The manager of a blue chip growth stock mutual fund is trying to fully hedge the $650 million portfolio position during the last two months of the calendar year.The current price of the S&P 500 Index futures contract is 1200.If the mutual fund has a beta of 1.24,how many contracts will be needed to hedge the fund?

Question

Quizplus · Accepted Answer

To fully hedge the fund, the manager needs to take a short position in S&P 500 futures. The value of the short position should be equal to the value of the portfolio. 
Value of the fund = $650 million
Value of S&P 500 futures contract = 1200 x $250 = $300,000
Number of contracts = value of the fund / (S&P 500 futures contract x index multiplier x beta)
Index multiplier for S&P 500 futures = $250 x 1 = $250
Number of contracts = $650,000,000 / ($300,000 x $250 x 1.24) = 3,032.67
Since the number of contracts must be a whole number, the manager needs to take a short position in 3,033 S&P 500 futures contracts to fully hedge the portfolio. Therefore, the correct answer is B.

The Manager of a Blue Chip Growth Stock Mutual Fund