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Chapter 12: Swaps

Chapter 12: Swaps. Markets are an evolving ecology. New risks arise all the time. Andrew Lo CFA Magazine , March-April, 2004, p. 31. Important Concepts. The concept of a swap Different types of swaps, based on underlying currency, interest rate, or equity Pricing and valuation of swaps

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Chapter 12: Swaps

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  1. Chapter 12: Swaps Markets are an evolving ecology. New risks arise all the time. Andrew Lo CFA Magazine, March-April, 2004, p. 31 An Introduction to Derivatives and Risk Management, 7th ed.

  2. Important Concepts • The concept of a swap • Different types of swaps, based on underlying currency, interest rate, or equity • Pricing and valuation of swaps • Strategies using swaps An Introduction to Derivatives and Risk Management, 7th ed.

  3. Nature of Swaps • A swap is an agreement to exchange cash flows at specified future times according to certain specified rules. An Introduction to Derivatives and Risk Management, 7th ed.

  4. SWAPS: Exchange assets now; return them later; in meantime, pay differential rent. Here’s your house back; thanks for returning my boat. Thanks for returning my house; here’s your boat back. JanuaryJuly I’ll use your house until July for $4,000/mo. I’ll use your boat until July for $3,000/mo. ($4,000 - $3,000)/mo = $1,000/mo

  5. Four types of swaps • Currency • Interest rate • Equity • Commodity • Characteristics of swaps • No cash up front • Notional principal • Settlement date, settlement period • Credit risk • Dealer market • See Figure 12.1, p. 407 for growth in world-wide notional principal An Introduction to Derivatives and Risk Management, 7th ed.

  6. Interest Rate Swaps • In an interest rate swap, two parties agree to exchange or swap a series of interest payments. • In a “plain vanilla” interest rate swap, one party agrees to make a series of fixed interest payments and the other agrees to make a series of variable or floating interest payments. An Introduction to Derivatives and Risk Management, 7th ed.

  7. Example of a “Plain Vanilla” Swap • An agreement by XYZ Corp 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.

  8. Cash Flows to XYZ Corp ---------Millions of Dollars--------- LIBOR FLOATING FIXED Net Date Rate Cash Flow Cash Flow Cash Flow Mar.5, 2004 4.2% Sept. 5, 2004 4.8% +2.10 –2.50 –0.40 Mar.5, 2005 5.3% +2.40 –2.50 –0.10 Sept. 5, 2005 5.5% +2.65 –2.50 +0.15 Mar.5, 2006 5.6% +2.75 –2.50 +0.25 Sept. 5, 2006 5.9% +2.80 –2.50 +0.30 Mar.5, 2007 6.4% +2.95 –2.50 +0.45

  9. 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

  10. Transforming a Liability 5% 5.2% ABC XYZ LIBOR+0.1% LIBOR

  11. When a Financial Institution is Involved 4.985% 5.015% 5.2% ABC F.I. XYZ LIBOR+0.1% LIBOR LIBOR

  12. Beaver Country Day School outside of Boston, and Tim Parson, its finance director.

  13. Transforming an Asset 5% 4.7% ABC XYZ LIBOR-0.2% LIBOR

  14. When a Financial Institution is Involved 4.985% 5.015% 4.7% F.I. XYZ ABC LIBOR-0.2% LIBOR LIBOR

  15. Quotes By a Swap Dealer

  16. The Comparative Advantage Argument Fixed Floating PQR Corp 4.00% 6-month LIBOR + 0.30% RST Corp 5.20% 6-month LIBOR + 1.00% • PQR Corp wants to borrow floating • RST Corp wants to borrow fixed

  17. The Swap 3.95% 4% PQR RST LIBOR+1% LIBOR

  18. When a Financial Institution is Involved 3.93% 3.97% 4% PQR F.I. RST LIBOR+1% LIBOR LIBOR

  19. Criticism of the Comparative Advantage Argument • The 4.0% and 5.2% rates available to PQR Corp and RST Corp in fixed rate markets are 5-year rates. • The LIBOR+0.3% and LIBOR+1% rates available in the floating rate market are six-month rates. • RST Corp’s fixed rate depends on the spread above LIBOR it borrows at in the future.

  20. 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.

  21. Interest Rate Swaps • The Structure of a Typical Interest Rate Swap • Example: On December 15 XYZ enters into $50 million NP swap with ABSwaps. Payments will be on 15th of March, June, September, December for one year, based on LIBOR. XYZ will pay 7.5% fixed and ABSwaps will pay LIBOR. Interest based on exact day count and 360 days (30 per month). In general the cash flow to the fixed payer will be An Introduction to Derivatives and Risk Management, 7th ed.

