Swaps Chapter 26. Swaps CBs and IBs are major participants –dealers –traders –users regulatory concerns regarding credit risk exposure five generic.

SwapsSwaps

Chapter 26Chapter 26

SwapsSwaps

CBs and IBs are major participantsCBs and IBs are major participants– dealersdealers– traderstraders– usersusers

regulatory concerns regarding credit risk exposureregulatory concerns regarding credit risk exposure five generic types of swapsfive generic types of swaps

– interest rate swapsinterest rate swaps– currency swapscurrency swaps– credit swapscredit swaps– commodity swapscommodity swaps– equity swapsequity swaps

Interest Rate SwapInterest Rate Swap

largest segment of global swap marketlargest segment of global swap market basically a succession of forward contracts basically a succession of forward contracts

on interest rates arranged by 2 partieson interest rates arranged by 2 parties FIs able to establish long-term hedge with FIs able to establish long-term hedge with

no need to roll over contracts like with no need to roll over contracts like with forwards and futuresforwards and futures

swap buyerswap buyer swap sellerswap seller

Plain Vanilla Interest Rate Swap Plain Vanilla Interest Rate Swap ExampleExample

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

DDAA - kD - kDLL < 0 < 0

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

DDAA - kD - kDLL > 0 > 0

Interest Rate SwapsInterest Rate Swaps

We depict this fixed-floating rate swap We depict this fixed-floating rate swap transaction in the followingtransaction in the following

Interest Rate SwapsInterest Rate Swaps

The expected net financing costs for the FIs are The expected net financing costs for the FIs are shown belowshown below

Interest Rate SwapsInterest Rate Swaps

Assume that the realized path of LIBOR over the 4 Assume that the realized path of LIBOR over the 4 year life of the contract would be as follows 9%, year life of the contract would be as follows 9%, 9%, 7%, and 6% at the end of each of the 4 years. 9%, 7%, and 6% at the end of each of the 4 years. The money center bank’s variable payments to The money center bank’s variable payments to the thrift are indexed to these rates by the formula:the thrift are indexed to these rates by the formula:

(LIBOR + 2%) * $100m(LIBOR + 2%) * $100m The annual payments made by the thrift were the The annual payments made by the thrift were the

same each yearsame each year

10% * $100m.10% * $100m.

End of year One-Year LIBOR

LIBOR + 2%

Pmt by MCB

Pmt by thrift Net Pmt by MCB

1 9% 11% 2 9% 11% 3 7% 9% 4 6% 8% TOTAL

Example 1Example 1

A U.S. insurer has a positive repricing gap of $50 A U.S. insurer has a positive repricing gap of $50 million and is worried that interest rates may fall, million and is worried that interest rates may fall, reducing their profitability. A bank with a reducing their profitability. A bank with a considerable amount of mortgage loans has a considerable amount of mortgage loans has a negative repricing gap of $50 million. The bank is negative repricing gap of $50 million. The bank is concerned that rates may rise, hurting their concerned that rates may rise, hurting their profitability. The insurer does not have enough profitability. The insurer does not have enough rate sensitive (variable rate or short maturity) rate sensitive (variable rate or short maturity) liabilities, and the bank has too many. How can liabilities, and the bank has too many. How can risk be reduced to both parties?risk be reduced to both parties?

Macrohedging with SwapsMacrohedging with Swaps

Assume a thrift has positive gap such thatAssume a thrift has positive gap such thatE = -(DE = -(DAA - kD - kDLL)A [)A [R/(1+R)] >0 if rates rise.R/(1+R)] >0 if rates rise.

Suppose choose to hedge with 10-year swaps. Suppose choose to hedge with 10-year swaps. Fixed-rate payments are equivalent to Fixed-rate payments are equivalent to payments on a 10-year T-bond. Floating-rate payments on a 10-year T-bond. Floating-rate payments repriced to LIBOR every year. payments repriced to LIBOR every year. Changes in swap value DS, depend on Changes in swap value DS, depend on duration difference (Dduration difference (D1010 - D - D11). ).

S = -(DS = -(DFixedFixed - D - DFloatFloat) × N) × NSS × [ × [R/(1+R)]R/(1+R)]

Macrohedging (continued)Macrohedging (continued)

Optimal notional value requiresOptimal notional value requiresS = S = EE

-(D-(DFixedFixed - D - DFloatFloat) × N) × NSS × [ × [R/(1+R)] R/(1+R)]

= -(D= -(DAA - kD - kDLL) × A × [) × A × [R/(1+R)]R/(1+R)]

NNS S = [(D= [(DAA - kD - kDLL) × A]/(D) × A]/(DFixedFixed - D - DFloatFloat))

Example 2Example 2

Suppose DSuppose DAA=5, D=5, DLL=3, k=.9, and =3, k=.9, and

A=$100,000,000. Also assume the duration A=$100,000,000. Also assume the duration of a current 10-year fixed-rate T-bond with of a current 10-year fixed-rate T-bond with the same coupon as the fixed rate on the the same coupon as the fixed rate on the swap in 7 years and the duration of a swap in 7 years and the duration of a floating-rate bond that reprices annually is 1 floating-rate bond that reprices annually is 1 year. Solve for Nyear. Solve for NSS..

