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.

Beta | R-square | Standard Deviation of Residuals |
---|---|---|

0.75 | 0.65 | 0.06 (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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