25) (9 points) You manage a risky portfolio with expected rate of return of 17% and standard deviation of 27%. The T-bill rate is 7%. a) Suppose that your client prefers to invest in your fund 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, y? What is the expected rate of return on the complete portfolio? b) Suppose your client's degree of risk aversion is A=4, what proportion, y, of the total investment should be invested in your fund? What is the expected return and standard deviation of this new portfolio? The utility function is U=log[E[R] - - A 02] (Hint: You first need to derive an explicit formula for the optimal portfolio weight by solving an optimization problem. The one I derived in the lecture is not valid here!). c) Suppose you have two risky asset, Asset A and Asset B. Asset A has an expected return of 10% and a standard deviation of 20%. Asset B has an expected return of 30% and a standard deviation of 60%. The correlation coefficient between Asset A and Asset B is -0.4. The T-bill rate is 7%. Write the optimization problem whose solution will give the optimal risky portfolio if short selling is not allowed in this market? (Do not solve the optimization problem!)