Decimal places: please keep at least 4 in the calculations, 2 in the final answers.

Q3 A fund manager has a portfolio worth $50 million with a beta of 1.8 . The manager is concerned about the performance of the market over the next two months and plans to use three-month futures contracts on a well-diversified index to hedge its risk. The current level of the index is 4,165 , one contract is on 250 times the index, the risk-free rate is 5% per annum, and the dividend yield on the index is 1.67% per annum. a) What position should the fund manager take to eliminate all exposure to the market over the next two months? b) Calculate the effect of your strategy on the fund manager's returns if the level of the market in two months is 3,900 and 4,400. c) What position should the fund manager take to reduce the beta to 0.7 ? To increase the beta to 2.2