1. Swaps Chapter 26 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. K. R. Stanton

2. McGraw-Hill/Irwin 26-2 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Overview The market for swaps has grown enormously and this has raised serious regulatory concerns regarding credit risk exposures. Such concerns motivated the BIS risk-based capital reforms. At the same time, the growth in exotic swaps such as inverse floater have also generated controversy (e.g., Orange County, CA). Generic swaps in order of quantitative importance: interest rate, currency, credit, commodity and equity swaps.

3. McGraw-Hill/Irwin 26-3 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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 interest rate swap Allows FIs to economically convert variable-rate instruments into fixed-rate (or vice versa) in order to better match the duration of assets and liabilities. Off-balance-sheet transaction.

4. McGraw-Hill/Irwin 26-4 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Plain Vanilla 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. D A - kD L < 0 Second party is savings bank with $100 million in fixed-rate mortgages of long duration funded with CDs having duration of 1 year. D A - kD L > 0

5. McGraw-Hill/Irwin 26-5 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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%.

6. McGraw-Hill/Irwin 26-6 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Realized Cash Flows on Swap  Suppose realized rates are as follows End of YearLIBOR 1 9% 2 9% 3 7% 4 6%

7. McGraw-Hill/Irwin 26-7 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Swap Payments End of LIBORMCBSavings MCB Year+ 2%PaymentBank Net 111%$11$10 +1 211 11 10 +1 39 9 10 - 1 48 8 10 - 2 Total 39 40 - 1

8. McGraw-Hill/Irwin 26-8 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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.

9. McGraw-Hill/Irwin 26-9 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Macrohedging with Swaps  Assume a thrift has positive gap such that  E = -(D A - kD L )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 (D 10 - D 1 ).  S = -(D Fixed - D Float ) × N S × [  R/(1+R)]

10. McGraw-Hill/Irwin 26-10 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Macrohedging (continued)  Optimal notional value requires  S =  E -(D Fixed - D Float ) × N S × [  R/(1+R)] = -(D A - kD L ) × A × [  R/(1+R)] N S = [(D A - kD L ) × A]/(D Fixed - D Float )

11. McGraw-Hill/Irwin 26-11 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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 on- the-run Treasury yield curve treating the individual payments as separate zero-coupon bonds and iterating forward.

12. McGraw-Hill/Irwin 26-12 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Solving the Discount Yield Curve* P 1 = 108/(1+R 1 ) = 100 ==> R 1 = 8% ==> d 1 = 8% P 2 = 9/(1+R 2 ) + 109/(1+R 2 ) 2 = 100 ==> R 2 = 9% 9/(1+d 1 ) + 109/(1+d 2 ) 2 = 100 ==> d 2 = 9.045% Similarly, d 3 = 9.58% and d 4 = 10.147%

13. McGraw-Hill/Irwin 26-13 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Solving Implied Forward Rates* d 1 = 8% ==> E(r 1 ) = 8% 1+ E(r 2 ) = (1+d 2 ) 2 /(1+d 1 ) ==> E(r 2 ) = 10.1% 1+ E(r 3 ) = (1+d 3 ) 3 /(1+d 2 ) 2 ==> E(r 3 ) = 10.658% 1+ E(r 4 ) = (1+d 4 ) 4 /(1+d 3 ) 3 ==> E(r 4 ) = 11.866%

14. McGraw-Hill/Irwin 26-14 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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.

15. McGraw-Hill/Irwin 26-15 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Cash Flows from Swap

16. McGraw-Hill/Irwin 26-16 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Fixed-Floating + Currency  Fixed-Floating currency swaps. Allows hedging of interest rate and currency exposures simultaneously

17. McGraw-Hill/Irwin 26-17 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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.

18. McGraw-Hill/Irwin 26-18 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Swaps and 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.  Greenspan claims that credit swap market has helped strengthen the banking system’s ability to deal with recession

19. McGraw-Hill/Irwin 26-19 © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Pertinent Websites BIS www.bis.orgwww.bis.org Moody’s Investor Services www.moodys.comwww.moodys.com