tm interest rate swap

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1

TREASURY MANAGEMENT

Chapter 14

Interest Rate Swap

Swaps

Two parties exchange recurring payments (most

commonly)

the feature of recurring payments distinguishes aswap from a forward contract

but, some swaps involve only a single exchange(Thus, in practice it’s a swap if it is written up on swapdocumentation. That is, it’s a swap if it’s called a swap.)

Similar to series of forward contracts

Common types:

interest rate, currency, equity, commodity

This class introduces interest rate swaps

Note: LIBOR is London Interbank Offered Rate

Fixed-Rate

Payer

Fixed-Rate

Receiver

Floating Rate

(LIBOR)

X Notional Principal

Fixed Rate

of 7.00%

X Notional

Principal

Cash flow diagram of interest rate swap



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Basic facts

Payments based on indices: interest rates (most common)

currency prices (actually an exchange of currencies)

commodity prices

equity prices or returns

Traded in “over-the-counter” markets -large dealers include: large U.S. commercial banks

large U.S. investment banks

some European banks (e.g. Swiss banks, DeutscheBank)

virtually all major banks do at least some swapsbusiness

Interest rates used as indices

3-month and 6-month LIBOR mostcommon

But also:

3-month U.S. Treasury bill yield

CMT (constant maturity Treasury) yields

commercial paper rates

almost any rate is possible

And of course, there are interest rateswaps in other currencies

Relevant parts of a swap confirmation

Contracting Parties: Little End-User (LEU) and Big Swap Dealer(BSD), with a guarantee to be provided by BigSwap Dealer Parent Corp.

Notional Amount: See Schedule A

Trade Date: January 18, 1989

Effective Date: January 20, 1989

Termination Date: January 15, 1992

Fixed Amounts:

Fixed Rate Payor: LEU

Fixed Rate PayorParyment Dates: Each January 15, April 15, July 15 and October

15 starting with April 15, 1989; subject toadjustment in accordance with the FollowingDay Banking Convention.

Fixed Rate and FixedRate Day Count Fraction: 10.05%, 30/360

(First page would be a cover letter; in addition, a swap with any but the simplest features

might include a few pages of definitions of the terms which appear in the confirmation.)



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Parts of a swap confirmation

Floating Amounts:

Floating Rate Payor: BSD

Floating Rate PayorPayment Dates: Each January 15, April 15, July 15 and October

15 starting with April 15, 1989; subject toadjustment in accordance with the FollowingBanking Day Convention.

Floating Rate for InitialCalculation Period: 9.742%

Floating Rate Option: LIBOR

Designated Maturity: 3 month

Adjustment to FloatingRate Option: 3-month LIBOR will be divided by .97 each

calculation period

Floating Rate Day CountFraction: Actual/360

Reset Dates: Two Days Prior to Each Floating Rate PaymentDate

*While this swap uses the Following Banking Day Convention, the use of the Modified Following Banking Day

Convention is more common. With payment dates in the middle of the month, the difference between these two

conventions is not relevant.

*

Parts of a swap confirmation

Schedule A

Date Notional Amount

1-20-89 - 1-15-90 $75,000,0001-16-90 - 1-15-91 70,000,0001-16-91 - 1-15-92 60,000,000

Contracting parties:

LEU is a telecommunications company

BSD is the derivatives subsidiary of an investment bank

Fixed rate payer/floating rate payer: fixed rate payer LUE pays fixed, receives floating

floating rate payer BSD pays floating, receives fixed

Payment dates, floating rate option, designatedmaturity:

payments based on 3-month LIBOR are exchangedevery 3 months

in US, also common to have payments based on 6-month LIBOR exchanged every 6 months

possible for fixed leg to have a different paymentfrequency than floating leg

Notional amount (or principal):

is not exchanged, but simply determines size of payments

*Not in the order in which items appear.

Features of the confirmation:*



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Discussion of the confirmation:Day-count fractions

Floating rate day-count fraction:

USD money market convention: Actual/360

floating leg generally follows money marketconvention in that currency (Act/360 orAct/365)

Fixed rate day count fraction:

U.S. bond market convention: 30/360

convention for fixed leg generally followsbond convention in that currency/region

Aside about day counts

What is the role of day counts?

