You are a Morgan Stanley portfolio manager of a risky portfolio with an expected rate of return of $17\%$ and a standard deviation of $28\%.$ The T$-$bill rate is $4\%.$ Suppose your client decides to invest in your risky portfolio a proportion $($y$)$ of his total investment budget so that his overall portfolio will have an expected return of $10\%.$Please choose all correct answers related to the following questions. a$.$ What is the proportion y$?$b$.$ What will be the standard deviation of your clients portfolio?c$.$ What is the Sharpe ratio of your portfolio?d$)$ Suppose your client is wondering if he should switch his money in your fund to a passive portfolio invested to mimic the S&P $500$ stock index yields an expected rate of return of $9\%$ with a standard deviation of $25\%.$ Show your client the maximum fee you could charge $($as a percent of the investment in your fund deducted at the end of the year$)$ that would still leave him at least as well off investing in your fund as in the passive one. $($Hint: The fee will lower the slope of your clients CAL by reducing the expected return net of the fee.$)$Please choose all correct answers. Please note that each incorrect answer will reduce the score by $10\%.$

The answer to part a is $46\mathrm{.}15\%$

The answer to part b is $12\mathrm{.}92\%$

the answer to part c is $46\mathrm{.}43\%$

The answer to part d is $7\mathrm{.}4\%$

The answer to part a is $50\%$

The answer to part $b$ is $14\%$

the answer to part c is $42\mathrm{.}8\%$

The answer to part d is $6\mathrm{.}4\%$

The answer to part a is $66\mathrm{.}15\%$

$($H$)$ The answer to part d is $6\mathrm{.}4\%$

The answer to part a is $66\mathrm{.}15\%$

The answer to part b is $14\mathrm{.}92\%$

the answer to part c is $56\mathrm{.}43\%$

The answer to part d is $8\mathrm{.}4\%$