dess swaps

7/31/2019 Dess Swaps

1/145

DrakeDRAKE UNIVERSITYUNIVERSITEDAUVERGNE

Swaps


2/145

UNIVERSITE

DAUVERGNE

DrakeDrake University

Introduction

An agreement between two parties to exchange cashflows in the future.

The agreement specifies the dates that the cash flows

are to be paid and the way that they are to becalculated.

A forward contract is an example of a simple swap. Witha forward contract, the result is an exchange of cash

flows at a single given date in the future.In the case of a swap the cash flows occur at several

dates in the future. In other words, you can think of aswap as a portfolio of forward contracts.


3/145

UNIVERSITE

DAUVERGNE


Mechanics of Swaps

The most commonly used swap agreement is anexchange of cash flows based upon a fixed andfloating rate.

Often referred to a plain vanilla swap, theagreement consists of one party paying a fixedinterest rate on a notional principal amount inexchange for the other party paying a floating

rate on the same notional principal amount for aset period of time.

In this case the currency of the agreement is thesame for both parties.


4/145

UNIVERSITE

DAUVERGNE


Notional Principal

The term notional principal implies that theprincipal itself is not exchanged. If it was

exchanged at the end of the swap, the exactsame cash flows would result.


5/145

UNIVERSITE

DAUVERGNE


An Example

Company B agrees to pay A 5% per annum on anotional principal of $100 million

Company A Agrees to pay B the 6 month LIBORrate prevailing 6 months prior to each paymentdate, on $100 million. (generally the floating rateis set at the beginning of the period for which it

is to be paid)


6/145

UNIVERSITE

DAUVERGNE


The Fixed Side

We assume that the exchange of cash flowsshould occur each six months (using a fixed rate

of 5% compounded semi annually).Company B will pay:

($100M)(.025) = $2.5 Million

to Firm A each 6 months.


7/145

UNIVERSITE

DAUVERGNE


Summary of Cash Flowsfor Firm B

Cash Flow Cash Flow Net

Date LIBOR Received Paid Cash Flow

3-1-98 4.2%

9-1-98 4.8% 2.10 2.5 -0.4

3-1-99 5.3% 2.40 2.5 -0.1

9-1-99 5.5% 2.65 2.5 0.15

3-1-00 5.6% 2.75 2.5 0.259-1-00 5.9% 2.80 2.5 0.30

3-1-01 6.4% 2.95 2.5 0.45


8/145

UNIVERSITE

DAUVERGNE


Swap Diagram

LIBOR

Company A Company B

5%


9/145

UNIVERSITE

DAUVERGNE


Offsetting Spot Position

Company A

Borrows (pays) 5.2%

Pays LIBOR

Receives 5%

Net LIBOR+.2%

Company B

Borrows (pays) LIBOR+.8%

Receives LIBOR

Pays 5%

Net 5.8%

Assume that A has a commitment to borrow at a fixed rate of

5.2% and that B has a commitment to borrow at a rate of

LIBOR + .8%


10/145

UNIVERSITE

DAUVERGNE


Swap Diagram

Company A Company B

The swap in effect transforms a fixed rate liability

or asset to a floating rate liability or asset (andvice versa) for the firms respectively.

5.2% LIBOR+.8%

LIBOR +.2% 5%

LIBOR

5.8%


11/145

UNIVERSITE

DAUVERGNE


Role of Intermediary

Usually a financial intermediary works toestablish the swap by bring the two parties

together.The intermediary then earns .03 to .04% perannum in exchange for arranging the swap.

The financial institution is actually entering into

two offsetting swap transactions, one with eachcompany.


12/145

UNIVERSITE

DAUVERGNE


Swap Diagram

Co A FI Co B

A pays LIBOR+.215%B pays 5.815%

The FI makes .03%

5.2% LIBOR+.8%

5.015%

LIBOR

4.985%

LIBOR


13/145

UNIVERSITE

DAUVERGNE


Day Count Conventions

The above example ignored the day countconventions on the short term rates.

For example the first floating payment was listedas 2.10. However since it is a money marketrate the six month LIBOR should be quoted onan actual /360 basis.

Assuming 184 days between payments the actualpayment should be

100(0.042)(184/360) = 2.1467


14/145

UNIVERSITE

DAUVERGNE


Day Count Conventions II

The fixed side must also be adjusted and as aresult the payment may not actually be equal on

each payment date.The fixed rate is often based off of a longermaturity instrument and may therefore uses adifferent day count convention than the LIBOR.

If the fixed rate is based off of a treasury notefor example, the note is based on a different dayconvention.


15/145

UNIVERSITE

DAUVERGNE


Role of the Intermediary

It is unlikely that a financial intermediary will becontacted by parties on both side of a swap atthe same time.

The intermediary must enter into the swapwithout the counter party. The intermediarythen hedges the interest rate risk using interestrate instruments while waiting for a counter

party to emerge.This practice is referred to as warehousingswaps.


16/145

UNIVERSITE

DAUVERGNE


Why enter into a swap?

The Comparative Advantage Argument

Fixed Floating

A 10% 6 mo LIBOR+.3B 11.2% 6 mo LIBOR + 1.0%

Difference between fixed rates = 1.2%Difference between floating rates = 0.7%

B Has an advantage in the floating rate.


17/145


18/145

UNIVERSITE

DAUVERGNE


Spread Differentials

Why do spread differentials exist?

Differences in business lines, credit history, asset

and liabilities, etc


19/145

UNIVERSITE

DAUVERGNE


Valuation of Interest Rate Swaps

After the swap is entered into it can be valued aseither:

A long position in one bond combined with a shortposition in another bond or

A portfolio of forward rate agreements.


20/145

UNIVERSITE

DAUVERGNE


Relationship of Swaps to Bonds

In the examples above the same relationshipcould have been written as

Company B lent company A $100 million at thesix month LIBOR rate

Company A lent company B $100 million at afixed 5% per annum

UNIVERSITE


21/145

UNIVERSITE

DAUVERGNE


Bond Valuation

Given the same floating rates as before the cashflow would be the same as in the swap example.

