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.)a) What is the theoretical futures price for the three-month futures contract?b) 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 managers returns if the level of the market in two months is 2,000, 2,200, 2,500, 2,800, and 3,000.