3. A fund manager has a portfolio worth $50 million with a beta of 0.87. 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 1250, one 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 1259.

a. What position should the fund manager take to eliminate all exposure to the market over the next two months? Please specify the position and the number of contracts.

b. Calculate the effect of your strategy on the fund managers returns if the level of the market in two months is 1,000, 1,100, 1,200, 1,300, and 1,400. Assume that the one- month futures price is 0.25% higher than the index level at this time.

4. A stock is expected to pay a dividend of $1 per share in two months and in five months. The stock price is $50, and the risk-free rate of interest is 8% per annum with continuous compounding for all maturities. An investor has just taken a short position in a six-month forward contract on the stock.

a. What are the forward price and the initial value of the forward contract?

b. Three months later, the price of the stock is $48 and the risk-free rate of interest is still

8% per annum. What are the forward price and the value of the short position in the forward contract?