Problem 1: Optimal Risky Portfolio with Risk-Free Asset and Risky Asset (10 points)

You manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 29%. The T-bill rate is 5%. Your clients degree of risk aversion is A = 2.5, assuming a utility function U = E(r) A. a. What proportion, y, of the total investment should be invested in your fund? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. What are the expected value and standard deviation of the rate of return on your clients optimized portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.)