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Problem 1 ( We consider an investment problem with 3 risky assets. You are given that • The expected return rate of these three risky assets are ₁ = 0.08, 7₂ = 0.13 and T3 = 0.16 repsectively. ● The variances of return rate of three risky assets are o2 = 0.02, o2 = 0.05 and 03= 0.1 respectively. We assume that the returns of the risky assets are mutually uncorrelated (i.e. cov(ri, rj) = 0 for all i ‡ j. (a) Find the minimum variance portfolio with expected return μp = 0.1 using Lagrange method. Is the portfolio efficient? Explain your answer. (*Note: You also need to demonstrate how do you solve the relevant equations in your solution.) (b) (True/False) Suppose that the investor is seeking for a portfolio which can achieve (1) smallest variance of portfolio return and (2) achieve expected return not less than up (i.e. Tp up), then the investor conjectures that the optimal portfolio must be the minimum variance portfolio with expected return µp. Give your comment on the correctness of investor's conjecture. (c) Suppose that the investor is seeking for a portfolio which the variance of portfolio cannot exceed omax = 0.5, find the portfolio with maximum expected return. Provide justification to your solution. LOU

Problem 1 ( We consider an investment problem with 3 risky assets. You are given that • The expected return rate of these three risky assets are ₁ = 0.08, 7₂ = 0.13 and T3 = 0.16 repsectively. ● The variances of return rate of three risky assets are o2 = 0.02, o2 = 0.05 and 03= 0.1 respectively. We assume that the returns of the risky assets are mutually uncorrelated (i.e. cov(ri, rj) = 0 for all i ‡ j. (a) Find the minimum variance portfolio with expected return μp = 0.1 using Lagrange method. Is the portfolio efficient? Explain your answer. (*Note: You also need to demonstrate how do you solve the relevant equations in your solution.) (b) (True/False) Suppose that the investor is seeking for a portfolio which can achieve (1) smallest variance of portfolio return and (2) achieve expected return not less than up (i.e. Tp up), then the investor conjectures that the optimal portfolio must be the minimum variance portfolio with expected return µp. Give your comment on the correctness of investor's conjecture. (c) Suppose that the investor is seeking for a portfolio which the variance of portfolio cannot exceed omax = 0.5, find the portfolio with maximum expected return. Provide justification to your solution. LOU

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section: Chapter Questions
Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...
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Problem 1 ( We consider an investment problem with 3 risky assets. You are given that The expected return rate of these three risky assets are ₁ = 0.08, 2₂ = 0.13 and T3 = 0.16 repsectively. The variances of return rate of three risky assets are o2 = 0.02, 0² = 0.05 and 03 = 0.1 respectively. ● ● ● We assume that the returns of the risky assets are mutually uncorrelated (i.e. cov(ri,ri) = 0 for all i ‡ j. (a) Find the minimum variance portfolio with expected return Up = 0.1 using Lagrange method. Is the portfolio efficient? Explain your answer. (*Note: You also need to demonstrate how do you solve the relevant equations in your solution.) (b) (True/False) Suppose that the investor is seeking for a portfolio which can achieve (1) smallest variance of portfolio return and (2) achieve expected return not less than μp (i.e. Tp Hp), then the investor conjectures that the optimal portfolio must be the minimum variance portfolio with expected return μp. Give your comment on the correctness of investor's conjecture. (c) Suppose that the investor is seeking for a portfolio which the variance of portfolio cannot exceed omax = 0.5, find the portfolio with maximum expected return. Provide justification to your solution. (Hint: For (b), you can get the answer using any method.)
Transcribed Image Text:Problem 1 ( We consider an investment problem with 3 risky assets. You are given that The expected return rate of these three risky assets are ₁ = 0.08, 2₂ = 0.13 and T3 = 0.16 repsectively. The variances of return rate of three risky assets are o2 = 0.02, 0² = 0.05 and 03 = 0.1 respectively. ● ● ● We assume that the returns of the risky assets are mutually uncorrelated (i.e. cov(ri,ri) = 0 for all i ‡ j. (a) Find the minimum variance portfolio with expected return Up = 0.1 using Lagrange method. Is the portfolio efficient? Explain your answer. (*Note: You also need to demonstrate how do you solve the relevant equations in your solution.) (b) (True/False) Suppose that the investor is seeking for a portfolio which can achieve (1) smallest variance of portfolio return and (2) achieve expected return not less than μp (i.e. Tp Hp), then the investor conjectures that the optimal portfolio must be the minimum variance portfolio with expected return μp. Give your comment on the correctness of investor's conjecture. (c) Suppose that the investor is seeking for a portfolio which the variance of portfolio cannot exceed omax = 0.5, find the portfolio with maximum expected return. Provide justification to your solution. (Hint: For (b), you can get the answer using any method.)
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