ptitdlib.ptit.edu.vn/bitstream/123456789/1516/1/bai giang c… · · 2017-02-242 chủ đề 2:...

BỘ THÔNG TIN VÀ TRUYỀN THÔNG

HỌC VIỆN CÔNG NGHỆ BƯU CHÍNH VIỄN THÔNG

*****

BÀI GIẢNG MÔN CFA

Mã môn học: FIA 1402

(03 tín chỉ)

Biên soạn

ThS. Nguyễn Đình Tú

Hà Nội – 2015

PTIT

MỤC LỤC

Lời mở đầu ........................................................................................................................................ 3

1. Chủ đề 1: Corporate Finance ........................................................................................................... 4

1.1 Capital Budgeting .................................................................................................................... 4

1.2 Cost of Capital .......................................................................................................................13

1.3 Measures of leverage .............................................................................................................24

1.4 Dividends and Share Repurchases ........................................................................................24

1.5 Working capital management ................................................................................................33

1.6 Corporate Governance ...........................................................................................................33

2 Chủ đề 2: Market Organization .....................................................................................................36

2.1 Market organization and structure .........................................................................................36

2.2 Security market indices .........................................................................................................56

2.3 Market efficiency ..................................................................................................................63

3 Chủ đề 3: Equity Analysis and Valuation .....................................................................................68

3.1 Overview of equity securities ................................................................................................68

3.2 Introduction to industry and company analysis .....................................................................75

3.3 Equity valuation: concepts and basic tools............................................................................85

4 Chủ đề 4: Portfolio Management ................................................................................................108

4.1 Portfolio management overview .........................................................................................108

4.2 Portfolio risk and return ......................................................................................................114

4.3 Portfolio planning and construction ....................................................................................152

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LỜI NÓI ĐẦU

Hiện nay trong chương trình đào tạo ngành Kế toán của Học viện Công nghệ Bưu chính

Viễn thông ngoài những môn học hướng tới ngành đào tạo còn có những môn học sử dụng tài

liệu tiếng Anh chuyên ngành như “CFA”, “Introduction to ACCA”. Những môn học này

ngoài việc bổ sung kiến thức tiếng Anh chyên ngành còn cung cấp kiến thức tài chính kế toán

theo hướng cập nhật các chuẩn mực quốc tế. Tuy nhiên với vốn tiếng Anh còn hạn chế của

sinh viên Học viện, đã tạo ra không ít khó khăn trong công tác giảng dạy và học tập các môn

học này. Nhận thấy vấn đề như trên, kết hợp với chủ trương của Học viện thực hiện biên soạn

bài giảng, giáo trình, slide cho các môn học nhằm đồng bộ hóa tài liệu, tác giả đã thực hiện

biên soạn bài giảng “CFA” dành riêng cho giảng viên và sinh viên ngành kế toán của Học

viện.

Bài giảng được thực hiện biên soạn trên tinh thần tiếp thu nội dung mới nhất những kiến

thức từ chứng chỉ tài chính quốc tế CFA và kế thừa phát huy những điểm mạnh trong bài

giảng của những trường đại học danh tiếng đồng thời dựa trên những kinh nghiệm thực tế

giảng dạy của tác giả. Bài giảng đã hệ thống những nội dung theo đề cương chi tiết đã được

Học viện ban hành: Corporate Finance, Market Organization, Equity Analysis and Valuation,

Portfolio Management

Để bài giảng thực sự trở thành tài liệu hữu ích phục vụ cho hoạt động giảng dạy và học

tập, tác giả mong muốn nhận được những góp ý với tinh thần xây dựng, chia sẻ chân thành từ

phía độc giả.

Xin chân thành cảm ơn!

Hà Nội 06/2015

CHỦ BIÊN

NGUYỄN ĐÌNH TÚ

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Chủ đề 1: Corporate Finance.

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1. Chủ đề 1: Corporate Finance

1.1 Capital Budgeting

Thecapital budgetingprocess istheprocessofidentifying andevaluating capitalprojects,

thatis,projectswherethecashflowtothefirmwillbereceivedoveraperiod longerthan

ayear.Anycorporate decisionswith animpact onfuture earningscanbe examined

usingthisframework. Decisions about whether tobuyanewmachine, expand

businessinanother geographic area,movethecorporate headquarters

toCleveland,orreplaceadeliverytruck, tonameafew,canbeexamined

usingacapitalbudgetinganalysis.

Foranumberofgoodreasons,capitalbudgeting m a ybethemostimportant responsibility

t h a t afinancialmanagerhas.First,becauseacapitalbudgeting decis ionoften

involvesthepurchase ofcostlylong-term asse t swithlivesofmanyyears,the

decisionsmademaydetermine thefuture successofthefirm.Second,theprinciples underlying

t h e capitalbudgeting processalsoapplytoother corporatedecisions, such

Asworking capitalmanagement a n d making strategicmergersandacquisitions. Finally,

making goodcapitalbudgeting d ec i s i on s isconsistent withmanagement’s primary

goalofmaximizing shareholdervalue.

The capitalbudgetingprocesshasfour administrativesteps:

Step1: Ideageneration.The mostimportantstepinthecapital budgetingprocess

Isgeneratinggoodproject ideas .Ideascancomefrom anumberofsources includingsenior

management,functionaldivisions, employees , orsources outside thecompany.

Step2: Analyzingprojectproposals.Becausethedecision toacceptorrejectacapital project

isbasedontheproject’s expectedfuture cashflows,acashflowforecast must

bemadeforeachproducttodetermine i t s expectedprofitability.

Step3: Createthefirm-widecapitalbudget.Firmsmust prioritizeprofitableprojects according

tothetiming oftheproject’s cashflows,availablecompany resources, andthecompany’s

overallstrategic plan. Many projectsthatareattractive

ind iv idua l l ymaynotmakesensestrategically.

Step4: Monitoring decis ionsandconductingapost-audit.

Itisimportanttofollowuponallcapital budgetingdecisions. Ananalyst should compare

theactual resultstotheprojectedresults, andproject managers should explain why

projectionsdidordid notmatch actual performance. Becausethecapital budgetingprocess

isonly asgood astheestimates ofthe inputs into themodel usedtoforecast cashflows,apost-

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auditshould beusedtoidentifysystematic errorsintheforecasting processandimprove

companyoperations.

Categories ofCapital Budgeting Projects

Capital budgetingprojects maybedivided intothefollowing categories:

Replacementprojectstomaintain t h e businessarenormallymadewithout

detailedanalysis.The onlyissuesarewhethertheexisting operationsshould continueand,

ifso,whetherexisting procedureso r processesshould bemaintained.

Replacementprojectsfor costreductiondeterminewhetherequipmentthat is obsolete,

butstillusable, shouldbereplaced. Afairlydetailed analysis isnecessary inthiscase.

Expansionprojectsaretaken onto growthebusiness andinvolveacomplexdecision-making

processbecause theyrequire anexplicit forecastoffuture demand.Averydetailed

analysisisrequired.

Newproduct ormarketdevelopmentalsoentails acomplex decision-makingprocessthat

willrequire adetailed analysisdueto thelargeamount o f uncertainty involved.

Mandatoryprojectsmayberequired byagovernmental agencyorinsurance company

andtypically involvesafety-related o r environmentalconcerns.These projects

typicallygeneratelittletonorevenue, buttheyaccompany n e w revenue

producingprojects undertakenbythecompany.

Otherprojects.Someprojects arenot easilyanalyzed throughthecapital budgetingprocess.

Suchprojects mayinclude apetproject ofsenior management(e.g., corporateperks) orahigh-

riskendeavor that isdifficulttoanalyzewith typical capital budgetingassessment

methods(e.g.,research anddevelopmentprojects).

The capitalbudgetingprocessinvolvesfivekeyprinciples:

1. Decisionsarebasedoncash flows, notaccountingincome.Therelevant cashflowsto

consider aspartofthecapital budgetingprocessareincrementalcashflows,the

changesincashflowsthatwilloccuriftheproject isundertaken.

Sunk costs arecoststhat cannotbe avoided, eveniftheproject isnot undertaken.

Becausethesecostsarenotaffected bytheaccept/rejectdecision, t he yshould

notbeincludedintheanalysis.Anexample ofasunk costisaconsultingfeepaid toa

marketingresearch firmtoestimate demandforanewproductprior toadecision

ontheproject.

Externalitiesaretheeffectstheacceptance o f aproject mayhaveonother firm cashflows.The

primaryoneisanegative externality calledcannibalization, whichoccurswhen anewproject

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takessalesfrom anexisting product.When

cons ider ingexternalities,thefullimplicationofthe newproject ( lossinsalesofexisting

products)should betaken intoaccount. Anexample ofcannibalizationiswhen asoftdrink

companyin t roducesadietversion ofanexistingbeverage.The analystshould

subtractthelostsalesoftheexisting beveragefrom theexpected newsales ofthedietversion

whenestimatedincrementalproject cashflows.Apositive externalityexistswhen

doingtheproject wouldhaveapositive effectonsalesofa firm'sother productlines.

Aproject hasaconventionalcashflowpattern ifthesignonthecashflows changes onlyonce,with

oneormore cashoutflows followedbyoneormore cashinflows.

Anunconventionalcashflowpattern hasmore thanonesignchange. Forexample, aproject

mighthaveaninitial investmentoutflow, aseriesofcash inflows, andacashoutflow

forassetretirementcostsattheendoftheproject's life.

2. Cash flowsarebasedonopportunity costs.Opportunity costsarecashflowsthat

afirmwilllosebyundertakingtheproject underanalysis.These arecashflowsgenerated

byanassetthefirmalreadyownsthatwould beforgone iftheproject

underconsiderationisundertaken.Opportunitycostsshould beincludedinproject

costs.Forexample,whenbuildingaplant, evenifthefirmalreadyownstheland,

Thecostofthelandshould bechargedtotheproject becauseitcouldbesoldifnot used.

3. Thetiming ofcash flowsisimportant. Capital budgetingdecisions accountforthe

timevalueofmoney,which meansthat cashflowsreceivedearlierareworth morethan

cashflowstobereceivedlater.

4. Cash flowsareanalyzedonanafter-tax basis.Theimpact oftaxesmust beconsidered

whenanalyzing allcapital budgetingprojects. Firmvalueisbasedoncashflowsthey

gettokeep,notthosetheysendtothegovernment.

5. Financingcostsarereflectedintheproject'srequiredrateofreturn.Donotconsider financing

costsspecifictotheproject whenestimatingincrementalcashflows.The

discountrateusedinthecapital budgetinganalysistakesaccountofthefirm'scostofcapital.

Onlyprojects thatareexpected toreturn morethan thecostofthecapital needed tofund

themwillincreasethevalueofthe firm.

Independentvs.MutuallyExclusiveProjects

Independent projectsareprojects thatareunrelatedtoeachother andallowforeach project

tobeevaluated basedonitsownprofitability.Forexample, ifprojects

AandBareindependent,andboth projectsareprofitable, then thefirmcould acceptboth

projects. Mutuallyexclusive means that onlyoneproject inasetofpossible projects

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canbeaccepted andthat theprojects compete with eachother. Ifprojects AandB

weremutuallyexclusive,thefirmcould accepteither ProjectAorProject B,but

notboth.Acapital budgetingdecision between twodifferentstampingmachines with

different costsandoutput would beanexample ofchoosing between twomutually

exclusiveprojects.

Project Sequencing

Someprojectsmust beundertakeninacertain order,orsequence, sothat investing in aproject

today createstheopportunitytoinvest inother projects inthefuture. For example, if a project

undertakentoday is profitable, that maycreate the opportunity to invest in a second project a

year from now. However, if the project undertakentoday turns out to be unprofitable, the

firm willnot investinthesecond project.

UnlimitedFunds vs.Capital R a t i o n i n g

Ifafirmhasunlimitedaccesstocapital, thefirmcanundertakeallprojects withexpected

returnsthatexceedthecostofcapital. Many firmshaveconstraintsonthe amount o f capital

theycanraiseandmust usecapitalrationing. Ifafirm'sprofitable project

opportunitiesexceedtheamount offundsavailable, thefirmmust ration, or

prioritize,itscapital expenditureswith thegoalofachieving themaximum increase in

valueforshareholders givenitsavailable capital.

Net PresentValue(NPV)

Wefirstexamined thecalculation ofnetpresent value(NPV) inQuantitative Methods.

The NPVisthesumofthepresent valuesofalltheexpected incrementalcashflowsifaproject

isundertaken.The discountrateusedisthefirm'scostofcapital,

adjustedfo r theriskleveloftheproject. Foranormal project, with aninitial cashoutflow

followed byaseriesofexpected after-tax cashinflows, theNPV isthe present

valueoftheexpected inflows minus the initial costoftheproject.

where:

CF0=initial investmentoutlay (anegative cashflow)

CFt=after-tax cash flowattime t

k =required ra t eofreturn forproject

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Apositive NPV project isexpected toincrease shareholder wealth, anegative NPV project

isexpected todecreaseshareholder wealth, and azeroNPV project hasno expected

effectonshareholder wealth.

Forindependent projects, theNPV decisionruleissimply toaccept anyproject with a positive

NPV andtorejectanyproject with anegative NPV.

Example: NPV analysis

Using the project cash flows presented Table 1, compute the NPV of each project’s cash

flows and determine for each project whether it should be accepted or rejected. Assume that

the cost of capital is 10%.

Table 1: Expected Net after - Tax Cash Flows

Year (t) Project A Project B

0 -$2,000 -$2,000

1 1,000 200

2 800 600

3 600 800

4 200 1,200

Answer:

Both Project A and Project B have positive NPVs, so both should be accepted.

InternalRateofReturn ( IRR)

Foranormal project,theinternalrate ofreturn (IRR) isthediscount ratethat makes thepresent

valueoftheexpected incremental after-tax cashinflowsjust equaltothe initial costoftheproject.

Moregenerally, theIRRisthediscount ratethat makes thepresent valuesofaproject'sestimated

cashinflowsequaltothepresent valueofthe project's estimated cashoutflows.That

is ,IRRisthediscount r a t e that makesthe following relationshiphold:

PV(inflows) =PV(outflows)

The IRRisalsothediscount r a t e forwhich theNPV ofaproject isequaltozero:

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TocalculatetheIRR,youmayusethetrial-and-error method. That i s ,just keepguessing

IRRsuntil yougettheright oneoryoumayuseafinancial ca l cu l a to r .

IRRdecisionrule:First, determinetherequired r a t e ofreturn foragivenproject.Thisisusually

thefirm'scostofcapital. Note that the required rateofreturn maybehigher orlowerthan

thefirm'scostofcapital toadjust fordifferences between project riskandthefirm'saverageproject

risk.

IfIRR>therequired ra t eofreturn, a c c e p t theproject.

IfIRR<therequired ra t e ofreturn,rejecttheproject.

Example: IRR

Continuing with the cash flows presented in Table 1 for the projects A and B, compute IRR

for each project, and determine whether to accept or reject each project under the assumptions

that the projects are independent and that required rate of return is 10%.

Answer:

Payback Period

Thepayback pe r iod ( PBP)isthenumberofyearsittakestorecovertheinitial costof

aninvestment.

Example: Paybackperiod

Calculate the payback periods for the two projects that have cash flows presented in Table

1. Note the Year 0 cash flow represents the initial cost of each project.

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Answer:

Note that the cumulative net cash flow (NCF) is just the running the total of the cash flow at

the end of each time period. Payback will occur when the cumulative NCF equals zero. To

find the payback periods, construct Table 4.

Table 4: Cumulative Net Cash Flows

Year 0 1 2 3 4

Project A Net cash flow -2,000 1,000 800 600 200

Cumulative -2,000 -1,000 -200 400 600

Project B Net cash flow -2,000 200 600 800 1,200

Cumulative -2,000 -1,800 -1,200 -400 800

The payback period is determined from the cumulative net cash flow table as follow:

payback period = full years until recovery +

Becausethepayback periodisameasure ofliquidity, forafirmwith liquidity concerns, theshorter

aproject’s paybackperiod, thebetter. However, projectdecisionsshould notbemade

onthebasisoftheir paybackperiodsbecauseofthemethod's drawbacks.

The main drawbacks ofthepayback period arethat itdoesnot takeinto account

eitherthetimevalueofmoney orcashflowsbeyond thepayback period, which means

terminalorsalvagevaluewouldn'tbeconsidered. These drawbacksmeanthatthepayback

periodisuselessasameasure ofprofitability.

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The mainbenefitof thepayback periodisthat itisagoodmeasure ofproject liquidity. Firmswith

limited accesstoadditionalliquidityoften impose amaximum payback period andthen

useameasure ofprofitability, suchasNPV orIRR, to evaluate projects that satisfythismaximum

payback period constraint.

DiscountedPayback Period

The discountedpayback period u s e s thepresent valuesoftheproject’s estimated c a s h

flows.Itisthe numberofyearsittakesaproject torecoveritsinitial investmentin present

valueterms and, therefore,must begreater than thepayback period without discounting.The

discountedpayback periodaddressesoneofthedrawbacks ofthepayback period

bydiscounting cashflowsattheproject’s required r a t eofreturn.However, thediscounted

payback period stilldoesnot consider anycashflowsbeyond thepayback period, which means

that itisapoor measure ofprofitability.Again, itsuseis primarily a s ameasure ofliquidity.

Profitability Index (PI)

Theprofitability index(PI)isthepresent valueofaproject’s future cashflowsdivided

bytheinitial cashoutlay:

The profitabilityindex isrelated closelytonetpresent value.The NPV isthe difference

between thepresent valueoffuture cashflowsandtheinitial cashoutlay, andthePIistheratio

ofthepresent valueoffuture cashflowstothe initial cash outlay.

IftheNPV ofaproject ispositive, thePIwillbegreater thanone. IftheNPV is negative,

thePIwillbelessthan one. Itfollowsthat thedecisionruleforthePIis:

If PI > 1.0, accept the project.

If PI < 1.0, reject the project

A project’s NPVprofile is agraph that shows aproject’s NPVfordifferentdiscount rates.The

NPVprofilesforthetwoprojects describedintheprevious example arepresented inFigure

1.The projectNPVsaresummarizedinthetable below the graph. The discount rates are on the

x-axis of theNPV profile,andthe corresponding NPVs are plotted on the y-axis.

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Figure 1: NPV Profiles

Discount Rate NPVA NPVB

0% 600.00 800.00

5% 360.84 413

10% 157.64 98.36

15% (16.66) (160.28)

Note that the projects' IRRs are the discount rates where the NPV profiles intersect the

x-axis, because these are the discount rates for which NPV equals zero. Recall that the

IRRis thediscount ratethat results in an NPV of zero.

Also notice inFigure 1that the NPV profiles intersect. They intersect at the discount rate for

which NPVs of the projects are equal, 7.2%. This rate at which the NPVs are equal is called

the crossover rate. At discount rates below 7.2% (to the left of the intersection), Project B

has the greater NPV, and at discount rates above 7.2%, Project A has a greater NPV.

Clearly, the discount rate used in the analysis can determine which one of two mutually

exclusive projects will be accepted. The NPVprofilesforprojects AandBintersect

b ecau s e ofadifference inthetiming ofthecashflows.Examining thecashflowsfortheprojects

(Table1),wecanseethat thetotal cashinflows forProject Baregreater ($2,800) than those

ofProject A ($2,600). Becausetheyboth havethesameinitial cost ($2,000) atadiscount rateof

zero, Project Bhasagreater NPV (2,800 - 2,000 = $800) than ProjectA(2,600 -2,000 = $600).

Wecanalsoseethat thecashflowsforProject Bcomelater intheproject’s life.That's whytheNPV

ofProject Bfallsfasterthan theNPV ofProjectAasthediscount rate increases, and theNPVs

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areeventually equalatadiscount rateof7.2%. Atdiscount ratesabove7.2%, thefactthat thetotal

cashflowsofProject Baregreater innominal dollars isoverridden bythefactthat Project

B'scashflowscomelater intheproject's lifethan those ofProject A.

Example: Crossover rate

Two projects have the following cash flows:

20X1 20X2 20X3 20X4

Project A -550 150 300 450

Project B -300 50 200 300

What is crossover rate for Project A and project B?

Answer:

The crossover rate is the discount rate that makes the NPVs of Projects A and B equal. That

is, it makes the NPV of the differences between the two projects’ cash flows equal zero.

To determine crossover rate, subtract the cash flows of the Project B from those of project A

and calculate the IRR of the differences.

20X1 20X2 20X3 20X4

Project A - Project B -250 100 100 150

CF0 = -250; CF1 = 100; CF2 = 100; CF3= 150; CPT IRR = 17.5%

1.2 Cost of Capital

The capitalbudgeting process involvesdiscounted c a s h flowanalysis.Toconductsuch

analysis,youmust knowthefirm'sproper discountrate .This topicreviewdiscusseshow,

asananalyst,youcandetermine t h e proper rateatwhich todiscountthecashflows

associatedwithacapitalbudgeting project .This discountrate isthefirm'sweighted

averagecostofcapital (WACC)andisalsoreferredtoasthemarginalcostofcapital (MCC).

Basicdefinitions.On theright (liability)sideofafirm'sbalancesheet,wehavedebt, preferred

stock,andcommon equi ty.Thesearenormally referredtoasthecapital

componentsofthefirm.Anyincreaseinafirm'stotalassetswillhavetobefinanced

throughanincreaseinatleastoneofthesecapitalaccounts. Thecostofeachofthese components

i s calledthecomponentcostofcapital.

Throughoutthisreview, wefocusonthefollowingcapitalcomponents a n d their

componentcosts:

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kid: The rateatwhich thefirmcanissuenewdebt.This istheyieldto

maturityonexistingdebt.This isalsocalledthebefore-tax component costofdebt.

Kd(l- t): The after-tax costofdebt. Here, tis thefirm'smarginal taxrate.The after

taxcomponentcostofdebt, kd(l-t),isusedtocalculate theWACC.

Kps: The costofpreferred stock.

Kce: The costofcommon equity.Itistherequired rateofreturn oncommon

stockandisgenerallydifficulttoestimate.

Inmanycountries, theinterest paidoncorporate debtistaxdeductible. Becauseweare interested

intheafter-tax costofcapital,weadjust thecostofdebt, kd,forthefirm's marginal

taxrate,t.Becausethereistypicallynotaxdeduction allowedforpayments to common orpreferred

stockholders, thereisnoequivalent deduction tokpsorkce·

Howacompany raisescapitalandhowitbudgetsorinvestsitareconsidered

independently. Mostcompanieshaveseparatedepartments forthetwotasks.Thefinancing

department isresponsibleforkeepingcostslowandusingabalanceoffunding sources: common

equity,preferredstock,anddebt.Generally,itisnecessarytoraiseeachtypeofcapitalinlargesums.Th

elargesumsmaytemporarily overweightthemostrecently

issuedcapital,butinthelongrun,thefirmwilladheretotargetweights.Becauseofthese

andotherfinancingconsiderations,eachinvestment decisionmustbemadeassuminga

WACC,whichincludeseachofthedifferentsourcesofcapitalandisbasedonthelong

runtargetweights.Acompanycreatesvaluebyproducing areturn onassetsthatishigher

thantherequiredrateofreturn onthecapitalneededtofundthoseassets.

TheWACC, aswehavedescribed it,isthecostoffinancing firmassets.Wecanview

thiscostasanopportunitycost.Consider howacompany couldreduceitscostsifit found

awaytoproduce itsoutput usingfewerassets,likelessworking capital. Ifweneedlessworking

capital,wecanusethefundsfreeduptobuybackourdebtandequity securitiesinamixthatjustmatches

ourtargetcapitalstructure. Our after-tax savings would

betheWACCbasedonourtargetcapitalstructure multiplied bythetotalvalueofthesecuritiesthat

arenolongeroutstanding.

Forthesereasons,anytimeweareconsidering aproject that requiresexpenditures, comparing

thereturn onthoseexpenditures totheWACC istheappropriate wayto determine whether

undertakingthat projectwillincreasethevalueofthefirm.This istheessenceofthecapitalbudgeting

decision. Becauseafirm'sWACCreflectstheaverage riskoftheprojects

thatmakeupthefirm,itisnotappropriate forevaluating allnew projects. Itshould beadjusted

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upward forprojectswithgreater-than-averageriskand downward forprojectswithless-than-

averagerisk.

Theweights inthecalculation ofafirm'sWACCaretheproportionsofeachsourceof capital

inafirm'scapitalstructure.

Calculating aCompany'sWeighted AverageCostofCapital

TheWACC isgivenby:

where:

wd= percentage ofdebtinthecapitalstructure

wps= percentage ofpreferred stockinthecapitalstructure

wce= percentage ofcommon stockinthecapitalstructure

Example: Computing WACC

Suppose Dexter, Inc.’s target capital structure is as follows:

Wd = 0.45, wps = 0.05, and wce = 0.50

Its before-tax cost of debt is 8%, its cost of equity is 10%, its cost of prefered stock is 8.4 %,

and its marginal tax rate is 40%. Calculate Dexter’s WACC?

Answer:

Dexter’s WACC will be:

WACC = (wd)(kd)(1 - t) + (wps)(kps) + (wce)(kce)

WACC = (0.45)(0.08)(0.6) + (0.05)(0.084) + (0.50)(0.12) = 0.0858 8.6%

Theweightsinthecalculation of WACC should bebasedonthefirm'starget capital structure;

that is, theproportions (basedonmarket values)ofdebt, preferred stock, andequitythat

thefirmexpectstoachieveovertime. Intheabsenceofanyexplicit information about

afirm'starget capitalstructure fromthefirmitself,ananalystmay simplyusethefirm'scurrent

capitalstructure (basedonmarket values)asthebestindication ofitstargetcapitalstructure.

Iftherehasbeenanoticeable trend inthefirm'scapitalstructure, theanalystmaywant

toincorporate thistrend intohisestimate ofthe firm'starget capitalstructure.

Forexample,ifafirmhasbeenreducing itsproportion of debtfinancing

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eachyearfortwoorthreeyears,theanalystmaywishtouseaweighton debtthat islowerthan

thefirm'scurrent weightondebtinconstructing thefirm'starget capitalstructure.

Alternatively, ananalystmaywishtousetheindustry averagecapitalstructure asthe

targetcapitalstructure forafirmunder analysis.

Example: Determiningtarget capital structureweights

The marketvaluesofafirm'scapitalareasfollows:

• Debt outstanding: $8million

• Preferredstockoutstanding: $2million

• Common stockoutstanding: $10million

• Totalcapital: $20million

What isthefirm'starget capitalstructure basedonitsexistingcapitalstructure?

Acompany increasesitsvalueandcreateswealth foritsshareholdersbyearningmoreon its

investment inassetsthan is required bythosewhoprovidethecapitalforthefirm.Afirm'sWACC

mayincreaseaslarger amountsofcapitalare raised.Thus,itsmarginal

costofcapital,thecostofraisingadditionalcapital,canincreaseaslargeramountsare

investedinnewprojects.Thisisillustrated bytheupward-slopingmarginalcostof capital curvein

Figure1. Given theexpected returns (IRRs)onpotentialprojects,we canorder

theexpendituresonadditionalprojectsfromhighest to lowest IRR.Thiswillallowustoconstruct a

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Figure 1: The Optimal Capital Budget

The intersectionoftheinvestmentopportunityschedulewith themarginal costof

capitalcurveidentifiestheamount oftheoptimalcapital budget. The intuitionhere isthat

thefirmshould undertakeallthoseprojectswithIRRsgreaterthan thecostof funds,

thesamecriteriondeveloped inthecapitalbudgetingtopicreview.Thiswill

maximizethevaluecreated.Atthesametime,noprojectswith IRRslessthan themarginal

costoftheadditionalcapitalrequiredtofundthem should

beundertaken,astheywillerodethevaluecreatedbythefirm.

One cautionarynoteregarding thesimplelogicbehind Figure1 isinorder.Allprojects

donothavethesamerisk.TheWACC istheappropriatediscountrateforprojects that

haveapproximatelythesamelevelofriskasthefirm'sexistingprojects.This isbecause

thecomponentcostsofcapitalusedtocalculatethefirm'sWACC arebasedonthe

existingleveloffirmrisk.Toevaluateaproject withgreaterthan

(thefirm's)averagerisk,adiscountrategreaterthan thefirm'sexistingWACC should

beused.Projectswithbelow-averageriskshould beevaluated usingadiscountratelessthan

thefirm's WACC.

Anadditionalissuetoconsider whenusingafirm's WACC (marginal costofcapital) to

evaluateaspecificproject isthat thereisanimplicitassumptionthat thecapitalstructure

ofthefirmwillremain atthetargetcapitalstructureoverthelifeoftheproject.

Thesecomplexities aside,wecanstillconclude that theNPVs ofpotentialprojects of firm-

averageriskshould becalculated usingthemarginal costofcapitalforthefirm. Projectsforwhich

Project IRR

Cost of

Capital (%)

Investment

Opportunity

Schedule

New Capital

Raised/Invested

($)

Optimal

Capital

Budget

Marginal

Cost of

Capital

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thepresent valueoftheafter-tax cashinflowsisgreaterthan the presentvalueoftheafter-tax

cashoutflowsshould beundertakenbythefirm.

Theafter-taxcostofdebt, kd(l-t),isusedincomputingtheWACC. Itisthe

interestrateatwhichfirmscanissuenewdebt (kd)netofthetaxsavingsfromthetax

deductibilityofinterest, kd(t):

after-taxcostofdebt= interest rate- taxsavings=kd- kd(t) =kd(l - t)

after-taxcostofdebt=kd(l - t)

IfamarketYTMisnotavailablebecausethefirm'sdebtisnotpublicly traded,

theanalystmayusetherating andmaturity ofthefirm'sexistingdebttoestimate thebefore•

taxcostofdebt. If,forexample,thefirm'sdebtcarriesasingle-Arating andhasan averagematurity

of15years,theanalystcanusetheyieldcurveforsingle-Arateddebttodetermine thecurrent market

ratefordebtwith a15-yearmaturity.This approachisanexampleofmatrix pricing orvaluingabond

basedontheyieldsofcomparable bonds.

Ifanycharacteristics ofthefirm'santicipated debtwould affecttheyield(e.g.,covenants

orseniority), theanalystshould maketheappropriate adjustment tohisestimatedbefore-tax

costofdebt.Forfirmsthatprimarily employfloating-

rate debt,theanalyst should estimate thelonger-term costofthefirm'sdebt usingthecurrent

yieldcurve (termstructure) fordebtoftheappropriate rating category.

The costofpreferred stock (kp) is:

kps=Dps/P

where:

Dps = preferred dividends

P = market priceofpreferred

Example: Cost of preferred stock

Suppose Dexter, Inc., has preferred stock that pays an $8 dividend per share and sells

for $100 per share. What is Dexter’s cost of preferred stock?

Answer:

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kps = Dps / P

kps = $8 / $100 = 0.08 = 8%

Note that the equation kps = Dps / P is just a rearrangement of the preferred stock

valuation model P = Dps / kps, where P is the market price.

The opportunitycostofequity capital (kce)istherequired rateofreturn onthefirm's common

stock.The rationale hereisthat thefirmcouldavoidpartofthecostof common stockoutstanding

byusingretained earnings tobuybacksharesofitsown stock.The costof(i.e.,therequired return

on)common equitycanbeestimated using oneofthefollowingthreeapproaches:

1. Thecapital assetpricing modelapproach.

StepI: Estimate therisk-freerate,RFR.Yieldsondefaultrisk-freedebtsuchas

U.S.Treasurynotesareusuallyused.The mostappropriate maturity to chooseisonethat

isclosetotheusefullifeoftheproject.

Step2:Estimate thestock'sbeta,(3.This isthestock'sriskmeasure.

Step3: Estimate theexpected rateofreturn onthemarket, E(Rmkt).

Step4: Usethecapitalassetpricing model (CAPM) equation toestimate the required

rateofreturn:

Example: Using CAPM to estimate kce

Suppose RFR = 6%, Rmkt 11%, and Dexter has a beta of 1.1. Estimate Dexter’s cost

of equity.

Answer:

The required rate of return for Dexter’s stock is:

kce = 6% + 1.1(11%—6%) = 11.5%

1. The dividend discount model approach. Ifdividends areexpectedtogrowata constant

rate,g,thenthecurrent valueofthestockisgivenbythedividend growth model:

where:

D1= nextyear'sdividend

kce = required rateofreturn oncommon equity

g = firm'sexpectedconstant growth rate

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Rearranging the terms, you can solve for kce:

Inorder touse kce = D1/P0 +g,youhaveto estimate theexpectedgrowth rate,g.This

canbedoneby:

Usingthegrowth rateasprojected bysecurityanalysts.

Usingthefollowingequation toestimate afirm'ssustainable growth rate:

g=(retention rate)(return onequity) =(1- payout rate)(ROE)

The difficultywith thismodel isestimating thefirm'sfuture growth rate.

Example: Estimating using the dividend discount model

Suppose Dexter’s stock sells for $21, next year’s dividend is expected to be $1, Dexter’s

expected ROE is 12%, and Dexter is expected to pay out 40% of its earnings. What is

Dexter’s cost of equity?