If you borrow/deposit $10 million for one year inthe interbank market when 1-year LIBOR is 5%:

you do not pay/receive $10(1.05) million at year-end

instead, you pay/receivemillion, where days is the actual number of days in

the period this is actual/360; actual/365 should be clear

In 30/360, when counting days you pretend thateach month has 30 days

)05.0)360 / (days1(10$ +

Payment conventions

What if the payment date specifiedin the contract is a weekend orholiday?

Need to consider two issues:

When is the payment date?

If the payment date is adjusted, do wealso adjust the amount of interestpaid?



6

Payment Date: Following and ModifiedFollowing Business Day Convention

The following business (banking) day conventionstates that the payment date is the first followingday that is a business day.

The modified following business (banking) dayconvention states that the payment date is thefirst following day that is a business day, unlessthat day falls in the next calendar month. In thiscase only, the maturity date will be the firstpreceeding business day.

Most common market practice is to use theModified Following Business Day Convention, butthe Following Business Day Convention issometimes used (for example, in the confirmationabove)

Adjusted versus unadjusted

Example from the fixed leg of a swap:

Fixed rate 6%, 30/360, Modified Following,scheduled payment date is 15 April,

But, 15 April is Saturday

Modified Following ⇒ payment is made/received onMonday, 17 April

Question: How large is the interest payment?

Is it (180/360)×0.06×N ? (N = notionalamount of swap)

Or do we add 2 days to the payment period, i.e. isthe payment (182/360)×0.06×N ?

(If we add 2 days to this payment period, we wouldalso then subtract 2 days from the next paymentperiod)

Adjusted versus unadjusted

Unadjusted: shift payment date, but do not change theamount of the payment

payment = (180/360)×0.06×N

Interest payments on bonds are generally unadjusted, i.e. if thepayment date gets shifted due to a weekend or holiday, thepayment amount is not changed

Adjusted: shift payment date and change the interestaccrual (that is, change the amount of the payment)

payment = (182/360)×0.06×N

Most commonly, but not always, swap payments are adjusted.Swap payments might be unadjusted if the swap is intended toexactly hedge an underlying bond on which payments areunadjusted.



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Discussion of the confirmation:Adjustment to floating rate option

Adjustment to floating rate option: if there is an adjustment to the floating

rate it usually comes in the form of adding or subtracting an amount, e.g.LIBOR + 40 basis points

in fact, the most common “adjustment” is no adjustment, i.e. LIBOR + 0 basispoints or “LIBOR flat”

In this deal, I have no idea why theadjustment comes in the form of dividing by 0.97

Confirmation: Notional amount

Notional amount (orprincipal):

Most commonly thenotional amount is justa number, e.g. $100million

In this swap thenotional amount variesover time because theswap was being usedto hedge a loan with aprincipal amount thatchanged over time asprincipal paymentswere made

Changes in notional amount reflect fact that:

(a) LEU borrowed $75 million(b) repaid $5 million on 15 Jan 1990

(c) Repaid $10 million on 15 Jan 1991

(d) Repaid the remaining $60 million on 15 Jan 1992

ScheduleA

Date Notional Amount

1-20-89- 1-15-90 $75,000,0001-16-90- 1-15-91 70,000,0001-16-91- 1-15-92 60,000,000

Cash flows (from perspective of LEU)

It is crucial to understand that the cash flow on say 7/17/89 is based on LIBOR observedon 4/13/89, …., cash flow on 1/15/92 is based on LIBOR observed on 10/11/91.

Days for Fraction Cash Flow Days for Fraction Cash Flow

Trade P ayment Reset Not ional LIBOR on Floating Float ing Due t o Floati ng Fi xed Fixed F ixed Due t o Fi xed Net C ashDate Date Date Amount reset date Payment Payment Payment Rate Payment Payment Payment Flow

1/18/1989 4/17/1989 $75,000,000 9.7420% 87 0.2417 $1,820,348 10.05% 87 0.24167 -$1,821,563 -$1,2151 /2 0/ 198 9 7/ 17 /1 989 4/ 13 /1 98 9 $7 5, 00 0, 00 0 1 0 .1 875% 9 1 0. 252 8 $1 ,99 1, 11 4 1 0. 05 % 90 0 .2 500 0 - $1 ,8 84 ,37 5 $ 106 ,7 39

