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Unformatted text preview: 11-1CHAPTER 11: ADVANCED FUTURES STRATEGIESEND-OF-CHAPTER QUESTIONS AND PROBLEMS1.A repurchase agreement (repo) is a type of loan in which the borrower sells a security such as a T-billwith the agreement to buy the security back at a later date. The security serves as a form of collateral. Thedifference between the price at which the investor purchases the security and the price at which theinvestor sells it reflects the rate of interest. Most repurchase agreements are short term, frequently for anovernight period; however, some repos are for as long as two weeks. In pricing futures, the reporepresents the cost of financing the spot position. The repo rate implied by the relationship between thefutures and spot prices is the implied repo rate. If the implied repo rate exceeds the actual rate on repofinancing, the cash-and-carry transaction should be done. Otherwise the reverse transaction should bedone. Of course, transaction costs must be covered.2.The price of the T-bill maturing on March 20, 139 days from November 1, is100 - 7.17(139/360) = 97.2316The T-bill futures price is100 - 7(90/360) = 98.25The implied repo rate is(98.25/97.2316)(365/48)- 1 = .08253.a.The March T-bill matures in 140 days; its price is100 - 7.17(140/360) = 97.2117The return on the March T-bill is(100/97.2117)(365/140)- 1 = .0765You buy the March futures at its price of(100 - 7.15(90/360) = 98.2125This guarantees that a T-bill can be purchased in March at an effective price of 98.2125. Thereturn on such a T-bill is(100/98.2125)(365/91)- 1 = .075The overall return on the synthetic security is(1.0765)(140/365)(1.075)(91/365)= (1 + r)(231/365)Solving for r givesr = .0759b.An actual June T-bill would have a price of100 - 7.31(231/360) = 95.3094This would imply a return of11-2(100/95.3094)(365/231)- 1 = .0789The actual T-bill has a higher return. The returns should be equal since they are essentially thesame security. Thus, an arbitrage profit is possible, which would drive the returns together.4.The contract permits delivery of any Treasury bond that does not mature or is not callable within 15 yearsof the first day of the delivery month. There are many bonds that meet the eligibility requirement; thecheapest bond to deliver is found by calculating the difference between the product of the futures price andthe conversion factor and the forward price. Since this difference is usually negative, the cheapest bond todeliver will have the smallest absolute value of this number.It is impossible to predict which bond will be the cheapest to deliver at expiration. Prior to expiration, thecalculations can be made for all eligible bonds, but changes in interest rates and futures prices can make adifferent bond become the cheapest to deliver at a later point in the contract's life....
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This note was uploaded on 03/09/2011 for the course FINA 4210 taught by Professor Staff during the Fall '08 term at North Texas.
- Fall '08