Problem $230$ points$)$you manage a risky portfolio with expected rate of return of $15\%$ and standard deviation of $34\%.$ The T$-$bill rate is $7\%.$a$.$ Your client 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 his portfolio?b$.$ Suppose that your risky portfolio includes the following investments in the given proportions:Stock A $15\%$Stock B $54\%$Stock C $31\%$What are the investment proportions of your client's overall portfolio, including the position in T$-$bills?What is the reward$-$to$-$volatility ratio $($S$)$ of your risky portfolio? Your client's?d$.$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 $16\%.$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?f$.$ Your client's degree of risk aversion is A $=4.$a$.$ What proportion, y$,$ of the total investment should be invested in your fund?b$.$ What is the expected value and standard deviation