Consider a two period economy. You can buy stocks in period 0, and then sell them in period 1. You can also enter into futures contracts in period 0, which expire in period 1.

1.  Suppose a stock has a β of 0.5. The stock pays no dividends, and is trading at $100. The market has an expected return of 10%. The interest rate is 2%. Suppose the CAPM holds. What is the stock’s expected return? What is the expected price of the stock in period 1?
2. Consider a futures contract on the stock, expiring at t = 1. What is the fair price of the futures contract, in t = 1 dollars?
3. Suppose you take a long position in the futures contract in period 0 (so, you promise to pay money, in exchange for getting the stock in period 1). When the futures contract expires in period 1, you receive the stock and immediately sell it. What is the expected amount you will pay in money for the stock? What is the expected amount you get from selling the stock?
4. Since buying single-stock futures appears to be a fairly profitable trade, you decide to invest in a futures strategy. You enter a long futures contract position, for exactly the amount you solved for in part 2). You also invest cash in period 0 at the risk-free rate, so you have just enough to pay for the futures contract at expiration. You plan to sell the stock just after expiration. What is the expected return on this trading strategy (in terms of expected period-1 dollars you get, per period-0 dollar invested)? How does this compare to your answer to part 1)?