Question 2

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 2.1% over the coming month. Required: a. If the fund holds a $3 million position in Waterworks stock and wishes to hedge market exposure for the next month using 1-month maturity S\&P 500 futures contracts, how many contracts should it enter? Should it 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 marketneutral strategy will lose money over the next month? Assume the risk-free rate is 0.6% per month. d. 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 on each of these stocks are independent of each other. What is the residual standard deviation of the portfolio? e. Calculate the probability of a loss on a market-neutral strategy involving equally weighted, market-hedged positions in the 100 stocks over the next month. Assume the risk-free rate is 0.6% per month. Complete this question by entering your answers in the tabs below. If the fund holds a $3 million position in Waterworks stock and wishes to hedge market exposure for the next month using 1month maturity S\&P 500 futures contracts, how many contracts should it enter? Should it buy or sell contracts? The S\&P 500 currently is at 1,000 and the contract multiplier is $250. 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 3% over the coming month. Now suppose that the manager misestimates the beta of Waterworks stock, believing it to be 0.50 instead of 1.00 . The standard deviation of the monthly market rate of return is 10%. 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 10% ? 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 month. 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 1.00 ? 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 0.5% per month. Complete this question by entering your answers in the tabs below. 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")