Question

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.

		Standard Deviation
Beta	R-square	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%.

a. What is the standard deviation of the (now improperly) hedged portfolio? (Do not round intermediate calculations. Round your 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 answer to 2 decimal places.)

Answer 1

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Answer:

a)

Calculate the Standard deviation of the now improperly hedged portfolio.

The variance of the (now improperly) hedged portfolio is,

Standard deviation is calculated as the square root of the variance. Hence, Standard Deviation is as follows:

Thus, the new standard deviation is ~ 6.13%

b)

Monthly market return has the expected value of 1% and standard deviation of 5%. The manager has not estimated properly the beta of Company W. The number of contracts sold for S&P 500 is as follows:

Thus, the number of contracts is 4.

The portfolio now is not hedged completely. Thus, the rate of return is not 2.5%. The new rate of return can be determined by computing the total dollar value of the stock plus future position.

The dollar value of the stock portfolio is as follows:

The proceeds of dollar from the future position are as follows:

The total value of the stock plus futures position in the month end is as follows:

The expected rate of return for the now improperly hedged portfolio is as follows:

The Z-value for zero rate of return is as follows:

Calculate the normal distribution value of -0.4283 using MS-EXCEL “NORMSDIST” Function as follows:

Therefore, the probability of negative return for .~ 0.33