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 $2\mathrm{.}2\%$ over the coming month.

Beta R$-$square Standard Deviation

of Residuals

$1\mathrm{.}450\mathrm{.}650\mathrm{.}11($i$.$e$.,11\%$ 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 on each of these stocks are independent of each other. What is the residual standard deviation of the portfolio? $($Round your answer to $1$ decimal place.$)$

b$.$ 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 $0\mathrm{.}2\%$ per month. $($Do not round intermediate calculations. Enter your answer as percent rounded to $5$ decimal places.$)$