A fund manager has a portfolio worth $50 million with a beta of 0.87. The manager is concerned about the performance of the market over the next 3 months and plans to use 4-month futures contracts on the S&P 500 to hedge the risk. The current level of the index is 2,835, one contract is on 250 times the index, the risk-free rate is 1.35% per annum, and the dividend yield on the index is 1.50% per annum. The current 4-month futures price is 2,845.

(a)What position should the fund manager take to eliminate all exposure to the market over the next 3 months?

(b)Calculate the effect of your strategy on the fund manager's returns if the level of the market in four months is 2,700, 2,800, 2,900, and 3,000. Assume that the 1-month futures price is 0.25% higher than the index level at this time.