Consider a stock that may produce the various possible returns for the next year:

Probability Stock Return T$-$Bill

Scenario $10\mathrm{.}220\%2\%$

Scenario $20\mathrm{.}1515\%2\%$

Scenario $30\mathrm{.}55\%2\%$

Scenario $40\mathrm{.}15-5\%2\%$

Calculate the standard deviation $(\backslash$sigma $)$ of the return on the stock.

$\backslash$sigma $^2=0\mathrm{.}2\backslash$times $()2+0\mathrm{.}15\backslash$times $()2+0\mathrm{.}5\backslash$times $()2+0\mathrm{.}15\backslash$times $()2$

$\backslash$sigma $^2=0\mathrm{.}2\backslash$times $()2+0\mathrm{.}15\backslash$times $()2+0\mathrm{.}5\backslash$times $(\_)2+0\mathrm{.}15\backslash$times $(\_\_)2$

$\backslash$sigma $=$

Find the standard deviation of the T$-$bill.