The value of the swap would then be thedifference between the value of the fixed ratebond and the floating rate bond.

UNIVERSITE


22/145

UNIVERSITE

DAUVERGNE


Fixed portion

The value of either bond can be found bydiscounting the cash flows from the bond (asalways). The fixed rate value is straight forward

it is given as:

where Q is the notional principal and k is thefixed interest payment

nnii trn

i

tr

fix QekeB

1

UNIVERSITE


23/145

UNIVERSITE

DAUVERGNE


Floating rate valuation

The floating rate is based on the fact that it is aseries of short term six months loans.

Immediately after a payment date Bfl is equal tothe notional principal Q. Allowing the time untilthe next payment to equal t1

where k* is the known next payment

1111 * trtr

fl ekQeB

UNIVERSITE


24/145

UNIVERSITE

DAUVERGNE


Swap Value

If the financial institution is paying fixed andreceiving floating the value of the swap is

Vswap = Bfl-Bfix

The other party will have a value of

Vswap = Bfix-Bfl

UNIVERSITE


25/145

UNIVERSITE

DAUVERGNE


Example

Pay 6 mo LIBOR & receive 8%

3 mo 10%

9 mo 10.5%15 mo 11%

Bfix = 4e.-1(.25)+4e-.105(.75)+104e-.11(1.25)=98.24M

Bfloat = 100e-.1(.25)

+ 5.1e-.1(.25)

=-102.5M-4.27 M

UNIVERSITE


26/145

UNIVERSITE

DAUVERGNE


A better valuation

Relationship of Swap value to Forward RteAgreements

Since the swap could be valued as a forward rateagreement (FRA) it is also possible to value theswap under the assumption that the forwardrates are realized.

UNIVERSITE


27/145

UNIVERSITE

DAUVERGNE


To do this you would need to:

Calculate the forward rates for each of the LIBORrates that will determine swap cash flows

Calculate swap cash flows using the forwardrates for the floating portion on the assumptionthat the LIBOR rates will equal the forward rates

Set the swap value equal to the present value of

these cash flows.

UNIVERSITE


28/145

UNIVERSITE

DAUVERGNE


Swap Rate

This works after you know the fixed rate.

When entering into the swap the value of theswap should be 0.

This implies that the PV of each of the two seriesof cash flows is equal. Each party is then willingto exchange the cash flows since they have thesame value.

The rate that makes the PV equal when used forthe fixed payments is the swap rate.

UNIVERSITE


29/145

UNIVERSITE

DAUVERGNE


Example

Assume that you are considering a swap wherethe party with the floating rate will pay the threemonth LIBOR on the $50 Million in principal.

The parties will swap quarterly payments eachquarter for the next year.

Both the fixed and floating rates are to be paid

on an actual/360 day basis.

UNIVERSITE


30/145

UNIVERSITE

DAUVERGNE


First floating payment

Assume that the current 3 month LIBOR rate is3.80% and that there are 93 days in the firstperiod.

The first floating payment would then be

3333.833,490000,000,50360

93038.

UNIVERSITE


31/145

UNIVERSITE

DAUVERGNE


Second floating payment

Assume that the three month futures price onthe Eurodollar futures is 96.05 implying aforward rate of 100-96.05 = 3.95

Given that there are 91 days in the period.

The second floating payment would then be

1111.236,499000,000,50360

910395.

UNIVERSITE


32/145

UNIVERSITE

DAUVERGNE


Example Floating side

PeriodDay

Count

FuturesPrice

Fwd

Rate

Floating

Cash flow

91 3.80

1 93 96.05 3.95 490,833.3333

2 91 95.55 4.45 499,236.1111

3 90 95.28 4.72 556,250.0000

4 91 596,555.5555

UNIVERSITE


33/145

UNIVERSITE

DAUVERGNE


PV of Floating cash flows

The PV of the floating cash flows is thencalculated using the same forward rates.

The first cash flow will have a PV of:

8263.061,486

360

93

038.1

3333.833,490

UNIVERSITE


34/145

UNIVERSITE

DAUVERGNE


PV of Floating cash flows

The PV of the floating cash flows is thencalculated using the same forward rates.

The second cash flow will have a PV of:

4412.495,489

360

910395.1360

93038.1

1111.236,499

UNIVERSITE


35/145

UNIVERSITE

DAUVERGNE


Example Floating side

PeriodDay

Count

Fwd

Rate

Floating

Cash flowPV of Floating CF

91 3.80

1 93 3.95 490,833.3333 486,061.8263

2 91 4.45 499,236.1111 489,495.4412

3 90 4.72 556,250.0000 539,396.1423

4 91 596,555.5555 525,668.5915

UNIVERSITE


36/145

UNIVERSITE

DAUVERGNE


PV of floating

The total PV of the floating cash flows is then thesum of the four PVs:

$2,040,622.0013

UNIVERSITE


37/145

DAUVERGNE


Swap rate

The fixed rate is then the rate that using thesame procedure will cause the PV of the fixedcash flows to have a PV equal to the same

amount.The fixed cash flows are discounted by the samerates as the floating rates.

Note: the fixed cash flows are not the same eachtime due to the changes in the number of days ineach period.

The resulting rate is 4.1294686

UNIVERSITE


38/145

DAUVERGNE


Example: Swap Cash Flows

PeriodDay

Count

Fwd

Rate

Floating

Cash flowFixed CF

91 3.80

1 93 3.95 490,833.3333 533,389.7003

2 91 4.45 499,236.1111 521,918.9541

3 90 4.72 556,250.0000 516,183.5810

4 91 596,555.5555 521,918.9541

UNIVERSITE


39/145

DAUVERGNE


Swap Spread

The swap spread would then be the differencebetween the swap rate and the on the runtreasury of the same maturity.

UNIVERSITE


40/145

DAUVERGNE


Swap valuation revisited

The value of the swap will change over time.

