Our Client Details: Assume that you manage a risky portfolio with an expected rate of return of $17\%$ and a standard deviation of $27\%.$ The T$-$bill rate is $7\%.$Your client chooses to invest $70\%$ of a portfolio in your fund and $30\%$ in a T$-$bill money market fund.

Pt$1.$ Suppose the client above decides 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 $15\%.$

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a$)$What is the proportion y$?$

b$)$What are your client$$s investment proportions in your three stocks and in T$-$bills?$$

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

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Pt$2.$ Suppose the same client as before prefers to invest in your portfolio 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 $20\%.$

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

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