Problem 2. Richard Green manages a portfolio of assets that are worth $50 million. The portfolio has a beta of 0.87 with respect to the S&P 500 index. Assume that the alpha and expense ratio of the portfolio are both zero. 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 hedge the 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. Assume that the dividend yield on the index is 3% per annum. Assignment 2: page 1 (a) What is the theoretical futures price for the three-month futures contract on the S&P 500 index? (b) Based on the formula in class, which ignores the mismatch between futures maturity and hedging period, how many futures contracts (in whole number) would the fund manager long or short, intending to eliminate the exposure to the market over the next two months? (c) How much does the portfolio manager gain (or lose) on his futures contracts if the market index at the end of hedging period is 1000, 1100, 1200, 1300, and 1400? Create a table to list the profit or loss (P/L) corresponding to each of the given index levels. (d) Suppose there are no idiosyncratic shocks to portfolio returns. (This is true if the asset portfolio consists of only the S&P 500 stocks and Treasury bills.) Calculate and report the P/L of the unhedged portfolio when the S&P 500 index finishes at the above given levels at the end of the hedging period. To simplify the calculation, you can approximate the two-month dividend yield by 3%