7 Interest Rate Risk

# T term structure equation 1

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Unformatted text preview: tial position π S = (F0 − Fτ) × 100 bonds × no. contracts Ec 174 INTEREST RATE RISK on × 9 × 0.005 = –\$225,000 (a loss) • ΔB/B0 = –Db*(Δry) = –12.25 × 0.005 = –6.125% • Fτ has dropped by 6.125% to 0.93875 × 1274.84 = \$1,196.76. • πshort = (F0 − Fτ) × units = (1274.84–1196.76) × 100×29 = \$226,432 (a gain). • Total net change in value is only 226,432 - 225,000 = \$1,432. Ec 174 INTEREST RATE RISK p. 12 of 17 E. Interest Rate Swaps {BKM §23.4} 1. Introduction to Swaps: a) A swap is an agreement between two entities (counterparties) to exchange a sequence of cash flows in each of several future periods. 1) The agreement specifies the formula for computation of the cash flows and the exact dates for their payment. 2) Typically, one cash flow stream is fixed, and the other is “floating” in that it depends on the future value of some market variable like an interest or exchange rate. b) A swap arrangement is like a multi- period series of forward contracts. For example, con- sider the following “one- cash- flow fixed- for- floating” swap. 1) Logan agrees to buy 100 oz. of gold in one year at forward price F0 = \$600/oz. Sharon, with gold to deliver, is the counterparty with the short position. 2) Once Logan takes delivery of the gold and pays Sharon, he can sell the gold at ST. 3) Logan has exchanged cash flows with Sharon. He will get the floating cash flow \$ST×100 (which depends on the market price of gold ST in one year), and she will get the fixed cash flow \$60,000 (known today). c) Three common types of swaps. 1) Interest rate swaps – one company pays interest at a fixed rate and receives it at a float- ing rate (usually LIBOR); the counterparty does the opposite. 2) Currency swaps – one company pays interest and principal in one currency and receives interest and principal in another, vis- à- vis a counterparty company. 3) Credit default swaps (CDSs) – not really swaps, but insurance policies. Company B holds a bond or loan or debt security from corporation X. B buys a default protection policy from insurance company S and makes periodic payments (insurance premiums). If X defaults on the bond payments, S pays the principal to B. 4) Swaps began about 1980; they became a major OTC derivative, with about \$300 trillion of open interest in 2008. AIG got hit hard on Notation (Interest Rate Swaps) CDSs. \$A Notional principal 2. Mechanics of Interest Rate Swaps: {Hull §7.1, 7.5 - 7.6} rℓ Floating rate (LIBOR) rx Fixed (swap) rate a) “Plain Vanilla” interest rate swaps. X party RECEIVING fixed CF 1) At time t = 0, parties X and F agree to: F party RECEIVING floating CF • a dollar value of notional principal (\$A) • a sequence of dates during the next few years for payments of cash flows • a fixed or predetermined interest rate (rx) • a market or floating rate (rℓ) which varies over the life of the swap agreement 2) X will pay \$rℓA of interest at floating or variable rate to F at regular intervals...
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