Answer:

g = (ROE)(retention race)

g = (0.12)(1 - 0.4) = 0.072 = 7.2%

kce = (1 / 21) + 0.072 = 0.12 or 12%

Aproject's betaisameasureofitssystematic ormarket risk.Justaswecanuseafirm's betatoestimate

itsrequired return onequity,wecanuseaproject's betatoadjustfor

differencesbetweenaspecificproject's riskandtheaverageriskofafirm'sprojects.

Becauseaspecificproject isnotrepresented byapublicly traded security,wetypically cannot

estimate aproject's betadirectly.Oneprocessthat canbeusedisbasedonthe equitybetaofapublicly

traded firmthat isengagedinabusinesssimilarto,andwith risksimilarto,theproject under

consideration. This isreferredtoasthepure-play method

becausewebeginwiththebetaofacompany orgroupofcompanies that are

purelyengagedinabusinesssimilartothat oftheproject andaretherefore comparable totheproject.

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Thus, usingthebetaofaconglomerate that isengagedinthesame businessastheproject would

beinappropriate becauseitsbetadepends onitsmany different linesofbusiness.

The betaofafirmisafunction notonlyofthebusinessrisksofitsprojects (linesof

business)butalsoofitsfinancialstructure. Foragivensetofprojects, thegreaterafirm's

relianceondebtfinancing, thegreateritsequitybeta. Forthisreason,wemust adjust the pure-play

betafromacomparable company (orgroup ofcompanies) forthecompany's

leverage(unleverit)andthenadjust it(re-leverit)basedonthefinancialstructure ofthe company

evaluating theproject. Wecanthen usethisequitybetatocalculate thecostof

equitytobeusedinevaluating theproject.

Togettheassetbetaforapublicly traded firm,weusethefollowingformula:

where:

D/E = comparable company's debt-to-equity ratio and tis its marginal tax rate

Togettheequitybetafortheproject, weusethesubject firm'staxrateanddebt-to-equity ratio:

The followingexampleillustrates thistechnique.

Example: Cost of capital for a project

Acme, Inc., is considering a project in the food distribution business. It has a D/E

ratio of 2, a marginal tax rate of 40%, and its debt currently has a yield of 14%.

Balfor, a publicly traded firm that operates only in the food distribution business, has

a D/E ratio of 1.5, a marginal tax rate of 30%, and an equity beta of 0.9. The risk-free

rate is 5%, and the expected return on the market portfolio is 12%. Calculate Balfor’s

asset beta, the project’s equity beta, and the appropriate WACC to use in evaluating

the project.

Answer:

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Balfor’s asset beta:

Equity beta for the project:

= 0.439[1 + (1- 0.4)(2)] = 0.966

Project cost of equity = 5% + 0.966(12% - 5%) = 11.762%

To get the weights of debt and equity, use the D/E ratio and give equity a value of 1.

Here, D/E = 2, so if E = 1, D = 2. The weight for debt, D/(D + E), is 2/(2 + 1) = 2/3,

and the weight for equity, E/(D + E), is 1/(2 + 1) = 1/3. The appropriate WACC for

the project is therefore:

While themethod istheoreticallycorrect, thereareseveralchallenging issuesinvolvedin

estimatingthebetaofthecomparable (orany)company's equity:

Betaisestimated usinghistorical returns data.Theestimate issensitivetothelength

oftimeusedandthefrequency (daily,weekly,etc.)ofthedata.The estimate isaffectedbywhich

indexischosentorepresentthemarket return. Betasarebelievedtoreverttoward 1 over time,

and the estimate may need to be adjusted for this tendency. Estimates ofbetaforsmall-

capitalization firmsmayneedtobeadjustedupwardtoreflectriskinherentinsmallfirmsthat

isnotcapturedbytheusualestimation methods.

UsingtheCAPM toestimate thecostofequityisproblematicindeveloping countries

becausebetadoesnotadequatelycapture countryrisk.Toreflecttheincreased risk

associatedwithinvesting inadeveloping country, acountry riskpremiumisadded to themarket

riskpremiumwhen usingtheCAPM.

Thegeneralriskofthedeveloping countryisreflectedinitssovereignyield spread.

Thisisthedifferenceinyieldsbetween thedeveloping country's governmentbonds

(denominatedinthedeveloped market's currency) andTreasurybonds ofasimilar

maturity.Toestimate anequity riskpremiumforthecountry, adjust thesovereignyield

spreadbytheratioofvolatility between thecountry's equity market anditsgovernment bond

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market (forbonds denominatedinthedeveloped market'scurrency). Amore

volatileequitymarket increasesthecountryriskpremium,other thingsequal.

The revisedCAPM equationisstated as:

where:

CRP= countryriskpremium

The countryriskpremiumcanbecalculated as:

where:

sovereignyieldspread=differencebetweentheyields ofgovernmentbondsinthe

developingcountryandTreasurybondsofsimilarmaturities

Example: Country risk premium

Robert Rodriguez, an analyst with Omni Corporation, is estimating the cost of equity

for a project Omni is starting in Venezuela. Rodriguez has compiled the following

information for his analysis:

Project beta =1.25.

Expected market return = 10.4%.

Risk-free rate = 4.2%.

Country risk premium = 5.53%.

Calculate the cost of equity for Omni’s Venezuelan project.

Answer

kce = RF + β⦋E(RMKT)-RF +CRP⦌

= 0.042 + 1.25[0.104 - 0.042 + 0.0553]

= 0.042 + 1.25[0.1173]

= 0.1886, or 18.86%

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1.3 Measures of leverage

Leverage,inthesenseweuseithere,referstotheamount offixedcostsafirmhas.These

fixedcostsmaybefixedoperating expenses,suchasbuilding orequipmentleases,orfixedfinancing

costs,suchasinterest payments ondebt. Greaterleverageleadstogreatervariability

ofthefirm'safter-taxoperating earnings andnetincome.Agivenchangein

saleswillleadtoagreaterchangeinoperating earningswhenthefirmemploysoperating

leverage;agivenchangeinoperating earningswillleadtoagreaterchangeinnetincome

whenthefirmemploysfinancialleverage.

Business riskreferstotheriskassociatedwith afirm'soperating income andistheresult

ofuncertainty about afirm'srevenuesandtheexpenditures necessarytoproduce those

revenues.Businessriskisthecombinationofsalesriskandoperating risk.

Salesriskistheuncertaintyabout thefirm'ssales.Operatingriskreferstotheadditional

uncertaintyabout operating earningscaused byfixedoperating

costs.Thegreatertheproportionoffixedcoststovariablecosts, thegreaterafirm'soperating risk.

Financial riskreferstotheadditional riskthat thefirm'scommon stockholders must

bearwhenafirmusesfixedcost(debt)financing. When acompany financesits operationswith

debt, ittakesonfixedexpensesintheformofinterest payments. The

greatertheproportionofdebtinafirm'scapitalstructure, thegreaterthefirm'sfinancial risk.

1.4 Dividends and Share Repurchases

Cashdividends,asthenameimplies, arepayments madetoshareholders incash.They

comeinthreeforms:

1. Regular dividends occurwhenacompany paysoutaportion ofprofitsona consistent

schedule (e.g.,quarterly). Along-term recordofstableorincreasing dividends

iswidelyviewedbyinvestorsasasignofacompany's financialstability.

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2. Specialdividends areusedwhenfavorablecircumstances allowthefirmtomakea one-time

cashpayment toshareholders, inadditiontoanyregulardividends the

firmpays.Manycyclicalfirms(e.g.,automakers) willuseaspecialdividend to shareprofitswith

shareholders whentimesaregoodbutmaintaintheflexibilityto

conservecashwhenprofitsaredown.Other namesforspecialdividends include

extradividendsandirregulardividends.

3. Liquidatingdividends occurwhenacompany goesoutofbusinessanddistributes

theproceeds toshareholders. Fortaxpurposes, aliquidatingdividend istreated asa return

ofcapitalandamounts overtheinvestor'staxbasisaretaxedascapitalgains.

Nomatterwhich formcashdividends take,theirneteffectistotransfer cashfromthe company

toitsshareholders. Thepayment ofacashdividend reducesacompany'sassets

andthemarketvalueofitsequity.This meansthat immediately afteradividend ispaid,

thepriceofthestockshould dropbytheamount ofthedividend. Forexample,ifa

company'sstockpriceis$25pershareandthecompany pays$1pershareasadividend,

thepriceofthestockshould immediately dropto$24persharetoaccount forthelower

assetandequityvaluesofthefirm.

Stockdividends aredividends paidoutinnewsharesofstockrather than

cash.Inthiscase,therewillbemoresharesoutstanding, buteachonewillbeworth less.Stock

dividends arecommonly expressedasapercentage. A20%stockdividend meansevery

shareholder gets20%morestock.On thefirm'sbalancesheet,issuingastockdividend

decreasesretained earnings andincreasescontributed capitalbythesameamount. Total

shareholders'equityremainsunchanged.

Example: Stock dividend

Dwight Craver owns loo shares of Carson Construction Company at a current price

of $30 per share. Carson has 1,000,000 shares of stock outstanding, and its earnings

per share (EPS) for the last year were $1.50. Carson declares a 20% stock dividend to

all shareholders of record as of June 30.

What is the effect of the stock dividend on the market price of the stock, and what is the

impact of the dividend on Craver’s ownership position in the company?

Answer

Impact of 20% Stock Dividend on Shareholders

Before Stock Dividend After Stock Dividend

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Shares outstanding 1,000,000

1,000,000 x 1.20 = 1,200,000

Earnings per share $1.50 $1.50 /1.20 = $1.25

Stock price $30.00 $30.00 / 1.20 $25.00

Total market value 1,000,000 x $30 = $30,000,000 1,200,000 x $25 = $30,000,000

Shares owned 100 100 x 1.20 = 120

Ownership value 100 x $30 = $3,000 120 x $25 = $3,000

Ownership stake 100 / 1,000,000 = 0.01% 120 / 1,200,000 = 0.01%

The effect of the stock dividend is to increase the number of shares outstanding by

20%. However, because company earnings stay the same, EPS decline and the price of the

firm’s stock drops from $30 to $25. Craver’s receipt of more shares is exactly offset by the

drop in stock price, and his wealth and ownership position in the company are unchanged.

Stocksplits divideeachexistingshareintomultiple shares,thuscreating moreshares. There

arenowmoreshares,butthepriceofeachsharewilldropcorrespondinglyto thenumber

ofsharescreated,sothereisnochangeintheowner'swealth. Splitsareexpressedasaratio. Ina3-for-1

stocksplit,eacholdshareissplitintothreenewshares. Stocksplitsaremorecommon todaythan

stockdividends.

Example: Stock split

Carson Construction Company declares a 3-for-2 stock split. The current stock price

is $30, earnings for last year were $1.50, dividends were $0.60 per share, and there

arc 1 million shares outstanding. What is the impact on Carson’s shares outstanding,

stock price, EPS, dividends per share, dividend yield, PIE, and market value?

Answer:

Impact of a 3-for-2 Stock Split on Shareholders

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Before Stock Split After Stock Split

Shares outstanding 1,000,000 1,000,000 x (3/2) = 1,500,000

Stock price $30.00 $30.00 / (3/2) = $20.00

Earnings per share $1.50 $1.50 / (3/2) = $1.00

Dividends per share $0.60 $0.60 / (3/2) = $0.40

Dividend yield $0.60 / $30.00 = 2.0% $0.40 / $20.00 = 2.0%

P/E ratio $30.00 / $1.50 = 20 $20.00 / $1.00 = 20

Total market value 1,000,000 x $30 = $30,000,000 1,500,000 x $20 = $30,000,000

The number of shares outstanding increases, but the stock price, EPS, and dividends

per share decrease by a proportional amount. The dividend yield, PIE ratio, and total

market value of the firm remain the same. As in our prior example, the effect on the

firm’s shareholders also remains the same. The number of shares would increase

(100 x 3 / 2 = 150), but the ownership value and stake are unchanged.

The bottom lineforstocksplitsandstockdividends isthat theyincreasethetotal number

ofsharesoutstanding, butbecausethestockpriceandearnings pershareare adjusted

proportionally, thevalueofashareholder's total sharesisunchanged.

Somefirmsusestocksplitsandstockdividends tokeepstockpriceswithin aperceived optimal

trading rangeof$20to$80pershare.What doesacademic researchhavetosay about this?

Stockpricestend toriseafterasplitorstockdividend.

Priceincreasesappeartooccurbecausestocksplitsaretakenasapositivesignalfrom

management about future earnings.

Ifareport ofgoodearnings doesnotfollowastocksplit,pricestend torevertto theiroriginal

(split-adjusted) levels.

Stocksplitsanddividends tend toreduceliquidity duetohigher percentage brokerage

feesonlower-priced stocks.

The conclusion isthat stocksplitsandstockdividends createmoresharesbut don't

increaseshareholder value.

Reversestocksplits are theopposite ofstock splits.Afterareversesplit,therearefewer shares

outstanding butahigher stock price. Becausethesefactors offsetoneanother, shareholder wealth

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is unchanged. Thelogic behind areverse stock splitis that the perceived optimalstock

pricerangeis$20to$80per share, andmostinvestorsconsider astock with apricelessthan

$5persharelessthan investment grade.Exchangesmay imposeaminimumstock priceanddelist

thosethat fallbelowthatprice.Acompany in financialdistresswhosestock hasfallendramatically

maydeclare areversestock splitto increasethestock price.

EffectsonFinancial Ratios

Paying a cash dividend decreases assets (cash) and shareholders' equity (retained

earnings). Other things equal, the decrease in cash will decrease a company's liquidity

ratios and increase its debt-to-assets ratio, while the decrease in shareholders' equity will

increase its debt-to-equity ratio.

Stock dividends, stock splits, and reverse stock splits have no effect on a company's

leverage ratios or liquidity ratios. These transactions do not change the value of a

company's assets or shareholders' equity; they merely change the number of equity

shares.

An example of a typical dividend payment schedule is shown in Figure 1.

Figure 1: Dividend Payment Chronology

Declaration date Ex-dividend date Holder-of-record

date

Payment date

August 25 September 15 September 17 September 30

Declarationdate.Thedatetheboardofdirectorsapprovespayment ofthedividend.

Ex-dividenddate.Thefirstdayashare ofstock tradeswithoutthedividend.Theex-dividend date

isalso thecutoffdateforreceiving thedividend andoccurstwo business daysbeforetheholder-of-

record date.Ifyoubuytheshare onorafterthe ex-dividend date,youwillnotreceive thedividend.

Holder-of-record date. The date on which the shareholders of record are designated to

receive the dividend.

Payment date. The date the dividend checks are mailed out or when the payment is

electronically transferred to shareholder accounts.

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Stocks are traded ex-dividend on and after the ex-dividend date, so stock prices should

fall by the amount of the dividend on the ex-dividend date. Because of taxes, however,

the drop in price may be closer to the after-tax value of dividends.

A share repurchase is a transaction in which a company buys back shares of its own

common stock. Companies use three methods to repurchase shares:

1. Buyinthe open market. Companies mayrepurchase stockintheopenmarket attheprevailing

market price.Asharerepurchase isauthorized bytheboardof directors foracertain

numberofshares.Buyingintheopenmarket givesthe company theflexibilityto choosethetiming

ofthetransaction.

2. Buyafixednumberofsharesatafixedprice. Acompany mayrepurchase stock bymaking

atender offerto repurchase aspecificnumberofsharesatapricethatisusuallyatapremium

tothecurrent market price.Shareholders maytender their sharesaccording

tothetermsoftheoffer.Ifshareholders trytotender moreshares than thetotalrepurchase,

thecompany willtypicallybuybackaprorataamount fromeachshareholder.The company

mayselectatender offerpriceoruseaDutch auction (described intheEconomics

topicreviewforDemandandSupplyAnalysis: Introduction)todetermine

thelowestpriceatwhich itcanrepurchase thenumber ofsharesdesired.

3. Repurchase bydirect negotiation.Companies maynegotiate directlywith alarge

shareholder tobuybackablockofshares,usuallyatapremium tothemarket price. Acompany

mayengageindirectnegotiation inordertokeepalargeblockofshares fromcoming intothemarket

andreducing thestockpriceortorepurchase shares fromapotentialacquirer afteranunsuccessful

takeoverattempt.Ifthefirmpays morethan market

valuefortheshares,theresultisanincreaseinwealthforthesellerandanequaldecreaseinwealthforre

maining firmshareholders.

Asharerepurchase willreducethenumberofsharesoutstanding,whichwilltend to

increaseearningspershare.On theotherhand, purchasing shareswith company funds

willreduceinterest income andearnings, andpurchasing shareswithborrowed funds

incursinterest costs,whichwillreduceearnings directlybytheafter-tax costoftheborrowed

funds.The relation ofthepercentage decreaseinearnings andthepercentage

decreaseinthenumber ofsharesusedtocalculateEPSwilldetermine whether theeffect

ofastockrepurchase onEPSwillbepositiveornegative.

Beforewelookatthecalculations involvedindetermining theeffectofashare repurchase

onEPS,consider thefollowing intuitive approach. The

earningsyieldforashareofstockissimplyEPSdivided bytheshareprice.A$20stockwith EPSof$1

hasanearningsyieldof5%.Iftheafter-taxyieldoncompany funds usedtorepurchase

shares,ortheafter-tax costofborrowed funds usedtorepurchase

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shares,isgreaterthan5%,EPSwillfallasaresultoftherepurchase. Iftheafter-taxyieldoncompany

fundsusedtorepurchase shares,ortheafter-tax costofborrowed funds usedtorepurchase

shares,islessthan 5%,EPSwillriseasaresultoftherepurchase.

Example: Share repurchase when after-tax cost of debt is less than earnings yield

Spencer Pharmaceuticals, Inc., (SPI) plans to borrow $30 million that it will use to

repurchase shares. SPI’s chief financial officer has compiled the following information:

Share price at the time of buyback = $50.

Shares outstanding before buyback = 20,000,000.

EPS before buyback = $5.00.

Earnings yield = $5.00 / $50 = 10%.

After-tax cost of borrowing = 8%.

Planned buyback = 600,000 shares.

Calculate the EPS after the buyback.

Answer:

total earnings = $5.00 x 20,000,000 = $100,000,000

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Because the 8% after-tax cost of borrowing is less than the 10% earnings yield (E/P)

of the shares, the share repurchase will increase the company’s EPS.

The conclusion isthat asharerepurchase usingborrowed fundswillincreaseEPSifthe after-

taxcostofdebtusedtobuybacksharesislessthan theearningsyieldoftheshares beforetherepurchase.

ItwilldecreaseEPSifthecostofdebtisgreaterthan theearnings

yield,anditwillnotchangeEPSifthetwoareequal.

Sharerepurchases mayalsohaveanimpact onthebookvalueofashareofstock.

Example: Effect of a share repurchase on book value per share

The share prices of Blue, Inc., and Red Company arc both $25 per share, and each

company has 20 million shares outstanding. Both companies have announced a

$10 million stock buyback. Blue, Inc., has a book value of $300 million, while Red

Company has a book value of $700 million.

Calculate the book value per share (BVPS) of each company after the share

repurchase.

Answer:

Share buyback for both companies = $10 million / $25 per share = 400,000 shares.

Remaining shares for both companies = 20 million - 400,000 = 19.6 million.

Blue, Inc.’s current BVPS = $300 million / 20 million = $15.

The market price per share of $25 is greater than the BVPS of $15.

Book value after repurchase: $300 million - $10 million = $290 million

BVPS = $290 million /19.6 million = $14.80

BVPS decreased by $0.20

Red Company’s current BVPS = $700 million / 20 million = $35.

The market price per share of $25 is less than the BVPS of $35.

Book value after repurchase: $700 million — $10 million = $690 million

BVPS $690 million / 19.6 million = $35.20

BVPS increased by $0.20

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The conclusion isthat BVPSwilldecreaseiftherepurchase priceisgreaterthan the original

BVPSandincreaseiftherepurchase priceislessthan theoriginal BVPS.

Becausesharesarerepurchased usingacompany's owncash,asharerepurchase can beconsidered

analternative toacashdividend asawayofdistributing earnings to shareholders.

Assuming thetaxtreatment ofthetwoalternatives isthesame,asharerepurchase has

thesameimpact onshareholder wealthasacashdividend payment ofanequalamount.

Example: Impact ofsharerepurchase andcashdividend ofequalamounts

Spencer Pharmaceuticals, Inc., (SPI) has 20,000,000 shares outstanding with a current market

value of $50 per share. SPI made $100 million in profits for the recent quarter, and because

only 70% of these profits will be reinvested back into the company, SPI’s Board of Directors

is considering two alternatives for distributing the remaining 30% to shareholders:

• Pay a cash dividend of $30,000,000 / 20,000,000 shares = $1.50 per share.

• Repurchase $30,000,000 worth of common stock.

Assume that dividends are received when the shares go ex-dividend, the stock can be

repurchased at the market price of $50 per share, and there arc no differences in tax

treatment between the two alternatives. How would the wealth of an SPI shareholder

be affected by the board’s decision on the method of distribution?

Answer:

(1) Cash dividend

After the shares go ex-dividend, a shareholder of a single share would have $1.50 in

cash and a share worth $50 - $1.50 = $48.50.

The ex-dividcnd value of $48.50 can also be calculated as the market value of equity

after the distribution of the $30 million, divided by the number of shares outstanding

after the dividend payment:

total wealth from the ownership of one share $48.50 + $1.50 = $50

(2) Share repurchase

With $30,000,000, SPI could repurchase $30,000,000 / $50 = 600,000 shares of

common stock. The share price after the rcpurchasc is calculated as the market value

of equity after the $30,000,000 repurchase divided by the shares outstanding after the

repurchase:

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1.5 Working capital management

Acompany's primarysourcesofliquidityarethesourcesofcashitusesinitsnormal day-to-day

operations. Thecompany's cashbalancesresultfromsellinggoodsand services,collecting

receivables,andgenerating cashfromother sourcessuchasshort-terminvestments.

Typicalsourcesofshort-termfundinginclude tradecreditfromvendors

andlinesofcreditfrombanks.Effectivecashflowmanagementofafirm's collections andpayments

canalsobeasourceofliquidityforacompany.

Secondary sourcesofliquidityinclude liquidatingshort-termorlong-lived assets, negotiating

debtagreements (i.e.,renegotiating), orfilingforbankruptcyand reorganizing

thecompany.While usingitsprimary sourcesofliquidity isunlikely to changethecompany's

normal operations, resorting tosecondary sourcesofliquidity

suchasthesecanchangethecompany'sfinancialstructureandoperations significantly

andmayindicate that itsfinancialposition isdeteriorating.

FactorsThat Influence aCompany'sLiquidityPosition

Ingeneral,acompany's liquidityposition improvesifitcangetcashtoflowinmore

quicklyandflowoutmoreslowly.Factorsthatweakenacompany's liquidityposition are

calleddragsandpullsonliquidity.

Drags onliquiditydelayorreducecashinflows,orincreaseborrowing costs.Examples include

uncollected receivablesandbaddebts, obsoleteinventory (takeslongertosell

andcanrequiresharppricediscounts), andtight short-term creditduetoeconomic conditions.

Pullsonliquidity acceleratecashoutflows.Examplesinclude payingvendors sooner than

isoptimal andchangesincredittermsthat requirerepayment ofoutstanding balances.

Somecompanies tend tohavechronically weakliquiditypositions, oftenduetospecific

factorsthat affectthecompany oritsindustry.These companies typicallyneedtoborrow

againsttheirlong-lived assetstoacquireworking capital.

1.6 Corporate Governance

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Corporate governance isthesetofinternal controls, processes, andprocedures by

whichfirmsaremanaged.Itdefinestheappropriate rights, roles,andresponsibilitiesof

management, theboardofdirectors, andshareholderswithin anorganization.Itisthe

firm'schecksandbalances.Good corporate governancepractices seektoensurethat:

The boardofdirectors protects shareholder interests.

The firmactslawfullyandethicallyindealingswith shareholders.

The rightsofshareholders areprotected andshareholders haveavoiceingovernance. The

boardactsindependentlyfrommanagement.

Properprocedures andcontrols covermanagement's day-to-day operations.

The firm'sfinancial, operating, andgovernance activitiesarereported toshareholders

inafair,accurate, andtimelymanner.

Thedutyoftheboardistoactintheshareholders' long-term interests. Aneffective board

needstohavetheindependence, experience, andresourcesnecessarytoperform

thisduty.Toproperly protect theirlong-term interests asshareholders, investorsshould consider

whether thefollowingstatements holdtrue:

Amajority oftheboardofdirectors iscomprised ofindependentmembers (not

management).

Theboardmeetsregularlyoutside thepresenceofmanagement.

Thechairman oftheboardisalsotheCEO oraformer CEO ofthefirm.This mayimpair

theabilityandwillingness ofindependentboardmembers toexpress opinions contrary

tothoseofmanagement.

Independentboardmembers haveaprimary orleadingboardmember incaseswhere

thechairman isnotindependent.

Boardmembers arecloselyalignedwithafirmsupplier, customer, share-option plan,

orpension adviser.Canboardmembers recusethemselvesonanypotentialareasof

conflict?

Anindependentboardisless likelytomakedecisionsthat unfairly orimproperly benefit

management andthosewhohaveinfluence overmanagement.

There isoften aneedforspecific,specialized,independentadviceonvariousfirmissues

andrisks,including compensation;mergersandacquisitions; legal,regulatory, and

financialmatters; andissuesrelating tothefirm'sreputation. Atrulyindependentboard

willhavetheabilitytohireexternalconsultants withoutmanagement approval.This

enablestheboardtoreceivespecializedadviceontechnical issuesandprovidestheboard with

independentadvicethat isnotinfluenced bymanagement interests.

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Chủ đề 2: Market Organization.

36

2 Chủ đề 2: Market Organization

2.1 Market organization and structure

Thethreemainfunctions ofthefinancialsystemareto:

1. Allowentities tosaveandborrowmoney,raiseequitycapital,manage risks,trade

assetscurrently orinthefuture,andtradebasedontheirestimates ofassetvalues.

2. Determine thereturns (i.e.,interest rates)that equate thetotalsupplyofsavings with

thetotaldemand forborrowing.

3. Allocatecapitaltoitsmostefficientuses.

Thefinancialsystemallowsthetransfer ofassetsandrisksfromoneentity toanother as

wellasacrosstime.Entities whoutilizethefinancialsysteminclude individuals, firms,

governments, charities, andothers.

Achievement ofPurposesintheFinancial System

Thefinancialsystemallowsentities tosave,borrow,issueequitycapital, managerisks,

exchangeassets,andtoutilizeinformation.

Thefinancialsystemisbestatfulfillingtheseroleswhenthemarkets areliquid, transactions

costsarelow,informationisreadily available,andwhenregulation ensurestheexecution

ofcontracts.

Savings.Individuals willsave(e.g.,forretirement) andexpectareturn that compensates

themforriskandtheuseoftheirmoney.Firmssaveaportion oftheirsalestofund future expenditures.

Vehiclesusedforsavinginclude stocks,bonds, certificatesof deposit, realassets,andother assets.

Borrowing.Individuals mayborrow inordertobuyahouse, fundacollegeeducation,

orforotherpurposes. Afirmmayborrow inordertofinancecapitalexpenditures and forother

activities. Governments mayissuedebttofund theirexpenditures. Lenders canrequirecollateral

toprotect them intheeventofborrower defaults, takeanequity position, orinvestigatethecredit

riskoftheborrower.

Issuingequity.Anothermethod ofraisingcapitalistoissueequity,wherethecapital

providerswillshareinanyfuture profits. Investment bankshelpwith issuance,analysts

valuetheequity,andregulators andaccountants encourage thedissemination of information.

Riskmanagement.Entities facerisksfromchanging interest rates,currencyvalues, commodities

values,anddefaults ondebt, amongother things. Forexample,afirm that owesaforeigncurrency

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in90dayscanlockinthepriceofthisforeigncurrency indomestic currency unitsbyentering

intoaforward contract. Future deliveryofthe foreigncurrency isguaranteed atadomestic-

currencypricesetatinception ofthe contract.Inthistransaction,

thefirmwouldbereferredtoasahedger.This hedging allowsthefirmtoenteramarket that itwould

otherwise bereluctanttoenterbyreducing theriskofthetransaction. Hedging instruments

areavailablefromexchanges, investment banks,insurance firms,andother institutions.

Exchangingassets.The financialsystemalsoallowsentities toexchangeassets.For

example,Proctor andGamblemaysellsoapinEurope buthavecostsdenominatedin

U.S.dollars.Proctor andGamble canexchangetheireurosfromsoapsalesfordollarsin thecurrency

markets.

Utilizinginformation. Investorswith information expecttoearnareturn onthat information

inadditiontotheir usualreturn. Investorswhocanidentify assetsthat are currently undervalued

orovervaluedinthemarket canearnextrareturns frominvesting

basedontheirinformation(whentheiranalysisiscorrect).

Return Determination

The financialsystemalsoprovidesamechanism todetermine therateofreturn

thatequatestheamount ofborrowing withtheamount oflending

(saving)inaneconomy.Lowratesofreturn increaseborrowing butreducesaving(increasecurrent

consumption). High ratesofreturn increasesavingbutreduceborrowing. The

equilibriuminterest rateistherateatwhichtheamount individuals, businesses,and governments

desiretoborrow isequaltotheamount that individuals, businesses,and governments

desiretolend.Equilibrium ratesfordifferent typesofborrowing

andlendingwilldifferduetodifferencesinrisk,liquidity, andmaturity.

Allocation ofCapital

With limited availability ofcapital,oneofthemostimportantfunctions ofafinancial

systemistoallocatecapitaltoitsmostefficientuses.Investorsweightheexpected risks andreturns

ofdifferent investments todetermine theirmostpreferred investments.As

longasinvestorsarewellinformed regarding riskandreturn andmarkets function well,

thisresultsinanallocation tocapitaltoitsmostvaluableuses.

Financial assetsinclude securities (stocksandbonds), derivativecontracts, and currencies.

Realassetsinclude realestate,equipment, commodities,andotherphysical assets.

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Financial securitiescanbeclassifiedasdebtorequity.Debt securities arepromisesto

repayborrowed funds.Equity securities represent ownership positions.

Public (publicly traded) securities aretraded onexchangesorthroughsecuritiesdealers

andaresubject toregulatory oversight. Securitiesthat arenottraded inpublic markets

arereferredtoasprivate securities.Privatesecuritiesareoftenilliquid andnotsubjectto regulation.

Derivative contractshavevaluesthat depend on(arederivedfrom)thevaluesofother

assets.Financial derivative contractsarebasedonequities, equityindexes,debt, debt

indexes,orother financialcontracts. Physical derivative contractsderivetheirvalues

fromthevaluesofphysicalassetssuchasgold,oil,andwheat.

Markets forimmediate deliveryarereferredtoasspotmarkets. Contracts forthefuture

deliveryofphysicalandfinancialassetsinclude forwards, futures, andoptions. Options provide

thebuyertheright, butnottheobligation, topurchase (orsell)assetsoversome period

oratsomefuture dateatpredeterminedprices.

Theprimarymarket isthemarket fornewlyissuedsecurities. Subsequent sales of

securitiesaresaidtooccurinthesecondary market.

Money markets refertomarketsfordebtsecuritieswithmaturities ofoneyearorless. Capital

markets refertomarkets forlonger-term debtsecuritiesandequitysecurities that

havenospecificmaturitydate.

Traditionalinvestmentmarkets refertothosefordebtandequity.Alternative markets

refertothoseforhedgefunds, commodities,realestate,collectibles, gemstones, leases,

andequipment. Alternative assetsareoftenmoredifficult tovalue,illiquid, require investor

duediligence, andtherefore oftensellatadiscount.

Assetscanbeclassifiedassecurities, currencies, contracts, commodities, andrealassets. Their

characteristics andsubtypesareasfollows.

Securities

Securitiescanbeclassifiedasfixedincome orequitysecurities, andindividual securities

canbecombined inpooled investment vehicles.Corporations andgovernments arethe

mostcommon issuersofindividual securities.The initial saleofasecurityiscalledan

issuewhenthesecurityissoldtothepublic.

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Fixedincome securities typicallyrefertodebtsecuritiesthat arepromises torepay borrowed

moneyinthefuture. Short-term fixedincome securitiesgenerallyhavea maturityoflessthan

oneortwoyears;long-term termmaturities arelongerthanfiveto tenyears,andintermediate

termmaturities fallinthemiddle ofthematurityrange.

Although thetermsareusedloosely,bondsaregenerallylongterm,whereasnotes areintermediate

term. Commercialpaperreferstoshort-termdebtissuedbyfirms. Governments

issuebillsandbanksissuecertificatesofdeposit.Inrepurchase agreements, theborrower

sellsahigh-quality assetandhasboth therightandobligation torepurchase it(atahigher

price)inthefuture. Repurchase agreements canbefortermsasshort asoneday.

