment priority arc the following:

• First lien or first mortgage.• Senior secured debt.• Junior secured debt.• Senior unsecured debt.• Senior subordinated debt.• Subordinated debt.• Junior subordinated debt.

All debt within the same category is said to rank pari passu, or have same prioriry ofclaims. All senior secured debt holders, for example, arc treated alike in a corporatebankruptcy.

Recovery rates arc highest for debt with the highest priority of claims and decrease witheach lower rank of seniority. The lower the seniority ranking of a bond, the higher itscredit risk. Investors require a higher yield to accept a lower seniority ranking.

In the event of a default or reorganiution, senior lenders have claims on the assetSbefore junior lenders and equity holders. A suict priority of claims, however, is notalways applied in practice. Although in theory the priority of claims is absolute, in many

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cases lower-priority debt holders (and even equity investors} may get paid even if seniordebt holders arc not paid in fuJI.

Bankruptcies can be costly and take a long time to settle. During banluuptcyproceedings, the value of a company's assets could deteriorate due to loss of customersand kcy employees, while: legal expenses mount. A bankruptcy reorganization plan isconfirmed by a vote among all classes of investors with less than 100% recovery rate.To avoid unncccssa.ty delays, negotiation and compromise among variow claimholdersm..y result in a reorganization plan that does not strictly conform to the origin ..1priorityof cl ..ims. By such .. vote or by order of the bankruptcy court, the fina.l plan m..y differfrom ..bsolute priority.

LOS 56.c: Distinguish between corporate issuer credit ratings and issue creditratings and describe me rating agency practice of "notching".

Credit rating ..gencies usign ratings to categories of bonds with similar credit risk.R.a.tingagencies rate both the issuer (i.e .• the comp ..ny issuing the bonds) ..nd the debtissues. or the bonds themselves. Issuer credit r..ting. arc called corporate family ratiogs(CFR), while issue-specific ratings arc called corporate credit ruiogs (CCR). Issuerr..tings ..re based on the overall creditworthiness of the eomp any. The issuers a re rated ontheir senior unsecured debt.

Figure 1 shows t..ting. scales used by Standard & Poor's. Moody·s.and Fitch. three of them ..jor credit r..ting ..gencies.

Figure 1: Credit R.a.tiog Ca.tegorie.

(a) Investment pde nting' (b) Non·inve.UMDt grade ratios.M~tI,~ SII'""",tl6Po",i. M-'!. S"""u'" d-Poo,i.

Fiuh FiuhAaa. AAA B ..I DB.Aa.1 M. Bol DBAa.2 AA Ba3 DB-

" ..3 M- BI B.AI A. B2 BA2 A B3 B-A3 A- Caal CCC.

D...I BDB. Ca.a.2 CCCBa.a.2 BBB Ca.a3 CCC-Ba.a3 BBB- Co CC

C CC 0

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Triple A (AAA or Aa2,) is the highest rating. Bonds with ratings of Baa3/BBB- or higherare considered investment grade. Bonds rated BaI/BB+ or lower are considered non-invc.tmcnt gradc and arc oftcn called highyi,iJ bDnds or junk bonds.

Bonds in default arc rated D by Standard & Poor's and Fitch and are included inMoody's lowest rating category, C. Whcn a company defaults on onc of its severaloutstanding bonds, provisions in bond indcntures may trigger default on the remainingissues as well. Such a provision is ailed a CTtJJJ tkfoult ptrJuiliDn.

A borrowcr can havc multiplc debt issues that vary not only by maturities and couponsbut also by credit rating. Issuc credit ratings depend on the seniority of a bond issue andits covcnants. Notching is the practice by rating agencies of assigning different ratings tobonds of thc same issuer. Notching is based on several factors, including seniority of thebonds and its impact on potential loss severity.

An example of a factor that rating agencies consider when notching an issue creditrating is slructural.ubordination. In a holding company structure, both the parentcompany and the subsidiarics may havc outstanding debt. A subsidiary's debt covenantsmay restrict the transfer of cash or assets "upstream" to the parent company before thesubsidiary's debt is serviced. In such a case, even though the parent company's bonds arcnot junior to the subsidiary's bonds, the subsidiary's bonds have a prioriry claim to thesubsidiary's cash Bows. Thus thc parent company's bonds are effectively subordinated tothe subsidiary's bonds.

Notching is less common for highly rated issuers than for lower-rated issuers, For lower-rated issuers, higher default risk leads to significant differences between recovery rates ofdebt with different senioriry, leading to morc notching.

LOS 5G.d: Explain risks in relying on ratings from credit rating agencies.

CF-A®PmgNm CMrriculum, Volume 5, page 542

Relying on ratings from credit rating agencies has some risks. Four specific risks are:

I. Credit ratings are dynamic. Credit ratings change over time. Rating agencies mayupdate their default risk assessments during the lift: of a bond. Higher credit ratingstend to be more stable than lower credit ratings.

2. Rating agencies arc not perfect. Ratings mistakes occur from time to time. Forexample, subprimc mortgage securities were assigned much higher ratings than theydeserved.

3. Event risk is difficult to assess. Risks that arc specific to a company or industry aredifficult to predict and incorporate into credit ratings. Litigation risk to tobaccocompanies is one example. Evcnts that arc difficult to anticipate, such as naturaldisasters, acquisitions, and equity buybacks using debt, are not easily captured incrcdit ratings.

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4. Credit ratings lag market pricing. Market prices and credit spreads change muchfaster than credit ratings. Additionally, twO bonds with same rating can trade atdifferent yields. Market prices reRea expected losses, while credit ratings only assessdefault risk.

LOS 56.e: Explain the components of uaditional credit analysis.

CF-A®Prog'Mmurriculum. Yolumt 5.pagt 547

A common way to categorize: the ltey components of credit analysis is by the four Cs ofcredit analysis: capacity. collateral, covenants, and character,

Capacicy

Capacity refers to a corporate borrower's ability repay its debt obligaticns on time.Analy.i. of capacity is similar to the process wed in equity analysis. Capacity analysisentails three levels of assessment: (1) industry structure. (2) industry fundamentals. and(3) company fundamental s.

InJwtry Strucrure

The firn level of a credit analyst's assessment is industry structure. Industry structurecan be described by Porter's five forces: rivalry among cxining competitors, threat ofnew entrants. threat of substitute products. bargaining power of buyers. and bargainingpower of suppliers.

~ Proftsrori Notr: WI tks"ib. inJIIS", analysis bas'" on Porttri fiw flrus in rh.~ StuJ, Stsrion on t'luity valuation.

InJwtry FunJamtntau

The next level of a credit analyst's assessment is industry fundamental s, including theinRuence of macroeconomic faaors on an indunry's growth prospects and profitability.Industry fundamentals evaluation focuses on:

• Industry cycIicality. Cyclical industries arc sensitive to economic performance.Cyclical industries tend to have more volatile earnings, revenues, and cash Rows.which make them more risky than noncyclical industries.

• Industry growth prospeas. Credirworthiness is most questionable for the weakercompanies in a slow-growing or declining industry.

• Industry published statistics. Industry statistics provided by rating agencies,investment banks. industry periodicals. and government agencies can be a source forindustry performance and fundamenta1s.

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Compllny FuntUmenrais

The last level of credit analysts' assessment is company fundamentals. A corporateborrower should be assessed on:

• Competitivc position. Market share changes oyer rime and cost structure relative topccrs arc some of the faCtors to analyzc:.

• Opcrating history. The pcrformancc of thc company ever diffcrcnt phases ofbusiness cycle, trends in margins and revenues, and current management's tenure,

• Management's stratcgy and eseeutien. This includes the soundness of the stratcgy,the ability to execute the strategy, and the effccu of management's decisions onbondholders.

• Ratios and ratio analysis. As we will discuss later in this ropic review, leverage andcovcragc ratios arc important rools for credit :tnalrsis.

Collateral

Collateral analysis is more important for less credicworthy companies. The markervalue of a company's asscts can be difficult to observe dirccdy. Issues to considcr whcnass<ssing collateral values Include:

• Intangiblc assets. Patents arc considered high-quality intangible assets because thcycan be morc casily sold to generate cash flows than other intangibles. Goodwill isnot considered a high-quality intangible asset and is usually wrirten down whcncompany perfcrmance is poor.

• Depreciatien. High depreciation expense relative to capital expenditures may signalthat m:tnagement is not investing sufficiently in the company. The quality of thecompany's assc:tsm:ty be poor, which may lead to reduced operating cash flow andpotentially high loss s~c:rity.

• Equiry market capitalization. A stock that trades below book value may indicatethat comp:tny assets are oflow quality.

• Human and intc:UcctuaI capital. These are difficult to value, but a company mayhave Intellectual propcrry that can function as collateral.

Covenants

Covenants an::the terms and conditions the borrowers and lenders have agreed to upart of a bond issue. Covenants protect lenders while leaving some operating flexibilityto the borrowers to run the company. There arc cwo types of covenants: (1) IlffirmariwCDwnllntsand (2) ntglltiut CDwnanlS.

Affirmativc covenants require the borrower to take certain actions, such as payinginterest, principal, and tuCI; catrying insurance on pledged assets; and maintainingcertain 6nancial ratios within prescribed limits.

Negativc covenants restrict the borrowcr from taking certain actions, such as incurringadditional debt or directing cash flows to sharcholders in the form of dividends andstock repurchases.

Covenants that arc overly restrictive of an issuer's operating activities may reducethc issuer's ability to rcpay. On the othcr hand, covenants create a legally binding

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contractual framework for repayment of the debt obligation, which reduces uncertaintyfor the debt holders. A careful credit analysis should include an assessment of whetherthe covenants protect the interests of the bondholders without unduly constraining theborrower's operating activities.

Character

Character refers [0 management's integrity and its commitment to repay the loan.Factors such as management's business qualifications and operating record a", importantfor c:vaIuating character. Character analysis includes an assessment of:

• Soundness of strategy. Management's ability to develop a sound strategy.• Track record. Management's past performance in executing its strategy and operating

the company without bankruptcies, restructurings, or other distress situations thatled to additional borrowing.

• Accounting policies and taX strategits. Usc of accounting policies and taxstrategies that may be hiding problems, such as revenue recognition issues, frequentrestatements, and frequendy changing auditors.

• Fraud and malfeasance record. Any record of fraud or other legal and regulatotyproblems.

• Prior t"'atment of bondholders. Benefits to equity holders at the expense of debtholders, through actions such as debt-financed acquisitions and special dividends,especially if they led to credit rating downgrades.

LOS 56.f: Calculate and interpret financial ratios used in credit analysis.

Ratio analysis is part of capacity analysis. Two primary categories of ratios for creditanalysis arc kwnzgt ,,,tios and C'fJvtTIlgtratios. Credit analysts calculate company ratios toassess the viability of a company, to find trends over time, and to compare companies toindustty averages and peers.

Profits and Cash Flows

Profits and cash Rows arc needed to service debt. Here we examine four profit and cashRow metrics commonly used in ratio analysis by credit analysts.

I. Earnings before Interest, taxes, depreciatinn, and amonizatinn (EBITDA).EBITDA is a commonly used measure that is calculated as operating incomc plusdepreciation and amortization. A drawback to using this measure for credit analysisis that it does not adjust for capital expenditures and changes in working capital,which aft' necessary uses of funds for a going concern. Cash needed for these uses i.not available to debt holders.

2. Funds from operations (FFO). Funds from operations a", net income fromcontinuing operations plus depreciation, amortization, deferred taXes, and noncashitems. FFO is similar to cash Row from operations (CFO) except that FFO excludeschanges in working capital.

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3. Free cash Sow before dividends. Free cash Sow before dividends is net income plusdepreciation and amortization minus capital expenditures minus increase in workingcapital. Free cash flow before dividends excludes non-recurring items.

4. Free cash Sow after dividends. This is free cash flow before dividends minus thedividends. If free cash flow after dividends is greater than zero, it reprcsena cash thatcould pay down debt or accumulate on the balance sheet. Either outcome is a formof dcleveraging, a positive indicator for creditworthiness.

Leverage Ratios

Analysts should adjust debr reported on the financial statements by including the firm'sobligations such as underfunded pension plans (net pension liabilities) and off-balance-sheet liabilities such as operating leases.

The three most common measures of leverage used by credit analysts arc the debt-to-capital ratio, the debt-to-EBITDA ratio, and the FFO-to-debt ratio.

1. Debt/capital. Capital is the sum of total debt and shareholders' equity. The debt-to-capital ratio is the percentage of the capital structure financed by debt. A lower ratioindicates less credit risk. If the financial statements list high values for intangibleassets such as goodwill, an analyst should calculate a second debe-to-capital ratioadjusted for a writedown of these asseu' after-taX value.

2. Debt/EBITDA. A higher ratio indicates higher leverage and higher credit risk. Thisratio is more volatile for firms in cyclical industries or with high operating leveragebecause of their high variability of EBIIDA.

3. FFO/debt. Because this ratio divides a cash flow measure by the value of debt, ahigher ratio indicates lower credit risk.

Coverage Ratios

Coverage ratios measure the borrower's ability to generate cash Bows to meet interestpaymcna. The two most commonly used arc EBITDA-to-inteteSt and EBIT-to-interest.

1. EBITDAlintcrcst apense. A higher ratio indicates lower credit risk. This ratio isused more often than the EBIT-to-intetcst expense ratio. Because depreciation andamortization are still included as part of the cash Bow measure, this ratio will behigher than the EBIT version.

2. EBIT/interen expense. A higher ratio indicates lower credit risk. This ratio is themore conservative measure because depreciation and amortization arc subtractedftom earnings,

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Ezample: Cm!jt -)'Su with &.w.c;aI rauoa (Pan l)

A credit analyst is usc-sins Suor. a U.S. multimedia company with the followingselected 6nancial information:

/" S ",Uti.1II 2OX1 2OX2 2OX3Operating income 5.205 6,456 7.726!WV'tnue 36.149 38.063 40,893Depreciation and amonization 1.631 1.713 1,841Capitll ClIpendi.ure. 1.753 2.110 3.559Cash Row from opctations 5.319 6.578 6.994Total deb. 12.701 12.480 13.977Total equity 33.734 37.519 37.385Dividends paid 648 653 756Intrrrst ClIJICAI! 300 330 360

Calculate the: cuh IIOWI and ratio. listed below. Free cash 11_ (FCF) is after dividendsfor all calculations.

20XI 2OX2 2OX3EBITDAFCF aficr dividendsOperating marginDebt/EBITDAEBITDAlin.rrcstFCF/dcbtDebt/capi ...1

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EBITDA. operating income + dcpm:.iation and amonization:20XI: 5.205 + 1.631 • $6.836 million20X2: 6.456 + 1.713. $8.169 million20X3: 7.726 + 1.841 • $9.567 million

FCF • cash Sow from operations - capital cxpenditun:s - dividends:20XI: 5.319-1.753-648. $2.918 million20X2: 6.578 - 2.110 - 653. $3.815 million20X3: 6.994 - 3.559 - 756 • $2.679 million

Operating margin. operating income 1 ~nue:20XI: 5.205 136.149. 14.4'11020X2: 6.456 1 38.063 • 17.0'If020X3: 7.726 1 40.893 • 18.9'110

DebtiEBITDA:20XI: 12,701 16.836 • 1.9'120X2: 12,480/8.169 = 1.5x20X3: 13.971 19.567 • 1.5x

EBITDAIintcn:st:20XI: 6.836/300 • 22.8x20X2: 8.169/330 • 24.8x20X3: 9.567 1360 = 26.6x

FCF/dcbe:20XI: 2.918/12.701 • 23.0'If020X2: 3.815 112.480 • 30.6'11020X3: 2.679/13.977 • 19.2'110

Debtlc:apital:20XI: 12,7011 (12.701 + 33.734).27.4'11020X2: 12,480 1 (12.480 + 37.519) • 25.0'11020X3: 13.9771 (13.977 + 37.385)·27.2'110

20XI 2OX2 20)(3

EBITDA 6.836 8.169 9.S67FCF afeer dividends 2.918 3.81S 2.679Operating margin 1."'% 17.~ 18.~DebtlEBlmA 1.9- I.S. I.S.EBITDAlinltrtl( 22.8. 24.8. 26.6.

FCF/debt 23.014t 30.6% 19.2'"Debtlcapital 27.4% 2S.~ 27.2'"

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Ezample: Cmlit _)'lis with 6aancial naaa (Part 2)

2. Coyote M.:dia is also a multimedia company and is • rival of Suor. Given thefollowing nrioc for Coyote over the lame period. calculate the 3-yar averages for bothSuor and Coyote and comment on which multimedia company is expected to haw: abetter ctcdit rating.

OperaJing musinDebt/EBITDAEBITDAliruemtFCF/dcbtDebt/capital

2DXI 20)(2 20X318.01(, 7.01(, 9.51(,1.9. 3.0. 2.0.

27.S. 12.7. 18.3.15.01(, 28.0110 26.61(,28.71(, 41.21(, "2.61(,

Operating musinDebt/EBITDAEBITDAlintemtFCF/dcbtDebt/capital

s"",r c.z.,.16.81(, 11.51(,

!.6x 2.3x24.7x 19.5x24.21(, 23.21(,26.S1(, 37.S1(,

All ratiol support a higher credit rating for Suor. Suor has a better operaling marginand better coycrage for inlelal (EBITOAIinlercsl) and for debt (FCF/dcbl). Lowerleverage as measured by debt-to-capital and dcbl-to-EBITDA also fa~r Suor.

LOS 56.g: Evaluate the credit quality of a corporate bond issuer and a bond ofthat issuer, given key financial ratios of the issuer and the industry.

CF-A®Program Clirrirllilim. Volllm~5. pag~ 555

Ratings agencies publish benchmark values for financial ralios Ihat arc associated witheach ratings classification. Credit analysIS can evaluate the potential for upgrades anddowngrades based on subject company ratios relative to these benchmarks.

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&ample: Credit radAp baed 00 ratiol (Pan I)

A credit nting a~ncy publishes the following benchmark ndos for bond issuesof multimedia companies in each of the investment gracK ntings. based on 3-yaravenges over the period 2OX1 to 20X3:

Cm/il hli"", AM M A BBBOptratina marain 2".5" 16.5% 10.0% 7.5"DtbrlEBITDA 1.3. I.a. 2.2. 2.5.EBITDAlillttrtSt 25.0. 20.0. 17.5. 15.0.FCF/dtbt 30.0% 2".~ 20.0% 17.~Debrlcapital 2S.~ 30.~ 35.0% 40.0%

Based on the ntios calculated in the previous example and the industry standards inthe table above. what a~ the expected issuer credit ratings for Coyote and Suor?

An __ r:

3-Y"" .........", 5.n, c."..1t c.,- s.-Operatinc nwain 16.8" 11.5% ... A M AM

c..,... s-DtbllEBITDA 1.6. 2.3. ... A M AM

c.,- s-EBITDAlinterat 2".7. 19.5. ... A M AM

c.,- s-FCF/dcbt 2".3" 23.2% ... A M AM

c.,- s-Dtbl/capital 26.6" 37.5% ... A M AM

Based on the ntio avenges. il is mosrlikcly thaI Suor', iauer rating is MandCoyote's issuer rating is A.

&ample: Credit radnp bued on ratios (Pan 2)

Coyote Media decides 10 spin off irs telc:vision division. The new company. CO)·TV.will issue new debl and wiD nol be a ~stricted subsidiary of Coyole Media. CoyTVis mo~ profitable and ~neratCl higher and less wlatile cash Rows. Describe possiblenotching for the Dew CoyTV issue and the: potential credit rating chan~ 10 Coyoa:Media.

An __ r:

Because CoyTV may be a better credit risk due to a better profit potential. the: newissue:may have a =dit nting one: notch aboY!:Coyote: Media.

Coyote Media may now be less profitable and could have more wlalile cash Rows. Thissuggests an incrcuc in credit risk that could lead to a credit rating downgrade.

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LOS 56.h: Describe factors that influence the level and volatility of yieldspreads.

CF-A®Program Curriculum, Vo'umt 5. fUJlt 568

We can think of the yield on an option-free corporare bond as the sum of the real risk-free interest rate, the expected inAation rate, a maturity premium, a liquidity premium.and a credit spread. All bond prices and yields arc affected by changes in the first threeof these components. The last twO components arc the yield spread:

yield spread. liquidity premium + credit sprcad

Yield spreads on corporate bonds arc affected primarily by five:interrelated factors:

I. Credit cycle. The market's perception of overall credit risk is cyclical. At the top ofthe credit cycle, the bond market perceives low credit risk and is gc:nerally buUish.Credit spreads narrow as the credit cycle improves. Credit sprcads widen as thecredit cycle deteriorates.

2. Economic conditions. Credit spreads narrow as the economy strengthens andinvestof$ expect firms' credit metries to improve. Conversely, credit spreads widen asthe economy weakens.

3. Financial market performance. Credit spreads narrow in mong-performing marketsoverall. including the equity market. Credit spreads widen in weak-performingmarkets. In steady-performing markets with low volatility of returns, credit spreadsalso tend to narrow as investors reach for yield.

4. Broker-dealer capital. Becawe most bonds trade ove:r the counter, invcstof$ needbroker-dealers to provide market-making capital for bond markets to function. Yieldspreads arc narrower when broker-dealers provide sufficient capital but can widenwhen market-making apital becomes scarce.

5. General market demand and supply. Credit spreads narrow in times of highdemand for bonds. Credit spreads widen in times of low demand for bonds. Excesssupply conditions, such as large issuance in a shon period of time, an lead towidening spreads.

Yield spreads on lower-quality issues tend to be more volatile than spreads on higher-quality issues.

LOS 56.i: Calculate the return impact of spread changes.

CFA® Progrttm CUTTi<u'um. Vo'umt 5, fUJgt 571

The return impact of spread changes is a combination of two facton: (I) the magnitudeof the spread change (tl.spread) and (2) the price sensitivity of the bond to interest ratechanges (i.e., the bond's modified duration).

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For small spread changes, the return impact (percent change in bond price) can beapproximated by:

return impact "" - modified duration )( Aspread

The negative sign in the equation reflecu the inverse relationship between prlces andyields. As spreads widen (the change in spread is positive), bond prices decrease and theimpact on return is negative. As spreads narrow (the change in spread is negative), bondprices increase and the impact on return is positive.

For larger spread changes, incorporating convexity improves the accuracy of returnimpact measurement.

return impact "" - modified duration x Asprcad + .!convcxity x (Asprcadt2

Profmor} Notr: Maltt S,," rh~ 114/'" ofconll""iry is sell/.d corrtCt/y. For option-ft'tt~ bonis, conlltxiry shou14 b~ M th. sam. ord~, of mllgniru4. as modifi'" Juoltiqn~ Sf/JIIlOd. FOT~xampk, ifYO" IIT~';Vtn that dU"'tion is 6. 0 and conlltXiry is 0.562.

dUTlllion squartd is 36.0 and the fOrTut!y mlltd fonvairy is 56.2.

Longer maturity bonds have higher duration and consequently higher spread sensitivity;their prices and returns arc more sensitive to changes in spread. The longer the maturity,the higher the uncertainty of the future creditworthiness of the debt issuer, implyinghigher credit spreads for longer maturity bonds. Longer maturity bonds also tend tohave larger bid-ask spreads (i.e., higher transaction casu), implying investors in longermaturity bonds would require higher spreads.

Credit curves or sprtlld C"'"'S show the relationship between spread and maturity.Because longer maturity bonds tend to have wider spreads, credit curves arc typicallyupward sloping.

Bond performance is positively affected by narrowing credit spreads and negativelyaffected by widening crcditspreads. To enhance bond portfolio perlOrmance, activebond managers need to forecast spread changes and expected credit losses for individualissues held and for the overall bond portfolio.

&ample: Impact 00 return

An S-year scmiaonual-pay corporate bond with a S.7S" coupon is priced at $10S.32.This bond's duration and reported convexity arc 6.4 aod O.S. The bond', credit 'preadnarrows by 7S basis poinu due to a credit rating upgrade. Estimate the return impactwith and without the convexity adjustment.

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return impact (without convexity adjustment) ... - modified durarion )( dsprcad... - 6.4 x -0.0075... 0.0480... 0.048 or 4.80%

return impaa with convexity adjustment

... - modi6cd duruion x 6sprcad + !convcxil)' x (dsprcad)22

... -6.4 x -0.0075 - !(SO.0)x(-0.0075)22

... 0.0480+0.0014

... 0.0494 or 4.94%

Notice that conouity needed to be corrected to match the scalc of duration.

We can calculate the actual change in the bond's price from the information given toillustrate the need for the convexity adjustment.

Beginning yield to maturity:

N. 16; PMT • 5.75 , 2.2.875; FV. 100; PV. -108.32;CPT -- IIY. 2.25 x 2. 4.SO

Yield to maturity after upgrade: 4.50 - 0.75 • 3.75%

Price alier upgrade:

IIY. 3.75 , 2 • 1.875; CPT .....PV. -113.71

The calculated bond price of5113.71 il an increase of(113.71' 108.32) -I .4.98%.The approximation is closer with the convexity adjustment.

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LOS 56.j: Explain special considerations when evaluating the credit of highyield, sovereign, and municipal debt issuers and issues.

CFA® Program Curriculum. Volume 5. palt 576

High Yield Debt

High yield or non-immtment I'm corporate bonds arc rated below Baa3/BBB by creditrating agencies. These bands arc also caUed junk HnJs because of their higher perceivedcredit risk.

Reasons for non-investment grade ratings may include:

• High kverage.Unproven operating history.Low or negative free cash 8ow.High sensitivity to business cycles.Low can6dencc in management.Unclear compctitive advantag es,Large off-balance-sheet liabilities.Industry in decline.

•••••••Because high yield bands have higher dcf.ault risk than investment grade bands. creditanalysu must pay marc auenticn to lass severity. Special considerations for high yieldbands includc their liquidity. 6nandal projections. debt structure. corporate structure,and covenants.

LitJuitiity. Liquidity or availability of cash is critical for high yield issuers. High yieldissucrs havc limitcd access to additional borrowings. and availablc funds tend to bemore expensivc for high yield issuers. Bad c.ompany-speci6c news and difficult 6nandalmarket conditions can quickly dry up the liquidity of debt markets. Many high yieldissuers arc privately owned and cannot access public equity markets for needed funds.

Analysu focus on six sources of liquidity (in ordcr of reliability):

J. Balance sheet cash.

2. Working capital.

3. Operating cash 80w (CFO).

4. Bank credit,

5. Equity issued.

6. Sales of asseu.

For a high yield issuer with few or unreliable sources of liquidity. signi6cant amaunuof debt coming due within a short time frame may indicate potential default. Runningout of cash with no access to external 6nancing to refinance or servic.c existing debt is

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the primary reason why high yield issuers default. For high yield financial firms thatarc highly levered and depend on funding long-term asseu with short-term liabilities.liquidity is critical.

FiNllllcw projections. Projecting future earnings and cash Rows. including stressscenarios and accounting for changes in capital expenditures and working capital. arcimportanr for revealing potential vulnerabilities to the inability to meet debt payments.

Debt strJietJUY. High yield issuers' capital structures often include different types of debtwith severallcvcls of seniority and hence varying levels of potential 10.. severity. Capitalstructures typically include secured bank debt. second lien debt. senior unsecured debt.subordinated debt, and preferred stock. Some of these, especially subordinated debt, maybe convertible to common shares.

A credit analysr will need to calculate leverage for each level of the debt structure whenan issuer has multiple layers of debt with a variety of expected recovery rates.

High yield companies for which secured bank debt is a high proportion of the capitalstructure arc said to be top htavy and have less capacity to borrow from banks infinancially stressful periods. Companies that have top-heavy capital structures arc morelikely to default and have lower recovery rates for unsecured debt issues.

Example: Debt ItruUun: aDd Icvcracc

Two European high yield compania in the same indusuy have the following 6nancialinformation:

I" e ",i/li.,. A BCash 100.0 50.0""ercst expense 40.0 20.0EBITDA 85.0 42.5Secured bank debt 500.0 125.0Senior II_Cured debt 200.0 50.0COD""nible bond, 50.0 200.0

1. Calculate total Icvcrap: through each Ic:vd of debt for both companies.

2. Calculate net levuagc: for both companies.

3. Comment on which company is mere attractive: to an unsecured debt investor.

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Answer:

A B

Stewed dd>1 lewnse:secureddcbclEBITDASeoior _wed levenF(secured • seniorUDlCCured debl)'EBITDATow debe !eYe .... :cow debdEBITDANel lnuage:(cow debe - cash)'EBITDA

500.01 85.0 • 5.!)x 125.0 , 42.5 • 2.9><

(500.0 • 200.0 • 50.0) ,85.0.8.8x

(125.0.50.0.200.0) ,42.5.8.8x

(500.0 • 200.0) , 85.0 • 8.2x (125.0. 50.0) 142.5 • 4.1x

(750.0 - 100.0) 185.0. 7.6x (375.0 - 50.0) '''2.5 • 7.Gx

Company B hat a lowu sccuRd debt Im:rage ratio than Company A, while total andnct leverage ratios are about the same. Company B is more attractive co unsceurcd debtholden becalllC it il len top hcaY)' and may have some capacity to borrow from banks,which "U8F'1S a lower probability of default. If it docs default, Company B may hafta higher percencagc of assets available to unsccuRd debt holders than Company A,cspcciaUy ifholdcrs of convcnible bonds haft excn:ised their options.

Q"po'lIr~ stnlctrl,~.Many high.yield companies usc a holding company structure. Aparent company receives dividends from the earnings of subsidiaries as its primary sourceof operating income. Because of structural subordination, subsiruarics' dividends paidupstream 10 a parent company are subordinate to interest paymenlS. These dividends canbe insufficient to pay the debt obligations of the parent, thus reducing the recovery ratefor debt holden of the parent company.

Despite structural subordination, a parent company's credit rating may be superior tosubsidiaries' ratings because the parent can bene6t from having access to multiple cashBows from diverse subsidiaries.

Some complex corporate structures have intermediate holding companies that carrytheir own debt and do not own 100% of their subsidiarics' stock. These companies aretypicaUya result of mergers, acquisitions, or leveraged buyoulS.

Default of one subsidiary may not necessarily result in cross default. Analysts need toscrutinize bonds' indentures and other legal documents to fully understand the impactof complex corporate structures. To analyze these companies, analysIS should calculateleverage ratios at each level of debt issuance and on a consolidated basis.

Q,,,enllnts. Important covenants for high yield debt include:

• Change of control put. This covenant gives debt holders the right to require theissuer to buy back debt (typically for par value or a value slighdy above par) inthe event of an acquisition. For investment grade bonds, a change of control PUI

typically applies only if an acquisition of the borrower results in a rating downgradeto below investment grade.

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• Restricted paymrnts. The covenant protrctS lenders by limiting the amount of cashthat may be paid to equity holders.

• Limitations on liens. The covenant limits the amount of secured debt that aborrower can carty. Unsecured debe holders prefer the issuer to have las secureddebr, which increases the recovety amount available to them in the event of default.

• Restricted versus unrestricted subsidiaries. Issuers can classify subsidiarirs asrest rieted or unrestricted. Restricted subsidiarid cash Rows and assets can be usedto service the debt of the parent holding company. This brnefits creditors of holdingcompanies because their debt is pari passu with the debt of restricted subsidiaria,rather than structurally subordinated. Restricted subsidiaries are typically theholding company's larger subsidiaries that have significant assets. Tax and rcgulatotyissues can fartor into the classification of subsidiary's restriction status. A subsidiary'sresericticn status is found in the bond indenture,

Bank eevenants are oftrn more restrictive than bond covenants, and when covenants arcviolated, banks can block additional loans until the violation is corrected, If a violationis not remedied, banks can triggrr a drfault by accderating the full repayment of a loan.

In trrms of the factors that affert their return, high yield bonds may be viewed as ahybrid of investment grade bonds and equity. Compared to investment gradr bonds,high yield bonds show greater price and spread volatility and are more highly correlatedwith the equity market,

High yicld analysis can indude some of the same techniques as equity market analysis,such as enterprise value. Entrrprisc value (EV) is rquity market capitalization plustotal debt minus excess cash. For high yidd companies that arc not publicly traded,comparable public company equity data can be used to estimate EV. Enterprise valueanalysis can indicate a firm's potential for additional leverage, or the potential creditdamage that might result from a leveraged buyout. An analyst can comparr firms basedon the differences between their EV/EBITDA and debtlEBITDA ratios. Firms witha wider difference betwecn these ratios have greater equity relative to their debt andtherefore have less credit risk.

Sovereign Debt

So""rcign debt is issued by national governmrnts. Sovereign credit analysis must assasboth the government's ability to servicc debt and its willingness to do so. The assessmentof willingness is important because bondholders usually have no legal recoursc if anational go""rnment refuses to pay its debts.

A basic framework for evaluating and assigning a credit rating to sovereign debt includesfive key arras:

1. Institutional effi:cti""ncss includes successful policymaking, absence of corruption,and commitment to honor debts.

2. Economic prospects include growth trends, demographics, income per capita, andsize of government relative to the private economy.

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3. International investment position includes the country's foreign reserves, itsexternal debt, and the ,tatw of its currency in international markets.

4. Fiscal ftcxibility includes the government's willingness and ability to increaserevenue or cut expenditures to ensure debt service, as well as trends in debt as apercentage of GOP.

5. Monetary Acxibility includes the ability to use monetary policy for domesticeconomic objectives (this might be lacking with exchange rate targeting ormembership in a monetary union) and the credibility and effectiveness of monetarypolicy.

Credit raring agencies assign each national government twO ratings: (I) a local currencydebt rating and (2) a foreign currency debt rating. The ratings are assigned separatelybecause defaults on foreign currency denominated debt have historically exceeded thoseon local currency debt. Foreign currency debt typically has a higher default rate anda lower credit raring because the government must purchase foreign currency in theopen market to make interest and principal payments, which exposes it to the risk ofsignificant local currency depreciation. In contrast, local currency debt can be repaid byraising taxes, controlling domestic spending, or simply printing more moncy. Ratingscan diffi:r as much as two notches for local and foreign currency bonds.

Sovereign defaults can be cawed by events such as war, political instability, severedevaluation of the currency, or large declines in the prices of the country's ""portcommodities. Aceess to debt markets can be diffirult for sovereigns in bad economictimes.

Municipal Debt

Municipal bond. arc issued by state and local governments or their agencies. Municipalbonds usually have 10001:rdefault rates than corporate bonds with same credit ratings.

Most municipal bonds can be classified as gefle",' obligation bontls or Tel/enlle bontls.General obligation (GO) bonds arc unsecured bonds backed by the fujI faith credit ofthe issuing governmental entiry, which is to say thcy arc supported by irs taXing power.

Unlike sovereigns, municipalities cannot usc monetary policy to service their debt andusually must balance their operating budgets. Municipal governments' abiliry to servicetheir general obligation debt depends ultimately on the local economy (i.e., the taXbase). Economic factors to assess include employment, trends in per capita income andper capita debt. tax base dimensions (depth. breadth and stability), demographics, andability to attract new jobs (location, infrastructure). Credit analysts must also observerevenue variability through economic cycles, Relying on highly variable taxes that arcsubject to economic cycles, such as capital gains and sales taxes. can signal higher creditrisk. Municipalitio may have long-term obligations such as underfunded pensions andpost-retirement benefits. Inconsistent reponing requirements for municipalities arc alsoan issue.

