A hedge fund has a $30 million portfolio with a beta of 2. The fund manager is concerned about the stock market over the next 3 months. He plans to use 4-month S&P 500 index futures to hedge his market exposure. One contract is worth $250 times the futures price. The S&P 500 index is currently at 3,800. The continuously compounded interest rate is 2% and the dividend yield of S&P 500 is 1.5%.

a) (3 points) How many contracts should the manager long or short to hedge out his market exposure?

b) (4 points) Calculate the effect of the hedging strategy on the funds return if the S&P 500 index increase to 3,900 in 3 months.

c) (2 points) Does the hedge always improve the fund return? If not, what is the point of hedging? Explain your answers.