1. Chapter 7 Swaps 1

2. Nature of Swaps A swap is an agreement to exchange cash flows at specified future times according to certain specified rules 2

3. An Example of a “Plain Vanilla” Interest Rate Swap An agreement by Microsoft to receive 6-month LIBOR & pay a fixed rate of 5% per annum every 6 months for 3 years on a notional principal of $100 million Next slide illustrates cash flows that could occur (Day count conventions are not considered) 3

4. One Possible Outcome for Cash Flows to Microsoft (Table 7.1, page 150) DateLIBORFloating Cash Flow Fixed Cash Flow Net Cash Flow Mar 5, 20124.20% Sep 5, 20124.80%+2.10−2.50−0.40 Mar 5, 20135.30%+2.40−2.50−0.10 Sep 5, 20135.50%+2.65−2.50+ 0.15 Mar 5, 20145.60%+2.75−2.50+0.25 Sep 5, 20145.90%+2.80−2.50+0.30 Mar 5, 2015+2.95−2.50+0.45 4

5. Typical Uses of an Interest Rate Swap 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

6. Intel and Microsoft (MS) Transform a Liability (Figure 7.2, page 151) 6 IntelMS LIBOR 5% LIBOR+0.1% 5.2%

7. Financial Institution is Involved (Figure 7.4, page 152) 7 F.I. LIBOR LIBOR+0.1 % 4.985% 5.015% 5.2% IntelMS Financial Institution has two offsetting swaps

8. Intel and Microsoft (MS) Transform an Asset ( Figure 7.3, page 152) 8 Intel MS LIBOR 5% LIBOR-0.2% 4.7%

9. Financial Institution is Involved (See Figure 7.5, page 153) 9 Intel F.I.MS LIBOR 4.7% 5.015%4.985% LIBOR-0.2%

10. Quotes By a Swap Market Maker (Table 7.3, page 154) 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

11. Day Count A day count convention is specified for for fixed and floating payment For example, LIBOR is likely to be actual/360 in the US because LIBOR is a money market rate 11

12. Confirmations Confirmations specify the terms of a transaction The International Swaps and Derivatives has developed Master Agreements that can be used to cover all agreements between two counterparties Governments now require central clearing to be used for most standardized derivatives 12

13. The Comparative Advantage Argument (Table 7.4, page 156) AAACorp wants to borrow floating BBBCorp wants to borrow fixed 13 FixedFloating AAACorp4.0%6 month LIBOR − 0.1% BBBCorp5.2%6 month LIBOR + 0.6%

14. The Swap (Figure 7.6, page 157) 14 AAACorp BBBCorp LIBOR LIBOR+0.6% 4.35% 4%

15. The Swap when a Financial Institution is Involved (Figure 7.7, page 157) 15 AAACorp F.I. BBBCorp 4% LIBOR LIBOR+0.6% 4.33% 4.37%

16. Criticism of the Comparative Advan tage Argument The 4.0% and 5.2% rates available to AAACorp and BBBCorp in fixed rate markets are 5-year rates The LIBOR−0.1% and LIBOR+0.6% rates available in the floating rate market are six- month rates BBBCorp’s fixed rate depends on the spread above LIBOR it borrows at in the future 16

17. The Nature of Swap Rates Six-month LIBOR is a short-term AA borrowing rate The 5-year swap rate has a risk corresponding to the situation where 10 six- month loans are made to AA borrowers at LIBOR This is because the lender can enter into a swap where income from the LIBOR loans is exchanged for the 5-year swap rate 17

18. Using Swap Rates to Bootstrap the LIBOR/Swap Zero Curve Consider a new swap where the fixed rate is the swap rate When principals are added to both sides on the final payment date the swap is the exchange of a fixed rate bond for a floating rate bond The floating-rate rate bond is worth par. The swap is worth zero. The fixed-rate bond must therefore also be worth par This shows that swap rates define par yield bonds that can be used to bootstrap the LIBOR (or LIBOR/swap) zero curve 18

19. Example of Bootstrapping the LIBOR/Swap Curve (Example 7.1, page 160) 6-month, 12-month, and 18-month LIBOR/swap rates are 4%, 4.5%, and 4.8% with continuous compounding. Two-year swap rate is 5% (semiannual) The 2-year LIBOR/swap rate, R, is 4.953% 19

20. Valuation of an Interest Rate Swap Initially interest rate swaps are worth close to zero At later times they can be valued as the difference between the value of a fixed- rate bond and the value of a floating-rate bond Alternatively, they can be valued as a portfolio of forward rate agreements (FRAs) 20

21. Valuation in Terms of Bonds The fixed rate bond is valued in the usual way The floating rate bond is valued by noting that it is worth par immediately after the next payment date 21

