5. (40 pts) There are three risky assets with (random) rates of return 11, 12, and...

 

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5. (40 pts) There are three risky assets with (random) rates of return 11, 12, and 13, respectively. Shorting is allowed in this market. The covariance matrix (2) and the expected rates of return (u) are 011 012 013] =21 22 23 031 032 033 Eri Erz Er (a) (5 pts) Write the Markowitz optimization problem to find the efficient portfolio with the mean return 0 (no need to solve it) (b) (10 pts) Derive the efficient equations for the efficient portfolio with the mean return 0 from (a) (no need to solve it) (c) (10 pts) Suppose the solution of (b) is (w, w, w). In addition, the efficient portfolio with the mean return 1 is (w, w, w). Find the efficient portfolio with mean return 0.1, and explain why. (d) (5 pts) Now a risk-free asset with return rf is available in this market. Write the optimization problem to find the one fund F. (e) (10 pts) Suppose the solution of (d) is (w, w2, w3) and its expected return is 0.2. Find the efficient portfolio with the expected return 0.4, and explain why. 5. (40 pts) There are three risky assets with (random) rates of return 11, 12, and 13, respectively. Shorting is allowed in this market. The covariance matrix (2) and the expected rates of return (u) are 011 012 013] =21 22 23 031 032 033 Eri Erz Er (a) (5 pts) Write the Markowitz optimization problem to find the efficient portfolio with the mean return 0 (no need to solve it) (b) (10 pts) Derive the efficient equations for the efficient portfolio with the mean return 0 from (a) (no need to solve it) (c) (10 pts) Suppose the solution of (b) is (w, w, w). In addition, the efficient portfolio with the mean return 1 is (w, w, w). Find the efficient portfolio with mean return 0.1, and explain why. (d) (5 pts) Now a risk-free asset with return rf is available in this market. Write the optimization problem to find the one fund F. (e) (10 pts) Suppose the solution of (d) is (w, w2, w3) and its expected return is 0.2. Find the efficient portfolio with the expected return 0.4, and explain why.