After the first payments are made, the futures

prices and corresponding interest rates havelikely changed.

The actual second payment will be based uponthe 3 month LIBOR at the end of the first period.

Therefore the value of the swap is recalculated.


41/145

UNIVERSITE


42/145

DAUVERGNE


A simple example

Assume that company A pays a fixed rate of 11% in sterling andreceives a fixed interest rate of 8% in dollars.

Let interest payments be made once a year and the principal amountsbe $15 million and L10 Million

Company A Dollar Cash Sterling CashFlow (millions) Flow (millions)

2/1/1999 -15.00 +10.002/1/2000 +1.20 -1.102/1/2001 +1.20 -1.10

2/1/2002 +1.20 -1.102/1/2003 +1.20 -1.102/1/2004 +16.20 -11.10

UNIVERSITE


43/145

DAUVERGNE


Intuition

Suppose A could issue bonds in the US for 8%interest, the swap allows it to use the 15 millionto actually borrow 10million sterling at 11% (Acan invest L 10M @ 11% but is afraid that $ willstrength it wants US denominated investment)

UNIVERSITE


44/145

DAUVERGNE


Comparative Advantage Again

The argument for this is very similar to thecomparative advantage argument presentedearlier for interest rate swaps.

It is likely that the domestic firm has anadvantage in borrowing in its home country.

UNIVERSITE


45/145

DAUVERGNE


Example using comparativeadvantage

Dollars AUD (Australian $)

Company A 5% 12.6%

Company B 7% 13.0%2% difference in $US .4% difference in AUD

UNIVERSITE


46/145

DAUVERGNE


The strategy

Company A borrows dollars at 5% per annum

Company B borrows AUD at 13% per annum

They enter into a swap

Result

Since the spread between the two companies isdifferent for each firm there is the ability of each

firm to benefit from the swap. We would expectthe gain to both parties to be 2 - 0.4 = 1.6%(the differences in the spreads).

UNIVERSITE


47/145

DAUVERGNE


Swap Diagram

Co A FI Co B

A pays 11.9% AUD instead of 12.6% AUDB pays 6.3% $US instead of 7% $US

The FI makes .2%

5% AUD 13%

6.3%

AUD 11.9%

5%

AUD 13%

UNIVERSITE

A G


48/145

DAUVERGNE


Valuation of Currency Swaps

Using Bond Techniques

Assuming there is no default risk the currency

swap can be decomposed into a position in twobonds, just like an interest rate swap.

In the example above the company is long asterling bond and short a dollar bond. The value

of the swap would then be the value of the twobonds adjusted for the spot exchange rate.

UNIVERSITE

DAUVERGNE


49/145

DAUVERGNE


Swap valuation

Let S = the spot exchange rate at the beginningof the swap, BF is the present value of theforeign denominated bond and BD is the present

value of the domestic bond. Then the value isgiven as

Vswap = SBF BD

The correct discount rate would then depend uponthe term structure of interest rates in each

country

UNIVERSITE

DAUVERGNE


50/145

DAUVERGNE


Other swaps

Swaps can be constructed from a large number ofunderlying assets.

Instead of the above examples swaps for floating rates

on both sides of the transaction.The principal can vary through out the life of the swap.

They can also include options such as the ability toextend the swap or put (cancel the swap).

The cash flows could even extend from another assetsuch as exchanging the dividends and capital gainsrealized on an equity index for a fixed or floating rate.

UNIVERSITE

DAUVERGNE


51/145

DAUVERGNE


Beyond Plain Vanilla Swaps

Amortizing Swap -- The notional principal isreduced over time. This decreases the fixedpayment. Useful for managing mortgageportfolios and mortgage backed securities.

Accreting Swap The notional principal increasesover the life of the swap. Useful in construction

finances. For example is the builder draws downan amount of financing each period for a numberof periods.

UNIVERSITE

DAUVERGNE


52/145

DAUVERGNE


Beyond Plain Vanilla

You can combine amortizing and accreting swapsto allow the notional principal to both increaseand decrease.

Seasonal Swap -- Increase and decrease ofnotional principal based of f of designated plan

Roller Coaster Swap -- notional principal firstincreases the amortizes to zero.

UNIVERSITE

DAUVERGNE


53/145

DAUVERGNE


Off Market Swap

The interest rate is set at a rate above marketvalue.

For example the fixed rate may pay 9% whenthe yield curve implies it should pay 8%.

The PV of the extra payments is transferred as aone time fee at the beginning of the swap (thus

keeping the initial value equal to zero)

UNIVERSITE

DAUVERGNEF d d


54/145

D AUVERGNE


Forward andExtension Swaps

Forward swap the payments are agreed tobegin at some point in time in the future

If the rates are based on the current forwardrate there should not be any exchange ofprincipal when the payments begin. Other wiseit is an off market swap and some form of

compensation is neededExtension Swap an agreement to extend thecurrent swap (a form of forward swap)

UNIVERSITE

DAUVERGNE


55/145

D AUVERGNE


Basis Swaps

Both parties pay floating rates based upondifferent indexes.

For example one party may pay the three monthLIBOR while the other pays the three month T-Bill.

The impact is that while the rates generally move

together the spread actually widens and narrows,Therefore the return on the swap is based uponthe spread.

UNIVERSITE

DAUVERGNE


56/145

D AUVERGNE


Yield Curve Swaps

Both parties pay floating but based off ofdifferent maturities. Is similar to a basis swapsince the effective result is based on the spreadbetween the two rates. A steepening curve thusbenefits the payer of the shorter maturity rate.

This is utilized by firms with a mismatch of

maturities in assets and liabilities (banks forexample). It can hedge against changes in theyield curve via the swap.

UNIVERSITE

DAUVERGNE


57/145

D AUVERGNE


Rate differential (diff) swap

Payments tied to rate indexes in differentcurrencies, but payments are made in only onecurrency.

UNIVERSITE

DAUVERGNE


58/145

D AUVERGNE


Corridor Swap

Payments obligation only occur in a given rangeof rates. For example if the LIBOR rate isbetween 5 and 7%.

