The following is part of the computer output from a regression of

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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% over the coming month.
 

BetaR-squareStandard Deviation
of Residuals
0.750.650.06 (i.e., 6% monthly)


Now suppose that the manager misestimates the beta of Waterworks stock, believing it to be 0.50 instead of 0.75. The standard deviation of the monthly market rate of return is 5%.

Required:

a. If he holds a $6 million portfolio of Waterworks stock and wishes to hedge market exposure for the next month using one-month maturity S&P 500 futures contracts, what is the standard deviation of the (now improperly) hedged portfolio? The S&P 500 currently is at 3,000 and the contract multiplier is $50. (Do not round intermediate calculations. Round your percentage answer to 2 decimal places.)

b. What is the probability of incurring a loss over the next month if the monthly market return has an expected value of 1% and a standard deviation of 5%? (Do not round intermediate calculations. Round your percentage answer to 2 decimal places.)

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