A fund manager has an all-equity portfolio worth $50 million with a beta of 1.25. 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 index to lower the beta of their investment to 0.75. The current level of the index is 1,300, one index futures contract is on $250 times the index, the risk-free rate is 6% per annum, and the dividend yield on the index is 3% per annum. The current 3- month futures price is 1309. 1. What position in index futures contracts should the fund manager take to reduce the beta to 0.75 over the next two months? (3 marks) 2. Calculate the effect of the strategy on the fund manager's returns if the fund manager decides to close out his futures position in two months when the level of the market is 1,400. Assume that the one-month futures price is 0.25% higher than the index level at this time. (7 marks) index is 3% per annum. The current 3- month futures price is 1309. 1. What position in index futures contracts should the fund manager take to reduce the beta to 0.75 over the next two months? (3 marks) 2. Calculate the effect of the strategy on the fund manager's returns if the fund manager decides to close out his futures position in two months when the level of the market is 1,400. Assume that the one-month futures price is 0.25% higher than the index level at this time. (7 marks) 3. When this strategy is more effective? When the market is bullish or when the market is bearish? What might prompt someone to halve the beta of their portfolio over the next 2 months? (4 marks)