1. Swaps Finance (Derivative Securities) 312 Tuesday, 5 September 2006 Readings: Chapter 7

2. Nature of Swaps  Agreement to exchange cash flows at specified future times according to certain rules  Example of a plain vanilla swap agreement by Microsoft to receive 6-month LIBOR & pay a fixed rate of 5% per annum every six months for three years on a notional principal of $100 million

3. Cash Flows ---------Millions of Dollars--------- LIBORFLOATINGFIXEDNet DateRateCash Flow Mar.5, 20014.2% Sept. 5, 20014.8%+2.10–2.50–0.40 Mar.5, 20025.3%+2.40–2.50–0.10 Sept. 5, 20025.5%+2.65–2.50+0.15 Mar.5, 20035.6%+2.75–2.50+0.25 Sept. 5, 20035.9%+2.80–2.50+0.30 Mar.5, 20046.4%+2.95–2.50+0.45

4. Use of Swaps  Converting a liability from fixed rate to floating rate floating rate to fixed rate  Converting an investment from fixed rate to floating rate floating rate to fixed rate

5. Transforming a Liability IntelMS LIBOR 5% LIBOR+0.1% 5.2%

6. Involving a Financial Institution F.I. LIBOR LIBOR+0.1% 4.985% 5.015% 5.2% IntelMS

7. Transforming an Asset Intel MS LIBOR 5% LIBOR–0.2% 4.7%

8. Involving a Financial Institution Intel F.I.MS LIBOR 4.7% 5.015%4.985% LIBOR–0.2%

9. Market Maker Quotes MaturityBid (%)Offer (%)Swap Rate (%) 2 years6.036.066.045 3 years6.216.246.225 4 years6.356.396.370 5 years6.476.516.490 7 years6.656.686.665 10 years6.836.876.850

10. Comparative Advantage  AAACorp wants to borrow floating  BBBCorp wants to borrow fixed FixedFloating AAACorp10.00%6-month LIBOR + 0.30% BBBCorp11.20%6-month LIBOR + 1.00%

11. The Swap AAA BBB LIBOR LIBOR+1% 9.95% 10%

12. Involving a Financial Institution AAAF.I.BBB 10% LIBOR LIBOR+1% 9.93% 9.97%

13. Critique  10.0% and 11.2% rates available to AAACorp and BBBCorp in fixed rate markets are 5-year rates  LIBOR+0.3% and LIBOR+1% rates available in the floating rate market are 6- month rates  BBBCorp’s fixed rate depends on the spread above LIBOR it borrows at in the future

14. Swap Rates  6-month LIBOR is a short-term AA borrowing rate  5-year swap rate has a risk corresponding to the situation where ten 6-month loans are made to AA borrowers at LIBOR Lender can enter into a swap where income from the LIBOR loans is exchanged for the 5- year swap rate

15. Valuation of Swaps  Valued as the difference between the value of a fixed-rate bond and the value of a floating-rate bond Fixed rate bond is valued in the usual way Floating rate bond is valued by noting that it is worth par immediately after the next payment date

16. Valuation of Swaps  Suppose that: A bank agrees to pay 6-month LIBOR and receive 8% p.a. with semiannual compounding on notional principal of $100m Remaining life of 1.25 years 3-month rate 10%, 6-month rate 10.2%, 9-month rate 10.5%, 15-month rate 11%  What is the value of this swap?

17. Valuation of Swaps * e -0.1(0.25) # 0.5 x 0.102 x 100 = 5.1 Value of swap: 98.238 – 102.505 = –4.267m TimeB fix CFB fl CFDiscount factor PV B fix CFPV B fl CF 0.254.0105.1 # 0.9753*3.901102.505 0.754.00.92433.697 1.25104.00.871590.640 Total98.238102.505

18. Valuation of Swaps  Alternatively, can be valued as a portfolio of forward rate agreements (FRAs) Each exchange of payments in an interest rate swap is an FRA FRAs can be valued on the assumption that today’s forward rates will be realised

19. Valuation of Swaps * e -0.1(0.25) # 0.5 x 0.102 x 100 = 5.1 † using rate [0.105(0.75) – 0.10(0.25)/0.5] = 0.1075 convert to semiannual compounding: 0.1044 TimeFixed CF Floating CF Net CFDiscount Factor PV Net CF 0.254.0-5.100 # -1.1000.9753*-1.073 0.754.0-5.522 † -1.5220.9243-1.407 1.254.0-6.051-2.0510.8715-1.787 Total-4.267

20. Currency Swaps  Agreement to pay 11% on a sterling principal of £10,000,000 & receive 8% on a US dollar principal of $15,000,000 every year for five years Principal is exchanged at the beginning and the end of the swap, unlike in an interest rate swap

21. Currency Swaps Year DollarsPounds $ ------millions------ 2001 –15.00 +10.00 2002 +1.20 –1.10 2003 +1.20 –1.10 2004 +1.20 –1.10 2005 +1.20 –1.10 2006+16.20 -11.10 £

22. Use of Currency Swaps  Conversion from a liability in one currency to a liability in another currency  Conversion from an investment in one currency to an investment in another currency

23. Comparative Advantage  General Motors wants to borrow AUD  Qantas wants to borrow USD  Can be valued either as the difference between two bonds or as a portfolio of forward contracts USDAUD General Motors 5.0%12.6% Qantas 7.0%13.0%

24. The Swap GMF.I. QAN USD 5.0% AUD 11.9% AUD 13.0% USD 5.0% USD 6.3%

25. Alternative Swap GMF.I. QAN USD 5.0% AUD 11.9% AUD 13.0% USD 5.0% USD 5.2%

26. Swaps v Forwards  Swaps can be regarded as a convenient way of packaging forward contracts  “Plain vanilla” interest rate swap in earlier example consisted of six FRAs  “Fixed for fixed” currency swap in other example consisted of a cash transaction & five forward contracts

27. Valuing Currency Swaps  Suppose that: Term structure of LIBOR/swap rates is flat in Japan and the US Japan rate is 4%, US rate is 9% p.a. (continuous compounding) A bank enters a swap paying 8% and receiving 5% p.a., USD10m against JPY1.2bn 3-year swap, current rate USD1 = JPY110  What is the value of the swap?

28. Valuation as Bonds Value of swap: 1,230.55/110 – 9.6439 = USD1.5430m TimeUSD CF PV ($)JPY CF PV (¥) 10.80.73116057.65 20.80.66826055.39 30.80.61076053.22 310.07.63381,2001,064.30 Total9.64391,230.55

29. Swaps v Forwards  Value of a swap is the sum of the values of the forward contracts underlying the swap  Swaps are normally “at the money” initially It costs nothing to enter into a swap It does not mean that each forward contract underlying a swap is “at the money” initially

30. Valuation as FRAs TimeUSD CF JPY CF Forward Rate JPY CF in USD Net CF in USD PV 1-0.8600.0095570.5734-0.2266-0.2071 2-0.8600.0100470.6028-0.1972-0.1647 3-0.8600.0105620.6337-0.1663-0.1269 3-10.01,2000.01056212.67462.67462.0417 Total1.5430

31. Credit Risk  A swap is worth zero to a company initially  At a future time its value is liable to be either positive or negative  Firm has credit risk exposure only when swap value is positive Exposure Swap Value