Given the six years of percentage linear return from Stock 1, 2 and 3 in the...

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Given the six years of percentage linear return from Stock 1, 2 and 3 in the following table Year Stock 1 return Stock 2 return Stock 3 return 2013 0.10 0.20 -0.05 2014 -0.15 -0.20 -0.3 2015 0.20 -0.10 0.25 2016 0.25 0.30 -0.1 2017 -0.30 -0.20 0.4 2018 0.20 0.60 0.15 Use the dataset from the previous exercise and assume Stock 3 to be the market portfolio, mkt, say the Standard and Poor's 500. 1. Write down the market model equation for Stock 1 and Stock 2 r = + ktrmkt + i 1 = + 3 + 2 2. For each Stock with i = {1,2} - compute the unbiased estimate of Brkt and interpret it compute the unbiased estimate of ai - compute the time series of the residuals {it=fit - a-beta; "mkt,t} - compute the unbiased estimate for the variance of the residuals 2 3. Write down the market model equation jointly for Stock 1 and Stock 2 using the matrix representation V^MM 0 report the vector that estimates the 21 vector a, is the market model a good statistical model given our data? why? - report the vector that estimates the 2 1 vector mkt, interpret the coefficient that you found - - Hint: follow the slides... report the 22 matrix containing the estimates for the diagonal variance covariance matrix of the error terms A = 0 0 0E2 compute the estimated 22 variance covariance matrix of Stock 1 and Stock 2 according to the market model and the available data: - compare it with the estimated variance-covariance matrix of just Stock 1 and Stock 2: how many estimates do the two covariance matrices require? does the market model help to reduce the number of estimates to estimate in this case? why? 4. For a generic portfolio of Stock 1 and Stock 2 0 = [1, 2] compute the estimated systematic and idiosyncratic component of the variance covariance matrix of the market model ^MM 0 5. Compute these components for the case of - Q = [1,0] - p = [0,1] - -=[0.5,0.5] 6. According to the market model which portfolio is better? why? Given the six years of percentage linear return from Stock 1, 2 and 3 in the following table Year Stock 1 return Stock 2 return Stock 3 return 2013 0.10 0.20 -0.05 2014 -0.15 -0.20 -0.3 2015 0.20 -0.10 0.25 2016 0.25 0.30 -0.1 2017 -0.30 -0.20 0.4 2018 0.20 0.60 0.15 Use the dataset from the previous exercise and assume Stock 3 to be the market portfolio, mkt, say the Standard and Poor's 500. 1. Write down the market model equation for Stock 1 and Stock 2 r = + ktrmkt + i 1 = + 3 + 2 2. For each Stock with i = {1,2} - compute the unbiased estimate of Brkt and interpret it compute the unbiased estimate of ai - compute the time series of the residuals {it=fit - a-beta; "mkt,t} - compute the unbiased estimate for the variance of the residuals 2 3. Write down the market model equation jointly for Stock 1 and Stock 2 using the matrix representation V^MM 0 report the vector that estimates the 21 vector a, is the market model a good statistical model given our data? why? - report the vector that estimates the 2 1 vector mkt, interpret the coefficient that you found - - Hint: follow the slides... report the 22 matrix containing the estimates for the diagonal variance covariance matrix of the error terms A = 0 0 0E2 compute the estimated 22 variance covariance matrix of Stock 1 and Stock 2 according to the market model and the available data: - compare it with the estimated variance-covariance matrix of just Stock 1 and Stock 2: how many estimates do the two covariance matrices require? does the market model help to reduce the number of estimates to estimate in this case? why? 4. For a generic portfolio of Stock 1 and Stock 2 0 = [1, 2] compute the estimated systematic and idiosyncratic component of the variance covariance matrix of the market model ^MM 0 5. Compute these components for the case of - Q = [1,0] - p = [0,1] - -=[0.5,0.5] 6. According to the market model which portfolio is better? why?