Consider the Markowitz model. Mr. Kang had received financial advice from a financial consultant. While reading the report, he realized that his utility function is U=E(r)-A\sigma2/2 and his risk aversion coefficient is 2. However, he had misplaced the report and his three-year old son tore the report to pieces. Fortunately, the most important page can be restored now. The page shows four portfolios, and one of them is the optimal risky portfolio. The optimal risky portfolio for him is one the following four portfolios: Portfolio A: E(rA)= 6% and \sigma_{}^{}_{A}^{2} = 1% Portfolio B: E(rB) = 7% and \sigma_{}^{}_{B}^{2} = 2.25% Portfolio C: E(rC) = 8% and \sigma_{C}^{2} = 4% Portfolio D: E(rD) =10% and \sigma _{D}^{2} = 6.25% The risk-free rate in the economy is 1%.
(a) Help Mr. Kang to find the optimal risky portfolio among the four portfolios.
(b) Find the overall optimal portfolio (the portfolio which maximizes Mr. Kang’s utility) for Mr. Kang. How can Mr. Kang construct the overall optimal portfolio? What are the expected rate of return and the variance of return at the overall optimal portfolio?
(c) Suppose that Mr. Kang realized that his risk aversion coefficient is 4 instead of 2 and that he cannot have short sales for the risk-free. Find the optimal risky portfolio.
(d) Find the overall optimal portfolio for Mr. Kang. How can Mr. Kang construct the optimal risky portfolio and overall optimal portfolio? What are the expected rate of return and the variance of return at the overall optimal portfolio?