8. Return again to Problem 6. 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%.

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 5%? Compare your answer to the probability you found in Problem 6.

c. What would be the probability of a loss using the data in Problem 7 if the manager similarly misestimated beta as .50 instead of .75? Compare your answer to the probability you found in Problem 7.

d. Why does the misestimation of beta matter so much more for the 100-stock portfolio than it does for the 1-stock portfolio?