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Swaps

Swaps. Chapter 7. Nature of Swaps. A swap is an agreement to exchange cash flows at specified future times according to certain specified rules. An Example of a “Plain Vanilla” Interest Rate Swap.

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Swaps

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  1. Swaps Chapter 7

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

  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. ---------Millions of Dollars--------- LIBOR FLOATING FIXED Net Date Rate Cash Flow Cash Flow Cash Flow Mar.5, 2007 4.2% Sept. 5, 2007 4.8% +2.10 –2.50 –0.40 Mar.5, 2008 5.3% +2.40 –2.50 –0.10 Sept. 5, 2008 5.5% +2.65 –2.50 +0.15 Mar.5, 2009 5.6% +2.75 –2.50 +0.25 Sept. 5, 2009 5.9% +2.80 –2.50 +0.30 Mar.5, 2010 6.4% +2.95 –2.50 +0.45 Cash Flows to Microsoft

  5. 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 Typical Uses of anInterest Rate Swap

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

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

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

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

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

  11. Fixed Floating AAACorp 4.00% 6-month LIBOR + 0.30% BBBCorp 5.20% 6-month LIBOR + 1.00% 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

  12. The Swap 3.95% 4% AAA BBB LIBOR+1% LIBOR 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. The Swap when a Financial Institution (earns 4 bps) is Involved 3.93% 3.97% 4% AAA F.I. BBB LIBOR+1% LIBOR LIBOR

  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. 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. 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. 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. 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. 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. 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. 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. F2 = 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. F2 = 12.1% T=1.25: CF = - 100Mx12.1%x.5 = -6.051M

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

  29. 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 Typical Uses of a Currency Swap

  30. USD AUD General Electric 5.0% 7.6% Qantas 7.0% 8.0% 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.

  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

  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. 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 Credit risk exposure only if Vswap > 0 Vswap to entity

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