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 believes that Waterworks is underpriced, with an alpha of 2% over the coming month. Now suppose that the manager misestimates the beta of Waterworks stock, believing it to be 0.50 instead of 0.85 . The standard deviation of the monthly market rate of return is 7%. If the fund holds a \$4 million position in Waterworks stock. The S\&P 500 currently is at 4,000 and the contract multiplier is $50. Required: a. What is the standard deviation of the (now improperly) hedged portfolio? 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 7% ? If the fund holds a $4 million position in Waterworks stock and wishes to hedge market exposure for the next month using 1-month maturity S\&P 500 futures contracts. The S\&P 500 currently is at 4,000 and the contract multiplier is $50. Assume the risk-free rate is 0.50% per morrth. c. What would be the probability of a loss if you hold an equally weighted portfolio of 100 stocks with the same alpha, beta, and residual standard deviation as Waterworks and the manager similarly misestimated beta as 0.50 instead of 0.85 ? If the fund holds a \$4 million position in Waterworks stock and wishes to hedge market exposure for the next month using 1-month maturity S\&P 500 futures contracts. The S\&P 500 currently is at 4,000 and the contract multiplier is $50. Assume the risk-free What is the standard deviation of the (now improperly) hedged portfolio? Note: Round your answer to 3 decimal places, Enter your answer as percentages and not as a numbers. (Eg: Enter "12\%" and not " 0.12). What is the probability of incurring a loss over the next month if the monthly market retum has an expected value of 1% and a standard deviation of 7% ? If the fund holds a $4 million position in Waterworks stock and wishes to hedge market exposure for the next month using 1 -month maturity 58.9500 futures contracts. The 58P500 currently is at 4,000 and the contract multiplier is $50. Assume the risk-free rate is 0.50% per month. Note: Round your answer to 2 decimal places, Enter your answer as percentages and not as a numbers. (Eg: Enter "12\%" and not "0.12"). Show less A What would be the probability of a loss if you hold an equally weighted portfolio of 100 stocks with the same alpha, beta, and residual standard deviation as Waterworks and the manager similarly misestimated beta as 0.50 instead of 0.85 ? If the fund holds a $4 million position in Waterworks stock and wishes to hedge market exposure for the next month using 1 -month maturity 58P500 futures contracts. The S\&P 500 currently is at 4,000 and the contract multiplier is $50. Assume the risk-free rate is 0.5% per month. Note: Round your answer to 2 decimal places, Enter your answer as percentages and not as a numbers. (Eg: Enter "12\%" and not "0.12")