The swap is basically a tool based on theuncertainty of rates.

UNIVERSITE

DAUVERGNE


59/145

D AUVERGNE


Flavored Currency Swaps

The basic currency swap can be modified similarto many of the modifications just discussed.

Swaps may also be combined to produce desiredoutcomes.

CIRCUS Swap (Combined interest rate andcurrency swap). Combines two basic swaps

UNIVERSITE

DAUVERGNE


60/145

D AUVERGNE


Circus Swap Diagram

LIBOR

Company A Company B

5% US$6% German Marks

Company A Company C

LIBOR

UNIVERSITE

DAUVERGNE


61/145

D AUVERGNE


Circus Swap Diagram

Company B

Company A 5% US$

6% German Marks

Company C

UNIVERSITE

DAUVERGNE


62/145

D AUVERGNE


Swapation

An option on a swap that specifies the tenor,notional principal fixed rate and floating rate

Price is usually set a a % of notional principal

Receiver Swapation

The holder has the right to enter into a swap asthe fixed rate receiver

Payer SwapationThe holder has the right to enter into a particularswap as the fixed rate payer.

UNIVERSITE

DAUVERGNESwapation as


63/145

D AUVERGNE


Swapation ascall (or put) Options

Receiver swapation similar to a call option on abond. The owner receives a fixed payment (likea coupon payment) and pays a floating rate (the

exercise price)

Payer swapation if exercised the owner ispaying a stream similar to the issue of a bond.

UNIVERSITE

DAUVERGNE


64/145

UV GN


In-the-Money Swapations

A receiver swapation is in the money if interestrates fall. The owner is paying a lower fixed ratein exchange for the fixed rate specified in the

contract.

Similarly a payer swapation is generally in themoney if interest rates increase since the owner

will receive a higher floating rate.

UNIVERSITE

DAUVERGNE


65/145


When to Exercise

The owner of the receiver swapation shouldexercise if the fixed rate on the swap underlyingthe swapation is greater than the market fixed

rate on a similar swap. In this case the swap ispaying a higher rate than that which is availablein the market.

UNIVERSITE

DAUVERGNEA fixed income


66/145


A fixed incomeswapation example

Consider a firm that has issued a corporate bondwith a call option at a given date in the future.

The firm has paid for the call option by being

forced to pay a higher coupon on the bond thanon a similar noncallable bond.

Assume that the firm has determined that it doesnot want to call the bond at its first call date at

some point in the future.The call option is worthless to the firm, but itshould theoretically have value.

UNIVERSITE

DAUVERGNECapturing the


67/145


Capturing thevalue of the call

The firm can sell a receiver swapation with termsthat match the call feature of the bond.

The firm would receive for this a premium that isequal to the value of the call option.

UNIVERSITE

DAUVERGNE


68/145


Example

Assume the firm has previously issued a 9%coupon bond that makes semiannual paymentsand matures in 7 years with a face value of $150

Million.

The bond has a call option for one year fromtoday.

UNIVERSITE

DAUVERGNE


69/145


Example continued

The firm can sell a European Receiver Swapation with anexpiration in one year. The Swapation terms are forsemiannual payments at a fixed rate of 9% in exchange forfloating payments at LIBOR.

The firm receives a premium for the swapation equal to afixed percentage of the $150 Million notional value (equalto the value of the call option).

The firm can keep the premium but has a potentialobligation in one year if the counter party exercises theswap.

UNIVERSITE

DAUVERGNE


70/145


Example Continued

In one year the fixed rate for this swap is 11%

The option will expire worthless since the ownercan earn a fixed 11% on a similar swap.

The firm gets to keep the premium.

UNIVERSITE

DAUVERGNE


71/145


Example Continued

If in one year the fixed rate of interest on asimilar swap is 7% the owner will exercise theswap since it calls for a 9% fixed rate.

The firm can call the bond since rates havedecreased. It can finance the call by issuing afloating rate note at LIBOR for the term of theswap.

The floating rate side of the swap pays for thenote and the firm is still paying the original 9%fixed, but it has also received the premium on theswapation

UNIVERSITE

DAUVERGNEExtendible and Cancelable


72/145


Extendible and Cancelableswaps

Similar to extension swaps except extensionswaps represent a firm commitment to extendthe swap. An extendible swap has the option to

extend the agreement.

Arranged via a plain vanilla swap an a swapation.

UNIVERSITE

DAUVERGNE


73/145


Extendible and Cancelable

Extendible pay fixed swap

= plain vanilla pay fixed plus payer swapation

Extendible Receive-Fixed Swap

= plain vanilla receive fixed swap + receiverswapation

Cancelable Pay Fixed Swap

= plain vanilla pay fixed swap + receiver swapation

Cancelable Receive Fixed Swap

=plain vanilla receive fixed swap + payableswapation

UNIVERSITE

DAUVERGNECreating synthetic


74/145


Creating syntheticsecurities using swaps

The origins of the swap market are based in thedebt market.

Previously there had been restrictions on the flowof currency.

A parallel loan market developed to get aroundrestrictions on the flow of currency from one

country to another, Especially restrictionsimposed by the Bank of England.

UNIVERSITE

DAUVERGNE


75/145


The Parallel Loan Market

Consider two firms, one British and oneAmerican, each with subsidiaries in bothcountries.

Assume that the free-market value of the poundis L1=$1.60 and the officially required exchangerate is L1=$1.44.

Assume the British Firm wants to undertake aproject in the US requiring an outlay of$100,000,000.

UNIVERSITE

DAUVERGNE


76/145


Parallel Loan Market

The cost of the project at the official exchangerate is 100,000,0000/1.44 = L69,444,000

The cost of the project at the free marketexchange rate is 100,000,0000/1.60 =L62,500,000

The firm is paying an extra L7,000,000

UNIVERSITE

DAUVERGNE


77/145


Parallel Loan Market

The British firm lends L62,500,000 pounds to theUS subsidiary operating in England at a floatingrate based on LIBOR and The US firm lends

$100,000,000 to the British firm at a fixed rate of7% in the US the official exchange rate isavoided.

