The following is part of the computer output from a regression of monthly returns on Waterworks stock agalnst the S&P $500$ index. A hedge fund manager belleves that Waterworks is underpriced, with an alpha of $21\%$ over the coming month.

$\backslash$table$[[,,$Standard Deviation$],[$Beta$,$R$-$square,of Residuals$],[1\mathrm{.}7,0\mathrm{.}65,$ nonthly$)]]$

a$.$ Suppose you hold an equally welghted 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 portfollo? $($Round your answer to $1$ decimal place.$)$

$\backslash$table$[[$Residual standard deviation,$1\mathrm{.}6]]$

b$.$ Calculate the probability of a loss on a market$-$neutral strategy involving equally welghted, market$-$hedged positions in the $100$ stocks over the next month. Assume the rlsk$-$free rate is $0\mathrm{.}6\%$ per month. $($Do not round intermedlate calculatlons. Enter your answer as percent rounded to $5$ decimal places.$)$

Probability of a loss

$\frac{17\mathrm{.}42507}{\%}$