Convertibledebtisdebtthat aninvestorcanexchangeforaspecifiednumberofequity

sharesoftheissuingfirm.

Equity securities represent ownership inafirmandinclude common stock,preferred

stock,andwarrants.

Commonstockisaresidualclaimonafirm'sassets.Commonstockdividends are

paidonlyafterinterest ispaidtodebtholders anddividends arepaidtopreferred stockholders.

Furthermore, intheeventoffirmliquidation,debtholders and preferred stockholders

havepriority overcommon stockholders andareusuallypaid infullbeforecommon stockholders

receiveanypayment.

Preferred stockisanequitysecuritywithscheduled dividends that

typicallydonotchangeoverthesecurity'slifeandmust bepaidbeforeanydividends oncommon

stockmaybepaid.

Warrantsaresimilartooptions inthat theygivetheholdertherighttobuyafirm's

equityshares(usuallycommon stock)atafixedexercisepriceprior tothewarrant's expiration.

Pooledinvestmentvehicles include mutual funds, depositories, andhedgefunds.The

termreferstostructures that combine thefunds ofmanyinvestorsinaportfolio ofinvestments. The

investor'sownership interests arereferredtoasshares,units,depository

receipts,orlimitedpartnershipinterests.

Mutual funds arepooled investment vehiclesinwhich investorscanpurchase shares,

eitherfromthefund itself(open-end funds) orinthesecondary market (closed-end

funds).

Exchange-traded funds (ETFs)andexchange-traded notes (ETNs) tradelike closed-

end fundsbuthavespecialprovisions allowingconversion intoindividual portfolio

securities, orexchangeofportfolio sharesforETFshares,that keeptheir market

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pricesclosetothevalueoftheirproportionalinterest intheoverallportfolio. Thesefunds

aresometimes referredtoasdepositories,withtheirsharesreferredtoas depositoryreceipts.

Asset-backed securities represent aclaimtoaportion ofapooloffinancialassets

suchasmortgages, carloans,orcreditcarddebt.The return fromtheassetsispassed

throughtoinvestors,with different classesofclaims(referredtoastranches)having

different levelsofrisk.

Hedge funds areorganized aslimited partnerships, with theinvestorsasthelimited

partners andthefund manager asthegeneralpartner.Hedgefunds utilizevarious

strategiesandpurchase isusuallyrestricted toinvestorsofsubstantial wealth and

investment knowledge.Hedgefundsoften useleverage.Hedgefund managersare

compensated basedontheamount ofassetsunder management aswellasontheir

investment results.

Currencies

Currencies areissuedbyagovernment's centralbank. Somearereferredtoasreserve currencies,

whicharethoseheldbygovernments andcentral banksworldwide. These include

thedollarandeuroand,secondarily, theBritishpound,Japaneseyen,andSwiss

franc.Inspotcurrency markets, currencies aretraded forimmediate delivery.

Contracts

Contractsareagreements betweentwoparties that requiresomeactioninthefuture,

suchasexchanging anassetforcash.Financial contracts areoftenbasedonsecurities, currencies,

commodities, orsecurityindexes(portfolios). They include futures, forwards, options,

swaps,andinsurance contracts.

Aforward contractisanagreement tobuyorsellanassetinthefuture ataprice

specifiedinthecontractatitsinception. Anagreement topurchase

100ouncesofgold90daysfromnowfor$1,000 perounce isaforward contract. Forward contracts

arenot traded onexchangesorindealermarkets.

Futures contractsaresimilartoforwardcontracts exceptthat theyarestandardized as

toamount,assetcharacteristics, anddeliverytimeandaretraded onanexchange(ina secondary

market) sothat theyareliquid investments.

Inaswapcontract,twopartiesmakepayments that areequivalent tooneassetbeing traded

(swapped)foranother. Inasimpleinterestrateswap,floatingrateinterest

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paymentsareexchangedforfixed-ratepayments overmultiple settlement dates.A

currencyswapinvolvesaloaninonecurrency fortheloanofanother currency fora period

oftime.Anequityswapinvolvestheexchangeofthereturn onanequity indexor portfolio

fortheinterest payment onadebtinstrument.

Anoption contractgivesitsownertherighttobuyorsellanassetataspecificexercise

priceatsomespecifiedtimeinthefuture. Acalloption givestheoption buyertheright

(butnottheobligation) tobuyanasset.Aput option givestheoption buyertheright

(butnottheobligation) tosellanasset.

Sellers,orwriters, ofcall(put) options receiveapayment, referredtoastheoption premium,

whentheyselltheoptions butincur theobligation tosell(buy)theassetatthe

specifiedpriceiftheoption ownerchoosestoexerciseit.

Optionsoncurrencies, stocks,stockindexes,futures, swaps,andpreciousmetalsare traded

onexchanges.Customized options contracts arealsosoldbydealersintheover• the-

countermarket.

Aninsurancecontractpaysacashamount ifafuture eventoccurs.Theyareusedto

hedgeagainstunfavorable, unexpected events.Examplesinclude life,liability,and automobile

insurance contracts. Insurance contracts cansometimes betraded toother

partiesandoftenhavetax-advantagedpayouts.

Credit default swapsareaformofinsurance thatmakesapayment ifanissuerdefaults

onitsbonds.They canbeusedbybond investorstohedgedefaultrisk.They canalsobe usedbyparties

thatwillexperiencelossesifanissuerexperiencesfinancial distressandby

otherswhoarespeculating that theissuerwillexperiencemoreorless financial trouble than

iscurrently expected.

Commodities

Commoditiestradeinspot,forward, andfutures markets.They include precious

metals,industrial metals,agricultural products, energyproducts, andcreditsforcarbon

reduction.

Futures andforwardsallowboth hedgersandspeculators toparticipate incommodity

marketswithouthavingtodeliverorstorethephysicalcommodities.

Real Assets

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Examplesofrealassetsarerealestate,equipment, andmachinery.Although theyhave

beentraditionally heldbyfirmsfortheiruseinproduction,realassetsareincreasingly

heldbyinstitutionalinvestorsboth directlyandindirectly.

Buyingrealassetsdirectlyoftenprovidesincome, taxadvantages, anddiversification benefits.

However,theyoftenentailsubstantial management costs.Furthermore,

becauseoftheirheterogeneity, theyusuallyrequire theinvestor todosubstantial duediligence

beforeinvesting.They areilliquid becausetheirspecialization mayresultinalimited

poolofinvestorsforaparticular realasset.

Rather thanbuying realassetsdirectly,aninvestormaychoosetobuythem indirectly

throughaninvestment suchasarealestateinvestmenttrust(REIT) ormasterlimited partnership

(MLP).The investorownsaninterest inthesevehicles,which holdtheassets

directly.Indirectownership interests aretypicallymoreliquid than ownership ofthe

assetsthemselves.Another indirect ownership method istobuythestockoffirmsthat

havelargeownership ofrealassets.

Financial intermediariesstandbetween buyersandsellers,facilitating theexchange

ofassets,capital, andrisk.Their servicesallowforgreaterefficiencyandarevitaltoa well-

functioning economy.Financial intermediaries include brokersandexchanges,

dealers,securitizers, depository institutions,insurance companies, arbitrageurs, and

clearinghouses.

Brokers,Dealers,andExchanges

Brokers helptheir clientsbuyandsellsecuritiesbyfinding counterparties totrades

inacostefficientmanner.They mayworkforlargebrokerage firms,forbanks,orat exchanges.

Blockbrokers helpwith theplacement oflargetrades.Typically,largetradesaredifficult

toplacewithoutmoving themarket. Forexample,alargesellordermight causea

security'spricetodecreasebeforetheordercanbefullyexecuted. Blockbrokershelp concealtheir

clients' intentionssothat themarket doesnotmoveagainstthem.

Investmentbanks helpcorporations sellcommon stock,preferred stock,anddebt

securitiestoinvestors.They alsoprovide advicetofirms,notably about mergers, acquisitions,

andraisingcapital.

Exchanges provide avenuewheretraderscanmeet.Exchangessometimes actasbrokers

byproviding electronic ordermatching. Exchangesregulatetheirmembers andrequire firmsthat

listontheexchangetoprovidetimelyfinancial disclosuresandtopromote shareholder

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democratization. Exchangesacquiretheirregulatory powerthroughmember agreement

orfromtheirgovernments.

Alternative trading systems (ATS),which servethesametrading function asexchanges

buthavenoregulatory function, arealsoknown as electroniccommunicationnetworks (ECNs)

ormultilateraltrading facilities (MTFs). ATSthat donotrevealcurrent client ordersareknown

asdarkpools.

Dealers facilitate trading bybuyingfororsellingfromtheirowninventory. Dealers

provideliquidityinthemarket andprofitprimarily fromthespread(difference) between

thepriceatwhichtheywillbuy(bidprice)andthepriceatwhichtheywillsell(ask

price)thesecurityorother asset.

Somedealersalsoactasbrokers. Broker-dealers haveaninherentconflict ofinterest.As brokers,

theyshould seekthebestpricesfortheirclients,butasdealers,theirgoalisto

profitthroughpricesorspreads.Asaresult,traderstypicallyplacelimitsonhowtheir

ordersarefilledwhentheytransact withbroker-dealers.

Dealersthat tradewith central bankswhenthebanksbuyorsellgovernment securities

inordertoaffectthemoneysupplyarereferredtoasprimarydealers.

Securitizers

Securitizers poollargeamounts ofsecuritiesorother assetsandthen sellinterests inthe pooltoother

investors.Thereturns fromthepool,netofthesecuritizer'sfees,arepassed throughtotheinvestors.

Bysecuritizing theassets,thesecuritizer createsadiversified poolofassetswith morepredictable

cashflowsthan theindividual assetsinthepool.This

createsliquidityintheassetsbecausetheownership interests

aremoreeasilyvaluedandtraded.There arealsoeconomies ofscaleinthemanagement

costsoflargepoolsof assetsandpotentialbenefitsfromthemanager'sselection ofassets.

Assetsthat areoftensecuritized include mortgages,

carloans,creditcardreceivables,bankloans,andequipmentleases.The primary

benefitofsecuritization istodecreasethe

fundingcostsfortheassetsinthepool.Afirmmaysetupaspecial purposevehicle (SPY) orspecial

purposeentity(SPE)tobuyfirmassets,whichremovesthem fromthefirm's

balancesheetandmayincreasetheirvaluebyremoving theriskthat financialtrouble at

thefirmwillgiveother investorsaclaimtotheassets'cashflows.

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The cashflowsfromsecuritized assetscanbesegregatedbyrisk.The different risk

categoriesarecalledtranches.Theseniortranches providethemostcertain cashflows,

whilethejunior tranches havegreaterrisk.

Depository Institutions

Examplesofdepositoryinstitutionsinclude banks,creditunions, andsavingsandloans.

Theypayinterest oncustomer deposits andprovidetransaction servicessuchaschecking

accounts.These financialintermediaries then makeloanswith thefunds,which offer

diversification benefits.The intermediaries haveexpertiseinevaluating creditquality and

managing theriskofaportfolio ofloansofvarioustypes.

Other intermediaries, suchaspaydaylendersandfactoring companies, lendmoneyto

firmsandindividuals onthebasisoftheirwages,accounts receivable,andotherfuture

cashflows.These intermediaries oftenfinancetheloansbyissuingcommercial paperor other

debtsecurities.

Securitiesbrokersprovideloanstoinvestorswhopurchase securitiesonmargin. When thismargin

lending istohedgefundsandother institutions,thebrokersarereferredto asprime brokers.

Theequityowners(stockholders) ofbanks,brokers, andother intermediaries absorbany

loanlossesbeforedepositors andother lenders.Themoreequitycapitalanintermediary

has,thelessriskfordepositors. Poorlycapitalized intermediaries (thosewith less equity)

havelessincentive toreducetheriskoftheirloanportfolios becausetheyhaveless capitalatrisk.

Insurance Companies

Insurancecompanies areintermediaries, inthat theycollectinsurance premiums in return

forproviding riskreduction totheinsured. The insurance firmcandothis

efficientlybecauseitprovidesprotectiontoadiversifiedpoolofpolicyholders, whose

risksoflossaretypicallyuncorrelated. Thisprovidesmorepredictable lossesandcash

flowscompared toasingleinsurance contract, inthesamewaythat abank'sdiversified portfolio

ofloansdiversifiestheriskofloandefaults.

Insurance firmsalsoprovide abenefittoinvestorsbymanaging therisksinherentin insurance:

moralhazard, adverseselection, andfraud. Moral hazard occursbecausethe insured

maytakemorerisksonceheisprotectedagainstlosses.Adverseselection occurs

whenthosemostlikelytoexperiencelossesarethepredominantbuyersofinsurance. In fraud,

theinsured purposely causesdamageorclaimsfictitious lossessohecancollecton hisinsurance

policy.

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Arbitrageurs

Initspure (riskless)form,arbitragereferstobuying anassetinonemarket andreselling itinanother

atahigherprice.Bydoingso,arbitrageurs actasintermediaries, providing liquiditytoparticipants

inthemarketwheretheassetispurchased andtransferring the assettothemarket whereitissold.

Inmarketswithgoodinformation, purearbitrage israrebecausetraderswillfavorthemarketswith

thebestprices.Morecommonly, arbitrageurs trytoexploitpricing

differencesforsimilarinstruments. Forexample,adealerwhosellsacalloption will

oftenalsobuythestockbecausethecallandstockpricearehighlycorrelated. Likewise, arbitrageurs

willattempt toexploitdiscrepancies inthepricing ofthecallandstock. Many (risk)arbitrageurs

usecomplexmodelsforvaluation ofrelatedsecuritiesandfor riskcontrol. Creating

similarpositions usingdifferent assetsisreferredtoasreplication. This

isalsoaformofintermediationbecausesimilarrisksaretraded indifferent forms andindifferent

markets.

Clearinghousesand Custodians

Clearinghouses actasintermediaries betweenbuyersandsellersinfinancialmarkets and

provide:

Escrowservices(transferring cashandassetstotherespectiveparties).

Guarantees ofcontractcompletion.

Assurancethat margin tradershaveadequate capital.

Limitsontheaggregatenetorderquantity(buyordersminus sellorders) of members.

Throughtheseactivities, clearinghouses limitcounterpartyrisk,theriskthat theother

partytoatransaction willnotfulfillitsobligation. Insomemarkets, theclearinghouse

ensuresonlythetradesofitsmember brokersanddealers,who,inturn, ensurethe

tradesoftheirretailcustomers.

Custodiansalsoimprovemarket integrity byholding clientsecuritiesandpreventing

theirlossduetofraudorother eventsthat affectthebroker orinvestment manager.

Aninvestorwhoownsanasset,orhastherightorobligation under acontractto purchase

anasset,issaidtohavealongposition.Ashort positioncanresultfrom borrowing

anassetandsellingit,with theobligation toreplacetheassetinthefuture (a

shortsale).Thepartytoacontractwhomust sellordeliveranassetinthefuture isalso

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saidtohaveashortposition. Ingeneral,investorswhoarelongbenefitfromanincrease

inthepriceofanassetandthosewhoareshort benefitwhentheassetpricedeclines.

Hedgers useshortpositions inoneassettohedgeanexistingriskfromalongposition inanother

assetthathasreturns that arestrongly correlated with thereturns ofthe assetshorted.

Forexample,wheatfarmersmaytakeashortpositionin(i.e.,sell)wheat futures contracts.

Ifwheatpricesfall,theresulting increaseinthevalueoftheshort futurespositionoffsets,partially

orfully,thelossinthevalueofthefarmer'scrop.

Thebuyerofanoption contractissaidtobelongtheoption. Thesellerisshort the option

andissaidtohavewritten theoption. Note that aninvestorwhoislong(buys) acalloption

onanassetprofitswhenthevalueoftheunderlying

assetincreasesinvalue,whilethepartyshorttheoption haslosses.Alongpositioninaput option

onan assethastherighttoselltheassetataspecifiedpriceandprofitswhen thepriceofthe underlying

assetfalls,whilethepartyshort theoption haslosses.

Inswaps,eachpartyislongoneassetandshorttheother,sothedesignation ofthelong

andshortsideisoftenarbitrary. Usually,however,thesidethatbenefitsfromanincrease inthequoted

priceorrateisreferredtoasthelongside.

Inacurrency contract, eachpartyislongonecurrency andshort theother.Forexample,

thebuyerofaeurofutures contractpriced indollarsislongtheeuroandshort the

dollar.

Short SalesandPositions

Inashort sale,theshortseller(1)simultaneouslyborrows andsellssecuritiesthrougha broker,

(2)must return thesecurities attherequestofthelender orwhentheshortsale isclosedout, and

(3)mustkeepaportion oftheproceeds oftheshortsaleondeposit with

thebroker.Shortsellershopetoprofitfromafallinthepriceofthesecurityor assetsoldshort, buying

atalowerpriceinthefuture inordertorepaytheloanofthe assetoriginally soldatahigher

price.Therepayment oftheborrowed securityorother assetisreferred

toas"coveringtheshortposition."

Inashortsale,theshortsellermustpayalldividends orinterest that thelenderwould

havereceivedfromthesecuritythathasbeenloaned totheshort seller.Thesepayments

arecalledpayments-in-lieuofdividends orinterest. Theshort sellermust alsodeposit

theproceeds oftheshortsaleascollateral toguarantee theeventual repurchase ofthe

security.Thebroker then earnsinterest onthesefunds andmayreturn aportion ofthis interest

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totheshortsellerataratereferredtoastheshort rebate rate.The shortrebate

rateisusuallyonlyprovided toinstitutionalinvestorsandistypically0.1%lessthan

overnight interest rates.Ifthesecurityisdifficulttoborrow,theshort

rebateratemaybelowerornegative.The differencebetweentheinterest earned ontheproceeds

fromthe shortsaleandtheshort rebatepaidisthereturn tothelender ofthesecurities.Ashort

salemayalsorequiretheshortsellertodeposit additional margin intheformofcashor short-

termrisklesssecurities.

LeveragedPositions

The useofborrowed funds topurchase anassetresultsinaleveragedpositionandthe investor

issaidtobeusingleverage.Investorswhouseleveragetobuysecuritiesby borrowing

fromtheirbrokers aresaidtobuyonmargin andtheborrowed fundsare referredtoasamargin

loan.Theinterest ratepaidonthefunds isthecallmoney rate, which isgenerallyhigher than

thegovernment billrate.The callmoneyrateislowerfor largerinvestorswithbetter collateral.

Atthetimeofanewmargin purchase, investorsarerequired toprovide aminimum amount

ofequity,referredtoastheinitial margin requirement.This requirement may

besetbythegovernment,exchange,clearinghouse,orbroker. Lowerriskinaninvestor's portfolio

willoftenresultinthebrokerlending morefunds.

Theuseofleveragemagnifiesboth thegainsandlossesfromchangesinthevalueofthe underlying

asset.The additional riskfromtheuseofborrowed funds isreferredtoasrisk fromfinancial

leverage.

Theleverageratio ofamargin investment isthevalueoftheassetdividedbythevalueof

theequityposition. Forexample,aninvestorwhosatisfiesaninitialmargin

requirementof50%equityhasa2-to-1 leverageratiosothata10%increase(decrease)inthepriceof

theassetresultsina20% increase(decrease)intheinvestor'sequityamount.

Toensurethat theloaniscoveredbythevalueoftheasset,aninvestor

mustmaintainaminimumequitypercentage, calledthemaintenancemargin requirement,inthe

account. This minimumistypically25%ofthecurrent position value,butbrokersmay

requireagreaterminimumequitypercentage forvolatilestocks.

Ifthepercentage ofequityinamargin account fallsbelowthemaintenancemargin

requirement,theinvestorwillreceiveamargin call,arequesttobring theequity percentage

intheaccount backuptothemaintenancemargin percentage. Aninvestor

cansatisfythisrequestbydepositing additional funds ordepositing other unmargined

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securitiesthatwillbring theequitypercentage uptotheminimumrequirement.Ifthe investor

doesnotmeetthemargin call,thebrokermust selltheposition.

Thestockpricewhich resultsinamargin callcanbecalculatedbyusingthefollowing formula:

where:

P0 = initial purchase price

Example: Margin call price

¡fan investor purchases a stock for $40 per share with an initial margin requirement

of 50% and the maintenance margin requirement is 25%, at what price will the

investor get a margin call?

Answer:

A margin call is triggered at a price below $26.67.

Inashortsale,theinvestormustdeposit initial margin equaltoapercentage ofthe

valueofthesharessoldshort toprotect thebroker incasethesharepriceincreases.An

increaseinthesharepricecandecreasethemargin percentage belowthemaintenance margin

percentage andgenerate amargin call.

Securitiesdealersprovidepricesatwhich theywillbuyandsellshares.The bidprice is

thepriceatwhichadealerwillbuyasecurity.Theaskorofferpriceisthepriceatwhich

adealerwillsellasecurity.The differencebetween thebidandaskpricesisreferred toasthebid-ask

spread andisthesourceofadealer'scompensation. Thebidandaskare quoted

forspecifictradesizes(bidsizeandasksize).

The quotationinthemarket isthehighest dealerbidandlowestdealeraskfromamong

alldealersinaparticular security.Moreliquid securitieshavemarket quotationswithbid-

askspreadsthat arelower(asapercentage ofshareprice)andtherefore havelower transactions

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costsforinvestors.Traderswhopostbidsandoffersaresaidtomakea

market,whilethosewhotradewiththem atpostedpricesaresaidtotakethemarket.

When investorswant tobuyorsell,theymust enterordersthat specifythesizeofthe

tradeandwhether tobuyorsell. The ordercanalsoinclude executioninstructionsthat specify

howtotrade,validityinstructionsthatspecify whentheordercanbefilled,and

clearinginstructionsthat specifyhowtosettlethetrade.

ExecutionInstructions

Themostcommon orders,interms ofexecution instructions,aremarket orlimit orders. Amarket

order instructsthebroker toexecutethetradeimmediately atthebestpossible price.Alimit

orderplacesaminimumexecution priceonsellordersandamaximum execution

priceonbuyorders. Forexample,abuyorderwith alimitof$6willbe

executedimmediatelyaslongasthesharescanbepurchased for$6orless.

Amarket orderisoftenappropriatewhenthetraderwantstoexecutequickly,as

whenthetraderhasinformationshebelievesisnotyetreflectedinmarket prices.The disadvantage

ofmarket ordersisthat theymayexecuteatunfavorable prices,especially

ifthesecurityhaslowtrading volume relativetotheordersize.Amarket

buyordermayexecuteatahighpriceoramarket sellordermayexecuteatalowprice.Executing

atanunfavorable pricerepresents aconcessionbythetrader forimmediate liquidity.

Unfortunately,thesepriceconcessions areunpredictable.

Toavoidpriceexecution uncertainty, atrader canplacealimitorderinstead ofthe market

order.Thedisadvantage ofthelimit orderisthat itmight notbefilled.For

example,ifatraderplacesalimitbuyorderof$50andnooneiswilling tosellat$50,

theorderwillnotbefilled.Furthermore, ifthestockpricerisesovertime,thetrader

missesoutonthegains.

Alimitbuyorderabovethebestaskoralimitsellorderbelowthebestbidaresaidto

bemarketableoraggressively

pricedbecauseatleastpartoftheorderislikelytoexecuteimmediately.Ifthelimitpriceisbetween

thebestbidandthebestask,alimitorder is

saidtobemakinganewmarketorinsidethemarket.Limitorderswaiting toexecuteare

calledstandinglimit orders.

Alimitbuyorder atthebestbidoralimitsellorderatthebestaskaresaidtomake

themarket.Again,theordermight notbefilled.Abuyorderwithalimitpricebelowthebestbid,

orasellorderwith alimitpriceabovethebestask,issaidtobebehindthe

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market.Itwilllikelynotexecuteuntil securitypricesmovetowardthelimitprice.A

limitbuyorderwith apriceconsiderablylowerthan thebestbid,oralimit sellorder with

apricesignificantly higher than thebestask,issaidtobefar.fromthemarket.

Other execution instructions concern thevolumeofthetrade.All-or-nothingorders

executeonlyifthewholeordercanbefilled.Orders canspecifytheminimumsizeofa trade,

whichisbeneficialwhentrading costsdepend onthenumberofexecutedtrades rather than

thesizeoftheorder.

Tradevisibilitycanalsobespecified.Hidden orders arethoseforwhich onlythebroker

orexchangeknowsthetradesize.These areusefulforinvestorsthathavealargeamount

totradeanddonotwant torevealtheirintentions.

Traderscanalsospecifydisplaysize,wheresomeofthetradeisvisibletothemarket,

buttherestisnot.These arealsoreferred toasicebergorders becausepart

ofmostoftheorderishidden fromview.They allowtheinvestor toadvertisesomeofthetrade,with

therestofthetradepotentially executedoncethevisibleparthasexecuted. Sometimes entering

tradesforpart ofthe positionthetraderwishestoestablishisawayto estimate

theliquidityof,orthebuying interest in,thesecurityinquestion.

ValidityInstructions

Validityinstructions specifywhen anordershould beexecuted.Mostordersareday orders,

meaning theyexpireifunfilledbytheendofthetrading day.Good-till-cancelled orderslastuntil

theyarefilled.Immediate-or-cancelordersarecancelledunlesstheycan

befilledimmediately.They arealsoknown asfill-or-kill orders.Good-on-

closeordersareonlyfilledattheendofthetrading day.Iftheyaremarket orders,theyarereferredto

asmarket-on-closeorders.These areoften usedbymutual funds becausetheirportfolios

arevaluedusingclosingprices.There arealsogood-on-openorders.

StopOrders

Stoporders arethosethat arenotexecutedunlessthestoppricehasbeenmet.Theyareoften

referredtoasstoplossorders becausetheycanbeusedtoprevent lossesorto protect

profits.Supposeaninvestorpurchases astockfor$50.Iftheinvestorwants to selloutoftheposition

ifthepricefalls10%to$45,hecanenterastop-sell order

at$45.Ifthestocktradesdownto$45orlower,thistriggersamarket ordertosell.There is noguarantee

that theorderwillexecuteat$45,andarapidlyfallingstockcouldbesold atapricesignificantly

lowerthan $45.

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Astop-buyisenteredwith atstop (trigger)abovethecurrent market price.There are twoprimary

reasonsatraderwould enterastop-buy order.(1)Atraderwithashortposition couldattempt

tolimitlossesfromanincreasing stockpricewithastop-buy order.(2)Itisoftensaid,"You

don'tgetpaidforbeingrightuntil themarket agreeswith you."With thisinmind,

aninvestorwhobelievesastockisundervalued, butdoesnot wishtoownituntil therearesignsthat

market participants arebeingconvinced ofthis undervaluation,mayplaceastop-buy

orderatapricesomespecificpercentage abovethe current price.

Note thatstopordersreinforcemarket momentum.Stop-sellordersexecutewhen market

pricesarefalling,andstop-buy ordersexecutewhenthemarket isrising. Execution

pricesforstopordersaretherefore oftenunfavorable.

ClearingInstructions

Clearing instructionstellthetrader howtoclearandsettleatrade.They areusually standing

instructionsandnotattached toanorder.Retailtradesaretypicallycleared

andsettledbythebroker,whereasinstitutionaltradesmaybesettledbyacustodian or another

broker,which might bethetrader'sprime broker.Usingtwobrokersallowsthe

investortokeeponebrokerasherprimebroker formargin andcustodial serviceswhile

usingavarietyofother brokersforspecializedexecution.

One importantclearinginstructioniswhether asellorderisashortsaleorlongsale.In

theformer,thebroker mustconfirm that thesecuritycanbeborrowed andinthelatter, that

thesecuritycanbedelivered.

Primarycapital markets refertothesaleofnewlyissuedsecurities.Newequity issues

involveeither:

Newsharesissuedbyfirmswhosesharesarealreadytrading inthemarketplace. These

issuesarecalledseasoned offerings orsecondary issues.

First-time issuesbyfirmswhosesharesarenotcurrently publicly traded.Theseare

calledinitial public offerings (IPOs).

Secondary financial markets arewheresecuritiestradeaftertheirinitial issuance.Placing

abuyorderontheLondon StockExchangeisanorderinthesecondary market andwill

resultinpurchase ofexistingsharesfromtheircurrent owner.

PrimaryMarket: PublicOfferings

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Corporate stockorbond issuesarealmostalwayssoldwiththeassistanceofan investmentbanking

firm.The investment bankfindsinvestorswhoagreetobuypart of theissue.These

arenotactualordersbutarereferredtoasindicationsofinterest.When

thenumberofsharescoveredbyindications ofinterest aregreater (less)than thenumber

ofsharesto beoffered,theofferingpricemaybeadjusted upward (downward). This

processofgathering indications ofinterest isreferredtoasbook

building.InLondon,thebookbuilder isreferredtoasthebookrunner. InEurope, anaccelerated

bookbuildoccurswhensecuritiesmust beissuedquickly.Tobuild abook, theinvestment bank

disseminates information about thefirm'sfinancialsandprospects.The issuermust also

makedisclosuresincluding howthefundswillbeused.

Themostcommon wayaninvestment bankassistswith

asecurityissuanceisthroughanunderwrittenoffering. Here,theinvestment bank

agreestopurchase theentireissue atapricethat isnegotiated betweentheissuerandbank.

Iftheissueisundersubscribed, theinvestment bankmust buytheunsold

portion.InthecaseofanIPO,theinvestment bankalsoagreestomakeamarket

inthestockforaperiod aftertheissuancetoprovide pricesupport fortheissue.

Aninvestment bank canalsoagreetodistributesharesofanIPO onabestefforts basis, rather than

agreeingtopurchase thewholeissue.Iftheissueisundersubscribed, thebank is notobligated

tobuytheunsold portion.

Note that investment bankshaveaconflictofinterest inanunderwrittenoffer.Asthe

issuer'sagents,theyshould setthepricehightoraisethemostfundsfortheissuer.But, asunderwriters,

theywouldpreferthat thepricebesetlowenough that thewholeissue sells.Thisalsoallowsthem

toallocateportions ofanundervalued IPO totheirclients. This

resultsinIPOstypicallybeingunderpriced.

IssuersalsocouldhaveaninterestinunderpricingtheIPO becauseofthenegativepublicity

whenanundersubscribed IPO initially tradesatapricebelowtheIPO priceinvestorspay.AnIPO

that is oversubscribedandhastheexpectation oftrading significantly aboveitsIPO priceis

referredtoasahot issue.

PrimaryMarket: Private PlacementsandOther Transactions

Inaprivate placement,securitiesaresolddirectlytoqualified investors, typicallywith

theassistanceofaninvestment bank. Qualified investorsarethosewithsubstantial

wealthandinvestment knowledge. Privateplacements donotrequire theissuerto discloseasmuch

informationastheymustwhenthesecuritiesarebeingsoldtothe public.The

issuancecostsarelesswith aprivateplacement andtheofferpriceisalso

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lowerbecausethesecuritiescannot beresoldinpublic markets, making themless

valuablethansharesregisteredforpublic trading.

Inashelfregistration,afirmmakesitspublic disclosuresasinaregularofferingbut

thenissuestheregisteredsecuritiesovertimewhenitneedscapitalandwhenthe markets

arefavorable.

Adividendreinvestmentplan (DRP orDRIP) allowsexistingshareholders tousetheir dividends

tobuynewsharesfromthefirmataslightdiscount.

Inarights offering, existingshareholders aregiventherighttobuynewsharesatadiscount

tothecurrent market price.Shareholders tend todislikerightsofferings becausetheirownership

isdiluted unlesstheyexercisetheirrightsandbuytheadditional shares.However,rightscanbetraded

separatelyfromthesharesthemselvesinsome circumstances.

Inaddition tofirmsissuingsecurities,governments issueshort-termandlong-term debt,

eitherbyauction orthroughinvestment banks.

ImportanceoftheSecondaryMarket

Secondary marketsareimportantbecausetheyprovideliquidityandprice/value

information.Liquid marketsarethoseinwhichasecuritycanbesoldquicklywithout incurring

adiscountfromthecurrent price.The better thesecondary market,

theeasieritisforfirmstoraiseexternalcapital intheprimary market, which resultsinalowercost

ofcapitalforfirmswith sharesthat haveadequate liquidity.

The trading ofsecurities inthesecondary markethasencouraged thedevelopment of market

structures tofacilitate trading. Trading canbeexamined according towhen securitiesaretraded

andhowtheyaretraded.

Securitiesmarketsmaybestructuredas callmarketsorcontinuous markets. Incall markets,

thestockis onlytraded atspecifictimes.Callmarketsarepotentially very

liquidwheninsessionbecausealltradersare present, buttheyareobviouslyilliquid

betweensessions.Inacallmarket, alltrades,bids,andasksaredeclared, andthenonenegotiated

priceissetthatclearsthemarket forthestock.Thismethod isusedin

smallermarkets butisalsousedtosetopening pricesandpricesaftertrading haltson

majorexchanges.

Incontinuousmarkets, tradesoccuratanytimethemarket isopen.Thepriceissetby

eithertheauction processorbydealerbid-askquotes.

