You manage a risky portfolio with an expected rate of return of $10\%$ and a standard deviation of $29\%.$ The T$-$bill rate is $3\%.$

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 $8\%.$

Required:

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

b$.$ 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?