Your client would like to invest $100,000 in both the risk-free asset with return of rf = 1% and the risky portfolio with expected return of m = 12% and standard deviation of m = 20%. Her utility function is U(, ) = 1 2 2 , where her risk aversion is 2.

a. [1pt] How much should you invest in the risky portfolio so that she can receive the greatest utility?

b. [1pt] What is the expected return of this optimal portfolio?

c. [1pt] What is the standard deviation of the returns of this optimal portfolio?

d. [2pts] Suppose that your risky portfolio consists of 40% Stock A and 60% Stock B. What are the investment proportions of your clients overall portfolio in Stock A, B, and risk-free asset?