1) Suppose that the risk-free rate is 10% p.a. with continuous compounding and that the dividend yield on a stock index is 4% p.a. The index is standing at 400, and the futures price for a contract deliverable in 4 months is 405. Identify the arbitrage opportunity, if any.
2) A trader buys two long July futures contracts on orange juice. Each contract is for the delivery of 15,000 pounds. The current futures price is 150 cents per pound, the initial margin is $6,000 per contract, and the maintenance margin is $4,500 per contract. What price change would lead to a margin call? Under what circumstances could $3,000 be withdrawn from the margin account?
3) Suppose that the standard deviation of quarterly changes in the price of a commodity is £0.50, the standard deviation of quarterly changes in the futures price of a closely related commodity is £0.75 and the coefficient of correlation between the two changes is 0.3 What is the optimal hedge ratio for a 3-month contract? Interpret it.
4) A company has a portfolio with a beta of 1.5 and valued at $30 million. It uses futures contracts on the S&P 500 to hedge its risk. The index futures is currently standing at 1,500 and each contract is for delivery of $250 times the index. What is the hedge that minimizes the risk? What should the company do if it wants to reduce the beta of the portfolio to 0.5?