A fund manager has a portfolio worth $100 million with a beta of 1.5. The manager is concerned about the performance of the market over the next two months and plans to use three-month futures contracts on the S&P 500 to hedge the risk. The current level of the index is 2250, one contract is on 250 times the index, the risk free rate is 2%, and the dividend yield on the index is 1.7% per year. (Assume all the rates are continuously compounded.)

- What is the theoretical futures price for the three-month futures contract?

- What position should the fund manger takes to eliminate all exposure to the market over the next two months?
- c) Calculate the effect of your strategy on the fund manager’s returns if the level of the market in two months is 2,000, 2,200, 2,500, 2,800, and 3,000.