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Market Structures

There arethreemain categoriesofsecuritiesmarkets: quote-drivenmarketswhere

investorstradewithdealers,order-drivenmarketswhererulesareusedtomatch buyers

andsellers,andbrokeredmarketswhereinvestorsusebrokers tolocateacounterpartyto atrade.

Quote-Driven Markets

Inquote-drivenmarkets, traderstransact with dealers(marketmakers)whopostbidand

askprices.Dealersmaintainaninventory ofsecurities. Quote-drivenmarketsarethus sometimes

calleddealermarkets, price-driven markets, orover-the-countermarkets. Mostsecuritiesother

than stockstradeinquote-drivenmarkets.Trading oftentakesplaceelectronically.

Order-Driven Markets

Inorder-drivenmarkets, ordersareexecutedusingtrading rules,which arenecessary

becausetraders areusuallyanonymous. Exchangesandautomatedtrading systemsare

examplesoforder-driven markets.Twosetsofrulesareusedinthesemarkets: order matching

rulesandtradepricing rules.

Order matchingrules establishanorderprecedencehierarchy.Pricepriority isone criteria,

wherethetradesgivenhighestpriority arethoseatthehighest bid(buy)and

lowestask(sell).Ifordersareatthesameprices,asecondaryprecedence rulegives priority tonon-

hiddenordersandearliestarrivingorders.These rulesencourage traders topricetheir

tradesaggressively, displaytheirentireorders, andtradeearlier,thereby improving liquidity.

Afterordersarecreatedusingordermatching rules,trade pricing rulesareusedto determine

theprice.Under theuniformpricingrule,allorderstradeatthesameprice, which isthepricethat

resultsinthehighestvolumeoftrading.The discriminatory

pricingruleusesthelimitpriceoftheorderthat arrivedfirstasthetradeprice.

Inanelectronic crossingnetwork, thetypicaltrader isaninstitution.Orders arebatched together

andcrossed(matched) atfixedpoints intimeduring thedayattheaverageof

thebidandaskquotesfromtheexchangewherethestockprimarily trades.This pricing

ruleisreferredtoasthederivativepricingrulebecauseitisderivedfromthesecurity's

mainmarket.Thepriceisnotdetermined byordersinthecrossingnetwork.

BrokeredMarkets

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Inbrokeredmarkets, brokersfindthecounterpartyinordertoexecuteatrade.This

serviceisespeciallyvaluablewhenthetraderhasasecuritythat is unique orilliquid.

Examplesarelargeblocksofstock,realestate,andartwork. Dealerstypicallydonot

carryaninventory oftheseassetsandtherearetoofewtradesfortheseassetstotradein order-driven

markets.

Market Information

Amarket issaidtobepre-tradetransparentifinvestorscanobtain pre-trade

information regarding quotesandorders.Amarket ispost-tradetransparentifinvestors

canobtain post-trade informationregarding completed tradepricesandsizes.

Buy-sidetradersvaluetransparency becauseitallowsthem tobetter understand security

valuesandtrading costs.Dealers,ontheotherhand, preferopaque markets becausethis

providesthemwithaninformational advantageovertraderswhotradeless frequently in

thesecurity.Transactions costsandbid-askspreadsarelargerinopaque markets.

Awell-functioningfinancialsystemallowsentities toachievetheirpurposes. More specifically,

complete markets fulfillthefollowing:

Investorscansave forthefuture atfairratesofreturn.

Creditworthyborrowers canobtain funds.

Hedgers canmanagetheir risks.

Traderscanobtain thecurrencies, commodities, andother assetstheyneed.

Ifamarket canperform thesefunctions atlowtrading costs(including commissions, bid-

askspreads,andpriceimpacts), itissaidtobeoperationallyefficient. Ifsecurity

pricesreflectalltheinformationassociatedwith fundamental valueinatimelyfashion,

thenthefinancialsystemisinformationallyefficient. Awell-functioningfinancial

systemhascomplete marketsthat areoperationally andinformationallyefficient,with pricesthat

reflectfundamental values.

Awell-functioningfinancialsystemhasfinancial intermediaries that:

Organize trading venues,including exchanges,brokerages, andalternative trading

systems.

Supplyliquidity.

Securitizeassetssothat borrowers canobtain fundsinexpensively.

Managebanksthat usedepositor capitaltofundborrowers.

Manageinsurance firmsthat poolunrelated risks.

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Manageinvestment advisoryservicesthat assistinvestorswithassetmanagement

inexpensively.

Provideclearinghouses thatsettletrades.

Managedepositories that provideforassetsafety.

Thebenefitsofawell-functioningfinancialsystemaretremendous. Saverscanfund

entrepreneurs whoneedcapitaltofund newcompanies. Company riskscanbe sharedsothat

riskycompanies canbefunded. Thesebenefitsareenhanced because thetransactions

canoccuramong strangers,widening theopportunitiesforcapital formation andrisksharing

intheeconomy.

Furthermore, ininformationallyefficientlymarkets, capitalisallocated toitsmost productive

use.That is,theyareallocationally efficient. Informational

efficiencyis broughtabout bytraderswhobidpricesupanddown inresponsetonewinformation

that changesestimates ofsecurities' fundamental values.If

markets areoperationally

efficient,securitypriceswillbemoreinformationallyefficientbecauselowtrading costs encourage

trading basedonnewinformation.

Theexistenceofaccounting standardsandfinancialreportingrequirements

alsoreducesthecostsofobtaininginformationand increasessecurityvalues.

2.2 Security market indices

Asecurity market indexisusedtorepresent theperformance ofanassetclass,security market,

orsegment ofamarket.They areusuallycreatedasportfolios

ofindividual securities,whicharereferredtoastheconstituent securities

oftheindex.Anindexhasanumerical valuethat iscalculated fromthemarket prices

(actualwhenavailable,orestimated) ofitsconstituentsecuritiesatapoint intime.Anindexreturn

isthe percentage changeintheindex'svalueoveraperiod oftime.

Anindexreturn maybecalculated usingapriceindex orareturn index.Apriceindex

usesonlythepricesoftheconstituentsecuritiesinthereturn calculation.Arateof return that

iscalculated basedonapriceindexisreferredtoasapricereturn.

Areturn indexincludes both pricesandincome fromtheconstituentsecurities.Arate ofreturn that

iscalculated basedonareturn indexiscalledatotal return.Iftheassets inanindexproduce interim

cashflowssuchasdividends orinterest payments, thetotal return willbegreaterthan

thepricereturn.

Oncereturns arecalculated foreachperiod, theythen canbecompoundedtogether to

arriveatthereturn forthemeasurement period:

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where:

RP = portfolio return during the measurement period

k = total number of subperiods

RSk = portfolio return during the subperiod k

For example, if the returns for the first two periods were 0.50% and 1.04%, they would be

geometrically linked to produce 1.55%:

Rp = (1 + Rs1)(1 + Rs2)-1 = (1.005)(1.0104)-1 = 0.0155 or 1.55%

If the starting index value is 100, its value after two periods would be 100 x 1.0155 =

101.55.

Indexproviders mustmakeseveraldecisions:

What isthetargetmarkettheindexisintendedtomeasure?

Which securitiesfromthetargetmarket should beincluded?

Howshould thesecuritiesbeweighted intheindex?

Howoftenshould theindexberebalanced?

When should theselection andweighting ofsecuritiesbere-examined?

Thetargetmarket maybedefinedverybroadly (e.g.,stocksintheUnited States)or narrowly

(e.g.,small-capvaluestocksintheUnited States).Itmayalsobedefinedby geographic

regionorbyeconomic sector(e.g.,cyclicalstocks).The constituentstocks

intheindexcouldbeallthestocksinthat market orjustarepresentative sample.Theselection

processmaybedetermined byanobjective ruleorsubjectively byacommittee.

Weighting schemesforstockindexesinclude priceweighting, equalweighting, market

capitalization weighting, float-adjusted market capitalization weighting, and fundamental

weighting.

Aprice-weightedindex issimplyanarithmetic averageofthepricesofthesecurities included

intheindex.The divisorofaprice-weighted indexisadjusted forstocksplits

andchangesinthecomposition oftheindexwhensecuritiesareaddedordeleted, such that

theindexvalueisunaffected bysuchchanges.

Theadvantage ofaprice-weighted indexisthat itscomputationissimple.One disadvantage isthat

agivenpercentage changeinthepriceofahigherpricedstockhas agreaterimpact

ontheindex'svaluethan doesanequalpercentage changeintheprice

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ofalowerpricedstock.Putanother way,higherpricedstockshavemoreweight inthe calculation

ofaprice-weighted index.Additionally,astock'sweightintheindexgoing

forwardchangesifthefirmsplitsitsstock,repurchases stock,orissuesstockdividends,

asalloftheseactionswillaffectthepriceofthestockandtherefore itsweightinthe index.Aportfolio

thathasanequalnumberofsharesineachoftheconstituentstocks

willhavepricereturns (ignoring dividends) thatwillmatch thereturns ofaprice-weighted index.

Twomajorprice-weighted indexesaretheDowJonesIndustrial Average(DJIA)andthe Nikkei

DowJonesStockAverage.The DJIAisaprice-weighted indexbasedon30U.S. stocks.TheNikkei

Dowisconstructed fromthepricesof225stocksthat tradeinthe firstsection

oftheTokyoStockExchange.

Anequal-weightedindex iscalculated asthearithmeticaveragereturn oftheindex

stocksand,foragiventimeperiod, would bematched bythereturns onaportfolio that

hadequaldollaramounts investedineachindexstock.Aswith aprice-weighted index, anadvantage

ofanequal-weightedindexisitssimplicity.

One complication with anequal-weightedindexreturn isthat amatching

portfoliowouldhavetobeadjusted periodically (rebalanced) aspriceschangesothat thevaluesof

allsecuritypositions aremadeequaleachperiod. Theportfolio rebalancing required to match

theperformance ofanequal-weightedindexcreateshightransactions coststhat would

decreaseportfolio returns.

Another concernwith anequal-weightedindexisthat theweightsplacedonthereturns

ofthesecuritiesofsmallercapitalization firmsaregreaterthan theirproportionsofthe

overallmarket valueoftheindexstocks.Conversely,theweightsonthereturns oflarge

capitalization firmsintheindexaresmallerthan theirproportionsoftheoverallmarket

valueoftheindexstocks.

TheValueLineComposite AverageandtheFinancialTimesOrdinaryShareIndexare well-

known examplesofequal-weightedindexes.

Amarket capitalization-weightedindex (orvalue-weightedindex)hasweightsbased

onthemarket capitalization ofeachindexstock(current stockpricemultiplied bythe number

ofsharesoutstanding) asaproportionofthetotalmarket capitalization ofall

thestocksintheindex.Amarket capitalization-weightedindexreturn canbematched

withaportfolio inwhichthevalueofeachsecuritypositionintheportfolio isthe

sameproportionofthetotalportfolio valueastheproportionofthat security'smarket

capitalization tothetotalmarket capitalization ofallofthesecuritiesincluded inthe

index.Thisweighting method morecloselyrepresents

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changesinaggregateinvestorwealththanpriceweighting.

Becausetheweightofanindexstockisbasedonitsmarket capitalization, amarket

capitalization-weightedindexdoesnotneedtobeadjusted when

astocksplitsorpaysastockdividend.

Analternative tousingafirm'smarket capitalization tocalculateitsweightinanindex

istouseitsmarket float.Afirm'smarket

floatisthetotalvalueofthesharesthatareactuallyavailabletotheinvestingpublic

andexcludesthevalueofsharesheldby controlling stockholders becausetheyareunlikely

toselltheirshares.Forexample, thefloatforMicrosoft would

excludesharesownedbyBillGatesandPaulAllen(the founders) andthoseofcertain other

largeshareholders aswell.Themarket floatis oftencalculated excluding

thosesharesheldbycorporations orgovernments aswell.

Sometimes themarket floatcalculation excludessharesthat

arenotavailabletoforeignbuyersandisthenreferredtoasthefreefloat.The reasonforthisistobetter

match theindexweightsofstockstotheirproportionsofthetotalvalueofallthesharesofindex

stocksthat areactuallyavailabletoinvestors.

Afloat-adjustedmarket capitalization-weightedindex isconstructed likeamarket

capitalization-weightedindex.Theweights, however,arebasedontheproportionate

valueofeachfirm'ssharesthat areavailabletoinvestorstothetotalmarketvalueof

thesharesofindexstocksthat areavailabletoinvestors. Firmswithrelativelylarge percentages

oftheirsharesheldbycontrolling stockholders willhavelessweightthan theyhaveinanunadjusted

market-capitalization index.

Theadvantage ofmarket capitalization-weightedindexesofeithertypeisthat index

securityweightsrepresent proportionsoftotalmarket value.Theprimary disadvantage ofvalue-

weightedindexesisthat therelativeimpact ofastock'sreturn ontheindex

increasesasitspricerisesanddecreasesasitspricefalls.Thismeansthatstocksthat

arepossiblyovervaluedaregivendisproportionately highweightsintheindexandstocksthat

arepossiblyundervalued aregivendisproportionately lowweights. Holding aportfolio that

tracksavalue-weightedindexis,therefore, similartofollowinga

momentumstrategy,underwhichthemostsuccessfulstocksaregiventhegreatest

weightsandpoorperforming stocksareunderweighted.

The Standard andPoor's500(S&P500)IndexComposite isanexampleofamarket capitalization-

weightedindex.

Anindexthat usesfundamentalweightingusesweightsbasedonfirmfundamentals,

suchasearnings, dividends, orcashflow. Incontrast tomarket capitalization index weights,

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theseweightsareunaffected bythesharepricesoftheindexstocks(although relatedtothem

overthelongterm). Fundamentalweightscanbebasedonasingle measureorsomecombination

offundamentalmeasures.

Anadvantage ofafundamental-weighted indexisthat itavoidsthebiasofmarket capitalization-

weightedindexestoward theperformance ofthesharesofovervaluedfirms

andawayfromtheperformance ofthesharesofundervalued firms.Afundamental• weighted

indexwillactuallyhaveavaluetilt, overweighting firmswithhighvalue-based

metricssuchasbook-to-marketratiosorearningsyields.Note that afirmwith ahigh

earningsyield(totalearnings tototal marketvalue)relativetoother indexfirmswillby

constructionhaveahigherweightinanearnings-weightedindexbecause,amongindex

stocks,itsearnings arehighrelativetoitsmarket value.

PriceWeighting

Aprice-weighted indexaddsthemarket pricesofeachstockintheindexanddividesthis

totalbythenumber ofstocksintheindex.Thedivisor,however,must beadjusted

forstocksplitsandother changesintheindexportfolio tomaintain thecontinuity ofthe

seriesovertime.

Example: Price-weighted index

Given the information for the three stocks presented in the following fgurc, calculate

a price-weighted index return over a 1-month period.

Index Firm Data

Share Price

December31, 20X6

Share Price

January 31. 20X7

Stock X $10 $20

StockY $20 $15

Stock Z $60 $40

Answer:

The price-weighted index is (10 + 20 + 60) / 3 = 30 as of December31 and (20 + 15

40) / 3 = 25 as of January 31. Hence, the price-weighted 1-month percentage return is:

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The returns onaprice-weighted indexcouldbematched bypurchasing anequalnumber

ofsharesofeachstockrepresented intheindex.Becausetheindexis priceweighted, a percentage

changeinahigh-priced stockwillhavearelativelygreatereffectontheindex than

thesamepercentage changeinalow-priced stock.

Market Capitalization Weighting

Amarket capitalization-weighted indexis calculated bysumming thetotalvalue(current

stockpricemultiplied bythenumber ofsharesoutstanding)

ofallthestocksintheindex.Thissumisthen divided byasimilarsumcalculated during

theselectedbaseperiod.The ratioisthen multiplied bytheindex'sbasevalue(typically 100).

Forexample,ifthetotalmarketvaluesoftheindexportfolio onDecember 31and January

31are$80million and$95million, respectively,theindexvalueattheendof January is:

Thus, the market capitalization-weighted index percentage return is: (118.75/100) - 1 =

18.75%

The followingexampleofprice-weighting versusmarketvalue-weighting showshow

thesetwoindexesarecalculated andhowtheydiffer.

Example: Price-weighted vs. market capitalization-weighted indexes

Consider che three firms described below. Compare the effects on a price-weighted

index and a market capitalization-weighted index if Stock A doubles in price or if

Stock C doubles in price. Assume the period shown in the table is the base period for

the market capitalization-weighted index and that its base value is l00.

Index Firm Data

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Company Number of Shares

Outstanding (000s)

Stock Price Capitalization

(000s)

A 100 $100 $10.000

B 1,000 $10 $10,000 $10 $10,000

C 20,000 $1 $20,000

Answer:

The price-weighted index equals:

If Stock A doubles in price to $200, the price-weighted index value is:

If Stock C doubles in price to $2, the price-weighted index value is:

If Stock A doubles in value, the index goes up 33.33 points, while if Stock C doubles

in value, the index only goes up 0.33 points. Changes in the value of the firm with

the highest stock price have a disproportionately large influence on a price-weighted

index.

For a market capialization-weighted index, the base period market capitalization is

(100,000 × $100) + (1,000,000 $10) + (20,000,000 $1) = $40,000,000.

If Stock A doubles in price to $200, the index goes to:

If Stock C doubles in price to $2, the index goes to:

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In the market capitalization-weighted index, the returns on Stock C have the greatest

influence on the index return because Stock C’s market capitalization is larger than

that of Stock A or Stock B.

Equal Weighting

Anequal-weighted indexplacesanequalweightonthereturns ofallindexstocks,

regardlessoftheirpricesormarket values.A$2changeinthepriceofa$20stockhas

thesameeffectontheindexasa$30changeinthepriceofa$300stockregardlessof

thesizeofthecompany.The return ofanequal-weighted indexoveragivenperiod is

oftencalculated asasimpleaverageofthereturns oftheindexstocks.

2.3 Market efficiency

Aninformationallyefficient capital market isoneinwhichthecurrent priceofa

securityfully,quickly,andrationally reflectsallavailableinformation about that security.This

isreallyastatistical concept. Anacademicmight say,"Givenallavailable information,current

securitiespricesareunbiased estimates oftheirvalues,sothat the expected return

onanysecurityisjusttheequilibrium return

necessarytocompensateinvestorsfortherisk(uncertainty) regarding itsfuture cashflows."This

concept isoftenput moreintuitively as,"Youcan'tbeatthemarket."

Inaperfectly efficientmarket, investorsshould useapassiveinvestmentstrategy(i.e.,buying

abroadmarket indexofstocksandholding it)becauseactiveinvestment

strategieswillunderperform duetotransactions costsandmanagement fees.However,

totheextent thatmarket pricesareinefficient, activeinvestment strategiescangenerate

positiverisk-adjusted returns.

One method ofmeasuring amarket'sefficiencyistodetermine thetimeittakesfor trading

activitytocauseinformationtobereflectedinsecurityprices(i.e.,thelagfrom

thetimeinformationisdisseminated tothetimepricesreflectthevalueimplications of that

information). Insomeveryefficientmarkets, suchasforeigncurrency markets, this

lagcanbeasshort asaminute. Ifthereisasignificant lag,informed traderscanusethe

informationtopotentially generatepositiverisk-adjusted returns.

Note that market pricesshould notbeaffectedbythereleaseofinformationthat is wellanticipated.

Onlynewinformation(information that isunexpected andchanges expectations) should

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moveprices.The announcementthat afirm'searningswereup45% overthelastquarter

maybegoodnewsiftheexpected increasewas20%. On theother hand,

thismaybebadnewsifa70%increasewasanticipated ornonewsatallifmarket participants

correctly anticipated quarterly earnings.

Themarket valueofanassetisitscurrent price.The intrinsicvalueorfundamental

valueofanassetisthevaluethatarational investorwith fullknowledge about theasset's

characteristics wouldwillinglypay.Forexample,abond investorwould fullyknowand

understandabond's coupon, maturity, default risk,liquidity, andother characteristicsandwould

usethesetoestimate itsintrinsicvalue.

Inmarkets that arehighlyefficient,investorscantypicallyexpectmarketvaluestoreflect

intrinsicvalues.Ifmarketsarenotcompletely efficient,activemanagerswillbuyassetsforwhich

theythink intrinsicvaluesaregreaterthan marketvaluesandsellassetsforwhichtheythink

intrinsicvaluesarelessthan marketvalues.

Intrinsicvaluescannot beknownwith certaintyandareestimated byinvestorswho

willhavediffering estimates ofanasset'sintrinsicvalue.The morecomplex anasset,

themoredifficultitistoestimate itsintrinsicvalue.Furthermore,intrinsicvalueis

constantlychanging asnew(unexpected) informationbecomesavailable.

Markets aregenerallyneither perfectly efficientnorcompletelyinefficient.The degreeof

informationalefficiencyvariesacrosscountries,time,andmarket types.Thefollowing

factorsaffectthedegreeofmarket efficiency.

Numberofmarket participants.Thelargerthenumberofinvestors, analysts,and

traderswhofollowanassetmarket,themoreefficientthemarket.The numberof participants

canvarythroughtimeandacrosscountries. Forexample,somecountries prevent foreigners

fromtrading intheirmarkets,reducing market efficiency.

Availability ofinformation.Themoreinformationisavailabletoinvestors, themore

efficientthemarket. Inlarge,developed markets suchastheNewYorkStockExchange,

informationisplentifulandmarkets arequite efficient.Inemerging markets, the

availabilityofinformationislower,andconsequently,market pricesarerelativelyless

efficient.Someassets,suchasbonds, currencies, swaps, forwards, mortgages, andmoney market

securitiesthat tradeinover-the-counter(OTC) markets, mayhavelessavailable information.

Accesstoinformationshould notfavoronepartyoveranother. Therefore, regulations

suchastheU.S.SecuritiesandExchangeCommission's Regulation FD(fairdisclosure) requirethat

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firmsdisclosethesameinformationtothepublic that theydisclosetostock analysts.Traderswith

material insideinformationabout afirmareprohibitedfrom trading onthat information.

Impedimentstotrading.Arbitragereferstobuying anassetinonemarket and

simultaneouslysellingitatahigher priceinanother market.This

buyingandsellingofassetswillcontinueuntil thepricesinthetwomarkets

areequal.Impedimentsto arbitrage, suchashightransactions costsorlackof

information,willlimit arbitrage activityandallowsomepriceinefficiencies (i.e.,mispricing

ofassets)topersist.

Shortsellingimprovesmarket efficiency.Thesales pressurefromshortsellingprevents

assetsfrombecoming overvalued. Restrictions onshortselling,suchas aninability to

borrowstockcheaply,canreducemarket efficiency.

Transactionandinformationcosts.Totheextent that thecostsofinformation,analysis,

andtrading aregreaterthan thepotentialprofitfromtrading misvalued securities,market

priceswillbeinefficient. Itisgenerallyaccepted thatmarkets areefficientif,after deducting

costs,therearenorisk-adjusted returns tobemadefromtrading basedon publicly

availableinformation.

ProfessorEugeneFamaoriginallydeveloped theconcept ofmarket efficiencyand identified

threeformsofmarket efficiency.Thedifference amongthem isthat eachis basedonadifferent

setofinformation.

1. Weak-form market efficiency.Theweakformoftheefficientmarketshypothesis (EMH)

statesthatcurrent securitypricesfully reflect allcurrentlyavailablesecurity marketdata.Thus,

pastpriceandvolume (market) informationwillhaveno predictivepoweraboutthefuturedirection

ofsecuritypricesbecausepricechanges willbeindependentfromoneperiodtothenext.Inaweak-

form efficientmarket, an investorcannot achievepositiverisk-adjusted returns

onaveragebyusingtechnical analysis.

2. Semi-strongformmarket efficiency.Thesemi-strong formoftheEMH holdsthat

securitypricesrapidlyadjustwithoutbiastothearrivalofallnewpublicinformation.

Assuch,current securitypricesfullyreflect all publiclyavailableinformation.Thesemi-strong

formsayssecuritypricesincludeallpastsecuritymarketinformationand

nonmarketinformationavailabletothepublic.Theimplication isthataninvestor

cannotachievepositiverisk-adjustedreturnsonaveragebyusingfundamental analysis.

3. Strong-formmarket efficiency.ThestrongformoftheEMH statesthatsecurity pricesfully

reflect all informationfrom bothpublicand private sources. Thestrongform

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includesalltypesofinformation:pastsecuritymarketinformation,public, and private

(inside)information.Thismeansthatnogroupofinvestorshasmonopolistic

accesstoinformationrelevanttotheformationofprices,andnoneshouldbeableto consistently

achievepositiveabnormal returns.

Giventheprohibitiononinsidertrading inmostmarkets, itwouldbeunrealistic to

expectmarketstoreflectallprivateinformation.Theevidencesupports theviewthat

marketsarenotstrong-formefficient.

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Chủ đề 3: Equity Analysis and Valuation

68

3 Chủ đề 3: Equity Analysis and Valuation

3.1 Overview of equity securities

Commonsharesarethemostcommon formofequityandrepresent anownership

interest.Commonshareholders havearesidualclaim(aftertheclaimsofdebtholders

andpreferred stockholders) onfirmassetsifthefirmisliquidated andgovernthe corporation

throughvoting rights. Firmsareunder noobligation to paydividends on common equity;

thefirmdetermines whatdividend willbepaidperiodically. Commonstockholders

areabletovotefortheboard ofdirectors,onmergerdecisions, andontheselection ofauditors.

Iftheyareunable toattend theannual meeting, shareholders can votebyproxy (havingsomeone

elsevoteastheydirectthem, ontheirbehalf).

Inastatutoryvoting system,eachshareheldisassignedonevoteintheelection ofeach member

oftheboardofdirectors. Under cumulative voting,shareholders canallocate

theirvotestooneormorecandidates astheychoose.Forexample,consider asituation

whereashareholder has100sharesandthreedirectors willbeelected.Under statutory voting,

theshareholder canvote100sharesforhisdirector choiceineachelection. Undercumulative

voting, theshareholder has300votes,which canbecastforasingle candidate

orspreadacrossmultiple candidates. The threereceivingthegreatestnumber

ofvotesareelected.Cumulative votingmakesitpossibleforaminorityshareholder to

havemoreproportionalrepresentation ontheboard.Thewaythemathworks,aholder

of30%ofthefirm'ssharescouldchoosethreeoftendirectorswith cumulative voting

butcouldelectnodirectors under statutoryvoting.

Callable commonsharesgivethefirmtherighttorepurchase thestockatapre-specified

callprice.Investors receiveafixedamount whenthefirmcallsthestock.The callfeature

benefitsthefirmbecausewhen thestock'smarket priceisgreaterthan

thecallprice,thefirmcancallthesharesandreissuethemlateratahigherprice. Calling theshares,

similarlytotherepurchase ofshares,allowsthefirmtoreduceitsdividend payments

withoutchanging itsper-share dividend.

Putable commonsharesgivetheshareholder therighttosellthesharesbacktothe

firmataspecificprice.Aputoption onthesharesbenefitstheshareholder

becauseiteffectivelyplacesafloorunder thesharevalue.Shareholders payfortheput option

becauseother things equal,putable sharesaresoldforhigherpricesthan non-putable

sharesandraisemorecapitalforthefirmwhentheyareissued.

Preference shares (orpreferredstock)havefeaturesofboth commonstockanddebt.

Aswithcommon stock,preferred stockdividends arenotacontractualobligation,the

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sharesusuallydonotmature, andthesharescanhaveput orcallfeatures. Likedebt, preferred

sharestypicallymakefixedperiodicpayments toinvestorsanddonotusually havevoting rights.

Cumulativepreferencesharesareusuallypromisedfixeddividends, andanydividends that

arenotpaidmust bemadeupbeforecommon shareholders canreceivedividends. Thedividends

ofnon-cumulativepreferencesharesdonotaccumulateovertimewhentheyarenotpaid,but

dividends foranyperiodmust bepaidbeforecommon shareholders canreceivedividends.

Preferredshareshaveastatedparvalueandpayapercentage dividendbasedonthepar

valueoftheshares.An$80parvaluepreferred

witha10%dividendpaysadividendof$8peryear.Investors

inparticipatingpreferencesharesreceiveextradividends iffirm

profitsexceedapredeterminedlevelandmayreceiveavaluegreaterthan

theparvalueofthepreferred stockifthefirmisliquidated.Non-

participatingpreferenceshareshaveaclaimequaltoparvalueintheeventofliquidationanddonots

hareinfirmprofits. Smallerandriskierfirmswhoseinvestorsmaybeconcernedabout

thefirm'sfuture often issueparticipatingpreferred

stocksoinvestorscanshareintheupsidepotentialofthe firm.

Convertiblepreferencesharescanbeexchanged forcommonstockataconversion ratio

determinedwhenthesharesareoriginallyissued.Ithasthefollowingadvantages:

Thepreferred dividend ishigherthan acommon dividend.

Ifthefirmisprofitable, theinvestor canshareintheprofitsbyconvertinghisshares

intocommon stock.

Theconversion option becomesmorevaluablewhenthecommonstockprice increases.

Preferredshareshavelessriskthan common sharesbecausethedividendisstable

andtheyhavepriority overcommon stockinreceivingdividends andintheeventof

liquidationofthefirm.

Becauseoftheirupsidepotential,convertible preferred sharesareoftenusedtofinance

riskyventure capitalandprivateequityfirms.Theconversion featurecompensates

investorsfortheadditionalrisktheytakewhen investing insuchfirms.

Afirmmayhavedifferent classesofcommon stock(e.g.,"ClassA"and"ClassB" shares).One class

mayhavegreatervoting powerandseniority ifthefirm'sassetsare liquidated.The

classesmayalsobetreated differently withrespecttodividends, stocksplits,andother transactions

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withshareholders. Informationontheownership and voting rightsofdifferent

classesofequitysharescanbefound inthecompany'sfilings withsecuritiesregulators,

suchastheSecuritiesandExchangeCommission inthe United States.

The discussionsofarhascentered onequitythat ispublicly traded. Private equity is

usuallyissuedtoinstitutionalinvestorsviaprivateplacements. Privateequity markets are

smallerthanpublic marketsbutaregrowingrapidly.

Compared topublic equity,privateequityhasthefollowingcharacteristics:

Lessliquiditybecausenopublic market forthesharesexists.

Sharepriceisnegotiated between thefirmanditsinvestors, notdetermined ina market.

Morelimited firmfinancialdisclosurebecausethereisnogovernment orexchange

requirement todoso.

Lowerreportingcostsbecauseoflessonerous reportingrequirements.

Potentially weakercorporate governance becauseofreduced reportingrequirements

andless public scrutiny.

Greaterabilitytofocusonlong-term prospects becausethereisnopublic pressure forshort-

termresults.

Potentially greaterreturn forinvestorsoncethefirmgoespublic.

The threemaintypesofprivateequity investments areventure capital, leveraged buyouts,

andprivateinvestments inpublic equity.

Venture capital referstothecapitalprovided tofirmsearlyintheirlifecyclestofund

theirdevelopment andgrowth. Venturecapitalfinancing atvariousstagesofafirm's development

isreferredtoasseedorstart-up,earlystage,ormezzanine financing.

Investorscanbefamily,friends,wealthyindividuals, orprivate

equityfunds.Venturecapitalinvestments areilliquid andinvestorsoftenhavetocommit

fundsforthreetoten yearsbeforetheycancashout (exit)theirinvestment.

Investorshopetoprofitwhenthey canselltheirsharesafter(oraspart of)aninitialpublic

offeringortoanestablished firm.

Inaleveraged buyout (LBO), investorsbuyallofafirm'sequity usingdebtfinancing

(leverage).Ifthebuyersarethefirm'scurrent management, theLBOis referredtoasa

managementbuyout (MBO). FirmsinLBOsusuallyhavecashflowthat isadequate to

servicetheissueddebtorhaveundervalued assetsthat canbesoldtopaydownthedebt overtime.

Inaprivate investmentinpublic equity (PIPE), apublic firmthat needscapitalquickly sells

privateequitytoinvestors.The firmmayhavegrowth opportunities,beindistress,

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orhavelargeamounts ofdebt.The investorscanoftenbuythestockatasizeable discount

toitsmarketprice.

When capitalflows freelyacrossborders, marketsaresaidtobeintegrated.Theworld's

financialmarkets havebecomemoreintegrated overtime, especiallyasaresultof improved

communications andtrading technologies. However,barrierstoglobalcapital

flowsstillexist.Somecountries restrict foreignownership oftheirdomestic stocks, primarily

toprevent foreigncontrol ofdomestic companies andtoreducethevariability

ofcapitalflowsinandoutoftheircountries.

Anincreasing number ofcountries havedroppedforeigncapitalrestrictions. Studies

haveshownthat reducing capitalbarriersimprovesequity market performance. Furthermore,

companies areincreasingly turning toforeigninvestorsforcapitalby

listingtheirstocksonforeignstockexchangesorbyencouraging foreignownership of shares.

