Assume an investor's universe consists of three stocks, Stock 1, 2 and 3. The return of each stock is denoted as ri where i E 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 Oi,j. 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 o w'w is given by the expression below. oi = wio? + wo + wzo3 + 2(w1W201,2 + w W301,3 + W2W302,3) = b) Confirm that rm w'r = Ewiri = W171 + W212 + W3r3. Also note that the covariance between the return of asset i and the market (which consists of these three assets) is given by Cov(ri, rm) = OiM = Cov(ri, W1r1 + w2r2 + W3r3) Using the above show that the market variance o = w;Oi,m , c) What is the relationship between Oi,m and of? Can we think of the ratio as the contribution om of a stock to the risk of the market portfolio? Assume an investor's universe consists of three stocks, Stock 1, 2 and 3. The return of each stock is denoted as ri where i E 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 Oi,j. 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 o w'w is given by the expression below. oi = wio? + wo + wzo3 + 2(w1W201,2 + w W301,3 + W2W302,3) = b) Confirm that rm w'r = Ewiri = W171 + W212 + W3r3. Also note that the covariance between the return of asset i and the market (which consists of these three assets) is given by Cov(ri, rm) = OiM = Cov(ri, W1r1 + w2r2 + W3r3) Using the above show that the market variance o = w;Oi,m , c) What is the relationship between Oi,m and of? Can we think of the ratio as the contribution om of a stock to the risk of the market portfolio