23 8 23 f s l r f t 580 105 609 if f 620 you could

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23. F 0 = S 0 (l + r f ) T = 580 × 1.05 = 609 If F 0 = 620, you could earn arbitrage profits as follows: CF Now CF in 1 year Buy gold 580 S T Short futures 0 620 S T Borrow $580 580 609 Total 0 11 The forward price must be 609 in order for this strategy to yield no profit. 24. 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. 25. 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 where FA stands for the future value factor for a level annuity with a given interest rate and number of payments. Thus, in order to induce storage, the expected price would have to be: $2.867 + $0.091 = $2.958 Because the expected spot price is only $2.94, you would not store corn. 23-9
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26. a. Delsing should sell stock index futures contracts and buy bond futures contracts. This strategy is justified because buying the bond futures and selling the stock index futures provides the same exposure as buying the bonds and selling the stocks. This strategy assumes high correlation between the bond futures and the bond portfolio, as well as high correlation between the stock index futures and the stock portfolio. b. The number of contracts in each case is: i. 5 × $200,000,000 × 0.0001 = $100,000 $100,000/97.85 = 1022 contracts ii. $200,000,000/($1,378 × 250) = 581 contracts 27. Situation A. The market value of the portfolio to be hedged is $20 million. The market value of the bonds controlled by one futures contract is $63,330. If we were to equate the market values of the portfolio and the futures contract, we would sell: $20,000,000/$63,330 = 315.806 contracts However, we must adjust this “naive” hedge for the price volatility of the bond portfolio relative to the futures contract. Price volatilities differ according to both the duration and the yield volatility of the bonds. In this case, the yield volatilities may be assumed equal, because any yield spread between the Treasury portfolio and the Treasury bond underlying the futures contract is likely to be stable. However, the duration of the Treasury portfolio is less than that of the futures contract. Adjusting
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