8 10.00 points value: is part of the computer output from a regression of monthl

Question

8 10.00 points value: 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 th at Waterworks is underpriced, with an alpha of 2% over the coming month. Standard Deviation of Residuals 06 (i.e., 6% monthly) Beta R-square 75 .65 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? (Round your answer to 2 decimal places.) Residual standard deviation 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. Assume the risk-free rate is .5% per month. (Do not round intermediate calculations. Round your answer to 5 decimal places.) Probability of a loss References eBook & Resources Worksheet Learning Objective: 20-02 Formulate "pure plays" on misaligned

Explanation / Answer

a. Computation of residual standard deviation of the portfolio:
Residual standard deviation = 0.6%
Explanation:
The residual variance of the portfolio is smaller by a factor of 100 = square root of 100 = 10.
Here, the standard deviation of the portfolio is smaller than each stock by 10.
Therefore, residual standard deviation is now 0.6%, instead of a residual standard deviation of 6%.

b. Probability of loss:
Probability of negative return = N* z-value for a rate of return of zero
Here, z-value for a rate of return of zero = -expected return of the market-neutral position
= -(risk free rate + alpha) / standard deviation
= -(0.5%+ 2% ) / 6%
= -2.5%/ 6%
Therefore, Probability of negative return = N* z-value for a rate of return of zero
= N* (-2.5/0.6%)
= N (-4.1667)
= 0.0000155

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