questions are attached...the help is much appreciated, thanks!

The following is part of the computer output from a regression of monthly returns on Waterworks stock against the S&P 500 fund manager believes that Waterworks is underpriced, with an alpha of 1% over the coming month. Beta .70 a. R-square .65 Standard Deviation of Residuals .05 (i.e., 5% monthly) Suppose you hold an equally weighted portfolio of 100 stocks with the same alpha, beta, and residual standard deviatio Waterworks. Assume the residual returns (the e terms in Equations 20.1 and 20.2) on each of these stocks are indepen 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 i over the next month. Assume the risk-free rate is .9% per month. (Do not round intermediate calculations. Round y decimal places.) Probability of a loss % A hedge fund charges an incentive fee of 15% of any investment returns above the T-bill rate, which currently is 3.0%. In fund suffers a loss of 7.2%. What rate of return must it earn in the second year to be eligible for an incentive fee? intermediate calculations. Round your answer to 2 decimal places.) Rate of return % 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 1% over the coming month. Beta .70 R-square .65 Standard Deviation of Residuals .05 (i.e., 5% monthly) 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 SD of Portfolio is smaller than each Stock's SD by a factor of Sqrt (100) = 10. So Resdiual SD of portfolio will be 5%/10 = 0.50% Residual standard deviation % b. Recalculate the probability of a loss on a market-neutral strategy involving equally weighted, markethedged positions in the 100 stocks over the next month. Assume the risk-free rate is 0.9% per month. (Do not round intermediate calculations. Round your answer to 5 decimal places.) Expected Return = Risk free rate + alpha = 0.9% + 1% = 1.9% So z-value for Rate of return of zero = Expected return/SD = -1.9%/0.5% = -3.80 So Prob of Loss = NORM.S.DIST(z) = NORM.S.DIST(-3.80) = 0.00007 or 0.00723% Probability of a loss % A hedge fund charges an incentive fee of 15% of any investment returns above the T-bill rate, which currently is 3.0%. In the first year, the fund suffers a loss of 7.2%. What rate of return must it earn in the second year to be eligible for an incentive fee? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Rate of return % Suppose initial investment in hedge fund is $100 And fund can charge 15% as an incentive fee for of any investment returns above the T-bill rate of 3% Therefore hedge fund is not eligible for incentive fee up to initial investment + 3% return of initial investment = $100 + 3% * $100 = $103.0 In the first year it suffered the loss of 7.2%, therefore investment value = $100 * (1-7.2%) = $92.80 Now in the second year to be eligible for an incentive fee, the value of investment must be more than $100 Therefore, rate of return must it earn in the second year to be eligible for an incentive fee should be more than [($100.0 - $92.80)/ $92.80]*100 = (7.2/ 92.8)*100 = 7.76% So Reqd return for Incentive = 7.76% + T-Bill = 7.76% + 3% = 10.76% 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 1% over the coming month. Beta .70 R-square .65 Standard Deviation of Residuals .05 (i.e., 5% monthly) 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 SD of Portfolio is smaller than each Stock's SD by a factor of Sqrt (100) = 10. So Resdiual SD of portfolio will be 5%/10 = 0.50% Residual standard deviation % b. Recalculate the probability of a loss on a market-neutral strategy involving equally weighted, markethedged positions in the 100 stocks over the next month. Assume the risk-free rate is 0.9% per month. (Do not round intermediate calculations. Round your answer to 5 decimal places.) Expected Return = Risk free rate + alpha = 0.9% + 1% = 1.9% So z-value for Rate of return of zero = Expected return/SD = -1.9%/0.5% = -3.80 So Prob of Loss = NORM.S.DIST(z) = NORM.S.DIST(-3.80) = 0.00007 or 0.00723% Probability of a loss % A hedge fund charges an incentive fee of 15% of any investment returns above the T-bill rate, which currently is 3.0%. In the first year, the fund suffers a loss of 7.2%. What rate of return must it earn in the second year to be eligible for an incentive fee? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Rate of return % Suppose initial investment in hedge fund is $100 And fund can charge 15% as an incentive fee for of any investment returns above the T-bill rate of 3% Therefore hedge fund is not eligible for incentive fee up to initial investment + 3% return of initial investment = $100 + 3% * $100 = $103.0 In the first year it suffered the loss of 7.2%, therefore investment value = $100 * (1-7.2%) = $92.80 Now in the second year to be eligible for an incentive fee, the value of investment must be more than $100 Therefore, rate of return must it earn in the second year to be eligible for an incentive fee should be more than [($100.0 - $92.80)/ $92.80]*100 = (7.2/ 92.8)*100 = 7.76% So Reqd return for Incentive = 7.76% + T-Bill = 7.76% + 3% = 10.76%