Assume that you manage a risky portfolio with an expected rate of return of $12\%$ and a standard deviation of $15\%.$ The T$-$bill rate is $5\%.$ Suppose your client decides to invest in your risky portfolio a proportion $($y$)$ of his total investment budget, with the remainder in a T$-$bill money market fund, aiming for an overall portfolio with an expected rate of return of $10\%.$ What is the weight of the money market fund?

Group of answer choices

$52\mathrm{.}4\%$

$28\mathrm{.}57\%$

$71\mathrm{.}43\%$

$46\mathrm{.}78\%$

$35\mathrm{.}5\%$