The result is a basic fixed for floating currency

swap. (In this case each loan is separatedefault on one loan does not constitute defaulton the other).

UNIVERSITE

DAUVERGNE


78/145


Synthetic Fixed Rate Debt

A firm with an existing floating rate debt caneasily transform it into a fixed rate debt via aninterest rate swap.

By receiving floating and paying fixed, the firmnets just a spread on the floating transactioncreating a fixed rate debt (the rate paid on the

swap plus the spread)

UNIVERSITE

DAUVERGNE


79/145


Synthetic Floating Rate Debt

Combining a fixed rate debt with a pay floating /receive fixed rate swap easily transforms thefixed rate. Again the fixed rates cancel out (or

result in a spread) leaving just a floating rate.

UNIVERSITE

DAUVERGNE


80/145


Synthetic Callable Debt

Consider a firm with an outstanding fixed ratedebt without any call option.

It can create a call option. If it had a call optionin place it would retire the debt if called. Look atthis as creating a new financing need (you needto finance the retirement of the debt.)

You want the ability to call the bond but not theobligation to do so.

UNIVERSITE

DAUVERGNE

h ll bl b


81/145


Synthetic Callable Debt

Buying a receiver swapation allows the firm toreceive a fixed rate, canceling out its currentfixed rate obligation.

It will pay a new floating rate as part of the swap(similar to financing the call with new floatingrate debt).

UNIVERSITEDAUVERGNE

h ll bl b


82/145


Synthetic non callable Debt

Basically the earlier example swapations.

UNIVERSITEDAUVERGNE

S h i D l C D b


83/145


Synthetic Dual Currency Debt

Dual Currency bond principal payments aredenominated in one currency and couponpayments denominated in another currency.

Assume you own a bond that makes itspayments in US dollars, but you would prefer thecoupon payments to be in another currency with

the principal repayment in dollars.A fixed for fixed currency swap would allow thisto happen

UNIVERSITEDAUVERGNE

S h i D l C D b


84/145


Synthetic Dual Currency Debt

Combine a receive fixed German marks and payUS dollars swap with the bond.

The dollars received from the bond are used topay the dollar commitment on the swap. Youthen just receive the German Marks.

UNIVERSITEDAUVERGNE

All i C t


85/145


All in Cost

The IRR for a given financing alternative, itincludes all costs including administration,flotation , and actual cash flows.

The cost is simply the rate that makes the PV ofthe cash flows equal to the current value of theborrowing.

UNIVERSITEDAUVERGNECompare two


86/145


Compare twoalternative proposals

A 10 year semiannual 7% coupon bond with aprincipal of $40 million priced at par

A loan of $40 million for 10 years at a floatingrate of LIBOR + 30 Bps reset every six monthswith the current LIBOR rate of 6.5%. Plus a swaptransforming the loan to a fixed rate

commitment. The swap will require the firm topay 6.5% fixed and receive floating.

UNIVERSITEDAUVERGNE

All i t


87/145


All in cost

The bond has a all in cost equal to its yield tomaturity, 7%

Assuming the firm must pay $400,000 to enter

into the swap so it only nest $39,600,000.Today. The net interest rate it pays is 6.8%implying semiannual payments of(.068/2)(40,000,000) = $1,360,000 plus a final

payment of 40,000,000. This implies a rate of.034703 every six months or .069406 every year.

UNIVERSITEDAUVERGNEBF Goodrich and Rabobank


88/145


BF Goodrich and RabobankAn early swap example*

In the early 1980s BF Goodrich needed to raisenew funds, but its credit rating had beendowngraded to BBB-. The firm needed

$50,000,000 to fund continuing operations.They wanted long term debt in the range of 8 to10 years and a fixed rate. Treasury rates wereat 10.1 % and BF Goodrich anticipated paying

approximately 12 to 12.5%

* taken from Kolb - Futures Options and Swaps

UNIVERSITEDAUVERGNE

R b b k


89/145


Rabobank

Rabobank was a large Dutch bankingorganization consisting of more than 1,000 smallagricultural banks. The bank was interested in

securing floating rate financing on approximately$50,000,000 in the Eurobond market.

With a AAA rating Rabobank could issue fixed

rate in the Eurobond market for approximately11% and for a floating rate of LIBOR plus .25%

UNIVERSITEDAUVERGNE

Th I t di


90/145


The Intermediary

Salomon Brothers suggested a swap agreementto each party.

This would require BF Goodrich to issue the firstpublic debt tied to LIBOR in the United States.Salomon Brothers felt that there would be amarket for the debt because of the increase in

deposits paying a floating rate due toderegulation.

UNIVERSITEDAUVERGNE

P bl


91/145


Problems

Rabobank was interested in the deal,but fearfulof credit risk. A direct swap would expose it tocredit risk. Without an active swap market it was

common for swaps to be arranged between thetwo counter parties.

The two finally reached an agreement to use

Morgan Guaranty as an intermediary.

UNIVERSITEDAUVERGNE

The ag eement


92/145


The agreement

BF Goodrich issued a noncallable 8 year floatingrate note with a principal value of $50,000,000paying the 3 month LIBOR rate plus .5%

semiannually. The bond was underwritten bySalomon.

Rabobank issued a $50,000,000 non callable 8

year Eurobond with annual payments of 11%Both entered into a swap with Morgan Guaranty

UNIVERSITEDAUVERGNE

The swaps


93/145


The swaps

BF Goodrich promised to pay Morgan Guaranty5,500,000 each year for eight years (matchingthe coupon on the Rabobanks debt). Morgan

agreed to pay BF Goodrich a semi annual ratetied to the 3 month LIBOR equal to:.5(50,000,000)(3 mo LIBOR-x)

x represents an undisclosed discountRabobank received $5,500,000 each year for 8years and paid semi annul payments of LIBOR-x

UNIVERSITEDAUVERGNE

The intermediary role


94/145


The intermediary role

The two swap agreements were independent ofeach other eliminating the credit risk concerns ofRabobank.