  22. Interest Rate Swaps • The Structure of a Typical Interest Rate Swap (continued) • The payments in this swap are • Payments are netted. • See Figure 12.2, p. 409 for payment pattern • See Table 12.1, p. 410 for sample of payments after-the-fact. An Introduction to Derivatives and Risk Management, 7th ed.

  23. Zero Rates • A zero rate (or spot rate), for maturity T is the rate of interest earned on an investment that provides a payoff only at time T

  24. Example

  25. Forward Rates • The forward rate is the future zero rate implied by today’s term structure of interest rates

  26. Forward Rates

  27. Forward Rates

  28. Formula for Forward Rates • Suppose that the zero rates for time periods T1and T2are R1 and R2 with both rates continuously compounded. • The forward rate for the period between times T1 and T2 is

  29. Calculation of Forward Rates Zero Rate for Forward Rate n n an -year Investment for th Year n Year ( ) (% per annum) (% per annum) 1 3.0 2 4.0 5.0 3 4.6 5.8 4 5.0 6.2 5 5.3 6.5

  30. Forward Rate Agreement • Forward Rate Agreement (FRA) is an agreement where interest at a predetermined rate, RK is exchanged for interest at the market rate. • An FRA can be valued by assuming that the forward interest rate is certain to be realized.

  31. Forward Rate Agreement • A contract made directly between 2 parties (a seller and a buyer) fixing the interest rate (at settlement date) that will apply to a notional principal sum of money for an agreed future time period (maturity date), such that at maturity date, • The FRA buyer: receives money from the seller if the reference benchmark interest rate is above the one agreed in the contract. • The FRA seller: receives money from the buyer if the reference benchmark interest rate is bellow the one agreed in the contract.

  32. Forward Rate Agreement

  33. Forward Rate Agreement

  34. Forward Rate Agreement

  35. FRA Valuation • Value of FRA where a fixed rate RK will be received on a principal L between times T1 and T2 is • Value of FRA where a fixed rate is paid is • RFis the forward rate for the period and R2 is the zero rate for maturity T2

  36. Example: FRA Valuation Suppose that the three-month LIBOR rate is 5% and the six-month LIBOR rate is 5.5% with continuous compounding. Consider an FRA where you will receive a rate 7% measured with quarterly compounding, on a principal of $1 million between the end of month 3 and the end of month 6. The forward rate is 6% percent with continuous compounding or 6.0452 with quarterly compounding. The value of the FRA is $1,000,000 x (.07– .060452) x 0.25 x e-0.055 x 0.5 = $2,322

  37. Example: FRA Valuation

  38. Valuation of an Outstanding Interest Rate Swap • An interest rate swap is worth zero, or close to zero, when it is initiated. After it has been in existence for some time, its value may become positive or negative. • Interest rate swaps can be valued as the difference between the value of a fixed-rate bond (Bfix) and the value of a floating-rate bond (Bfl). • Alternatively, they can be valued as a portfolio of FRAs.

  39. Valuation in Terms of Bonds • The fixed rate bond is valued in the usual way as present value of future cash flows. • The floating rate bond is valued by noting that it is worth par immediately after the next payment date. • Then the value of the swap (VSWAP) is • VSWAP = Bfix - Bfl

  40. Example Suppose that PDQ Corp pays six-month LIBOR and receives 8% per annum (with semiannual compounding) on a swap with notional principal of $100 million and the remaining payment are in 3, 9, and 15 months. The swap has a remaining life of 15 months. The LIBOR rates with continuous compounding for 3-month, 9-month, and 15-month maturities are 10%, 10.5%, and 11%. The 6-month LIBOR rate at the last payment date was 10.2% (with semiannual compounding). What is the value of the swap?

  41. Swap Valuation Bfix = 4e-0.1x3/12 + 4e-0.105x9/12 + 104e-0.11x15/12 = $98.24 million Bfl = 105.1e-0.1x3/12 = $102.51 million The value of the swap is VSWAP= $98.24 million - $102.51 million = - $4.27 million If PDQ Corp had been paying fixed and receiving floating, the value of the swap would be + $4.27 million.

  42. 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. • The procedure is as follows: • Calculate forward rates for each of the LIBOR rates that will determine swap cash flows. • Calculate swap cash flows assuming that the LIBOR rates will equal the forward rates. • Set the swap value equal to the present value of these cash flows.

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