© K. Cuthbertson and D. Nitzsche 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 t0t0 t*t* t1t1 t2t2 r1r1 r2r2 t 12, f 12 Futures protection period = t 12 Exposure period, t 0 to t 1 t 1 = Maturity of futures contract

© K. Cuthbertson and D. Nitzsche Figure 5.3 : Hedge using US T-Bill Futures Purchase T-Bill future with Sept. delivery date $1m cash receipts Maturity date Sept. T-Bill futures contract 3 month exposure period Desired investment period = 6-months May Aug. Sept. Feb.Dec. Futures protection period

© K. Cuthbertson and D. Nitzsche Figure 5.4 : Eurodollar futures hedge Sept. future maturity MayJuneJulyAugustSeptember L0L0 Loan ends L1L1 L2L2 F 0 (Sept.) = Reset dates

© K. Cuthbertson and D. Nitzsche Figure 5.5 : Pricing an interest rate futures contract Receive $100 face value of 2-year T-bill Buy 2-year T-bill for $S with face value $100 A r2r2 r2r2 Receive $100 face value of T-bill underlying the F.C. Buy 1-year T-bill for F/(1 + r 1 ) B. 012 r1r1 f 12 Maturity of T-bill receive $F Portfolio A : 2-year T-bill Portfolio B : 1-year T-bill plus interest rate futures contract Go long a T-bill futures (at zero cost today) Pay $F for F.C. on 1-year T-bill

© K. Cuthbertson and D. Nitzsche Figure A5.1 : Forward rates from spot rates r 0.32, Derived forward rates at t= Days Days f 32,122 r 0.122, r 0.212, r 0.32, f 122,212 Current observed spot rates at t=0 90 days