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Study SHsion 16Cross-~fmDce to CFA Irutiwle Assigned Reading '56 - Fundamentals of Credit Analysis

Revenue bonds 6nancc specific projects. Revenue bonds often have higher credit riskthan GO bonds because the project is the sole source of funds to service the debt.Analysis of revenue bonds combines analysis of the project, wing techniques similar tothose for analyzing corporate bonds, with analysis of the 6nancing of the project.

A key metric for revenue bonds is the debt service coverage ratio (DSCR), which isthe ratio of the project's net revenue to the required interest and principal paymentson the bonds. Many revenue bonds include a covenant requiring a minimum debtservice coverage ratio to protect the lenders' interests. Lenders prefer higher debt servicecoverage ratios, as this represents lower default risk (better creditwonhineu).

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KEy CONCEPTS

LOS 56.aCredit risk refers to the possibility that a borrower fails to make the scheduled interestpayments or return of principal. Credit risk is composed of default risk, which is theprobability of default, and loss severity, which is the ponion of the value of a bondor loan a lender or investor will lose if the bcrrcwer defaults. The expected loss is theprobability of default multiplied by the loss severity.

Spread risk is the possibility that a bond loses value because its credit spread widensrelative to its benchmark. Spread risk includes credit migration or downgrade risk andmarket liquidity risk.

LOS 56.bCorporate debt is ranked by seniority or priority of claims. Secured debt is a direct claimon specific firm assets and has priority over unsecured debt. Secured or unsecured debtmay be fun her ranked as senior or subordinated. Priority of claims may be summari:r.cdas follows:• First mongage or first lien.• Second or subsequent lien.• Senior secured debt.• Senior unsecured debt.• Senior subordinated debt.• Subordinated debt.• Junior subordinated debt.

LOS 56.cIssuer credit ratings, or corporate family ratings, reAect a debt issuer's overallcreditworthiness and typically apply to a firm's senior unsecured debt.

Issue credit ratings, or corporate credit ratings, reAect the credit risk of a specific debtissue. Notching refers to the practice of adjusting an issue credit rating upward ordownward from the issuer credit rating to reAcct the seniority and other provisions of adebt issue.

LOS 56.dLenders and bond investors should not rely exclusively on credit ratings from ratingagencies for the following reasons:• Credit ratings can change during the life of a debt issue.• lUting agencies cannot always judge credit risk accurately.• Firms arc subject to risk of unforeseen events that credit ratings do not reAcct.• Market prices of bonds often adjust more rapidly than credit ratings.

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LOS 56.cComponents of traditional credit analysis arc known as the four Cs:o Capacity! The borrower's ability to make timely payments on its debt.o Collateral: The value of assets pledged against a debt issue or available to creditors if

the issuer defaults.o Covenants: Provisions of a bond issue that protect creditors by requ.iring or

prohibiting actions by an issuer's management.o Character: Assessment of an issuer's management, nrategy, quality of earnings, and

past treatment of bondholders.

LOS56.fCredit analyns usc profitability, cash 1I0w,and leverage and coverage ratios to assess debt. , .ISsuers capaCIty.o Profitability refers to operating income and operating profit margin, with operating

income typically defined as earnings before interest and taxes (EBln.o Cash lIow may be measured as earnings before interest, taxes, depreciation, and

amortization (EBITDA); funds from operations (FFO); free cash IIow beforedividends; or free cash 1I0wafter dividends.

o Leverage ratios include debt-to-capital, debt-to-EBITDA, and FFO-to-debt_o Coverage ratios include EBIT-to-interest expense and EBITDA-to-interest expense.

LOS 56.gLower leverage, higher interest coverage, and greater free cash 1I0wimply lower creditrisk and a higher credit rating for a firm. When calculating leverage ratiO$, analystsshould include in a firm's toral debt its obligations such as underfunded pensions andoff-balance-sheet financing.

For a specific debt issue. secured collateral implies lower credit risk compared tounsecured debt, and higher seniority implies lower credit risk compared to lowerseniority,

LOS 56.hCorporate bond yields comprise the real risk-free rate, expected inllation rate. creditspread, maturity premium, and liqu.idity premium. An issue's yield spread to itsbenchmark includes its credit spread and liquidity premium.

The level and volatility of yield spreads arc affected by the credit and business cycles.the performance of financial markets as a whole, availability of capital from broker-dealers. and supply and demand for debt issues. Yield spreads tend to narrow whenthe credit cycle is improving. the economy is expanding, and financial markets andinvestor demand for new debt issues arc strong. Yield spreads tend to widen when thecredit cycle, the economy. and financial markets arc weakening, and in periods whenthe supply of new debt issues is heavy or broker-dealer capital i. insufficient for marketmaking.

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LOS 56.iAnalysts can usc duration and convexity to estimate the impact on return (thepercentage change in bond price) of a change in credit spread.

For small spread changes:

return irnpace se -duration x ll.sprcad

For larger spread changes:

return impact ... -duration x ll.spread + iconvc:xity x (6sprcad)2

LOS 56.JHigh yield bonds arc more likely to default than investment grade bonds. whichincreases the importance of estimating loss severity. Analysis of high yield debt shouldfocus on liquidity, projected financial performance, the issuer's corporate and debtstructures, and debt covenants.

Credit risk of sovereign debt indud es the issuing country's ability and willingness topay. Ability to pay is greater for debt issued in the country's own currency than for debtissued in a foreign currency. Willingness refers to the possibility that a country refuses torepay its debts.

Analysis of general obligation municipal debt is similar to analysis of sovereign debt,focusing on the strength of the local economy and its effect on tax revenues. Analysis ofmunicipal revenue bonds is similar to analysis of corporate debt. focusing on the abilityof a project to generate sufficient revenue to service the bonds.

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Page 132

CONCEPT CHECKERS

1. Expected lou can decrease with an increase in a bond's:A. default risk.B. los.sseverity.C. recovery rate.

2. Absolute priority of claims in a bankruptcy might be violated because:A. of the p"Ti !"IIII principle.B. creditors negotiate a different outcome.C. available funds must be distributed equally among creditors.

3. "Notching" is 11m described as a differcnce between a(n):A. issuer credit rating and an issue credit rating.B. company credit rating and an indwtty average credit rating.C. investment grade credit rating and a non-investment grade credit rating.

4. Which of the following natements is killt liltt/y a limitation of relying on ratingsfrom credit rating agencies?A. Credit ratings are dynamic.B. Firm-specific risks are diffieultto rate.C. Credit ratings adjWt quickly to changes in bond prices.

5. Ratio analysis is most liltt/y used to assess a borrower's:A. capacity.B. character.C. collateral.

6. Higher credit risk is indicated by a higher:A. FFO/debt ratio.B. debtlEBITDA ratio.C. EBITDAlintercst expense ratio.

7. Compared to other firms in the same industry, an issuer with a credit rating ofAAA should have a lower:A. FFO/debt ratio.B. operating margin.C. debtlcapital ratio.

8. Credit spreads tend to widen as:A. the credit cycle improves.B. economic conditions woescn.C. broker-dealers become more waling to provide capital.

9. Compared to shorter duration bonds, longcr duration bonds:A. have smaller bid-ask spreads.B. arc ku sensitive: to credit spreads.C. have less certainty reg;arding future creditworthiness.

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Study S... ion 16Cro&s-lUftrtn~ to CFA I",ulult Assigned Reading '56 - Fundamtnuls of Cttdil Analysis

10. One key difference between sovereign bonds and municipal bonds is thatsovercign issuers:A. can print money.B. have governmental taXing power.C. arc affected by economic ccnditions.

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Study S...ion 16Cross-lUft~DC>e to CFA lrutillllt As$igntd Rtading '56 - Fuodamtntals of Credit Analysis

CHALLENGE PROBLEM

Woden,lnc., is a high yield bond issuer with a credit rating of Ba2IBB. Woden presentsthe following balance sheet for the most recent year (in millions of dollars):

Cash 10 Accounts payable 10

AccountS receivable 15 Short-term deb, 5

Inventories ~ Cwn:n, portion of long-cerm dc:bt ....3Curml< ~ts 80 Currenl Uabililics 18

land 10 Long-term bank loans 30Propcrey, plam, and equipment, nC! 85 Secured bonds 10

Goodwill .25. Unsccurtd bonds ....2llNon-curren; asstlS 120 Tow long-term debr GO

Tow~ts 200 Ner pension liabiJjey ~Tow liabililics 100

Paid-in capital 10

Retained cunings ....20Tow sharcholdtrs' oqwry 100

Tow liabjJj,ics and oquiey 200

For the year, Woden's earnings before interest, taxes, depreciation, and amortization(EBITDA) were $45 million.

For firms in Woden's industry, credit rating standards for an investment grade (Baa31BBB-) credit rating include a debt-to-EBITDA ratio less than 1.8x and a debt-to-capitalratio (based on all sowces of financing) less than 40%. On a conference call with analysts,Woden's management states that they believe Woden should be upgraded to investmentgrade, based on its debt-to-EBITDA ratio of 1.5x and its debt-to-apical ratio of34%.

Why might a credit analyst disagree with management's assessment?

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Study Session 16Cross-lUfor<n'" to CFA Institult Assignod Rtadlng '56 - Fundam..,ta!s of Crtdit Analysis

ANSWERS - CONCEPT CHECKERS

I. C An inc«asc in the lecovuy rato mcans that the loss severity has deer essed. whichdecreases expected loss.

2. B A negotiated bankruptcy seulement does nOI always follow !he absolute pliolity ofclaims,

3. A NOlching lefers 10 the credit lating agency practice of diStinguishing berween the creditrating of an issuer (gone rally fOI its senior unsecured debt) and the credit rating ofpatticulu debt issuos from !hal iuuel. which may diff., from !he issnellaling because ofprovisions such U seniolity.

4. C Bond plices and aedit spleads chang. much fUI., !han credit ralings.

5. A Rario antl,..is is used 10 assess a colporale borrower's capacity 10 «pay its debtobligation. on time.

6. B A bigher debt/EBITOA ratio is .ign ofhighellcverage and bigher credit risk. HigherFFO/debt and EBITOiVintelen expense ralios indicate 10"''''' credit risk.

7. C A low debt/capita! ratio is an indicator of low loverage. An iuucr raeed AM is Iikdy tohave a high oporating margin and a high FFO/debt ratio eompa«d 10 its industty group.

8. B Credil sprnds widen U economic conditions worsen. Spleads narrow U the credit cycleimproves and U broker-dealers provide more capital to bond markets.

9. C umger duration bond. usually have longer maturities and carty mort uncertalnty offuture crediewerthiness.

10. A Sove«ign entities can print money 10 repay debt. while municipal borrowers cannot.Both sove«ign and municipal entities have Wling powers, and both are alfectod byeconcmic conditions.

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Study Session 16Cro$S-~fmDC>e to CFA lrutiwt. Assignod R.ading '56 - Fundamentals of Cmiit AnaI) ..i,

ANSWERS - CHALLENGE PROBLEM

The debt ratios cakulated by managemont are based on thelirm', short-term and long-term deb"

Total debt _ 5 • 3 + 30 + 10 + 20 _ 68

Debt/EBITDA • 68 1"5 • 1.5.

Debt/capital _ 68 1 200 - 34%

A credit analyst, however, should add Woden', net pension liability to iu tOtal deb"

Debt. net pension liability _ 68 + 22 _ 90

Adjusted debtlEBITDA • 90/45 • 2.0.

Adjusted dobt/capital _ 90 I 200 - 45%

Additionally, a credit analyst may calcubte what the debt-to-capital ratio would be if Wodenwrote down tbe value of iu balance sheet goodwiU and reduced retained e.rnings by the sameamount:

Adjusted capital - 200 - 25 - 175

Adjustod debi ladjuSled capital » 90 1175.51%

These adjustmenu suggest Wodon docs not meet the r<quiremenu for an investment grade creditrating.

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SELF-TEsT: FIXED INCOME INVESTMENTS

14 questions, 21 minutes

1. An estimate of the incre .. e in an option-free bond's price, based only on itsduration:A. will be too small.B. will be too large,C. may be either too small or too large,

2. Three companies in the same industry have exhibited the following av~rag~ratios over a 5-y= period:

5-Y~r Averages AIM" &rrtlW Col/il4"Operaling margin 13.3% 15.0% 20.7%OebtiEBITDA 4.6. 0.9. 2.8.EBIT/ln,uCoS' 3.6. 8.9. 5.7.FFO/Oeb, 12.5% 14.6% 11.5%DebtiCapital 60.8% 23.6% 29.6%

Based only on the infOrmation given, the company that mott likt/y hOI thehigh~st credit rating is:A. A1d~n.B. Barrow.C. Collison.

3. The difTer~nc~ between a convertible bond and a bond with warrants is that abondholder who exercises warrants:A. docs not pay cash fOr the common stock.B. obtains common stock at a Iowa price pa share,C. continua to hold the bond aft~r uercising the warrants.

4. Which of the fOllowing is !tast likt/y a common form of external creditenhancement!A. Overcollateralizatioe.B. A corporate guarant~~.C. A letter of credit from a bank.

5. A bond with an embedded put option hOI a modified duration of7, an ~fTectiv~duration of 6 and an effective convexity of 125. If interest rata rise 25 basispoints, the bond's price will change by IIpproximatt/y:A. 1.46%.B. 1.50%.C. 1.54%.

6. Which of the fOllowing bonds would appreciate the most if the yield curve shiftsdown by 50 basi. points at all maturities?A. 4-~ar 8%, 8% YTM.B. 5-~r 8%, 7.5% YTM.C. 5-~ar 8.5%, 8% YTM.

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Sdf-Teot: Fued Income In~.unenu

7.

8.

9.

~138

Which of the following provisions would mOJr /ilt~1yincrease the required yieldto maturity on a debt security?A. Call option.B. Put option.C. Floor on a floating-rate security.

Other things equal, a corporate bond's yield spread is likely to be mOlrvolatile ifthe bond is rated:A. Mwith 5 years to maturity.B. AM with 3 years to maturity.C. BBB with 15 years to maturity.

A commercial paper issue with 320 days until marurity has a yield of 2.20%.This commercial paper most /iIt~Iy:A. was issued in the United States.B. is quoted on a discount yield basis.C. is supported by a backup line of credit.

10. An investor in longer-term coupon bonds who has a short investment horizon ismDI' 'ilt~1y:A. more concerned with market price risk than reinvestment risk.B. more concerned with reinvestment risk than market price risk.C. equally concerned about market price risk and reinvestment risk.

II. A bank loan department is trying to determine the correct rate for a 2-year loanto be made two years from now. If current implied Treasury effective annualspot rates are: I-year; 2%, 2-ycar ; 3%, 3-year ; 3.5%, 4-ycar ; 4.5%, the base(risk-free) forward rate for the loan before adding a risk premium is closes: to:A. 4.5%.B. 6.0%.C.9.0%.

12. Ceyore Corporation has an issuer credit rating of M but its most reeendy issuedbonds have an issue credit rating of AA-. This difference is most likely due tothe newly issued bonds having:A. been issued as senior subordinated debt.B. been affected by restricted subsidiary status.C. additional covenants that protect the bondholders.

13. An 8% semiannual coupon, $ 1,000 par value 5-year bond is issued onDecember 30, 2OX2 and matures on December 30, 20X7. The bond pays itscoupons on June 30 and December 30 of each year. On February 15 of 20X2the bond has a yield to maturity of 6.5%. Accrued interest on this date using the30/360 method is c/gmt to:A. SI5.00.B. S20.00.C. $25.00.

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14. Which of the following statements Ittlft tlCCUTtltt/y describes a form of riskassociated with inv~sting in fix~d income securities!A. Credit risk has only two compon~nu, default ruk and downgrade risk.B. Other things equal, a bond is more valuable to an investor when it has las

liquidity risk.C. Bonds that are callable or amonizing have more reinvestment risk than

otherwise equivalent bonds without these featur~s.

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Sdf-Test: Fued Income In~stmcnu

SELF-TEsT ANSWERS: FIXED INCOME INVESTMENTS

I. A Duration is a linear measure, but the relationship between bond price and yield for anoption. free bond is eonv ex, For a gi~n decrease in yield, !h. estimated price increaseusing duration alone will be smaller than the actual price incr ease.

2. B Four of the five credit m.uies giv.n indicate that Burow should have the highest creditrating of these three companies. Barrow has higher interest coverage and lower leverage!han either Ald.n or Collison.

3. C Warran ts give holders the option to buy shares of the issuer's common srock at apredetermined pric e. A bondholder who exercises warrantS pays !h•••• rei•• price to theissuer and reee ives common shares, but continues to hold the bond. With ccnvertiblebonds, a bondholder who exercises the conversion option exchanges the bond for apredetermined number of common shares. Excrcise pric•• of wuran .. and conv.rsionprices of eenvenible bonds are not necwuily related.

4. A External credit eehaneemenu are financial guarantees from !hird parties that gcnerallysuppOrt the performance of the bond. Ov.rcollateralization is a form of internal credilenhancemeru,

5. A Effectivc duration must be used with bonds !hat have embedded options.

6P • (-)(EO)(6y) + (1/2)(EC)(6y)1

6P. (-)(6)(0.0025) + (1/2)(125)(0.0025)1. -0.015. 0.00039. -0.014610% or-10461%

6. B The bond wi!h !h. high." duration will benefit !he moS! from a decrease in rates. Thelower rhe coupon, low.r the yield 10 maturity, and longer the lime to malurity, rhebigher will be the duration.

7. A Call options favor !he issuer and increase th. required YTM. A PUIoption or alloorpretec .. the bondholder agaiDS!falling rates, which reduces. bond's required YTM.

8. C Spread volatility is typically gr.al." for lo" .. r quality and longer malurities. The BBBrated 15-year corporate bond has !h. lowest credit quality and longest maturity of !hethree choices.

9. C Commeedal paper issu.rs often maintain backup lines of eredh wi!h banks. Based oni.. 320 days to malurity, this issue is mosllikely Eurocommereia! pap.r (ECP), which isissued with original maturhies up to 364 days. Commercial paper issued in the UnitedStales Iypically bas an original maturilY of 270 days or less. ECP rates are quoted as add-on yields.

10. A Over a short investm.nl horizon, an increase in int .... t ralCSis lik.ly to decrease thereturn on a coupon bond because the decrease in price more than offs.ts ehe increasein reinvestment income. Over a long invalmeDt horizon. a decrease in interest ratesis likely 10 decrease lhe return on a coupon bond because the decrease in reinv.Slmentincome more than offseu me increase in price. Therefore, an investor with a shotthorizon is more concerned with market price risk and an investor with a long horizon ismore concerned with reinvestment risk.

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1I. B The forward rate is (1.04541 1.032)112 - 1 .6.02%, or use the approximation(4.5(4) - 3(2»)12 .6.

12. A The issuer', corpor ate family rating (CFR) is M while th. bond', corpcrate credit rating(CCR) is lower,M-. One possible reason for this notching diff.rence is thar the bondmay have a lower seniori!), ranking. CFR ratings are based on senior unsecured debt.If the newly issued bond is a senior subordinated deb" it has a lo.... r priori!}' of claimsand hence a lower rating. Restricted status would afTeet both CFR and CCR. Additionalcov.. nants that protect bondholders would enhance the issue's CCR.

13. B For a semiannual coupon bond, accrued interest using the 30/360 method is based on30-day months and a 180-day coupon period. The number of days over which couponinterest has accrued is 30 Uanuary) + 15 (February) • 45. Accrued interest. S 1,000 •8% • 45/180 • S20.

14. A Even if a bond does not default and is not downgraded, it still faces credit spread risk uthe premium in the market for the bond's credit risk may increase. Lo....r liquidity risk(i.e., higher liquidi!}') is preferred by investors, reduces a bond's required rate of return,and inc.reues iu value, other things equal. Reinvemnent risk is higher for callable oramortizing bond. u these features l•• d to a greater probabili!}' of receiving principalrepayment earlier, which means the re lie more fund. to be reinvested over the lif. of thebond.

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The (011~;ng is • rnicw of the DcrinbWI principles dellped to addrus the leuai.ng outcome.talCtDcnu .et forth by CfA In.tituk. Thil topic i. allG c~rcd iD:

DERIVATIVE MARKETS ANDINSTRUMENTS

Study SHslon 17

ExAM FocusThis topic review contains introductory material for the upcoming reviews of specifictypes of derivatives. Derivarives-specifie definition. and terminology arc presented alongwith information about derivatives markets. Upon completion of this review. candidatesshould be familiar with the basic concepts that underlie derivatives and the generalarbitrage framework. There is little contained in this review that will not be elaboratedupon in the five reviews that follow.

LOS 57.a: Define a derivative, and distinguish between exchange-traded andover-the-counter derivatives.

CF-A'"Progr4m Cu"icu/um. Vq{umt 6; p4gt 6

A derivative i. a .ccurity that Mriuts its value from the value or return of another user orsecurity,

A physical exchange exists for many options contracts and futures contracts.Exchange-traded dc:rivatives arc standardized and backed by a clearinghouse.

Forw4rds and SUN/pS arc custom instruments and arc traded/created by dealers in a marketwith no central location. A dealer market with no central location is referred to u anover-the-counter market. They arc largely unregulated markets and each contract is witha counterparty. which may ""pose the owner of a derivative to default risk {when thecountcrparty does not honor their commitment}.

Some options trade in the over-the-counter marker. noubly bond options.

LOS 57.b: Contrast forward commitments with contingent claims.

CF-A'"Progr4m Cumcu/um. Vq/umt 6; p4gt 7

A forward commitment is a legally binding promise to perform some action in thefuture. Forward commitments include forward contracts. futures contracts. and swaps.Forward contracts and futures contracts can be written on equities. indexes, bonds.physical assets, or interest rates.

A contingent claim is a claim (to a payoff) that depends on a particular event. Optionsarc contingent claims that dcpend on a stock pricc at some future date. While forwards.future s, and swaps have payments that arc made based on a price or rate outcome

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Study Seuion 17Cross·Rd".rtnce to CFA Instinll' A.. i~ Rtadinll '57 - Dtrivativt MathIS and Insuwn.nlS

whether the movement is up or down, contingent claims only require a payment if acertain threshold price is broken (e.g., if the price is above X or the rate is below Y). Ittakes cwo options to replicate a future or forward.

Credit derivatives are contingent claims that depend on a credit event such as a default.

LOS 57.c: Define forward contracts, futures contracts, options (calls and puts),swaps, and credit derivatives, and compare their basic characteristics.

In a forward contract, one parry agrees to buy, and the counterparty to sell, a physicalasset or a security at a specific price on a specific date in the future. If the future price ofthe asset increases, the buyer (at the older, lower price) has a gain, and the seller a loss.

A futun:& contraet is a forward contract that is standardized and exchange-traded. Themain differences with forwards are that futures are traded in an active secondary market,are regulated, backed by the clearinghouse, and require a daily set dement of gains andlosses.

A swap is a series of forward contracts. In the simplest swap, one party agrees to pay theshort-term (floating) rate of interest on some principal amount, and the counterpartyagrees to pay a certain (fixed) rate of interest in return. Swaps of different currencies andequity returns arc also common.

An option to buy an asset at a particular price is termed a call option. The seller ofthe option has an obliglltion to sell the asset at the agreed-upon price, if the call buyerchooses to exercise the right to buy the asset.

An option to seUan asset at a particular price is termed a put option. The seller of theoption has an obliglltion to purchase the asset at the agreed-upon price, if the put buyerchooses to exercise the right to sell the asset.

PTOftllOTiNow To T~m~mb~Tth~u terms, no" thllt th~ own" of II ,"1/ 'lin ","1/tb« IIIltt in" (i.e., bUl it); th~ own" of IIput hili tht Tight UJ "put tb« IIlltt to"th~ writtT of tb« put.

A credit derivative is a contract that provides a bondholder (lender) with protectionagainst a downgrade or a default by the borrower. The most common type of creditderivative is a credit default swap (CDS), which is essentially an insurance contractagainst default. A bondholder pays a series of cash flows to a credit protection seller andreceives a payment if the bond issuer dcfaulu.

Another type of credit derivative is a credit spread option, typicaUy a call option thatis based on a bond's yield spread against a benchmark. If the bond's credit qualitydecreases, iu yield spread will increase and the bondholder will collect a pa)"Cffon theoption.

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LOS 57.d: Describe purposes of, and controversies related to, derivativemarkets.

cr~"PrDgramCUfTiCfllum, Volumt 6,pagt 39

The critieism of tUrivatillts is that they are "tOOrisley,· especially to investors with limitedknowledge of sometimes complex instruments. Because of the high leverage involved inderivatives payoffs, they are sometimes likened to gambling.

The btntfiu of tUrivatillts markets are that they:

• Provide price information.• Allow risk to be managed and shifted among market participants.• Reduce transactions costs.

LOS 57.e: Explain arbitrage and the role it plays in determining prices andpromoting marker efficiency.

cr~»Program Curriculum, Volumt 6, fNlgt 47

Arbitrage is an important concept in valuing (pricing) derivative securities. In its purestsense, arbitrage is riskless. If a return greater than the risk-free rate can be earned byholding a portfolio of assets that produces a certain {riskless} return, then an arbitrageopportunity exislS.

Arbitrage opportunities arise when assets arc mispriccd. Trading by arbitrageurs willcontinue until they alfea supply and demand enough to bring asset prices to efficient{no-arbitrage} levels.

There are two arbitrage arguments that arc particularly useful in the study and usc ofderivatives.

The first is based on the law of one price. Two securities or portfolios that have identicalcash Rows in the future, regardless of future events, should have the same price. If A andB have the identical future payoffs, and A is priced lower than B, buy A and sell B. Youhave an immediate profit, and the payoff on A willntisfy the (future) liabiUty of beingshort on B.

The second type of arbitrage is used where two securities with uncertain returns can becombined in a portfolio that will have a certain payoff. If a portfolio consisting of A andB has a certain payoff, the portfolio should yield the risk-free rate. If this no-arbitragecondition is violated in that the certain return of A and B together is higher than therisk-free rate, an arbitrage opportunity exists. An arbi trageur could borrow at therisk-free rate, buy the A + B portfolio, and carn arbitrage profits when the certain payoffoccurs. The payoff will be more than is required to pay back the loan at the risk-freerate.

o P,oftJIor~ Not«: Wt wi/I ducull arbitragt forth" in our rtlJitw of options.

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KEy CONCEPTS

LOS 57.aA derivative has a value that is derived from the value of another asser or interest rate.

Exchange-traded derivatives, notably futures and some options, arc traded in centralizedlocations and arc standardized, regulated, and default risk free.

Forwards and swaps are customized contracts (over-the-counter derivatives) created bydealers and by financial institutions. There is very limited trading of these contracts insecondary markers and default (counterparry) risk must be considered.

LOS 57.bA forward commitment is a binding promise to buy or sell an asset or make apayment in the future. Forward contracts, futures conrracts, and swaps arc all forwardcommitments.

A contingent claim u an asset that has value only if some future event takes place(e.g., asset price is greater than a specified price). Options and credit derivatives arccontingent claims.

LOS 57.cForward contracts obligatc one party to buy, and anoth er to sell, a specific asset at apredetermincd price at a specific timc in the future.

Swaps contracts are equivalent to a series of forward contracts on interest rates,currencies, or equity returns.

Futures contracts arc much like forward contracts, but arc exchange-traded, quite liquid,and require daily settlement of any gains or losses.

A call option gives the holder the right, but not the obligation. to buy an asset at apredetermined price at some time in the future.

A put option gives the holder the right, but not the obligation. to sell an asset at apredetermined price at some time in the future.

A credit derivative is a contract that provides a payoff if a credit event occurs.

LOS 57.dDerivative markets arc criticized for their risky nature. However. many marketparticipants we derivatives to manage and reduce existing risk exposures.

Derivative securities play an important role in promoting efficient market prices andreducing transaction costs.

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LOS 57.cRisklen arbitrage refers to carning more than the risk-fre,e rate of return with no risk. orcarning an immediate gain wirh no possible future Iiabiliry.

Arbitrage can be expected to force the prices of two securities or portfolios of securitiesto be equal if they have the same future cash flows regardless of future events.

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Study Session 17Cro.. ·Rd'.rtncr to CFA InSUtu!.A&sisntd Rtadinll '57 - Dtrivativt Mathu and Insuwu.DU

I

CoNCEPT CHECKERS

I. Which of the rollowing most IIU,,,,ltt" describes a derivative security?A derivative:A. always increases risk.B. has no expiration date.C. has a payoff based on another asset.

2. Which of the rollowing derivatives is a forward commitment?A. Put option.B. Cwrency swap.e. Credit default swap.

3. Which of the following statements about exchange-traded derivatives is ItllstIlrcultlt~?A. They arc liquid.B. Thcy are standardized contracts.C. They carry signi6cant default risk.

4. A customized agreement to purchase a certain T-bond next Thursday for 51,000is!A. an option.B. a futures contract,e. a forward commitment.

5. A swap is:A. highly regulated.B. a series of rorward contracts.e. the exchange of one asset for another.

6. A call option gives the holder:A. the right to sell at a speci6c price.B. the right to buy at a specific price.e. an obHgation to sell at a certain price.

7. Arbitrage prevents:A. market efficiency.B. pr06t higher than the risk-free rate of return,e. two assets with identical payoffs from selling at different prices.

8. Derivatives arc It/1st liltt" to provide or improve:A. liquidlty.B. price information.C. inLtion reduction.

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ANSWERS - CONCEPT CHECKERS

1. C A derivative's value is derived from another asset.

2. B A cur~ncy swap is a forward commitment because both ecunterparti .. have obligationsto make paymenu in the futu~. Options and credit derivatives art contingent claimsbecause one of the counrerparties only has an obligalion if certain conditions are met.

3. C Exchange-traded derivatives ha,.. rdatively low default risk because the clearinghouseslands between the counterparries involved in men contracts .

.(. C This non-srandudiud t~ of contract is a forward commitment.

5. B A twap is an agreement to buy or sell an underlying auet periodically over the life of theswap contracr. It is cqwva]cnt [0 a series offorwud contracts.

G. B A call gives the owner the right 10 callan asset away (buy it) from the seller,

7. C Arbitrage ferces rwo auelS with the same expccted future value to sell for the samecurrent price. If this were not the case. you could simultaneously buy the cheaper assetand selithe more expensive one for a guaranteed riskless profit.

8. C Inflation is a monetary phenomenon. unaffeered by derivatives.

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The following is a rnicw of the Derivatiwi principici designed to address t.be laming outcomeIUtemen" set fOnA by CFA INfinite. This topic i, also covered in:

FORWARD MARKETS AND CONTRACTS

Study Sosdon 17

EXAll1 FocusThis topic review introduces forward contracts in general and covers the characteristicsof forward contracts on various financial securities, as well as interest rates. It is noteasy material. and you should take the time to Icarn it wdl. This material on forwardcontracts provides a good basis for futures contractS and many of the charactcristics ofboth rypcs of contracts are the samc. Takc the time to undcrstand the intuition behindthe valuation of forward ratc agreements.

FORWARD CONTRACTS

A forward contract is a bilateral contract that obligates one party to buy and the otherto seU a specific quantity of an asset. at a sct price. on a specific date in the future.Typically. neither party to the contract pays anything to get into the contract. If theexpected futute price of the assee increases over the lifc of the contract. the right to buyat the contract price will have positive value. and the obligation to sell will have an equalnegative value. If the future price of the asset falls below the contract price. the resultis opposite and the right to sell (at an above-market price) will have the positive value.The parties may enter into the contract as a speculation on the future price. More of'tcn.a party seeks to enter into a forward contract to hedge a risk it already has. The forwardcontract is used to eliminate uncertainty about the futurc price of an asset it plans to buyor sell at a later date. Forward contracts on physical assets. such as agricultural products.have existed for centuries. The Level I CFA curriculum. however, focuses on their (morerecent) usc for financial assets. such as T-bills. bonds. equicies, and foreign currencies.

LOS 58.a: Explain delivery/settlement and default risk for both long and shorrpositions in a forward contract.

CFA'" PrDpm Curriculum. Volumt 6. pllgt 62

The party to the forward contract that agrees to buy the financial or physical asset hasa long forward position and is called thc IDng. The party to the forward contract thatagrees to sell or deliver the asset has a sbort forward position and is called the short.

We will illustrate the mechanics of the basic forward contract through an example basedon thc purchase and sale of a Treasury bill. Note that while forward and futures contractson T-bills are usually quoted in terms of a discount percentage from face value. we willuse dollar prices to make the example easy to foUow. Actual pricing conventions andcalculations are among the contract characteristics covered later in this review.

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Study S.Won 17CroSs-~ft~Dce to CFA lruticutt ~td Reading '58 - Forward Marlccuand CoDltaCU

Consider a contract under which Party A agrees to buy a 51.000 face value. 90-dayTreasury bill from Party B 30 days from now at a price of 5990. Party A is the long andParty B is the short. Both panics have removed uncertainty about the price they willpay/receive for the T-bill at the future date. If 30 days from now T-bills are trading at5992. the short must deliver the T-biJI to the long in exchange for a 5990 payment. IfT-biJls are trading at 5988 on the future date. the long mwt purchase the T-bill from theshort for 5990. the contract price.

Each party to a forward contract is exposed to default risk (or eounterparty risk). theprobability that the other party (the counterparty) will not perform as promised. It isunusual for any cash to actually be exchanged at the inception of a forward contract .•unlike futures contracts in which each party posts an initial deposit (margin) as aguarantee of performance.

At any point in time. including the settlement date. only one party to the forwardcontract will owe money. meaning that side of the contract has a negative value. Theother side of the contract will have a positive value of an equal amount. Following theexample. if the T-bill price is 5992 at the (future) settlement date and the short does notdeliver the T-bill for S990 as promised. the short has defaulted.

LOS 58.b: Describe the procedures for settling a forward contract atexpiration, and how termination prior to expiration can affect credit risk.

The previous example was for a deliverable forward contract. The short contracted todeliver the aetual instrument. in this case a $1,000 face value, 90-day T-bin.

This is one procedure for settling a forward contract at the stttkmtnt dArt or expirationdate specified in the contract.

An alternative settlement method is cash settlement. Under this method. the party thathas a position with negative value is obligated to pay that amount to the other party.In the previow example. if the price of the T-biJI were S992 on the expiration date. theshort would satisfy thc contract by paying 52 to the long, Ignoring transactions costs,this method yields the same result as asset delivery. If the short had the T-bill. it couldbe sold in the market for S992. The short's net proceeds. however. would be 5990 aftersubtracting the 52 payment to the long. If the T-bill price at the settlement date wcre5988. thc long would make a $2 payment to the short. Purchasing a T-bill at the marketprice of S988. together with this 52 payment. would make the toral cost 5990. just as itwould be if it were a deliverable contract.

On the expiration (or scrtlement) date of the contract. the long receives a payment if theprice of the asset is above the agreed-upon (forward) price; the short receives a paymentif the price of the asset is below the contract price.

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Terminating a Position Prior to Expiration

A party to a forward contract can terminate the position prior to expiration by enteringinto an opposite forward contract with an expiration date equal to the time tcmainingon the original contract,

Recall our example and assume that ten daY' after inception (it was originally a 30-daycontract), the 20-day forward price ofa $1,000 face value, 90-dayT-bill is 5992. Theshort, expecting the price to be even higher by the delivery date, wishes to terminatethe contract. Sincc the short is obligated to sell the T-bill 20 days in the future, he caneffectively exit the contract by entering into a new (20-day) forward contract to buy anidentical T-bill (a long position) at the current forward price of 5992.

