1. 7.1 Swaps Chapter 7

2. 7.2 Nature of Swaps A swap is an agreement to exchange cash flows at specified future times according to certain specified rules

3. 7.3 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 Uncertainty about LIBOR receipt at end of reset period (6 months) is resolved at start of the reset period: the start of the 6-month period is the reset date

4. 7.4 ---------Millions of Dollars--------- LIBORFLOATINGFIXEDNet DateRateCash Flow Mar.5, 20074.2% Sept. 5, 20074.8%+2.10–2.50–0.40 Mar.5, 20085.3%+2.40–2.50–0.10 Sept. 5, 20085.5%+2.65–2.50+0.15 Mar.5, 20095.6%+2.75–2.50+0.25 Sept. 5, 20095.9%+2.80–2.50+0.30 Mar.5, 20106.4%+2.95–2.50+0.45 Cash Flows to Microsoft

5. 7.5 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

6. 7.6 Intel and Microsoft (MS) Transform a Liability IntelMS LIBOR 5% LIBOR+0.1% 5.2% Result: MS pays fixed 5.1%; Intel pays float. L+0.2%

7. 7.7 Financial Institution is Involved F.I. LIBOR LIBOR+0.1% 4.985% 5.015% 5.2% IntelMS F.I. earns 3 basis points, i.e. 0.03%

8. 7.8 Intel and Microsoft (MS) Transform an Asset Intel MS LIBOR 5% LIBOR-0.2% 4.7% Result: MS earns float. L-0.3%; Intel earns fixed 4. 8%

9. 7.9 Financial Institution is Involved Intel F.I.MS LIBOR 4.7% 5.015%4.985% LIBOR-0.2%

10. 7.10 Quotes of a Swap Market Maker F.I. 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 F.I. pays Bid to receive LIBOR; F.I. requires Offer to pay LIBOR

11. 7.11 The Comparative Advantage Argument: for both counterparties desired loan differs from that in which comparative advantage lies AAACorp (less default risk) absolute advantage in both types AAACorp wants to borrow floating but comp. ad. in fixed BBBCorp wants to borrow fixed but comp. ad. in floating Comparative advantage: interest rate differences are different Fixed 120 bps, Floating 70 bps Total gain = difference of differences = 50 bps FixedFloating AAACorp4.00%6-month LIBOR + 0.30% BBBCorp5.20% 6-month LIBOR + 1.00%

12. 7.12 The Swap AAA BBB LIBOR LIBOR+1% 3.95% 4% Each counterparty initially issues debt in which comp. advantage lies then enters into swap to obtain desired debt financing

13. Total Gain (50 bps) partitioned Gain = interest rate paid in absence of swap – interest rate paid via swap AAA gain: (L +.3%) – (L +.05%) = 25 bps BBB gain: 5.2% - 4.95 % = 25 bps

14. 7.14 The Swap when a Financial Institution (earns 4 bps) is Involved AAAF.I.BBB 4% LIBOR LIBOR+1% 3.93% 3.97%

15. Total Gain (50 bps) partitioned AAA gain: (L+.3%) – (L+.07%) = 23 bps BBB gain: 5.2% - 4.97% = 23 bps Bank gain: 3.97% - 3.93% = 4 bps

16. 7.16 Criticism of the Comparative Advantage Argument The 4.0% and 5.2% fixed rates available to AAACorp and BBBCorp are 5-year rates The LIBOR+0.3% and LIBOR+1% rates available to the same corps. are six-month rates Floating rate loans have more scope for renegotiation than fixed rate loans BBBCorp’s fixed rate depends on the spread above LIBOR it borrows at in the future

17. 7.17 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

18. Swap Rate = Par Yield (N-year) Used in boot strapping procedure True if swap reset period is 6 months Otherwise, must calculate equivalent interest rate with semiannual compound. For newly issued float rate Bfloat = 100 For newly issued swap Bfloat = Bfix; swap rate is the coupon rate of fix rate bond Bfix = 100; thus swap rate = par yield

19. 7.19 Valuation (post-inception) of an Interest Rate Swap Interest rate swaps 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. 7.20 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 Bfloat = PV ( next payment* + par value ) *next payment is know at start of the reset period

21. 7.21 Example Receive 8% and pay floating LIBOR both semiannually on a principal of $100 million 1.25 years to go and next floating payment ($5.1 million) will occur 3 months from now On last reset date (3 months ago) LIBOR = 10.2% 3-, 9-, 15- month zero rates are 10%, 10.5%, 11 % Swap value = 98.238 −102.505= − 4.267; Why negative?

22. 7.22 Valuation (post-inception) in Terms of portfolio of staggered 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

23. 7.23 Example ($ amounts in M)

24. Float. CF for T=.75 is -5.522 Infer F pertaining to T=.25 to T=.75 F = (10.5%(.75)+10%(.25)) /.5 = 10.75% Convert from cc to semiannual compound. F 2 = 11.044% T=.75: CF = -100Mx11.044%x.5 = -.522M

25. Float. CF for T=1.25 is -6.051 Infer F pertaining to T=.75 to T=1.25 F = (11%(1.25)+10.5%(.75)) /.5 = 11.75% Convert from cc to semiannual compound. F 2 = 12.1% T=1.25: CF = - 100Mx12.1%x.5 = -6.051M

26. 7.26 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

27. 7.27 Exchange of Principal In an interest rate swap the principal is not exchanged In a currency swap the principal is exchanged at the beginning and the end of the swap Difference shows up in swap valuation approach via portfolio of staggered forwards

28. 7.28 The Cash Flows Year DollarsPounds $ ------millions------ 2007 –18.00 +10.00 2008 +1.08 –0.5 2009 +1.08 –0.5 2010 +1.08 –0.5 2011 +1.08 –0.5 2012+19.08 –10.5 £

29. 7.29 Typical Uses of a Currency Swap 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

30. 7.30 Comparative Advantage Argument for Currency Swaps General Electric wants to borrow AUD but comp. ad. in USD Qantas wants to borrow USD but comp. ad. in AUD. Precondition for viable swap satisfied! Comparative advantage: interest rate differences are different USD: 200 bps; AUD: 40 bps; Total Swap Gain = 160 bps. USDAUD General Electric 5.0%7.6% Qantas 7.0%8.0%

31. 7.31 Valuation (post-inception) 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

32. Currency Swap Valuation: difference between 2 bonds approach Test Bank 7.5

33. Currency Swap Valuation: portfolios of forwards approach Bank previously entered into a swap: receives 5% in JPY, pays 8% in USD Zero curves are flat: JPY 4%, USD 9% Principals: USD10M, JPY1,200M Current spot = JPY110/USD Swap has 3 years remaining CF exchange occurs annually; a CF exchange has recently occurred Intuition: Vswap > 0 since JPY R has dropped, USD R has risen. Also, JPY has appreciated; USD has depreciated since contract signed.

34. Swap Value = USD 1.543M = PV of last column entries TimeUSD CFJPY CFForward Rates NCF in USD 1-.860104.64-.2266 2-.86099.53-.1647 3-10.81,26094.681.9148

35. 7.35 Swaps & Forwards A swap can be regarded as a convenient way of packaging forward contracts When a swap is initiated the swap has zero value, but typically some forwards have a positive value and some have a negative value

36. 7.36 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

37. Credit Risk Exposure of Entity Vswap to entity Credit risk exposure only if Vswap > 0