Consider the following problem max f(w) = autw (1 a)w"Pw subject to WTI, = 1 where a (0,1), u = [M1, M2, ..., Men]" 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 = 0.1, M2 = 0.15, 43 = 0.05, p = 0.12, o = 0.04, o = 0.09, o = 0.0625, 0 = 0.0625, 012 0.005, 013 = -0.002,014 = 0,023 0.007, 024 = 0,034 = 0 = If you have $1 million, how will you set up the portfolio, when a = 0.3? Consider the following problem max f(w) = autw (1 a)w"Pw subject to WTI, = 1 where a (0,1), u = [M1, M2, ..., Men]" 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 = 0.1, M2 = 0.15, 43 = 0.05, p = 0.12, o = 0.04, o = 0.09, o = 0.0625, 0 = 0.0625, 012 0.005, 013 = -0.002,014 = 0,023 0.007, 024 = 0,034 = 0 = If you have $1 million, how will you set up the portfolio, when a = 0.3