1. 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 coecient of correlation between the two changes is 0.8. What is the optimal hedge ratio for a three-month contract? What does it mean?

2. A company has a $20 million portfolio with a beta of 1.2. It would like to use futures contracts on a well-diversied stock index to hedge its risk. The index futures price is currently 1080, and each contract is for delivery of $250 times the index. What is the hedge that minimizes risk? What should the company do if it wants to reduce the beta of the portfolio to 0.6?

3. In the CME Groups corn futures contract, the following delivery months are available:March, May, July, September, and December. State the contract that should be used for hedging when the expiration of the hedge is in (a) June, (b) July, and (c) January.

4. Explain why a short hedgers position improves when the basis strengthens unexpectedly and worsens when the basis weakens unexpectedly.