The S&P/ASX 200 index is currently at 4000. You manage a $4 million indexed equity portfolio. The S&P/ASX 200 futures contract has a multiplier of $25.

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 government pay 2% per six months and the semi-annual 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 part (a) provide a return equal to the government bond rate.