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3. Assume an investor's universe consists of three stocks, Stock 1, 2 and 3. The return of each stock is denoted as r; where i 1,2,3. The weight of each stock in the market portfolio is denoted as w. The standard deviation of each stock is o and lastly, the covariance between two stocks is given by 0u). Let w be a 3 x 1 matrix of weights and be a 3 x 3 variance-covariance matrix. a) Show that the variance of the market portfolio of = w'w is given by the expression below. oh = wo? + wo + wo + 2(W,W201,2 + W;W302,3 + W3W302.3) b) Confirm that I'm = w'r = {win = win + W212 + W373. Also note that the covariance between the return of asset i and the market (which consists of these three assets) is given by Cov(n,r) = 0 = Cov(n,win + W2r2 + W3r3) Using the above show that the market variance of = w;0.M c) What is the relationship between in and o? Can we think of the ratio M as the contribution of a stock to the risk of the market portfolio? 3. Assume an investor's universe consists of three stocks, Stock 1, 2 and 3. The return of each stock is denoted as r; where i 1,2,3. The weight of each stock in the market portfolio is denoted as w. The standard deviation of each stock is o and lastly, the covariance between two stocks is given by 0u). Let w be a 3 x 1 matrix of weights and be a 3 x 3 variance-covariance matrix. a) Show that the variance of the market portfolio of = w'w is given by the expression below. oh = wo? + wo + wo + 2(W,W201,2 + W;W302,3 + W3W302.3) b) Confirm that I'm = w'r = {win = win + W212 + W373. Also note that the covariance between the return of asset i and the market (which consists of these three assets) is given by Cov(n,r) = 0 = Cov(n,win + W2r2 + W3r3) Using the above show that the market variance of = w;0.M c) What is the relationship between in and o? Can we think of the ratio M as the contribution of a stock to the risk of the market portfolio

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