(1 point) Let P2(w1,w2) be the variance of a portfolio composed of two assets weighted w1,w2 Suppose P2(W1,W2) attains its minimum value at (W1:W2) Then for all wi, '2 Taking the square root of each side of the inequality (1) gives Taking the square root preserves the direction of the inequality) lt follows that the standard deviation P wl wa) attains it's minimum value at the same point wi w2 that minimizes the variance P2(w1 w2 Let plwi, u 2) be the standard deviation of a portfolio composed of two assets weighted wi,u, Suppose r(w1, w2) attains its minimum value at (U1,W2) Then for all w1, "2 Also, since (wl, w2) > 0 and P(w1, w2)2 0 Multiplying (2) and (3) gives (The product of two expressions, each 0, is also 0). Then for all w1, "2 lt follows that the variance P2(w1, wa) attains it's minimum value at the same point wi,w2) that minimizes the standard deviation Although this analysis shows minimizing the variance is equivalent to minimizing the standard deviation, in practice most people would choose to minimize the y because