Problem 3 Consider the following problem max f(w) = au'w (1 - a)w Pw subject to w1,=1 where a (0,1), u = [M1, M2, ..., fin]T are the expected rates of return of n different assets in a portfolio with weight vector w = [W1, W2, ..., wn] and covariance matrix P = PT> 0. (a) Find the value of w* that maximizes f(w) and state any conditions to be satisfied. (b) Use the results in (a) to find the optimum portfolio of 4 stocks with the following characteristics: Mi = 0.08, M2 = 0.10, M3 = 0.25, p = 0.05, 01 = 0.04, o2 = 0.06, o = 0.09, 020.009, 012 = 0.001, 013 = 0.008,014 = 0,023 = 0,024 = 0,034 = 0.002 If you have $1 million, how will you set up the portfolio? Problem 3 Consider the following problem max f(w) = au'w (1 - a)w Pw subject to w1,=1 where a (0,1), u = [M1, M2, ..., fin]T are the expected rates of return of n different assets in a portfolio with weight vector w = [W1, W2, ..., wn] and covariance matrix P = PT> 0. (a) Find the value of w* that maximizes f(w) and state any conditions to be satisfied. (b) Use the results in (a) to find the optimum portfolio of 4 stocks with the following characteristics: Mi = 0.08, M2 = 0.10, M3 = 0.25, p = 0.05, 01 = 0.04, o2 = 0.06, o = 0.09, 020.009, 012 = 0.001, 013 = 0.008,014 = 0,023 = 0,024 = 0,034 = 0.002 If you have $1 million, how will you set up the portfolio