3 (30 points) Futures The current stock price of IBM is So = 100 per share. The futures price of IBM futures that mature 2 days from today is F0,2 = 100.05. Suppose IBM does not pay any dividend. The risk-free rate is constant. (i) (10 points) What is the annual continuously-compounded risk-free rate implied by the futures price Fo.2? (ii) (12 points) Suppose the futures prices at t = 1 and t = 2 are F1.2 = 99 and F2,2 = 102, respectively. What are the implied stock prices S, and S2 at t=1 and t=2? Calculate the profits and losses on day 1 and day 2 for buying (long position) one futures contract. (iii) (8 points) An investor Bob holds $1,000,500 IBM stock at t = 0. Bob wants to hedge his stock position for two days using the above futures contract. What position should Bob take short or long)? How many futures contracts should Bob long/short? Show clearly why this is a perfect hedge. For this question, let us ignore the interest earnings on your margin account so that you do not need to change your futures position over time 3 (30 points) Futures The current stock price of IBM is So = 100 per share. The futures price of IBM futures that mature 2 days from today is F0,2 = 100.05. Suppose IBM does not pay any dividend. The risk-free rate is constant. (i) (10 points) What is the annual continuously-compounded risk-free rate implied by the futures price Fo.2? (ii) (12 points) Suppose the futures prices at t = 1 and t = 2 are F1.2 = 99 and F2,2 = 102, respectively. What are the implied stock prices S, and S2 at t=1 and t=2? Calculate the profits and losses on day 1 and day 2 for buying (long position) one futures contract. (iii) (8 points) An investor Bob holds $1,000,500 IBM stock at t = 0. Bob wants to hedge his stock position for two days using the above futures contract. What position should Bob take short or long)? How many futures contracts should Bob long/short? Show clearly why this is a perfect hedge. For this question, let us ignore the interest earnings on your margin account so that you do not need to change your futures position over time