The S&P 500 Index is currently at 1,800. You manage a $9m indexed equity portfolio. The S&P 500 futures contract has a multiplier of $250.

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?

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

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