$1.$ You manage a risky portfolio with an expected rate of return of $17\%$ and a standard

deviation of $27\%.$ The Treasury$-$bill rate is $7\%.$

a$.$ One of your clients chooses to invest $70\%$ of a portfolio in your fund and $30\%$ in a

T$-$bill money market fund. What is the expected value and standard deviation of

the rate of return on your client$$s portfolio?

b$.$ Suppose that your client decides to invest in your portfolio a proportion y of the

total investment budget so that the overall portfolio will have an expected rate of

return of $15\%.$

i$.$ What is the proportion y$?$

ii$.$ Further suppose that your risky portfolio includes the following

investments in the given proportions: Stock A $(27\%),$ Stock B $(33\%),$ and

Stock C $(40\%).$ What are your client$$s investment proportions in your

three stocks and the T$-$bill fund.

c$.$ Now suppose that your client prefers to invest in your fund a proportion y that

maximizes the expected return on the overall portfolio subject to the constraint

that the overall portfolio$$s standard deviation will not exceed $20\%.$

i$.$ What is the investment proportion, y$?$

ii$.$ What is the expected rate of return on the overall portfolio?

d$.$ Suppose that your client$$s degree of risk aversion is A $=3\mathrm{.}5.$ What proportion, y$,$

of the total investment should you suggest that he invest in your fund?

e$.$ You estimate that a passive portfolio $($that is$,$ one entirely invested in a risky

portfolio that mimics the S&P $500$ stock index$)$ yields an expected rate of return

of $13\%$ with a standard deviation of $25\%.$

i$.$ What is the slope of the CML$?$

ii$.$ Characterize in one short paragraph the advantage of your fund over the

passive fund.

iii. Your client is considering whether to switch to the passive portfolio the $70\%$

of his wealth currently invested in your fund. Show your client that he is better

off staying with you.

iv$.$ What is the maximum fee at which client will be indifferent?