It is July 16. A company has a portfolio of stocks worth $100 million. The beta of the portfolio is 1.6. The company would like to use the CME December futures contract on the S&P 500 to change the beta of the portfolio to 0.3 during the period July 16 to November 16. The December S&P 500 index futures price is currently 1,000, and each contract is on $250 times the index.

(a) What position should the company take? How many December S&P 500 futures contracts should the company buy or sell now?

(b) Suppose that the company changes its mind and decides to increase the beta of the portfolio from 1.6 to 1.8. What position in futures contracts should it take? How many December S&P 500 futures contracts should the company buy or sell now?