A fund manager wants to hedge her portfolio against market movements over the next two months. The portfolio is worth $40 million and its CAPM beta is 0.8. The manager plans to use three-month futures contracts on a well-diversified index to hedge its risk. The current level of the index is 3200, one contract is on $50 times the index, the risk-free rate is 2.4% per annum, and the dividend yield on the index is 1.8% per annum. The current 3-month futures price is 3205.

1. (a) What position should the fund manager take to eliminate all exposure to the market over the next two months?

2. (b) Calculate the expected gain or loss of the fund managers hedged position under four cases: the index value in two months is 2,500, 3,000, 3,500, and 4,000. In each case, assume that the one-month futures price after two months is 0.05% higher than the index level at that time. Your portfolio value at that time is not provided for these cases. To calculate the expected value of your portfolio after two months in any case, determine the excess return on market as the percentage increase in the index plus the dividend yield over two months minus the risk-free rate over two months. Multiply by the beta of the portfolio to get expected excess return on the portfolio. Add risk-free rate over two months to get the expected return on the index over two months. For this problem you can ignore compounding so that, for example, 2.4% per annum is equivalent to 2.4% 1/12 = 0.2% per month.