The position of the original short now is two-fold, an obligation to sell a T-bill in 20days for 5990 (under the original contract) and an obligation to purchase an identicalT-bill in 20 days for 5992. He has locked in a 52 loss, but has effectively exited thecontract since the amount owed at settlement is $2, regardless of the market price of theT-bill at the settlement date. No matter what the price of a 90·day T-bill is 20 days fromnow, he has the contractual right and obligation to buy one at 5992 and to sell one at5990.

However, if the short's new forward contract is with a different parry than the firstforward contract, some credit risk remains. If the price of the T-bill at the expirationdate is above S992, and the counterparry to the second forward contract fails toperform, the short's losses could exceed 52.

An alternative is to enter into the second (offsetting) contract with the same parry as theoriginal contract. This would avoid credit risk since the short could make a 52 paymentto the counterparty at contract expiration, the amount of his net exposure. In filc.t,ifthe original counterparry were willing to take the short position in the second (20-day)contract at the S992 price, a payment of the present value of the S2 (diseounted forthe 20 daY' until the settlement date) would be an equivalent transaction. The originalcounterparty would be wiDing to allow termination of the original contract for animmediate payment of that amount.

If the original counterparty requires a payment larger than the present value of 52to exit the contract, the short must weight this additional cost to exit the contractagainst the default risk he bears by entering into the offsetting contract with a differentcounterparry at a forward price of 5992.

LOS 58.c: Distinguish between a dealer and an end user of a forward contract.

CFA- Progmm Cu"irulum. ~lumt 6. pagt 64

The end user of a forward contract is typically a corporation, government unit, ornonprofit institution that has existing risk they wish to avoid by locking in the futureprice of an asset. A U.S. corporation that has an obligation to make a payment inEuros 60 days from now can eliminate its exchange rate risk by entering into a forward

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contract to purchase the required amount of Euros for a certain dollar-denominatedpayment with a settlement date 60 days in the future.

Dealers arc often banks, but can also be nonbank financial institutions such as securitiesbrokers. Ideally, dealers will balance their overall long positions with their overall shortpositions by entering forwud contracts with end users who have opposite existingrisk exposures. A dealer's quote desk will quote a buying price (at wbich they willassume a long position) and a .<lightlyhigher selling price (at which they will assumea short position). The bid/ask spread between the two is the dealer's compensationfor administrative com as well as bearing default risk and any asset price risk fromunbalanced (unhedgcd) positions. Dealers will also enter into contracts with otherdealers to hedge a net long or net short position.

LOS 58.d: Describe characteristics of equity forward contracts and forwardcontracts on uro-coupon and coupon bonds.

cr~"Program CUTTj",/um, Yo/uml 6, pagl 66

Equity forwW contracts where the underlying asset is a single stock, a portfolio ofstocks, or a stock index, work in much the same manner as other forward contracts. Aninvestor who wishes to sclllO,OOO shares of IBM stock 90 days from now and wishesto avoid the uncertainty about the stock price on that date, could do so by ulcing ashort position in a forward contract covering 10,000 IBM shares, (We will leave themotivation for this and the pricing of such a contract aside for now.)

A dealer might quote a price ofSIOO per share, agreeing to pay $1 million for the10,000 shares 90 days from now. The contract may be deliverable or seeded in cash asdesc.ribcd above. The stock seller bas locked in the selling price of the shares and willget no more if the price (in 90 days) is actually higher, and will get no less if the priceactually lower.

A portfolio manager wbo wishes to sell a portfolio of several stocks 60 days from nowcan similarly request a quote, giving the dealer the company names and the number ofshares of each stock in the portfolio. The only difference between this type of forwardcontract and several forward contracts each covering a single stock. is that the pricingwould be better (a higher total price) for the portfolio because overall administrationlorigination costs would be less for the portfolio forward contract.

A forward contract on a stock index is similar except that the contract will be based on anotional amount and will very likely be a cash-settlement contract.

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Eumple:: Equity ina fo...... d contne ..

A portfolio manager desirca to generate S10 million 100 days from now from aportfolio that is quite similar in composition to the S&P 100 index. She requests aquote on a short position in a 100-day forward contract based on the index with anotional amount of SI0 miUion and gelS a quote of S2S.2. If the index level at thesctdcmcnt date b S3S.7. calculate the amount the manager wiU payor receive to scalethe contracL

S3S.7 I S2S.2 - I .0.02 • 2%

Answer:

The actual index bel is 2% .b_ the contract price. or:

As the short party. the portfolio manager must pay 2% of the SIO million notionalamount, S200.000. to the long.

Alternatively. if the index were 1% below the contract level. the portfolio managerwould receive a payment from the long of S 100.000. which would approximately oRiClany decrease in the portfolio value.

Dividend. arc usually not included in equity forward contracts, as the uncertainty aboutdividend amounts and payment dates is small comparod to the uncertainty about futureequity prices. Since forward contracts arc custom instruments. the parties could spccifya total return value (including dividends) rather than simply the index value. This wouldeffectivcly remove dividend uncertainty as well.

Forward Contracts on Zero-Coupon a.nd Coupon Bonds

Forward contracts on short-term, zero·coupon bonds (T-bills in the United States) andcoupon interest-paying bonds arc quite similar to those on equities. However. whileequities do not havc a maturity date. bonds do. and the forward contract must settlebefore the bond matures.

As we noted earlier, T-bill prices arc often quoted as a percentage discount from facevalue. The percentage discount for T-bills is annualized so that a 90·day T-bill quoted ata ,,% discount will be:priced at a (90 I 360) )( ,,% • I % discount from face value. This isequivalent to a price quote of (l- 0.01) )( $1.000 5 5990 per 51.000 of face value.

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&ample: T-biU forwanb

A forwud contract am:ring a 510 million face value ofT-bills thaI will have 100 daysto maturity at eontna sc:tdement il priced at 1.96 on a discount yield basil. Computeme dollar amount the Ions mUll pay at sc:rdcmcnt for the T-bills.

0.0196 x (tOO I 360) • 0.0054+t is me actual discount.

The 1.96% annualized discount must be ·unannualizcd" based on me 100 days tomaturity.

The doDar serdcmcnt price is (t- 0.005444) x $10 million. 59.945.560.

Please: note that when marker intetat rates inCICISC.discouna incrcasc:. and T-bmprices fall. A long. who is obligated to purchase me bonds. will haye losses on theforward contract when inrctat rares risco and gainlon the contract when interest ratesfall. The outcomes for the shan will be opposite.

The price specified in forward contracts on coupon-bearing bonds is typically staled as ayield 10 maturity as of the settlement dale. exclusive of accrued interest. If the contractis on bonds with me possibility of default. there must be provisions in the contract todefine default and specify the obligations of the parties in me event of default. Specialprovisions must also be included if the bonds have embedded options such as callfeatures or conversion features. Forward conuacts can be constructed covering individualbonds or portfolios of bonds.

LOS 58.e: Describe characteristics of the Eurodollu time deposit market, anddefine UBOR and Euribor.

CF<A"PrDgram Cu"ie-ulum. Volume 6.pagt 70

Eurodollar deposit is me term for deposits in large banks outside the United Statesdenominated in U.S. dollars. The lending rate on doUar-denominated loans betweenbanks is ealled me London Interbank Offered Rate (UBOR). It is quoted as anannualiu:d rate based on a 360-<lay year. In ecnUasl to T-biU discount yields. UBOR isan add-on rate. like a yield quote on a short-term certificate of deposit. UBOR is usedas a reference rate for Aoating rate U.S. dollar-denominated loans worldwide.

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Study Session 17CrolS-Rtftrtnae 10 CFA Instirutt Assiped Rtadin, ,SS - Forwanl Marktu and Conlncts

Eumple: UBOR-hued loaDS

Compulr the amount thar muse be repaid on a SI million loan for 30 days if 3O-dayUBOR is quoted at 6%.

Answer:

The add-on inlrrcst is calculated as $) million" 0.06 " (30 / 360) • SS,ooo. Theborrower would repay SI,OOO,OOO+ SS,ooo • S1.00S,OOO at the end of 30 days.

UBOR is published daily by the British Banker's Auociation and is compiled fromquotes from a number of large banks; some arc large multinational banks based in othercounuies that have London offices.

There is also an equivalent Euro lending rate called Euribor, or Europe InterbankOffered Rate. Euribor, established in Frankfurt. is published by the European CcnualBank.

The Roating rates are for various periods and arc quoted as such. For example, theterminology is 30-ciay UBOR (or Euribor). 90-ciay UBOR. and ISO-day UBOR.depending on the term of the loan. For longer-term Roating-rate loans. the interest rateis reset periodically based on the then-current UBOR for the relevant period.

LOS 58.f: Describe forward rate agreements (FRAs) and calculate the gain/losson a FRA.

LOS 58.g: Calculate and interpret the payoff of a FRA and explain each of thecomponent terms of the payoff formula.

CFA'" ProgTllm Currinllum. Volumt 6. pflg. 71

A forward rate agreement (FRA) can be viewed as a forward contract to borrowllendmoney at a certain rate at some future date. In practice. these contracts settle in cash.but no actual loan is made at the settlement date. Thls means that the creditworthinessof the parties to the contract need not be considered in the forward interest rate, so anessentially riskless rate. such as UBOR. can be specified in the contract. (The parrles tothe contract may still be exposed to default risk on the amount owed at settlement.)

The long position in an FRA u the party that would borrow the money (long the loanwith the contract price being the interest rate on the loan). If the Roating rate at contractexpiration (UBOR or Euribor) is above the rate specified in the forward agreement. thelong position in the contract an be viewed as the right to borrow at below market ratesand the long will receive a payment. If the reference rate at the expiration date il belowthe contract rate. the short will receive a cash payment from the long. (The right to lendat rates high" rhfln market rates would have a positive value.)

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To calculate the cash payment at settlement for a forward rate agreement. we need tocalculate the value as of the settlement date of making a loan at a rate that is either aboveor below the market rate. Since the interest savings would come at the end of the loanperiod. the cash payment at settlement of the forward is the present value of the interestsavings. We need to calculate the discounted value at the settlement date of the interestsavings or excess interest at the end of the loan period. An example will illustrate thecalculation of the payment at expiration and some terminology of FRAs.

&ample: FRAs

Consider an FRA that:

• Expires/setdes in 30 days.• h based on a notional principal amount of $1 million.• h based on 9O-day UDOR.• Specifics a forward rate of S%.

Assume that the aaual 9O-day UDOR 30-days from now (at expiration) is 6%.Compute me cash setdement payment at expimion. and identify wbicb party makc:sthe payment.

Answer:

If me long could borrow at the contract rate of S.,.. rathct than the market rate of6%. the interest saved on a 90-day 5Imillion loan would be:

(0.06 - 0.OS)(90 / 360) " I miDion • 0.0025 " Imillion. 52.500

The 52.SOD in intctcst savings would not come until tbe e:nd of the 90·tlay loanperiod. The: value: at settlement is the: present value:of thnc savin". The correctdiscount rate to use is the actual rate: at setdement. 6%, not the:contract rate of 5%.

The payment at lcedcment from the short to the long i"

2,500 = 52 463.05r- [(0.06) x (90 1360») ,

In doing the calculation of the settlement payment. remember that the term of the FRAand the term of the underlying "loan" need not be the same and arc "tit interchangeable.While the settlement date can be any future date, in practice it is usually some multipleof 30 days. The speeific market rate on which we calculate the value of the contract wiDtypically be similar. 30·day. 60-day. 90·day. or I BO·day UDOR. If Wedescribe an FRAas a 60-day FRA on 90·tlay UBOl. settlement or expiration is 60 days from now andthe payment at settlement is based on 90-day UBOR 60 days from now. Such an FRAcould be quoted in (30·day) months. and would be described as a 2·by· 5 FRA (or 2 " 5FRA). The 2 refers to the number of months until contract expiration and the 5 refers tothe total time until the end of the interest rate period (2 ~ 3 : 5).

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The general formula for the payment to the long at settlement is:

(floating _ forwa.rd)( days)

(notional principal) I (d 3)60

1I + (floating) ays

360

where:days = number of days in the loan rerm

The numerator is the interest savings in percent, and the denominator is the discountfactor.

Note that if the floating rate underlying the agreement turns out to be below the forwardrate specified in the contract, the numerator in the formula is negative and the shortreceives a payment from the long.

FRAs for non-standard periods (e.g., a 45-day FRA on 132-day UBOR) arc termedoff-the-run FRAs.

LOS 58.h: Describe characteristics of currency forward contracts.

CFA'" Prt1grrzm CurriC'Ulum, Volum, 6. pagt 72

Under the terms of a CUrTencyforward contract, one party agrees to exchange a cerrainamount of one currency for a certain amount of another currency at a future date. Thistype of forward contract in practice will specify an exchange rate at which one partycan buy a fixed amount of the currency underlying the contract. If we need to exchange10 million Euros for U.s. doUars 60 days in the future, we might receive a quote ofUSDO.95. The forward contract specifies that we (the long) will purchase USD9.5miUion for EURIO miDion at settlement, Currency forward contracts can bc deliverableor sctded in cash. As with other forward contracts, the cash set dement amount is theamount necessary to compensate the party who would be disadvantaged by the actualchange in market rates as of the setdement date. An example wiD illustrate thi •.

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&ample: Currency forwanb

Gc:mco c:xpeCISro receive EURSO million thn:e months from now and enlers into acub lerdemcnt cum:ncy forward 10 exchange these wros for U.S. dollan at USD1.23per wro.lfthe marker c:xcbange rate is USD1.25 per ewo at settlement, what is theamount of the payment 10 be n:ccivcd or paid by Gemco!

AnswI:r:

Under lhe lerms of rhc conuacr Gemco would receive:

EURSO million x ~~ 1.23 • USD6J.5 million

Withoul the forward canlraa, Gemco would receive:

EURSO million IC USD 1.25. USD62.5 millionEUR

The eounlerpany would be disadvanragcd by Ihe difFc:n:nccbelWCCnthe contraCI rateand lhe marker rate in an amounl equal 10 the advanrage Ihal would have accrued 10Gcmco had thcy nOI entered inro the currency forward.

Gc:mco musl make. paymenl of USDJ.O million 10 the counlCrparry.

A diICa calculation of the value of lhe long (USD) position at scttIemenl is:

(USD1.23_ USD 1.2S)X EURSO milJjon= -USD1.0 millionEUR EUR

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KEy CONCEPTS

LOS 58.0A deliverable forward contract on an uset specifics that the long (the buyer) will paya certain amount at a futule date to the shon, who will deliver a cenain amount of anassn.

Default risk in • forward contract is the risk that the other pany to the contract will notperform at settlement, because typially no money changes hands at the initiation of thecontract.

LOS 58.bA forwud contract with ash settlement docs not require delivery of the underlyingasset, but a ash payment at the settlement date from one counterputy to the oth er,based on the contract price and the muket price of the asset at setdement.

Euly termination of a forward contract an be accomplished by ent cring into a newforward contract with the opposite position, at the then-current expected forward price.This early termination wiU fix the amount of the gain or loss at the setdement date.If this new forward is with a different counterparty than the original, there is creditor default risk to consider since one of the two counterputies may fail to honor itsobliguion under the forward contract.

LOS 58.cAn end user of a forward contract is most often a corporation hedging an existing risk.

Forward dealers, luge banks. or brokerages originate forward contracts and take thelong side in some contracts and the short side in others. with a spread in pricing tocompensate them for actual costs, bearing default risk, and any unhedged price risk theymustbeu.

LOS 58.dAn equity forwud contract may be on a single stock. a customized ponfolio, or anequity index, and is used to hedge the risk of equity prices at some future date.• Equity forward contracts an be written on a total return buis (including

dividcnds), but are typically based solely on an index value.• Index forwards senle in ash based on the notional amount and the percentage

difference between the index value in the forward contract and the actual index levelat settlement.

Forward contracts in which bonds are the underlying u.et may be quoted in terms ofthe discount on zcro-<:oupon bond. (e.g .•T·bill.) or in terms of the yield to maturityon coupon bonds. Forwards on corporate bonds must contain special provisions to dealwith the possibility of default u well .. with .ny call or conversion features. Forwardcontracts may also be written on portfolics of fixed income securities or on bond indexes.

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LOS 58.eEurodollar time deposits are USD-denominatcd short-term unsecured loans to largemoncy-center banks outside the United Slates.

The London Interbank Offered Rate (UBOR) is an international reference rate forEurodollar deposits and is quoted for 30-day, 60-day, 90-day, 180-day, or 360-day(I-year) terms.

Euribor is the equivalent for short-term Euro-denominated bank deposits (loans tobanks).

For both L1BOR and Euribor, rates arc expressed as annual rates and actual interest isbased on the loan term as a proportion of a 360-day year.

LOS 58.fForward rate agreements (FRAs) serve to hedge the uncertainty about short-term rates(e.g., 30- or 90-day L1BOR) that will prevail in the future. If rates rise, the long receivesa payment at settlement. The short receives a payment if the specified rate falls to a levelbelow the contract rate,

LOS 58.gThe payment to the long at settlement on an FRA is:

j<) days in loan term I. .. reference rate at se!dement - FRA rate 360

notional prindpal amount [d . I ]d ttl ays In Dan term1+ r erence rate at sc emen eX 360

The numerator is the difrerence between the rate on a loan for the specified period at theforward eonuact rate and the rate at settlement, and the denominator is to discount thisinterest differential back to the settlement date at the market rate at settlement.

LOS 58.hCurrency forward contracts specify that one party will deliver a certain amount of onecurrency at the sctdement date in exchange for a certain amount of another currency.

Under cash settlement, a single cash payment is made at settlement based on thedifrerence between the exchange rate fixed in the contract and the market exchange rateat the settlement date.

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CONCEPT CHECKERS

I. The short in a deliverable forward contract:A. has no default risk.B. is obligated to deliver the specified asset.C. makes a cash payment to the long at settlement.

2. On the settlement date of a forward contract:A. the shon may be required to sell the asset.B. the long must sell the asset or make a cuh payment.C. at least one parry must make a cash payment to the other.

3. Which of the following statements regarding early termination of a forwardcontract is mOlt aCCIITllti!

A. A party who enters into an offsetting contract to terminate has no risk.B. A party who terminates a forward contract early must make a cash payment.C. Early termination through an offsetting transaction with the original

counterparty eliminates default risk.

4. A dealer in the forward contract marker:A. cannot be a bank.B. may enter into a contract with another dealer.C. gets a small payment for each contract at initiation.

S. Which of the following statements regarding equity forward contracts is kasrIl(,(,u'"t~?A. Equity forwards may be settled in cash.B. Dividends arc never included in index forwards.C. A short position in an cq uity forward could not hedge the risk of a purchase

of that equity in the future.

6. Which of the following statements regarding forward contracts on 9D-day T-billsis most UC1lrllt~?A. The face value must be paid by the long at settlement.B. There is no default risk on these forwards because T-bills arc

government-backed.C. If short-rerm yields increase unexpectedly after contract initiation. the short

will pro6t on the contract.

7. A Eurodollar time deposit:A. is priced on a discount basis.B. may be issued by a Japanese bank.C. is a certificate of deposit denominated in Euros.

8. One difference between L1BOR and Euribor is that:A. L1BOR is for London deposits.B. they are for diffi:rent currencies.C. L1BOR is slightly higher due to default risk.

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9.

10.

11.

12.

13.

14.

Page 162

Which of the following statements regarding a UBDR-based FRA is mosta" .. ratt?A. The short will settle the contract by making a loan.B. FRAs can be based on interest rates for 30-. 60-. or 90-day periods.C. IfUBDR increases unexpectedly over the contract term. the long wiu be

required to make a cash payment at settlement,

Consider a S2 million FRA with a contract rate of5% on 60-day UBDR-If60-day UBDR is 6% at settlement. the long will:A. pay 53.333.B. receive S3.300.C. receive S3.333.

Party A has entered a currency forward contract to purchase €1 0 million at anexchange rate of 50.98 per euro, At settlement. the exchange rate is $0.97 peteuro. If the contract is settled in cash. Patty A will:A. make a payment of $1 00.000.B. receive a payment ofS100.000.C. receive a payment ofS103.090.

If the quoted discount yield on a 128-day. $1 million T-bill decreases from3.15% to 3.07%. how much has the holder of the T-bill gained or lost?A. Lost $284.B. Gained 5284.C. Gained S800.

90-day UBDR is quoted as 3.58%. How much interest ·...ould be owed atmaturity for a 90-day loan of S 1.5 million :u UBDR + 1.3%1A. SI7,612.B. SI8.300.C. S32,925.

A company treasurer needs to borrow 10 million euros for 180 days. 60 daysfrom now. The type of FRA and the position he should take to hedge theinterest rate risk of this transaction arc:

ERA EasiljocA. 2x6 ShortB. 2x8 LongC. 2x8 Short

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ANSWERS - CONCEPT CHECKERS

I. B The shert in a forward conuaCI is obligaled 10 deliver the speci6ed aJ£e1al the contractprice on the seulemenr dale. Either parlY may have defaull risk if rhere is any probabilitythaI lhe counlerparty may not perform under the lerms of the conrract,

2. A A forw:ard conuact may call for serdement in cash or for delivery of she asset, Under adeliverable ccntrace, the shorl is required 10deliver the asset al seltlemenl, nOI to make acash payment.

3. C Terminalin!: a forward cemract early by entering into an offsetting forward contraCtwith a different counterparlY exposes a party 10 default risk. If the offselting transactionis witb the original counterparty, default risk is eliminated. ~o cash payment is requiredif an offselting contract;' used for early rerminauon,

4. B Forwanl contracts deale" are commonly banks and large brokerage houses. Theyfrequendy ent .. into forward ocntracts wilh other deale" to offset long or sboltcxposun. No payment is rypically made a[ contract initiafion.

5. B Index forward conuaclS may be wrilten as tctal return conuacu, which includedividends. Contracu may be written to seule in cash, or to be deliverable. A {o"tposition is used 10 reduce the price risk of an expected fUlure purchase,

6. C When sheri-term rates increase, T-bill prices fall and the sbon position will pr06t.The price of a T-bill prior 10 malurilY is always less Iban ilS face value. The deliverablesecurity is a T-bill with 90 days to malurity. There is defaull risk on Ihe flrwa,tI. eventhough Ibe underlying a,sel is considered risk free.

7. B EurodoUar time deposiu are U.S. dollar-denominated accounu wilb banks outside IbeUnned Slales and a", quoted as an add-on yield rather than on a discoum basis.

8. B UBOR is for U.S. doUar-denominated accounu while Euribor is for euro-dencmlnatedsccounu, Neither is lccaricn-specific. Differences in these ralcs are due 10 Ibe differentcurrencies involved. nOI differences in default risk.

9. B A LlBOR-based contract can be based on lIBOR for various lerms. Tbey are settled incasb. Tbelong will receive a payment wben lIBOR is higber Iban the contraCI rare alseulernent.

10. B (0.06 - 0.05) x (60 1 360) x 52 million x 1 1(1 • 0.06/6) • 53.300.33.

II. A (SO.98 - SO.97) x 10 million. 5100.000 loss. The long. Puty A. is obligated 10 buyeuros al 50.98 wben they are only worth SO.97 and must pay 50.01 x 10 million.5100.000.

12. B The actUal discount has deer eased by:

128(0.0315-0.0307)x 360 ~ 0.0284% ofSI.ooo.OOO. or S284.

A decrease in the diseeum is an incr ease in value.

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13. 0 (0.0358. 0.013>(:0)t.5 miUion- $18,300.Doth LIBOR and any pn:miwn '0 UOOR

arc quoted as annualized ta,.s.

14. 0 This requires along posi,ion in a 2.8 FRA.

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The foUowing is a rnicw of the Derivatiwi principle. designed to address t.be laming outcome.tatemenu set fortb. by CFA INtitute. This topic i. allO covered in:

FUTURES MARKETS AND CONTRACTS

S,udy Sossion 17

EXA1II FocusCandidates should focus on the terminology of futures markets, how futures diJfer fromforwards. the mechanics of margin deposits. and the process of marking to market.Other important concepts here include limit price moves. delivery options. and thecharacteristics of the basic rypes of financial futures contracts. Learn the ways a futuresposition ean be terminated prior to contract expiration and understand how cashsettlement is accomplished by the final mark-to-market at contract expiration.

LOS 59.a: Describe the characteristics of futures contracts.

LOS 59.b: Compare futures contracts and forward contracts.

CFA'" Progrtlm Curriculum. Yolum, 6. pllg, 77

Futures contracts are very much like the forward contracts we learned about in theprevious topic review, They are simi"" in that both:

• Can be either deliverable or cash settlement contracts.• Are priced to have zero value at the time an investor enters into the contract.

Futures contracts diffir from forward contracts in the following ways:

• Futures contracts trade on organized exchanges. Forwards are private contracts anddo not trade.

• Futures contracts are highly standardized. Forwards are cwtomized contractssatisfying the needs of the parties involved.

• A single clearinghouse is the counterparty to all futures contracts. Forwards arecontracts with the originating counterparty.

• The government regulates futures markets. Forward contracts arc wually notregulated.

Cbaracteristics of Futures Contracts

Standard.iution. A major difference between forwards and futures is that futurescontracts have standardized contract terms. Futures conuacts specify the quality andquantity of goods that can be delivered. the delivery time. and the manner of delivery.The exchange also sets the minimum price fluctuation (which is called the tick siz.c:).For example. the basic price movement. or tick. for a 5.000·bwhel grain contract is aquarter of a point (1 point. 50.01) per bushel. or $12.50 per contract. Contracts alsohave a daily price limit. which sets the maximum price movement allowed in a singleday. For example, wheat cannot move more than $0.20 from its close the preceding day.

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The maximum price limits expand during periods of high volatility and an: not in efTc:ctduring the delivery month. The exchange also sets the trading times for each contract.

Itwould appear that these rules would restrict trading activity, but in fact, they stimulatetrading. Why? Standardization tells traders c:xacdywhat is being traded and theconditions of the transaction. Uniformity promom marl,., [iqui"ity.

The: purchaser of a futures contract is said to have gone long or taken a longpo,ition,while the: seller of a future. e:ontract is said to have gone: short or taken a short position.For each contract traded, there is a buyer and a seller. The long has contracted to buythe asset at the contract price at contract expiration, and the short has an obligation tosell at that price. Futures contracts arc used by ,p«ulaton to gain exposurc to changes inthe price of the asset underlying a futures contract. A h~ag~r, in contrast, will we futurescontracts to reduce exposure to price changes in the asset (hedge their asset price risk).An example is a wheat farmer who sells wheat futures to reduce: the uncertainty aboutthe price of wheat at harvest time.

Clearinghouse. Each exchange has a cuaringhou1l. The clearinghouse guarantees thattraders in the futures market will honor their obligations. The clearinghouse does thisby splitting each trade once it is made: and acting as the opposite: side of each position.The clearinghouse acts as the buyer to eY<:ryseller and the seller to cv<:rybuyer. By doingthi., the clearinghouse: allows either side of the trade to reverse positions at a future datewithout having to contact the other side of the initial trade. This allows traders to enterthe market knowing that they wiU be able to reverse their posit.ion. Traders arc also freedfrom having to worry about the counterparty defaulting since the counterparty is nowthe clearinghouse. In the history of U.S. futures trading, the clearinghouse has neverdefaulted on a trade.

Proftnor~ Now The ttrmino[oD is that you ·bought" bona forurn ifyoumttr~a into th~ (ontract with th~ tong po,ition. In my t"1'trimu, thisttrmin%D has (au1l" confusion for many canaidattJ. YDutiDn'tpureha1l th~cantrec«, you enter into it. YDua" contracting to buy an asstt on th~ "'ng sitk.·Bu," meen: tak~ th~ long sitk, ana ·1I1l" means talt~ th~ short sid~ in fotum.

LOS 59.c: Distinguish between margin in the securities markets and marginin the futures markets. and explain the role of initial margin. maintenancemargin. variation margin. and settlement in futures trading,

cr~"Program Curriculum, Volum~ 6, pag~ 82

In securities markets, margin on a stock or bond purchase is a percentage of the marketvalue of the asset. Initially, 50% of the steek purchase amount may be: borrowed, andthe remaining amount, the equity in the account, must be paid in cash. There is interestcharged on the borrowed amount, the margin loan. The margin percentage, the percentof the security value that is owned, will vary over time and must be maintained at someminimum percentage of market value.

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Study Seuion 17Cross.Rd".r.nce to CFA hutitulC Assigntd Rndl", '59 - Futurt. Markou aAd Contncu

In the futures markets. margin is a performance guarantee. It is money deposited byboth the long and the shon. There is no loan involved and. conscquendy. no interestcharges.

Each futures exchange has a clearinghouse. To safoguard the clearinghouse. the exchangerequires traders to post margin and sonic thoir accounts on a daily basis. Before trading.the trader must deposit funds (called margin) with a broker (who. in tum. will postmargin with tho clearinghouse).

In securities markets, tho cash deposited is paid to the seller of tho security. with thobalance of tho purchase price provided by tho broker. This is why tho unpaid balance is aloan. with interest charged to the buyer who purchased on margin.

Initial margin is the money that must be deposited in a futures account before anytrading takes place. It is set for each type of underlying asset. Initial margin per contractis relatlvely low and equals about one day's maximum price fluctuation on tho total valueof the contract's underlying asset.

Maiotenance margin is the amount of margin that must be maintained in a futuresaccount. If the margin balance in tho account falls bdow the maintenance margin dueto a change in the contract price for the underlying asset. additional funds must bedeposited to bring the margin balance back up to the initilll margin requirement,

This is in contrast to equity account margins. which require investors only to bring themargin percentage up to the maintenance margin. not back to the initial margin level.

Variatioo margin is the funds that must be deposited into the account to bring it backto the initial margin amount. If account margin exceeds the initial margin requirement,funds can be withdrawn or used as initial margin for additional positions.

The settlement price is analogous to the closing price for a stock but is not simply theprice of the last trade. It is an average of the prices of the trades during the last periodof trading. called the closing period. which is set by the exchange. This feature of thesettlement price provents manipulation by traders. The settlement price is used to makemargin calculations at the end of each trading day.

Initial and minimum margins in securities accounts arc set by the Federal Reserve.although brokerage houses can require more. Initial and maintenance margins in thefutures market are set by the clearinghouse and arc based on historical daily pricevolatility of the underlying asset since margin i. reseeded daily in futures accounts.Margin in future. accounts is typically milch IIJUHT as a percentage of the value of theassets covered by the futures contract. This means that the loverage. based on the actualcash required. is much higher for futures accounts.

How a Futures Trade Takes Place

In contrast to forward contracts in which a bank or brokerage is usually the counterpartyto the contract. there is a buyer and a seller on each side of a futures trade. The futut<Sexchange selects the contracts that will trade. The asset. the amount of the asset. and the

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settlement/delivery date are standardized in this manner (e.g., a June futures contract on90-day T-bills with a face amount of S1 million). Each time ehere is a trade, the deliveryprice for that contract is the equilibrium priee at that point in tim", which depends onsupply (by those wishing to be short) and demand (by those wishing to be long).

The mechanism by which supply and demand determine this equilibrium is open outcryat a particular location on the exchange Roor called a pir. Each trade is reported to theexchange so that the equilibrium price, at any point in tim", is known to all traders.

LOS 59.d: Describe price limits and the process of marking to market, andcalculate and interpret the margin balance, given the previous day's balance andthe change in the futures price.

Many futur"s contracts have price limiu, which are exchange-imposed Iimirs on howmuch the contract price can change from the previous day's settlement price. Exchangemembers arc prohibited from executing trades at prices outside these lim irs. If the(equilibrium) price at which traders would willingly trade is above the upp"r limit orbdow the lower limit, trades cannot rake place.

Consider a futures contract that has daily price limits of rwo cents and settled theprevious day at $1.04. If, on the following trading day, traders wish to trade at $1.07because of changes in mark", conditions or expectations, no trades will take place. Thesettlement price will be reported as $1.06 (for the purposes of marking-to-marker). Thecontract will be said to have made a limit move, and the price is said to be limit up(from the previous day). If market conditions had changed such that the price at whichtraders arc willing to trade is below $1.02, $1.02 will be the setdement priec, and theprice is said to be limit down. If trades cannot take place because of a limit move. eitherup or down, the price is said to be locked limit sinee no trades can take place and tradersarc locked into their existing positions.

Marking-tn-market is the process of adjusting the margin balance in a futures accounteach day for the change in the value of the contract assees from the previous trading day,based on the new settlement price,

The futures exchanges can require a mark-to-market more frequently (than daily) underextraordinary circumstances.

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Computing the Margin Balance

Eumple: MarJin balance

Consider a long position of 6~ July wheal CORlnas. each of which coven 5.000bushels. Assume chal me conuacl price is 52.00 and mal each conlracl requires aninitial margin deposit ofS150 and a mainlenance margin of S100. The lOW inidalmargin required for me 5-conlracl uade is S750. The mainICnana: margin for Iheacx:ounl is 5500. Compute chc margin balance for chis posidon after a 2o<ent decreasein price on Day 1. a l-eene incrcase: in price on Day 2. and a l-cenl dec~e in priceon Day 3.

Each conuacI is for 5.000 bushels so chal a price change of SO.OI per bushel changesme conuacr value by 550. or 5250 for me 6~ conrraca: (0.01)(5)(5.000) • S25O.oo.

The following 6gu~ U1usuares chc change in me margin halana: u me price ofmis contract changes each day. Nore chat me initial balana: is me initial marginrequi~enr of 5750 and mal me required deposir is bued on me previous day's pricechange.

Margin Balancca

d., Rlf-irM o.,.i, PrinlB"w1 o.ilJ ClMn,. GttinilMs BttIn«

o (Purdwc) 5750 52.00 0 0 5750

0 $1.98 -$0.02 -S500 5250

2 5500 $I.?? +50.01 +5250 $1.000

3 0 $1.98 -$0.01 -S250 5750

Ar me dose on Day 1. me margin balance bas gone below me minimum ormainrenana: margin level of 5500. Therefore. a deposit of 5500 is required ro bringme margin back 10 me initial margin levd of $750. We can inrerpm Ihe marginbalance at any poinr u me amount me inYalOr would rcallze ifme position wereclosed our by a reversing uade at me mosr recenr scrdernent price used 10 calculareme margin balance.

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LOS 59.e: Describe how a futures contract can be terminated at or prior toexpiration.

cr:A" Program Cu"i(llium. Volumt 6.pagt 88

TheI'C arc four ways to terminate a futures contract:

1. A short can terminate the contract by delivering the goods, and a long can terminatethe contract by aceepting delivery and paying the contract price to the shorr. This iscalled delivery. The location for delivery (for physical assets), terms of delivery, anddetails of exacdy what is to be delivered arc all specified in the contract. Deliveriesrepresent less than 1% of all contract terminations.

2. In a cash-settlement contract, delivery is not an option. The futures account ismarked-to-market based on the setdement price on the last day of trading.

3. You may make a reverse, or offsetting, trade in the futures market. This is similar tothe way we described cxiting a forwud contract prior to expiration. With futures,however. the other side of your position is held by the cleuinghousc-if you makean exact opposite trade (maturiry, quantiry, and good) to your current position, theclearinghouse will net your positions out, leaving you with a zero balance. This ishow most futures positions arc sertled. The contract price can difl'cr between therwo contracts. If you inirially arc long one contract at $370 per ounce of gold andsubsequendy sell (rake the shorr position in) an identical gold contract when theprice is S35010L, $20 times the number of ounces of gold speci6ed in the contractwill be deducted from the margin deposit{s) in your account. The sale of rhe fururescontract ends the exposure to future price 8uctuations on the first contract. Yourposition has been Ttl/trwi, or closed out, by a rlosing trade.

