Consider the following problem max f(w) = autw (1 a)w'Pw 1 subject to wTI, where a (0,1), p = (M1, M2, Men] are the expected rates of return of n different assets in a portfolio with weight vector w = [wi, 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: 0.005, Hi = 0.1, M2 = 0.15, M3 = 0.05, p = 0.12,01 = 0.04, o2 = 0.09, o = 0.0625, 02 = 0.0625,012 :-0.002,014 = 0,023 0.007,0 24 = 0,034 = 0 = 013 = 0.3? If you have $1 million, how will you set up the portfolio, when a = Consider the following problem max f(w) = autw (1 a)w'Pw 1 subject to wTI, where a (0,1), p = (M1, M2, Men] are the expected rates of return of n different assets in a portfolio with weight vector w = [wi, 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: 0.005, Hi = 0.1, M2 = 0.15, M3 = 0.05, p = 0.12,01 = 0.04, o2 = 0.09, o = 0.0625, 02 = 0.0625,012 :-0.002,014 = 0,023 0.007,0 24 = 0,034 = 0 = 013 = 0.3? If you have $1 million, how will you set up the portfolio, when a =