A fund manager has a portfolio worth $200 million with a beta against the S&P 500 of 1.3. The manager is concerned about the performance of the market over the next 2 months and plans to use 3-month futures contracts on the S&P 500 to hedge the risk. The current 3-month futures price is 2050 and one contract is written on 250 times the index. The risk free rate is 1% per annum and the dividend yield on the index is 2% per annum. Both rates are continuously compounded. The spot S&P 500 index is 2065. Given these assumptions:
- Compute the fair price of the 3-month S&P 500 futures assuming that the fair price is the forward price. For the calculation, assume that 3 months is .25 year.
- What position should the fund manager take in the three month futures to hedge all exposure to the market over the next 2 months?
- Calculate the effect of the hedging strategy on the fund manager's returns if the index in 2 months is 1800, 2050 and 2200. Assume that the then 1 month S&P 500 futures price is equal to 0.995 times the corresponding index level at this time. Assume that the rate of return on the unhedged portfolio is given by the CAPM Security Market Line.