Currency SwapsCurrency Swaps

swaps can be used to hedge currency risk similar swaps can be used to hedge currency risk similar to the way they are used to hedge interest rate riskto the way they are used to hedge interest rate risk– immunize FI against exchange rate risk when they immunize FI against exchange rate risk when they

mismatch currencies of assets and liabilitiesmismatch currencies of assets and liabilities Consider FI with all fixed-rate assets denominated Consider FI with all fixed-rate assets denominated

in dollars – financing part of asset portfolio with in dollars – financing part of asset portfolio with 50m issue of 4 year medium term British pound 50m issue of 4 year medium term British pound sterling notes that have fixed annual coupon of sterling notes that have fixed annual coupon of 10%. There is a UK FI that has all assets 10%. There is a UK FI that has all assets denominated in sterling – partly funding those denominated in sterling – partly funding those assets with $100m issue of 4-year, medium-term assets with $100m issue of 4-year, medium-term dollar notes with a fixed annual coupon of 10%.dollar notes with a fixed annual coupon of 10%.

Currency SwapsCurrency Swaps

Off the balance sheet, the U.K. and U.S. FIs can enter into a fixed-fixed currency swap by which the U.K. FI sends annual payments in pounds to cover the coupon and principal repayments of the U.S. FI’s pound note issue, and the U.S. FI sends annual dollar payments to the U.K. FI to cover the interest and principal payments on its dollar note issue.

Currency SwapsCurrency Swaps

Currency SwapsCurrency Swaps

Example 3Example 3

Ohio Bank has all of its assets in dollars but Ohio Bank has all of its assets in dollars but is financing some of them with an issue of is financing some of them with an issue of the equivalent of $75 million of 5 year fixed the equivalent of $75 million of 5 year fixed rate notes denominated in British pounds. rate notes denominated in British pounds. Bulldog Bank, a British FI, has a net $75 Bulldog Bank, a British FI, has a net $75 million dollar fixed rate liability exposure. million dollar fixed rate liability exposure. How should the FIs manage their exposure? How should the FIs manage their exposure?

Total Return SwapsTotal Return Swaps

swap involving an obligation to pay interest swap involving an obligation to pay interest at a specified fixed or floating rate for at a specified fixed or floating rate for payments representing the total return on a payments representing the total return on a loan or bond (interest and principal value loan or bond (interest and principal value changes) of a specified amountchanges) of a specified amount

ExampleExample Suppose that an FI lends $100m to a Brazilian manufacturing firm at a Suppose that an FI lends $100m to a Brazilian manufacturing firm at a

fixed rate of 10%. If the firm’s credit risk increases unexpectedly over fixed rate of 10%. If the firm’s credit risk increases unexpectedly over the life of the loan, the market value of the loan and consequently the the life of the loan, the market value of the loan and consequently the FI’s net worth will fall. The FI can hedge an unexpected increase in FI’s net worth will fall. The FI can hedge an unexpected increase in the borrower’s credit risk by entering into a total return swap in which it the borrower’s credit risk by entering into a total return swap in which it agrees to pay a total return based on an annual fixed rate plus agrees to pay a total return based on an annual fixed rate plus changes in the market value of Brazilian government debt (changes in changes in the market value of Brazilian government debt (changes in the value of these bonds reflect the political and economic events in the value of these bonds reflect the political and economic events in the firm’s home country and thus will be correlated with the credit risk the firm’s home country and thus will be correlated with the credit risk of the Brazilian borrowing firm.) Also the bonds are in the same of the Brazilian borrowing firm.) Also the bonds are in the same currency (US dollars) as the loans.currency (US dollars) as the loans.

The FI benefits from the total return swap if the Brazilian bond value The FI benefits from the total return swap if the Brazilian bond value deteriorates as a result of a political or economic shock. Assuming deteriorates as a result of a political or economic shock. Assuming that the Brazilian firm’s credit risk deteriorates along with the local that the Brazilian firm’s credit risk deteriorates along with the local economy, the FI will offset some of this loss of the Brazilian loan on its economy, the FI will offset some of this loss of the Brazilian loan on its balance sheet with a gain from the total return swap.balance sheet with a gain from the total return swap.

Pure Credit SwapsPure Credit Swaps

pure credit swap strips interest rate sensitive pure credit swap strips interest rate sensitive element of total return swap – swap by which an FI element of total return swap – swap by which an FI receives the par value of the loan on default in receives the par value of the loan on default in return for paying a periodic swap fee (like an return for paying a periodic swap fee (like an insurance premium)insurance premium)– if no default on loan, FI lender receives nothing back if no default on loan, FI lender receives nothing back

from counterpartyfrom counterparty– if loan defaults, FI counterparty will cover default loss by if loan defaults, FI counterparty will cover default loss by

making a default payment that is often equal to he par making a default payment that is often equal to he par value of the original loan minus the secondary market value of the original loan minus the secondary market value of the defaulted loan (at time of default)value of the defaulted loan (at time of default)

Credit Risk with SwapsCredit Risk with Swaps

Credit risk on swaps is however generally much lower than Credit risk on swaps is however generally much lower than on loans of equivalent principle amounts becauseon loans of equivalent principle amounts because

1. Only the net payment is due on the swap payment 1. Only the net payment is due on the swap payment dates, and this amount will be less than the typical interest dates, and this amount will be less than the typical interest payment on a equivalent principle loan.payment on a equivalent principle loan.

2.2. Swap payments are often interest only and not Swap payments are often interest only and not principle, so the notional principle is not at risk.principle, so the notional principle is not at risk.

3.3. If a swap partner is worried about the counterparty’s If a swap partner is worried about the counterparty’s creditworthiness they may require the counterparty to creditworthiness they may require the counterparty to obtain a standby letter of credit or to post collateral.obtain a standby letter of credit or to post collateral.