22. Valution of Floating-Rate Bond 22 0t*t* Valuation Date First Pmt Date Floating Pmt =k * Second Pmt Date Maturity Date Value = L Value = L+k * Value = PV of L+k * at t *

23. Example Pay six-month LIBOR, receive 8% (s.a. compounding) on a principal of $100 million Remaining life 1.25 years LIBOR rates for 3-months, 9-months and 15-months are 10%, 10.5%, and 11% (cont comp) 6-month LIBOR on last payment date was 10.2% (s.a. compounding) 23

24. Valuation Using Bonds (page 161) 24 TimeB fix cash flow B fl cash flow Disc factor PV B fix PV B fl 0.254.0105.1000.97533.901102.505 0.754.00.92433.697 1.25104.00.871590.640 Total98.238102.505 Swap value = 98.238 − 102.505 = −4.267

25. Valuation in Terms of FRAs Each exchange of payments in an interest rate swap is an FRA The FRAs can be valued on the assumption that today’s forward rates are realized 25

26. Valuation of Example Using FRAs (page 163) TimeFixed cash flow Floating cash flow Net Cash Flow Disc factorPV B fl 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 26

27. Overnight Indexed Swaps Fixed rate for a period is exchanged for the geometric average of the overnight rates Should OIS rate equal the LIBOR rate? A bank can –Borrow $100 million in the overnight market, rolling forward for 3 months –Enter into an OIS swap to convert this to the 3-month OIS rate –Lend the funds to another bank at LIBOR for 3 months 27

28. Overnight Indexed Swaps continued...but it bears the credit risk of another bank in this arrangement The OIS rate is now regarded as a better proxy for the short-term risk-free rate than LIBOR The excess of LIBOR over the OIS rate is the LIBOR-OIS spread. It is usually about 10 basis points but spiked at an all time high of 364 basis points in October 2008 28

29. An Example of a Currency Swap An agreement to pay 5% on a sterling principal of £10,000,000 & receive 6% on a US$ principal of $18,000,000 every year for 5 years 29

30. Exchange of Principal In an interest rate swap the principal is not exchanged In a currency swap the principal is usually exchanged at the beginning and the end of the swap’s life 30

31. The Cash Flows (Table 7.7, page 166) 31 DateDollar Cash Flows (millions) Sterling cash flow (millions) Feb 1, 2011-18.0+10.0 Feb 1, 2012+1.08−0.50 Feb 1, 2012+1.08−0.50 Feb 1, 2014+1.08−0.50 Feb 1, 2015+1.08−0.50 Feb 1, 2016+19.08−10.50

32. Typical Uses of a Currency Swap Convert a liability in one currency to a liability in another currency Convert an investment in one currency to an investment in another currency 32

33. Comparative Advantage May Be Real Because of Taxes General Electric wants to borrow AUD Quantas wants to borrow USD Cost after adjusting for the differential impact of taxes 33 USDAUD General Electric5.0%7.6% Quantas7.0%8.0%

34. Valuation of Currency Swaps Like interest rate swaps, currency swaps can be valued either as the difference between 2 bonds or as a portfolio of forward contracts 34

35. Example All Japanese LIBOR/swap rates are 4% All USD LIBOR/swap rates are 9% 5% is received in yen; 8% is paid in dollars. Payments are made annually Principals are $10 million and 1,200 million yen Swap will last for 3 more years Current exchange rate is 110 yen per dollar 35

36. Valuation in Terms of Bonds (Table 7.9, page 169) TimeCash Flows ($)PV ($)Cash flows (yen)PV (yen) 10.80.73116057.65 20.80.66826055.39 30.80.61076053.22 310.07.63381,2001,064.30 Total9.64391,230.55 36 Value of Swap = 1230.55/110 − 9.6439 = 1.5430

37. Valuation in Terms of Forwards (Table 7.10, page 170) 37 Time$ cash flow Yen cash flow Forward Exch rate Yen cash flow in $ Net Cash Flow Present value 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 3-10.012000.01056212.6746+2.674 6 2.0417 Total1.5430

38. Swaps & Forwards A swap can be regarded as a convenient way of packaging forward contracts Although the swap contract is usually worth close to zero at the outset, each of the underlying forward contracts are not worth zero 38

39. 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 The company has credit risk exposure only when its value is positive Some swaps are more likely to lead to credit risk exposure than others What is the situation if early forward rates have a positive value? What is the situation when the early forward rates have a negative value? 39

40. Other Types of Swaps Floating-for-floating interest rate swaps, amortizing swaps, step up swaps, forward swaps, constant maturity swaps, compounding swaps, LIBOR-in-arrears swaps, accrual swaps, diff swaps, cross currency interest rate swaps, equity swaps, extendable swaps, puttable swaps, swaptions, commodity swaps, volatility swaps…….. 40