Financial Math Problem: Mean-Variance Portfolio Selection Theory (25 marks)

There are 1 riskfree asset and 3 risky assets available for trade in the market. The following table summarizes the expected return and variances of return of each of the assets Riskfree Risky asset 1 Risky asset Risky asset Risky asset asset 2 3 4 Expected 2% 3% 5% 8% 10% return i Variance of Nil 0.0064 0.01 0.04 0.03 return o? The correlation coefficients of these 4 assets are P12 = 0.2, P13 = P14 = P23 = P24 = P34 = 0. Questions: Solve the following problems using Lagrange method: (a) Suppose that an investor is seeking for the minimum variance portfolio, which contains risky assets 2, 3 and 4 only that has expected return equal 7%, find this portfolio (b) Suppose that another investor is seeking for a minimum variance portfolio, which consists of riskfree asset, risky asset1 and risky asset 2, that has expected return equal 3%, find this portfolio. There are 1 riskfree asset and 3 risky assets available for trade in the market. The following table summarizes the expected return and variances of return of each of the assets Riskfree Risky asset 1 Risky asset Risky asset Risky asset asset 2 3 4 Expected 2% 3% 5% 8% 10% return i Variance of Nil 0.0064 0.01 0.04 0.03 return o? The correlation coefficients of these 4 assets are P12 = 0.2, P13 = P14 = P23 = P24 = P34 = 0. Questions: Solve the following problems using Lagrange method: (a) Suppose that an investor is seeking for the minimum variance portfolio, which contains risky assets 2, 3 and 4 only that has expected return equal 7%, find this portfolio (b) Suppose that another investor is seeking for a minimum variance portfolio, which consists of riskfree asset, risky asset1 and risky asset 2, that has expected return equal 3%, find this portfolio