4. A position may a1,0 be settled through an exchange for physicals. Here, you finda trader with an opposite position to your own and deliver the goods and settle upberween yourselves. off thc 800r of the exchange (called an ex-pit transaction). Thisis the sale exception to the fcderallaw that requires that all trades take place onthe 800r of the exchange. You must then contact the clearinghouse and tell rhemwhat happened. An exchange for physicals differs from a delivery in that the tradersactually exchange the goods, the contract is not closed on the 800r of the exchange,and rhe two traders privately negotiate the terms of the transaction. Regular deliveryinvolves only one rrader and the clearinghouse.

Delivery Options in Futures Contracts

Some futures contracts grant delivery options to the short, oprions on whar, where. andwhen to deliver. Some Treasury bond contracts give the shorr a choice of several bondsthat are acceptable to deliver and options as to when to deliver during the expirationmonth. Physical assets, such as gold or corn, may offer a choice: of delivery locations torhe shorr. These options can be of significant value to the holder of the shorr position ina futures contract.

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LOS 59.f: Describe characteristics of the following types of futures contracts:Treasury bill, Eurodollar, Treasury bond, stock index, and currency.

CFA'" Progrttm Curriculum. Yolumt 6. pllgt 92

Let's introduce 6nancial futures by 6rn examining the mechanics of a T·biJI futurescontract. Treasury bill futures cont.racu arc based on a $1 million face value 90·day(13·wcek) T-biU and settle in cash. The price quotes arc 100 minus the annualizeddiscount in percent on the T-biUs.

A price quote of98.52 represents an annualized discount of 1.48%. an actual discountfrom face of 0.0148 x (90 I 360) • 0.0037. and a delivery price of (1 - 0.003nx I million = $996.300.

T-bill futures contracts are not as important as they once were. Their prices arc heavilyin8uenced by U.S. Federal Reserve operations and overall monetary policy. T-biUfutures have lost importance in favor of Eurodollar futures contracts. which representa more free-market and more global measure of short-term interest rates to top qualiryborrowers for U.S. dollar-denominated loans.

Eurodollar futures arc based on 90-day LIBOR. which is an add-on yield. rather than adiscount yield. By convention, however. the price quotes follow the same convention asT-bills and arc calculated as (100 - annualized UBOR in percent). These contracts sertlein cash. and the minimum price change is one tidl, which is a price change of 0.0001 =0.01 %, representing $25 per $1 million contract. A quote of97.60 corresponds to anannualized LIBOR of (100 - 97.6) = 2.4% and an effective 90-day yield of2.4/4 =0.6%.

P'0foSJo,'sNow Eu",Jol/4, fotUrtfll,t p,ietJ such thllt tht long position glliNVIIlut whtn interest '1I1tl ucrtast. This is JijfiTtnt from foTWllrtI ret« 1I1'ttmtntsIInJ interest ret« clllioptions. whtTt tht long position glliN whtn interet» reminereet«.o ant of tht first things II ntw T-biUfotUTtS tTau, leern: is thllt tllch chllngt inp,iet ofO. Olin tht p,iet of II T-bill fotuTtS conlTllct is worth $25. 1/you toolt IIlong position lit 98.52 IInti tb« prier foil to 98.50. JOU' lOll is $50 pt, contrsc«,Beceus« Eu,otltzl/4, contrllcts on 90-tltzy UBOR IITt th. sem« sizt IInti p,ietJ inIIsimi[a, foshion. IIp,iet chllngt of 0.01 repretent« II $25 chllngt in valut fo'tbtSt liS wtlL

Treasury bond futures contracts:

• Are traded for Treasury bonds with maturities greater than IS years.• Arc a deliverable contract.• Have a facc value of S I00.000.• Arc quoted as a percent and fractions of I% (measured in 1/32nds) of face value.

The short in a Treasury bond futures contract has the option to deliver any of severalbonds that will satisfy the delivery terms of the contract. This is called a delivery optionand is valuable to the short because at expiration. one particular Treasury bond will bethe cheapest-to-deliver bond.

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Study SHaon 17Cro, s-~ft~Dceto CFA lrutitute Assiptd ~ading '59 - Futures MarktU aruI ContraCtS

Each bond is given a crJnlltniDn fono" which is used to adjust the long's paymentat delivery so that the more valuable bonds receive a higher payment. These factorsarc multipliers for the futures price at settlement. The long pays the futures price atexpiration times the conversion factor.

Stock index futures. The most popular stock index future is the S&P 500 Index Futurethat trades in Chicago. Settlement is in cash and is based on a multiplier of250.

The value of a contract is 250 times the level of the index stated in the contract ..Withan index level of 1,000, the value of each contract is S250,OOO. Each index point in thefutures price represents a gain or loss of S250 per contract. A long stock index futuresposition on S&P 500 index futures at 1,051 would show a gain of SI,750 in the trader'saccount if the index were 1,058 at the settlement date (5250 x 7. $1,750). A smallercontract is traded on the same index and has a multiplier of 50.

Futures contracts covering several other popular indices arc traded, and the pricingand contract valuation arc the same, although the multiplier can vary from contract tocontract.

Currency futures. The currency futures market is smaller in volume than the forwardcurrency market ...'" described in the previous topic review. In the United States,currency contracts trade on the euro (EUR), Mexican peso (MXP), and yen UPy),among others. Contracts arc set in units of the foreign currency, and the price is statedin USD/unit. The size of the peso contract is MXP500,Ooo, and the euro contract ison EURI25,OOO. A change in the price of the currency unit ofUSDO.OOOl translatesinto a gain or loss ofUSD50 on a MXP500,OOO unit contract and USD12.50 on aEUR125,OOO unit contract.

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KEy CONCEPTSI

LOS 59.aLike forward contracts, futures contracts are most commonly for delivery ofcommodities and financial assets at a future date and can require delivery or settlementin cash,

LOS 59.bCompared to forward contracts, futures contracts:• Ate more liquid, trade on exchanges, and can be closed OUtby an offsetting trade.• Do not have counterpany risk; the clearinghouse acts as counterparry to each side of

the contract.• Have lower transactions costs.• Require margin deposits and arc marked to market daily.• Are srandardized contracts as to asset quantity, quality, settlement dates, and delivery

requirements.

LOS 59.eFutures margin deposits arc not loans, but deposits to ensure performance under theterms of the contract.

Initial margin is the deposit required to initiate a futures position.

Maintenance margin is the minimum margin amount. When margin falls below thisamount, it must be brought back up to its initial level by depositing variation margin.

Margin calculations are based on the daily settlement price, the average of the prices fortrades during a closing period set by the exchange.

LOS 59.dTrades cannot take place at prices that differ from the previous day's settlement prices bymore than the price limit and arc said to be limit down (up) when the new equilibriumprice is below (above) the minimum (maximum) price for the day.

Marking-to-market is the process of adding gain. to or subtracting losses from themargin account daily, based on the change in settlement prices from one day to the next.

The mark-to-market adjustment either adds the day's gains in contract value to thelong'. margin balance and subtracts them from the short's margin balance, or subtractsthe day's loss in contract value from the long's margin balance and adds them to theshort's margin balance.

LOS 59.cA futures position can be terminated in the following ways:• An offsetting trade, entering into an opposite position in the same contract,• Cash payment at expiration (cash-settlement contract).• Delivery of the asset specified in the contract.• An exchange for physicals (asset delivery off the exchange).

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LOS 59.fEurodoUar furures contracts are for a face value ofSl,OOO,OOO, arc quoted as JOOminusannualized 90·day L1BOR in percent, and settle in cash.

Treasury bond contracts arc for a face value of $100,000, give the short a choice ofbonds to deliver, and use conversion factors to adjust the contract price for the bondthat is delivered.

Stock index futures have a multiplier that is multiplied by the index to calculate thecontract value, and setde in cash.

Currency futures arc for delivery of standardized amounts of foreign currency.

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Study Session 17Crou-Rd"trmce to CFA InstitulC Assigned RndiDg '59 - Future. Markets and Contna.

CONCEPT CHECKERS

1. Which of the following statements about futures markets is klZJt accuftlu?A. Hedgers trade to reduce some preexisting risk exposure.B. The dcaringhowe guarantees that traders in the futures market will honor

their obligations.C. If an account rises to or exceeds the maintenance margin, the trader mwt

deposit variation margin.

2. The daily process of adjusting the margin in a futures account is called:A. variation margin.B. marking-to-market.C. maintenance margin.

3. A trader buys (takes a long position in) a Eurodollar futures contract (SI millionface value) at 98.1-4 and closes it out at a price of 98.27. On this contract, thetrader has:A. lost 5325.B. gained S325.C. gained S1,300.

-4. In the futures market, a contract docs not trade for two days because trades arcnot permitted at the equilibrium price. The market for this contract is:A. limit up.B. limit down.C. locked limit.

5. The existence of a delivery option with respeet to Treasury bond futures meansthat the:A. short can choose which bond to deliver.B. short has the option to settle in cash or by delivery.C. long chooses which of a number of bonds will be delivered.

6. Assume the holder of a long futures position negotiates privately with the holderof a short futures position to accept delivery to dose out both the long andshort positions. Which of the following statements about the transaction is mostaccurau? The transaction is:A. also known as delivery.B. also known as an exchange for physicals.C. the most common way to close a futures position.

7. A conversion factor in a Treasury bond contract is:A. wed to adjust the number of bonds to be delivered.B. multiplied by the face value to determine the delivery price.C. multiplied by the futures price to determine the delivery price.

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Page 176

8. Three 125,000 euro futures contracts are sold at a price of $1.0234. The nextday the price senles at $1.0180. The mark-to-market for this account changesthe previous day's margin bY'A. +$675.B. -$675.C. +$2,025.

9. In the futures marker, the clearinghouse is leesr liluly to:A. decide which contracts will trade.B. set initial and maintenance margins.C. act as the counterparty to every trade.

10. Funds deposited to meet a margin call arc termed:A. daily margin.B. settlement costs.C. variation margin.

11. Compared to forward contracts, future. contracts arc Ull" lilttly to be:A. standardized.B. larger in size.C. less subject to default risk.

02013 Kaplan. Inc.

Study Session 17Cross.Rd'erOJ>Ceto CFA InstitulC Assigned !lndiog '59 - Futures Marktu aDd Contracts

ANSWERS - CONCEPT CHECKERS

I. C If an account rises 10 or exceeds the mainlenan~ margin. no payment needs to be made.and [h. trad., has [h. opricn [0 remove the .'~SI funds from the account. Only if anaccount falls below the maintenance margin does variallon margin need 10 be paid tobring the level of [he account back up [0 the level of the inilial margin.

2. B The pTOttll is called rnarking-te-market, Varialion margin is the funds thaI must bedeposired when marking·[o-market draws the margin balance below the maintenancemargin.

3. B The price is quoted as 100 minus the annuali.ed discount in percent. Remember thatthe gains and losses on T-bill and Eurodollar fUlures are 525 per basis point of [he pricequote. The price is up U licks. and U• 525 is a gain of 5325 for along posillon.

4. C This describes the situation when the equilibrium price is either above or below [heprior days seule price by more [han the permitted (limil) daily prlee move. We do nOlknow whtmtr it is limit up or limit down.

5. A The shot[ has Ihe option 10 deliver any of a number of perrnined bonds. The deliveryprice iI adjusted by a conversion factor thar is calculated for each permiued bond.

6. B When ehe holder of a long pesition negotiates directly wirh the holder of the shot[position 10 accepl d.liv.ry of the undctlying commodity 10 close OUtboth pesition s, thisis called an ,xth.nt' forph"lt.u. (Thil is a private tratuaaion lhal occurs ,x-pi, and isone excepticn 10 the federal law lhal all trades take place on rhe exchange floor.) Notethat the exchange for physicals differs from an offse[[ing trade in which no delivery takesplace and also diff.,. from delivery in which the commodity is simply delivered as aresulr of the fUlures expiration with no secondaty agreemenl. MoSt fulures posilions aresettled by an .ffimint ,""',.

7. C It adjusu the delivory price based on tho fulurts price at contract oxpiralion.

8. C (1.0234 - 1.0180) • 125.000 • 3 • 52.025. The contractS wore sold and tho pricedeclined, so tho adjuSlmonl is an addition 10 the account margin.

9. A The exchango derermines which contracu will trade.

10. C When insufficienl funds exist tc satisfy margin requirements, a variation margin musl beposred.

II. B Siu is not one of ehe things Ih.. distinguilhes forwards and futures. although thecontraa .iu of fulure. is lIandardi.ed. whereas forwards are cusrcmhed for each parlY.

02013 Kaplan. Inc.

Thc (011~;ng is • rnicw of thc Dcrivatiw. ptincjplc.l dCI'ped to addrul the Icaraing outcomcIcalement •• ct fonh by CfA 1"lacute. Thil tOpic:il allO coveted in:

OPTION MARKETS AND CONTRACTS

Study ~ .. ion 17

ExAM FocusThis derivatives review introduces options. describes their terms and trading. and providesderivations of several options valuation raul ts. Candidates should spend some timeunderstanding how me payoffs on several types of options arc determined. This includesoptions on stocks. bonds, stock indices. interest rates. currencies. and futures. The assignedmaterial on establishing upper and lower bounds is extensive. so it should not be ignored.Candidates must learn at least one of me put-call patity relations and how to construct anarbitrage strategy. The notation. formulas. and relations may seem daunting, but if youput in me time to understand what me notation is saying (and why). you can master theimportant points.

LOS 60.a: Describe call and put options.

CFA'" Program Cu"iru/um. Vo/umt 6; patt JOB

An option eentraet gives its owner the right, but not the legal obligation. to conduct atransaction involving an underlying asset at a predetermined future date (me exercisedate) and at a predetermined price (the exercise price or strike price). Options give meoption buyer me right to decide whether or not me uade will c:v<:ntuallytake place. Theseller of the option has me obligation to perform if me buyer exercises the option.

• The owner of a call option has me right to purchase me underlying asset at a specific:price for a specified time period.

• The owner of a put option has me right to sdl the underlying asset at a specific pricefor a specified time period.

For every owner of an option. there must be a seller. The seller of the option is alsocalled me option writer. There arc four possible options positions:

1. Long call: me buyer of a call option-has the right to buy an underlying asset.

2. Short call: me writer (sdkr) of a call option-has me obligation to sell the underlyingasset.

3. Long put: me buyer of a PUt option-has me right to sell the underlying asset.

4. Short put: the writer (seller) of a put option-has the obligation to buy the underlyingasSC:L

To acquire these rights, owners of options must buy them by paying a price called meoption premium to me seller of the option.

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Listed stock option contracts trade on exchanges and arc normally for 100 shares ofstock. After issuance. stock option contracu arc adjustc:d for stock splits but not cashdividends.

To sec how an option contract works, consider the stock of ABC Company. It sells forSSS and has a call option available on it that sells for a premium ofSIO. This call optionhas an exercise price of $50 and has an expiration date in five months.

Profmori No"_' The oprion p"mium is limply rh. pri" of th. option. PI", se aonot confou thil with th e exerei .. pri" of th. option. which is th. pri" at whichth. una"lying alut will b. bought/10M if th. option is rxerci... ".

If the ABC call option is purchased for $10, the buyer can purchase ABC stock fromthe option seller over the next five months for S50. The seller, or writer. of the optiongets to keep the $10 premium no matter what the stock does during this time period.If the option buyer exercises the option. the seller will receive the $50 strike price andmust deliver to the buyer a share of ABC stock. If the price of ABC stock falls to 550 orbelow, the buyer is not obligated to exercise the option. Note that option holders willonly exercise their right to act if it is profitable to do so. The option writer. however, hasan obligation to act at the request of the option holder.

A put option on ABC stock is the same as a call option, except the buyer of the put(long position) has the right to sell a share of ABC for 550 at any time during the nextfive months. The put "Titer (short position) has the obligation to buy ABC stock at theexercise priee in the event that the option is exercised.

The owner of the option is the one who decides whether or not to exercise the option.If the option has value, the buyer may either exercise the option or sell the option toanother buyer in the secondary options market.

LOS 60.b: Distinguish between European and American options.

American options may be exercised at any time up to and including the contract'sexpiration date.

European options can be exercised only on the contract's expiration date.

~ Profmori Not«: Tb« nam« of tM option JoN not imply wh." tM optioll rraatl-~ th~ a" jUlr nema,

At expiration. an American option and a European option on the same asset with thesame mike price arc identical. They may either be exercised or allowed to expire. Beforeexpiration, however. they are different and may have different values, so you mustdistinguish between the two.

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Study S... ion 17Cro.. -~ft~Dceto CFA Institute Ani&ntd Ruding ,GO - Option Mwu and Conuaas

If two options arc identical (maturity. underlying stock. strike price. cre.) in all ways.except that one is a European option and the other is an American option. the value ofthe American option will equal or exceed the value of the European oprion. Why? Theearly exercise feature of the American option gives it more flexibility. so it should beworth at least as much and possibly more.

LOS 60_c: Define the concept of moneyness of an option.

CFA'" Progmm Curriculum. VIIlumt 6. Pillt J J J

Moneyness refers to whether an option is in tM mont] or out of tht mont]. If immediateexercise of the option would 8"nerate a positive payoff, it is in the money, If immediateexercise would result in a loss (negative payoff). it is out of the money. When the currentasset price equals the exercise price. exercise will generate neither a gain nor loss, and theoption is lit tht monry.

The following describe the conditions for a call option to be in. out of. or at the money.

o In-th .. mont] cilIIoptiom. If S - X > O. a call option is in the money. S - X is theamount of the payoff a call holder would receive from immediate exercise. buying ashare for X and selling it in the market for a greater price S.

o Out-<lftht-mont] '''// options. If S - X < O. a call option is out of the money.o At-tht-mont] ,,,II optiom. If S = X. a call option is said to be at the money.

The following describe the conditions for a put option to be in. out of. or at the money.

o In-tht-mont] put DptiDm. If X - s > O. a put option is in the money. X - S is theamount of the payoff from immediate exercise, buying a share for S and exercisingthe put to receive X for the share.

o Out-oftht-mont] put options. When the stock's price is greater than the strike price,a put option is said to be out of the money. If X - S < 0, a put option is out of themoney.

o At-tht-mont] put options. If S • X. a put option is said to be at the money.

&ample:: MCNlC)'RCII

Consider a July 40 call and a July 40 put, both on a stock that is currmdy sdling for537/shate. Calcularc: how much these options arc in or out of the money.

~ Proftsso,~ No": A '"" 40 ("II " " ("II tlpti." with "" ""re",priu 1I{$40 ""tI~ "" 'xpil'tltilln tItIl4 in ,tJ,.

Amwcr:

The call is 53 OUtof the money because S - X • -53.00_ The put is 53 in the moneybecause X - S • 53.00.

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Study Seuion 17Cross-Rtre~nct to CFA Institute Assigned RtadiAg ,GO - Option Marktu aAd Contracts

LOS 60_d: Compare exchange-traded options and over-the-counter options.

CPA" Program CIU,;(Ulum. Volume 6. pflg~ 112

Exchange-traded or lilted options arc regulated. standardized. liquid. and backed by theOptions Clearing Corporation for Chicago Board Options Exchange transactions. Mostexchange-listed options have: expiration dates within two to four months of the currentdate. Exchanges also list long-term equity anticipatory securities (LEAPS). which areequity options with expiration dates longer than one year.

Over-the-counter (OTC) options on stocks for the retail trade all but disappeared withthe growth of the organized exchanges in me 1970s. There is now. however. an activemarket in OTC options on currencies. swaps. and equities. primarily for institutionalbuyers. Like the forward market. the OTC options market is largely unregulated.consists of custom options. involves counterparty risk. and is faeilitated by dealers inmuch the same way forwards markets are.

LOS 60.10:Identify the types of options in terms of the underlying instruments.

CPA" Program Curri(Ulum. Volume 6. pag~ 116

The three types of options we consider are (1) financial options. (2) options on futures.and (3) commodity options.

Fina.ncial options include equity options and other options based on stock indices.Treasury bonds. interest rates. and currencies. The strike price for financial options canbe in terms of yield-to-maturity on bonds. an index level, or an exchange rate for fo"il"(11'""9 options_ UBOR-based inttrtsr M" options have payoffs based on the differencebetween UBOR at expiration and the strike rate in the option.

Bond options are most often based on Treasury bonds because of their active trading.There are relatively f<:VIlisted options on bonds-most are over-the-counter options.Bond options can be deliverable or settle in cash. The mechanics of bond options arelike those of equity options. but are based on bond prices and a specific face value of thebond. The buyer of a call option on a bond will gain if interest rates fall and bond pricesrise. A put buyer will gain when rates rise and bond prices fall.

[ndne options settle in cash. nothing is delivered. and the payoff is made directly to theoption holder's account. The payoff on an index call (long) is the amount (if any) bywhich the index level at expiration exceeds the index level spccilied in the option (themike price). multiplied by the (ontrtUf muhipli~'. An equal amount will be deductedfrom the account of the index caU option writer.

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Study Snsion 17Cross-lUfe~Dceto CFA lrutitute Assigned Reading ,GO - Option Mwu and ContncU

&ample: Inda optioa.

Assume thu you own a call option on th~ SeeP SOO Index with an exercise:price equalto 9S0. The multiplier for this conuact is2S0. Compute the payoff on this optionassuming lhallh~ inda is962 al expiration.

Answer:

This is a call,.o the expiration da~ payoff is (962 - 9S0) x S2S0 • 53,000.

Options on fulul'C$, sometimes called futures options, give the holder the right to buyor sell a specified fulures contract on or before a given date at a given futures price, thestrike price.

o Call options on futures contracts give the holder the right to enter into the long sideof a fulures contract at a given futures price. Assume that you hold a caU optionon a bond future at 98 (percent of face) and at expiration the futures price on thebond contract is 99. By exercising the call, you take on a long position in the futurescontract, and the account is immediately marked to market based on the setdementprice. Your account would be credited with cash in an amount equal to 1% (99 - 98)of the face value of thc bonds covered by the contract. The seller of the exercised callwill take on the short position in the futures contract. and the mark-to-market valueof this position will generate the cash deposited to YOUt account.

o Put options on futures conuacu give the holder the option to take on a short futuresposition at a futures price equal to the mike price. The writer has the obligation totake on the opposite (long) position if the option is exercised.

Commodity options give the holder the right to either buy or sell a fixed quantity ofsome physical asset at a fixed (mike) price.

Some capital in,'Csunent projects have provisions that give the company flexibility toadjust the project's cash flows while it is in progrcss (for example. an option to abandonthe project before completion). Such rcal options have value that should be consideredwhen evaluating a project's NPY.

~ Proftssor's Note: Evaluatinl projats with rtaloptiDns is (ow"d in tht Study~ Seuion on (orporart jinan<t at ulltl II.

LOS 60.f: Compare interesl rate options with forward rate agreements (FRAs).

CFA'" Pror;rllmCu"i(uu.m. Volumt 6. palt J J 8

Inlel'C$t rate options are similar to the stock options except that the exercise price is aninterest rate and the underlying asset i. a reference rate such as UBOR. Interest rateoptions are also similar to FRAs because there is no deliverable asset. Instead they arcsettled in cash, in an amount that is based on a notional amount and the spread betweenthe strike rate and the reference rsre, Most interest rate options are European options.

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To see how interest rate options work, consider a long position in a l-year UBOR·bas<dinterest rate call option with a notional amount of $1,000,000 and a mike rate of 5%.For our example, let's assume thai this opncn is costless for simplicity. If at expiration,UBOR is great<f than 5%, tho option can be exercised and tho owner will receive51,000.000 x (UBOR- 5%).lfUBOR i.I<55 than 5%, the eprlon expires worthlessand the owner receives nothing.

Now, let's consider a shott position in a UBOR·based interest rate put option withthe same features as the call that we just discussed. Again, the option i. assumed to becostless, with a strike rate of 5% and notional amount of 5 1.000,000. If at expiration,UBOR f.tIls below 5%. the option writer (short) must pay the put holder an amountequal to $1,000,000 x (5% - UBOR). If at expiration, UBOR is greater than 5%, theoption expires worthless and the put writer makes no payments. If the rate is for lessthan one year, the payoff' is adjusted. For example, if the reference rate for the option is60.day UBOR.lhe payoff' would be $1,000,000 x (5% - UBOR)(60/360) because thoactual UBOR rate and the mike rate arc annualized rates.

Notice the one-sided payoff' on rh ese interest rate options. The long call receives a payoff'when UBOR exceeds the mike rate and receives nothing if UBOR is below tho strikerate. On the other hand. the shot! PUI position makes payments ifLiBOR is below thestrike rate, and makes no paymenls when UBOR exceeds the strike rate,

The combination of the long interest tale call option plus a shot! interest rate PUI optionhas the same payoff' as a forward rate agreom<nt (FRA). To soc this, eonsidee thefixed-rare payer in a 5% fixed-rare, 51,000,000 notional. UBOR·based FRA. Like ourlong call position, tho fixed·rat< payer will reeeive 51.000,000 x (UBOR - 5%). And,like our short PUI position. tho fixed-rate payer win pay $1,000,000 x (5% - UBOR).

~ Profissori Not«: For the tum. you ntta to Imow thllt II long inurnt rat« ,"1/~ combinta with II short interest rat«put 'lin hllllt tht SlImepllyoff liSalong

position in lin ERA.

LOS 60.g: Define interest rate caps, Boors, and collars.

An interest tate <ap is a series of interest rate call options. having expiration dales thatcorrespond to tho reset dales on a Boaling.rale loan. Caps are often used 10 prolect aBoaling.rat< borrower from an incrc:.. e in inreresr rates. Caps place a maximum (upperlimit) on the interest paymc:nts on a Boating·ratc: loan.

Caps pay when rates rise above the cap rare. In this regard, a cap can be viewed as aseries of interest rate call options with strike rates equal 10 the cap rate. Each oprion in acap is called a caplet.

An inlc:resl tate Boor is a series of interest rate PUI options, having expiration dales thatcorrespond to the reset data on a Boating.ratc: loan. floors arc:oftc:n used 10 protect

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a floating-rate lender from a decline in interest rates. Floors place a minimum (lowerlimit) on the interest payments that are received from a floating-rate loan.

An interest rate floor on a loan operates jwt the opposite of a cap. The floor rate is aminimum rate on the paymenu on a floating-rate loan.

Floors pay when rates fall below the floor rate. In this regard, a floor can be viewed as aseries of interest rate put options with strike rates equal to the floor rate. Each option ina floor is called a jllHJrltt.

An interest rate collar combines a cap and a floor. A borrower with a floating-rate loanmay buy a cap for protcction against rates above the cap and sell a floor in order to defraysome of the cost of the cap.

Let's review the information in Figure I, which illustrates the payments from a cap and aAoor. On each reset date of a Aoating-rate loan, the interest for the next period (e.g., 90days) is determined on the basis of some reference rate. Here, we assume that L1BOR isthe reference rate and that we have quarterly payment dates on the loan.

The figure shows the effect of a cap that is set at 10%. In the event that UBOR risesabove 10%, the cap will make a payment to the cap buyer to offset any interest expensein excess of an annual rate of 10%. A cap may be structured to cover a certain numberof periods or for the entire life of a loan. The cap will make a payment at any futureinterest payment due date whenever the reference rate (L1BOR in our example) exceedsthe cap rate. As indicated in the figure, the cap's payment is based on the differencebetween the reference rate and the cap rate. The amount of the payment will equal thenotional amount specified in the cap contract times the difference between the cap rateand the reference rate. When used to hedge a loan, the notional amount is usually equalto the loan amount.

Figure 1 also illustrates a floor of S% for our L1BOR-bascd loan. For any payment wherethe reference rate on the loan falls below S%, there is an additional payment requiredby the floor to bring the total payment to S% (I.2S% quarterly on a 90-day L1BOR-based loan). Note that the issuer of a Aoating-rate note with both a cap and a floor (acollar) is long a cap and short (has sold) a floor. The note issuer receives a payment whenrates arc above the cap, and makes an additional payment when rates arc below the Aoor(compared to just paying the reference rate).

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Figure I: Interest Rate Caps and Floors

Loan lUte

I~ .........•..•.•.•...•....•...•.....•.•

Loon Rare wi,houl C'I" 0' Floors

5%

1 Received h.e.pow,,;,10% Cop

5% Hoor

LlBOR0% 5% 10%

LOS 60.h: Calculate and interpret option payoffs and explain how interest rateoptions differ from other types of options.

CFA" Program Curriculum. Volume 6. pagt 123

Calculating the payoff for a srock option, or other type of option "ith a monetary-based exercise price, is straightforward. At expiration, a call owner receives any amountby which the asset price exceeds the strike price, and zero otherwise. The holder of a putwill receive any amount that the asset price is below the strike price at expiration. andzero otherwise.

While bond. arc quoted in terms of yield-to-maturity, T-bill. in discount yield, indicesin index points. and currencies as an exchange rate, the same principle applies. That is.in each case, to get the payoff per unit of the relevant asset, we need to translate the assetvalue to a dollar value and the: strike price (or rate, or yield) to a dollar strike price. Wecan then multiply this payoff times however many units of the asset arc covered by theoptions contract.

• For a stock index option. we saw that these dollar values wert obtained frommultiplying the index level and the strike level by the multiplier specified in thecontract. The resulting dollar payoffs arc pcr contract.

• The payoff on options on futures is the cash the option holdcr receives when heexercises the option and the raulting futures position is marked to market.

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The payoffs on interest rate options are different. For example, a call option based on90-day UBOR makes a payment based on a stated notional amount and the differencebetween 90-day UBOR and the option's strike rate, times 90 I 360 to adjust for theinterest rate period. The payment is made, not at option expiration, but at a future datecotresponding to the term of the reference rate. For example, an option based on90-day UBOR will make a payment 90 days after the expiration date of the option.This payment date often corresponds to the date on which a UBOR-based borrowerwould make the next interest payment on a loan .

.Example: Computiag the payoff fw aD intCJ'ell rate option

Assume you bought a 6O-day call option on 9O-day UBOR with • notional principal of$1 million and a suike rare of 5'111.Compute the:payment that you wiU receive: if90-cIay UBOR is 6'111at contract expiration, and determine whc:n the payment will bereeebed.

Imillion x (0_06 - 0.05)(90 I 360) • $2,500

Answ.:r:

The interest savings on a $1 million 90-day loan It 5'111-..:nus6'111is:

This is the amount that will be paid by the call wrirer 90 days after expiration.

LOS 60.i: Define intrinsic value and time value, and explain their relationship.

CFA" ProgrrtmCllrrifllillm, Yoillm' 6,Pl1lf' 124

An option's intrinsic value is the amount by which the option is in-the-money, It is theamount that the option owner would receive if the option were exercised. An option haszero intrinsic value if it is at the money or out of the money, regardless of whether it is acall or a put option.

Let's look at the value of a call option I1Itapi,4tilln. If the expiration date price of thestock exceeds the strike price of the option, the call owner will exercise the option andreceive S - X. If the price of the stock is less than or equal to the strike price, the callholder will let the option expire and get nothing.

The intrinsic IIIJI/u' 0/IJI call option is the greater of (S - X) or O. That is:

C = mulO, S - XI

Similarly, the intrinsic will' 11/4pllt option is (X - S) or 0, whichever is greater. That is:

P • mulO, X - SI

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stock price. S55: C .. mu[O. S - X) • mu(O. (55 - 50») • S5

stock price. S50: C. mu[O. S - X) • max(O. (50 - 50») • SO

stock price. S45: c. mu[O. S - X) • mu(O. (45 - 50») • SO

Notice that at expiration. if me stock is worth S50 or below. the caD option is wonh SO-Why? BccaUIC a rational option holder will not aen:i1C me caUoption and take meloss. This one-sided feature of call options is illustrated in the option payoff diagrampresented in Figure 2 for me call option '" ha~ used in mis example.

Example: Illuinsic value

Consider a call option with a strike price ofS50. Compute me intrinsic value of thisoption for stockpricCl ofS55. S50. and 545.

~ hoftss"ri N"r~:Opti"" ,.,.11Jitlpl"IS." "",,,,,,,,t, IIS~IlIIIis I" illllSt,..t~~ tIN ""I,,,11[." "pn"" ., "";,.,tio,,.

Figure 2: Call Option Payoff Diagram

Value

-$5

OJ- ..........._ ...........-('.· .: "..... .. .· '.,........................... :" ~'"· .· '.· .: ".: -'.· .1 ". Short coli

Long call

S5

'-----------''-----''-------- SlUck priceZit CXIHraUOJlx = $50 555

As indicated in Figure 2. the expiration date payoff to the owner is either zero or theamount that the option is in the moncy. For a call option ·...riter (sellerj. rhe payoff iseither zero or minus the amount it is in the money. There are no positive payoffs for anoption writer. The option writer receives the premium and takes on the obligation to paywhatever the call owner gains.

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With reference to Figure 2, you should make the foUowing observations:

• The payoff to a long call position (the solid line) is a Bat line which angles upwardto the right at a 45 degree angle from the strike price, X.

• The payoff to the writer of a call (dotted line), is a Aat line which angles downwardto the right at a 45 degree angle from the strike price, X.

• Options arc a zero-sum game. If you add the long call option's payoff to the shortoption's payoff, you will get a net payoff of zero.

• At a stock price of $55, the payoff to the long is $5, whieh is a $5 loss to the short.

Similar to our payoff diagram for a call option, Figure 3 illustrates thc at-expirationpayoff values for a put option. Iu indicated here, if the price of the stock is less than thestrike price, the put owner will exercise the option and receive (X - S). If the price of thestock is greater than or equal to the strike price, the PUt holder will let the put optionexpire and gct nothing (0). At a stock price of $40, the payoff on a long put is $10; theseller of the put (the short) would have a negative payoff because he must buy the stockat $50 and receive stock worth $40.

Figure 3: Put Option Payoff Diagram

\',lIut'

x

SIO

-$10

o , "- __ _: .~~... :. . .: ............. ...~..... :... :... :. .... :

···Short PUI l-x

S40 X. $50Stockprice

The time value of an option is the amount by which thc option prcmium exceedsthe intrinsic value and is sometimes called the speculative value of the option. Thisrelationship can be written as:

option value = intrinsic value + time value

As we discwsed earlier thc intrinsic value of an option is the amount by which theoption is in the moncy. At any point during the life of an options contract, its valuewill typicaUy be greater than its intrinsic value. This is because thcre is some probabilitythat the stock price will change in an amount that gives the option a positive payoffat expiration greater than the (current) intrinsic value. Recall that an option's intrinsic

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value (to a buyer) is the amount of the payoff at expiration and is bounded by zero,When an option reaches expiration there is no time remaining and the time value iszero. For American options and in most cases for European options, the longer the timeto expiration, the greater the time value and, other things equal, the greater the option'spremium (priee).

LOS 60.;: Determine the minimum and maximum values of European optionsand AmericaJl options.

CFA" PrDgrilm Curriculum, Volume 6, pag' 128

The following is some option terminology that we will use when addressing these LOS:

S, z the price of the underlying stock at time t

X = the exercise price of the optionT • the time to expirationc, • the price of a European call at any time t prior to expiration at

time. TC, = the price of an American call at any time t prior to expiration at

time.Tp, z the price of a European put at any time t prior to expiration at

time = TP, • the price of an American put at any time t prior to expiration at

time. TRFR z the risk-free rate

ProftsSDTi Nott.' Pleesr notiu thllt IOIlHT(IIStletten IITt ustd to npTtStntEUTop,"n-styk opti.ns.

