The expected rate of return of the market portfolio is $18\%$ and the standard deviation of the

market portfolio is $28\%.$ The T$-$bill rate is $8\%.$

a$.$ Your client chooses to invest $70\%$ of a portfolio in the market portfolio and $30\%$ in a T$-$bill

money market fund. What is the expected return and the standard deviation of his portfolio?

b$.$ Draw the CAL of your portfolio on an expected return$$standard deviation diagram. What is the

slope of the CAL? Show the position of your client on your fund$$s CAL.

c$.$ Suppose that your client prefers to invest in the market a proportion y that maximizes the

expected return on the complete portfolio subject to the constraint that the complete portfolio$$s

standard deviation will not exceed $18\%.$ What is the investment proportion in the market

portfolio? What is the expected rate of return on the complete portfolio?

d$.$ Suppose that your client decides to invest in the market a proportion y of the total investment

budget so that the overall portfolio will have an expected rate of return of $16\%.$ What is the

proportion the client invests in the market portfolio and what is your client$$s portfolio standard

deviation?