Question

3. A fund manager is concerned about the performance of the market over the next year and plans to use one-year futures contracts on the S&P 500 to hedge the risk. The current index level is 1,200, and the one-year risk-free interest rate is 4% p.a. with continuous compounding. The current one-year futures price on a stock-index portfolio is 1,220. Assume that a dividend of $20 is expected after a year for a $1,200 investment in the market portfolio.

   1. a) (4 points) Is the contract mispriced? Why? If yes, by how much is it overpriced (underpriced)?

   2. b) (8 points) Identify an arbitrage opportunity such that you can obtain a riskless profit equal to the futures mispricing.

   3. c) (8 points) Suppose that when you short sell the stocks in the market index, you do not receive any interest on the funds; instead, the broker receive it. Is there still an arbitrage opportunity now (assuming you don’t own the shares originally)? Explain the reason.

   4. d) (10 points) Under the assumption of (c), i.e., you do not receive any interest on the funds if you short sell the stocks, whhat is the no-arbitrage range? That is, how high and how low can the futures price be such that there is no arbitrage opportunity?

Answer 1