LOIIHTbound. Theoretically, no option will sell for less than its intrinsic value and nooption can take on a negative value. This means that the lower bound for any option iszero. Tb« f4WtT bound DfUfO .pplits to both AmtTirlln.nd EuTDpt.n options.

UPP'T bound foT (111/ options. The maximum value of either an American or a European(.lloption at any time t is the time-t share price of the underlying stock. This maltasense because no one would pay a price for the right to buy an asset that exceeded theasset's value. It would be cheaper to simply buy the underlying asset. At time t • 0, theupper boundary condition can be expressed respectively for American and European calloptions as:

UP!'T bound foT put options. The price for an American put option cannot be morethan its strike price. This is the exercise value in the event the underlying stock pricegoes to zero. However. since European puts cannot be exercised prior to expiration, themaximum value is the present value of the exercise price discounted at the risk-free rate.Even if the stock price goes to zero, and is expected to stay at zero, the intrinsic value,

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X, will not be received until the expiration date. At time t = 0, the upper boundarycondition can be expressed for American and European put options, respectively, as:

xPo sX and Po s T

(I+RFR)

The minimum and maximum boundary conditions for the various types of options atany time tare summarized in Figure 4.

Figure 4: Option Value Limits

Opli.n Minimum Va"'t MlIXimum VIII"t

European call e, <!: 0 e, S S,

American call C, <!: 0 C, S S,

European pu, P, <!: 0 P, S XI( I • RFR)(T-I)

American PUt P, <!: 0 P,S X

~ Proft11ori Nou: Th« "alutf in 1M tablt art tht IMorakallimitl on th« "alut Df~ option>.In Iht nal section, _ will tflablilh mort mtriai"t limiu for oplion

priCll.

LOS 60.k: Calculate and interpret the lowest prices of European and Americancalls and puts based on the rules for minimum values and lower bounds.

CFA" PrDgramCurrirulum. Volumt 6. pagt J28

Proftuori Not« TM option bou"",, ronailionl thllt _ diuull btlow will btimponant whm you study option priring motit". For now. ifyou flibJw thtlogic /tllding up to th« multi pm",,,d in Piprt 5. you will bt p"partd to d.IIIwith tMu LOS. Knowing ana undtntanding tht mulls in Fiprt 5 latilfi thtrt'luirtmmu ofthtlt LOS: tht following dtrilHJtion of thou rtfulu nltd not btmtmtlrnttl.

At this point, we know that for American-style options, which can be immediatelyexercised, the minimum price has to be the option's intrinsic value. For at-the-moneyand out-of-the money options, this minimum is zero, because options cannot havenegative values. Foe in-the-money American options. the minima are simply the intrinsicvalues 5 - X for calls, and X - 5 for puts. If this were not the case, you could buy theoption for less than its intrinsic value and immediately exercise it for a guaranteed profit.50, for American options, we can express the Io_r bound on tht option prirt at any timeI prior to expiration as:

C, • mu[O, 5, - XIP, = mu[O, X - 5,1

For European options. however, the minima are not so obvious because these optionsarc not exercisable immediately. To determine the lower bounds for European options,

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we can examine the value of a portfolio in which the option is combined with a long orshort position in the stock and a pure discount bond.

For a EuroptlJn CIJ" DptiDn. construct the foUowing portfolio:

• A long at-the-money European call option with exercise price X. expiring at timet =T.

• A long discount bond priced to yield the risk-free rate that pays X at optionexpiration.

• A short position in one share of the underlying stock priced at So • X.

The current value of this portfolio is Co- So + X 1(1 + RFR)T.

At expiration time. t • T. this portfolio will pay Cr - Sr + X. That is. we will collectCr • max[O. ST - XI on the call option. pay ST to cover our short stock position. andcoUect X from the maturing bond.

• If ST ;:: X. the call is in-the-money. and the portfolio will have a zero payoff becausethe call pays ST - X. the bond pays +x, and we pay -ST to cover our short position.That is. the time t • T payoff is: ST - X + X - ST • O.

• If X > ST the call is out-of-the-money. and the portfolio has a positive payoff equalto X - ST because the call value. Cr. is zero, we collect X on the bond. and pay -STto cover the short position. So. the time t = T payoff is: 0 + X - S1' = X - Sr.

Note that no matter whether the option expires in-the-money. at-the-money. or out-of-the-money. the portfolio value wiD be equal to or greater than zero. We will never haveto make a payment.

To prevent arbitrage. any portfolio that has no possibiliry of a negative payoff cannothave a negative value. Thus. we can state the value of the portfolio IJt timr t. 0 as:

which allows us to conclude that:

Combining this result with the earlier minimum on the call value of zero, we can write:

Note that X I (I + RFR)r is the present value of a pure discount bond with a face valueofX.

Based on these results. we can now state the lower bound for the price of an Americancall as:

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How can we say this? This conclusion follows from the following twO facts:

I. The early exercise feature on an American eall makes it worth at lean as much as anequivalent European call (i.e., C, 2: c,).

2. The lower bound for the value of a European caU is equal to or greater than thetheoretical lower bound for an American call. For example, mulO, So- X I(I • RFR)TI 2: mulO, So - XI.

ProftssoTi Now Don't gtt ""tV" ""run ber« wt jUJt USt tht foct thllt lin~ Americlln cllil is worth lit lelUt liSmuch lIS II EMmptiln ,aU to claim that tht~ lDwer bound on lin Americe» ,aU is lit lettSt lIS much liS tht 14w" bound on II

EUTOPtll","0.

Derive the minimum value of a European PUt option by forming the followingportfolio at time t = 0:

• A long at-the-money European PUt option with exercise price X, expiring at t 5 T.A short position on a risk-free bond priced at X I (1 • RFR)T. This is the same asborrowing an amount equal to X I (J • RFR)T.A long position in a share of the underlying stock priced at So'

•

•At expiration time t • T, this portfolio will pay Pr • Sr - X. That is, we will collect Pr= mulO, X - SrI on the put option, receive Sr from the stock, and pay -X on the bondissue (loan).

• If Sr > X, the payoff will equal: Pr • ST - X • Sr - X.• If Sr S X, the payoff will be zero.

Again, a no-arbitrage argument can be made that the portfolio value must be zero orgrearer, because there are no negative payoffs to the portfolio.

At timc t = 0, this condition can be written as:

and rearranged to state the minimum value for a European PUt option at time t = 0 as:

Po 2: XI (I. RFR)T -So

We have now established the minimum bound on the price of a European PUt optionas:

Po 2: mulO, X I (1 • RFR)T - Sol

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PrtIpssDr, ND'" NDtict thllt the ID=, bou"d 0" II EU'DP'Il" put is b,Iow thllt Df~ II" AmtrUll" put DptiO" (i.e .• max/O. X - Sol). This is bUlluu wht" its in the~ mD"ry. tht Ameri(Il" put optiD" (II" bt txt7(i~d imm6iillu/y for II pllJDif of

X-Sq

Figure 5 summarizes what we now know regarding the boundary prices for Americanand European options at any time t prior to expiration at rime t = T.

Figure 5: Lower and Upper Bounds for OptioDs

Opti." Minim"", VAlu~ Maximum V../",

European call e, ~ mulO. S, - X I (I • RFR)T"J

c, ~ mulO. S, - X 1(1 • RFR)T~J

p. ~ mulO. X I (1 • RFR) T·, - S,J

5,

American call 5,

X 1(1 • RFR)T-.

X

European put

American pur P, ~ mulO. X - 5.1

~ ProftssDrj NDu: For mt tum. ImDw tht p,iet limi" in Figu" 5. :t&u will "Dt b,~ aslr,d to tU,iw them. but JDu mil) be '''p«ud to uu them.

Example: MiDimum prices for American ..s. European pUIS

Compute: the lowest pomble price for .-month American and European 65 pUt5on astoCk that is trading at 63 when the risk-free: rate: is 5,.,.

Annvcr:

American put: Po ~ mulO, X - So) • maxI0.2) • S2

European put: Po ~ mulO, X 1(1 + RFR)T - Sol- mulO, 65/1.05°333 - 63) -SO.95

Example: MiDimum ptices for American ..s, European calls

Compute: the lowest posAble: price for 3-month American ond European 65 call. on astock that is uading at 68 when the risk-free rau: is 5,.,.

Answer.

Co ~ mulO, So - X I (1 + RFR) T) • mulO, 68 - 65/1.05°.25) • S3.79

Co ~ mulO,So-XI (l + RFR)T). mulO, 68-65 11.05°.2'1.53.79

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LOS 60.1: Explain how option prices are affected by the exercise price and thetime to expiration.

CFA'"ProgramCII"i(lIll1m.Volllmr6. pagt 133

The result we arc after here is a simple and somewhat inruitive one. That is. giventwo puts that arc identical in all respects except exercise price. the one with the higherexercise price "ill have at least as much value as the one with the lower exercise price.This is because the underlying stock can be sold at a higher price. Similarly. given twocalls that arc identical in every rcspea exccpt cxercisc price. the onc with the lowcrexcrcise price will have at least as much value as the one with the higher exercise price.This is because the underlying stock can be purchased at a lower price.

~ P'.fiss.,i Net«: Tb« atrivati." .fthis ,ttlllt;s ;"dllata htrt alth.llgh;t is ".t~ txpliritly rt'{lIirta by tht LOS.

The method here. for both puts and calls, is to combine two options with differentexercise prices into a portfolio and examine the portfolio payoffs at expiration for thethree possible stock price ranges. We usc the fact that a portfolio with no possibiliry of anegative payoff cannot have a negative value to establish the pricing relations for optionswith differing times to expiration.

For Xl < Xz. consider a portfolio at time t that holds the following positions:

",(XI) • a long call with an exercise price of XI

C,(Xl) = a short call with an exercise price ofX2

The three expiration date (t • n conditions and payoffs that need to be considered herearc summarized in Figure 6.

Figure 6: Exercise Price VI. Call Price

Expirll,iD" DIIUOp,i." v"llIt Portfolio P",.ffC."Ji,i."

ST s Xl ey(X,) • ey(X·2) • 0 0

x, < s,< Xl ey(X,) • s,. - X, ST-X,>Oey(X2) • 0

Xl s ST ~(X,) • s,. - X, (ST- X,) - (ST - X;~(X2) • s,. - X2 .Xz-X, >0

With no negative payoffs at expiration, the current portfolio of co(XI) - eo(X2) musthave a value greater than or equal to zero, and we have provcn that cO(XI) ~ co(Xz).

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Similarly, consider a portfolio shore a put with exercise price XI and long a put withexercise price X2, where XI < Xr The expiration date payoffs that we need 10 considerare summarized in Figure 7.

Figu.n: 7: Exercise Price v•. Put Price

&p;rlll;O"D"uOption v"b" 1'(",[0/;. P90ffu"J;I;on

ST~'S Pr09 • Pr(X2l • 0 0

Xl> ST > X, PT(X,l·O 'S-Sr>OPT(X2l • X2 - Sr

XI ~ ST PT(Xll • XI - Sr ('S - Srl - (X, - STlPT<Xzl • 'S - Sr .Xz-X,>O

Here again, with no negative payoffs at expiration, the current portfolio ofPo(X2) - Po(X,) must have a value greater than or equal to zero, which prove. thatPo(X2) ~ PO(Xl)'

In summary, we have shown that, all else being equal:

• Call prices arc inversely related to exercise prices.• Put price. arc directly related to exercise price.

In general, a longer time to expiration will increase an option'. value. For far out-of-the-money options, the extra time may have no effect, but we can say the longer-term optionwill be no less valuable that the shorter-term option.

The case that doesn't lit this pattern is the European put. Recall that the minimum valueof an in-the-money European put at any time r prior to expiration is X / (1 + RFR)T-< - St'Whilc longer time to expiration Increases option value through increased volatility, itdecreases the present value of any option payoff at expiration. For this reason, we cannotstate positively that the value of a longer European put will be greater than the value of ashorter-term put.

If volatility is high and the discount rate low, the extra time value will be the dominantfactor and the longer-term put will be more valuable. Low volatility and high interestrates have the opposite effect and the value of a longer-term in-the-money put optioncan be less than the value of a shorter-term put option.

LOS 60.m: Explain put-call parity for European options, and explain how put-call patity is related to arbitrage and the construction of synthetic options,

CFA" Progrllm Curriculum, Volume 6, pag. 135

Our derivation of put-all parity is based on the payoffs of two portfolio combinations,a liduciaty call and a protective put.

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Ajiauciary call is a combination of a pure-discount, riskless bond that pa)'SX at maturityand a call with exercise price X. The payoff for a fiduciary call at expiration is X whenthe call is out of the money, and X • (S - X) • S when the call is in the money.

A prottrtiw put is a share of stock together with a put option on the stock. Thecxpiration dare payoff for a protective put is (X - S) • S • X when thc put is in themoney. and S when the put is out of the money.

~ Profissor's Now Whtn working with pur-<all parity. it is important to mitt that~ th, exerciseprius on th, put ana th, <allana th, fou valu, of th, riskless bona

"" all 'qual ttJ X

When the put is in the money, the call is out of the money, and both portfolios pay X atexpiration.

Similarly, when the put is out of the money and the call is in the money, both portfoliospay S at expiration.

Put-call parity holds that portfolios with identical payoffs must sell for the same price toprc:vent arbitrage. We can express the put-call parity relationship as:

e .. X / (I • RFR)T • S • p

Equivalencies for each of the individual securities in the put-call parity relationship canbe expressod as:

S ~ c - p • X / (I • RFR)TP • c - S • X / (I • RFR)Tc=S.p-X/(I.RFR)TX/(I. RFR)T =S. p-c

The single securities on the left-hand side of the equations aU have exacdy the samepayoffs as the portfolios on the right-hand side. The portfolios on the right-hand sidearc the synthetic equivalents of the securities on the left. Note that the options mustbe European-style and the puu and caUs must have the same exercise price for theserelations to hold.

For example, to synthetically produce the payoff for a long position in a share of stock,usc the following relationship:

S • c - p • X I (I • RFR)T

This mean. that the payoff on a long stock can be synthetically created with a long call,a shon put, and a long position in a risk-free discount bond.

The other securities in the put-call parity relationship can be constructed in a similarmanner.

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Study Session 17Cro .. ·Rtre~nu to CFA Institllle Assip<! Rtading ,GO - Option Mulotu aM Contracts

Proftuor" Now Afur ~xprruinK th~put-caU parity rri4tionthip in ttrmlofthe~ IUII';ty JDIIwant to lJnthttitally create, tht lign on the inJilliJu./,tcllriti" wiU~ inaitau wh~th~rJDu nml a ilmgpolition (. lip) or a thort pOlilion (-lip) in

th~ rnp~ttillt securities,

Eumple Call option ...Io.tmn using put-call parity

Suppose dun the currentllodt price: is 5S2 and the risk-frc:c:rate is S'MI.You have: founda quote fora 3-month put option with an c:xercise:price ofSSO. The: put price is 51.S0.but due to light trading in rhc:call options. there was aot a listed quote for the3-month. SSOcall. Estimate the price of rhc: 3-month call option.

Answer:

Rearranging put-all parity. we find that the call price is:

call = put + stock - present value(X)

SSOca1I=SI.SO+SS2-I.OS~I.2S $4.11

This means that ifa 3-month. SSOcall is aYailabie. it should be: priced at S4.11 permare.

LOS 60.n: Explain how cash Bows on the underlying asset affect put-call parityand the lower bounds of option prices.

CFA- Program Cumtll/um, Volume 6, pal' 142

If the asset has positive cash Bows over the period of the option. the eesr of the assetis less by the present value of the cash Bows. You can think of buying a stock for S andsimultaneously borrowing the present value of the cash Bows, PV CF' The cash Bow(s)will provide the payoff of the loan(s), and the loan(s) wiU reduce the net cost of the assetto S - PV CF •Therefore, for assets with positive cash Bows over the term of the option.we can substitute this (lower) net COli. S - PVCF' for S in the lower bound conditionsand in all the parity relations.

The lower bounds for European options at time t • 0 can be expressed as:TCo ~ maxlO. So - pVcp- X 1(1 • RFR) l. and

Po ~ maxlO. X 1(1. RFR)T - (So - PVc.,>l

The put-call parity relations can be adjusted to account for asset cash Bows in the samemanner.

(So - PVCF) = c- p • X I (1 • RFR)T. andc. XI (1. RFR)T = (So-PVC">. P

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LOS 60.0: Determine the directional effect of an interest rate change orvolatility change on an option's price.

CFA"' ProFm o.rricuillm, Voillmt 6.pagt J 42

When interest rates increase, the value of a call option increases and the value of a putoption decreases (holding the price of the underlying security constant). This generalresult may not apply to interest rate options or to bond or T-bill options, where a changein the risk-free rate may affi:a the value of the underlying asset.

The no-arbirrage relations for puts and calls make these statements obvious:

C.S~P-X/(I ~RFR)TP 5 C - S ~ X I (I ~ RFR)T

Here we can sec that an increase in RFR decreases X I (1 ~ RFR)T. This will have theeffect of increasing the value of the call, and decreasing the value of the put. A decreasein interest rates will decrease the value of a call option and increase the value of a PUtoption.

~ Profmo,s Now A"mitwl!y. this is a partial analysis of thtu t'l"ations, bllt it~ aOtSgillt tht right air«tions for tht t/focrs of interett mt« changts and will htlp

)011 rtmtmbtr thtm if this ,./Arion is ttlUa on tht exem.

Greater volatility in the value of an asset or interest rate underlying an option conuactincreases the values of both puts and calls (and caps and 1I00rs). The reason is thatoptions are one-sided. Since an option's value falls no lower than zero when it expiresout of the money, the increased upside potential (with no greater downside ri.k) fromincreased volatility, increases the option'. value.

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KEy CONCEPTS

LOS GO_aA call option on a financial or physical a.ssetgives the option's owner the right, but notthe obligation, to buy a specified quantity of the a.sset from the option writer at theexercise price specified in the option for a given time period. The writer of a call optionis obligated to sell the asset at the exercise price if the option's owner chooses to exerciseit.

A put option on a financial or physical a.ssctgives the option's owner the right, butnot the obligation, to sell a specified quantity of the asset to the option writer at theexercise price specified in the option for a given time period. The writer of a PUt optionis obligated to purchase the asset at the exercise price if the option's owner chooses toexercise ir,

The owner (buyer) of an option is said to be long the option, and the writer (seller) ofan option is said to be short the option.

LOS60.bAmerican options can be exercised at any time up to the option's expiration date.

European options can be exercised only at the option's expiration date.

LOS 60.cMoncyncss for puts and calls is determined by the difl'crence between the strike price (X)and the market price of the underlying stock (5):

c.lI Op,;o" !'II, Op,i4"In the moneyAI the moneyOUI of the money

L0560.dExchange-traded options arc standardized, regulated, and backed by a clearinghouse.Over-the-counter options arc largely unregulated custom options that have counterpartyrisk.

L0560.eOptions arc available on financial securities, futures contracts, interest rates, andcommodities.

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Study Somon 17CroSs-~ft~Dce to CFA IrutiNte Assij;nedRtading ,GO- OptiODMwts and Conuacu

LOS 60.(Interest rate option payoffs arc me difference between the market and strike rates,adjusted for me loan period, multiplied by the principal amount.

At expiration, an interest rate call receives a payment when me reference rate is above thestrike rare, and an interest rate put receives a payment when me reference rate is belowthe mike rate.

An FRA can be replicated with twO interest rate options: a long call and a short put.

LOS 60.gInterest rate caps put a maximum (upper limit) on the payments on a Roating-rate loanand arc equivalent (from me borrower's perspective) to a series of long interest rate callsat me cap rate.

Interest rate Roors put a minimum (lo...."'r limit) on the payments on a Roating-rate loanand arc equivalent (from me borrower's perspective) to a series of shon interest rate pUtsat me Boor rate.

An interest rate collar combines a cap and a Roor. A borrower can create a collar on aRoating-rate loan by buying a cap and selling a Roor.

LOS 60.hThe payoff to me holder of a call or put option on a stock is the option's intrinsic value.Payment occurs at expiration of the option.

Payoffs on interest rate options arc paid after expiration, at me end of me interest rate(loan) period specified in the contract.

LOS 60.iThe intrinsic value of an option is me payoff from immediate exercise if the option is inthe money, and zero otherwise.

The time (speculative) value of an option is the difference berwcen its premium (marketprice) and its intrinsic value. At expiration, time value is zero.

LOS 60.j,kMinimum and maximum option values:

Opli." Mi"imum v"lut M""imum Vttlut

European callAm<rican allEuropean PUt

Am<rican put

e, ;:: max[O, S, - X I (1 + RFR)T"JC, ;:: mu[O, S, - X 1(1 + RFR)T"JP, ;:: mu[O, X 1(1 • RFR)T., - S)

P. > mulO, X - S,)

S,

S,X 1(1 + RFR)T.,

X

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L0560.1CaIIJ with lower exercise prices are worth at least as much as otherwise identical callswith higher exercise prices (and typically more).

Puts with higher exercise prices arc wonh at least as much as otherwise identical putswith lower exercise prices (and typicaUy more).

Otherwise identical options arc worth more when there is more time to expiration, withtwo exceptions:• Far out-of-the-money options with different expiration dates may be equal in value.• With European puts, longer time to expiration may decrease an option's value when

they are deep in the money.

L0560.mA fiduciary call (a caU option and a risk-free :z.c:ro-couponbond that pays the strike priceX at expiration) and a protective put (a share of stock and a put at X) have the samepayoffs at expiration, so arbitrage wiU foree these positions to have equal prices:c + X I (1 + RFR) T • 5 + p. This establishes put-call parity for European options.

Based on the put-call parity relation, a synthetic security (stock, bond, call, or put) canbe created by combining long and shon positions in the other three securiti es,• c. 5 + p - X I (1 + RFR)T• P = c - S + X 1(1 • RFR)T• 5 = e - p + X 1(1 + RFR)T• X I (1 + RFR)T • 5 + P - c

L0560.0When the underlying asset has positive cash flows, the minima, maxima, and put-callparity relations arc adjusted by subtracting the present value of the expected cash flowsfrom the assets over the life of the option. That is, S can be replaced by (S - PV ofexpected cash flows).

LOS 60.0An increase in the risk-free rate wiU increase call values and decrease PUt values (foroptions that do not explicitly depend on interest rates or bond values).

Increased volatility of the underlying asset or interest rate increases both put values andcall values.

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CONCEPT CHECKERS

1. Which of the following statements about moneyness is Itan tzuurllu? When:A. S - X is > 0, a call option is in the money.B. S - X 5 0, a call option is at the money.C. S > X, a put option is in the money.

2. Which of the following statements about American and European options ismatt Il(CUTIlIt?A. There will always be some price difference bcrween American and European

options because of exchange-rate risk.B. European options allow for exercise on or before the option expiration date.C. Prior to expiration. an American option may havc a higher value than an

equivalent European option.

3. Which of the following statements about put and call options is kllit tz«uratt?A. The price of the option is less volatile than the price of the underlying stock,B. Option prices arc generally higher the longer the time until the option

expires.C. For put options. the higher the strike price relative to the stock's underlying

price. the more the put is worth.

4. Which of the following statements about options is mott Il«urlltt?A. The writer of a put option has the obligation to sell the asset to the holder

of the put option.B. The bolder of a call option has the obligation to sdl to the option writer if

the stoek's price rises above the strike price.C. The holder of a put option has the right to sell to the writer of the option.

5. A durtllSt in the risk-Ieee rate of interest will:A. increase put and caU prices.B. decrease put prices and increase call prices.C. increase put prices and decrease call prices.

6. A 540 calIon a stock trading at $43 is priced at $5. The time value of the optionis:A. S2.B. SS.C. S8.

7. Prior to expiration. an American put option on a stock:A. is bounded by S - X, (1 + RFR)'I:B. will never sell for less than its inuinsic value.C. can never sell for more than its intrinsic value.

8. The owner of a call option on oil futures with a strike price of $68.70:A. can exercise the option and take delivery of the oil.B. can exercise the option and take a long position in oil futures.C. would never exercise the option when the spOt price of oil is less than the

strike price.

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9. The lowcr bound for a European put option is:A. max(O, S - X).B. max[O, X I 0 + RFR)T_ SI.C. max[O, S - X I (1 + RFR)TJ.

10. The lowcr bound for an American call option is:A. max(O, S - X).B. max[O, X 1(1 + RFR)T- S).C. max[O, S - X I (1 + RFR)T).

II. To account for positive cash Bows from the underlying .. set, we need to adjustthe put-call parity formula by:A. adding the future value of the cash Bows to S.B. adding the furure value of the cash Bows to X.C. subtracting the present value of the cash Bows from S.

12. A forward rate agreement is equivalent to the following interest rate options:A. long a call and a put.B. short a call and long a pUt.C. long a call and shorr a put.

13. The payoff on an interest rate option:A. comes only at exercise.B. is greater the higher the "strike" rate.C. comes some period after option expiration.

14. An interest rate Boor on a Boating-rate note (from the issuer's perspective) isequivalent to a series of:A. long interest rate puu.B. short interest rate puts.C. short interest rate calls.

15. Which of the following relations is kart liltdy accurate?A. p. C-S + XI (I + RFR)T.B. C e S - P + X I (I + RFR)T.C. X/O+RFR)T_p.S-c.

16. A stock is selling at $40, a 3-month put at $50 is selling for $11, a 3-month callat 550 is sdling for $1, and the risk-free rate is 6%. How much, if anything, canbe made on an arbitrage?A. 50 (no arbitrage).B. 50.28.C. 50.72.

17. Which of the following will increas« the value of a put option!A. An increase in volatility.B. A deere ase in the exercise price.C. A decrease in time to expiration.

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ANSWERS - CONCEPT CHECKERS

I. C A PUI cption is OUIof the money when S > X and in the money when 5 < X. The otherstatemenu ale true.

2. C American and European options both givc the holder Ihe righl 10 exercise rhe optionat expiration. An American option a1.0 gives the holder the righl of carly exercise. soAmerican options will be worth more than European oprlcns when the righl 10 earlyexercise is valuable. and lhey will have equal value when il is nOI. C, ;:: c, and P, ;:: P•.

3. A Option prices are m.rt volatile than the price of the underlying stock. The olh erstalemenu are true. Options have lime value. which means prices are higher Ihelongerthe time until the option expires, and a higher strike price increases me value of a putoption.

4. C The holder of a PUI option h .. the righllO sell ro the writer of the opticn. The wriler ofthe PUI option h .. Ihe obligation 10 bu)·. and the holder of the call oprion has the righl.bUI nOI the obligation 10 buy.

5. C Interese rales are inversely related 10 PUI prices and directly related 10 caU prices.

G. A The intrinsic value is 5 - X • SH - $<10 • 53. So. the lime value is 55 - 53 • $2.

7. B AI any time r, an American PUI will never sell below intriruic value, bUI may sell formore than that. The lower bound is mulO, X - 5,1.

8. B A calion a fuiures contract gives the holder the right to buy (go long) a futures contractat thc exercise pricc of the call. It is not the current spot price of the a.. et underlyingthe futures conlract that determines whether a fUlures oplion i. in the money, il is rhefUlures contract price (which may be higher).

9. B The lower bound for a European PUI ranges from zero 10 the presenl value of theexercise price less the prevailing stock price, where the exercise price is discounted at therisk-free rate.

10. C The lower bound for an American call rang es from zero to the prevailing stock price lessthe present value of the exercise price discounted at the risk-free rate.

II. C If the underlying as.. 1 uscd to establish the put-call parity relationship generale. a ca5bflow prior to expiration, the .... I·Svalue mU$1be reduced by the present value of thecash flow discoumed at the risk-free rate,

12. C The payoff to a FRA is equivalent to that of a long inter est rate call oplion and a shortinterest rare put option.

13. C The paymenl on along PUI increases as the strike rare increases, bUI nOI for calls. Therei. only one payment and it come. after option expiration by the term of the underlyingrate.

14. B 5hon interest rare puts require a payment when the markel rate at expiration is belowthe strike rate. just as lower rates can require a payment from a 1I00r.

15. B The put-call pariI)' rdatioruhip is S • p. C. X I (I • RFR)T. All individual sec..rilicscan be expres sed .. rearrangements of this b .. ic relationship.

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IG. C A synthetic stock is: S • C - P + X I (I + RFR)T. SI - SI1 + 50 I (l.OG)0.2S • S39.28.Since the stock is selling for S.(O. you can short a sh are of stock for S40 and buy thesynthetic for an immcdiatt ubitngt profit of SO.72.

17. A Increased volatility of the und.r1ying asst, increases both pu, values a.nd ca.1Ivaluts.

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The (011~;ng is • rnicw of the Dcrintiw. princjple.s de"ped to addrul the leuaing outcome,talcmenu let forth by CfA In.tituk. Thil topic: i, also coveted iD:

SWAP MARKETS AND CONTRACTS

Study ~SJion 17

ExAM Focus

This topic rcview introduces swaps. The first thing you mwt learn is the mechaniesof swaps so that you can calculate the payments on any of the types of swaps covered.Bcyond that. you should be able to rccogni zc that the ca.sh lIows of a swap can beduplicated with capital markets transactions (make a loan. issue a bond) or with otherdcrivatives (a series of forward rate agreements or interest rate options). Commonmistakes include forgetting that the current-period lIoating rate determines the nextpayment. forgetting to adjust the interest rates for the payment period. forgetting to addany margin above the lIoating rate specified in the swap, and forgetting that currencyswaps involve an exchange of currencies at the initiation and termination of the swap.Don't do these things.

SWAP CHARACTEJUsTICs

Before we get into the derails of swaps, a simple introduction may help as you gothrough the different types of swaps. You can view interest rate swap. as the exchange ofone loan for another. If you lend me 510,000 at alloating rate, and 1 lend you $10,000at a fixed rate, we have created a swap. There is no rcason for the $10,000 to aauallychange hands. The two equal loans make this poindess. At each payment date. I willmake a payment to you based on the lIoating rate, and you will make one to me basedon the fixed rate. Again. it makes no sense to exchange the full amounts; the one withthe larger payment liability will make a payment of the difference to the other. Thisdescribes the payments of a fixed-for-lloating or "plain vanilla swap.

A currency swap can be vicwed the same way. If I lend you 1,000,000 euros at the eurorate of interest. and you lend me the equivalent amount of yen ar roday's exchangerate at the yen rate of interest. we have done a currency swap. We will "swap· backthese same amounts of currency at the maturity date of the two loans. In the interim, Iborrowed yen. so I make yen interest payments, and you borrowed euros and must makeinterest payments in euros.

For other types of swaps. we jun need to deseribe how the payments arc calculated onthe loans. For an equity swap, I could promise to make quarterly payments on your loanto me equal to the return on a stock index, and you could promise to make fixed-rate(or lIoating-rate) payments to me. If the stock index goe. down, my payments to you arcnegative (i.e., you make a fixed-rate payment to me and a payment equal to the declinein the index over the quarrer). If the index went up over the quarter. I would make apayment based on the percentage increase in the index. Again. the payments could be"netted" so that only the difference changes hands.

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Study Seuion 17Cross-Rtf_nce 10 CFA Institute Assigned Rtading ,61 - Swap Markets aAd Contraas

This intuitive explanation of swaps should make the following a bit e... ier to understand.Now let's dive into the mechanics and tcrminology of swaps. We have to spceify cxactlyhow the intcrest payments will be:calculated, how oftcn they are made, how much is tobe loaned, and how long the loan. ate for. Swaps are custom instruments, and we canspc:cify any terms both of us can agte:e on.

LOS 61.a: Describe characteristics of swap contracts and explain how swaps arcterminated.

CFA" Program Curriculum, Volume 6, pag' 156

Swaps arc agreemcnts to exchange a series of cash flows on periodic settlement datn ovcra certain time: pe:riod (e.g., quarre:rly payme:nts over two years), In the: simplest type: ofswap, one: patry makes fix,d'Tau interest payments on the notional principal specified inthe: swap in return fot flDating-raft payments from the other patty. At each settlementdate, the two payments arc nttud so that only one (ne:t) payme:nt is made:. The: pattywith the: gre:atcr liability make:s a payme:nt to the: other parry. The length of the swap istermed the tenor of the swap and the contract ends on the termination date. A swap canbe decomposed into a series of forward contracts (FRAs) that expire on the setdementdates.

In many respeets, swaps arc similar to forwards:

• Swaps typically requite no payment by either parry at initiation.• Swaps arc custom instruments.• Swap. arc not traded in any organized secondary market.• Swaps ate largely unregulated.• Default risk is an important ...peet of the contracts.• Most participants in the swaps market arc large institutions.• Individuals arc rardy swaps market participants.

There arc swaps facilitators who bring together parties with needs for the opposite sidesof swaps. There arc also dealers, large banks and brokerage firms, who act ... principalsin trades just as they do in forward contracts, It is a large business; the total notionalprincipal of swaps contracts is estimated at over 550 trillion.

How Swaps arc Terminated

There arc four ways to terminate a swap prior to its original termination date.

). Mutual termination, A ca.shpayment can be made by one patry that is acceptable tothe other parry. Like forwards, swap. can accumulate value ... market prices or interestrates change. If the party that has been disadvantaged by the market movements iswilling to make a payment of the sv.-ap'svalue to the: eountcrpatty, and thecounterparry is willing to accept it, they can mutually terminate the swap.

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2. O./fitttinl contract,Just as with forwards. if the terms of the original counterpartyoffers for early termination arc unacceptable. thc alternative is to cnter an offsettingswap. [f our S-ycar quarterly-pay Aoaring swap has IWO years to go. wc can seek acurrent price on a pay-fixed (receive Aoating) swap that will provide our Aoatingpayments and leave us with a fixed-rate liability.

Just as with forwards. exiting a swap may involve taking a loss. Consider the casewhere we receive 3% fixed on our original S-year pay Aoating swap. but must pay4% fixed on the offietting swap. We have locked in a loss because we must pay [%higher rates on the offsening swap than we receive on the swap we arc offsetting. Wemust make quarterly payments for the next twO years. and receive nothing in return.Exiting a swap through an offietting swap with other than the original counterpartywill also expose the investor to default risk. just as with forwards.

3. Rmllt.Ie is possible to sell the swap to another party. with the permission of thecounterparty to the swap. This would be unusual. however. as there is not afunctioning seeondary market.

4. SWllption.A swaption is an option to enter into a swap. The option to enter into anoffietting swap provides an option to terminate an existing swap. Consider that. in thecase of the previous S-year pay Aoating swap. we purchased a 3-year call option on a2-year pay fixed swap at 3%. Exercising this swap would give us the offietting swap toexit our original swap. The COStfor such protection is the swaption premium.

LOS 61.b: Describe, calculate, and interpret the payments of currency swaps,plain vanilla interest rate swaps, and equity swaps.

In a currency swap. one party makes payments denominated in one currency. while thepayments from the other party arc madc in a second currency. Typically. the notionalamounts of the contract. expressed in both currencies at the current exchange rate. arcexchanged at contraa initiation and returned at the contract termination date in thesame amounu.

An example of a currency swap is as follows: Party 1 pays Party 2 S10 million at contractinitiation in return for €9.8 million. On each of the settlement dates, Pany I. havingreceived euros, makes payments at a 6% annualized rate in euros on the €9.8 million toPany 2. Party 2 makes payments at an annualized rate ofS% on the $10 million toParty 1.These settlement payments arc both made. They arc not netted as they arc in asingle currency interest rate swap.

