A stock has an expected return, over the next year, of $10\%.$ You believe that it is equally likely that the stock's actual return will be either $15$ percentage points lower or higher than this expected return, and that these returns both have a $30\%$ chance of occurring. The stock also has a $40\%$ chance of obtaining a return exactly equal to its $10\%$ expected value. What is the standard deviation of this stock?

A$.11\mathrm{.}6\%(\mathrm{.}116)$

B$.12\mathrm{.}2\%(\mathrm{.}122)$

C$.15\mathrm{.}0\%(\mathrm{.}150)$

D$.15\mathrm{.}3\%(\mathrm{.}153)$

E$.21\mathrm{.}2\%(\mathrm{.}212)$