Morgan received a one time fee of $125,000 paidby BF Goodrich plus an annual fee of 8 to 37 Bp($40,000 to $185,000) also paid by BF Goodrich.

UNIVERSITEDAUVERGNE

BF Goodrich


95/145


BF Goodrich

Assuming that the discount from LIBOR was 50Bp and that the service fee was 22.5 BP (themidpoint of the range). BF Goodrich paid an all

in cost of 11.9488 % annually compared to 12 to12.5% if they had issued the debt on their own.

UNIVERSITEDAUVERGNE

D kRabobanks Position


96/145


Rabobank s Position

At the time of financing it would have paid LIBORplus 25 to 50 Bp. Given that it paid no fees andthe fixed rate canceled out it ended up paying

LIBOR - x.

UNIVERSITEDAUVERGNE

D kSecuring financing


97/145


Securing financing

BF Goodrich was able to secure financing via itsuse of the swaps market, this is a common useof the market.

The example provides a good illustration of theidea of the comparative advantage argumentswe discussed earlier.

UNIVERSITEDAUVERGNE

D kA Second Example of securing


98/145


p gfinancing*

It is possible for swaps to increases accessibilitytwo the debt market

Mexcobre (Mexicana de Corbre) is the copper

exporting subsidiary of Grupo Mexico. In the late1980s it would have had a difficult timeborrowing in international credit markets due toconcerns or default risk

However it was able to borrow $210 million for38 months from a group of banks led by Paribas

* from Managing Financial Risk by Smithson, Smith and Wilford

UNIVERSITEDAUVERGNE

D kThe original loan


99/145


The original loan

The banks lent the firm $210 Million at a fixedrate of 11.48%. The debt replaced borrowingfrom the Mexican government which had cost the

firm 23%.A Belgian company Sogem agreed to buy 4,000tons of copper per month at the prevailing spotrate from Mexcobre making payments into an

escrow account in New York that was used toservice the debt with any extra funds returned toMexcobre.

UNIVERSITEDAUVERGNE

D k


100/145


Banks Escrow

Mexcobre SOGEM4,000 tons of copper

per month

Cash based

on Spot Price

Quarterly payments of 11.48%

interest plus principal

$210

million

loan

Excess cash

if it builds

up

UNIVERSITEDAUVERGNE

D kSwaps


101/145


Swaps

Swaps were added between Paribas and theescrow account to hedge the price risk of copperand between Paribas and the banks to change

the banks position to a floating rate

Paribas


102/145

Banks Escrow

Mexcobre SOGEM4,000 tons of copper

per month

Cash per

ton based

on Spot Price

Quarterly payments of 11.48%

interest plus principal

$210

million

loan

Excess cash

if it builds

up

Paribas

Spot

Priceper ton

FloatingFixed $2,000

per ton

UNIVERSITEDAUVERGNE

D kDuration of Interest


103/145

DrakeDrake UniversityRate Swaps*

A plain vanilla swap can be valued as a portfolioof two bonds, therefore the duration of the swapshould equal the duration of the bond portfolio.

The duration can be either positive or negativedepending on the side of the swap

* Kolb, Futures Options and Swaps

UNIVERSITEDAUVERGNE

D kDuration of Swaps


104/145


Duration of Swaps

Duration of Receive Fixed Swap =

Duration of Underlying coupon bond

- Duration of underlying floating Rate Bond

>0

Duration of Pay Fixed Swap =

Duration of underlying floating Rate Bond

- Duration of Underlying coupon bond


105/145


Example

Consider a swap with a semiannual fixed rate of7% and a floating rate that resets each sixmonths.

The duration of the fixed rate side (assuming a100 notional principal) is 5.65139 years

Duration of Receive Fixed Swap

=5.65139-0.5=5.15369Duration of Pay Fixed Swap

=0.5-5.65139=-5.15369

UNIVERSITEDAUVERGNE

DrakeCalculating Duration


106/145


Calculating Duration

Duration of floating rate security is equal to thetime between resetting of the rate.

Therefore the duration of the swap actually

depends upon the duration of the fixed rate side.

Receive Fixed rate swaps will then usuallylengthen the duration of an existing position

while pay fixed swaps will shorten the duration ofan existing position.

UNIVERSITEDAUVERGNE

DrakeImmunization with Swaps


107/145


Immunization with Swaps

Swaps can be used to hedge interest rate risk byimpacting the duration of the assets andliabilities on the balance sheet.

Going to look at a fictional financial services firmFSF

UNIVERSITEDAUVERGNE

DrakeBalance Sheet for FSF


108/145


Balance Sheet for FSF

AssetsCash $7,000,000

Marketable Sec $18,000,000

(6 mo mat Yield 7%)

Amortizing loans $130,467,133

(10 yr avg mat

semiannual

8% avg yield)

Total Assets $1555,467,133

Liabilities6mo money mkt $75,000,000

(avg yield 6%)

Floating Rate Notes $40,000,000(5 yr mat7.3% yld semi)

Coupon Bond $24,111,725

(10 yr semi 6.5% coup

$25,000,000 par, 7% YTM

Net worth $16,355,408

Total Liab & NW $155,467,133

UNIVERSITEDAUVERGNE

DrakeBasic Duration


109/145


Basic Duration

iassetofDurationMacaulayDa

AssetsAllofValueMarket

Assetwwhere

DawDAPortfolioAssetofDurationWeighted$

i

ii

i

N

1ii

jLiabilityofDurationMacaulayDl

sLiabilitieAllofValueMarket

Assetwwhere

DlwDLPortfolioLiabilityof

DurationWeighted$

j

j

j

j

N

1j

j

UNIVERSITEDAUVERGNE

DrakeDuration


110/145


Duration

Assets

Duration

Cash 0.00

Marketable Sec 0.500

Amortizing loans 4.604562

Total Duration

(7,000,000/155,467,133)0.000

+(18,000,000/155,467,133)0.500+(130,467,133/155,467,133)4.605

3.922013

Liabilities

Duration

6mo money mkt 0.5000

Floating Rate Notes 0.5000

Coupon Bond 7.453369

Total Duration

(75,000,000/155,467,133)0.500

+(40,000,000/155,467,133)0.500+(24,111,725/155,467,133)7.45337

1.705202

UNIVERSITEDAUVERGNE

DrakeHedging the


111/145

DrakeDrake Universityportfolios separately

It is easy to use duration to hedge the interestrate risk of the portfolio.

