A fund manager has a portfolio worth $50 million with a beta of 0.95. 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 level of the index is 2,300, one contract is on

250 times the index, the risk-free rate is 5% per annum, and the dividend yield on the index is 2%

per annum.

a) Calculate the theoretical futures price of a 3-month S&P 500 futures price.

b) How many futures contracts should the manager buy or sell to hedge the exposure to the

market over the next 2 months?

c) Calculate the value of the hedged position (stock and futures) if the index in 2 months is 2000.