Fromthefirm'sperspective, listingonforeignstockexchangesincreasespublicity forthe

firm'sproducts andtheliquidityofthefirm'sshares.Foreignlistingalsoincreasesfirm transparency

duetothestricter disclosurerequirements ofmanyforeignmarkets.

Direct investing inthesecuritiesofforeigncompanies simplyreferstobuying aforeign

firm'ssecuritiesinforeignmarkets. Someobstaclestodirectforeigninvestment arethat:

Theinvestment andreturn aredenominatedinaforeigncurrency.

Theforeignstockexchangemaybeilliquid.

Thereportingrequirements offoreignstockexchangesmaybeless strict,impeding

analysis.

Investors mustbefamiliarwith theregulations andprocedures ofeachmarket in which

theyinvest.

Other methods forinvesting inforeigncompanies areprovided byglobaldepository receipts

(GDRs), American depository receipts (ADRs),globalregisteredshares(GRSs),

andbasketsoflisted depository receipts (BLDRs).

Depositoryreceipts (DRs)represent ownership inaforeignfirmandaretraded inthe markets

ofother countries inlocalmarket currencies. Abank depositssharesofthe foreignfirmandthen

issuesreceiptsrepresenting ownership ofaspecificnumberofthe foreignshares.The

depositorybank actsasacustodian andmanagesdividends, stock splits,andother

events.Although theinvestordoesnothavetoconverttotheforeign

currency,thevalueoftheDRisaffectedbyexchangeratechanges,aswellasfirm fundamentals,

economic events,andanyother factorsthat affectthevalueofanystock.

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Ifthefirmisinvolvedwiththeissue,thedepository receiptisasponsored DR;

otherwise,itisanunsponsoredDR.Asponsored DRprovidestheinvestorvoting rights

andisusuallysubject togreaterdisclosurerequirements.Inanunsponsored DR, the depository

bankretainsthevoting rights.

Global depositoryreceipts (GDRs) areissuedoutside theUnited Statesandtheissuer's

homecountry. MostGDRs aretraded ontheLondon andLuxembourg exchanges. Although

notlistedonU.S.exchanges,theyareusuallydenominatedinU.S.dollarsandcanbesoldtoU.S.instit

utionalinvestors. GDRs arenotsubjecttothecapitalflow restrictions imposed bygovernments

andthusofferthefirmandtheinvestorgreater opportunitiesforforeigninvestment. The

firmusuallychoosestolisttheGDR ina marketwheremanyinvestorsarefamiliarwith thefirm.

American depositoryreceipts (ADRs)aredenominatedinU.S.dollarsandtradeinthe United

States.The securityonwhichtheADR isbasedistheAmerican depositoryshare

(ADS),whichtradesinthefirm'sdomestic market. SomeADRsallowfirmstoraise

capitalintheUnited Statesorusethesharestoacquireother firms.MostrequireU.S.

SecuritiesandExchangeCommission (SEC)registration, butsomeareprivatelyplaced

(Rule144AorRegulation S receipts).

ThefourtypesofADRs,with different levelsoftrading availabilityandfirm requirements,

aresummarized inFigure1.

Figure 1: Types of ADRs

Level I Level II Level III Rule 144A

Trading location Over-the-

counter (OTC)

NYSE, Nasdaq,

and AMEX

NYSE, Nasdaq,

and AMEX

Private

SEC registration

required

Yes

Yes

Yes

No

Ability to raise

capical in

United States

No No Yes

Yes

Firm listing

expenses

Low High High Low

Global registered shares (GRS)aretraded indifferent currencies onstockexchanges around

theworld.

Abasket oflisted depositoryreceipts (BLDR)isanexchange-tradedfund (ETF) that is

acollection ofDRs.ETFsharestradeinmarketsjustlikecommon stocks.

The returns onequity investments consistofpricechanges,dividend payments, and,in

thecaseofequities denominatedinaforeigncurrency,gainsorlossesfromchangesin

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exchangerates.AJapaneseinvestorwhoinvestsineuro-denorninated shareswillhave

greateryen-based returns iftheeuroappreciates relativetotheyen.

Gainsfromdividends andthereinvestment ofdividends havebeenanimportantpart

ofequityinvestors' long-term returns. Forexample,$1investedinU.S.stocksin1900

wouldhavebeenworth $834 inrealtermsin2011with dividends reinvestedbut only$8.10

withpriceappreciation alone.Overthesametimeperiod, theterminal wealth for bonds

andbillswouldhavebeen$9.30and$2.80, respectively.

The riskofequitysecuritiesismostcommonly measured asthestandard deviation of returns.

Preferredstockislessriskythan common stockbecausepreferred stockpaysa known,

fixeddividend toinvestorsthat isalargepartofthereturn, whereascommon dividends

arevariableandcanvarywith earnings.Also,preferred stockholders receive

theirdistributionsbeforecommon shareholders andhaveaclaiminliquidationequalto

theparvalueoftheirsharesthathaspriority overtheclaimsofcommon stockowners.

Becauseitislessrisky,preferred stockhasaloweraveragereturn than common stock.

Cumulative preferred shareshavelessriskthan non-cumulativepreferred sharesbecause

theyretaintherighttoreceiveanymisseddividends beforeanycommon stockdividends canbepaid.

Forboth common andpreferred shares,putable sharesarelessriskyandcallableshares

aremoreriskycompared toshareswith neither option. Putablesharesarelessrisky

becauseifthemarket pricedrops, theinvestorcanput thesharesbacktothefirmata

fixedprice(assuming thefirmhasthecapitaltohonor theput).Becauseofthisfeature, putable

sharesusuallypayalowerdividend yieldthan non-putableshares.

Callablesharesarethemostriskybecauseifthemarket pricerises,thefirmcancallthe shares,limiting

theupsidepotentialoftheshares.Callableshares,therefore,usuallyhave higher dividend

yieldsthan non-callable shares.

Equity capitalisusedforthepurchase oflong-term assets,equipment, researchand development,

andexpansion intonewbusinessesorgeographic areas.Equity securities provide thefirmwith

"currency"that canbeusedtobuyother companies orthat canbe offeredtoemployeesasincentive

compensation. Having publicly traded equitysecurities providesliquidity,

whichmaybeespeciallyimportanttofirmsthat needtomeet regulatory requirements,

capitaladequacyratios,andliquidity ratios.

Theprimary goaloffirmmanagement istoincreasethebookvalueofthefirm'sequity andthereby

increasethemarketvalueofitsequity.Thebookvalueofequity isthevalue

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ofthefirm'sassetsonthebalancesheetminus itsliabilities.

Itincreaseswhenthefirmhaspositivenetincome andretained earnings

thatflowintotheequityaccount. Whenmanagement makesdecisionsthat increaseincome

andretained earnings, theyincrease thebookvalueofequity.

Themarket valueofequity

isthetotalvalueofafirm'soutstandingequitysharesbasedonmarketpricesandreflectstheexpectati

ons ofinvestorsabout thefirm'sfuture performance. Investors usetheirperceptions

ofthefirm'sriskandtheamounts and timing offuture cashflowstodetermine

themarketvalueofequity.Themarket value andbookvalueofequityareseldomequal.Although

management maybemaximizing

thebookvalueofequity,thismaynotbereflectedinthemarketvalueofequitybecause

bookvaluedoesnotreflectinvestor expectations about future firmperformance.

Akeyratiousedtodetermine management efficiencyistheaccounting return on

equity,usuallyreferredtosimplyasthereturn onequity (ROE).ROEiscalculated as netincome

availabletocommon (netincome minus preferred dividends) dividedbythe

averagebookvalueofcommon equity overtheperiod:

Alternatively, ROEisoftencalculated usingonlybeginning-of-yearbookvalueofequity

(i.e.,bookvalueofequityforendofyeart- 1):

Thefirstmethod ismoreappropriate whenitistheindustryconvention orwhenbook

valueisvolatile.Thelattermethod ismoreappropriate when examining ROEfora number

ofyearsorwhenbookvalueisstable.

Higher ROEisgenerallyviewedasapositiveforafirm,butthereasonforanincrease should

beexamined.Forexample,ifbookvalueisdecreasingmorerapidlythan net income,

ROEwillincrease.This isnot,however,apositiveforthefirm.Afirmcanalso issuedebttorepurchase

equity,therebydecreasingthebookvalueofequity.Thiswould

increasetheROEbutalsomakethefirm'ssharesriskierduetotheincreasedfinancial leverage(debt).

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Thebookvalueofequity reflectsafirm'sfinancialdecisionsandoperating resultssince itsinception,

whereasthemarket valueofequityreflectsthemarket's consensusviewofafirm's future

performance. The price-to-book ratio (also called the market-to-book ratio)isthe

market value ofafirm's equity divided bythe book value ofitsequity. Themoreoptimistic

investors are about the firm's future growth, the greater itsprice-to-bookratio.The price-

to-book ratio isused asameasure of relative value. Often, firms withlow price-to-book

ratios are considered valuestocks,whilefirmswithhighprice-to-bookratiosareconsidered

growthstocks.

Investors'RequiredReturn andtheCostofEquity

Afirm'scostofequity istheexpectedequilibrium totalreturn (including

dividends)onitssharesinthemarket. Itisusuallyestimated inpractice usingadividend-discount

modelorthecapitalassetpricing model.Atanypoint intime,

adecreaseinsharepricewillincreasetheexpectedreturn

onthesharesandanincreaseinsharepricewilldecreaseexpectedreturns, other things

equal.Becausetheintrinsic valueofafirm's sharesisthediscounted presentvalueofitsfuture

cashflows,anincrease(decrease)in therequired return usedtodiscountfuture

cashflowswilldecrease(increase)intrinsic value.

Investorsalsoestimate theexpectedmarket returns onequitysharesandcompare thisto

theminimumreturn theywillacceptforbearing theriskinherentinaparticular stock.

Ifaninvestor estimates theexpectedreturn onastocktobegreaterthanherminimum required

rateofreturn ontheshares,giventheir risk,then thesharesareanattractive investment. Investors

canhavedifferent required ratesofreturn foragivenrisk, different estimates ofafirm'sfuture

cashflows,anddifferent estimates oftheriskofa firm'sequityshares.Afirm'scostofequity

canbeinterpretedastheminimumrateof return required byinvestors

(intheaggregate)tocompensate them fortheriskofthe firm'sequityshares.

3.2 Introduction to industry and company analysis

Industryanalysisisimportantforcompany analysisbecauseitprovidesaframework for

understandingthefirm.Analystswilloftenfocusonagroup ofspecificindustries sothat

theycanbetter understand thebusinessconditions thefirmsinthoseindustries face.

Understandingafirm'sbusinessenvironment canprovideinsight about thefirm's

potentialgrowth, competition,andrisks.Foracreditanalyst,industryconditions can provide

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importantinformationaboutwhether afirmwillbeabletomeetitsobligations during

thenextrecession.

Inanactivemanagement strategy,industryanalysiscanidentify industries that are undervalued

orovervaluedinordertoweightthemappropriately. Someinvestorsengage

inindustryrotation,which isoverweighting orunderweightingindustries basedonthe current

phaseofthebusinesscycle. Afirm'sindustryhasbeenfound tobeasimportant asitshome country

indeterminingitsperformance.

Inperformance attributionanalysis,thesourcesofportfolio return aredetermined

relativetoabenchmark. The industryrepresentation within aportfolio isoftena significant

componentofattributionanalysis.

Onewaytogroup companies intoanindustryisbytheproductsandservicestheyoffer.

Forexample,thefirmsthatproduce automobiles constitutetheautoindustry.Asectorisagroup

ofsimilarindustries. Hospitals, doctors, pharmaceutical firms,andother industries areincluded

inthehealth caresector.Systemsthat aregrouped byproducts

andservicesusuallyuseafirm'sprincipalbusiness activity (thelargestsourceofsales orearnings)

toclassifyfirms.Examplesofthesesystemsarediscussedinthefollowingandinclude

theGlobalIndustryClassification Standard (GICS),

RussellGlobalSectors(RGS),andIndustryClassification Benchmark.

Firmscanalsobeclassifiedbytheirsensitivitytobusinesscycles.Thissystemhastwomain

classifications:cyclicalandnon-cyclical firms.

Statisticalmethods,suchasclusteranalysis,canalsobeused.This method groupsfirms

thathistorically havehadhighlycorrelated returns. The groups (i.e.,industries) formed

willthenhavelowerreturns correlations between groups.

Thismethod hasseverallimitations:

Historical correlations maynotbethesameasfuture correlations.

The groupings offirmsmaydifferovertimeandacrosscountries.

The grouping offirmsissometimes non-intuitive.

The method issusceptible tostatistical error (i.e., firmscanbegrouped bya relationship

that occursbychance, ornotgrouped together when theyshould be).

Acyclicalfirmisonewhoseearnings arehighlydependentonthestageofthebusiness cycle.These

firmshavehighearningsvolatility andhighoperating leverage.Their products

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areoftenexpensive,non-necessitieswhosepurchase canbedelayeduntiltheeconomy improves.

Examplesofcyclicalindustries include basicmaterials and processing, consumer discretionary,

energy,financialservices,industrial andproducer durables, andtechnology.

Incontrast, anon-cyclical firmproduces goodsandservicesforwhich demand is

relativelystableoverthebusinesscycle.Examplesofnon-cyclical industries include health

care,utilities, telecommunications, andconsumer staples.

Sectorscanalsobeclassifiedbytheirsensitivity tothephaseofthebusinesscycle.

Cyclicalsectorexamplesinclude energy,financials, technology, materials, andconsumer

discretionary. Non-cyclical sectorexamplesinclude health care,utilities, andconsumer staples.

Non-cyclical industries canbefurther separated into defensive(stable)orgrowth industries.

Defensive industriesarethosethat areleastaffectedbythestageofthe businesscycleandinclude

utilities, consumer staples(suchasfoodproducers), andbasic

services(suchasdrugstores).Growthindustrieshavedemand sostrong theyarelargely

unaffected bythestageofthebusinesscycle.

Descriptors suchas"growth," "defensive,"and"cyclical"should beusedwithcaution.

Cyclicalindustries, which aresupposed tobedependentonthebusinesscycle,often include

growth firmsthat arelessdependentonthebusinesscycle.Non-cyclical

industriescanbeaffectedbysevererecessions,aswasthecaseinthe2008-09downturn.

Defensiveindustries maynotalwaysbesafeinvestments.

Forexample,grocerystoresareclassifiedasdefensive,buttheyaresubject tointense

pricecompetitionthat reducesearnings. Defensiveindustries mayalsocontain

sometrulydefensiveandsomegrowth firms.Becausebusinesscyclephasesdifferacrosscountries

andregions,twocyclical firmsoperating indifferent countries

maybesimultaneouslyexperiencing different cyclicaleffectsonearningsgrowth.

Apeergroup isa setofsimilarcompanies ananalystwilluseforvaluation comparisons.

Morespecifically,a peergroupwillconsistofcompanies withsimilarbusinessactivities, demand

drivers,coststructuredrivers,andavailabilityofcapital.

Toformapeergroup, ananalystwilloftenstartbyidentifying companies

inthesameindustryclassification, usingthecommercial classificationproviderspreviously

described. Usually,theanalystwilluseother informationtoverifythat thefirmsinan

industryareindeed peers.Ananalystmight include acompany inmorethan onepeer group.

Thefollowingarestepsananalystwould usetoformapeergroup:

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Usecommercial classificationproviders todetermine whichfirmsareinthesame industry.

Examine firms'annual reports toseeiftheyidentify keycompetitors.

Examine competitors' annual reports toseeifother competitors arenamed.

Useindustrytradepublications toidentify competitors.

Confirm that comparable firmshavesimilarsourcesofsalesandearnings, have

similarsourcesofdemand, andareinsimilargeographic markets.

Adjust financialstatements ofnon-financial companies foranyfinancing subsidiary

datatheyinclude.

Athoroughindustryanalysisshould include thefollowingelements:

Evaluatetherelationships between macroeconomicvariablesandindustrytrends

usinginformationfromindustrygroups, firmsintheindustry, competitors, suppliers,

andcustomers.

Estimate industryvariablesusingdifferent approaches andscenarios.

Compare with other analysts'forecastsofindustryvariablestoconfirm thevalidity

oftheanalysisandpotentially findindustries that aremisvalued asaresultof

consensusforecasts.

Determine therelativevaluation ofdifferent industries.

Compare thevaluations ofindustries acrosstimetodetermine thevolatility oftheir

performance overthelongrun andduring different phasesofthebusinesscycle.

Thisisusefulforlong-term investing aswellasshort-termindustryrotationbased

onthecurrent economic environment.

Analyzeindustryprospects basedonstrategic groups, which aregroupsoffirmsthat

aredistinct fromtherestoftheindustryduetothedeliveryorcomplexity oftheir products

orbarrierstoentry.Forexample,full-servicehotelsareadistinct market segmentwithin

thehotelindustry.

Classifyindustries bylife-cyclestage,whetheritisembryonic, growth, shakeout, mature,

ordeclining.

Position theindustryontheexperience curve,whichshowsthecostperunit relative

tooutput. Thecurvedeclinesbecauseofincreasesinproductivityandeconomies of

scale,especiallyinindustries withhighfixedcosts.

Consider theforcesthat affectindustries, which include demographic,

macroeconomic,governmental, social,andtechnological influences.

Examine theforcesthat determine competition within anindustry.

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Industries differmarkedly inprofitability becauseofdifferencesineconomic fundamentals,

industrystructure, anddegreeofcompetition.Insomeindustries, competition isintense

andfewfirmsearneconomic profits.Economic profits, thereturn oninvestedcapitalminus

itscost,aregreaterthan 20%insomeindustries andnegative inothers.The degreeofeconomic

profitsdepends inpart onpricing power(elasticityof demand forthefirm'sproducts).

Ananalystshould understandthat industryconditions andprofitscanchangedramatically

overtime,soindustryanalysisshould beforward-looking.

One componentofananalyst'sindustryanalysisshould bestrategicanalysis,which

examineshowanindustry's competitiveenvironmentinfluencesafirm'sstrategy.The

analysisframework developed byMichael Porterdelineates fiveforcesthat determine

industrycompetition.

1. Rivalryamongexistingcompetitors.Rivalryincreaseswhen manyfirmsofrelatively

equalsizecompetewithin anindustry. Slowgrowth leadstocompetitionasfirms fightformarket

share,andhighfixedcostsleadtopricedecreasesasfirmstryto operate

atfullcapacity.Forexample,thehighfixedcostsintheautoindustryfrom capital investments

andlaborcontracts forcefirmstoproducealargenumberof vehiclesthat

theycanonlysellatlowmargins. Industrieswithproductsthat are

undifferentiatedorhavebarriers (arecostly)toexittend tohavehighlevelsof competition.

2. Threatofnewentrants.Industriesthat havesignificant barriers toentry (e.g.,large

capitaloutlaysforfacilities)willfinditeasiertomaintainpremiumpricing. Itis

costlytoenterthesteeloroilproductionindustries.Those industrieshavelarge barriers

toentryandthuslesscompetitionfromnewcomers.Ananalystshould identifyfactorsthat

discourage newentrants,suchaseconomies ofscale.

3. Threatofsubstitute products.Substituteproductslimit theprofitpotentialofan

industrybecausetheylimit thepricesfirmscanchargebyincreasing theelasticityof

demand.Commodity-likeproductshavehighlevelsofcompetitionandlowprofit

margins.Themoredifferentiatedtheproductsarewithin anindustry,theless price

competitiontherewillbe.Forexample,inthepharmaceuticalindustry,patents protect

aproducerfromcompetitioninthemarkets forpatenteddrugs.

4. Bargainingpowerofbuyers.Buyers'abilitytobargain forlowerpricesorhigher quality

influencesindustryprofitability. Bargaining bygovernments andever-larger health

careprovidershaveput downward pressureevenonpatenteddrugs.

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5. Bargainingpowerofsuppliers.Suppliers' abilitytoraisepricesorlimit supply influences

industryprofitability. Suppliers aremorepowerful iftherearejustafew ofthem

andtheirproductsarescarce.Forexample,Microsoftisoneofthefew suppliers

ofoperatingsystemsoftwareandthushaspricing power.

Thefirsttwoforcesdeservefurther attentionbecausealmostallfirmsmustbeconcerned about

thethreat ofnewentrantsandcompetitionthatwould erodeprofits. Studying

theseforcesalsohelpstheanalystbetter understandthesubject firm'scompetitorsandprospects.

Thefollowingsummarydescribeshowthesetwofactorsinfluence the

competitiveenvironmentinanindustry:

Higher barriers toentry reducecompetition.

Greater concentration(asmallnumberoffirmscontrol alargepartofthemarket)

reducescompetition, whereasmarket fragmentation(alargenumberoffirms,each with

asmallmarket share)increasescompetition.

Unusedcapacityinanindustry, especiallyifprolonged,resultsinintense price

competition.Forexample,underutilizedcapacityintheautoindustryhasresulted in

verycompetitivepricing.

Morepricesensitivity incustomer buying decisionsresultsingreatercompetition.

Greater maturityofanindustryresultsinslowinggrowth.

BarrierstoEntry

Highbarrierstoentrybenefitexistingindustry firmsbecausetheyprevent new competitors

fromcompeting formarket shareandreducing theexistingfirms'return oncapital. Inindustries

with lowbarriers toentry,firmshavelittlepricing powerand

competitionreducesexistingfirms'return oncapital.Toassesstheeaseofentry,the analystshould

determine howeasilyanewentrant totheindustrycould obtain thecapital,intellectual property,

andcustomer baseneeded tobesuccessful.Onemethod ofdetermining theeaseofentry

istoexaminethecomposition oftheindustryovertime.Ifthesamefirmsdominate

theindustrytodayastenyearsago,entry isprobably difficult.

Highbarrierstoentrydonotnecessarilymeanfirmpricing powerishigh.Industries

withhighbarrierstoentrymayhavestrong competitionamongexistingfirms.This is

morelikelywhentheproducts soldareundifferentiatedandcommodity-likeorwhen

highbarrierstoexitresultinovercapacity.Forexample,anautomobile factorymayhave

alowvalueinanalternative use,making firmownersless likelytoexittheindustry.They continue

tooperate evenwhenlosingmoney,hoping toturn things around,

whichcanresultinindustryovercapacityandintense pricecompetition.

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Lowbarrierstoentrydonotensuresuccessfornewentrants. Barrierstoentry may

changeovertime,andsomight thecompetitive environment.

IndustryConcentration

High industryconcentrationdoesnotguarantee pricing power.

Absolute market sharemaynotmatter asmuch asafirm'smarket

sharerelativetoitscompetitors. Afirmmayhavea50%marketshare,but

ifasinglecompetitorhas theother 50%, their 50%sharewould

notresultinagreatdegreeofpricing power. Return oncapitalislimited byintense

competition betweenthetwofirms.

Conversely,afirmthat hasa10%market sharewhennocompetitorhasmorethan

2%mayhaveagooddegreeofpricing powerandhigh return oncapital.

Ifindustryproducts areundifferentiatedandcommodity-like,then consumers will

switchtothelowest-pricedproducer. The moreimportance consumers placeon

price,thegreaterthecompetitioninanindustry. Greater competitionleadstolower

return oncapital.

Industries withgreaterproductdifferentiation inregardtofeatures,reliability,and

serviceafterthesalewillhavegreaterpricing power.Return oncapitalcanbehigher

forfirmsthat canbetter differentiate theirproducts.

Iftheindustryiscapitalintensive, andtherefore costlytoenterorexit,overcapacity

canresultinintensepricecompetition.

Tobacco, alcohol, andconfections areexamplesofhighlyconcentrated industries in which

firms'pricing powerisrelativelystrong.Automobiles, aircraft, andoilrefiningare

examplesofhighlyconcentratedindustries with relativelyweakpricing power.

Although industryconcentrationdoesnotguarantee pricing power,afragmented market

doesusuallyresultinstrong competition. When therearemanyindustrymembers, firms cannot

coordinate pricing, firmswillactindependently, andbecauseeachmember has

suchasmallmarket share,anyincremental increaseinmarket sharemaymakeaprice

decreaseprofitable.

IndustryCapacity

Industrycapacityhasaclearimpact onpricing power.Undercapacity,asituation in which

demand exceedssupplyatcurrent prices,resultsinpricing powerandhigher return oncapital.

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Overcapacity, with supplygreaterthan demand atcurrent prices,will resultindownward

pressureonpriceandlowerreturn oncapital.

Ananalystshould befamiliarwith theindustry's current capacityanditsplanned investment

inadditional capacity.Capacity isfixedintheshort runandvariableinthe longrun.

Inotherwords,givenenough time,producers willbuild enough factoriesandraiseenough

capitaltomeetdemand atapriceclosetominimumaveragecost.However,producers

mayovershoot theoptimal industrycapacity,especiallyincyclical markets.

Forexample,producers maystarttoordernewequipmentduring aneconomic expansion

toincreasecapacity.Bythetimetheybring theadditional productionontothemarket, theeconomy

maybeinarecessionwith decreaseddemand. Adiligent analystcanlookforsignsthat

theplannedcapacityincreasesofallproducers (whomay nottakeinto account

thecapacityincreasesofother firms)sumtomoreoutput than industrydemand willsupport.

Capacity isnotnecessarilyphysical. Forexample,anincreaseindemand forinsurance

canbemoreeasilyandquicklymetthan anincreaseindemand foraproductrequiring

physicalcapacity,suchaselectricity orrefinedpetroleum products.

Ifcapacityisphysicalandspecialized,overcapacity canexistforanextended period if producers

expand toomuch overthecourseofabusinesscycle.Specializedphysical

capacitymayhavealowliquidationvalueandbecostlytoreallocatetoadifferent product.Non-

physical capacity (e.g.,financialcapital) canbereallocated morequickly tonewindustries than

physicalcapacity.

Market ShareStability

Ananalystshould examinewhether firms'market sharesinanindustryhavebeen stable over

time. Market shares that are highly variable likely indicate a highly competitive industry

in which firms have little pricing power. More stable market shares likely indicate less

intense competition in the industry.

Factors that affect market share stability include barriers to entry, introductions of

new products and innovations, and the switching costs that customers face when

changing from one firm's products to another. Switching costs, such as the time and

expense of learning to use a competitor's product, tend to be higher for specialized or

differentiated products. High switching costs contribute to market share stability and

pricing power.

Industry life cycle analysis should be a component of an analyst's strategic analysis.

An industry's stage in the cycle has an impact on industry competition, growth, and

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profits. An industry's stage will change over time, so the analyst must monitor the

industry on an ongoing basis. The five phases of the industry life-cycle model are

illustrated in Figure 1.

Figure 1: Stages of the Industry Life Cycle

The externalinfluencesonindustrygrowth, profitability,andriskshould

beacomponentofananalyst'sstrategic analysis.Theseexternalfactorsinclude

macroeconomic,technological, demographic, governmental, andsocialinfluences.

Macroeconomicfactorscanbecyclicalorstructural(longer-term) trends, most notably

economic output asmeasured byGDP orsomeother measure. Interest ratesaffect financing

costsforfirmsandindividuals, aswellasfinancialinstitutionprofitability. Credit

availabilityaffectsconsumer andbusinessexpenditures andfunding. Inflation

affectscosts,prices,interest rates,andbusinessandconsumerconfidence. Anexampleof

astructuraleconomic factoristheeducation leveloftheworkforce.Moreeducation can

increaseworkers'productivityandrealwages,whichinturn canincreasetheirdemand

forconsumer goods.

Technology canchangeanindustrydramatically throughtheintroductionofnew

orimproved products. Computerhardware

isanexampleofanindustrythathasundergone dramatic transformation.

Radicalimprovements incircuitry were assistedbytransformations inother industries,

includingthecomputersoftwareandtelecommunications industries.

Anotherexampleofanindustrythat hasbeenchanged bytechnology isphotography,

which haslargelymovedfromfilmtodigitalmedia.

Embryonic

Mature

Shakeout

Growth

Demand

Time

Decline

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Demographicfactorsinclude agedistributionandpopulationsize,aswellasother changes

inthecomposition ofthepopulation.Asalargesegment ofthepopulationreachestheir twenties,

residential construction,furniture, andrelatedindustries seeincreaseddemand.

Anagingoftheoverallpopulationcanmeansignificant growth forthehealth care

industryanddevelopersofretirement communities. Forexample,theagingofthepost-

WorldWarIIBabyBoomersisanexampleofdemographics thatwillincreasedemand in

theseindustries.

Governmentshaveanimportantandwidespread effectonbusinessesthroughvarious channels,

including taxesandregulation. Theleveloftaxratescertainly affects industries, but

analystsshould alsobeawareofthedifferential taxation applied tosome goods.Forexample,

tobacco isheavilytaxedintheUnited States.Specificregulations applytomanyindustries. Entry

intothehealth careindustry, forexample,iscontrolledbygovernments thatlicensedoctors

andother providers. Governments canalsoempowerself-regulatory organizations,

suchasstockexchangesthat regulatetheirmembers. Some industries,

suchastheU.S.defenseindustry, depend heavilyongovernment purchasesofgoodsandservices.

Socialinfluencesrelatetohowpeoplework,play,spend

theirmoney,andconducttheirlives;thesefactorscanhavealargeimpact

onindustries.Forexample,whenwomenentered theU.S.workforce,therestaurant

industrybenefitted becausetherewaslesscooking athome.Child care,women'sclothing,

andother industries werealso dramatically affected.

Having gainedunderstandingofanindustry's external environment,

ananalystcanthenfocusoncompanyanalysis.This

involvesanalyzingthefirm'sfinancialcondition, products andservices,andcompetitivestrategy.

Competitive strategyishowafirm responds totheopportunitiesandthreats oftheexternal

environment. Thestrategymay bedefensiveoroffensive.

Porterhasidentified twoimportantcompetitive strategiesthat canbeemployed byfirmswithin

anindustry: acostleadership (low-cost) strategyoraproductorservice differentiationstrategy.

According toPorter,afirmmust decidetofocusononeofthese twoareastocompete effectively.

Inalow-coststrategy,thefirmseekstohavethelowestcostsofproductioninitsindustry,

offerthelowestprices,andgenerate enough volume tomakeasuperior return. The

strategycanbeuseddefensivelytoprotect market shareoroffensivelytogainmarket

share.Ifindustrycompetition isintense, pricing

canbeaggressiveorevenpredatory.Inpredatorypricing, thefirmhopestodriveoutcompetitors

andlaterincreaseprices.Although thereareoftenlawsprohibitingpredatory pricing,

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itcanbehardtoproveifthefirm'scostsarenoteasilytraced toaparticular product.Alow-

coststrategyfirm should havemanagerial incentives that aregearedtoward improving operating

efficiency.

Inadifferentiation strategy,thefirm'sproducts andservicesshould bedistinctive interms

oftype,quality,ordelivery.Forsuccess,thefirm'scostofdifferentiation mustbelessthan

thepricepremium buyersplaceonproductdifferentiation. Thepricepremium should

alsobesustainable overtime.Successfuldifferentiators willhaveoutstanding marketing

researchteamsandcreativepersonnel.

Acompany analysisshould include thefollowingelements:

Firmoverview,including information onoperations, governance, andstrengths and

weaknesses.

Industrycharacteristics.

Product demand.

Productcosts.

Pricingenvironment.

Financial ratios,with comparisons tootherfirmsandovertime.

Projected financialstatements andfirmvaluation.

Afirm'sreturn onequity(ROE)should bepartofthefinancialanalysis.The ROEisa function

ofprofitability, totalassetturnover, andfinancialleverage(debt).

3.3 Equity valuation: concepts and basic tools

RecallfromthetopicreviewofMarket Efficiencythat intrinsicvalueorfundamental

valueisdefinedastherational valueinvestorswould placeontheassetiftheyhadfull knowledge

oftheasset'scharacteristics. Analystsusevaluation modelstoestimate the intrinsic

valuesofstocksandcompare them tothestocks'market pricestodetermine whether individual

stocksareovervalued, undervalued, orfairlyvalued.Indoing valuation

analysisforstocks,analystsareassumingthat somestocks'pricesdeviate significantly

fromtheirintrinsic values.

Totheextent that market pricesdeviatefromintrinsic values,analystswhocanestimate

astock'sintrinsic valuebetter than themarket canearnabnormal profitsifthestock's market

pricemovestowarditsintrinsic valueovertime.There areseveralthingsto

consider,however,indecidingwhether toinvestbasedondifferencesbetween market

pricesandestimated intrinsic values.

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1.Thelargerthepercentage differencebetweenmarket pricesandestimated values,the

morelikelytheinvestoristotakeapositionbasedontheestimate ofintrinsic value.

Smalldifferencesbetween market pricesandestimates ofintrinsic valuesaretobe expected.

2.Themoreconfident theinvestor isabout theappropriatenessofthevaluation model

used,themorelikelytheinvestor istotakeaninvestment position inastockthat is identified

asovervaluedorundervalued.