The idea is to construct a portfolio with a

duration of zero.Let MVi be the market value and Di be theDuration of the assets (A), liabilities (L) orhedge vehicle (H) then

MVA(DA)+MVH(DH) = 0and

MVL(DL)+MVH(DH) = 0

UNIVERSITEDAUVERGNE

DrakeSwap notional value


112/145


Swap notional value

Given the duration of the hedge (a swap) it isthen possible to solve for a notional value (ormarket value) of the swap that would make the

portfolio duration zero.Previously we found the duration of a swap:

Duration of Receive Fixed Swap

=5.65139-0.5=5.15369Duration of Pay Fixed Swap

=0.5-5.65139=-5.15369

UNIVERSITEDAUVERGNE

DrakeAsset Hedge


113/145


Asset Hedge

The asset can then be hedged by solving for thenotional value (MVH) of the pay fixed swap

MVA(DA)+MVH(DH) = 0

155,467,133(3.922)+(-5.15369)(MVH) =0

MVH=$118,365,451

UNIVERSITEDAUVERGNE

DrakeLiability Hedge


114/145


Liability Hedge

The liabilities can then be hedged by solving forthe notional value (MVH) of the receive fixedswap

MVL(DL)+MVH(DH) = 0

(-139,111,725)(1.705202)+(5.15369)(MVH) =0

MVH=$46,048,651

UNIVERSITEDAUVERGNE

DrakeHedging Assets andLi bili i h


115/145

DrakeDrake UniversityLiabilities together

The entire balance sheet can be hedged with oneinterest rate swap by using GAP analysis.

UNIVERSITEDAUVERGNE

DrakeStatic GAP Analysis

(Th i i d l)


116/145

DrakeDrake University(The repricing model)

Repricing GAP

The difference between the value of interestsensitive assets and interest sensitive liabilities of

a given maturity.Measures the amount of rate sensitive (asset orliability will be repriced to reflect changes ininterest rates) assets and liabilities for a given

time frame.

UNIVERSITEDAUVERGNE

DrakeGAP Analysis


117/145


GAP Analysis

Static GAP-- Goal is to manage interest rateincome in the short run (over a given period oftime)

Measuring Interest rate risk calculating GAPover a broad range of time intervals provides a

better measure of long term interest rate risk.

UNIVERSITEDAUVERGNE

DrakeInterest Sensitive GAP


118/145


Interest Sensitive GAP

Given the Gap it is easy to investigate thechange in the net interest income (NII) of the

financial institution.

sLiabilitieSensistiveRate-AssetsSensistiveRateGAP

R)(GAP)(NII

Rates)inge(GAP)(ChanNIIinChange

UNIVERSITEDAUVERGNE

DrakeExample


119/145


Example

Over next 6 Months:

Rate Sensitive Liabilities = $120 million

Rate Sensitive Assets = $100 Million

GAP = 100M 120M = - 20 Million

If rate are expected to decline by 1%

Change in net interest income

= (-20M)(-.01)= $200,000

UNIVERSITEDAUVERGNE

DrakeGAP Analysis


120/145


GAP Analysis

Asset sensitive GAP (Positive GAP)

RSA RSL > 0

If interest rates h NII will h

If interest rates i NII will iLiability sensitive GAP (Negative GAP)

RSA RSL < 0

If interest rates h NII will i

If interest rates i NII will h

Would you expect a commercial bank to beasset or liability sensitive for 6 mos? 5 years?

UNIVERSITEDAUVERGNE

DrakeImportant things to note:


121/145


Important things to note:

Assuming book value accounting is used -- onlythe income statement is impacted, the bookvalue on the balance sheet remains the same.

The GAP varies based on the bucket or timeframe calculated.

It assumes that all rates move together.

UNIVERSITEDAUVERGNE

DrakeSteps in Calculating GAP


122/145


p g

Select time Interval

Develop Interest Rate Forecast

Group Assets and Liabilities by the time interval(according to first repricing)

Forecast the change in net interest income.

UNIVERSITEDAUVERGNE

DrakeAlternative measures of GAP


123/145

a eDrake University

Cumulative GAP

Totals the GAP over a range of of possiblematurities (all maturities less than one year for

example).Total GAP including all maturities

UNIVERSITEDAUVERGNE

DrakeOther useful measures using

GAP


124/145

Drake UniversityGAP

Relative Interest sensitivity GAP (GAP ratio)

GAP / Bank Size

The higher the number the higher the risk that is

present

Interest Sensitivity Ratio

SensitiveAsset1

SensitiveLiability1

sLiabilitieSensitiveRate

AssetsSensitiveRate

UNIVERSITEDAUVERGNE

DrakeWhat is Rate Sensitive


125/145

Drake University

Any Asset or Liability that matures during thetime frame

Any principal payment on a loan is rate sensitive

if it is to be recorded during the time period

Assets or liabilities linked to an index

Interest rates applied to outstanding principal

changes during the interval

UNIVERSITEDAUVERGNE

DrakeUnequal changes in interest

rates


126/145

Drake Universityrates

So far we have assumed that the change thelevel of interest rates will be the same for bothassets and liabilities.

If it isnt you need to calculate GAP using therespective change.

