You Are a Portfolio Manager Who Has Just Discovered the Possibilities

Essay

You are a portfolio manager who has just discovered the possibilities of stock-index futures.Assume that today is January 12.
a. Assume that you have the resources to buy and hold the stocks in the S&P 500. The current level of S&P 500 index is 258.90, the June S&P 500 futures contract is selling for 260.15, the annualized rate on the T-bill expiring on the expiration date of the futures contract is 6%, and the annualized dividend yield on S&P 500 stocks is 3%. Assume that dividends are paid out continuously over the year. Is there a potential for arbitrage, and, if so, how would you go about setting up the arbitrage?
b. Assume now that you are known for your stock selection skills. You have 10,000 shares of Texacola (now selling for 38) in your portfolio, and you are worried about the direction of the market until June. You would like to protect yourself against market risk by using the December S&P 500 futures contract (which is currently at 260.15). If Texacola's beta is 0.8, how would you go about creating this protection?