3. The moreconfident theinvestorisabout theestimated inputs usedinthevaluation model,

themorelikelytheinvestoristotakeaninvestment position inastockthatisidentified

asovervaluedorundervalued. Analystsmustalsoconsider thesensitivity

ofamodelvaluetoeachofitsinputs indecidingwhether toactonadifference between

modelvaluesandmarket prices.Ifadecreaseofone-halfpercent inthelong-term growth

rateusedinthevaluation modelwould produce anestimated valueequaltothemarket

price,ananalystwouldhavetobequitesureofthe model'sgrowth estimate totakeaposition

inthestockbasedonitsestimated value.

4. Evenif weassumethat market pricessometimes deviatefromintrinsic values, market

pricesmustbetreated asfairlyreliableindications ofintrinsic value. Investorsmustconsider

whyastockismispriced inthemarket. Investorsmaybe moreconfident about estimates

ofvaluethat differfrommarket priceswhenfew analystsfollowaparticular security.

5. Finally,totakeapositioninastockidentified asmispriced inthemarket, an investormust

believethat themarket pricewillactuallymovetoward (andcertainly

notawayfrom)itsestimated intrinsic valueandthat itwilldosotoasignificant extentwithin

theinvestment timehorizon.

Analystsuseavarietyofmodelsto estimate thevalueofequities. Usually,ananalystwill

usemorethan onemodelwith severaldifferent setsofinputs todetermine arangeof

possiblestockvalues.

Indiscountedcashflowmodels (orpresent valuemodels),

astock'svalueisestimatedasthepresentvalueofcashdistributedtoshareholders

(dividenddiscountmodels)orthe presentvalueofcashavailabletoshareholders

afterthefirmmeetsitsnecessarycapital expenditures andworking capitalexpenses(free cashflow

to equity models).

There aretwobasictypesofmultipliermodels (ormarket multiplemodels) that

canbeusedtoestimate intrinsic values.Inthefirsttype,theratioofstockpricetosuch fundamentals

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asearnings, sales,bookvalue,orcashflowpershareisusedtodetermine if astockisfairlyvalued.

Forexample,thepricetoearnings (P/E)ratioisfrequently used byanalysts.

Thesecondtypeofmultiplier model isbasedontheratioofenterprisevaluetoeither

earningsbeforeinterest, taxes,depreciation, andamortization (EBITDA) orrevenue. Enterprise

valueisthemarket valueofallafirm'soutstandingsecuritiesminus cashand short-

terminvestments. Commonstockvaluecanbeestimated bysubtracting thevalue ofliabilities

andpreferred stockfromanestimate ofenterprise value.

Inasset-based models, theintrinsic valueofcommon stockisestimated astotalasset valueminus

liabilitiesandpreferred stock.Analyststypicallyadjust thebookvaluesof

thefirm'sassetsandliabilities totheirfairvalueswhenestimating themarket valueofits

equitywithanasset-basedmodel.

Thedividend discountmodel (DDM) isbasedontherationale that theintrinsic value

ofstockisthepresentvalueofitsfuture dividends.

Themostgeneralformofthemodelisasfollows:

where:

V0 = current stock value

Dt = dividend at time t

ke = required rate of return on common equity

One-year holdingperiod DDM.Foraholding period ofoneyear,thevalueofthestock

todayisthepresentvalueofanydividends during theyearplusthepresentvalueofthe

expectedpriceofthestockattheendoftheyear(referredtoasitsterminalvalue).

Theone-yearholding period DDM issimply:

Example: One-period DDM valuation

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Calculate the value of a stock that paid a $1 dividend last year, if next year’s dividend

will be 5% higher and the stock will sell for $13.45 at year-end. The required return is

13.2%.

Answer:

The next dividend is the current dividend increased by the estimated growth rate. In this

case, we have:

The present value of the expected future cash flows is:

.

The current value based on the investor’s expectations is:

Multiple-year holding period DOM.With amultiple-year holding period, wesimply

sumthepresentvaluesoftheestimated dividends overtheholding period andthe estimated

terminal value.

Foratwo-yearholding period, wehave:

Example: Multiple-period DDM valuation

A stock recently paid a dividend of $1.00 which is expected to grow at 5% per year. The

required rate of return of 13.2%. Calculate the value of this stock assuming that it will be

priced at $14.12 two years from now.

Answer:

Find the PV of the future dividends:

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Find the PV of the future price:

Add the present values. The current value based on the investor’s expectations is

$1.79 + $11.02 = $12.81.

The mostgeneralformoftheDOM usesaninfiniteholding period becausea corporation

hasanindefinite life.Inaninfinite-period DDM model, thepresentvalue ofallexpectedfuture

dividends iscalculated andthereisnoexplicitterminal valuefor thestock.Inpractice,

aswewillsee,aterminal valuecanbecalculated atatimeinthe future afterwhichthegrowth

rateofdividends isexpectedtobeconstant.

Freecashflowtoequity (FCFE) isoftenusedindiscounted cashflowmodelsinstead of dividends

becauseitrepresents thepotential amount ofcashthat couldbepaidouttocommon shareholders.

That is,FCFE reflectsthefirm'scapacitytopaydividends. FCFEisalsousefulforfirmsthat

donotcurrently paydividends.

FCFE isdefinedasthecashremaining afterafirmmeetsallofitsdebtobligations

andprovidesforthecapitalexpenditures necessarytomaintainexistingassetsandto purchase

thenewassetsneeded tosupport theassumedgrowth ofthefirm.Inother words, itis

thecashavailabletothefirm'sequityholders afterafirmmeetsallofits other obligations.

FCFEforaperiod isoftencalculated as:

FCFE = netincome + depreciation - increaseinworking capital- fixedcapital investment

(FClnv) - debtprincipal repayments + newdebtissues

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FCFE canalsobecalculated as:

FCFE = cashflowfromoperations - FCinv +netborrowing

Inthesecondformula, net borrowingistheincreaseindebtduring theperiod (i.e., amount

borrowed minus amount repaid) andisassumedtobeavailabletoshareholders.

Fixedcapitalinvestment must besubtracted becausethefirmmust investinassetsto

sustainitself.FCFE isprojected forfuture periods usingthefirm'sfinancialstatements.

Restating thegeneralformoftheDDM intermsof FCFE,wehave:

Estimating theRequired Returnfor Equity

The capital asset pricing model (CAPM) provides an estimate of the required rate of return

( ) for security i as a function of its systematic risk ( , the risk-free rate (Rf), and the

expected return on the market [E(Rmkt)] as:

There issomecontroversy overwhether theCAPM isthebestmodeltocalculatethe required

return onequity.Also,different analystswilllikelyusedifferent inputs, sothere isnosinglenumber

that iscorrect.

RecallfromthetopicreviewofCostofCapital that forfirmswithpublicly traded debt, analystsoften

estimate therequired return onthefirm'scommon equitybyadding arisk premium

tothefirm'scurrent bondyield.Ifthefirmdoesnothavepublicly traded debt,

ananalystcanaddalargerriskpremium toagovernment bond yield.

Preferred stockpaysadividend that isusuallyfixedandusuallyhasanindefinite maturity. When

thedividend isfixedandthestreamofdividends isinfinite, theinfinite period dividend discount

model reducestoasimpleratio:

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Example: Preferred stock valuation

A company’s $100 par preferred stock pays a $5.00 annual dividend and has a required return

of 8%. Calculate the value of the preferred stock.

Answer:

Value of the preferred stock: Dp / kp = $5.00 / 0.08 = $62.50

In the previous example, if the dividends were paid semiannually and the preferred stock

had a maturity of one year, we would use a formula similar to the one we examined earlier

for common stock. Instead of the price, we would use the par value (F) paid by the firm.

Instead of the required return on common, we would use the required return on preferred:

With a1-year maturity, therearetwosemiannual dividends of$2.50remaining, and

witharequired semiannual return of4%wehave:

The Gordon growth model (or constant growth model) assumes the annual growth rate of

dividends, gc, is constant. Hence, next period's dividend, D1, is D0(1 + g), the second

year's dividend, D2, is D0(1 + g)2, and so on. The extended equation using this

assumption gives the present value of the expected future dividends (V0) as:

When thegrowth rateofdividends isconstant, thisequation simplifiestotheGordon(constant)

growth model:

The assumptions oftheGordon growth modelare:

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Dividends aretheappropriate measureofshareholder wealth.

The constant dividend growth rate, gc, and required return on stock, ke, are never

expected to change.

ke must be greater than gc. If not, the math will not work.

Ifanyoneoftheseassumptions isnotmet,themodel isnotappropriate.

Example: Gordon growth model valuation

Calculate the value of a stock that paid a $2 dividend last year, if dividends are

expected to grow at 5% forever and the required return on equity is 12%.

Answer:

Determine D1: D0(l + gc) = $2(1.05) = $2.10

Calculate the stock’s value = D1 / (ke – gc)

= $2.10 / (0.12 - 0.05)

= $30.00

This exampledemonstratesthat thestock'svalueisdetermined bytherelationship between

theinvestor's required rate of return on equity, ke, and the projected growth rate of

dividends, gc:

As the difference between ke; and gc widens, the value of the stock falls.

As the difference narrows, the value of the stock rises.

Small changes in the difference between ke and gc can cause large changes in the

stock's value.

Becausetheestimated stockvalueisverysensitivetothedenominator,ananalystshould

calculateseveraldifferent valueestimates usingarangeofrequired returns andgrowth rates.

AnanalystcanalsousetheGordon growth model todetermine howmuch ofthe estimated

stockvalueisduetodividend growth.Todothis,assumethegrowth rateis

zeroandcalculateavalue.Then, subtract thisvaluefromthestockvalueestimated using

apositivegrowth rate.

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Example: Amount of estimated stock value due to dividend growth

Using the data from the previous example, calculate how much of the estimated stock value is

due to dividend growth.

Answer:

The estimated stock value with a growth rate of zero is:

The amount of the estimated stock value due to estimated dividend growth is:

EstimatingtheGrowthRateinDividends

Toestimate thegrowth rateindividends, theanalystcanusethreemethods:

1. Usethehistorical growth individends forthefirm.

2. Usethemedian industrydividend growth rate.

3. Estimate thesustainable growth rate.

Thesustainable growth rate istherateatwhichequity,earnings, anddividends can continue

togrowindefinitely assuming that ROEisconstant, thedividend payout ratio isconstant,

andnonewequityissold.

sustainable growth= (1 - dividend payout ratio) x ROE

Thequantity (1 - dividendpayout ratio) is also referredtoastheretentionrate, the

proportionofnetincome that isnotpaidoutasdividends andgoestoretained earnings,

thusincreasing equity.

Example: Sustainable growth rate

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Green, Inc., is expected to pay dividends equal to 25% of earnings. Green’s ROE is

21%. Calculate and interpre its sustainable growth rate.

Answer:

With long-run economic growth typically in the single digits, it is unlikely that a firm

could sustain 15.75% growth forever. The analyst should also examine the growth

rate for the industry and the firm’s historical growth rate to determine whether the

estimate is reasonable.

Somefirmsdonotcurrently paydividends butareexpected tobeginpayingdividends atsomepoint

inthefuture.Afirmmaynotcurrently payadividend becauseitisin financialdistressandcannot

affordtopayoutcashorbecausethereturn thefirmcan earnbyreinvesting cashisgreaterthanwhat

stockholders couldexpecttoearnby investing dividends elsewhere.

Forthesefirms,ananalystmust estimate theamount andtiming ofthefirstdividend in

ordertousetheGordon growth model. Becausetheseparameters arehighlyuncertain,

theanalystshould checktheestimate fromtheGordon growth model againstestimates

madeusingothermodels.

Example: A firm with no current dividend

A firm currently pays no dividend but is expected to pay a dividend at the end of Year 4. Year

4 earnings are expected to be $1.64, and the firm will maintain a payout ratio of 50%.

Assuming a constant growth rate of 5% and a required rate of return of 10%, estimate the

current value of this stock.

Answer:

The first step is to find the value of the stock at the end of Year 3. Remember, P3 is

the present value of dividends in Years 4 through infinity, calculated at the end of Year 3, one

period before the first dividend is paid.

Calculate D4, the estimate of the dividend that will be paid at the end of Year 4:

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Apply the constant growth model to estimate

The second step is to calculate the current value, :

Multistage Dividend Growth Models

Afirmmaytemporarily experienceagrowth ratethatexceedstherequired rateofreturn

onthefirm'sequity,butnofirmcanmaintain thisrelationship

indefinitely.Afirmwithanextremelyhighgrowthratewillattract competition, anditsgrowth

ratewilleventuallyfall.Wemustassumethefirmwillreturn toamoresustainable rateofgrowth

atsome point inthefuture inordertocalculatethepresentvalueofexpectedfuture dividends.

Onewaytovalueadividend-paying firmthat isexperiencing temporarily

highgrowthistoaddthepresentvaluesofdividends expectedduring thehigh-growth period tothe

presentvalueoftheconstant growthvalueofthefirmattheendofthehigh-growth period.This

isreferredtoasthemultistage dividend discount model.

where

is the terminal stock value, assuming that dividends at

and beyond grow at a constant rate of gc

Stepsinusingthemultistage model:

Determine the discount rate, ke.

Project the size and duration of the high initial dividend growth rate, g*.

Estimate dividends during the high-growth period.

Estimate the constant growth rate at the end of the high-growth period, gc.

Estimate the first dividend that will grow at the constant rate.

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Use the constant growth value to calculate the stock value at the end of the high-

growth period.

Add the PVs of all dividends to the PV of the terminal value of the stock.

Example: Multistage growth

Consider a stock with dividends that are expected to grow at 20% per year for four

years, after which they are expected to grow at 5% per year, indefinitely. The last

dividend paid was $1.00, and ke = 10%. Calculate the value of this stock using the

multistage growth model.

Answer:

Calculate the dividends over the high-growth period:

Although we increase D3 by the high growth rate of 20% to get D4, D4 will grow at

the constant growth rate of 5% for the foreseeable future. This property of D4 allows

us to use the constant growth model formula with D4 to get P3, a time = 3 value for

all the (infinite) dividends expected from time = 4 onward.

Finally, we can sum the present values of dividends 1, 2, and 3 and of P3 to get the

present value of all the expected future dividends during both the high- and constant

growth periods:

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The Gordongrowth model usesasingleconstant growth rateofdividends andismost

appropriate forvaluingstableandmature, non-cyclical,dividend-payingfirms.

Fordividend-payingfirmswithdividends that areexpectedtogrowrapidly,slowly,or

erraticallyoversomeperiod, followedbyconstant dividend growth, someformofthe multistage

growth modelshould beemployed.The importantpoints arethat dividends must beestimable

andmustgrowataconstant rateaftersomeinitial period sothat the constant growth

modelcanbeusedtodetermine theterminal valueofthestock.Thus, wecanapplymultistage

dividend growth modelstoafirmwith highcurrent growth that will drop to a stable rate in the

future or to a firm that is temporarily losing market share and growing slowly or getting

smaller, as long as its growth is expected to stabilize to a constant rate at some point in the

future.

One variant of a multistage growth model assumes that the firm has three stages of

dividend growth, not just two. These three stages can be categorized as growth,

transition, and maturity. A 3-stage model would be suitable for firms with an initial high

growth rate, followed by a lower growth rate during a second, transitional period,

followed by the constant growth rate in the long run, such as a young firm still in the high

growth phase.

When a firm does not pay dividends, estimates of dividend payments some years in the

future are highly speculative. In this case, and in any case where future dividends cannot

be estimated with much confidence, valuation based on FCFE is appropriate as long as

growth rates of earnings can be estimated. In other cases, valuation based on price

multiples may be more appropriate.

Because the dividend discount model is very sensitive to its inputs, many investors rely on

other methods. In a price multiple approach, an analyst compares a stock's price multiple

to a benchmark value based on an index, industry group of firms, or a peer group of firms

within an industry. Common price multiples used for valuation include price-to-earnings,

price-to-cash flow, price-to-sales, and price-to-book value ratios.

Price multiples are widely used by analysts and readily available in numerous media outlets.

Price multiples are easily calculated and can be used in time series and cross sectional

comparisons. Many of these ratios have been shown to be useful for predicting stock returns,

with low multiples associated with higher future returns.

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A critique of price multiples is that they reflect only the past because historical (trailing)

data are often used in the denominator. For this reason, many practitioners use forward

(leading or prospective) values in the denominator (sales, book value, earnings, etc.). The

use of projected values can result in much different ratios. An analyst should be sure to use

price multiple calculations consistently across firms.

When we compare a price multiple, such as P/E, for a firm to those of other firms based

on market prices, we are using price multiples based on comparables. By contrast, price

multiples based on fundamentals tell us what a multiple should be based on some valuation

model and therefore are not dependent on the current market prices of other companies to

establish value.

Price multiples used for valuation include:

Price-earnings (P/E) ratio: The P/E ratio is a firm's stock price divided by earnings

per share and is widely used by analysts and cited in the press.

Price-sales (P/S) ratio: The P/S ratio is a firm's stock price divided by sales per

share.

Price-book value (P/B) ratio: The P/B ratio is a firm's stock price divided by book

value of equity per share.

Price-cash flow (P/CF) ratio: The P/CF ratio is a firm's stock price divided by cash

flow per share, where cash flow may be defined as operating cash flow or free cash

flow.

Other multiples can be used that are industry specific. For example, in the cable television

industry, stock market capitalization is compared to the number of subscribers.

Multiples Based on Fundamentals

To understand fundamental price multiples, consider the Gordon growth valuation model:

If we divide both sides of the equation by next year's projected earnings, E1, we get:

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which is the leading P/E for this stock if it is valued in the market

according to the constant growth DDM.

This P/E based on fundamentals is also referred to as a justified P/E. It is "justified"

because, assuming we have the correct inputs for D1, E1, ke, and g, the equation above will

provide a P/E ratio that is based on the present value of the future cash flows. We refer to

this as a leading P/E ratio because it is based on expected earnings next period, not on actual

earnings for the previous period, which would produce a lagging or trailing P/E ratio.

One advantage of this approach is that it makes clear how the firm's P/E ratio should be

related to its fundamentals. It illustrates that the P/E ratio is a function of:

• D1/E1 = expected dividend payout ratio.

• k = required rate of return on the stock.

• g = expected constant growth rate of dividends.

Example: P/E based on fundamentals

A firm has an expected dividend payout ratio of 60%, a required rate of return of

11%, and an expected dividend growth rate of 5%. Calculate the firm’s fundamental

(justified) leading P/E ratio.

Answer:

expected P/E ratio:

The justified P/E ratio serves as a benchmark for the price at which the stock should trade.

In the previous example, if the firm's actual P/E ratio (based on the market price and

expected earnings) was 16, the stock would be considered overvalued. If the firm's market

P/E ratio was 7, the stock would be considered undervalued.

P/E ratios based on fundamentals are very sensitive to the inputs (especially the

denominator, k - g), so the analyst should use several different sets of inputs to indicate a

range for the justified P/E.

Because we started with the equation for the constant growth DDM, the P/E ratio

calculated in this way is the P/E ratio consistent with the constant growth DDM. We can

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see from the formula that, other things equal, the P/E ratio we have defined here will

increase with (1) a higher dividend payout rate, (2) a higher growth rate, or (3) a lower

required rate of return. So, if the subject firm has a higher dividend payout ratio, higher

growth rate, and lower required return than its peers, a higher P/E ratio may be justified.

In practice, other things are not equal. An increase in the dividend payout ratio, for

example, will reduce the firm's sustainable growth rate. While higher dividends will

increase firm value, a lower growth rate will decrease firm value. This relationship is

referred to as the dividend displacement of earnings. The net effect on firm value of

increasing the dividend payout ratio is ambiguous. As intuition would suggest, firms

cannot continually increase their P/Es or market values by increasing the dividend payout

ratio. Otherwise, all firms would have 100% payout ratios.

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Example: Fundamental P/E ratio comparison

Holt Industries makes decorative items. The figures below are for Holt and its

industry.

Holt Industries Industry Average

Dividend payout ratio 25% 16%

Sales growth 7.5% 3.9%

Toral debt to equity 113% 68%

Which of these factors suggest a higher fundamental P/E ratio for Holt?

Answer:

• The higher dividend payout ratio supports Holt having a higher PIE ratio than the

industry.

• Higher growth in sales suggests that Holt will be able to increase dividends at a faster

rate, which supports Holt having a higher P/E ratio than the industry.

• The higher level of debt, however, indicates that Holt has higher risk and a higher

required return on equity, which supports Holt having a lower P/E ratio than the

industry.

Multiples Based on Comparables

Valuation based on price multiple comparables (or comps) involves using a price multiple

to evaluate whether an asset is valued properly relative to a benchmark. Common

benchmarks include the stock's historical average (a time series comparison) or similar

stocks and industry averages (a cross-sectional comparison). Comparing firms within an

industry is useful for analysts who are familiar with a particular industry. Price multiples

are readily calculated and provided by many media outlets.

The economic principle guiding this method is the law of one price, which

asserts that two identical assets should sell at the same price, or in this case, two

comparable assets should have approximately the same multiple.

The analyst should be sure that any comparables used really are comparable.

Price multiples may not be comparable across firms if the firms are different sizes,

are in different industries, or will grow at different rates. Furthermore, using P/E

ratios for cyclical firms is complicated due to their sensitivity to economic conditions. In

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this case, the P/S ratio may be favored over the P/E ratio because the sales are less volatile

than earnings due to both operating and financial leverage.

The disadvantages of using price multiples based on comparables are (1) a stock may

appear overvalued by the comparable method but undervalued by the fundamental method,

or vice versa; (2) different accounting methods can result in price multiples that are not

comparable across firms, especially internationally; and (3) price multiples for cyclical

firms may be greatly affected by economic conditions at a given point in time.

Example: Valuation using comparables

The following figures are for Renee’s Bakery. All figures except the stock price are in

millions.

Fiscal Year-End 20X3 20X2 20X1

Total stockholder’s equity

$55.60 $54.10

$52.60

Net revenues

$77.30

$73.60

$70.80

Net income

$3.20

$1.10

$0.40

Net cash flow from operations

$17.90

$15.20

$12.20

Stock price

$11.40

$14.40 $12.05

Shares outstanding

4.476

3.994

3.823

Calculate Renee’s lagging PIE, P/CF, P/S, and P/B ratios. Judge whether the firm is

undcrvalucd or overvalued using the following relevant industry averages for 20X3

and the firm’s historical trend.

Lagging Industry Ratios 20X3

Price-to-earnings 8.6

Price-to-cash flow 4.6

Price-to-salcs 1 .4

Price-to-book value 3.6

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Answer:

To calculate the lagging price multiples, first divide the relevant financial statement

items by the number of shares to get per-share amounts. Then, divide the stock price

by this figure.

For example, for the P/S ratio for 20X3, divide net revenue (net sales) by the number

of shares:

Then, divide the stock price by sales per share:

Using the net income for earnings, the net cash flow from operations for the cash

flow, and stockholder’s equity for book value, the ratios for Renee’s Bakery are:

20X3 20X2 20X1

P/E 15.9 52.3 115.2

P/CF 2.9 3.8 3.8

P/S 0.7 0.8 0.7

P/B 0.9 1.1 0.9

Comparing Renee’s Bakery’s ratios to the industry averages for 20X3, the price

multiples arc lower in all cases except for the P/E multiple. This cross-sectional

evidence suggests that Renee’s Bakery is undervalued.

The P/E ratio merits further investigation. Rcnee’s Bakery may have a higher P/E

because its earnings are depressed by high depreciation, interest expense, or taxes.

Calculating the price-EBITDA ratio would provide an alternative measure that is

unaffected by these expenses.

On a time series basis, the ratios are trending downward. This indicates that Renee’s

Bakery may be currently undervalued relative to its past valuations. We could also

calculate average price multiples for the ratios over 20X1-20X3 as a benchmark for

the current values:

Company average P/E 20X1-20X3 61.1

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Company average P/CF 20X1-20X3 3.5

Company average P/S 20X1-20X3 0.7

Company average P/B 20X1-20X3 1.0

The current P/E, P/CF, and P/B ratios are lower than their 3-year averages. This indicates that

Renec’s Bakery may be currently undervalued. It also may be the case,

however, that P/E ratios for the market as a whole have been decreasing over the

period due to systematic factors.

Enterprise value (EV) measures total company value. EV can be viewed as what it would

cost to acquire the firm:

EV= market value of common and preferred stock + market value of debt - cash and short-

term investments

Cash and short-term investments are subtracted because an acquirer's cost for a firm would

be decreased by the amount of the target's liquid assets. Although an acquirer assumes the

firm's debt, it also receives the firm's cash and short-term investments. Enterprise value is

appropriate when an analyst wants to compare the values of firms that have significant

differences in capital structure.

EBITDA (earnings before interest, taxes, depreciation, and amortization are subtracted) is

probably the most frequently used denominator for EV multiples; operating income can

also be used. Because the numerator represents total company value, it should be compared

to earnings of both debt and equity owners. An advantage of using EBITDA instead of net

income is that EBITDA is usually positive even when earnings are not. When net income

is negative, value multiples based on earnings are meaningless. A disadvantage of using

EBITDA is that it often includes non-cash revenues and expenses.

A potential problem with using enterprise value is that the market value of a firm's debt is

often not available. In this case, the analyst can use the market values of similar bonds or can

use their book values. Book value, however, may not be a good estimate of market value if

firm and market conditions have changed significantly since the bonds were issued.

Example: Calculating EV/EBITDA multiples

Daniel, Inc., is a manufacturer of small refrigerators and other appliances. The

following figures are from Daniel’s most recent financial statements except for the

market value of long-term debt, which has been estimated from financial market data.

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Stock price $30.00

Shares outstanding 300,000

Marke value of long-term debt $800,000

Book value of long-term debt $1,100,000

Book value of total debt $2,600,000

Cash and marketable securities $300,000

EBITDA $1,200,000

Calculare the EV/EBITDA multiple.

Answer:

First, we must estimate the market value of the firm’s short-term debt and liabilities.

To do so, subtract the book value of long-term debt from the book value of total

debt: $2,600,000 - $1,100,000 = $1,500,000. This is the book value of the firm’s

short-term debt. We can assume the market value of these short-term items is close

to their book value. (As we will see in the Study Session on fixed income valuation,

the market values of debt instruments approach their face values as they get close to

maturity.)

Add the market value of long-term debt to get the market value of total debt:

The market value of equity is the stock price multiplied by the number of shares:

The enterprise value of the firm is the sum of debt and equity minus cash:

EV/EBITDA = $11,000,000 / $1,200,000 = 9.2.

If the competitor or industry average EV/EBITDA is above 9.2, Daniel is relatively

undervalued, lithe competitor or industry average EV/EBITDA is below 9.2, Daniel

is relatively overvalued.

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Our third category of valuation model is asset-based models, which are based on the idea

that equity value is the market or fair value of assets minus the market or fair value of

liabilities. Because market values of firm assets are usually difficult to obtain, the analyst

typically starts with the balance sheet to determine the values of assets and liabilities. In

most cases, market values are not equal to book values. Possible approaches to valuing assets

are to value them at their depreciated values, inflation-adjusted depreciated values, or

estimated replacement values.

Applying asset-based models is especially problematic for a firm that has a large amount of

intangible assets, on or off the balance sheet. The effect of the loss of the current owners'

talents and customer relationships on forward earnings may be quite difficult to measure.

Analysts often consider asset-based model values as floor or minimum values when

significant intangibles, such as business reputation, are involved. An analyst should

consider supplementing an asset-based valuation with a more forward-looking valuation,

such as one from a discounted cash flow model.

Asset-based model valuations are most reliable when the firm has primarily tangible short-

term assets, assets with ready market values (e.g., financial or natural resource firms), or

when the firm will cease to operate and is being liquidated. Asset-based models are often

used to value private companies but may be increasingly useful for public firms as they

move toward fair value reporting on the balance sheet.

Example: Using an asset-based model for a public firm

Williams Optical is a publicly traded firm. An analyst estimates that the market value

of net fixed assets is 120% of book value. Liability and short-term asset market values are

assumed to equal their book values. The firm has 2,000 shares outstanding.

Using the selected financial results in the table, calculate the value of the firm’s net

assets on a per-share basis.

Cash $10,000

Accounts receivable $20,000

Inventories $50,000

Net fixed assets $120.000

Total assets $200,000

Accounts payable $5,000

Notes payable $30,000

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Term loans $45,000

Common stockholder equity $120.000

Total assets $200,000

Answer:

Estimate the market value of assets, adjusting the fixed assets for the analyst’s

estimates of their market values:

Determine the market value of liabilities:

Calculate the adjusted equity value:

Calculate the adjusted equity value per share:

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4 Chủ đề 4: Portfolio Management

4.1 Portfolio management overview

Theportfolioperspective referstoevaluating individual investments bytheir

contributiontotheriskandreturn ofaninvestor'sportfolio. Thealternative totaking aportfolio

perspective istoexaminetheriskandreturn ofindividual investments

inisolation.Aninvestorwhoholdsallhiswealthinasinglestockbecausehebelievesittobethebeststoc

kavailableisnottaking theportfolio perspective-hisportfolio isvery riskycompared

toholdingadiversifiedportfolio ofstocks.Modern portfolio theory concludes that

theextrariskfromholding onlyasinglesecurityisnotrewardedwith higherexpectedinvestment

returns. Conversely,diversification allowsaninvestorto reduceportfolio

riskwithoutnecessarilyreducing theportfolio's expected return.

Intheearly1950s,theresearchofProfessorHarry Markowitz provided aframework for

measuring therisk-reduction benefitsofdiversification.Usingthestandard deviation of returns

asthemeasureofinvestment risk,heinvestigated howcombining riskysecurities intoaportfolio

affectedtheportfolio's riskandexpectedreturn.One important conclusion ofhismodel isthat

unlessthereturns oftheriskyassetsareperfectly positivelycorrelated,

riskisreducedbydiversifyingacrossassets.

Inthe 1960s,professorsTreynor,Sharpe,Mossin, andLintner independently extended

thisworkintowhathasbecomeknown asmodern portfolio theory (MPT).MPT

resultsinequilibrium expected returns forsecuritiesandportfolios that arealinearfunction

ofeachsecurity'sorportfolio'smarket risk(theriskthat cannot bereduced by diversification).

Onemeasureofthebenefitsofdiversification isthediversificationratio. Itiscalculated

astheratiooftheriskofanequallyweighted portfolio ofnsecurities (measured byits standard

deviation ofreturns) totheriskofasinglesecurityselectedatrandom fromthensecurities. Note that

theexpectedreturn ofanequal-weightedportfolio isalsothe expected return

fromselectingoneofthenportfolio securitiesatrandom (thesimple

averageofexpectedsecurityreturns inboth instances). Iftheaveragestandard deviation ofreturns

forthenstocksis25%, andthestandard deviation ofreturns foranequally weighted portfolio

ofthenstocksis18%,thediversificationratiois18/25= 0.72.

While thediversification ratioprovidesaquickmeasureofthepotentialbenefitsof

diversification,anequal-weightedportfolio isnotnecessarilytheportfolio thatprovides

thegreatestreduction inrisk.Computeroptimization cancalculatetheportfolio weights

thatwillproduce thelowestportfolio risk(standard deviation ofreturns) foragiven

groupofsecurities.

Portfolio diversification worksbestwhenfinancialmarkets areoperating normally;

diversification provideslessreductionofriskduring market turmoil, suchasthecredit contagion

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of2008. During periods offinancialcrisis,correlations tendtoincrease, which

reducesthebenefitsofdiversification.

Individualinvestors saveandinvestforavarietyofreasons,including purchasing a

houseoreducating theirchildren. Inmanycountries, specialaccounts allowcitizensto

investforretirement andtodeferanytaxesoninvestment income andgainsuntilthe

fundsarewithdrawn. Defined contributionpension plansarepopular vehiclesforthese

investments. Pensionplansaredescribed laterinthistopicreview.

Manytypesofinstitutionshavelargeinvestment portfolios. Anendowmentisafund that

isdedicated toproviding financialsupport onanongoing basisforaspecific purpose.

Forexample,intheUnited States,manyuniversities havelargeendowment fundstosupport

theirprograms. Afoundationisafund established forcharitable purposes tosupport

specifictypesofactivitiesortofund researchrelatedtoaparticular

disease.Atypicalfoundation'sinvestment objective istofund theactivityorresearchon

acontinuingbasiswithoutdecreasingthereal(inflation adjusted) valueoftheportfolio

assets.Foundations andendowments typicallyhavelonginvestment horizons, highrisktolerance,

and,asidefromtheirplannedspending needs,littleneedforadditional

liquidity.

The investment objectiveofabank, simplyput, istoearnmoreonthebank'sloansand investments

than thebankpaysfordeposits ofvarioustypes.Banksseektokeeprisklow andneedadequate

liquidity tomeetinvestorwithdrawals astheyoccur.

Insurancecompanies investcustomer premiums with theobjectiveoffundingcustomer

claimsastheyoccur.Lifeinsurance companies havearelativelylong-term investment horizon,

whileproperty andcasualty(P&C) insurershaveashorter investment horizon

becauseclaimsareexpectedtoarisesoonerthan forlifeinsurers.

