Return again to the previous problem. Now suppose that the manager misestimates the beta...

Return again to the previous problem. Now suppose that the manager misestimates the beta of Waterworks stock, believing it to be .50 instead of .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 12.

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

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

Previous problem. Return to the previous problem.

a. Suppose you hold an equally weighted portfolio of 100 stocks with the same alpha, beta, and residual standard deviation as Waterworks. Assume the residual returns (the e terms in Equations 20.1 and 20.2 ) on each of these stocks are independent of each other. What is the residual standard deviation of the portfolio?

b. Recalculate the probability of a loss on a market-neutral strategy involving equally weighted, market-hedged positions in the 100 stocks over the next month.

Problem 12.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.

a. If he holds a $3 million portfolio of Waterworks stock, and wishes to hedge market exposure for the next month using one-month maturity S&P 500 futures contracts, how many contracts should he enter? Should he buy or sell contracts? The S&P 500 currently is at 1,000 and the contract multiplier is $250.

b. What is the standard deviation of the monthly return of the hedged portfolio?

c. Assuming that monthly returns are approximately normally distributed, what is the probability that this market-neutral strategy will lose money over the next month? Assume the risk-free rate is .5% per month.

Equations 20.1 and 20.2.