A hedge fund has a $20 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 3,200. The continuously compounded interest rate is 2% and the dividend yield of S&P 500 is 1.5%.

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

(b) Calculate the effect of the hedging strategy on the fund managers return if S&P 500 drops to 3,000 in 3 months.

(c) What is the cost of carry for the S&P 500 index futures? Intuitively (not mathematically), why a higher dividend yield would lower the futures price?