1. It is July 16. A company has a portfolio of stocks worth $100 million. The beta of the portfolio is 1.2. The company would like to use the CME December futures contract on the S&P 500 to change the beta of the portfolio to 0.5 during the period July 16 to November 16. The index is currently 1,000, and each contract is on $250 times the index. (a) What position should the company take? (b) Suppose that the company changes its mind and decides to in- crease the beta of the portfolio from 1.2 to 1.5. What position in futures contracts should it take? 2. 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 the S&P 500 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, 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 ex- posure to the market over the next two months? (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. Suppose that a beef packer in Amarillo has a plant-capacity of slaugh- tering 1,000 fed cattle per month. Each fed cattle weight approximately 1,200 lbs. It is Oct 19. The cash price for live cattle is 75 cents/lb in the local market, and Feb CME Live Cattle futures settled at 85 cents/lb. To fully cover her expected cash position in February, the beef packer needs CME Live Cattle futures (because the size of CME Live Cattle futures is 40,000 lbs.) The beef packer plans to purchase live cattle in February from the local market, but is worried that cash price for live cattle may increase to 80 cents/lb in February. The beef packer may hedge against the increasing price risk by long hedging. (a) Calculate net payment (cash payment + profit/loss from futures transaction) and net price paid with zero basis risk. (b) Calculate net payment and net price paid when basis expands to 15 cents/lb. (c) Calculate net payment and net price paid when basis shrinks to 5 cents/lb