Swaps

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. ---------Millions of Dollars--------- LIBOR FLOATING FIXED Net Date Rate Cash Flow Cash Flow Cash Flow Mar.5, 2001 4.2% Sept. 5, 2001 4.8% +2.10 –2.50 –0.40 Mar.5, 2002 5.3% +2.40 –2.50 –0.10 Sept. 5, 2002 5.5% +2.65 –2.50 +0.15 Mar.5, 2003 5.6% +2.75 –2.50 +0.25 Sept. 5, 2003 5.9% +2.80 –2.50 +0.30 Mar.5, 2004 6.4% +2.95 –2.50 +0.45 Cash Flows

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 5% 5.2% Intel MS LIBOR+0.1% LIBOR

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

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

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

9. Market Maker Quotes

10. Fixed Floating AAACorp 10.00% 6-month LIBOR + 0.30% BBBCorp 11.20% 6-month LIBOR + 1.00% Comparative Advantage • AAACorp wants to borrow floating • BBBCorp wants to borrow fixed

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

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

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

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

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 Dollars Pounds $ £ Year ------millions------ 2001 –15.00 +10.00 +1.20 2002 –1.10 +1.20 –1.10 2003 2004 +1.20 –1.10 +1.20 –1.10 2005 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. USD AUD General Motors 5.0% 12.6% Qantas 7.0% 13.0% 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

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

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

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

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

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