A company has a 20,000,000  portfolio with a beta of 1.2. It would like to use futures contracts on a well-diversified 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?

ANSWER：
The formula for the number of contracts that should be shorted gives 1.2*[2,000,000/(1080*250)]=88.9
Rounding to the nearest whole number, 89 contracts should be shorted. To reduce the beta to 0.6, half of this position, or a short position in 44 contracts, is required.