Answer part (a) and (b) and please show your work.

Question 1: A fund manager has a portfolio worth $50 million with a beta of 0.9. The manager is concerned about the performance of the market over the next two months and plans to use 3-month futures contracts on the S&P 500 to hedge the risk. The current level of the index is 1,500, one contract is 250 times the index. The risk-free rate is 5% per annum, and the dividend yield is 3% per annum. The current 3-month futures price is 1510. a) What position should the fund manager take to hedge all exposure to the market over the next two months? b) Calculate the effect of your strategy on the fund's returns if the index level in 2 months is 1250, 1350, 1450, 1550, 1650. Assume that the futures price in 2 months is 0.3% higher than the corresponding index level level. Question 1: A fund manager has a portfolio worth $50 million with a beta of 0.9. The manager is concerned about the performance of the market over the next two months and plans to use 3-month futures contracts on the S&P 500 to hedge the risk. The current level of the index is 1,500, one contract is 250 times the index. The risk-free rate is 5% per annum, and the dividend yield is 3% per annum. The current 3-month futures price is 1510. a) What position should the fund manager take to hedge all exposure to the market over the next two months? b) Calculate the effect of your strategy on the fund's returns if the index level in 2 months is 1250, 1350, 1450, 1550, 1650. Assume that the futures price in 2 months is 0.3% higher than the corresponding index level level