As an example of what motivates a currency swap. consider that a U.S. firm. Party A.wishcs to establish opcrations in Ausualia and wants to finance thc costs in Australiandollars (AUO). The firm finds. however. that issuing debt in AUO is relatively morcexpensive than issuing USO-denominated debt. because they arc relatively unknown inAusualian fmancial markets. An altcrnative to issuing AUO-denominated debt is toissue USO debt and cnter into a USO/AUO currcncy swap. Through a swaps facilitator.the U.S. firm finds an Australian firm. Party B. that faces the same situation in reverse.They with to issue AUO debt and swap into a USO exposure.

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There arc four possible types of currency swaps available.

1. Party A pays a fixed rare on AUD received, and Parry B pays a fixed rate on USDreceived.

2. Party A pays a Roating rare on AUD received, and Parry B pays a fixed rare on USDreceived.

3. Parry A pays a fixed rare on AUD received, and Party B pays a Roating rate on USDreceived.

4. Party A pays a Roating rate on AUD received, and Parry B pays a Roating rate on USDreceived.

Following ore the steps in a fixed-for-fixed currency swap:

Sup i: The notional principal actually changes hands at the beginning of the swap.Parry A gives USD to Parry B and gets AUD back. Why? Because the motivationof Party A was to get AUD and the motivation of Party B ·...as to get USD.Notional p,ittdpal illlllappta as initiation.

Sup 2: Interest payments arc made without netting. Party A, who got AUD, pays theAustralian interest rate on the notional amount of AUD to Parry B. Parry B,who got USD, pays the U.S. interest rate on the notional amount of USDreceived to Parry A. Since the payments arc made in different currencies, nettingis not a typical practice. F"IIII intemr palmmtl art ",changttl at tach stnltmttttalllt, tllCh in IIaifftrtnt (u,"nC]>

Sltp 3: At the termination of the swap agreement (maturiry), the eounterparties giveeach other back the exchanged norional amounts. Notiottal p,indpal is llllapptaIIgllin lit the ttrnli1llltion o/tht IIgrttmtttt. The cash Rows associated with thiscurrency swap arc illustrated in Figure 1.

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Figure 1: Fixed-for-FIXed Currency Swap

SWAI' INITIATION

111t Amtr:lluu firlll ,,"l1i1S USD.Sw.1" AUO for USO

11><U.S. firm W3"ISAUD.Has or C'3Jl borrow t\UD. I los or a" borrow USO.

SW31"USO for AUO

SWAP INTERI:ST PAYMENTS

"lbe Au.s.tr.1Jian firmAuser.li.n p.ys USI) interest

lho U.S. firm hashas usc of ,h. USD. "'0 of the AUO.

U.s. firm p.)'s AUI) inco... !

SWAI'TERMINAl"ION

USD returnedThe AII~'r.,ll.1nfirm returns 'Ihc U.S. firm returnscit. usn borrow.. l. tho ,\UI) borrowed.

AUOltturnod

Calculating the Payments on a Currency Swap

Example: FllICd-for-liKd cuncncy &Wap

BB can borrow in the Unired SQICSfor 9%, while M has to pay 10% to borrow in theUnited States. M can borrow in Australia for 7%, while BB hu to pay 8% to borrow inAusrralia. BB will be doing business inAustralia and needs AUD, while M wiUbedoing business in the United SUtes and needs USD. The exchange rare is 2AUD/USD.M needs USD1.0 million and BB needs AUD2.0 million. They decide to borrow thefunds locally and swap the borrowed funds. The swap period is for live yean. Calculatethe cash Sows for this swap.

M .". BB ,.ch to ,. Ibn,."", umntic II.1I1r:

• M borrows AUD2.0 million, agreeing to pay the bank 7%, or AUDI40,OOOannually.

• BB borrows USDI.O miUion, agreeing to pay the bank 9%, or USD90,OOOannually.

Mand BB swap currencies:

• M g~s USD1.0 million, agreeing to pay BB 10% interest in USD annually.• BB gets AUD2.0 million, agreeing to pay M 8% intereSt in AUD annually.

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1'bt] PIll nlLhIIrkr ,II, tin",..} i",~o M owes BB USD 100,000 in interell to be paid on each settlement date.o BB owcsMAUD160.000 in inten:st to be paid on each settlement date.

TM] ncb 111« ,IItir 11111" Md- tilt tItI",..} i"umt PtIJ",mt:

o M pays the Attstralian bank AUD 140.000 (butgcuAUDI60.000 from BB. anAUD20,OOO gain).

o BB pays the U.S. bank USD90.000 (but Fts USD100.000 from AA. aUSD 10.000 gain).

o They both gain by swapping (M is ahead AUD20,OOO and BB is ahead USD10.000).

I" filM JH'I. thq rrwn, ,lit slUtl/. Tilt] rrtIIrn ,lit "",;.".1prilltipd

o M Fts AUD2.0 miUion from BB and then pays back the Auaualian bank.o BB gets USDl.O million from M and then pays back the U.S. bank.

Interest Rate Swaps

The plain vanilla inrerest rate swap involves uading fixed interest rate payments forfloating.rate payments. (A basis SW2pinvolves trading one set of floating rate paymentsfor another.)

The party who wants floating-rate interest payments ageees to pay fixed-rate interest andhas the p4y-fixed side of the swap. The counterparry, who receives the fi.xcdpayments andageccs to pay variable-rate interest. has the pily-floating side of the swap and is called thejI4llring-rllu p4)V1r.

The floating rate quoted is generally the London Interbank Olttred Rate (UBOR). flator plus a spread.

Let's look at the cash flows that occur in a pillin uenill« intern: "'u SWllp.

o Because the notional principal swapped is the same for both counterpartics and isin the same currency units. there is no need to actually exchange the cash. Notionlllprincip"l is generalJy no' sWllpped in single currency swap •.

• The determination of the variable rate is at the beginning of the settlementperiod. and the cash interest payment is made at the end of the settlement period.Because the interest payments arc in the same currency. there is no need for bothcounterpartics to actually transfer the cash. The difference between the fixed-ratepayment and the variable-rate payment is calculated and paid to the appropriatecounterparry. Net inurrsr is pdid by ,he one who own it.

o At the conclusion of the swap. since the notional principal was not swapped. there isno transfer of funds.

You should note that swaps arc a 'Zero-sum game. What one party gains. the other partyloses.

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The net formula for the fixtti-rllu PIlJ". based on a 360-day year and a floating rate ofL1BORis:

( )(nun\berof days)(Ott fixed,,,"r payment), = swap fixed rate - U80R,.t 360 (notiorW principal)

If this number is positive. the fixed-rate payer OI«S a net payment to the floating-ratepany. If this number is negative, then the fixed-ratc payer rt((illtJa net flow from thefloating-rate payer.

Profmor's Now For tht exem, remember thllt with pwin tlllnilwswllps. one~ pllT" PfIJsfixtd lind tht other PIlYSIljlo"tint ret«. SomttimtssWilp p"Jmtnts Ilrt~ billed on II 365-d1lJ 1'llr. For tXllmpk. tht SWllpwill Sptrifj whtther !JO/36()or

90/365 should bt IIItd to clllcuwu " qUllrttrly SWllppllymtnt. &mtmbtr. thtu"" custom instruments.

Eumple: Interat nte risk

Consider a bank. 115deposiu represent Iiabllities and are most likely short term innature. In other words. deposits represent bting-rate liabilitica. The bank uscu areprimarily loans.. Man loans carry fixed rateS ofintemt. The bank UselS an: fixed-rateand bank liabilities arc Soating. Explain the naNIC of the inccrcst rate risk that the bankmes, and describe how an interest rate swap may be used to hedge this risk.

Answer:

The risk the bank faces is that shore-term interest rates wiD rise, causing cash paymenton deposits to incrcuc. This would not be a major problem if cash in80ws also increaseas interest rates risco but with a fixed-rate loan portfolio they will not. If the bankremains unhedgcd u interest rala rise. cash ouc8ows rise and bank profits faD.

The bank can hedge this risk by entering into .fixed-for-Roating swap u the fixed-ratepayer. The Soating-rate paymcnlS received would ofFset any incrcuc in the flo.ting-ratepayments on deposits. Nocc mac if rala faD, the banlc's COStsdo noc. They still pay fixedfor the term of the swap and n:ccivc (lower) floating-rate payments that correspond totheir lower COSIS on deposits.

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Calculating the Payments on an Interest Rate Swap

Eumple: Calculatins thc payments OD an intcrest ratc swap

Bank A enters into a $ 1,000,000 quarterly.pay plain vanilla interest rate swap as mc6xc:d-ratc payer at a fixc:draee of 6% based on a 360-day year. The Soatins-rate payerapea to pay 9O-day UBOR pltu a 1% margin; 90-day UBOR is currcntly 4%.

9O-day UBOR rates atc: 4.5%5.0%5.5%6.0%

90 days &om now180 days from now270 days from now360 days from now

Calculuc the amounts Bank A pays or rcccivcs90, 270, and 360 days (rom now.

Answer:

The payment 90 days &om now depends on current UBOR and the fixed rate (don'tforsenhe 1% marlJin).

Fixed-rate payer pays:

10.06(:) -(0.04 ~0.01)( :)Ix 1,000,000 = S2.500

270 days from now, the payment is based on UBOR 180 days (tom now, which is 5%.AddinS the 1% marpn makes the lloanns·rate 6%, which is equal to the fixed rate, sothere is no net third quancrly payment.

The bank's ·payment" 360 days &om now is:

10.06(:) - (0.055 -o.OI)(:)jx 1,000,000 = -$1,250

Because the lIoatins-rate payment exceeds the fixed-rate payment, Bank A will ""i.$ 1.250 at the fourth payment date.

EqwtySwaps

In an equity swap, the return on a stock, a portfolio, or a stock index is paid each periodb)· one party in return for a fixed-rate or floaring-ratc payment. The return can be thecapital appreeiation or the total return including dividends on the stock. portfolio. orindex.

In order to reduce equity risk. a portfolio manager might enter into a I-year quarterly-pay S&P 500 index swap and agree to receive a fixed rate. The percentage increase in theindex each quarter is netted against the fixed rate to determine the payment to be made.If the index return is negative, the fixc:d-rate payer must also pay the percentage decline

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in the index to the portfolio manager. Uniquely among swaps, equity swap paymentscan be floating on both sides and the payments arc not known until the end of thequarter. With interest rate swaps, both the fixed and floating payments arc known at thebeginning of period for which they will be paid.

A swap on a single stock can be motivated by a desire to protect the value of a positionover the period of the swap. To protect a large capital gain in a single stock, and to avoida sale for tax or control reasons, an investor could enter into an equity swap as theequity-returns payer and receive a fIXedrate in return. Any decline in the stock pricewould be paid to the investor at the settlement dates, plus the fixed-rate payment. If thestock appreciates, the investor must pay the appreciation less the fixed payment.

Calculating the Payments on an Equity Swap

Example: Equity swap paymCIIU

Ms. Smith enters into a 2-ycar $ 10 million quartcrly swap as the fixed payer and willreeebe the index return on the S&P 500. The fixed rate is 8'16, and the index iscurrcndyat 986. At the end of the next thrce quartcrs, the index level is: 1030,968,and 989.

Calculate the net payment for each of the next three quarters and identify the directionof the payment.

Amwer:

The percentage change in the index each quarter, Q, is: QI .4.46'16, Q2 • -6.02'16,and Q3 • 2.17'16. The index return payer will receive 0.08 14 • 2'16each quarter andpay the index return, therefore:

Q I: Index mum payer pays 4.46'110- 2.00'16 c 2.46'16 or $246,000.Q2: Index return payer receives 6.02'110+ 2.00'16 • 8.02'110or $802,000.Q3: Index return payer pays 2.17'110- 2.00'16 • 0.17'16 or 517,000.

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Study 5«.ion 17Cross-Rtf_nce to CFAlnltitule A£.""ed Rtading '61 - Swap Markets aAd Con"ac ..

KEy CONCEPTS,

LOS 61.aSwaps are based on a notional amount of principal. Each p:trty is obligated to p:ty apercentage return on the notional amount :It periodic settlement dues over the life(tenor) of the sw:tp. Percentage payments are based on :t Aoating rate. fixed rate, or thereturn on an equity index or portfolio.

Except in the case of a currency swap. no money eh:tnges hands ae the inception of theswap and periodic payments are netted (the parry wt owes the larger amount pays thedifference to the other).

Swaps are custom instruments. are largely unregulated, do not trade in secondarymarkets. and are subject to counterp:trty (default) risk.

Swaps can be terminated prior to their stated termination dates by:• Entering into an offsetting swap. sometimes by exercising a swaption {most

common}.• Agreeing with the counterp:trty to terminate (likely involves making or receiving

compensation).• Selling the sw:tp to a third patty with the consent of the original counterparty

(uncommon).

LOS61.bIn a plain nnill:t (fixed-for-Aoating) interest-rate sw:tp. one patty :tgrees to p:ty :t Ao:ttingrate of interest on the notional amount and the counterp:trty :>greesto pay a fixed rate ofinterest.

The formul:t for the net p:tyment by the fixed-rate p:tycr. based on a 360-d:ty ycu andthe number of days in the sctdcment period is:

(net Iixcd rate p:tyment),

.(swap fixed rate - UBOR,.!)( num~f days ) (noaonal princip:tl)

In :on equity swap. the returns p:tyer makes payments hued on the return on a stock.portfolio. or index. in exchange for fixed- or Aoating-rue p:tyments. If the stock.portfolio. or index. declines in value over the period. the returns p:tycr receives theinterest payment and a p:tyment based on the pereent:>ge decline in value.

In .. currency swap. the notional principal (in two different currencies) is exchangedat the inception of the swap. periodic interest p:tyments in twO different currencies areexchanged on settlement dates. and the same notional amounts are exchanged (repaid)on the termination due of the swap.

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CONCEPT CHECKERS

1. Which of the following statements about swaps is Itast /ilttly correct?A. In an interest rate swap. the notional principal is swapped.B. The dd'ault problem is the most important limitation to the swap market.C. In a plain vanilla interest rate swap. fixed rates are traded for variable rates.

2. Which of the following statements about swaps is laut lilttly correct?A. The time frame of a swap is called its tenor.B. In a currency swap. only net interest payments are made.C. In a currency swap. the notional principal is actually swapped twice. once at

the beginning of the swap and again at the termination of the swap.

3. Which of the following statements is uast fjltt/y an advantage of swaps? Swaps:A. have little or no regulation.B. minimize default risk.C. have cusrcmized contracts.

4. In an equity swap:A. settlement is made only at swap termination.B. shares are exchanged for the notional principal.C. returns on an index an be swapped for fixed-rate payments.

5. In a plain vanilla interest rate swap:A. the notional principal is swapped.B. only the net interest payments are made.C. the notional principal is returned at the end of the swap.

6. Which of the following statements about swap markets is Itasr /ilrt/y correct?A. In an interest rate swap only the net interest is exchanged.B. The notional principal is swapped at inception and at termination of a

currency swap.C. Only the net difference between the dollar interest and the forcign interest is

exchanged in a currency swap.

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Usc the following data ro answer Questions 7 through 10.

Consider a 3·year annual currency swap that rakes place between a foreign firm (FF)wirh FC currency units and a U.S. firm (USF) with $ currency units. USF is the fixed·rate payer and FF is the floating-rate payer. The fixed interest rate at the initiation of theswap is 7%, and 8% at the end of the swap. The variable rate is 5% currendy; 6% at theend of year I; 8% at rhe end of year 2; and 7% at the end of year 3. At the beginning ofthe swap, $1.0 million is exchanged at an exchange rate ofFC2.0 = $1.0. At the end ofthe swap period, the exchange tate is FC 1.5. $1.0.

Note: With this currency swap, end-of-period payments arc based on bcginning-of-period interest rates.

7. At the initiation of the swap, which of the following statements is mDrt liltt"correct?A. FF gives USF $1.0 million.B. USF gives FF $1.0 million.C. USF gives FF FC2.0 million.

8. At the end of year 2:A. USF pays FCI40,000; FF pays S60,000.B. USF pays FC60,OOO; FF pays 570,000.C. USF pays USD70,OOO; FF pays FC60,OOO.

9. At the termination of the swap, FF gives USF which of the following notionalamounts?A. 51 million.B. FC2,000,000.C. FC 1,500,000.

10. At the end of year 3, FF will pay which of the foUowing total amounts?A. 51,080,000.B. 51,070,000.C. FC2,160,OOO

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Usc the following information to answer Questions 11 through 13.

Lambda Corp. has a floating-rate liability and wants a fixed-rate exposure. They enterinto a 2-year quarterly-pay S4,OOO,OOOfIXed-far-floating swap as the fixed-rate payer.The eounterparty is Gamma Corp. The fixed rate is 6% and the floating rate is 90-dayUBOR + I%, with both calculated based on a 360-day year. Realizations ofUBOR arc:

~nualizcd.J.IllQJ!.Current 5.0%In 1 quarter 5.5%In 2 quarters 5.4%In 3 quarters 5.8%In 4 quarters 6.0%

11. The first swap payment is:A. from Gamma to Lambda.B. known at the initiation of the swap.C. S5,OOO.

12. The second net swap payment is:A. S5,OOOfrom Lambda to Gamma.B. S4,OOOfrom Gamma to Lambda.c. S5,OOOfrom Gamma to Lambda.

13. The fifth net quarterly payment on the swap is:A. o.B. SI0,OOO.C. S40,OOO.

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ANSWERS - CONCEPT CHECKERS

I. A In an int ...... ra te swap. the notional principal is only used to calcula te Ih. inlu,,,paymenu and dots not change hands. The notional principal is only <xchangtd in acurrency SY.'ap.

2. B In a currency swap, paym.nts art not netted beaus e th.y art mad. in differ.ntcurrencies. Full inte test paym<nu a", made, and ehe no,ional principal is also txchangtd.

3. B Sv.-apsdo nor minimize default risk. Swaps art agrecmrnu between ","'0 or more parties,and there at. no guaran tees that on. of the pat,i es will nOI d.faul t, Not< ,bal swaps dogive traders privacy and. being privaee uansactions. have linle to no ~gulation and off«the ability to customize contracts [0 specific needs.

4. C Equity swaps involve one party paying the "'turn or 10lal return on a stock or indexperiodically in uchange for a fixed return.

5. B In a plain vanilla intcresl rate swap, interest paym.nu a", nened. Note Iba. nctionalprincipal is nOI exchanged and i. only used as a basis for calculating interest paym.nu.

6. C In a currency swap, full int.r.n paym.nts are mad e, and .h. notional principal isexchangtd.

7. B Because this u a currency swap, we know that the notiona! principal is exchangtd.Because USF holds dollats. it will b. handing over dollars 10 FF.

8. A Remember, the eur rency sv.'2pis pay 800ling on dollars and pay fix.d on foreign.Floaling at tho end of year I i. 6% of SI.O million. Since paym.nts are made in arrears,FF pays S6O,OOOand USF pays FCI40,OOO at the end of reat 2.

9. A The notional principal is txchangtd at termination. FF gives back what it berrewed,S 1.0 million, and ehe Itrminal exchange tal. is no. u ••d.

10. A FF is the Boating-rate dollar pay"r. FF will pay the return ofSI.O million in principala•• h. t.rmina.ion of the swap. plus the Boa.ing rat. paym.nt (in arrears ) of 8% • SI.Omillion. S80,OOO. The total paym.nt will be SI,080.000.

II. B The first paymem is based on the fix.d ra te and curr.n. LlBOR • I %, which a", both6%. ncr. i. no net paymenl mad. al the finl quarterly payment date and this i. knownat I.he initiation of th. swap.

12. C The second quart er paym.nt is b... d on th. ",a1iution of UBOR at ihe end of th. finl

quarter, 5.5%. Th. floaling nit u: (5.5%+1%)(:]4.000.000- 565.000. ne fixtd

ra te payment is S6O.000, making the ner paym.nt S5.000 from Gamma 10 Lambda.

13. B The fif,hqua" er ly ft02ting-ra,. paymen. is b ... d on the ",a1iu,ion of LIBOR a. rheend of the fourth quarter. which is 6%. With the 1% margin. the Boadng rare u 7%eempared te 6% lixtd, 10 the net paym.n. is SIO,OOO.

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The (011~;ng is • mint of the Dcrivatiw. princjple.l del'ped to .deltal the Icarai.ng outcomeItatemenu lel forth by CfA InlOtuk. Thil topic: il allO coveted in:

RISK MANAGEMENT ApPLICATIONS OFOPTION STRATEGIES

Study S.ssion 17

ExAM FocusThe most important asprct of this topic review is the interpretation of option profitdiagrams. Payoff diagrams for single put or single call positions wac covered in ouroptions review. In this review, we introduce profit diagrams and twO option mategies thatcombine stock with options. In a protective put position. we combine a share of stock anda pUt. With this strategy. we essentially purchase downside protettion for the stock (likeinsurance), A covered call position consists of buying a share of stock and selling a call onit. This strategy equates to sdling the upside potential on the stock in return for the addedincome from the sale of the call. On the Levell CFA~ EX2tn, you will not be required todraw payoff diagrams. but you are expected to know how to inrerpret them and find thebreakcvcn prier. maximum gains and losses. and the gaiN and 1055esfor any stock price atoption expiration.

LOS 62 .a: Determine the value at expiration, the profit, maximum profit,maximum loss, breakeven underlying price at expiration, and payoff grapb ofthe strategies of buying and selling calls and puts and determine the potentialoutcomes for investors using these strategies.

CFA!' Program CII"icu/um. VII/llmt 6, pagt J 83

Call Option Profits and Losses

Consider a call option with a premium of 55 and a strike price of S50. This means thebuyer pays S5 to the writer. At expi ration, if the price of the stock is less than or equalto the S50 strike price (the option has zero value), the buyer of the option is out S5, andthe writer of the option is ahead $5. As the Stock's price exceeds $50. the buyer of theoption starts to gain (brcakeven will come at S55, when the value of the stock equals thestrike price and the option premium). However, as the price of the stock moves upward,the seller of the option starts to lose (negative figures will start at S55, when the value ofthe stock equals the mike price and the option premium).

The profitlloss diagram for the buyer (long) and writer (short) of the call option we havebeen discussing at expiration is presented in Figure 1. This profitlloss diagram illustratesthe following:

• The maximum loss for the buyer of a call is the loss of the 55 premium(at any S :$ 550).

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• The breakeven point for the buyer and seller is the strike price plus the premium(at S • $SS).

o The profit potential to the buyer of the option is unlimited. and, conversely, thepotential loss to the writer of the call option is unlimircd.

• The call holder will exercise the option whenever the stock's price exceeds the strikeprice at the expiration date.

o The greatest profit the writer can make is the $S premium (at any S ::; SSO).• The sum of the profits between the buyer and seller of the call option is always zero;

thus, options trading is a U1'tJ·sumgltm~. There arc no net profits or losses in themarket. The long profits equal the shon losses.

Pro!wo,'s Now P/~lls~noticr thllt option profit dillgrllms show tbe gllin or loss~ to the long lind/or short option positionJ. Thty diff" from th~pllJoff dillgrtlml~ thllt w~ us~d in our options rtui~w in thllt prefir dillgrllml ,tjl«t th~ cosr o!th~

option [i,e •• the option premium}.

Figun: 1: ProfitlLoss Diagram for a Call Option

Proh.

Long all

.55 1---------,...o 0(- Brcakevcn IX • I'rrmium)

~5~------------~

Shon nIl

'----------~---------- Stock pricex = $50 $55

Put Option Profits and Losses

To examine the profits/lolses associated with trading put options, consider a put optionwith a $S premium. The buyer pays $5 to the writer. When the price of the stock atexpiration is greatct tha:l or equal to the 550 strike price. the put has zero value. Thebuyer of the option has a loss of $5. and the writer of the option has a gain of $5. &the stock's price falls below 550, the buyer of the put option starts to gain (breakcvenwill come at S4S. when the value of the stock equals the strike price less the optionpremium). However, as the price of the stock moves downward, the seller of the optionstarts to lose (negative profits will start at $45. when the value of the stock equals thestrike price less the option premium).

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Study S""OIl 17Ctos,s.RtftftDc:eto CFA INtitute Aui£ntd Rtading ,62 - Illik Managtmtut AppUcatioosof Option Suattgies

Figure 2 shows the profit/loss diagram for the buyer Oong) and seller (short) of the putoption that we have been discussing. This profitlloss diagram illusuates that:

o The maximum loss for the buyer of a put is the loss of the S5 premium(at any S ::=: S50).

o The maximum gain to the buyer of a put is limited to the strike price less thepremium (S50 - S5 = S45). The potential loss to the writer of the put is the sameamount.

o The breakeven price of a put buyer (sc11er) is at the strike price minus th e optionpremium (S50 - S5 = S45).

o The greatest profit the writer of a put can make is the S5 premium (S ::=: S50).o The sum of the profits between the buyer and seller of the put option is always zero.

Trading put options is a ;z.tTII-JUmgam~. In other words, the buy.-r's profit.s equal thewriter's losses,

Figure 2: ProfitfLoss Diagram for a Put Option

)'rotit

$45

Shon puto .•...•.•.•.•••.. ....;.__ Breakeven (X = Premium}. .

-S5 ••••.••.••.• . . lonS put

-S45

L-----~_;'----------Slock priceS45 X· S50

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Example: OptiOA profit calculatioDs

Suppose that both a all option and a put option have been wrinen on a stock with anexercise price of540. The current stock price is 542, and the calland put p~miums are53 and $0.75, rnpcctivcly.

Calculate the profit to the long and short positions for both the put and the all with anexpiration day stock price of535 and with a price at expiration ofS43.

Ans_r:Pnfit win be computed as ending opcion valuation - initial option cost.

StIKIr.t $35:

• Long call: SO- $3 • -$3. The option finished out-of-the-moncy, so thepremium is lost.

• Shon all: S3 - SO • 53. Because the option finished out-of-the-moncy, thecall writCf's gain equals the premium.

• Long put: $5 - 50.75. S4.25. You paid SO.75 for an option that is nowwonhS5.

• Shon put: SO.75 - S5 • -S4.25. You received SO.75 for writing the option,but you face a S5 lOISbecause the option is in-the-money.

• Long call: -53 + S3 • SO. You paid $3 for the option, and it is now worth S3.Hence, your net profit is zero.

• Shon call: S3 - 53 • SO. You received 53 for writing the option and now facea -53 valuation for a net profit of zero.

• Long put: -$0.75 - 50. -50.75. You paid SO.75 for the PUt option and theoption is now worthless. Your net profit is -$0.75_

• Shon pUt: SO.75 - 50. SO.75. You received 50.75 for writing the option andkccp the premium because the option finished out-of-thc-money.

A buyer of puu or a seller of ails will profit when the prlce of the underlying :wetdecreases. A buyer of calls or a seller of puu will profit when the price of the underlyingasset increases. In general, a put buyer believes the underlying asset is overvalued andwill decline in price. while a all buyer anticipates an increase in the underlying assct'sprice,

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Study Session 17Cro,,-~ft~Dce to CFA IrutilUte Asaigntd Reading 162 - RUk MaJUAtmmt Applications of Option Suategies

LOS 62.b: Determine the value at expiration, profit, maximum profit,maximum loss, breakeven underlying price at expiration, and payoff graphof a covered call strategy and a protective put strategy, and explain the riskmanagement application of each strategy.

CFA'" Prof7'1m Cu"i(ulum, Yolulnt 6, patt 189

Prllfmor's Note: Whtntvtr UN' combint IIptions with IISlttsor oth., IIptions, tht~ net cost of tht ,0mbintJ position is simply tht sum of tht prius paid for lht lont~ IIptumslassttl minus tht prllut/Is from tht option/lISltt salts (short pllsitillns). The

prllfits anJ IlIsstslin a positilln art simply tht valut IIf all tht IlSsm/llptillns in th«positions at apiratum minou tht net cest.

In writing covered call" the term (IIVtrtJ means that owning the stock covers theobligation to deliver stock assumed in writing thr call. Why would you write a coveredcall? You feel the stock's price will not go up any time soon, and you want to increaseyour income by collecting the call option premium. To add some insurance that thestock won't grt called away, the call writer can write out-of-the-money calls. You shouldknow that this strategy for enhancing onr's income is not without risk. The ,a/lwrittr istraJing the st«lti upsitUplluntial for tht caUprtmium.

Figure 3 illustrates the profit/loss of a covered call position at option expiration date.When the call was written, thr stock's price was S50. The calI's strike price was S55, andthe call premium was S4. The call is out-of-the-money, From Figure 3, we can observethat at expiration:

• If the stock doses bdow S50, the option will expire worthless, and the optionwriter's loss is offset by the premium income of S4.

• Breakeven for tht position is at S46 • S50 - S4. Brcakcven price. So - call premium.• If the stock doses between S50 and S55, the option will expire worthless. Because

this option was an out-of-the-money call, the option writer will get any stockappreciation above the original stock price and bdow the strike price. So the gain(premium plus stock appreciation) will be between S4 and $9.

• If stock closes above S55, the strike price, the writer will gc:tnothing morro Themaximum gain is S9 on the covered out-of-the-money call.

• The maximum loss occurs if the stock price goes to zero; the net cost of the position($46 = S50 stock loss offset by $4 premium income) is the maximum loss.

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Figure 3: Covered Call Profit and Lo ss for 5 = 50. C " 4. X = 55

Profit

o - - - - - --- - - - - - - - - - ",,! ---.' ,. ,.' ,

stock

maximum gain$9 ----------------------------~--- .' ,. ,

call prC'mium .,,' I

$4 ---------------------~,.- - - - - -- - - ---- covered call

.'

.................-$46

-$50o

Stock price

The desirabiliey of writing a covered call to cnhance income depends upon the chancethat the stock price will exceed the exercise price at which the trader writes the call. Inthis example, the writer of the call thinks the stock's upside potential is less than thebuyer expects. The buyer of the call is paying 54 to get any gain above 555. while theseller ha.s traded the upside potential above $55 for a payment of 54.

A protective put is an investment management technique designed to protect a stockfrom a decline in value. It is constructed by buying a stock and put option on that stock,

Look at the profitlloss diagrams in Figure 4. The diagraln on the left is the profit fromholding the stock. If the stock's value is up, your profit is positive and if the stock's valueis down, your profit is negative. Profit equals the end price, S,., 1= the initial price St'That is, profit. S... - 5" The diagram on the right side of Figure 4 is the profit graphfrom holding a long put, If the market is up, you lose your premium payment. and if themarket is down. )'ou have a profit.

The value of the put at termination wiII be max[O, X - STI. Your profit will bemax[O, X - s...lless the price of the put.

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Study 50"'011 17Ctoss-Rtfttenc:e to CFA IlIItilul. Asai£ntd Ruding .62 - RhI< Managtmtnt AppUcatiODl of Option Suattgies

Figure 4: Protective Put Components

Stock Long put

Profit Profit

Stock"'---s._---- value•

~ ~ Stockvaluex

Figure 5 shows the profia from the combination of a long put and a long stock (l.e .• aprotective put). Here it is assumed that the stock is purchased at $100 and that a putwith a strike price ofS100 is purchased for $4. Note that the put described in Figure 5 isat the money.

Figure 5: Protective Put

rtori,S,ock ...-, .

.'. .........Or----~.c.~..~.~.~------~(. .

-$4 I-----....-'.~.;1;: ... ~... ... ....... long pili.......Stock valueo S100 $104

What we should observe in Figure 5 is Ihal:

• A protective put cua your downside loues (maximum loss. S4) but leaves theupside potential alone (unlimited upside gains).Your maximum loss occurs al any price below S100.Losses between SO and $4 occur for stock prices between S100 and $104.You will not make a profit until the stock price exceeds $104 (breakeven),Breakeven price = So ~ premium.

••••

Note that a prrJUttiw PI" (st«/t plus a put) hIlStht sam« shap~profit diagram lIS a 101lg (ail.II could be replicated with a bond Ihat pays (X - premium) at expiration and a call at X.

ProftSSOTS Nou: R«all that this "/Ation wllSth~ bllSisfor our drriuation Df put-(all paTity. Th« PtJJ6/fi at ncpirrJtuma" Ulrntkal for a prot«ti,,~ put (S ~ P) ando a fidudllr, (111/1 (1+~ )T -t +cJ. a call with an exereis« priu ~I[U(JI to X and a

PU" discount bond that pays X at ocpirrJtion.

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KEy CONCEPTS,

LOS 62.aCall option value at expiration is Max (0, 5 - Xl and profit (loss) isMax (0, 5 - Xl - option cost.

Cell Optil'"

Buyer (long)SeUer (short)

Breakeven

MllXimwm u,u Mu;",u", win

Option CostUnlimited

UnlimitedOption CoS!

x • Option COst

Put value at expiration is Max (0, X - 5) and profit (I.,...) isMax (0, X - S) - option cost.

Pwt Opti."

Buyer (long)S.II., (short)

Breakeven

MIIJtimum L." MllXimwm Gm"Option Co.. x - Option Cost

x - Option COil Option Cost

X - Option eost

A all buyer (call seller) anticipates an increase (decrease) in the value of the underlyingassn.

A put buyer (put seller) anticipates a decrease (increase) in the value of the underlyingasset.

LOS 62.bA covered call position is a share of stock and a short (writren) call. Profits and losses arcmeasured relative to the net cost of this combination (So - premium).• The purposc of seUing a covered call is to enhance income by trading the stock's

upside potential for the call premium.• The upside potential on a covered call is Iimitcd to (X - SO>+ call prcmium received,

The maximum loss is the net cost (So - premium).

A protective PUt consists of buying a share of stock and buying a put. Profits and lossesarc measured rdative to the net cost (So + premium).• A protective put is a suategy to protect against a decline in the value of the stock.• Maximum gains on a protective put are unlimited, but reduced by the put premium

paid. Maximum losses arc limited to (So - Xl + put prcmium paid.

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CONCEPT CHECKERS

I. A call option sells for 54 on a S25 stock with a strike price of S30. Which of thefollowing statements is kast aeNlratr.A. At expiration, the buyer of the call will not make a profit unless the stock's

price exceeds 530.B. At cxpiration, the writer of the call will only experience a net loss if the price

of the stock exceeds S34.C. A covered call position at these prices has a maximum gain of 59 and the

maximum loss of the stock price less the premium.

2. An investor buys a put on a stock selling for S60, with a strike price of S55 for aS5 premium. The maximum gain is:A. S50.B. S55.C. S60.

3. Which of the following is the riskiest single-option transaction?A. Writing a call.B. Buying a put.C. Writing a put.

4. An investor will Ii/uly exercise a put option when the price of the stock is:A. above the mike price.B. below the mike price plus the premium.C. below the strike price.

5. A put with a strike price of $75 sells for $10. Which of the following statementsis leesr aCNI",u? The greatest:A. profit the writer of the put option can make is 510.B. profit the buyer of a put option can make is 565.C. loss the writer of a put option can have is $75.

6. At expiration, the value of a call option must equal:A. the larger of the strike price less the stock price or zero,B. the stock price minus the strike price, or arbitrage will occur.C. the larger of zero, or the stock's price less the mike price.

7. An investor writes a covered callan a $40 stock with an exercise price of 550 fora premium of S2. The investor's maximum:A. gain will be 512.B. loss will be S40.C. loss wiD be unlimited.

8. Which of the following combinations of options and underlying investmentshave similarly shaped profit/loss diagrams? IeA. covered call, and a short stock combined with a long call.B. short PUt option combined with a long call option, and a protective put.C. long call option combined with a short put option, and a long stock

position.

