8. Consider the following problem: maximize f(w) = ouw (1 a)w"Pw TW subject to w Tiy - 1, = = 9 W = where a (0,1), p = (M1, M2, ..., Men]" is the vector with 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 specify any conditions that need to be satisfied (b) Use the result in (a) to find the optimum portfolio of four stocks with the following characteristics: Mi 0.08, M2 0.10, M3 0.25, M4 0.05, 07 0.04, o 0.06, o} 0.09, o = 0.09, 012 0.001,013 0,023 0,034 0.002. If you have $1 million, how will you set up the portfolio? = 0.008, 014 0,024 8. Consider the following problem: maximize f(w) = ouw (1 a)w"Pw TW subject to w Tiy - 1, = = 9 W = where a (0,1), p = (M1, M2, ..., Men]" is the vector with 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 specify any conditions that need to be satisfied (b) Use the result in (a) to find the optimum portfolio of four stocks with the following characteristics: Mi 0.08, M2 0.10, M3 0.25, M4 0.05, 07 0.04, o 0.06, o} 0.09, o = 0.09, 012 0.001,013 0,023 0,034 0.002. If you have $1 million, how will you set up the portfolio? = 0.008, 014 0,024