Investment companies manage the pooled funds ofmany investors. Mutual funds

manage these pooled funds in particular styles (e.g., index investing, growth investing,

bond investing) and restrict their investments to particular subcategories

ofinvestments (e.g., large-firm stocks, energy stocks, speculative bonds) or particular

regions (emerging market stocks, international bonds, Asian-firm stocks).

Sovereign wealth funds refer to pools ofassets owned byagovernment. For example,

theAbu Dhabi Investment Authority, asovereign wealth fund in the United Arab

Emirates funded byAbu Dhabi government surpluses, has an estimated US$627 billion

in assets.

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Figure1 provides asummary oftherisktolerance, investment horizon, liquidityneeds,

andincome objectivesfordifferent typesofinvestors.

Figure 1: Characteristics of Different Types of Investors

Investor Risk olerance Investment Horizon Liquidity Needs Income Needs

Individuals Depends on

individual

Depends on

individual

Depends on

individual

Depends on

individual

Banks Low Short High Pay interest

Endowments High Long Low Spending

level

Insurance Low Long— life

Short—P&C

High Low

Mutual funds

Depends on

fund

Depends on fund High Depends on

fund

Defined

benefit

pensions

High Long Low Depends on

age

Adefined contributionpensionplan isaretirement planinwhich thefirmcontributes

asumeachperiod totheemployee'sretirement account.

Thefirm'scontributioncanbebasedonanynumberoffactors, including

yearsofservice,theemployee'sage, compensation, profitability, orevenapercentage

oftheemployee'scontribution.Inanyevent,thefirmmakesnopromise totheemployeeregarding

thefuture valueofthe planassets.Theinvestment decisions

arelefttotheemployee,whoassumesallofthe investment risk.

Inadefined benefit pensionplan, thefirmpromises tomakeperiodic payments

toemployeesafterretirement. Thebenefitisusuallybasedontheemployee'syears

ofserviceandtheemployee'scompensation at,ornear,retirement.

Forexample,anemployeemight earnaretirement benefitof2%ofherfinalsalary

foreachyear ofservice.Consequently,

anemployeewith20yearsofserviceandafinalsalaryof$100,000, would receive$40,000

($100,000 finalsalaryx2%x 20yearsofservice) eachyearupon retirement until death.

Becausetheemployee's future benefit is defined, the employer assumes the investment risk.

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The employer makes contributions to a fund established to provide the promised future

benefits. Poor investment performance will increase the amount of required employer

contributions to the fund. There are three major steps in the portfolio management process:

Step 1: The planning step begins with an analysis of the investor's risk tolerance, return

objectives, time horizon, tax exposure, liquidity needs, incomeneeds,andany unique

circumstances orinvestor preferences.

This analysisresultsinaninvestmentpolicy statement(IPS)that details

theinvestor'sinvestment objectivesandconstraints.Itshould alsospecifyan objectivebenchmark

(suchasanindexreturn) againstwhichthesuccessofthe portfolio management

processwillbemeasured.The IPSshould beupdatedat

leasteveryfewyearsandanytimetheinvestor'sobjectivesorconstraints change significantly.

Step2:Theexecution stepinvolvesananalysisoftheriskandreturn characteristics

ofvariousassetclassestodetermine howfundswillbeallocatedtothevarious assettypes.Often,

inwhat isreferredtoasatop-downanalysis,aportfolio managerwillexaminecurrent economic

conditions andforecastsofsuch macroeconomicvariablesasGDP growth, inflation, andinterest

rates,inorder toidentify theassetclassesthat aremostattractive. The resulting portfolio is

typicallydiversifiedacrosssuchassetclassesascash,fixed-income securities, publicly traded

equities,hedgefunds, privateequity,andrealestate,aswellas commodities andother realassets.

Once theassetclassallocations aredetermined, portfolio managers mayattempt toidentify

themostattractive securitieswithin theassetclass.Securityanalysts usemodelvaluations

forsecuritiestoidentify thosethat appearundervalued in what istermed bottom-

upsecurityanalysis.

Step3: Thefeedback stepisthefinalstep.Overtime, investorcircumstances will change,

riskandreturn characteristics ofassetclasses will change,andtheactual

weightsoftheassetsintheportfolio willchangewithassetprices.Theportfolio manager must

monitorthesechangesandrebalance theportfolio periodicallyinresponse,adjusting

theallocations tothevariousassetclassesbacktotheir desiredpercentages. The manager

mustalsomeasureportfolio performance and evaluateitrelativetothereturn onthebenchmark

portfolio identifiedintheIPS.

Mutual funds areoneformofpooled investments(i.e.,asingleportfolio

thatcontainsinvestment funds frommultiple investors ). Eachinvestor

ownssharesrepresentingownership ofaportion o f theoverallportfolio. The

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totalnetvalueoftheassetsinthe fund (pool)dividedbythenumber

ofsuchsharesissuedisreferredtoasthenetasset value (NAV)ofeachshare.

With anopen-endfund, investorscanbuynewlyissuedsharesattheNAV.Newly

investedcashisinvestedbythemutual fund managers inadditional portfolio securities.

Investorscanredeem theirshares(sellthembacktothefund) atNAVaswell.All mutualfunds

chargeafeefortheongoing management oftheportfolio assets,which isexpressedasapercentage

ofthenetassetvalueofthefund. No-loadfunds donotchargeadditional feesforpurchasing

shares(up-front fees)orforredeeming shares(redemption fees).Loadfunds chargeeitherup-

frontfees,redemptionfees,orboth.

Closed-endfunds areprofessionally managed poolsofinvestor moneythat donottake

newinvestments into thefund orredeeminvestorshares.Thesharesofaclosed-end fund

tradelikeequityshares(onexchangesorover-the-counter).Aswith open-end funds,

theportfolio management firmchargesongoing management fees.

TypesofMutual Funds

Money market funds investinshort-termdebtsecurities andprovideinterest income

withverylowriskofchangesinsharevalue.FundNAVsaretypicallysettoonecurrency unit,

buttherehavebeeninstances overrecentyearsinwhich theNAVofsomefundsdeclined

whenthesecuritiestheyhelddroppeddramatically invalue.Fundsare differentiated

bythetypesofmoneymarket securitiestheypurchase andtheir average maturities.

Bondmutual funds investinfixed-income securities.Theyaredifferentiated bybond maturities,

creditratings,issuers,andtypes.Examplesinclude government bond funds, tax-exempt bond

funds, high-yield (lowerratedcorporate) bond funds, andglobalbond funds.

Agreatvarietyofstockmutual funds areavailabletoinvestors.Index funds are

passivelymanaged; that is,theportfolio isconstructed tomatch theperformance ofa particular

index,suchastheStandard &Poor's500Index.Activelymanagedfunds

refertofundswherethemanagement s e l e c t s individual securitieswith thegoalofproducing

returns greaterthan thoseoftheirbenchmark i n d e x e s .Annual management feesare

higherforactivelymanaged funds, andactivelymanaged fundshavehigherturnover of portfolio

securities (thepercentage ofinvestments that arechanged during theyear).This

leadstogreatertax liabilities comparedtopassively managedindexfunds.

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Other FormsofPooledInvestments

Exchange-traded funds(ETFs)aresimilartoclosed-end fundsinthose purchases

andsalesaremadeinthemarket ratherthanwith thefunditself.There areimportant

differences,however.While closed-end fundsareoftenactivelymanaged, ETFsaremost

ofteninvestedtomatch aparticular index (passivelymanaged). With closed-end funds,

themarket priceofsharescandiffersignificantly fromtheirNAVduetoimbalancesbetween

investorsupplyanddemand forsharesatanypoint intime.Specialredemption provisions

forETFsaredesignedtokeeptheirmarket pricesveryclosetotheirNAVs.

ETFscanbesoldshort, purchased onmargin, andtraded atintraday prices,whereas open-end

funds aretypicallysoldandredeemed onlydaily,basedontheshareNAV calculated with

closingassetprices.Investors inETFsmust paybrokerage commissions when theytrade,

andthereisaspreadbetween thebidpriceatwhich market makers

willbuysharesandtheaskpriceatwhichmarket makerswillsellshares.With mostETFs,

investorsreceiveanydividend incomeonportfolio s tocksincash,whileopen

endfundsofferthealternative ofreinvesting dividends inadditional fundshares.One

finaldifference isthatETFsmayproduce less capitalgainsliability compared toopen•

endindexfunds.This isbecauseinvestor sales ofETFsharesdonotrequirethefund to

sellanysecurities. Ifanopen-end fundhassignificant redemptions that causeittosell appreciated

portfolio shares,shareholdersincur acapitalgainstaxliability.

Aseparately managedaccountisaportfolio that isownedbyasingleinvestor and managed

according tothat investor'sneedsandpreferences.Nosharesareissued,asthe singleinvestor

ownstheentireaccount.

Hedge funds arepoolsofinvestorfundsthat arenot regulated totheextentthat mutual funds

are.Hedgefunds arelimited

inthenumberofinvestorswhocaninvestinthefundandareoftensoldonlytoqualifiedinvestorswhoh

aveaminimumamount ofoverallportfolio wealth.Minimuminvestments canbequitehigh,

oftenbetween$250,000 and$1million.

There isagreatvarietyofhedgefundstrategies,andmajorhedgefund categoriesare

basedontheinvestment strategythat thefundspursue:

Long/shortfunds buysecuritiesthat areexpected tooutperformtheoverallmarket

andsellsecuritiesshort that areexpectedtounderperformtheoverallmarket.

Equity market-neutralfunds arelong/shortfundswithlongstockpositions that are

justoffsetinvaluebystockssoldshort.Thesefunds aredesignedtobeneutral with

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respecttooverallmarket movements sothat theycanbeprofitable inboth upand

downmarkets aslongastheirlongsoutperform theirshorts.

Anequityhedgefundwith abiasisalong/shortfund dedicated toalargerlong position

relativetoshortsales(alongbias)ortoagreatershortposition relativeto longpositions

(ashort bias).

Event-drivenfunds investinresponsetoone-time corporate events,suchasmergers

andacquisitions.

Fixed-incomearbitragefunds takelongandshortpositions indebtsecurities,

attemptingtoprofitfromminor mispricing whileminimizing theeffectsofinterest

ratechangesonportfolio values.

Convertiblebond arbitragefunds takelongandshort positions inconvertible bonds

andtheequitysharestheycanbeconverted intoinordertoprofitfroma relativemispricing

between thetwo.

Global macro funds speculate onchangesininternationalinterest ratesandcurrency

exchangerates,oftenusingderivativesecuritiesandagreatamount ofleverage.

Buyout funds (private equity funds) typicallybuyentirepublic companies andtake them private

(theirsharesnolongertrade).Thepurchase ofthecompanies isoften funded withasignificant

increaseinthefirm'sdebt (aleveragedbuyout). The fundattempts

toreorganizethefirmtoincreaseitscashflow,paydownitsdebt, increasethe

valueofitsequity,andthen selltherestructured firmoritsparts inapublic offeringor toanother

company overafairlyshort timehorizon ofthreetofiveyears.

Venture capital funds typicallyinvestincompanies intheirstart-upphase,with the intent

togrowthem intovaluablecompanies that

canbesoldpubliclyviaanIPOorsoldtoanestablished firm.Bothbuyout fundsandventure

capitalfunds arevery involvedinthemanagement oftheirportfolio companies

andoftenhaveexpertiseinthe industries onwhich theyfocus.

4.2 Portfolio risk and return

Holding period return (HPR) issimplythepercentage increaseinthevalueofan investment

overagiventimeperiod:

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Ifastockisvaluedat€20 atthebeginning oftheperiod, pays€1 individends overthe period,

andattheendoftheperiod isvaluedat€22, theHPR is:

HPR =(22+ 1)/20- 1 =0.15= 15%

AverageReturns

Thearithmeticmean return isthesimpleaverageofaseriesofperiodic returns. Ithasthestatistical

propertyofbeinganunbiased estimator ofthetruemeanoftheunderlying distributionofreturns:

Thegeometric mean return isacompound annual rate.When periodic ratesofreturn

varyfromperiod toperiod, thegeometric meanreturn willhaveavalueless than the arithmetic

meanreturn:

Forexample,forreturns Rtoverthreeannual periods, thegeometric meanreturn is calculated

asfollows:

Example: Return measures

An investor purchased $1,000 of a mutual fund’s shares. The fund had the following

total returns over a 3-year period: +5%, -8%, + 12%. Calculate the value at the end

of the 3-year period, the holding period return, the mean annual return, and the

geometric mean annual return.

Answer:

, which can also

be calculated as

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, which can

also be calculated as geometric mean return

Themoney-weightedrateofreturn istheinternal rateofreturn onaportfolio based

onallofitscashinflowsandoutflows.Tocalculateamoney-weightedrateofreturn, consider

thebeginning valueandadditional deposits ofcashbytheinvestor tobe

inflowsandconsiderwithdrawals ofcash,interest, anddividends (whichareadditional

cashavailabletobewithdrawn) andtheendingvaluetobeoutflows.

Example: Money-weighted rate of return

Assume an investor buys a share of stock for $80 at t = 0 and at the end of the next

year (t =1), she buys an additional share for $70. At the end of Year 2, the investor

sells both shares for $85 each. At the end of each year in the holding period the stock

paid a $1.50 per share dividend. What is the money-weighted rate of return?

Answer:

Step 1: Determine the timing of each cash flow and whether the cash flow is an

inflow (+), into the account, or an outflow (-), available from the account.

t = 0: purchase of first share = +$80.00 inflow to account

t = 1:

purchase of second share = + $70.00

dividend from first share =

Subtotal, t = 1 + 468.50 inflow to account

t = 2: dividend from two shares =

proceeds from selling shares =

Subtotal, t = 2

Step 2: Net the cash flows for each time period and set the PV of cash inflows equal

to the present value of cash outflows.

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Step 3: Solve for r to find the money-weighted rate of return.

Net cash flows:

The money-weighted rate of return is 10.35%.

Inthepreviousexample,thecashflowsinandoutoftheaccount occuratI-year

intervalssothatwesolvedforanannual money-weightedrateofreturn. Moregenerally,

wemustusetheshortest period betweensignificant cashflowsintooroutoftheaccount whensetting

uptheinternal rateofreturn calculation. Forexample, if weuseonemonth asourperiod

(zerocashflowformonths with nocashflows),theinternal rateofreturn calculation

willyieldamonthlyrateofreturn. Inthat case,wewould needto compound themonthlymoney-

weightedreturn for12months totranslate itintoan effectiveannual rate.

Other Return Measures

Grossreturn referstothetotal return onasecurityportfolio beforededucting feesfor

themanagement andadministration oftheinvestment account. Net return referstothe return

afterthesefeeshavebeendeducted. Note that commissions ontradesandothercoststhat

arenecessarytogenerate theinvestment returns arededucted inboth gross andnetreturn

measures.

Pretax nominal return referstothereturn priortopayingtaxes.Dividend income, interest income,

short-termcapitalgains,andlong-term capitalgainsmayallbetaxedat different rates.

After-tax nominal return referstothereturn afterthetaxliability isdeducted.

Realreturn isnominal return adjusted forinflation.Consider aninvestorwhoearnsa nominal

return of7%overayearwheninflation is2%.The investor'sapproximate real return issimply7- 2=

5%.The investor'sexactrealreturn isslightlylower,1.07/1.02- 1 = 0.049=4.9%.

Realreturn measurestheincreaseinaninvestor'spurchasing power:howmuch more

goodsshecanpurchase attheendofoneyearduetotheincreaseinthevalueofher

investments.Ifsheinvests$1,000 andearnsanominal return of 7%, shewillhave$1,070

attheendoftheyear.Ifthepriceofthegoodssheconsumes hasgoneup2%, from$1.00 to$1.02,

shewillbeabletoconsume 1,070I1.02= 1,049units. Shehas givenupconsuming 1,000units

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todaybutinstead isabletopurchase 1,049 unitsatthe endofoneyear.Herpurchasing

powerhasgoneup4.9%; thisisherrealreturn.

Aleveraged return referstoareturn toaninvestor that isamultiple ofthereturn onthe underlying

asset.Theleveragedreturn iscalculated asthegainorlossontheinvestment asapercentage

ofaninvestor'scashinvestment.Aninvestment inaderivativesecurity, suchasafutures contract,

produces a

leveragedreturn becausethecashdeposited isonlyafraction ofthevalueoftheassetsunderlying

thefutures contract. Leveraged investments

inrealestateareverycommon:investorspayforonlypartofthecostof thepropertywith

theirowncash,andtherestoftheamount ispaidforwith borrowed money.

Anexamination ofthereturns andstandard deviation ofreturns forthemajorinvestable

assetclassessupports theideaofatradeoffbetween riskandreturn.UsingU.S. data over the

period 1926-2008 as an example, shown in Figure 1, small-capitalizationstockshave

hadthegreatestaveragereturns andgreatestriskovertheperiod.T-billshadthelowest

averagereturns andtheloweststandard deviation ofreturns.

Figure 1:RiskandReturn ofMajorAssetClassesintheUnited States (1926-2008)

AssetsClass

AverageAnnual

Return

(GeometricMean)

Standard Deviation

(Annualized

Monthly) Small-cap

stocks

11.7% 33.0%

Large-cap

stocks

9.6% 20.9%

Long-term

corporate

bonds 5.9% 8.4%

Long-term Treasury

bonds

5.7% 9.4%

Treasury bills 3.7% 3.1%

Inflation 3.0% 4.2%

Resultsforother marketsaround theworldaresimilar:assetclasseswith thegreatest

averagereturns alsohavethehigheststandard deviations ofreturns.

The annual nominal return onU.S.equitieshasvariedgreatlyfromyeartoyear,

rangingfromlossesgreaterthan 40%togainsofmorethan 50%.Wecanapproximate

therealreturns overtheperiod bysubtracting inflation. The asset class with the least risk, T-

bills, had a real return of only approximately 0. 7% over the period, while the

approximate real return on U.S. large-cap stocks was 6.6%. Because annual inflation

fluctuated greatly over the period, realreturns havebeenmuch morestablethan nominal

returns.

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Evaluating investments usingexpectedreturn andvarianceofreturns isasimplification

becausereturns donotfollowanormal distribution;distributions arenegativelyskewed,

withgreaterkurtosis (fattertails)than anormal distribution.Thenegativeskewreflectsatendency

towardslargedownside deviations, whilethepositiveexcesskurtosis reflects frequent

extremedeviations on both the upside and downside. These non-normal characteristics of

skewness (# 0) and kurtosis ( # 3) should be taken into account when analyzing

investments.

Liquidity isanadditional characteristic toconsiderwhenchoosing investments because liquidity

canaffectthepriceand,therefore, theexpectedreturn ofasecurity.Liquidity canbeamajorconcern

inemerging markets andforsecuritiesthat tradeinfrequently, suchaslow-quality corporate

bonds.

Variance(StandardDeviation)ofReturns foranIndividualSecurity

Infinance,thevarianceandstandard deviation ofreturns arecommon measuresof investment

risk.Bothofthesearemeasuresofthevariability ofadistributionofreturns about

itsmeanorexpectedvalue.

Wecancalculatethepopulation variance, , whenweknowthereturnRtforeachperiod, thetotal

number periods (T), andthemeanorexpectedvalueofthepopulation's distribution(µ),

asfollows:

Intheworld offinance,wearetypicallyanalyzingonlyasampleofreturns data, rather than

theentirepopulation.Tocalculatesamplevariance,s2,usingasampleofT historicalreturns

andthemean, oftheobservations,weusethefollowingformula:

CovarianceandCorrelationofReturnsforTwoSecurities

Covariance measurestheextent towhich twovariablesmovetogether overtime.A

positivecovariancemeansthat thevariables(e.g.,ratesofreturn ontwostocks)tend

tomovetogether. Negativecovariancemeansthat thetwovariablestend tomoveinopposite

directions. Acovarianceofzeromeansthereisnolinearrelationship

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betweenthetwovariables.Toput itanother way,ifthecovarianceofreturns between twoassets

iszero,knowing thereturn forthenextperiod ononeoftheassetstellsyounothing about thereturn

oftheother assetfortheperiod.

Herewewillfocusonthecalculation ofthecovariancebetween twoassets'returnsusinghistorical

data.The calculation ofthesamplecovarianceisbasedonthefollowing formula:

Where:

Rt,1= return on Asset 1 in period t

Rt,2= return on Asset 2 in period t

1

n = number of periods

Themagnitude ofthecovariancedepends onthemagnitude oftheindividual stocks' standard

deviations andtherelationship between theirco-movements.Covariance isan absolute

measureandismeasured inreturn units squared.The covarianceofthereturns

oftwosecuritiescanbestandardized bydividing bythe productofthestandard deviations

ofthetwosecurities.This standardized measureof co-movement

iscalledcorrelationandiscomputed as:

The relation can also be written as:

The term iscalledthecorrelation coefficient between thereturns ofsecurities 1 and2. The

correlation coefficienthasnounits. Itisapuremeasureoftheco-movement ofthe twostocks'returns

andisboundedby-1 and+1.

Howshouldyouinterpretthecorrelation coefficient?

Acorrelation coefficientof +1 meansthat deviations fromthemeanorexpected

return arealwaysproportionalinthesamedirection.That is,theyareperfectly

positivelycorrelated.

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Acorrelation coefficientof -1 meansthat deviations fromthemeanorexpected

return arealwaysproportionalinopposite directions. That is,theyareperfectly

negativelycorrelated.

Acorrelation coefficientofzeromeansthat thereisnolinearrelationship between

thetwostocks'returns. Theyareuncorrelated.Onewaytointerpretacorrelation

(orcovariance)ofzeroisthat, inanyperiod, knowing theactualvalueofone

variabletellsyounothingabout thevalueoftheother.

Example: Calculating mean return, returns variance, returns covariance,

and correlation

Given the six years of percentage returns for Stocks 1 and 2 in the following table,

calculate the mean return, sample variance, sample covariance, and correlation for the two

returns series.

Year

Stock 1

Return

Stock 2

Return

)

)

) )

20X4

+0.20

20X5

20X6

20X7

+0.30

20X8

20X9

+ 0.60

= 0.05

=0.10

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Answer:

To calculate the mean returns for the samples, we sum the returns for each stock and

divide by the number of years. The mean returns are for Stock 1 and

for Stock 2.

Using the deviations of each year’s returns from the mean return for Stock 1, we can

calculate the sample variance as follows:

Using the deviations of each year’s returns from the mean return for Stock 2, we can

calculate the sample variance as follows:

In the right-hand column of the table, we have summed the products of the

deviations of Stocks 1 and 2 from their means to get 0.255.

The sample covariance is calculated as 0.255 I (6— 1) 0.051.

To convert the covariance into correlation, we use the sample standard deviations of

returns for the two stocks:

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Finally, we can calculate the correlation coefficient for the two stocks’ returns as

follows:

Arisk-averse investor issimplyonethat dislikesrisk(i.e.,preferslessrisktomorerisk).

Giventwoinvestments thathaveequalexpected returns, arisk-averseinvestorwill

choosetheonewithlessrisk(standarddeviation, ).

Arisk-seeking (risk-loving) investor actuallyprefersmorerisktoless and,givenequal

expectedreturns, willchoosethemoreriskyinvestment. Arisk-neutralinvestorhasno preference

regarding riskandwouldbeindifferent betweentwosuchinvestments.

Consider thisgamble:Acoinwillbeflipped; ifitcomesupheads,youreceive $100; if it comes up

tails, you receive nothing. The expected payoff is 0.5($100) + 0.5($0) = $50. A risk-averse

investor would choose a payment of $50 (a certain outcome) overthegamble. Arisk-seeking

investorwould preferthegambletoacertain payment of$50.Arisk-neutral investorwould

beindifferent between thegambleandacertain payment of$50.

Ifexpectedreturns areidentical, arisk-averseinvestorwillalwayschoosetheinvestment

withtheleastrisk.However,aninvestormayselectaveryriskyportfolio despitebeing

riskaverse;arisk-averseinvestorwillholdveryriskyassetsifhefeelsthat theextra return

heexpectstoearnisadequate compensation fortheadditional risk.

Thevarianceofreturns foraportfolio oftworiskyassetsiscalculated asfollows:

wherew1istheproportionoftheportfolio investedinAsset1,andw2istheproportion oftheportfolio

investedinAsset 2.W2 must equal(1-w1 ).

Previously,weestablished that thecorrelation ofreturns fortwoassetsiscalculated as:

Substituting thisterm forCov12intheformula forthevarianceofreturns foraportfolio

oftworiskyassets,wehavethefollowing:

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:

Writing theformula inthisformallowsustoeasilyseetheeffectofthecorrelation of returns between

thetwoassetsonportfolio risk.

Iftworiskyassetreturns areperfectlypositivelycorrelated, p12 = +1,then thesquareroot

ofportfolio variance (theportfolio standard deviation ofreturns) isequalto:

In this unique case, with p12 = l, theportfolio standard deviation issimplyaweighted

averageofthestandard deviations oftheindividual assetreturns.Aportfolio 25% investedinAsset

1and75% investedinAsset2willhaveastandard deviation ofreturns equalto25%ofthestandard

deviation ( ) ofAsset1 's return, plus75%ofthestandard deviation ( ) ofAsset2'sreturn.

Focusingonreturns correlation, wecanseethat thegreatestportfolio riskresultswhen

thecorrelation between assetreturns is+1. Foranyvalueofcorrelation lessthan +1, portfolio

varianceisreduced. Note that foracorrelation ofzero,theentirethird termin theportfolio

varianceequation iszero.Fornegativevaluesofcorrelation p12, thethird

termbecomesnegativeandfurther reducesportfolio varianceandstandard deviation.

Wewillillustrate thispropertywith anexample.

Example: Portfolio risk as correlation varies

Consider two risky assets chat have returns variances of 0.0625 and 0.0324,

respectively. The assets’ standard deviations of returns arc then 25% and 18%,

respectively. Calculate the variances and standard deviations of portfolio returns for an equal-

weighted portfolio of the two assets when their correlation of returns is 1, 0.5, 0, and 0.5.

The calculations are as follows:

+

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:

:

Note thatportfolio riskfallsasthecorrelation betweentheassets'returns decreases.This

isanimportant resultoftheanalysisofportfolio risk:The lowerthecorrelation ofasset returns,

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thegreatertheriskreduction (diversification) benefitofcombining assetsina

portfolio.Ifassetreturns wereperfectly negativelycorrelated, portfolio riskcouldbe eliminated

altogether foraspecificsetofassetweights.

Weshowtheserelations graphically inFigure2byplotting theportfolio riskandreturn

forallportfolios oftworiskyassets,forassumedvaluesoftheassets'returns correlation.

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Figure 2: Risk and Return for Different Values of p

Fromtheseanalyses,therisk-reductionbenefitsofinvesting inassetswithlowreturn correlations

shouldbeclear.The desiretoreduceriskiswhat drivesinvestorstoinvestin notjustdomestic

stocks,butalsobonds, foreignstocks,realestate,andother assets.

Foreachlevelofexpectedportfolio re tu rn , wecanvarytheportfolio weightsonthe individual

assets todetermine t h e portfolio t ha t hastheleastrisk.Theseportfolios

thathavetheloweststandard deviat ionofallportfolios withagivenexpectedreturn areknown

asminimum-varianceportfolios.Together theymakeuptheminimum-variance frontier.

Onariskversusreturn graph, theportfolio that isfarthest totheleft(hasthe leastrisk)isknown

astheglobalminimum-varianceportfolio.

Assuming thatinvestorsareriskaverse,investorsprefertheportfolio t ha thasthegreatest

expected returnwhenchoosing amongportfolios thathavethesamestandard

deviationofreturns. Those portfoliosthathavethegreatestexpectedreturn foreachlevelofrisk

(standard deviation) makeuptheefficient frontier.The efficientfrontier coincideswith

thetopportion o f theminimum-variancefrontier. Arisk-averseinvestorwould only

chooseportfolios that areontheefficientfrontier becauseallavailableportfolios that are

notontheefficientfrontier havelowerexpected returns than anefficientportfolio with

thesamerisk.Theportfolio on theefficientfrontier thathastheleastriskistheglobal minimum-

varianceportfolio.

Theseconcepts areillustrated inFigure3.

E (RP)

100% Asset A

100% Asset B B

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Figure 3: Minimum-Variance and Efficient Frontiers

An investor's utility functionrepresents the investor's preferences in terms of risk and return

(i.e., his degree of risk aversion). An indifference curve is a tool from economics that, in

this application, plots combinations of risk (standard deviation) and expected return

amongwhich aninvestor is indifferent. In constructing indifference curves for portfolios

based on only their expected return and standard deviation of returns, we are assuming

that these are the only portfolio characteristics that investors care about. In Figure 4, we

show three indifference curves for an investor. The investor's expected utility is

thesameforallpoints alongasingleindifference curve. Indifference curve I1represents the

most preferred portfolios in Figure 4; ourinvestorwillpreferanyportfolio

alongI1toanyportfolio oneitherI2orI3

Figure 4: Risk-Averse Investor’s Indifference Curves

Global Minimum

Variance Portfolio

E(R)

Individual Security

Efficient frontier

(All Efficient portfolios)

Inefficient portfolios

E(R)

I1

I2

I3

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Indifference curvesslopeupward forrisk-averseinvestorsbecausetheywillonlytakeon

morerisk(standard deviationofreturns) iftheyarecompensated wi thgreaterexpected returns.

Aninvestorwhoisrelativelymoreriskaverserequiresarelativelygreater increaseinexpected

returntocompensate foragivenincreaseinrisk.Inotherwords,amorerisk-

averseinvestorwillhavesteeperindifference curves ,reflectingahigher riskaversion coefficient.

Inourpreviousillustration o f efficientportfolios availableinthemarket, weincluded

onlyriskyassets.Nowwewillintroduce a risk-freeassetinto ouruniverseofavailable

assets,andwewillconsider theriskandreturn characteristics ofaportfolio thatcombines

aportfolio of riskyassetsandtherisk-freeasset.RecallfromQuantitative Methods

thatwecancalculatetheexpectedreturn andstandard deviationofaportfoliowithweight

WAallocated to risky Asset A and weight WB allocated to risky Asset B using the following

formulas:

AllowAssetBtobetherisk-freeassetandAssetAtobetheriskyassetportfolio.Because arisk-

freeassethaszerostandard deviationandzerocorrelation ofreturns withthoseofariskyportfolio,

t h i s resultsinthereduced equation:

The intuitionofthisresultisquite simple:Ifweput X% ofourportfolio intotherisky assetportfolio,

the resulting portfolio will have standard deviation of returns equal to X% of the standard

deviation of the risky asset portfolio. The relationship betweenportfolio risk and return for

various portfolio allocations is linear, as illustrated in Figure 5.

Combining a risky portfolio with a risk-free asset is the process that supports the two fund

separation theorem, which states that all investors' optimum portfolios will be made up of

some combination of an optimal portfolio of risky assets and the risk-free asset. The line

representing these possible combinations of risk-free assets and the optimal risky asset

portfolio is referred to as the capital allocation line.

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Point X on the capital allocation line in Figure 5 represents a portfolio that is 40% invested in

the risky asset portfolio and 60% invested in the risk-free asset. Its expected return will be

0.40[E(R risky asset portfolio)] + 0.60(Rf), and its standard deviation will be 0.40(J risky asset

portfolio)

Figure 5: Capital Allocation Line and Risky Asset Weights

Now that we have constructed a set of the possible efficient portfolios (the capital

allocation line), we can combine this with indifference curves representing an

individual's preferences for risk and return to illustrate the logic of selecting an optimal

portfolio (i.e., one that maximizes the investor's expected utility). In Figure 6, we can

see that Investor A, with preferences represented byindifference curves I1, I2, and I3, can

reach the level of expected utility on I1 by selecting portfolio X. This is the optimal

portfolio for this investor, as any portfolio that lies on I2 is preferred to all portfolios that

lie on I3 (and in fact to any portfolios that lie between I2 and I3). Portfolios on I1 are

preferred to those on I2, but none of the portfolios that lie on I1 are available in the

market.

Figure 6: Risk-Averse Investor’s Indifference Curves

X

E(

E(R)

E(

Capital

Allocation Line

I3

X

I1

I2

E(R)

Capital

Allocation

Line

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Thefinalresultofouranalysishereisnotsurprising; investorswhoarelessriskaverse

willselectportfolios thataremorerisky.Recallthat thelessaninvestor'sriskaversion,

theflatterhisindifference curves.Asillustrated inFigure7,theflatterindifference curve

forInvestor B(IB)resultsinanoptimal (tangency) portfolio thatliestotherightofthe onethat

resultsfromasteeperindifference curve,suchasthatforInvestorA(IA).An

investorwhoislessriskaverseshould optimallychooseaportfolio withmoreinvestedin

theriskyassetportfolio andlessinvestedintherisk-freeasset.

Figure 7: Portfolio Choices Based on Investor’s Indifference Curves

Intheprevioustopicreview, wecoveredthemathematics ofcalculating theriskand

returnofaportfolio with apercentage weightofWA investedinariskyportfolio (P) and a weight

of WB = 1- WA invested in a risk-free asset.

