Let X1 be a random variable denoting the return of stock 1, and X2 be a random variable denoting the return of stock 2. Accordingly, let pl = E[X1], 1,12 = E[X2], 012 = Var(X1), 022 = Var(X2), and 012 = C ov(X1,X2). Also assume that 1.11 > 1,42. The return on a portfolio of stocks, H, is then a weighted average of X1 and Xzthat is, H(w) = le + (1 w)X2, where 1:) denotes the weight that the portfolio places on stock 1. In other words, 10 represents the fraction of the portfolio that stock 1 makes up. In this example, we'll require 10 6 [0, 1], so that negative weights are not allowed.2 1. (1) Suppose you wanted to maximize the expected return of your portfolio, B[H(w)]. What weights :4) and 1 It) would you choose? (Hint: You don't need calculus to answer this.) 2. (1) Express the variance of your portfolio's return, Var[H(w)], in terms of the given parameters. 3. (2) Now suppose you wanted to minimize the variance of your portfolio's return. Find the value of 1:) that accomplishes this. (Hint: This time, you do need calculus: Take the appropriate derivative and solve for the optimal w and 1 w.) 4. (1) Now suppose 012 = 0, so returns are uncorrelated. Rewrite your answer to 3 given this information. Then, give a brief, non-technical interpretation of the new variance minimizing weights. In other words, explain why the optimal w and 1 1:) look the way they do, to someone who has never taken a class in probability or statistics