The state-dependent returns on securities A and B are estimated as below: Bear Normal Bull -0.15 0.20 0.30 -0.05 0.25 -0.03 0.15 0.55 0.30 State Return on security A Return on security B Probability The risk-free return is 5%. (a) Calculate the expected returns and covariance matrix of securities A and B. (b) Is security A more mean-variance efficient than security B? Why or why not? (c) Calculate the weights of the minimum variance portfolio of securities A and B. (d) What are the optimal risky portfolio weights? Calculate the expected return and risk of the optimal risky portfolio. (e) What is the expected return of an efficient portfolio with a standard deviation of 10%? Calculate the portfolio weights. (f) Suppose the optimal risky portfolio is identical to the market portfolio. What are the systematic and idiosyncratic risk of securities A and B? 1

Che state-dependent returns on securities A and B are estimated as below: The risk-free return is 5%. (a) Calculate the expected returns and covariance matrix of securities A and B. (b) Is security A more mean-variance efficient than security B? Why or why not? (c) Calculate the weights of the minimum variance portfolio of securities A and B. (d) What are the optimal risky portfolio weights? Calculate the expected return and risk of the optimal risky portfolio. (e) What is the expected return of an efficient portfolio with a standard deviation of 10% ? Calculate the portfolio weights. (f) Suppose the optimal risky portfolio is identical to the market portfolio. What are the systematic and idiosyncratic risk of securities A and B