Assume that you manage a risky portfolio with an expected rate of return of $20\%$ and a standard deviation of $25\%.$ The T$-$bill rate is $7\%.$ Suppose that you have a client that prefers to invest in your risky portfolio a proportion $(y)$ of his total investment budget so that his overall portfolio will have an expected rate of return of $15\%.$

$($a$)$ What is the investment proportion, $y?$

$($b$)$ What is the standard deviation of the rate of return on your client's portfolio?

$0\mathrm{.}615,6\mathrm{.}32\%$

$0\mathrm{.}515,6\mathrm{.}32\%$

$0\mathrm{.}615,7\mathrm{.}32\%$

$0\mathrm{.}515,7\mathrm{.}32\%$

$0\mathrm{.}715,6\mathrm{.}32\%$