Under what circumstances are (a) a short hedge and (b) a long hedge appropriate? (5 marks) Explain what is meant by a perfect hedge. Does a perfect hedge always lead to a better outcome than an imperfect hedge? Explain your answer. (5 marks) 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? (10 marks) Explain why a short hedger's position improves when tile basis strengthens unexpectedly and worsens when the basis weakens unexpectedly. (5 marks) What is the difference between the forward price and the value of a forward contract? (5 marks) 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. What are the forward price and the initial value of the forward contract? Six months later, the price of the stock is $45 and the risk-free interest rate is stil110%" What are the forward price and the value of the forward contract? (10 marks)