Ch9Sols - 9-1CHAPTER 9: PRINCIPLES OF FORWARD AND FUTURES

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Unformatted text preview: 9-1CHAPTER 9: PRINCIPLES OF FORWARD AND FUTURES PRICINGEND-OF-CHAPTER QUESTIONS AND PROBLEMS1.The original forward contract is worth the present value of the difference between the current forwardprice and the original forward price($54 - $45)(1.10)-.5= $8.58Suppose the original forward contract is bought on January 1 when the price is $45. It expires onDecember 31. The current date is July 1, halfway during the life of the contract. New forward contractscan be sold at a price of $54. If one new contract is sold, in six months the cash flow will be $45 paid forthe commodity on the original contract and $54 received for delivery of the commodity on the newcontract. Thus, the total net cash flow is $9. This amount is known for certain on July 1. So on July 1,the value of a long position in the original contract and a short position in the new contract is the presentvalue of $9 or $8.58. But the value of the new forward contract is zero, so the value of the overall positionmust equal the value of the old forward contract. Thus, $8.58 must be the value of the old forwardcontract.2.Other than the insignificant margin requirement, a futures contract requires no initial outlay of funds.Immediately after buying the contract and before the price changes, the holder of the contract cannotreceive anything for selling it. Since you cannot receive anything for it, it has no value. The spotcommodity, however, requires payment and it can be resold immediately for cash. Thus, it has valueequal to whatever price it will fetch in the market, the current spot price.3.The value at the opening is699.70 - 699.30 = .40In dollars, this is.40($500) = $200An instant before the close, the value is(699.10 - 699.30) = -.20In dollars, that is-.20($500) = -$100After the market has closed, the contract is marked-to-market, the gain or loss is distributed, and the valueis zero.4.a.If the interest rate is known to be constant, then the forward and futures prices should be equal.Here the futures price exceeds the forward price. To generate an arbitrage profit, you should buyone forward contract and sell 1.05-(1/365)futures contracts.b.On March 14, you close out the 1.05-(1/365)futures contracts. The daily settlement produces acash flow of-1.05-(1/365)(353.35 - 353.625).Since this is positive, it is invested in risk-free bonds for one day. If it were negative, it would befinanced by issuing a one-day risk-free loan. The next day this cash flow will have grown to avalue of9-2-1.05-(1/365)(353.35 - 353.625)1.05(1/365)= -(353.35 - 353.625) = .275.Then on March 14 you sell one new futures contract. The contract is marked-to-market onMarch 15 for a cash flow of-(350.125 - 353.35) = 3.225....
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Ch9Sols - 9-1CHAPTER 9: PRINCIPLES OF FORWARD AND FUTURES

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