A fund manager has a portfolio worth $20 million with a beta of 1.4. The manager is concerned about the performance of the market over the next two months and plans to use threemonth futures contracts on the S&P 500 to hedge the risk. The current index level is 1,850 and one futures contract is on 250 times the index (i.e., the index multiplier is 250). The riskfree rate is 4.0% per annum and the dividend yield on the index is 2.0% per annum. The current threemonth futures price is $1,900. a. What position should the fund manager take to hedge exposure to the market over the next two months? In other words, how many futures contracts does the manager have to buy or sell? Specify whether it’s a long (=buy) or short (=sell) position. b. Calculate the effect of your strategy on the fund manager’s returns if the index in two months is 1600, 1700, 1800, 1900 and 2000. Assume in 2 months, the onemonth futures price will be 0.25% higher than the index level. For example, if the index is 1600 two months from now, the index futures price will be 1.0025*1600 = 1604.00. c. Are the total values (hedged values = stock portfolio plus futures position) always greater than the stock (=unhedged) values, no matter what the index becomes in 2 months? If not, does it mean the hedge was unsuccessful? Explain.