(1) Consider portfolios mixing 3 risky assets K1, K2, K3. Following the book's notation, we write E[K] = mi for the mean returns and cij-Cov(Ki, Kj) for the covariance matrix. Suppose the mean returns are 0.1 m= | m2|-| 0.05 0.05 m1 m3 and the covariance matrix is 1 0 -1 010 C11 C12 C13 C13 C23 C33 Note: usually solving linear systems by hand is tedious. But for this problem it's easy, since C1 1 0.] Recall that mean-variance analysis characterizes the minimum-variance portfolio with mean return as the solution of 5 linear equations in 5 unknowns (w1, w2,w3, 1, 2), namely the three equations (in which u | | | ), combined with the two equations (a) Show that if you set 1-0 and drop the equation wim1 +w2m2 +W3m3-, the resulting system of 4 equations for (w1,W2,W3, 2) describe the minimum variance portfolio. (This requires only a sentence or two of explanation.) (b) Find the minimum variance portfolio by observing that w 2Cu, then choos- ing 2 so that w1 + w2 +W3 1. (1) Consider portfolios mixing 3 risky assets K1, K2, K3. Following the book's notation, we write E[K] = mi for the mean returns and cij-Cov(Ki, Kj) for the covariance matrix. Suppose the mean returns are 0.1 m= | m2|-| 0.05 0.05 m1 m3 and the covariance matrix is 1 0 -1 010 C11 C12 C13 C13 C23 C33 Note: usually solving linear systems by hand is tedious. But for this problem it's easy, since C1 1 0.] Recall that mean-variance analysis characterizes the minimum-variance portfolio with mean return as the solution of 5 linear equations in 5 unknowns (w1, w2,w3, 1, 2), namely the three equations (in which u | | | ), combined with the two equations (a) Show that if you set 1-0 and drop the equation wim1 +w2m2 +W3m3-, the resulting system of 4 equations for (w1,W2,W3, 2) describe the minimum variance portfolio. (This requires only a sentence or two of explanation.) (b) Find the minimum variance portfolio by observing that w 2Cu, then choos- ing 2 so that w1 + w2 +W3 1