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Swaps

Swaps. 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

  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 • Next slide illustrates cash flows

  4. ---------Millions of Dollars--------- LIBOR FLOATING FIXED Net Date Rate Cash Flow Cash Flow Cash Flow Mar.1, 1998 4.2% Sept. 1, 1998 4.8% +2.10 –2.50 –0.40 Mar.1, 1999 5.3% +2.40 –2.50 –0.10 Sept. 1, 1999 5.5% +2.65 –2.50 +0.15 Mar.1, 2000 5.6% +2.75 –2.50 +0.25 Sept. 1, 2000 5.9% +2.80 –2.50 +0.30 Mar.1, 2001 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. Valuation 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 with the same par value • Par values will cancel at maturity

  7. Swap Valuation • Fixed Receive: Vswap = Vfixed – Vfloating • Fixed Pay: Vswap = Vfloating - Vfixed • The fixed rate bond is valued using the term structure of interest rates • The floating rate stream is valued by noting that it is worth par immediately after the next payment date

  8. Floating Rate Bond • To create a floating rate bond, invest principal value in 6-month LIBOR • At the end of 6-months, pay the interest and reinvest the principal value at the new 6-month LIBOR • At maturity pay last interest payment and principal value • Therefore, the cost of a floating rate bond is the principal value • It always sells for its par value immediately after interest payment

  9. Swap Valuation • The swap is structured such that initial value is zero to either party • Set Vswap = 0 • Vfixed = Vfloating = M • Since the bond is selling at par, CR = C/M = y • For the swap to have zero value the fixed rate must equal the yield to maturity on a par bond • The swap rate is the coupon rate on a fixed rate bond that causes it to be worth par

  10. Example • Zero coupon LIBOR curve is 5%, 6%, and 7% for one, two, and three years • What is the swap rate on a three year interest rate swap? • Assume payments are annual and yields are compounded annually • Solve for LIBOR par yield • M = CRxM(d1 + d2 + d3) + Md3

  11. Example Continued • Solution:

  12. Interest Rate Risk • Receive Fixed: Vswap = Vfixed – Vfloating • Pay Fixed: Vswap = Vfloating – Vfixed

  13. An Example of a Currency Swap An agreement to pay 11% on a sterling principal of £10,000,000 & receive 8% on a US$ principal of $15,000,000 every year for 5 years

  14. 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

  15. Three Cash Flow Components • t = 0: exchange principal based upon current exchange rates Pay: $15 M Rcv: £ 10 M • t = 1, 2, 3, 4, 5: Pay: .11x10 = £1.1 M Rcv: .08x15 = $1.2 M • t = 5: Pay: £ 10 M Rcv: $ 15 M

  16. The Cash Flow Dollars Pounds $ £ Years ------millions------ 0 –15.00 +10.00 +1.20 1 –1.10 2 +1.20 –1.10 3 +1.20 –1.10 4 +1.20 –1.10 5 +16.20 -11.10

  17. 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

  18. Valuationof 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

  19. Swaps & Forwards • A swap can be regarded as a convenient way of packaging forward contracts • The “plain vanilla” interest rate swap in our example consisted of 6 Fraps • The “fixed for fixed” currency swap in our example consisted of a cash transaction & 5 forward contracts

  20. Swaps & Forwards(continued) • The value of the swap is the sum of the values of the forward contracts underlying the swap • Swaps are normally “at the money” initially • This means that it costs nothing to enter into a swap • It does not mean that each forward contract underlying a swap is “at the money” initially

  21. 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

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