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 $2\mathrm{.}3\%$ over the coming month.

$\backslash$table$[[$Beta$,$R$-$square,$\backslash$table$[[$Standard Deviation$],[$of Residuals$]]],[1\mathrm{.}2,0\mathrm{.}65,0\mathrm{.}06($i$.$e$.,6\%$ monthly$)]]$

Now suppose that the manager misestimates the beta of Waterworks stock, believing it to be $0\mathrm{.}5$ instead of $1\mathrm{.}2.$ The standard deviation of the monthly market rate of return is $5\%.$ If he holds a $$5,000,000$ portfolio of Waterworks stock. The S&P $500$ currently is at $2,000$ and the contract multiplier is $$50.$

a$.$ What is the standard deviation of the $($now improperly$)$ hedged portfolio? $($Round your answer to $3$ decimal places.$)$

Standard deviation