Problem 3 Consider the following problem max f(w)au w - (1 - a)wTPw subject to wTIy 1 where a E (0, 1), u = [ii, ^2, . .. , f^n] are the expected rates of return of n different assets in a portfolio with weight vector w Wn and covariance matrix P = PT0. w1, W2 (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: 0.25, u 0.05, o= 0.04, o 0.06, o = 0.09, o0.009, o12 0.001, 0.08, 2 0.10, 3 013 0.008, 014 = 0,023 = 0,o24 = 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)wTPw subject to wTIy 1 where a E (0, 1), u = [ii, ^2, . .. , f^n] are the expected rates of return of n different assets in a portfolio with weight vector w Wn and covariance matrix P = PT0. w1, W2 (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: 0.25, u 0.05, o= 0.04, o 0.06, o = 0.09, o0.009, o12 0.001, 0.08, 2 0.10, 3 013 0.008, 014 = 0,023 = 0,o24 = 0,034 = 0.002 If you have $1 million, how will you set up the portfolio