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
Chapter6: Exponential And Logarithmic Functions
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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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