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ANSWERS - CONCEPT CHECKERS

1. A The buyer will no. have a net profit unless the stock price exceeds S3~ (suike price plusthe premium). The other ,u.emenu are true. At S3() ehe option will be exercised, butthe writer will only lose money in a net sense when .he Stock's price exceed.X • C • 530 • 54. The coveted call's maximum gain is ~ premium plus55 appreciation.

2. A This .. sumes the price of Ihe stock falls 10 uro and you gel 10 sell for S55. Your profilwould be $55 - 5 • S50.

3. A When buying either a call or a pur. the loss is limited '0 the amounl of the premium.When writing a put, the loss is limited to m~strike price if the stock falls 10 zero(bown'er, the writer keeps rhe premium). When wriling an uncovered call •• he $lOck

could go up infinil<iy, and rhe wri.er would be forced 10 buy the seeek in the openmarket and deliver at the strilce price-potential lossesare unlimited.

4. C The owner of a PUI profiu when the sloek falls. The PUI would be exercised whenthe price of the stock is bl"'", rhe strike price. The amount of .he premium is used .0de. ermine net profiu .0 each party.

5. C The greatest loss the pu. wriler can have is the strike price minus the premium receivedequals S65. The o.her sUlementS are true, The greatCSI profil lhc put wri.cr can make isrhe arnouru of the premium. The gre..... profi. for a pu. buyer occurs if the stock falls.0 lero and the bu)'Cr mak es the suike price minus the premium. Since op.ions are asere-sum game. Ihe maximum profit 10 the writer of the PUt must equal the maximumloss .0 the buyer of the pur,

6. C At .. pi ration. the value of a call mu.t be equal 10 its intrinsic value. which isMaxIO, 5 - XI. If the value of the stock is les. than rhe strike price. the inrrinsie value iszero. If the value of the stock is grater than the suike price •• he call is in-the-money andthe value of the call is the slock price minus rhe strike price. or S - X.

7. A As soon .. the Stock rises 10 the exercise price, the covered call wriler will cease to reali zea profit because the shon call move. inro-the-mcney, Each dollar gain on the stock;. then offset with a dollar los. on the short call. Since the option i, $10 cut-of-the-money, the covered call writer can gain this amount plus the $2 call premium. Thus.the nlaximum gain i.S2 + S10. S12. However. because the investor owns the stock.he or she could lose 540 if the stock goes to zero, but gain $2 from the call premium.Maximum loss is $38.

8. C A combined long call and a shon put, with exercise prices equal to the current stockprice. will have profiullosses at expiration nearly identiallo those of along stockposition.

~ p,.[tII'Jr~ '!.0It: TIN llUinl _, I.Itt lhil it I. JTlIUItIN ,.) ..ff Jittgrllm for Ihl NlmbinlJ~ 0l'ttJn ptlSlllons.

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The following is • rnkw of the Alkm2tn-c lnwltmmu principles dcsignrd to 2ddttss th~lel-mingoutcome: lutemcnt' Jct forth by CfA lnJtitute. Thi. topic is, also cO\'trcd ift!

INTRODUCTION TO ALTERNATIVEINVESTMENTS

Study S... ioo 18

ExAM Focus

"Alternative investments" collectively refers to the many asset classes tbat fall outside thetraditional dc6nitions of stocks and bonds. Tbis catcgory includes hedge funds. printccquity. real estate. commodities, and other alternative investments, primarily collectibles.Eacb of these alternative investments hao unique characteristics that require a diffcrcntapproach by the analyst. You should be aware of the diffcrent strategies. fcc structures.due diligence, and issues in valuing and c:alculating returns with each of the alternativeinvestments discussed in this topic review.

LOS 63.a: Compare alternative investments with traditional investments.

CF-A®Program Cllrritll/llm. VII/llmt 6; pagt 210

Alternauve investments differ from traditional investments (publicly traded stocks.bonds. cash) both in thc types of asscts and securities included in this asset class andin the structure of the investment vehicles in which these assets arc held, Manage rs ofalternative investment portfolios may usc derivatives and leverage, invest in illiquidassets, and short securities. Many types of rc:alestate investment arc consideredalternatives to traditional investment as well. Types of alternative investment structuresinclude hedge funds. private equity funds. various types of rc:alestate investments,and some ETFs. Fee structures for alternative investments arc different than thoseof traditional investments. with higher management fcc. on average and ofren withadditional incentive fccs based on performance. Alternative investments as a group havehad low returns correlations with traditional investments, Compared to traditionalinvestments, alternaeive invesuncnu cxhibit:

• Less liquidity of asseu held.• More specialization by investment managers.• Less regulation and transparcncy.• Morc problcmatic and less availablc historic:al return and volatility data.• Diffcrent legal issues and tax treatments,

LOS 63.b: Describe categories of alternative investments.

CFA® Program CllrrifJ//um. VII/llmt 6; pagt 214

We will cxamine 6vc catcgories of alternative investments in detail in this topic review,Here we introduce each of those categories.

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1. Hedge funds. These fund. may use leverage, hold long and short positions. usederivatives, and invest in illiquid assets, Managrrs of hedge funds use a greatmany dilfrrrnt stratrgics in attempting to grnrratr invesrmene g;:ains, They do notnecessarily hedge risk as the name might imply.

2. Private rquiry funds. 11$ the name suggr.ts. private equity fund. invest in thr equityof companies that are not publicly traded or in the equity of publicly traded firm.that thr fund intends to eake private. Leveraged buyout (LBO) funds use borrowedmoney to purchase rquity in established companies and comprise the majority ofprivaee equity investmenr funds. A much .mallrr portion of these funds. venturecapital funds. invest in or finance young unprovrn compania at various .tagcsearly in their existence. For our purposes here we will also consider invcsting in thesecurities of financially distressed companies to be privare equity, although hedgefunds may hold these also.

3. Real estate, Real estate investments indoor residential or commercial properties aswell as real estate backed debt. These investments are held in a varirty of Structuresincluding full or leveraged ownership of individual properties, individual real estatebacked loans, private and publicly traded securities backed by pools of properties ormortgagcs. and limited partnership s,

4. Commoditirs. To gain exposurr to changcs in commoditics prices, investors canown physiw commodities, commodities derivatives, or the equity of commodityproducing firms. Some funds seek exposurr to the returns on various commodityindices. oftrn by holding derivatives contracts that are expected to track a spreificcommodity index,

5. Other, This catrgory includes investment in tangible collectible assets such asfinr wines, stamps. automobiles, antique furnieure, and art, as well as patents, anintangible a55et.

LOS 63.c: Describe potential benefits of alternative investments in the contextof portfolio management.

CFA® Program CIU,icu/um. Yo/UIM 6. pagt 217

Alrernaeive investment returns have had low correlations with those of traditionalinvestments over long periods, The primary motivation for holding alternativeinvestments is their historically low cerrelaeion of returns with those of traditionalinvestments. which can reduce an invcstor's overall portlOlio risk. However, therisk measures we usc lOr traditional assets may not be adequate to capture the riskcharacteristics of alternative investments, Managrrs ofien consider measures of riskother than standard deviation of return •• such as worst month or historical frequency ofdownside returns.

Historical returns lOr alternative investments have bern highrr on avrragr than fortraditional investments, so adding alternative investments to a uaditional portfolio mayincrease expected returns. The rrasons lOr these higher returns are thought to be thatsome alternative investments are less rffieirndy priced than uaditional assets (providing

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Sludy Stsslon 18Cros$-~fmoce 10 CFA lrutitutt Assigned~adin8 .63 - Inuoduction to A11.malM! Inwsunenu

opponunities for skilled managers). that airernarive investments may ofTerextra returnsfor bcing illiquid. and that alternative investments often use leverage.

While it seems that adding alternative investments to a portfolio wiu improve bothportfolio risk and expected return. choosing the optimal portfolio allocation toalternative investments is complex and there are potential problems with historicalreturns data and traditional risk measures. SUnlillO"hip bilts refrrs to the upward bias ofreturns if data only for currently existing (surviving) firms is included. Since survivingfirms tend to be those that had better-than-average returns. excluding the returns datafor failed firms results in average returns that arc biased upward. &ultfill bias refers tobias introduced by including the previous performance data for firms recently added to abenchmark index. Since firms that are newly added to an index must be those that havesurvived and done better than avcra~. including their returns for prior years (withoutincluding the previous and current returns for funds that have not been added to theindex) tends to bias index returns upward.

LOS 63.d: Describe hedge funds, private equity, real estate, commodities,and other alternative investments, including, as applicable, strategies, sub-categories, potential benefits and risks, fee structures, and due diligence,

LOS 63.e: Describe issues in valuing, and calculating returns on, hedge funds,private equity, real estate, and commodities.

HEDGE FUNDS

Hedge funds employ a large number of different strategies. Hedge fund managershave more Bexibility than mana~rs of traditional investments. Hedge funds can uscleverage, take short equity positions. and take long or shon positions in derivatives.The complex nature of hedge fund transaetions leads managers to trade through primebrokers. who provide many services including custodial services. administrative services.money lending, securities lending for shon sales. and trading. Hedge fund managerscan negotiate various service parameters with the prime brokers. such as marginrequirements.

Hedge fund return objectives can be stated on an absolute basis (e.g .• 10%) or ona relative basis (e.g .• returns 5% above a specific benchmark return) depending onthe fund strategy. Hedge funds arc kss 'q;ulllt~d than traditional investments. Likeprivate equity funds, hedge funds arc typically set up as limited partnerships. withthe investors as the limited (liability) partners. A hedge fund limited pannership maynot include more than a proscribed number of investors. who must possess adequatewealth. sufficient liquidity. and an acceptable degree of investment sophistication. Themana~ment firm is the general partner and typically receives both a mana~ent fccbased on the value of assets managed and an incentive fcc based on fund returns.

Hedge fund investments arc less liquid than traditional. publicly traded investments.Restrictions on redemptions may include a lockup period and/or a notice period.A lockup period is a time after initial investment during which withdrawals arc not

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allowed, A notice period, typir:ally 30 to 90 days, is the amount of time a fund has aftcrrc:ceiving a redemption «quest to fulfill the request. Additionalli:cs may be chargedat redemption. All of these, of course, discourage redempdcns. Hedge fund managersoften incur signifir:ant transactions cosu when they redeem shares. Redemption feescan offset these:cosu. Notice periods allow time for managers to reduce positions inan orderly manner, Redemptions often increase when hedge fund performance is poorover a period, and the cosu of honoring redemptions may furthc:r decrease: the value ofpartnership interests, This is an additional source: of risk for hedge fund investors.

A fund of funds is an investment company that invests in hedge funds, giving investorsdiversification among hedge fund strategies and allowing smaller investors to accesshedge funds in which they may not be able to invest direcdy, Fund of funds managerscharge an additional layer of fees beyond the fecs charged by me individual hedge fundsin the portfolio.

Hedge Fund Strategies

Similar to categorizing alternative investments, classifying hedge funds can also bechallenging. Acc:ording to Hedge Fund Research, Inc., there arc: four main dassifir:ationsof hedge fund strategies:

1. Evcnt-drivcn strategies are typically based on a corporate restructuring oracquisition that creates profit opportunities for long or short positions in commonequiey, preferred equiey, or debt of a spc:c:i6ecorporation. Subcategories are:• Merger arbilf2&C: Buy the shares of a firm being acquired and sdl short me firm

maldng the acquisition.• Disucsscd/rc:suucturing: Buy the (undervalued) securities of finns in

financial distress when analysis indicates value will be increased by a successfulrestructuring; possibly short overvalued security types at the same time.

• Activist shareholder: Buy sufficient cquiey shares to inAuenee a company'spolicics with me goal of increasing company value.

• Special situations: Invest in the securities of firms that arc issuing orrepurchasing securities, spinning off divisions, selling assets, or distributingcapital.

2. Rrlativc value stratc:gies involve buying a securiey and sdling short a related securieywith the goal of profiting when a perceived pricing discrepancy between the two isresolved.• Convertible ubitrage 6xc:d income: Exploit pricing discrepancies between

convertible bonds and the common stock of the issuing companies.• Asset·backed fixed income: Exploit pricing discrepancies among vuious

mortgage· backed securities (MBS) or asset-backed securities (ABS).• General fixed income: Exploit pricing discrepancies between fixed income

securities of various rypcs.• Volatility: Exploit pricing discrepancies arising from differences between returns

volatiliey implied by options prices and manager cxpectarions of future volatiliey.• Multi-strategy: Exploit pricing discrepancies among securities in asset classes

different from those previously listed and across asset classes and markets.

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3. Macro suategie. arc based on global economic trends and events and may involvelong or shorr positions in equities, fixed income, currencies, or commodities.

4. Equity hedge fund straregles seck to profit from long or short positions in publiclyuaded equities and derivatives with equities as their underlying assets.• Market neutral: Usc technic:al or fundamental analysis to select undervalued

equities to be held long, and to select overvalued equities to be sold short, inapproximately equal amounts to profit from their relative price movementswithout exposure to market risk.

• Fundamental growth: Usc fundamental analysis to find high-growth companies.Identify and buy equities of companies that are expected to sustain relativelyhigh rates of capital appreciation.

• Fundamental value: Buy equity shares that arc believed to be undervaluedbased on fundamental analysis. Here it is the hedge fund structure, ratherthan the type of assets purchased, that results in classification as an alternativeinvestment.

• Quantitative directional: Buy equity securities believed to be undervalued andshort securities believed to be overvalued based on technical analysis. Marketexposure may vaty depending on relative size of long and short portfoliopositions.

• Shon bias: Employ predominantly short positions in overvalued equities,possibly with smaller long positions, but with negative market exposure overall.

Many hedge funds tend to specialize in a specific strategy at fim and over time maydevelop or add additional areas of expertise, becoming multi-strategy funds.

Hedge Fund Potential Benefits and Risks

Hedge fund returns have tended to be better than those of global equities in downequity markets and to lag the returns of global equities in up markets. Different hedgefund strategies have the best returns during different time periods. Statements about theperformance and diversification benefits of hedge funds arc problematic because of thegreat variety of mategies used. Less-than-perfect correlation with global equity returnsmay offer some diversification benefits, but correlations tend to increase during periodsof financial crisis.

Hedge Fund Valuation

Hedge fund values arc based on market values for traded securities in their portfolios,but must usc modd (estimated) values for non-traded securities, For traded securitiesit is most conservative to usc the prices at which a position could be closed: bid pricesfor long positions and ask prices for shorr positions. Some funds usc the average of thebid and ask prices instead. In the case of illiquid securities, quoted market prices may bereduced for the degree of illiquidity. based on position sizc compared to the tOtal valueof such securities outstanding and their average trading volume. Some funds calculatea "trading NAY" using such adjustments for illiquidity. Trading NAY is different fromthe c:alculated net asset value required by accounting standards, which is based on eithermarket or model prices,

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Hedge Fund Due Diligence

Selecting hedge funds (or funds of funds) requires significant invcstigation of theavailable funds. This may be somewhat hampered by a lack of transparency by fundsthat consider their strategies and systems to be proprietary information. The fact thatthe regulatory requirements for hedge fund disclosures arc minimal presents additionalchallenges. A partial list of faCtors to consider when selecting a hedge fund or a fund offunds includes an examination of the fund's:

• Investment strategy.• Investment process.• Source of competitive advantages.• Historical returns.• Valuation and returns calculation methods.• Longevity.• Amount of assets under management.• Management style.• Key person risk.• Reputation.• Growth plans.• Systems for risk management.• Appropriateness of benchmarks.

The analysis of these factors is challenging because a lack of persistence in returns maymean that funds with better historical returns will not provide better- than-averagereturns in the future. Additionally, many of the items for due diligence, such asreputation, risk management systems, and management style, are difficult to quantify ina way that provides clear choices for potential investors. Further, previously profitablesuatcgies to exploit pricing inefficiencies are likely to become less profitable as morefunds pursue the same strategy.

PRIVATE EQUITY

The majority of private equity funds invest either in private companica or publiccompanies thcy intend to take private (leveraged buyout funds}, or in early stagecompanies (venture apical funds). Two additional, but smaller, categories of privateequity funds are distressed investment funds and developmental capital funds.

A private equity fund may also charge fees for arranging buyouts, fees for a deal thatdocs not happen, or fees for handling asset divestitures after a buyout.

Private Equity Strategies

Leveraged buyouts (LBOs) are the most common type of private equity fundinvestment. "Leveraged" refers to the fact that the fund's purchase of the portfoliocompany is funded primarily by debt. This may be bank debt (leveraged debt), high-yield bonds, or mezzanine financing. Mezzanine financing refers to debt or preferredshares that arc subordinate to the high-yield bonds issued and carry warrants orconversion fcatures that give investors parcicipation in equity value increases.

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PrI1/ml1r'sNom ~ wiU uu a similar tum, "mtt:Z4nint-J14gt financing, •~ whtn Ttfi"ing to a lau-Jtagt investment in a IItnturt capi141cl1mpan, that is~ prtparing tl1gl1public vUt an fPO. Hut wt art "/r"ing tl1a 'lpt D/ucuri'l

ramtr than a 'lpt D/ investment.

Two typc:s ofLBOs arc management buyouts (MBOs), in which the existingmanagement team is involved in the purchase, and management buy-ins (MBIs), inwhich an external management tearn will replace the existing management tam.

In an LBO, the private equity firm seeks to increase the value of the firm through somecombination of new management, management incentives, restructuring. COStreduction,or revenue enhancement. Firms with high cash Row are attractive LBO candidatesbecause their cash Row can be used to service and eventually pay down the debt taken onfor acquisition.

Yentu"' apital (YC) funds invest in companies in the early stages of their development.The investment often is in the form of equity but can be in convertible preferred sharesor convenible debt. While the risk of start-up companies is often grato returns onsuceessful companies can be very high. This is often the case when a company has grownto the point where it is sold (at least in part) to the public via an IPO.

The companies in which a venture capital fund is invested are referred to as its ponfoliocompanies. Yenture capital fund managers are closely involved in the development ofportfolio companies, often sitting on their boards or filling key management roles.

Categorization of venture capital investments is based on the company's stage ofdevelopment- Terminology used to identify venture firm investment at different stages ofthe company's life includes the following:

I. The formative stage refers to investments made during a firm's earliest period andcomprises three distinct phases.• Angel investing refers to investments made very early in a firm's life. often the

"idea" stage. and the investment funds are used for business plans and assessingmarket potential. The funding source is usually individuals ("angels") ratherthan venture capital funds.

• The seed stage refers to investmenu made for product development, marketing.and market research. This is typically the stage during which venture capitalfunds make initial investments, through ordinary or convenible preferred shares.

• Early stage refers to investments made to fund initial commercial productionand sales.

2. Later lIage investment refers to the suge of development where a company alreadyhas production and tala and is operating as a commercial entity. Investmentfunds provided at this stage ate typically used for expansion of production andlorincreasing sales though an expanded marketing ampaign.

3. Meuaoine-stage financing refers to capital provided to prepare the firm for an IPO.The term refers to the timing of the financing (between private company and publiccompany) rather than the type of financing.

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Other Private Equity Strategies

Developmental capital or minority equity investing refers to the provision of capitalfor business growth or restructuring. The firms financed may be public or private. In thecase of public companies, such financing is referred 10 as private investment in publicequities (PIPEs).

Distressed invesling involves buying debt of mature companies Ihal arc experiencingfinancial difficulties (potenrlally or currently in default, or in bankruptcy proceedings).Investors in distressed debe oft.n take an active role in the turnaround by workingwith manag.m.nl on reorganization or 10 determine the direction the company shouldrake. Distressed debt investors arc sometimes referred 10 as lIu/rurl inveuon. Note thaIalthough distressed debt investing is included in Ihe private equity calegOry, some hedgefunds invest in the debt of financially distressed companies uwell.

Private Equity Structure and Fees

Similar to hedge funds, private equity funds arc typically structured as limitedpartnerships. Committ.d capital is the amount of capiral provided 10 the fund byinvestors, The committed capital amount is typically not all invested immediatelybut is "drawn down" (invested) as securities are identified and added 10 the portfolio.Committed capital is usually drawn down over three 10 five years, bUI the drawdown'triod i. al the discreticn of the fund manager. Management fees arc typically 1% to 3%of committed caplral, rather than invested capital.

Incentive fccs for private equity funds are typically 20% of profits, bUI these fees arenot earned until after the fund has returned investors' initial capital. II is possible lhatincentive fees paid over time may exceed 20% of the profits realized when all portfoliocompanies have been liquidated. This situation arises when returns on portfoliocompanies are high early and decline later, A dawback provision requires the manager 10

return any periodic incentive fees 10 investors that would result in investors receiving lessthan 80% of the profits generated by portfolio investments as a whole.

Private Equity &it Strategies

The average holding period for companies in private equity portfolios is five years. Therearc several primary methods of exiting an investment in a portfolio company:

1. Trade sale: Sell a portfolio company 10 a competitor or another strategic buyer.

2. [PO: Sell all or some shares of a portfolio company 10 the public.

3. Recapitalization: The company issues debt to fund a dividend distribution 10 equityholders (the fund). This is nOI an exit, in thaI the fund still controls the company,but is ofte.n a step toward an nit.

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4. Secondary sale: Sell a ponfolio company to anomer privatt equity firm or a groupof investors.

5. Write-offlliquidation: Reassess and adjust to take losses from an unsuccessfuloutcome.

Private Equity Potential Benefits and Risks

There is evidence mat over me last 20 years returns on private equity funds have beenhigher on average than overall stock returns. Less-than-perfect cerrelarion of privateequity returns with traditional investment returns suggests that mere may be portfoliodiversification benefits from including private equity in portfolios. The standarddeviation of private equity returns has been higher man the standard deviation of equityindex returns. suggesting grcattr risk. As with hedge fund returns data. private equityreturns data may suffer from survivorship bias and backfill bias (both lead to overstatedreturns). Because portfolio companies arc revalued infrequendy. reponed standarddeviations of returns and correlations of returns wim equity returns may both be biaseddownward.

Evidence suggests that choosing skilled fund managers is important. Differencesbetween the returns to tOP quartile funds and bottom quartile funds are significant andperformance rank shows persistence over time.

Private Equity Company Valuation

Valuation for private equity portfolio companies is essentially me same as valuing apublidy traded company. almough me discount rate or multiples used may be differentfor private companies.

• Market/comparables approach: Market or private transaction values of similarcompanies may be used to estimate multiples of EBITDA. net income. or revenue tousc in estimating the portfolio company's value.

• Discounted cash flow approach: A dividend discount model falls into this category.as does calculating the prescnt value of free cash flow to the firm or free cash flow toequity.

• Asset-based approach: Either the liquidation values or fair market values of assetscan be used. Liquidation values will be lower as they arc values that could be realizedquickly in a situation of financial distress or termination of company operations.Liabilities arc subtracted so that only the equity ponion of the firm's valuc is beingestimated.

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Example: Ponfolio c:ompaay c:ompuablcs approach

A private equity fund is valuing a French private manufacturing company. EBITDAand marlu:t values for four publicly traded European companies in the same industryan: shown in the foll_ing table (in millions of .uros):

Company I:Company 2:Company 3:Company 4:

EBITPA£100£250£250£275

Market Value£1.000E2.000£1.500E2.200

The: estimated EBITDA for the French company is £175 million. Using an aft rage ofthe four companies as the industry multiple. eSDmate the marlu:t value for the Frenchcompany.

ADIIWCr:

Company I:Company 2:Company 3:Company 4:

EBIIDAldIIhiplc£1.000 I £100.10,.£2.000 I £250 • ax£1.500 I £250.6,.£2.200 I £275 • 8,.

The: aftrage multiple for thc:sc four companies is 8,.. Based on the French company'sexpected EBITDA of £175 million. its estimated value is £175 million,. 8 • £1.400million or £1.4 billion.

Private Equity Due Diligence

Because of the high leverage typically wed for private equity funds. investors shouldconsider how interest rates and the availability of capital may affect any requiredre6nancing of portfolio company debt, The choice of managrr (general partner) is quiteimportant and many of the factors we listed for hedge fund due diligence also apply toprivate equity fund investments. Spcci6cally, the operating and 6nancial experience ofthe manager. the valuation methods used, the incentive fcc structures, and drawdownprocedures arc all important areas to investigate prior to investing.

REAL ESTATE

Investment in real estate can provide income in the form of rents as well as the potentialfor capital ga.ins. Real estate as an asset class can provide diversi6cation bene6ts to aninvestor's portfolio and a potential in Ration hedge because rents and real estate valucstend to increase with inAation. Real estate investments can be differentiated accordingto their underlying assets. Assets included under the heading of real estate investmentsinclude:

• Residential property-single.famiJy homes.

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• Commercial property-produces income.• Loans with residential or commercial property as collateral-mortgages ("whole

loans"), construction loans.

Forms of Real Estate Investment

Residential property is considered a direct investment in real estate. Some buyers paycash but most take on a mortgage (borrow) to purchase, The issuer (lender) of themortgage has a direct investment in a whole loan and is said to "hold the mortgage."Issuers often sell the mortgages they originate and the mOrtgages arc then pooled(securitized) as publicly traded mortgage-backed securities (MBS), which represent anindirect investment in the mortgage loan pool. Property purchased with a mortgage isreferred to as a kllmJtta investmmr and the owner's equity is the propetty value minusthe outstanding loan amount. Changes in property value over time, therefore, affect theproperty owner's equity in the property.

Commercial real estate properties generate income from renrs. Homes purchased forrental income arc considered investment in commercial property. Large properties (e.g.,an office building) arc a form of direct investment for institutions or wealthy individuals,either purchased for cash or leveraged (a mortgage loan is taken for a portion of thepurchase price). Long time horizons, illiquidity, the large size of investment needed, andthe complexity of the investments make commercial real estate inappropriate for manyinvestors. Commercial real estate properties can also be hcld by a limited partnership inwhich the partners have limited liability and the general partner manages the investmentand the properties, or by a real estate investment trust (REin.

As. with residential mortgages, whole loans (commercial property mortgages) areconsidered a direct investment. but loans can be pooled into commercial mongage-backed securities (CMBS) that represent an indirect investment.

Real estate investment trusts (REITs) issue shares that trade publicly like shares ofstock. RElTs arc often identified by the type of real estate assets they hold: mortgages.hotel properties. malls. office buildings. or other commercial propctty. Income is wedto pay dividends. Typically. 90% of income mwt be distributed to shareholders to avoidtaxes on this income that would have to be paid by the REIT before distribution toshareholders.

Other Real Estate Assets

Two additional assets considered as real estate are timberland and farmland. forwhich one component of returns comes from sales of timber or agricultural products.Timberland returns also include price changes on timberland. which depend onexpectations of lumber prices in the future and how much timber has been harvested.Farmland returns arc based on land price changes. changes in farm commodity prices,and the quality and quantity of the crops produced.

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Potential Benefits and Risks of Real Estate

Real estate performance is measured by three different types of indices. An appraisalindex, such as those: prepared by the National Council of Real Estate InvestmentFiduciaries (NCREIF), is based on periodic estimates of property values. Appraisalindex returns arc smoother than those based on actual sales and have the lowest standarddeviation of return. of the various index methods. A rcpnt sale. index is based on pricechanges for properties that have sold multiple times. The sample of properties sold andthus included in the index is not necessarily random and may not be representative ofthe broad spectrum of properties available (an example of sample selection bias). REITindices arc based on the actual trading prices of REIT shares, similar to equity indices.

Historically, REIT index returns and global equity returns have had a relatively strongcorrelation (on the order ofO.G) because business cycles affeet RElTs and global equitiessimilarly. The correlation between global bond returns and REIT returns has beenvery low historically. In either case diversification bcndits can result from includingreal estate in an investor's portfolio. However, the methods of index construction(e.g., appraisal or repeat sales indices) may be a factor in the low reported correlations,in which case actual diversification bene6ts may be less than expected.

Real Estate Valuation

Three methods arc commonly used to value real estate:

• The comparable sales approach bases valuation on recent sales of similar properties.Values for individual properties include adjustments for differences between thecharaceeristics of the specific property and those of the properties for which recentsales prices arc available, such as age, location, condition, and size.

• The income approach estimates property values by calculating the present value ofexpected furure cash Bows from property ownership or by dividing the net opcratingincome (NO!) for a property by a capitalization (cap) rate. The cap rate is a discountrate minus a growth rate and is estimated based on factors such as general businessconditions, property qualities, management effectiveness, and sales of comparableproperties. Nore tbat dividing by a cap rate of 12.5% is the same as using a multipleof 8 times NOI (II 0.125 • 8).

• The cost approach estimates the replacement cost of a property. The cost of landand the cost of rebuilding at current construction costs arc added to estimatereplacement COst.

Value estimates for real estate investment trusts can be income based or asset based.The income- based approach ;s similar to the income approach for a specific propertyand uses some measure of cash Bow and a cap rate based on the factors we notedpreviously for the income approach. One measure of cash flow for a RElT is fundsfrom operations (FFO). FFO is calculated from net income with depreciation addedback (because depreciation is a non-cash charge) and with gains from property salessubtracted and losses on property sales added (because these gains and looses arc assumedto be nonrecurring). A second measure of cash Bow is adjusted funds from operations(AFFO), which is FFO with recurring capital expenditures subtracted. AFFO is similarto frec cash Bow. The asset-based approach provides an estimate of the net asset value ofthe REIT by subtracting total liabilities from the total value of the real estate assets anddividing by the number of shares outstanding.

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Real Estate Investment Due Diligence

Property values Aucruate because of global and national economic factors. localmarket conditions. and interest rate levels. Other specific risks include variation inthe abilities of managers to select and manage properties, and changes in regulations.Decisions regarding selecting. financing. and managing rcal estate projects directlyaffect performance. The degree of leverage used in a real estate investment is importantbecause leverage amplifies losses as well as gains.

Dinrtsua pTrJp~rri~1investing has additional risk f.actors compared to investing inproperties with sound financials and stable operating histories. &41 estat« aewlDpmt1lthas additional risk f.actors including regulatoty issues such as zoning. permitting. andenvironmental considerations or remediation. and economic changes and financingdecisions over the development period. The possible inability to get long-term financingat the appropriate time for properties initially developed with temporary (short-term]financing presents an additional risk.

COMMODITIl!S

While it is possible to invest directly in commodities such as grain and gold. the mostcommonly used instruments to gain exposure to commodity prices arc derivatives.Commodities themselves arc physical goods and thus incur costs for storage andtransponation. Returns arc based on price changes and not on income streams.

Futures. forwards. options. and swaps arc all available forms of commodity derivatives.Futures trade on exchanges; some options trade on exchanges while others trade overthe counter; and forwards and swaps arc over-the-counter instruments originated bydealers. Futures and forwards arc conrracrual obligations to buy or sell a commodity at aspecified price and time. Options convey the right. but not the obligation. to buy or sella commodity at a specified price and time. Other methods of exposures to commoditiesinclude the following:

• Exchange-traded funds (commodity ETFs) arc suitable for investors who arc limitedto buying equity shares. ETFs can invest in commodities or commodity futures andcan track prices or indices.

• Equities that are dirccsly linked to a commodity include shares of a commodityproducer. such as an oil producer or a gold mining firm, and give investorsexposure to price changes of the produced commodity. One potential drawback tocommodity-linked equities is that the price movements of the stock and the pricemovements of the commodity may not be perfectly correlated.

• Managed futures funds arc actively managed. Some managers concentrate onspecific sectors (e.g.• agricultwal commodities) while others arc more diversified.Managed futwe funds can be structured as limited partnerships with fees like thoseof hedge funds (e.g .• 2 and 20) and restrictions on the number. net worth. andliquidity of the investors. They can also be structured like mutual funds with sharesthat arc publicly traded so that retail investors can also benefit from professionalmanagement. Additionally. such a structure allows a lower minimum investment andgreater liquidity compared to a limited partnership structure.

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• Individual managed accounu provide an alternative to pooled funds for high networth individuals and institutions. Accounts arc tailored to the needs of the specificlnvesrcr,

• Specialized funds in specific commodity sectors can be organized under any of thestructures we have discussed and focus on certain commodities, such as oil and gas,grains, precious metals, or industrial metals.

Potential Benefits and Risks of Commodities

Returns on commodities over time have been lower than returns on global stocksor bonds. Sharpe ratios for commodities as an asset class have been low due to theselower returns and the high volatility of commodities prices. As with other investments.speculators can carn high returns over short periods when their expectations about short-term commodity price movements arc correct and they act on them.

Historically. correlations of commodity returns with those of global equities and globalbonds have been low, typically less than 0.2, so that adding commodities to a traditionalportfolio can provide diversification benefits. Because commodity prices tend to movewith inRation rates, holding commodities can act as a hedge of inAation risk. To theextent that commodities prices move with inAation the rca! return over time would bezero, although futures contracts may offer positive real returns.

Commodity Prices and Investments

Spot prices for commodities arc a function of supply and demand. Demand is affectedby the value of the commodity to end-users and by global economic conditions andejeles. Supply is affected by production and storage costs and existing inventories. Bothsupply and demand arc affected by the purchase. and sales of non-hedging investors(speculators).

For many commodities, supply is inelasric in the shon run because of long lead timesto alter production levels (e.g .• drill oil wells, plane crops. or decide to plant less ofthem). As a result, commodity prices can be volatile when demand changes significantlyover the economic cycle. Production of some commodities, especially agriculturalcommodities, can be significantly affected by the weather, leading to high prices whenproduction is low and low prices when production is high. Costs of extracting oil andminerals increase as more expensive methods or morc remote arcas arc used. To estimatefuture needs, commodities producers analyze economic events, government policy, andforecasts of future supply. Investors analyze inventory levels, forecasts of production,changes in government policy, and expectations of economic growth in order to forecastcommodity prices.

Commodity Futures Pricing

Whelt today and wheat six months from today are different products. Purchasing thecommodity today wiJI give the buyer the usc of it if needed, while contracting for wheat

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to be delivered six months from today avoids storage costs and having cash tied up. Anequation that considers these aspecu is:

future. price '" .pot price (1 + risk-free rate) + storage cosrs - convenience yield

Convenience yield is the value of having the physical commodity for we over theperiod of the futures contract. If this equation docs not hold. an arbitrage uansaction ifpossible.

If there is lirde or no convenience yield. futures prices will be higher than spOt prices. asituation termed contango. When the convenience yield is high. futures prices will beless than spot prices. a situation referred to as backwardation.

Three sources of commodities futurcs returns are:

I. Roll yield-The yield due to a difference between the spot price and futures price.or a difference between tWOfutures prices with different expiration dates. Futuresprices converge toward spot prices as contracts get closer to expiration. RoD yield i.positive for a market in backwardation and negative for a markct in contango.

2. Collateral yield-The interest carned on collateral required to enter into a futurescontract.

3. Change in spot priccs- The total price return is a combination of the change inspot prices and the convergence of futures prices to spot prices over the term of thefutures contract.

Other Alternation: Investments

Variou. types of tangible collectibles are considered investments, including rare wines.art. rare coins and stamps. valuable jewelry and watches. and sport. memorabilia. Thereis no income generation but owners do get enjoyment from usc. as with a collectibleautomobile. Storage cosu may be significant. especiaDy with art and wine. Specializedknowledge is required. the markets for many collectibles arc illiquid. and gains resultonly from increases in the priccs of these assets.

LOS 63_f: Describe, calculate, and interpret management and incentive feesand net-of-fees returns to hedge funds.

