4. For a portfolio of n risky assets with the expected return m = (M1, M2, ..., jin) and the covariance matrix C = (Cij)nxn. Consider the following mean-variance portfolio problem max mut WER SwCw" uc-1u7 and u = (1,1, ... ,1) is a 1 x n vector of ones. (i) What is the maximum expected mean? (5 marks (ii) What is the optimal Lagrange multiplier? (5 marks] (iii) Show that the optimal portfolio is w* = V oo KI (m - Ku)C-1 + Kuc-, K VK- where K1 = uC-147, K2 = uC-Im? and K3 = mc-Im?. (10 marks 4. For a portfolio of n risky assets with the expected return m = (M1, M2, ..., jin) and the covariance matrix C = (Cij)nxn. Consider the following mean-variance portfolio problem max mut WER SwCw" uc-1u7 and u = (1,1, ... ,1) is a 1 x n vector of ones. (i) What is the maximum expected mean? (5 marks (ii) What is the optimal Lagrange multiplier? (5 marks] (iii) Show that the optimal portfolio is w* = V oo KI (m - Ku)C-1 + Kuc-, K VK- where K1 = uC-147, K2 = uC-Im? and K3 = mc-Im?. (10 marks