1 0/ 16 /1 989 7/ 13 /1 98 9 $ 75 ,00 0, 00 0 8 .8 125% 9 1 0. 252 8 $1 ,72 2, 37 4 1 0. 05 % 89 0 .2 472 2 - $1 ,8 63 ,43 8 - $141 ,0 631/ 15 /1 990 1 0/ 12 /1 98 9 $ 75 ,00 0, 00 0 8 .7 500% 9 1 0. 252 8 $1 ,71 0, 15 9 1 0. 05 % 89 0 .2 472 2 - $1 ,8 63 ,43 8 - $153 ,2 79

4/16/1990 1/ 11/1990 $70,000, 000 8.1875% 91 0. 2528 $1, 493,539 10. 05% 91 0.25278 -$1,778,292 -$284,753

7/16/1990 4/ 12/1990 $70,000, 000 8.4375% 91 0. 2528 $1, 539,143 10. 05% 90 0.25000 -$1,758,750 -$219,6071 0/ 15 /1 990 7/ 12 /1 99 0 $ 70 ,00 0, 00 0 8 .3 125% 9 1 0. 252 8 $1 ,51 6, 34 1 1 0. 05 % 89 0 .2 472 2 - $1 ,7 39 ,20 8 - $222 ,8 67

1/ 15 /1 991 1 0/ 11 /1 99 0 $ 70 ,00 0, 00 0 8 .2 500% 9 2 0. 255 6 $1 ,52 1, 47 8 1 0. 05 % 90 0 .2 500 0 - $1 ,7 58 ,75 0 - $237 ,2 724/15/1991 1/ 11/1991 $60,000, 000 7.3125% 90 0. 2500 $1, 130,799 10. 05% 90 0.25000 -$1,507,500 -$376,701

7/15/1991 4/ 11/1991 $60,000, 000 6.1250% 91 0. 2528 $957,689 10. 05% 90 0.25000 -$1,507,500 -$549,81110/15/1991 7/ 11/1991 $60,000, 000 5.9375% 92 0. 2556 $938,574 10. 05% 90 0.25000 -$1,507,500 -$568,926

1/15/1992 10/ 11/1991 $60,000, 000 5.3750% 92 0. 2556 $849,656 10. 05% 90 0.25000 -$1,507,500 -$657,844

Note that this column reflects the “adjustmentTo floating rate option,” that is the floating

Rate is divided by 0.97



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Why did LEU do the deal?

LEU was a relatively new telecom. company

Borrowed $75 million from a bank on a 3-yearnote

floating rate loan

interest payments every 3 months based on 3-monthLIBOR

partial principal payments discussed above

Condition of loan was that LEU swap from floatingto fixed

LEU receives floating, pays fixed on swap

Pays floating on bank loan

Net effect is that LEU has a synthetic fixed-rate loan

How does the dealer profit?

For this swap, dealer

receives 10.05%

Pays 3-month LIBOR

In an ideal world, dealer would doanother swap (of same size) in which it:

Pays 9.95%

Receives 3-month LIBOR Dealer gross profit is 0.10% or 10 basis

points

Exactly offsetting swaps only rarely (if ever) occur

Steps in Dealing

Negotiate terms by telephone

convention is LIBOR flat

as a result, dealer quotes the fixed rate

fixed rate is chosen so that the swap has value0 on the trade date

Fax confirmation (this is what you have)

Exchange signed ISDA Master Agreement

ISDA master defines terms, contains detailedprovisions



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Swap quotes

Hypothetical Indicative U.S. Dollar Interest Rate Swap Quotes

Maturity /tenor

Spread over Treasuryyield if dealer pays fixed

Spread over Treasury yieldif dealer receives fixed

2Y 25 basis points 27 basis points3Y 28 basis points 30 basis points4Y 30 basis points 34 basis points5Y 30 basis points 35 basis points7Y 33 basis points 38 basis points10Y 37 basis points 42 basis points

For each maturity/tenor, the spread would be added to the yield on the “current” Treasury note of the same maturity. For example, if the dealer pays fixed on a 5 year swap, the fixed rate of theswap would be equal to the yield on the 5 year note plus 30 basis. If the dealer pays floating andreceives fixed, the fixed rate of the swap would be equal to the yield on the 5 year note plus 35basis points.

