A fund manager has a portfolio worth $100 million with a beta of 0.8. The manager is concerned about the performance of the market over the next 1 month and plans to use 3-month futures contracts on the S&P 500 to hedge the risk. The current level of the index is 2,900, one contract is on 250 times the index, the risk-free rate is 3% 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 month?

c) Calculate the value of the hedged position (stock and futures) if the index in 1 month is 2700.