A fund manager has a portfolio worth $200 million. The managers portfolio return changes have a 0.7 correlation with ASX 200 index return changes. The manager's portfolio return change has a standard deviation that is 35% greater than return changes in ASX index return. 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 ASX 200 to hedge the risk. The current level of the index is 5840, one contract is on 250 times the index, the risk-free rate is 4% per annum, and the dividend yield on the index is 2.4% per annum. The current 3 month futures price is 5887.

a. What position should the fund manager take to eliminate all exposure to the market over the next two months? How many futures contracts should the manager take? Please show your calculation. (4 marks)

b. Calculate the effect (net gain) of the fund manager (if the strategy in part a was employed) if the level of the ASX 200 in two months is 5103. Assume that the three-month futures price is 0.8% higher than the index level at this time. (6 marks)