Swap Quotes from GovPX

(4.420+4.416)/2 + 0.51 = 4.928

Using a swap: A stylized example

Company issued a $200 millionfloating rate note with interestpayments based on 3-mo. LIBOR

assume quarterly payments

Interest payment: LIBOR × 0.25 ×

$200 Million

LIBOR currently is 7%

Company exposed to risk of increases in LIBOR



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as ow a eac n . paymendate(<0 because int. exp. is an outflow)

3-mo. LIBOR

C a s h f l o w

a t i n t . p y m n t . d a t e ( $ m i l l i o n s )

-8

-6

-4

-2

0

2

4

6

0% 5% 10% 15%

7%, -$3.5 million

Interest expense at each interestpayment date

3-mo. LIBOR

I n t . e x p . a t i n t . p y m n t . d a t e ( $ m i l l i o n s )

0

2

4

6

0% 5% 10% 15%

7%, -$3.5 million

Fixed-Rate

Payer

Company with

Exposure

Bank or Other

IntermediaryReceive Floating Rate

(LIBOR) × 0.25 ×

Notional Amount

Pay 7.00%

Fixed Rate × 0.25 ×

Notional Principal

Risk Management Tool:

Interest Rate Swap

Fixed-Rate

Receiver



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Risk management tool: interestrate swap

Pay fixed, receive floating swap withfixed rate of 7%, notional prin. =$200m (quarterly payments)

3-mo. LIBOR

I n t . e x p . a t i n t . p y m n t . d a t e ( $ m i l l i o n s )

-4

-2

0

2

4

6

0% 5% 10% 15%

pay LIBOR= 7%,rec. fixed rate of 7%

Net cash flow at each interestpayment date

3-mo. LIBOR

N e t c a s h f l o w

a t i n t . p y m n t . d a t e ( $ m i l l i o n s )

-6

-4

-2

0

2

4

0% 5% 10% 15%

Cash flow = -$3.5 million

Swap cash flows

A tabular representation is also useful:

Here:

cash flows are from perspective of counterparty whois receiving floating, paying fixed

r t (t , t +0.25) is a floating interest rate observed at

time t, for a deposit/loan from time t to time t + 0.25

7% is the fixed rate

we ignore notional principal (notional = $1) and thedetails of day-counts

Time 0 0.25 0.5 ... T

Swap CashFlows

0 0.25[r 0(0, 0.25) − 0.07] 0.25[r 0.25(0.25, 0.5) − 0.07] ... 0.25[r T -0.25(T −0.25, T ) − 0.07]



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Transaction Cash Flows

Here is a tabular summary of the transaction:

Here the end-user has hedged cash flows(interest expense) by swapping from floatingto fixed

Time 0 0.25 0.5 ... T

Cash flows of original position

1 −0.25r 0(0, 0.25) −0.25r 0.25(0.25, 0.5) ... −[1 + 0.25r T -0.25(T −0.25, T )]

Swap CashFlows (pay fixed,receive floating)

0 0.25[r 0(0, 0.25) − 0.07] 0.25[r 0.25(0.25, 0.5) − 0.07] ... 0.25[r T -0.25(T −0.25, T ) − 0.07]

Net Cash Flows(orig. position +swap = syntheticfixed rate note)

1 −0.25( 0.07) −0.25( 0.07) ... −[1 + 0.25(0.07)]

Swapping from fixed to floating

This table shows swapping from fixed tofloating:

The net position is a synthetic floating ratebond

Time 0 0.25 0.5 ... T

Cash flows of original position

1 −0.25( 0.07) −0.25( 0.07) ... −[1 + 0.25(0.07)]

Swap CashFlows (payfloating, rec.fixed)

0 0.25[0.07−r 0(0, 0.25)] 0.25[0.07−r 0.25(0.25, 0.5)] ... 0.25[0.07−r T -0.25(T −0.25, T )]

Net Cash Flows(orig. position +swap = syntheticfloating ratenote)

1 −0.25r 0(0, 0.25) −0.25r 0.25(0.25, 0.5) ... −[1 + 0.25r T -0.25(T −0.25, T )]

Which is hedging?

