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 2.4% over the coming month.
Standard Deviation: 0.95
Beta: 0.65
R-square of Residuals: 0.1 (i.e., 10% monthly)
Now suppose that the manager misestimates the beta of Waterworks stock, believing it to be 0.5 instead of 0.95. The standard deviation of the monthly market rate of return is 9%. If he holds a $2,000,000 portfolio of Waterworks stock, the S&P 500 currently is at 2,000 and the contract multiplier is $50.
a. What is the standard deviation of the (now improperly) hedged portfolio? (Round your answer to 3 decimal places.)
b. What is the probability of incurring a loss on the improperly hedged portfolio over the next month if the monthly market return has an expected value of 1% and a standard deviation of 9%? The manager holds a $2 million portfolio of 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 2,000 and the contract multiplier is $50. Assume the risk-free rate is 0.5% per month. (Round your answer to 2 decimal places. Enter your answer as percentages and not as numbers. (Eg: Enter "12%" and not "0.12").)