Question

The following is part of the computer output from a regression of monthly returns on Waterworks stock against the S&P 500 index. A hedge fund manager believes that Waterworks is underpriced, with an alpha of 2.1% over the coming month. Beta R-square Standard Deviation of Residuals 1.5 0.65 0.16 (i.e., 16% monthly) a-1. If he holds a $3 million portfolio of Waterworks stock, and wishes to hedge market exposure for the next month using 1-month maturity S&P 500 futures contracts, how many contracts should he enter? The S&P 500 currently is at 1,000 and the contract multiplier is $250.

Answer 1

To hedge a $3 million portfolio of Waterworks stock that has a beta of 1.5 against the S&P 500 index, a hedge fund manager would need to purchase 18 S&P 500 futures contracts. This calculation is based on the current value of the S&P 500 index being at 1,000 and the contract multiplier being $250.

Step-by-step explanation:

The student has provided data from a regression analysis and wants to know how many S&P 500 futures contracts to purchase in order to hedge a $3 million portfolio of Waterworks stock for one month. Given the beta of 1.5, R-square of 0.65, and standard deviation of residuals of 16%, our calculation boils down to finding the 'hedge ratio,' which indicates how much of the portfolio's value must be hedged.

First, we calculate the total value that needs to be hedged: $3 million multiplied by the portfolio's beta (1.5), which gives us $4.5 million. Next, we divide this value by the notional value of one S&P 500 futures contract. With the S&P 500 at 1,000 and the futures contract multiplier at $250, the notional value of one contract is 1,000 * $250 = $250,000.

Finally, we divide $4.5 million by $250,000, and we get 18 contracts. Therefore, the manager should enter into 18 S&P 500 futures contracts to hedge market exposure.