Assume that you are the manager of a very successful portfolio with an historical expected rate of return of 15% and a standard deviation of 22%. One of your biggest clients is willing to invest in your portfolio, she faces a lending rate of rf = 7% and a borrowing rate of r = 9%. Your client's utility function is U = E(r)-1/2x Ao. 1. Draw your fund's capital allocation line (CAL) on an expected return-standard devia- tion diagram. 2. You estimate that your client's risk aversion index is A = 4. Obtain the optimal propor- tion invested in your fund, y, as well as the utility level, the expected rate of return and standard deviation on your client's complete portfolio. 3. Now assume that A = 0.9. With this new parameter, obtain the optimal proportion invested in your fund, y, as well as the utility level, the expected rate of return and standard deviation on your client's complete portfolio. 4. Continue to assume that A=0.9, but now let r = rB = 7%. With equal lending and borrowing rates, compute the optimal proportion invested in your fund, y, as well as the utility level, the expected rate of return and standard deviation on your client's complete portfolio. 5. Is the utility level obtained in (3) greater, less or equal than the one in (4)? Please explain your answer and provide some intuition.