# With the covering of interest rate risk action now cf

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with the covering of interest rate risk: Action Now CF in \$ Action at period-end CF in \$ Borrow \$2.00 in U.S. \$2.00 Repay loan –\$2.00 × 1.04 Convert borrowed dollars to pounds; lend £1 pound in U.K. –\$2.00 Collect repayment; exchange proceeds for dollars 1.07 × E 1 Sell forward £1.07 at F 0 = \$1.98 0 Unwind forward 1.07 × (\$1.98 – E 1 ) Total 0 Total \$0.0386 13. The farmer must sell forward: 100,000 × (1/0.90) = 111,111 bushels of yellow corn This requires selling: 111,111/5,000 = 22.2 contracts 14. The closing futures price will be: 100 - 4.80 = 95.20 The initial futures price was 95.4525, so the loss to the long side is 25.25 basis points or: 25.25 basis points × \$25 per basis point = \$631.25 The loss can also be computed as: 0.002525 × ¼ × \$1,000,000 = \$631.25 15. Suppose the yield on your portfolio increases by 1.5 basis points. Then the yield on the T-bond contract is likely to increase by 1 basis point. The loss on your portfolio will be: \$1 million ×∆ y × D* = \$1,000,000 × 0.00015 × 4 = \$600 The change in the futures price (per \$100 par value) will be: \$95 × 0.0001 × 9 = \$0.0855 This is a change of \$85.50 on a \$100,000 par value contract. Therefore you should sell: \$600/\$85.50 = 7 contracts 23-5

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Chapter 23 - Futures, Swaps, and Risk Management 16. She must sell: 8 . 0 \$ 10 8 million 1 \$ = × million of T-bonds 17. If yield changes on the bond and the contracts are each 1 basis point, then the bond value will change by: \$10,000,000 × 0.0001 × 8 = \$8,000 The contract will result in a cash flow of: \$100,000 × 0.0001 × 6 = \$60 Therefore, the firm should sell: 8,000/60 = 133 contracts The firm sells the contracts because you need profits on the contract to offset losses as a bond issuer if interest rates increase. 18. F 0 = S 0 (l + r f ) T = 880 × 1.04 = 915.20 If F 0 = 920, you could earn arbitrage profits as follows: CF Now CF in 1 year Buy gold - 880 S T Short futures 0 920 - S T Borrow \$880 880 - 915.20 Total 0 4.80 The forward price must be 915.20 in order for this strategy to yield no profit. 19. If a poor harvest today indicates a worse than average harvest in future years, then the futures prices will rise in response to today’s harvest, although presumably the two-year price will change by less than the one-year price. The same reasoning holds if corn is stored across the harvest. Next year’s price is determined by the available supply at harvest time, which is the actual harvest plus the stored corn. A smaller harvest today means less stored corn for next year which can lead to higher prices. Suppose first that corn is never stored across a harvest, and second that the quality of a harvest is not related to the quality of past harvests. Under these circumstances, there is no link between the current price of corn and the expected future price of corn. The quantity of corn stored will fall to zero before the next harvest, and thus the quantity of corn and the price in one year will depend solely on the quantity of next year’s harvest, which has nothing to do with this year’s harvest. 23-6
Chapter 23 - Futures, Swaps, and Risk Management 20. The required rate of return on an asset with the same risk as corn is: 1% + 0.5(1.8% – 1%) = 1.4% per month Thus, in the absence of storage costs, three months from now corn would sell for: \$2.75 × 1.014 3 = \$2.867 The future value of 3 month’s storage costs is: \$0.03 × FA(1%, 3) = \$0.091

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