(1 point) Suppose three assets have expected rates of return r1 0.07 r2 = 0.03 variances 120.5 22-0.8 T3"0.2 and covariances Find the weights and expected rate of return for the minimum variance portfolio by using Lagrange multipliers Let f(w1, w2, w3) p (type wi as w1, w2 as w2, w3 as w3) The partial derivatives of F with respect to wl, w2 w3 and are (type A as lambda) (type A as lambda) (type A as lambda) 13 Consider the equations 0, Fu0, and Fu0 After replacing wi with wi w2 with w2 and w3 with w3 in these equations. solving for wi, W2 and w3 gives For the equation F-0 to be satisfied. must be such that iA + w2 + w3-1, so lt follows that the weights w! = ,-w1/wtotal, tv2-W2-w2/wtotal-tv3 = 3-W3/wtotal, are 02 The expected rate of return of the minimum variance portfolio is TP