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SwapsChapter 26

Financial Institutions Management, 3/e

By Anthony Saunders

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Introduction

Market for swaps has grown enormously Serious regulatory concerns regarding credit risk

exposures• Motivated BIS risk-based capital reforms• Growth in exotic swaps such as inverse floater

generated controversy (e.g., Orange County, CA). Generic swaps in order of quantitative

importance: interest rate, currency, commodity.

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Interest Rate Swaps

Interest rate swap as succession of forwards.• Swap buyer agrees to pay fixed-rate• Swap seller agrees to pay floating-rate.

Purpose of swap• Allows FIs to economically convert variable-

rate instruments into fixed-rate (or vice versa) in order to better match assets and liabilities.

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Interest Rate Swap Example

• Consider money center bank that has raised $100 million by issuing 4-year notes with 10% fixed coupons. On asset side: C&I loans linked to LIBOR. Duration gap is negative.

DA - kDL < 0

• Second party is savings bank with $100 million in fixed-rate mortgages of long duration funded with CDs having duration of 1 year.

DA - kDL > 0

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Example (continued)

• Savings bank can reduce duration gap by buying a swap (taking fixed-payment side).

• Notional value of the swap is $100 million.• Maturity is 4 years with 10% fixed-payments.• Suppose that LIBOR currently equals 8% and

bank agrees to pay LIBOR + 2%.

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Realized Cash Flows on Swap

Suppose realized rates are as follows

End of Year LIBOR

1 9%

2 9%

3 7%

4 6%

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Swap Payments

End of LIBOR MCB Savings

Year + 2% Payment Bank Net

1 11% $11 $10 +1

2 11 11 10 +1

3 9 9 10 - 1

4 8 8 10 - 2

Total 39 40 - 1

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Off-market Swaps

Swaps can be molded to suit needs• Special interest terms• Varying notional value

» Increasing or decreasing over life of swap.

• Structured-note inverse floater» Example: Government agency issues note with

coupon equal to 7 percent minus LIBOR and converts it into a LIBOR liability through a swap.

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Macrohedging with Swaps

Assume a thrift has positive gap such thatE = -(DA - kDL)A [R/(1+R)] >0 if rates rise.

Suppose choose to hedge with 10-year swaps. Fixed-rate payments are equivalent to payments on a 10-year T-bond. Floating-rate payments repriced to LIBOR every year. Changes in swap value DS, depend on duration difference (D10 - D1).

S = -(DFixed - DFloat) × NS × [R/(1+R)]

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Macrohedging (continued)

Optimal notional value requiresS = E

-(DFixed - DFloat) × NS × [R/(1+R)]

= -(DA - kDL) × A × [R/(1+R)]

NS = [(DA - kDL) × A]/(DFixed - DFloat)

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Pricing an Interest Rate Swap

Example:• Assume 4-year swap with fixed payments at

end of year.• We derive expected one-year rates from the

yield curve treating the individual payments as separate zero-coupon bonds and iterating forward.

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Currency Swaps

Fixed-Fixed • Example: U.S. bank with fixed-rate assets

denominated in dollars, partly financed with £50 million in 4-year 10 percent (fixed) notes. By comparison, U.K. bank has assets partly funded by $100 million 4-year 10 percent notes.

• Solution: Enter into currency swap. Fixed-Floating currency swaps.

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Credit Swaps

Credit swaps designed to hedge credit risk. Total return swap Pure credit swap

• Interest-rate sensitive element stripped out leaving only the credit risk.

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Credit Risk Concerns

Credit risk concerns partly mitigated by netting of swap payments.

Netting by novation• When there are many contracts between parties.

Payment flows are interest and not principal.

Standby letters of credit may be required.