Figures for Chapter 5 SHORTTERM INTEREST RATE FUTURES

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Figures for Chapter 5 SHORT-TERM INTEREST RATE FUTURES (Financial Engineering : Derivatives and Risk

Figures for Chapter 5 SHORT-TERM INTEREST RATE FUTURES (Financial Engineering : Derivatives and Risk Management) © K. Cuthbertson and D. Nitzsche

Figure 5. 2 : Interest rate futures contract r 2 r 1 t 0

Figure 5. 2 : Interest rate futures contract r 2 r 1 t 0 Futures protection period = t 12 t* t 1 Exposure period, t 0 to t 1 = Maturity of futures contract © K. Cuthbertson and D. Nitzsche t 2 t 12, f 12

Figure 5. 3 : Hedge using US T-Bill Futures 3 month exposure period May

Figure 5. 3 : Hedge using US T-Bill Futures 3 month exposure period May Desired investment period = 6 -months Aug. Sept. Dec. Futures protection period Purchase T-Bill future with Sept. delivery date $1 m cash receipts Maturity date Sept. T-Bill futures contract © K. Cuthbertson and D. Nitzsche Feb.

Figure 5. 4 : Eurodollar futures hedge Sept. future maturity Loan ends L 0

Figure 5. 4 : Eurodollar futures hedge Sept. future maturity Loan ends L 0 L 1 L 2 May June July Reset dates F 0 (Sept. ) = 97. 56 © K. Cuthbertson and D. Nitzsche August September

Figure 5. 5 : Pricing an interest rate futures contract Buy 2 -year T-bill

Figure 5. 5 : Pricing an interest rate futures contract Buy 2 -year T-bill for $S with face value $100 A. r 2 0 Buy 1 -year T-bill for F/(1 + r 1) B. Receive $100 face value of 2 -year T-bill r 2 2 1 r 1 0 Maturity of T-bill receive $F f 12 Receive $100 face value of T-bill underlying the F. C. 1 Go long a T-bill futures (at zero cost today) Pay $F for F. C. on 1 -year T-bill Portfolio A : 2 -year T-bill Portfolio B : 1 -year T-bill plus interest rate futures contract © K. Cuthbertson and D. Nitzsche 2

Figure A 5. 1 : Forward rates from spot rates Current observed spot rates

Figure A 5. 1 : Forward rates from spot rates Current observed spot rates at t=0 r 0. 212, r 0. 122, r 0. 32, 0 32 90 days 122 90 days 212 Days Derived forward rates at t=0 r 0. 32, 0 f 122, 212 f 32, 122 32 122 © K. Cuthbertson and D. Nitzsche