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 2.3% over the coming month.
Beta R-square Standard Deviation of Residuals
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1.19 0.65 0.18 (i.e., 18% monthly)
a-1. If he holds a $4 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.
Number of contracts _________
a-2. Should he buy or sell contracts? multiple choice
b. What is the standard deviation of the monthly return of the hedged portfolio?
Standard deviation ________%
c. Assuming that monthly returns are approximately normally distributed, what is the probability that this market-neutral strategy will lose money over the next month? Assume the risk-free rate is 0.6% per month. (Enter your answer as percent rounded to 2 decimal places, e.g., enter “12.53%” and not “0.1253.”)