The S&P 500 Index is currently at 3,000. You manage a $15 million indexed equity portfolio. The S&P 500 futures contract has a multiplier of $50.

a. If you are temporarily bearish on the stock market, how many contracts should you sell to fully eliminate your exposure over the next six months? 

b. If T-bills pay 2% per six months and the semiannual dividend yield is 1%, what is the parity value of the futures price? 

c. Show that if the contract is fairly priced, the total risk-free proceeds on the hedged strategy in part (a) provide a return equal to the T-bill rate.