Swapping from floating to fixed creates asynthetic fixed-rate bond

Swapping from fixed to floating creates asynthetic floating-rate bond

Which is less risky:

a fixed rate bond?; or

a floating rate bond?

Which is “hedging,” swapping fromfloating to fixed? Or fixed to floating?



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The first Gibson/BT transaction

On 21 Nov. 1991 Gibson and BT enteredinto the following two interest rate swaptransactions:

A 5-year swap based on 6-month LIBOR:

Gibson pays (BT receives) floating

BT pays (Gibson receives) 7.12% fixed

A 2-year swap based on 6-month LIBOR:

BT pays (Gibson receives) floating

Gibson pays (BT receives) 5.91% fixed

Both swaps had a notional amount of $30million

2-year swap

-$1,000,000

-$500,000

$0

$500,000

$1,000,000

$1,500,000

0 1 2 3 4 5

Time (years)

S w

a p p a y m e n t s

Fixed payments

Hypothetical floating payments

5-year swap

-$1,500,000

-$1,000,000

-$500,000

$0

$500,000

$1,000,000

$1,500,000

0 1 2 3 4 5

Time (years)

S w a p p a y m e n t s


Fixed payments



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Net cash flows

-$1,500,000

-$1,000,000

-$500,000

$0

$500,000

$1,000,000

$1,500,000

0 1 2 3 4 5

Time (years)

S w a p p a y m e n t s

Fixed payments


Net cash flows

-$1,500,000

-$1,000,000

-$500,000

$0

$500,000

$1,000,000

$1,500,000

0 1 2 3 4 5

Time (years)

S w a

p p a y m e n t s

Fixed payments


Net payment in years

3-5 must have negative

present value

The first Gibson/BT transaction Cash flows from perspective of Gibson (per $1 of

notional principal; to get actual cash flows, multiply by $30

million):Time in years

(Nov. 1991 =time 0)

0 0.5 ... 2.0 ... 2.5 ...

5-year swap

(receive7.12%, payfloating)

0 0.5[0.0712−r 0(0, 0.5)] ... 0.5[0.0712−r 1.5(1.5, 2.0)] ... 0.5[0.0712−r 2(2, 2.5)] ...

2-year swap

(pay 5.91%,rec. floating)

0 0.5[r 0(0, 0.5) −0.0591] ... 0.5[r 1.5(1.5, 2.0)−0.0591]

Net CashFlows

0 0.5[0.0712−0.0591] ... 0.5[0.0712−0.0591] ... 0.5[0.0712−r 2(2, 2.5)] ...

Positive cash flows

Cash flows with negative present value



The first Gibson/BT transaction

What is going on in this transaction? Each swap has value = 0 on the trade date (that is, the

present value of the cash flows over the life of swap = 0)

Thus, PV of the net cash flows of the 2 swaps together = 0

But, cash flows over first 2 years (times 0.5, 1, 1.5, 2) > 0

Thus, the present value of the cash flows during the nextthree years (times 2.5, …, 5) must be < 0

Gibson has shifted income from years 3through 5 into years 1 and 2.

Remarks re the Gibson/BTtransaction

This transaction “worked” to shift income because the 5-year swap rate (7.12%) exceeded the 2-year swap rate(5.91%)

If the 2-year rate was greater than the 5-year rate, thenthe opposite positions in the swaps would achieve thesame effect

Gibson could shift as much income as it wanted byincreasing the notional principal of the swaps

Why might such a transaction be appealing to Gibson?

The transaction will not shift income if the swaps areaccounted for on a fair value or “mark-to-market” basis(but it will still shift cash flows, that is it will still beequivalent to borrowing)

Other swaps

Ordinary (“plain-vanilla”) swap: swapfixed for floating

Basis swap: swap one floating rate foranother

Currency swaps: the two legs aredenominated in different currencies

Both, either, or neither legs may be fixed

In a currency swap, principals typically areexchanged

tm interest rate swap

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