Problem:

A fund manager has a portfolio worth $50 million with a beta of 1.35. The manager is concerned about the performance of the market over the next three months and plans to use four-month Mini S&P 500 futures contract to hedge the risk. The current level of the index is 1,560, the risk-free rate is 0.60% per annum, and the dividend yield on the index is 1.7% per annum. The current four-month futures price is 1,555. One futures contract covers $50 times the index.

Required:

Question 1: What position should the fund manager take to eliminate all exposure to the market over the next three months?

Question 2: Calculate the effect of your strategy on the fund manager's returns if the level of the market in three months is 1,600, and 1,700. Assume that the interest rate and the dividend yield will be unchanged.

Note: Explain all steps comprehensively.