Becausearisk-freeassethaszerostandard deviationandzerocorrelation o f returns

withariskyportfolio, a l l o w i n g AssetBtobetherisk-freeassetandAssetAtobetherisky

assetportfolio resu l t s inthefollowingreduced equation:

Our resultisthat therisk(standard deviationofreturns) andexpectedreturn ofportfolios

withvaryingweightsintherisk-freeassetandariskyportfolio canbe

E(R)

A

B

Capital

Allocation Line

IA

IB

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Plotted asalinethatbeginsattherisk-freerateofreturn andextendsthroughtherisky portfolio.This

resultisillustrated inFigure 1.

Figure 1: Combining a Risk-Free Asset with a Risky Asset

Thelineofpossibleportfolio r i skandreturn combinationsgiventherisk-freerateand

theriskandreturn ofaportfolio ofriskyassetsisreferredtoasthecapital allocationline

(CAL).Foranindividual investor, thebestCAListheonethat offersthemost preferred

setofpossibleportfolios intermsoftheirriskandreturn. Figure2illustrates threepossibleinvestor

CALsforthreedifferent riskyportfolios A,B,andC.The optimal riskyportfolio for thisinvestor

isPortfolioAbecauseitresultsinthemostpreferred setofpossibleportfolios

constructedb y combining t h e risk-freeassetwith theriskyportfolio. Ofalltheportfolios

availabletotheinvestor,acombination oftherisk freeassetwith

riskyPortfolioAofferstheinvestorthegreatestexpected utility.

E(RA)

E(Rportfolio)

Rf

0

Risk free

Asset

Portfolio with

WA

Invested in the

Risky Asset

Risky Asset

E(RP)

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Figure 2: Risky Portfolios and Their Associated Capital Allocation Line

Ifeachinvestor hasdifferent expectations about theexpectedreturns of,standard deviations

of,orcorrelations betweenriskyassetreturns, eachinvestorwillhavea different optimal

riskyassetportfolio andadifferent CAL.

Asimplifying assumption underlying modern portfolio theory (andthecapitalasset pricing

model,which isintroducedlaterinthistopic review)isthat investorshave

homogeneousexpectations (i.e.,theyallhavethesameestimates ofrisk,return, and correlations

with other riskyassetsforallriskyassets).Under thisassumption,

a l l investorsfacethesameefficientfrontier ofriskyportfolios andwillallhavethesame optimal

riskyportfolio andCAL.

Figure3illustrates thedeterminationoftheoptimal riskyportfolio andoptimal

CALforallinvestors undertheassumption o fhomogeneousexpectations.Note that,

underthisassumption, t h e optimal CALforanyinvestor istheonethat isjusttangent tothe

efficientfrontier. Depending o n theirpreferencesforriskandreturn ( theirindifference

curves),investorsmaychoosedifferent portfolio weightsfortherisk-freeassetandthe

risky(tangency) portfolio. Everyinvestor,however,willusethesameriskyportfolio. When

thisisthecase,thatportfolio mustbethemarket portfolioofallriskyassets

becauseallinvestorsthathold anyriskyassetshold thesameportfolio o f riskyassets.

E(R)

CALA

A

B

CALC

CALB

C

Indiffe

rence

curve

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Figure 3: Determining the Optimal Risky Portfolio and Optimal CAL Assuming

Homogeneous Expectations

Under theassumption o fhomogeneousexpectations,thisoptimal CALforallinvestors

istermed thecapital marketline(CML).Alongthisline,expectedportfolio return, E(Rp),is

alinearfunction ofportfolio risk, p· The equation ofthislineisasfollows:

They-interceptofthislineisRfandtheslope(riseoverrun) ofthislineisasfollows:

The intuitionofthisrelation isstraightforward.Aninvestorwhochoosestotakeonno risk( p = O)

will earntherisk-freerate,Rf.The differencebetween theexpected returnonthemarket

andtherisk-freerateistermed themarket r iskpremium.Ifwerewrite theCMLequation as

wecanseethat aninvestor canexpecttogetoneunit ofmarket riskpremium in additional return

(abovetherisk-freerate)foreveryunit ofmarket risk, M,that the investoriswillingtoaccept.

Capital Market Line

Rf Risk free asset

Efficient

Frontier

E(R)

Optimal Risky

portfolio

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Ifweassumethat investorscanboth lend (investintherisk-freeasset)attherisk-freerateandborrow

(aswith amargin account) attherisk-freerate,theycanselect portfoliostotheright ofthemarket

portfolio inFigure3.Anexamplewillillustrate thecalculations.

Example: Portfolio risk and return with borrowing and lending

Assume that the risk-free rate, is 5%; the expected rate of return on the market,

E ( ), is 11%; and that the standard deviation of returns on the market portfolio, is 20%.

Calculate the expected return and standard deviation of returns for

Portfolios that are 25%, 75%, and 125% invested in the market portfolio. We will use to

represent these portfolio weights.

Expected portfolio returns are calculated as E ( ) = (1 WM) x Rf. + WM x E (RM), we have

the following:

Portfolio standard deviation is calculated as , so we have the following:

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Figure 4: Borrowing and Lending Portfolios

Note thatwithaweight (ofinvestorassets)of125%inthemarket portfolio, t h e investorborrows

anamount equa l to25%ofhisportfolio asse t sat5%.Aninvestor with $10,000

wouldthenborrow$2,500 andinvestatotalof$12,500 i n themarket portfolio. This

leveragedportfolio willhaveanexpected returnof12.5%andstandard deviation of25%.

Investorswhobelievemarket pricesareinformationallyefficientoftenfollowapassive

investmentstrategy(i.e.,investinanindexofriskyassetsthat servesasaproxyforthe market

portfolioandallocateaportion o f theirinvestableassetstoarisk-freeasset,such asshort-

termgovernment s e c u r i t i e s ). Inpractice, manyinvestorsandportfolio

managersbelievetheirestimates ofsecurityvaluesarecorrectandmarket pricesareincorrect.

Such investorswillnotusetheweights ofthemarket portfoliobutwillinvestmorethan

themarketweightsinsecuritiesthat theybelieveareundervalued a n d lessthan themarket

weightsinsecuritieswhich theybelieveareovervalued.This isreferredtoasactive

portfoliomanagementtodifferentiate i t fromapassiveinvestment s t r a t eg y that

utilizesamarket indexfortheoptimal riskyassetportfolio.

When aninvestor diversifiesacrossassetsthat arenotperfectlycorrelated, theportfolio's

riskislessthan theweighted averageoftherisksoftheindividual securit ies inthe portfolio.The

riskthat iseliminated b ydiversification iscalledunsystematicrisk(also

Lending portfolios

E(RM)=11%

Rf=5%

0

WM=75%

WM=125%

WM=20%

E(RP) Borrowing portfolios

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calledunique,diversifiable,orfirm-specificrisk).Becausethemarket

portfolioconta insallriskyassets,itmustbeawell-diversifiedportfolio.Alltheriskthat

canbediversifiedawayhasbeen.Theriskthat remainscannotbediversifiedawayandiscalledthe

systematic risk(alsocallednondiversifiableriskormarketrisk).

The conceptofsystematicriskappliestoindividual securitiesaswellastoportfolios.

Somesecurities’ returns arehighlycorrelated withoverallmarket returns. Examplesof firmsthat

arehighlycorrelated withmarket returnsareluxurygoodsmanufacturers

suchasFerrariautomobiles andHarleyDavidson motorcycles. Thesefirmshavehigh

systematic risk(i.e.,theyareveryresponsivetomarket,orsystematic, changes). Other

firms,suchasutility companies, respond verylittletochangesinthesystematic riskfactors.These

firmshaveverylittlesystematic risk.Hence, totalrisk(asmeasured bystandard deviation)

canbebroken downinto itscomponentparts: unsystematic r iskand systematic

risk.Mathematically:

Doyouactuallyhavetobuyallthesecuritiesinthemarket todiversifyaway unsystematic

r isk?No.Academicstudieshaveshownthat asyouincreasethenumber ofstocksinaportfolio,

t h e portfolio’s riskfallstowardthelevelofmarket risk.Onestudy showedthatitonlytookabout

12to18 stocksinaportfolio t o achieve90%of themaximum

d ivers i f i ca t ion possible.Another studyindicatedittook30securities. Whatever

thenumber,itis significantlylessthanallthesecurities. Figure5providesa general

r e p r e s e n t a t i o n ofthisconcept.Note,inthefigure,thatonceyougetto30 o r so

securitiesinaportfolio,thestandard deviationremainsconstant. Theremaining

r i sk issystematic, ornondiversifiable, risk.Wewilldevelopthisconceptlaterwhenwe discuss

beta, a measure of systematic risk.

Figure 5: Risk vs. Number of Portfolio Assets

σ

(Risk)

Market

Risk

(σmkt)

Unsystematic

Risk

Number of securities in the

portfolio

Systematic Risky

Total Risk

(unsystematic risk

+ systematic risk)

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Systematic Risk is Relevant in Portfolios

One important conclusion of capital market theory is that equilibrium security returns

depend on a stock's or a portfolio's systematic risk, not its total risk as measured by

standard deviation. One of the assumptions ofthe modelis that diversificationis free. The

reasoning isthat investors will not be compensated for bearing risk that can be eliminated at

no cost. If you think about the costs of a no-load index fund compared to buying

individual stocks, diversification is actually very low cost if not actually free.

The implications of this conclusion are very important to asset pricing (expected returns).

The riskiest stock, with risk measured as standard deviation of returns, does not

necessarily have the greatest expected return. Consider a biotech stock with one new drug

product that is in clinical trials todetermine its effectiveness. If it turns out that the drug is

effective and safe, stock returns willbe quite high. If, on the other hand, the subjects in the

clinical trials are killed or otherwise harmed by the drug, the stock will fall to

approximately zero and returns will be quite poor. This describes a stock with high standard

deviation of returns (i.e., hightotal risk).

The high risk of our biotech stock, however, is primarily from firm-specific factors, so its

unsystematic risk is high. Because market factors such as economic growth rates have

little to do with the eventual outcome for this stock, systematic risk is a small proportion

of the total risk of the stock. Capital market theory says that the equilibrium return on

this stock may be less than that of a stock with much less firm-specific risk but more

sensitivity to the factors that drive the return of the overall market. An established

manufacturer of machine tools may not be a very risky investment in terms of total

risk,butmayhaveagreatersensitivity tomarket (systematic) riskfactors(e.g.,GDP growth

rates)than ourbiotech stock.Giventhisscenario, thestockwith moretotalrisk(the biotech

stock)hasless systematic riskandwilltherefore havealowerequilibrium r a t e of return

accordingtocapitalmarket theory.

Note thatholding manybiotech firmsinaportfolio willdiversifyawaythefirm-specific

risk.Somewillhaveblockbuster products andsomewillfail,butyoucanimagine that when

50or100suchstocksarecombined intoaportfolio, theuncertaintyabout the portfolio return

ismuch lessthan theuncertaintyabout thereturn ofasinglebiotech firmstock.

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Tosumup,unsystematic r iskisnotcompensated i n equilibrium b e c a u s e itcanbeeliminated

fo r freethroughdiversification.Systematicriskismeasured bythe

contributionofasecuritytotheriskofawell-diversifiedportfolio, a n d theexpected equilibrium

r e t u r n (required return) onanindividual securitywilldepend onlyonits systematic risk.

Return generat ingmodels areusedtoestimate theexpectedreturns onriskysecurities

basedonspecificfactors. Foreachsecurity,wemust estimatethesensitivity ofits returns

toeachspecificfactor.Factorsthat explainsecurityreturns

canbeclassifiedasmacroeconomic,fundamental, andstatistical factors.Multifactormodels

mostcommonly usemacroeconomicfactorssuchasGDP growth, inflation, orconsumer

confidence,alongwithfundamentalfactorssuchasearnings,earningsgrowth, firmsize,

andresearchexpenditures. Statisticalfactorsoftenhavenobasisinfinancetheory

andaresuspectinthat theymayrepresent onlyrelations foraspecifictimeperiodwhich

havebeenidentified bydatamining (repeated testsonasingledataset).

Thegeneralformofamultifactor m o d e l withk factorsisasfollows:

This modelstatesthat theexpectedexcessreturn (abovetherisk-freerate)forAssetiis

thesumofeachfactor sensitivityorfactor loading (the(βs) forAssetimultiplied bythe

expectedvalueofthat factorfortheperiod.The firstfactorisoftentheexpected excessreturn

onthemarket, E (Rm- Rf).

One multifactorm o d e l that isoften usedisthat ofFamaandFrench.They estimated the

sensitivity ofsecurityreturns tothreefactors:firmsize,firmbookvaluetomarket value ratio,

andthereturn onthemarket portfolio minus therisk-freerate(excessreturn onthemarket

portfolio). Carhart suggestsafourth factor that measurespricemomentum usingprior

periodreturns. Together, thesefourfactorsdoarelativelygoodjobof explaining

returnsdifferencesforU.S.equitysecuritiesovertheperiod forwhichthe

modelhasbeenestimated.

Thesimplestfactormodel isasingle-factormodel. Asingle-factor modelwith thereturn

onthemarket, Rm’asitsonlyriskfactorcanbewritten ( inexcess returns fo rm)as:

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Here, theexpected excessreturn (return abovetherisk-freerate)istheproductofthe

factorweightorfactorsensitivity,Betai, andtheriskfactor,whichinthismodel isthe excessreturn

onthemarket portfolio ormarket index,sothat thisisalsosometimes calledasingle-index model.

Asimplifiedformofasingle-index model isthemarket model,whichisusedtoestimate

asecurity's(orportfolio's) betaandtoestimate asecurity'sabnormal return (return above

itsexpected return) basedontheactualmarket return.

Theformofthemarket modelisasfollows:

Where:

Ri = Return on Asset i

Rm = Market return

= Slope coefficient

= Intercept

= Abnormal return on Asset i

The intercept αi and slope coefficient βi areestimated fromhistorical return data. We can

require that αi is the risk-free rate times (1 - βi) to be consistent with the general form of a

single-index model in excess returns form.

The expected return on Asset i is αi + βi E(Rm). A deviation from the expected return in

a given period is the abnormal return on Asset i, ei, or Ri - (αi + βi Rm).

In the market model, the factor sensitivity or beta for Asset i is a measure of how sensitive

the return on Asset i is to the return on the overall market portfolio (market index).

The sensitivity of an asset’s return to the return on the market index in the context of the

market model isreferredtoasitsbeta.Betaisastandardized m e a s u r e ofthe

covarianceoftheasset’s returnwiththemarket return.Betacanbecalculated asfollows:

Wecanusethedefinition ofthecorrelation b e tween thereturns onAssetiwith thereturns

onthemarket index:

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Substituting f o r Covim intheequation for , we canalsocalculatebetaas:

Example: Calculating an asset’s beta

The standard deviation of the return on the market index is estimated as 20%.

1. If Asset A’s standard deviation is 30% and its correlation of returns with the

Market index is 0.8, what is Asset A’s beta?

2. If the covariance of Asset A’s returns with the returns on the market index is 0.048,

what is the beta of Asset A?

Inpractice, weestimate assetbetasbyregressingreturns ontheassetonthoseofthe market

index.While regressionisaLevelIIconcept, forourpurposes, youcanthink ofitasamathematical

e s t i m a t i o n procedu re that fitsalinetoadataplot.InFigure5,we represent theexcessreturns

onAssetiasthedependentvariableandtheexcessreturns onthemarket

indexastheindependentvariable.The leastsquaresregression lineisthe linethat

minimizesthesumofthesquared distancesofthepoints plottedfromtheline (this iswhat ismeant

bythelineofbest fit). Theslopeofthislineisourestimate ofbeta. InFigure6,thelineissteeperthan

45degrees,theslopeisgreaterthan one, and the asset’s estimated betaisgreaterthan one.Our

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interpretationisthat thereturns onAsseti aremorevariableinresponsetosystematic

riskfactorsthan istheoverallmarket, whichhasabetaofone.

Figure 6: Regression of Asset Excess Returns against Market Asset Returns

This regression line is referred to as the asset's security characteristic line. Mathematically,

the slope of the security characteristic line is Covim/ which is the same formula we used

earlier to calculate beta.

Given that the only relevant (priced) risk for an individual Asset i is measured by the

covariance between the asset's returns and the returns on the market, Covi,mkt we can plot

the relationship between risk and return for individual assets using Covi,mkt as our measure

of systematic risk. The resulting line, plotted in Figure 7, is one version of what is referred to

as the security market line (SML).

Figure 7: Security Market Line

Market Excess Return (Rm-Rf)

Asset

Excess

Return

Security

Characteristic Line

E(R) Security Market

Line (SML)

Rf

Market portfolio

Systematic Risk

(

E(Rmkt)

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The equation of the SML is:

Which can be rearranged and stated as:

The line described by this last equation is presented in Figure 8, where we let the

Standardized covariance term, , be defined as beta,

This is the most common means of describing the SML, and this relation between beta

(systematic risk) and expected return is known as the capital asset pricing model

(CAPM).

Figure 8: The Capital Asset Pricing Model

So, we can define beta, , as a standardized measure ofsystematic risk.

Beta measures the relation between a security's excess returns and the excess returns to the

market portfolio.

E(Ri) Security Market

Line (SML)

Rf

Market portfolio

Systematic Risk

E(Rmkt)

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Formally, the CAPM is stated as:

The CAPM holds that, in equilibrium, the expected return on risky asset E(R) is the

risk-free rate (Rf) plus a beta-adjusted market risk premium, βi [E(Rmkt) - Rf]. Beta

measures systematic (market or covariance) risk.

The assumptions of the CAPM are:

Risk aversion. To accept a greater degree of risk, investors require ahigher expected

return.

Utility maximizing investors. Investors choose the portfolio, based on their

individual preferences, with the risk and return combination that maximizes their

(expected) utility.

Frictionless markets. There are no taxes, transaction costs, or other impediments to

trading.

One-period horizon. All investors have the same one-period time horizon.

Homogeneous expectations. All investors have the same expectations for assets'

expected returns, standard deviation of returns, and returns correlations between

assets.

Divisible assets. All investments are infinitely divisible.

Competitive markets. Investors take the market price as given and no investor

caninfluence priceswith their trades.

Comparing t h e CMLandtheSML

It is important to recognize that the CML and SML are very different. Recall the equation of

the CML:

The CML usestotal risk = on the x-axis. Hence, onlyefficient portfolios will plot on the

CML. On theother hand, the SML uses beta (systematic risk) on the x-axis. So in a CAPM

world, all properly priced securities and portfolios of securities will plot on the SML, as

shown in Figure 9.

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Figure 9: Comparing the CML and the SML

Portfolios that are not well diversified (efficient) plot inside the efficient frontier and are

represented by risk-return combinations such as points A, B, and C in panel (a) of Figure

9. Individual securitiesare one example of such inefficient portfolios. According to the

CAPM, theexpected returns on all portfolios, well diversified or not, aredetermined by their

systematic risk. Thus, according to the CAPM, Point A represents a high-beta stock or

portfolio, Point B a stock or portfolio with a beta of one, and Point C a low-beta stock or

portfolio. We know this because the expected return at Point B is equal to the expected

(b) Security Market line

E

A

B

C

D

PM+T-bills

(a) Capital Market Line E(R) CML

Rf

M

E(RM)

PM w/margin

A

E

C

D

E(R) SML

Rf

B

E(RM) PTIT


146

return on the market, and the expected returns at Point A and Care greater and less than the

expected return on the market (tangency) portfolio, respectively.

Note that a low-beta stock, such as represented by Point C, is not necessarily low-risk when

total risk is considered. While its contribution to the risk of a well-diversified portfolio may

be low, its risk when held by itself can be considered quite high. A firm whose only activity is

developing a new, but as yet unproven, drug may be quite speculative with highly uncertain

returns. It may also have quite low systematic risk if the uncertainty about itsfuture returns

depends primarily on firm-specific factors.

All stocks and portfolios that plot along the line labeled β = 1 in Figure 9 have the same

expected return as the market portfolio and, thus, according to the CAPM, have the same

systematic risk as the market portfolio (i.e., they all have betas of one).

All points on the CML (except the tangency point) represent the risk-return characteristics

of portfolios formed by either combining the market portfolio with the risk-

freeassetorborrowing attherisk-freerateinordertoinvestmorethan 100%of theportfolio's

netvalueintheriskymarket portfolio (investing onmargin). Point DinFigure8represents

aportfolio that combines themarket portfolio with therisk-free asset,whilepoints

abovethepoint oftangency,suchasPointE,represent portfolios createdbyborrowing attherisk-

freeratetoinvestinthemarket portfolio.Portfolios that

donotlieontheCMLarenotefficientandtherefore haveriskthatwillnotbe rewardedwithhigher

expectedreturns inequilibrium.

According totheCAPM, allsecuritiesandportfolios, d iv e r s i f i ed ornot,willplotontheSMLin

equilibrium. In fact, all stocks and portfolios along the line labeled β = 1 in

Figure9,including themarket portfolio,willplotatthesamepoint ontheSML.They

willplotatthepoint ontheSMLwith betaequaltooneandexpectedreturn equalto theexpected

returnonthemarket, regardless of their totalrisk.

The CAPMisoneofthemostfundamental concepts ininvestment theor y.The

CAPMisanequilibrium m o d e l thatpredicts theexpected returnonastock,giventheexpected

return onthemarket, thestock'sbetacoefficient, andtherisk-freerate.

BecausetheSMLshowstheequilibrium (required) returnforanysecurityorportfolio

basedonitsbeta (systematicrisk),analystsoftencompare theirforecastofasecurity's return

toitsrequired returnbasedonitsbetarisk.Thefollowingexampleillustrates this technique.

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Example: Identifying mispriced securities

The following figure contains information based on analyst’s forecasts for three stocks.

Assume a risk-free rate of 7% and a market return of 15%. Compute the expected and

required return on each stock, determine whether each stock is undervalued, overvalued,

or properly valued, and outline an appropriate trading strategy.

Forecast Data

Stock Price Today

E(Price) in 1 Year E(Dividend) in 1 Year

Beta

A $25

$27

$1.00

1.0

B 40

45

2.00

0.8

C 15

17

0.50

1.2

Answer:

Expected and required returns computations are shown in the following figure.

Forecasts vs. Required Returns

Stock Forecast Return Required Return

A

B

C

• Stock A is overvalued. It is expected to earn 12%, but based on its systematic risk,

it should earn 15%. It plots below the SML.

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• Stock B is undervalued. It is expected to earn 17.5%, but based on its systematic

risk, it should earn 13.4%. It plots above the SML.

• Stock C is properly valued. It is expected to earn 16.6%, and based on its

systematic risk, it should earn 16.6%. It plots on the SML.

The appropriate trading strategy is:

• Short sell Stock A.

• Buy Stock B.

• Buy, sell, or ignore Stock C.

We can do this same analysis graphically. The expected return/beta combinations of all

three stocks are graphed in the following figure relative to the SML.

Identifying Mispriced Securities

Remember, allstocks should plot on the SML; anystock not plotting on the SML is mispriced.

Notice that Stock A falls below the SML, Stock B lies above the SML, and Stock C is on the

SML. If you plot a stock’s expectedreturn and it falls below the SML, the stock is

overpriced. That is, the stock's expected return is too low given itssystematic risk. If a stock

plots above the SML, it is underpriced and is offering an expected return greater than

required for its systematic risk. If it plots on the SML, the stock is properly priced.

A

C

B

E (R)

7

Beta risk

SML

0.8 1 1.2

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Because the equation of the SML is thecapital assetpricing model, you can determine if a

stock is over- or underpriced graphically or mathematically. Your answers willalways be

the same.

When we evaluate the performance of a portfolio with risk that differs from that of a

benchmark, we need to adjust the portfolio returns for the risk of the portfolio. There

are several measures of risk-adjusted returns that are used to evaluate relative portfolio

One such measure is the Sharpe ratio

The Sharpe ratio of a portfolio is its excess returns per unit of total portfolio risk, and

higher Sharpe ratios indicate better risk-adjusted portfolio performance. Note that this

is a slope measure and, as illustrated in Figure 9, the Sharpe ratios of all portfolios

along the CML are the same. Because the Sharpe ratio uses total risk, rather than

systematic risk, it accounts for any unsystematic risk that the portfolio manager has taken.

Note that the value of the Sharpe ratiois only useful for comparison with the Sharpe ratio of

another portfolio.

In Figure 10, we illustrate that the Sharpe ratio is the slope of the CAL for the portfolio

and can be compared to the slope of the CML, which is the Sharpe ratio for any portfolio

along the CML.

Figure 10: Sharpe Ratios as Slopes

E (R)

Rf

RPI

RM

RP2

P1

P2

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~--~

The M-squared (M2) measure produces the same portfolio rankings as the Sharpe ratiobut is

stated in percentage terms. It is calculated as

The intuition of this measure is that the first term is the excess return on a Portfolio P*,

constructed by taking a leveraged position in Portfolio P so that P* has the same total

risk, M, as the market portfolio. As shown in Figure 11, the excess return on such a

leveraged portfolio is greater than the return on the market portfolio by the vertical

distance M2.

Figure 11: M-squared for a Portfolio

Two measures of risk-adjusted returns based on systematic risk (beta) rather than totalrisk

are theTreynor measure and Jensen's alpha. They are similar to the Sharpe ratio and M2 in

that the Treynor measure is based on slope and Jensen's alpha is a measure of percentage

returns in excess of those from a portfolio that has the same beta but lies on the SML.

The Treynor measure is calculated as , interpreted as excess returns per unit of

systematic risk, and represented by the slope of a line as illustrated in Figure 12.

Jensen's alpha for Portfolio Pi calculated as = R - [Rf + βp(RM - Rf)] and is the

percentage portfolio return above that of a portfolio (or security) with the same beta as

the portfolio that lies on the SML, as illustrated in Figure 12.

E (R)

Rf

RP

RM

P

M

P*

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Figure 12: Treynor Measure and Jensen’s Alpha

Whether risk adjustment should be based on total risk or systematic risk depends on

whether a fund bears the nonsystematic risk of a manager's portfolio. If a single manager

is used, then the total risk (including any nonsystematic risk) is the relevant measure

and risk adjustment using total risk, as with the Sharpe and M2 measures, is appropriate. If

a fund usesmultiple managers so that the overall fund portfolio is well diversified (has no

nonsystematic risk), then performance measures based on systematic (beta) risk, such as the

Treynor measure and Jensen's alpha, are appropriate.

These measures of risk-adjusted returns areoften used to compare theperformance of actively

managed funds to passively managed funds. Note in Figures 10 and 11 that portfolios that lie

above the CML have Sharpe ratios greater than those of any portfolios along the CML and

have positive M2 measures. Similarly, in Figure 12, we can see that portfolios that lie above

the SML have Treynor measures greater than those of any security or portfolio that lies along

the SML and also have positive values for Jensen's alpha.

One final note of caution isthat estimating the values needed to apply these theoretical models

and performance measures is often difficult and is done with error. The expected return on the

market, and thus the market risk premium, may not be equal to its average historical value.

Estimating security and portfolio betas is done with error as well.

Jensen’s alpha

E (R)

Rf

RP

RM

P

1

M

SML

Slope = Treynor measure for

Portfolio P

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4.3 Portfolio planning and construction

Aninvestment manager isveryunlikelytoproduce agoodresultforaclientwithout

understandingthat client’sneeds,circumstances, andconstraints.

Awritten investmentpolicy statementwilltypicallybeginwith

theinvestor'sgoalsintermsofriskandreturn. These should bedetermined j o i n t l y ,

asthegoalsofhighreturnsandlowrisk(whilequitepopular) arelikelytobemutually

exclusiveinpractice. Investorexpectations intermsofreturns mustbecompatible

wi th investor'stolerance forrisk(uncertaintyabout portfolioperformance).

Themajorcomponents ofanIPStypicallyaddressthefollowing:

DescriptionofClientcircumstances, s i t ua t ion , a n d investment object ives .

Statementof thePurposeoftheIPS.

StatementofDutiesandResponsibilitiesofinvestment manager, custodianofassets,

andtheclient.

Procedures toupdate IPSandtorespond tovariouspossiblesituations.

Investment Objectivesderivedfromcommunicationswith theclient.

Investment Constraintsthat mustbeconsidered intheplan.

Investment Guidelinessuchashowthepolicywillbeexecuted, assettypespermitted,

andleveragetobeused.

Evaluationof Performance,thebenchmark p o r t fo l i o forevaluating

investmentperformance, a n d other informationonevaluation ofinvestment r e s u l t s .

Appendicescontaininginformationonstrategic (baseline)assetallocation

andpermitteddeviations frompolicyportfolio al locations , aswellashowandwhenthe

portfolio al locationsshouldberebalanced.

Inanycase,theIPSwill,ataminimum,contain aclearstatement o f client circumstances

andconstraints, a n investment strategybasedonthese,andsome benchmark

a g a i n s t whichtoevaluatetheaccount performance.

Theriskobjectives inanIPSmaytakeseveralforms.Anabsolute r iskobjective

mightbeto"havenodecreaseinportfolio valueduring any12-month p e r i o d ” orto"not

decreaseinvaluebymorethan2%atanypoint overany12-month p e r i o d ." Low

absolutepercentage riskobjectivessuchasthesemayresultinportfolios madeupof securitiesthat

offerguaranteed re turns (e.g., U.S.Treasurybills).

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Absolute riskobjectivescanalsobestated intermsoftheprobability o f specificportfolio

results,percentage lossesordollarlosses,rather thanstrictlimitsonportfolio

results.Examplesareasfollows:

"Nogreaterthan a5%probability o f returns below-5% i n any12-month p e r i o d ."

"Nogreaterthan a4%probability o f alossofmorethan $20,000 overany12-month p e r i o d ."

Anabsolute returnobjectivemaybestatedinnominal terms, suchas"anoverallreturn

ofatleast6%perannum,"orinrealreturns, suchas"areturn of3%morethan theannual

inflationrateeachyear."

Relativeriskobjectives relatetoaspecificbenchmark andcanalsobestrict, suchas, "Returns

willnotbeless than 12-montheuroLIBOR overany12-monthperiod," or

statedintermsofprobability, suchas,"Nogreaterthan a5%probability ofreturns

morethan4%belowthereturn ontheMSCIWorld Indexoverany12-month period."

Return objectivescanberelativetoabenchmark p o r t fo l io re tu rn , suchas,"Exceedthereturn

ontheS&P500Indexby2%perannum."Forabank,thereturn

objectivemayberelativetothebank'scostoffunds (deposit rate).While itispossibleforan

institutiontousereturns onpeerportfolios, suchasanendowment w i t h astated

objectivetobeinthetopquartile ofendowment f u n d returns, peerperformance benchmarks

suffer fromnotbeinginvestableportfolios. There is no way to match thisinvestment return

byportfolio construction before the fact.

Inanyevent,theaccount managermust makesurethat thestatedriskandreturn

objectivesarecompatible, g i v e n therealityofexpectedinvestment r e s u l t s and uncertainty

overtime.

Aninvestor'sability tobearriskdepends onfinancialcircumstances. Longerinvestment horizons

(20yearsrather than 2years),greaterassetsversusliabilities (morewealth), moreinsurance

againstunexpected occurrences, andasecurejoballsuggestagreater abilitytobearinvestment

riskintermsofuncertaintyabout periodic investment performance.

Aninvestor'swillingness t o bearriskisbasedprimarily ontheinvestor'sattitudes andbeliefsabout

investments( variousassettypes).Theassessmentofaninvestor'sattitude about

riskisquitesubjectiveandissometimes donewith ashort questionnairet h a t attempts

t o categorizetheinvestor'sriskaversionorrisktolerance.

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When theadviser'sassessmentsofaninvestor'sabilityandwillingness totakeinvestment

riskarecompatible, t h e r e isnorealproblem selectinganappropriate l e v e l ofinvestment

risk.Iftheinvestor'swillingness totakeoninvestment r i s k ishighbuttheinvestor's

abilitytotakeonriskislow,thelowabilitytotakeoninvestment r i skwillprevailinthe

adviser'sassessment.

In situations where ability is high but willingness is low, the adviser may attempt to educate

the investor about investment risk and correct any misconceptions that may be contributing

to the investor's low stated willingness to take on investment risk. However, the adviser's

job is not to change theinvestor'spersonality

characteristics thatcontributetoalowwillingness totakeoninvestment r i sk .The approach

willmostlikelybeto conform totheloweroftheinvestor'sabilityorwillingness

tobearrisk,asconstructingaportfolio withalevelofriskthat theclientisclearlyuncomfortable

withwillnotlikelyleadtoagoodoutcome intheinvestor'sview investmentconstraintsinclude

theinvestor'sliquidity needs,timehorizon, tax considerations,legalandregulatory

constraints, a n d unique needsandpreferences.

TÀI LIỆU THAM KHẢO

1. Schweser Notes CFA Level 1, Kaplan Schweser, 2011

2. CFA Program Curriculum Level 1, CFA Institute, 2011

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