Use these inputs for Problems $13$ through $19$: You manage a risky portfolio with an expected rate of return of $\backslash (18\backslash \%\backslash )$ and a

standard deviation of $\backslash (28\backslash \%\backslash ).$ The T$-$bill rate is $\backslash (8\backslash \%\backslash ).$

$13.$ Your client chooses to invest $\backslash (70\backslash \%\backslash )$ of a portfolio in your fund and $\backslash (30\backslash \%\backslash )$ in an essentially risk$-$free money market fund. What are the expected value and standard deviation of the rate of return on his portfolio?

$14.$ Suppose that your risky portfolio includes the following investments in the given proportions:

What are the investment proportions of your client's overall portfolio, including the position in T$-$bills?

$17.$ Suppose that your client decides to invest in your portfolio a proportion $\backslash ($ y $\backslash )$ of the total investment budget so that the overall portfolio will have an expected rate of return of $\backslash (16\backslash \%\backslash ).$

a$.$ What is the proportion $\backslash ($ y $\backslash )?$

$\backslash ($ b $\backslash ).$ What are your client's investment proportions in your three stocks and the T$-$bill fund?

c$.$ What is the standard deviation of the rate of return on your client's portfolio?

$18.$ Suppose that your client prefers to invest in your fund a proportion $\backslash ($ y $\backslash )$ that maximizes the expected return on the complete portfolio subject to the constraint that the complete portfolio's standard deviation will not exceed $\backslash (18\backslash \%\backslash ).$

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

b$.$ What is the expected rate of return on the complete portfolio?