CFA® Program CUTTiculum. v"lumt 6. pagt 226

Hedge Fund Fees

The total fee paid by investors in a hedge fund consists of a management fee and anincentive fcc. The managemcnt fcc is carned regardless ofinvc:stment performance andincentive fees arc a portion of profits. The most common fcc structure for a hedge fundis "2 and 20' or "2 plus: 2% of the value of the assets under management plw anincentive fcc of20% of profits.

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Profies can be (1) any gains in value, (2) any gains in value in excess of the managementfcc, or (3) gains in excess of a hurdle rate. A hurdle rate can be set either as a percentage(e.g., 4%) or a rate plus a premium (e.g., UBOR + 2%). A harrl hurrlk ftlU means thatincentive fc:esarc earned only on rei urns in excess of the benchmark. A IDft hurrlh 'lilt

means that incentive fees arc paid on all proSu, but only if the hurdle rate is met.

Another fearure that is ofeen included is called a high WlIter mark. This means thatthe incentive fcc is not paid on gains that just offiel prior losses. Thus incentive feesare only paid to the extent that the current value of an investor's account is above thehights! value previously recorded. This fearure ensures that investors will not be chargedincentive fees twice on the same gains in their portfolio values.

Investors in funds of funds incur additional fees from the managers of the funds offunds. A common fcc structure from funds of funds is ·1 and 10." A 1% managementfcc and a 10% incentive fcc arc charged in addition to any fees charged by the individualhedge funds within the fund-of-funds structure,

Fcc calculations for both management fees and incentive fees can differ not only bythe schedule of rates but also method of fc:edetermlnation. Management fees may becalculated on either the beginning-of·period or end-of-period values of ...SClS undermanagement. Incentive fees may be calculated net of management fees (value increaseless management fees) or independent of management fees. Although the most commonhedge fund fee rates tend to be the "2 and 20" and "I and 10' for funds of funds, fccstructures can vary. Price breaks to investors, competitive conditions. and historicalperformance can in8uence negotiated rates.

Fcc structures and their impact on investors' resulu arc iIIunrated in the followingexample.

Example: Hedge Nud fCCl

BJI Funds is a hedge fund with a value of$IOO million at the bcginnins of me year(an all-time hip). BJI Funds chUSes a 2% management fcc hued on assets undermanagement at me bcginrUDI!of me year and a 20'111incentive fcc with a 5% hardhurdle rate and uscs a high water mark. Incentive fccs arc calculated on gains nel ofmanasement fc:cs. The endins values before fees arc:

Year 1: s125.75 millionYear 2: $127.40 millionYear 3: s138.44 million

Calculate me total fc:cs and investor's net return for all mree years.

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Year 1:Management fcc: 100" 2% • 2Gross value end of'ymr (give:n): $125.75 millionIntenti.., fcc: (125.75 - 100 - 2 - (100 x 5%»)" 2O'Ko • 53.75 millionTotal fcc: 2 + 3.75 • S5.75 millionEnding value nct offcx:s: 125.75 - 5.75. S120.00 miUionNet return to investors: (120/100) - J .20.00%

Year 2:Management fcc: 120 x 2%.52.40 miUionGrou value end of)'alr (give:n): S127.40 millionInccnci.., fcc: (127.40 - J20 - 2.40 - (120 " 5.0%)] x 20% • -$0.20 million. Sinccthis result is negative: there is no incentive fcc. The return did not esceed the hurdle:rate.Total fcc: S2.40 millionEnding value nct of fcc: 127.40 - 2.40. S125.00 miUionNet return: (125 I 120) - 1 • 4.17%The net return of less than 5% is consistent with no intenti.., fcc.

Year 3:Management fcc: 125 x 2.0% • $2.50 millionGross value end of ymr (Jiven): S138.« millionInccnti.., fcc: (138.« - 125.00 - 2.50 - (125.00" 5.0%») " 20% • $0.94 millionTotal fcc: 2.50 + 0.94 • 53.44 miUionEnding value net of fcc: 138.« - 3.44 • S135.00 miUionNet return: (135 I 125) - I • 8.00%

The high water mark was ncvcr an issue because this hedge fund bad positive: returnsovc:reach of the three )'airs.

LOS 63.g: Describe risk management of alternative investments.

cr~®Program Curriculum. Volumt 6. PIlgt 261

Risk management of alternative investments requires additional understanding of theunique set of cireumstances for each category. We can summarize some of the moreimportant risk considerations as follows:

• Standard deviation of returns may be a misleading measure of risk for twO reasons.First, returns distributions are not approximately normal; they tend to be Ieptokurtic(fat tails) and negatively skewed (possibility of extreme negative outcomes). Second.for alternative assets that use appraisal or models to estimate values. returns arcsmoothed so that standard deviation of returns (and correlations with returns oftraditional investments) will be understated. Even market- based returns can havethese same limitations when transactions arc infrequent. These problems can bias

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Sharpe measures upward and make estimates of beta misleading as wrU. Investorsshould consider downside risk measures such as value at risk (VaR). which is anestimate of the sizc of a potential decline over a period that will OCCUI. for example.less than 5% of the time; or the Sortino ratio. which measures risk as downsidedeviation rather than standard deviation. For publicly traded securities. such asREITs and ETFs. market returns arc used and standard definitions of risk arc moreapplicable.

• Usc: of derivatives introduces operational. financial. counterpany. and liquidity risk.• Prrformance for some alternatlve investment categories is primarily determined by

management expertise and execution, so risk is not just that of holding an asset classbut also risk of management underperformance.

• Hedge funds and prlvste equity funds arc much less transparent than traditionalinvcstments as they release less information and may consider their strategiC5 to beproprietary information.

• Many alternative investments arc iUiquid. Returns should rrBeet a premium forlack of liquidity to compensate investors for liquidity risk or the inability to redeemsecurities at all during lockup periods.

• When calculating optimal allocations. indices of historical returns and standarddeviations may not be good indicators of future returns and volatility.

• Correlations vary across periods and arc affected by events.

Due Diligence

A listing of kcy items for due diligence for alternative investments includes sixmajor categories: organization. portfolio management. opentions and controls. riskmanagement. legal review, and fund terms.

1. Otganization: Experience. quality, and compensation of management and staff;analysis of all their prior and current fund results; alignment of manager andinvestor interests; and reputation and quality of third-party service providers used.

2. Portfolio management: Management of the investment process; target markets, assettypes. and strategies; investment sources; operating partners' roles; underwriting;environmental and engineering review; integration of asset management,acquisitions, and dispositions; and the process for dispositions.

3. Operations and controls: Reporting and accounting methods; audited financialstatements; internal controls; frequency of valuations; valuation approaches;insurance; and contingency plans.

4. Risk management: Fund policies and limits; portfolio risk and kcy factors; andconstraints on leverage and currencies and hedging of related risks.

5. Legal review: Fund legal structure:; registrations; and current and past litigation.

6. Fund terms: Fees, both management and incentive, and expenses; contractualterms; investment period; fund term and extensions; carried interest; distributions;conSiets; rights of limited partners; and termination procedures for kcy personnel.

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Study ~soion 18Cross-~fmoce to CFA lrutiwlt Assigned~adin8 .63 - Introduction to Alternative Inwsuntnu

KEY CONCEPTS

LOS 63.a"Traditional investments' refen to long-only positions in stocks, bonds, and cash.-Alternative- investments" Ie-fees to some ty~s of assets such as real estate, commodities.and various collectables, as well as some specific structures of investment vehicles.Hedge funds and private equity funds (including venture capital funds) arc oftenstructured as limited partnerships; real estate investment trusts (REITs) are similar tomutual funds; and ETFs can contain alternative investments as well,

Compared to traditional investments, a1ternat.ive investments typically have lowerliquidity; less regulation and disclosure; higher management fees and more specializedmanagement; potential diversification benefits; more we of leverage. use of derivatives;potentially higher returns; limited and possibly biased historical returns data;problematic historical risk measures; and unique legal and taX considerations.

LOS 63.bHedge funds arc invesunent companies that we a variety of strategies and may be highlyleveraged, use long and short positions, and we derivatives.

Private equity funds wually invest in the equity of private companies or companieswanting to become private, financing their assets with high levels of debt. This categoryalso includes venture capital funds, which provide capital to companies early in theirdevelopment.

Real estate as an asset class includes residential and commercial real estate, individualmortgages, and pools of mortgages or properties. It includes direct investment in singleproperties or loans as well as indirect invcsunent in limited partnerships, which arcprivate securities, and mortgage-backed securities and real estate investment trusts,which arc publicly traded.

Commodities refer to physical assets such as agricultural products, metals, oil and gas,and other raw materials used in production. Commodities marlcct exposure can providean inflation hedge and divcuification benefits.

Various types of collectibles, such as cars, wines, and art, are considered alternativeinvestments as well.

LOS 63.cThe primary motivation for adding alternative investments to a portfolio is to reduceportfolio risk based on the less-than-perfect correlation between alternative asset returnsand traditional asset returns. For many alternative investments, the expert ise of themanager can be an important determinant of returns.

02013 Kaplan, Ine.

Study Session 18Cross-Rd'tn!n<e ro CFA In.niNlt Assigned Reading 163 -Inuoduction to A1ttmative In_tmtllrs

LOS 63_dHedge Funds• Ewnt-tlriwn strategies include merger arbitrage. distressed/reseructudng, activist

shareholder and special situations.• Rrl4tiv~IHJ/'" strategies seck profits from unusual pricing issues.• M4(1"O INtlg~strategies are "top down" strategies based on global economic trends.• Equity h~tlg~strategies are "bottom up" stratcgies tru.t take long and short positions

in equities and equity derivatives. Strategies include market neutral. fundamcntalgrowth. fundamental value, quantitative directional. short bias, and sector specific,

In periods of financial crisis. the correlation of returns between global equities and hedgefunds tends to increase. which limits hedge funds' effeaiveness as a diversifying assetclass.

Due diligence factors for bedge funds arc investment strategy. investment process.competitive advantages, track record. longevity of fund. and size (assets undermanagcment). Other qualitative factors include management style. key person risk.reputation. investor relations, growth plans. and management of systematic risk,

Private Equity

L~wr4g~tIbuyouts (LBOs) and wn"'" (Apiu/ are the two dominant strategies. Otherstrategies include developmental capital and distressed securities.

Types of LBOs include management buyouts, in which the existing management tcamis involved in the purchase. and management buy-ins. in which an external managementtcam replaces the existing management.

Stages of venture capital investing include the formative stage (composed of the angelinvesting. seed. and early stages): the later stage (expansion): and the mezzanine stage(prepare for IPO).

Methods for exiting investments in porrfoUo companies include trade sale (sell toa competitor or another strategic buyer): IPO (sell some or aU shares to investors):recapitalization (issue pottfolio company debt): secondary sale (sell to another privateequity firm or other investors); or wtite-offlliquidat.ion.

Private equity has some historical record of potcntial divcrsification benefits. An investormust idcntify top performing private equity managers to benefit from private equity.

Due diligencc factors for private equity include the manager's experience. valuationmethods used. fcc structure, and drawdown procedures for committcd capital.

Real Estate

Reasons to invest in real estate include potential long-term total returns, incomc fromrent payments. diversification benefits. and hedging against inAation.

02013 Kaplan. Inc.

Study Seuioo 18erou-lUftreo<e to CFA lrutitute Auigned Reading .63 - Inuoduc:tion to AlternatM: lowsuntou

F f calorrns o r estate Invc:stlllg:Pub/i( (InJimr) !'ri .. te (Dirrrt)

D,br • Mortgase-bachd securities • Mortgages• Collateral ned mortg;tge obligaliOI\$ • Consrruecion loans

Et{Mity • Real estate corporation ,hans • Sale ownership• Real eseare investment (rust shafts • Joint ventures

• Limited pucnerships• Commingled funds

R.. l esrare investment categori.s include residential properties, commercial real estate,REITs, mortgage-backed securities, and timberland and farmland.

Historically, real estate returns arc bighly correlated with global equity returns but Iesscorrelated with global bond returns. The construction method of real estate indexes maycontribute to the low correlation with bond returns.

Due diligence factors for real estate include global and national economic factors, localmarket conditions, interest rates, and preperty-specific risks including r.gulations andabilities of managers. Distressed properties invating and real estate development haveadditional risk factors to consider.

Commodities

The most common "''''y to invest in commodities is with derivatives. Other methodsinclude exchange-traded funds, equities that are directly linked to a commodity,managed futures funds, individual managed accounts, and specialized funds in speci6ccommodity sectors.

Beyond the potcntial for higher returns and lewer volatility benc6u to a portfolio,commodity .. an .. set class may offer inflation protection. Commcdlries can offsetinflation, .sp.cially if commodity prices are used to determine inflation indices.

Spot prices for commodities are a function of supply and demand. Global economies,production costs, and storage costs, along with value to user, all factor into prices.

LOS 63.eHedge funds oft.n invest in seeuriries that arc not actively traded and must estimatetheir values, and invest in securities that are illiquid relative to the size of a hedge fund'sposition. Hedge funds may calculate a trading NAY that adjusts for the illiquidity ofthese securities.

A private .quity portfolio company may b. valued using a mark<tlcomparables approach(muhiple-b ased) approach, a discounted cash flow approach, or an .... t-b ased approach.

Real estate property valuation approaches include the comparable sales approach, theincome approach (mulriples or discounted cash flows), and the cost approach. REITs canb. valued using an income-based approach or an asset-based approach.

A commodity futures price is approximately equal to the spot price compounded at therisk-free rare, plus storage costs, minus the eenvenienee yield.

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Study Session 18Crou·R.rtn!lIte to CFA (nUiNt. AssignedReading 163 -Illuoduction to Ah.tmative III_m,tIlU

LOS 63.fThe toul fee for a hedge fund consim of a management fcc and an incentive fcc. Otherfee structure specifications include hurdle rates and high water marks. Funds of fundsincur an additionallevcl of management fees. Fee calculations for both management feesand incentive fees can differ by the schedule and method of fee determination.

LOS 63.gRisk management of alternative investments requires undersunding of the uniquecircumstances for cach category.• Sundard deviation of returns may be misleading as a measure of risk.• Usc of derivatives introduces operational. financial. counterp:my. and liquidiry risks.• Performance for some alternative investment categories depends primarily on

management expertise.• Hedge funds and private equiry funds arc less transparent than traditional

investments.• Many alternative investments arc illiquid.• Indices of historical returns and stalldard deviations may not be good indicators of

future returns and volatiliry.• Correlations vary across periods and arc affected by events.

Key item. for due diligence include organization. portfolio management. operations andcontrols. risk management, legal review. and fund terms.

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Study S... ioo 18CroIs-~f_Dce to CFA Institute Assigned ~ading .63 - Introduction to Alternative IOWltrnoou

Page 252

CONCEPT CHECKERS

1. Compared to managers of traditional investments. managers of alternativeinvcstments arc likely to have li:wcr restrictions on:A. holding cash.B. buying stocks.C. using derivatives.

2. Compared to alternative investments. traditional investments tend to:A. be less liquid.B. be less regulated.C. require lower fees,

3. In which category of alternative investments is an investor mDIt lillt/y to uscderivatives?A. Real estate.B. Commodities.C. Collcctibles.

4. An investor who chooses a fund of funds as an alternative to a single hedge fundis most li"t/y to benefit from:A. lower fees,B. higher returns.C. more due diligence.

s. In a leveraged buyout. covenants in leveraged loans can:A. restrict additional borrowing.B. require lenders to provide transparency.C. provide protection for the general partners.

6. Direct commereial real estate ownership ItlUt li"t/y requires investing in:A. large amounts.B. illiquid assets.C. a short time horizon.

7. Diversification benefits from adding hedge funds to an equity ponfolio may belimited because:A. correlations tend to increase during periods of financial crisis.B. hedge fund returns arc less than perfectly correlated with global equities.C. hedge funds tend to perform better when global equity prices arc declining.

8. A private equity valuation approach that uses estimated multiples of cash flowsto value a portfolio company is the:A. asset-based approach.B. discount cash flow approach.C. market/comparables approach.

02013 Kaplan. Inc.

Study Session 18Cross·ReI'tn!nl:e 10 CFA Instilule Assigned Reading 163 -Inuoduction 10 A1ltmative In_uutllu

9. A real estate propert), valuation would leesr lilttly use a(n):A. ineomc approach.B. asset-based approach.c. comparable sales approach.

10. A high water mark of £150 million was established two years ago for a Britishhedge fund. The end-of-year value before fees for last year was £140 million.This year's end-of-year value before fees is £155 million. The fund ehuges"2and 20.' Management fees are paid independently of incentive fees and arecalculated on end-of-year values. What is the total fee paid this year?A. £3.1 million.B. £4.1 million.C. £6.1 million.

) 1. Standard deviation is ulJsr lil"Iy an appropriate measure of risk for:A. hedge funds.B. publicly traded REITs.C. exchange-traded funds.

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Study Session 18Cross.-!WftreDce to CFA Institu~ Auign.d !Wading ,63 - Inuoduaion to Alccrnativ. Inw,un«nu

ANSWERS - CONCEPT CHECKERS

I. C Traditional managers can hold cash and buy stocla but may b. Itsuictcd from usingderivarives.

2. C Traditional investm.nu typically require lower fees. are more regulated. and are moltliquid than alternative investments.

3. B Commodities investing frequently involves the use offuturcs contractS. Derivatives areless o';en employed in real es.. te or collecubles investing.

4. C A fund of funds manager is expected to provide more due diligence and beuerredemprion term s. Funds of funds charg. an addirional Ia)"r off ees. InveICing in fund offunds may provide more diwrsi6cation but may not neu...,ily provide highe, returns.

S. A Debt covenantS in leveraged buyout loan. may ... trict addirional borrowing by theacquired 6rm. CovenantS ..,mict and require borrowers' actions. net lenders' actions.Covenants in leveraged loans provide protection for the lenders, not the gen.ral partn.rs.

6. C Comm.rcial real estate ownership requires long tim. horizon. and purchasing illiquidauea that requiee la~ investm.nt amounu.

7. A Adding hedge funds to traditional portfolios may not provide tb e expecteddiversification to an .quity portfolio because return correlations rend to incresse duringperiods of financial crisis.

8. C The markn/comparabl es approach uses markn or private transaction valu.s ofsimilar companies to estimate multiples of EmmA. ntt ieccme, or revenue to use in.stimating the portfolio company's value.

9. B The three approach es to valuing a property are Incom e, comparable sales. and COSI. Anasset-based approach can be used for real estate investment uusu, but not for valuingindividual real e"ate properties.

10. B Management fee is LISS million x 0.02.0.1 million.

Ineemivefee is (LISS million - LISO million) x 0.20. L1.0 million.

Total fee is 0.1 million + L1.0 mimon • L4.1 million.

II. A Hedge funds may hold UJiquid asseu that may use estimaeed values to calculate returns.Risk as measured by standard deviarion could be undersrated. For publicly tradedsecurities. such as REITs and ETFs. Standard definitions of risk are more applicable.

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SELF-TEsT: DERIVATIVES AND ALTERNATIVEINVESTMENTS

10 questions, 15 minutes

1. Which of the following is leest likt/y a similarity between a forward rateagreement based on UBOR + 1.5% and an interest rate option on UBOR?A. A long position in either one will result in a posinve payment if interest

rates increase above the contract rate,B. The payments to either arc based on the difference between a contract rate

and a market {ref'crence}rate.C. If both have the same contract rate. notional principal. expiration date. and

reference rate, they will make equal payments to their (long) owners.

2. Adam Vernon took a long position in four 100-ouncc July gold futures contractsat 685 when spot gold was 670. Initial margin is S4.000 per contract andmaintenance margin is S3.200 per contract. If the account is marked to marketwhen spot gold is 660 and the fururcs price is 672. the additional margin theinvestor must deposit to keep the position open is <"'lttt to:A. S2.0OO.B. S4.OO0.C. S5.000.

3. The value of a call option on a stock is uast likt/y to inaeasc as a result of.A. an increase in asset price volatility.B. a decrease in the risk-free rate of interest.C. a decrease in the strike price of the option.

4. Kurt Crawford purchased shares of Acme. Inc .• for $38 and sold call options atS40. covering all his sharcs for S2 each. The sum of the maximum per-share gainand maximum per-share loss {as an absolute value} on the covered call position is:A. S36.B. S40.C. unlimited.

5. Ccaig Grant has entered into a S10 miUion quarterly-pay equity swap based onthe NASDAQ stock index as the 8% fixed rate payer when the index is at 2.750.Which of the following is most IlccuratdA. He will make a payment of $200.000 on the second payment date if the

index is 2.750.B. He will neither make nor receive a payment on the first settlement date if

the index is 2.805.C. If the index at the first settlement date is 2.782. he must make a payment at

the second settlement date.

6. It is Itlllt likt/y that a forward contract on a zero-coupon bond:A. hal counterparty risk.B. can be settled in cash.e. requires a margin deposit.

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StIr-Test: Derivuiws and A1lunww Inwsuntnu

7. Survivorship bias in reported hedge fund index returns will molt lilttly result inindex:A. returns and risk that arc biased upward.B. returns and risk that arc biased downward.C. risk that is biased downward and returns that arc biased upward.

8. A hedge fund with a 2 and 20 fcc structure has a hard hurdle rate of 5%. Ifthe incentive fcc and management fee arc calculated independently and themanagement fcc is based on beginning-of-period asset values, an investor's netreturn over a period during which the gross value of the fund has increased 22%is closat to:A. 16.4%B. 16.6%C. 17.0%

9. Measures of downside risk for asset classes with asymmetric return distributionsarc kast li"~/yto include:A. value at risk (VaR).B. the Sortino ratio.C. kurtosis-adjusted standard deviation.

10. The type of real estate index that most li"~/yexhibits sample selection bias isa(n):A. REIT index.B. appraisal index.C. repeat sales index.

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s.el{·Ttsl: OtrivatiW$ and A1ttmati,-e In_ImtnlS

SELF-TEsT ANSWERS: DERIVATIVES ANDALTERNATIVE INVESTMENTS

I. C Because the FRA pays at the expiration of the forward contract, it pays the present valueof the interest Iavings that would be reali~ at the end of the (hypothetical) loan term.The interest rate option wiU pay the interest savings on the (hypoth.tical) loan afttrexpiration at the end of thtloan term and its paymtnt will be greattr (since it's notdiscounted baa to the expirauon date).

2. C The initial margin is 4 • 54,000 • 516,000 and the ma;ntenance margin is 4 • 53,200 •512,800. The loss on the position is (672 - 685).4. 100. -55,200, leaving a balanceof 516,000 - S5,200 • SIO,800. Because the account has fall.n below the maintenaneemargin, a deposit of 55,200 is required to bring the balanC%back up to the initialmargjn.

3. B A decrease in the risk- free rate of interest will decrease call values, The other changes willtend to increase the value of a call option.

4. B The net COStof the covered call position u 38 - 2 • 36, so the maximum loss (if theSlack price goes to zero) U 536. The maximum gain (if the stock price goes to 40 ormore) is 54. The sum;' 36 • 4 .40.

5. B If the index has risen to 2,805 (.2%), rhe index paytr'sliability (2% • SIO million) JUStoffsets the fixed rate payer'sliability (8% 14. $10 million). The payment at the secondsetdemem date cannot be determined without knowing the change in the index 1.... 1between the 6rst and second settlement dates. The indtx level at the fitst senlemem datedoes not determine the payment at the second settlement date.

6. C Forward conuaeu typically do not require a margin deposit. They are custominstruments that may require seulemem in cash or delivery of the underlying as.", andthey have coumerpany risk.

7. C Surviving firms are more likely to have had good past returns and have taken on It .. riskthan the .verage fund, leading to upward bias in index t<turru and downward bias inindex risk measur es,

8. B The manog.m.nt fee is 2% of the beginning 'SKt valu., which reduces an investor',gross If turn by 2% to 22 - 2 • 20%. The incentive fee is 20% of the .XCe.. gross If turnOVOI the hurdle rate, or 0.20(0.22 - 0.05) • 3.4%. Tbe investor return ntt of fees is22% - 2% - 3.4%.16.6%.

9. C Value at risk (VaR) and the SOllino ratio based on downside deviations from the meanare measures of downside risk, Kwtods.adjustcd standard deviation is not a conctptpresented in the curriculum.

10. C A repeat sales index includes prices of properties that have recently sold. Because theseproperties may not be representative of overall property values (n....y be biased towardproperties that have declined or incrased th. most in value of the period), there is therisk of sample selection bias. An apprilial index ora REIT index u gen<tally construcredfor a sample of representati ... properties or REIT plOperty pools.

02013 Kaplan, Inc. Page 257

FORMULAS

for an annual-coupon bond with N )",ars to maturity:

. _ coupon .... coupon + + coupon + principalpncc - (1+ YrM) . (I+ YrM)2 •.. (1+ YrM)X

for a scmiannual-coupon bond with N years to maturity:

price = ( CO'fm) +( coy: r +...+ co{upo~~n)·~~r1+ 1+-- 1+--

2 2 2

bond valuc wing spot rates:

.... . ipal_-,-. . coupon + coupon + coupon . pnncInO-awltrage pnce = + ...(1+St) (1+S2)2 (1+SN)N

full price between coupon payment dates:

par x (1+ YrM)tIT

where r is the numbcr of days from the last coupon payment date until the date thebond trade will settle. and Tis the number of days between the last coupon paymentand the nexr

ield annual cash coupon paymentcurrent yl =bond price

forward and spot rates: (1 • S2)2 = (1 • SI)(1 • 1y1y)

option-adjusted spread: OAS • Z-spread - option value

od·,,-~ d . Macaulay durationm lncu. uranon =1+YrM

v -vapproximate modified duration = - ±

2VoLl.YfM

_tr • d . _V...;;_~-_V-,+;;_cnl:Cb.vc unoon =2VoLl.cwvc

money duration. annual modified duration x full price of bond position

money duration per 100 units of par value =annual modified duration x full bond price per 100 of par value

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Book 5 _ FIXed Income, Derivatives, and A1t<rnaliv.InvesunenuFormulas

price: value of a basis point: PVBP = [(V__ V) /21 )( par value )(0.01

approximat. oonvcxity =V_+V+-2Vo

(t.YTM)2Vo

V_ +V+-2VO

(t.rurvc)2 Voapproximat< dfc:ctiv< oonvcxity =

%t. full bond price • -annual modified duration(t. YTM) ~ ~ annual oonvaity(t. YTM)2

duration gap = Maaulay duration _ Investment horizon

return impact :::::-duration x t.spr<ad + .!.convaity x (t.spr<ad)22

(floating - forward)( ~)value of a long fRA at sertlemenn (notional principal) [ [3)r

1+ (Boating) ~~

intrinsic value of a all: C = Max[O, S _ X]

intrinsic value of a put: P • Max[O, X _ Sl

option value = intrinsic value + tim. value

lower and upper bounds for options:

Opli~"European allAmetian call

European PUt

American puc:

e, ~ Max[O, S, _ X / (1 + RFR)T-'lc- ~ Max[O, S, _ X / {I ~RFR)T-'llp, ~ Max[O, X / {I ~RFR)T-, _ S,lP, ~ Max[O, X - S,l

S,S,

X/ (1 ~ RFR)T-<X

put-all parity: c ~ X / (I ~RFR)" = S ~ P

pur-call parity with asset cash Bows: C ~ X / (I ~RFR) T • (So _ PVc~ ~ P

plain-vanilla interest rat. swap:

(net fIXed-ratepaym.nt), = (swap fixed rare _ UBOR,_.>( num~: days)x notional principal

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INDEX

A

ab",lut. basis 232add-on yitld 33aIlirmati"" cov.nanu 113a&tllcy bonds 31alternative invesun.nts 230Am.rian options 179angt! investing 236annualiud holding period ra te of return 80appraisal index 241approximat. modifitd duration 87arbitrag. 144

B

backup lines of cttdit 32backwardation 244btnchrnarlc bonds 31btnchrnarlc spread 63btu elTom ofTerint 29bilat<ralloan 32bond equivalent yield 56bond options 181bridge financing 32

ccall option 143.178. 182call option profilS and loss.. 220cap 183capiw mark.t securiti .. 27capler 183carrying valu. 81cash Row yidd 90cash setdement (forwards) 150cash sculem.nt (futurcs) 170central bank funds market 34central bank funds ratts 34certificates of deposie (CDs) 34cheapest-to-delivee 171clawback 237clean price 47clearinghouse 166closing tradc 170collar 184colla reral yidd 244comm.rciaI papee 32commercial real ...... 240commit eed capital 237commoditi .. 242

Pagt260 02013 Kaplan. Inc.

comparable sal .. approach 241constant.yitld price U2j<ClOry 45contango 244ccmingenr chim 142contract multiplier 181convenlence yidd 244convexiry 93corpora te bonds 33corpora re crtdit ratings 110corpora« family ratings 110COStapproach 241counttrparty risk 150covered call 224credit curves 121crtdit dtfault swap 143credit derivati,"" 143ceedir migration risk 109credit rating 110credir risk 108,151crtdit sprtad 120credir sprtad option 143currtncy forward contract 157eurrtncy futum 172currtncy options 181currtncy swap 208eurrem yidd 52

Dd.bt Stmo< eov<ragt ratio 128d.fault risk 108. 150deliverable forward contract ISOddivtry 170delivery options 170d.rivativcs 142

criticism of 144developed markeu 28develcpmenral capital 237dirty price 47discount margin 54distressed investing 237downgrad. risk 109duration 85duration gap 98

Etarly sage (ventUft capiw) 236.ff<ctivt convexity 94.ffuu"" duration 88.ff<cti"" yidd 50

.nl.rsing nwk<u 28

.nt.rprise valu. 126equiry forward contncts 152equiry hedge fund n ...tegies 23~.quiry swap 213Euribor 155Eurodollar deposit 154Eurodollar futuru 171European options 179event-driven stmegies 233exchang. for physicals 170exchangc-rradcd derivatives 1~2exchang e-traded options 181expected loss 108

F

fiduciatycall 196financial options 181fl2L prier 47Roating .... te not. yi.1ds 53Roor 183Roorlet 184foccign currency options 181focmativ. srag. 236focward commitmenr 142focward contract 143. 149focward ...te agreem.nt 155focward ntes 58focward yi.1d curve 58feur Cs of credit analysis 112full prier 47fund of funds 233futures COntracts 143. 165

G

&en.nl obligadon bonds 127grey market 29G.spread ~

HhaircUt 35high wal<r mark 245high yield 123hurdle ...re 2~5

I

incentive fcc 244income approach 241inde x-linked bonds 28index options 181inicial m"l\in 167interbank funds 34interbank money market 28int.rest m. cap 183

Book 5 - FIXedIncome. Derivadves, and A1ttrnative Inv<SlmentsIndex

in teres t rate coUar 184in ter... rate 800r 183in terest rate opclons 181.182. 186in teres t rate "''''p' 211in eerpolated spreads (I-spreads) ~in.tho-money call option 180inuiruic valu. of an option 186.187invesun.nt grad. IIIinvesun.nt hori2.0n 81invoier price 47

Jjunior debt 109

Llat.r srage (venture capital) 236law of on. price 144lev.raged buyouts (lBOs) 235limit move (up. down) 168listed options 181locked limit 168lockup period 232London Interbank Offered Rat. (L1BOR) 155.

182.211long forv.'lIrd po.ition 149long.term equity anticipatory securities (LEAPS)

18110$sseve ril)' 108

MMacaulay duration 85macro strategies 234main tenance margin 167managem.nt buy.ins 236managem.nt buyouts 236managem.nt fcc 244market liquidiry risk 109marking to mark.. 168material adverse change 32matrix pricing 48medium-term notes (MTN.) 33nlaunin.financing (in LBO,) 235maunine.nage financin& (venture capital) 236minimum and maximum values of options 189minimum value of a European put option 192minimum value of an American aU option 191minoriry equiry investing 237modified duration 86nloney duration 91money mark er securities 27moneyness 180municipal bonds 28. 127mutual te rmination of a swap 207

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Book 5 - FlXtd Incom e, Derivatives, and Altttnativ. Inv.. tmtntsInd""

Nnegativ. co,..nants 113n<soliabl. cortiScat .. of d<posit 34no-arbit",. price 46non-inv .. tmene grad. I I Inonsovmign govo,nmtnt bonds 3 Inotching II Inotice period 232notional principal 209

ooffsetting conu..." (10 terminate a swap) 208off.. uing track (to •• it a fu,w .. position) 170option.adjuSltd .pmd (OAS) 65op,ion.adjuSltd yitld 53option cemract 178option payoff. 185optlon premium 178option p,oS, diagrams 220optlons 142options on futur .. 182option wrile' 178out-of.the-mon<y all option 180ov<rnight r.po 34ever-ibe-ccumer detivui ... 142ov<r-the-counter options 181

p

parallel shift 9 Ipar bond yield curve 58pari passu 109p.riodidty 50plain vanala inter es, rare swap 21 IpOllfolio companies 236premium of an option 179prepayment option 89priee limits 168price valu. of a basis point (PVBP) 92primary dtaltn 29primary marko, 29prim. brok ... 232priority of claims 109privale in... unenr in public equiti es 237pri.... ptac.m.nt 29prottcti ve put 196. 225public ofT.ring 29put-call parity 195. 196. 197put option 143.178.182put option proSts and los... 221

Qquasi-gov.rnmrot bonds 31quoted m:ugin 54

!'ag.262

Rrating agonei.. 110rea1 .... te investment 'fU.U (REITs) 240rea1 optiOll$ 182rec:ovrty rat. 108REIT indica 241relati ve buis 232rebUve valu<ltratcgi es 233re pear sal .. index 241repe daee 35repo margin 35repo rat. 34repwchast (repe) agmmont 34re quired margin 5.(re sale of a swap 208resickntial proporry 240... enue bonds 128.... rse repo agreemem 35... erse ttad. (to <Xita futut<S position) 170roUov.r ri.k 32roUyidd 244

SstCOndary marktu 30.. cured d.bt 109.. ed Stago (ventu re capital) 236stmiannual bond basis 50stniority ranlting 109serial bond issue 33seulemem date 150.207.209stttltm.nt price 167shelf rtgistration 30short forward position 149simple yield 52Sottino ratio 247sou .... of return from eommodiri .. 244sove re ign bonds 30. 126spot ralCS 45spot rate yitld curve 57spr<ad risk 109stoekind .. futut<S InSCfC<t con_tion 51strip curve 57SlruCtural.ubordination 11 Istructured security 33subo,dinattd debemures 109supranational bond. 3 Iswaps 142.207swaption 208swap. ways to twninale 207syndicate 29syndicattd loan 32synth.tic options 196

02013 Kapbn. Inc.

TT-bal (orward, 154tenor 207[erminating a (orward c:onuact 151[erminating a furo"" contract 170term maturity structure 33term repe 35term structure 57rerm ,UUctUfeo( )ield ,'Olatility 96[ime ,..Jue 188T"''''ury bill (U[ures 171T",...ury bond futures 171nue yield 51

uunderwritten offering 2!)unsecured debt IO!)upper bound (or call options 189upper bound for puc options 18!)

Dook 5 - FIXedInoome. Derivati ves, and A1ternath .. InvestmcnuIndex

Vy..Jueat risk (VaR) 247variation matgin 167venture capital 236

y

yield curve 57yield curve (or coupon bonds 57yields (or money market instruments 55yield spread 63. 108yield-to-call 52yield-to-maturity (YTM) 41yield-to-wofSl 52

zuro-c:oupon rates 45zero curve 57zero-volatility spread (Z-sp",ad) 65

02013 Kaplan. Inc. Page 263

Notes

Notes