Problem
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%.
Task
1) 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.
2) 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%?