Spread effect The spread between assets and

liabilities may change as rates rise or decrease

)R(RSL)(-)R(RSA)(NII liabiltiesassets

UNIVERSITEDAUVERGNE

DrakeStrengths of GAP


127/145

Drake University

g

Easy to understand and calculate

Allows you to identify specific balance sheet

items that are responsible for risk

Provides analysis based on different time frames.

UNIVERSITEDAUVERGNE

DrakeWeaknesses of Static GAP


128/145

Drake University

Market Value Effects

Basic repricing model the changes in marketvalue. The PV of the future cash flows should

change as the level of interest rates change.(ignores TVM)

Over aggregation

Repricing may occur at different times within thebucket (assets may be early and liabilities latewithin the time frame)

Many large banks look at daily buckets.

UNIVERSITEDAUVERGNE

DrakeWeaknesses of Static GAP


129/145

Drake University

Runoffs

Periodic payment of principal and interest that canbe reinvested and is itself rate sensitive.

You can include runoff in your measure of ratesensitive assets and rate sensitive liabilities.

Note: the amount of runoffs may be sensitive torate changes also (prepayments on mortgages forexample)

UNIVERSITEDAUVERGNE

DrakeWeaknesses of GAP


130/145

Drake University

Off Balance Sheet Activities

Basic GAP ignores changes in off balance sheetactivities that may also be sensitive to changes in

the level of interest rates.Ignores changes in the level of demand deposits

UNIVERSITEDAUVERGNE

DrakeBasic Duration Gap


131/145

Drake University

p

Duration Gap

DLDADGAPBasic

PortfolioLibailityofDurationWeighted$

PortfolioAssetofDurationWeighted$DGAPBasic

UNIVERSITEDAUVERGNE

DrakeBasic DGAP


132/145

Drake University

If the Basic DGAP is +

If Rates h

i in the value of assets > i in value of liab

Owners equity will decrease

If Rate i

h in the value of assets > h in value of liab

Owners equity will increase

UNIVERSITEDAUVERGNE

DrakeBasic DGAP


133/145

Drake University

If the Basic DGAP is (-)

If Rates h

i in the value of assets < i in value of liab

Owners equity will increase

If Rate i

h in the value of assets < h in value of liab

Owners equity will decrease

UNIVERSITEDAUVERGNE

DrakeBasic DGAP


134/145

Drake University

Does that imply that if DA = DL the financialinstitution has hedged its interest rate risk?

No, because the $ amount of assets > $ amountof liabilities otherwise the institution would beinsolvent.

UNIVERSITEDAUVERGNE

DrakeDGAP


135/145

Drake University

Let MVL = market value of liabilities and MVA =market value of assets

Then to immunize the balance sheet we can use

the following identity:

MVA

MVLDLDADGAP

MVA

MVLDLDA

UNIVERSITEDAUVERGNE

DrakeDGAP calculation


136/145

Drake University

396201.2

133,467,155

725,111,139705202.1922013.3DGAP

MVA

MVLDLDADGAP

UNIVERSITEDAUVERGNE

DrakeHedging with DGAP


137/145

Drake University

The net cash flows represented on the balancesheet have the same properties as a longposition in a bond with a duration of 2.396201.

We can hedge using our equation from beforeand the duration of the interest rate swap.

UNIVERSITEDAUVERGNE

DrakeD k U i i

Hedging with DGAP


138/145

Drake University

Since the duration of our position is positive wewant the duration of the hedge to be negative.This requires the pay fixed swap from before

with a notional value equal to MVH below.

MVi(Di)+MVH(DH) = 0

$155,467,725(2.396201)+(-5.151369)MVH=0MVH=$72,316,800

UNIVERSITEDAUVERGNE

DrakeD k U i it

DGAP and owners equity


139/145

Drake University

Let MVE = MVAMVL

We can find MVA &MVL using duration

From our definition of duration:

MVLy1

y-DLMVL

MVAy1

y

-DAMVA

formulatheApplyingPi)(1

iDP

UNIVERSITEDAUVERGNE

DrakeD k U i it


140/145

Drake University

MVAy1

y-DGAPMVE

MVAy1

y

MVA

MVL(DL)-(DA)-

y1y(DL)MVL-(DA)MVA-

MVLy1

yDL--MVA

y1

y-DA

MVL-MVAMVE

UNIVERSITEDAUVERGNE

DrakeDrake Uni ersit

DGAP Analysis


141/145

Drake University

If DGAP is (+)

An h in rates will cause MVE to i

An i in rates will cause MVE to h

If DGAP is (-)

An h in rates will cause MVE to h

An i in rates will cause MVE to i

The closer DGAP is to zero the smaller thepotential change in the market value of equity.

UNIVERSITEDAUVERGNE


Weaknesses of DGAP


142/145

Drake University

It is difficult to calculate duration accurately(especially accounting for options)

Each CF needs to be discounted at a distinct rate

can use the forward rates from treasury spotcurve

Must continually monitor and adjust duration

It is difficult to measure duration for non interestearning assets.

UNIVERSITEDAUVERGNE


More General Problems


143/145

Drake University

Interest rate forecasts are often wrong

To be effective management must beat the abilityof the market to forecast rates

Varying GAP and DGAP can come at the expenseof yield

Offer a range of products, customers may notprefer the ones that help GAP or DGAP Need tooffer more attractive yields to entice thisdecreases profitability.

UNIVERSITEDAUVERGNE


Changing Duration


144/145

Drake University

You can also manipulate the duration of yourcash flows. This allows you to lower yourinterest rate sensitivity instead of eliminating it.

Let DG* be the desired duration gap, DG be thecurrent duration gap, DS be the duration of theSwap, and MVH* be the notional value ofrequired for the swap.

AssetsTotal

MVDDD

*H

SG*G

UNIVERSITEDAUVERGNE


Decreasing Duration GAPto One year


145/145

Drake Universityto One year

The negative sign just indicate that we need a payfi d (th d ti ld th b ti

025,137,42MV

33$155,467,1

MV

15369.5396201.20.1

AssetsTotal

MVDDD

*H

*H

*H

SG*G

dess swaps

Documents