Q.1 An investor enters into a short forward contract to sell 100,000 British pounds for U.S. dollars at an exchange rate of 1.9000 U.S. dollars per pound. How much does the investor gain or lose if the exchange rate at the end of the contract is (a) 1.8900 and (b) 1.9200?
Q.2 Suppose that on October 24, 2009, a company sells one April 2010 live-cattle futures contract. It closes out its position on January 21, 2010. The futures price (per pound) is 91.20 cents when it enters into contract, 88.30 cents when it closes out its position, and 88.80 cents at the end of December 2009. One contract is for the delivery of 40,000 pounds of cattle. What is the total profit? How is it taxed if the company is (a) a hedger and (b) a speculator? Assume that the company has a December 31 year end.
Q.3 Suppose that the standard deviation of quarterly changes in the prices of a commodity is $0.65, the standard deviation of quarterly changes in a futures price on the commodity is $0.81, and the coefficient of correlation between the two changes is 0.8. What is the optimal hedge ratio for a three-month contract? What does it mean?
Q.4 A one-year long forward contract on a non-dividend-paying stock is entered into when the stock price is $40 and the risk-free rate of interest is 10% per annum with continuous compounding.
(a) What are the forward price and the initial value of the forward contract?
(b) Six months later, the price of the stock is $45 and the risk-free interest rate is still 10%. What are the forward price and the value of the forward contract?
Q.5 Suppose that the risk-free interest rate is 10% per annum with continuous compounding and that the dividend yield on a stock index is 4% per annum. The index is standing at 400, and the futures price for a contract deliverable in four months is 405. What arbitrage opportunities does it create? Please specify the correct arbitrage strategy based on your calculation.