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11-Covariance
Covariance/Correlation Example 1. Compute the mean of the returns on Stock A. The means of the returns on Stocks B and C have been provided for you. State Probability Ret. Stock A Ret. Stock B Ret. Stock C Boom .20 .15 .40 –.10 Normal .60 .05 .10 .03 Bust .20 –.05 –.20 .15 ?A = ______ ?B = .10 ?C = .028 ?A = (.2 x .15) + (.6 x .05) + (.2 x -.05) = .03 + .03 + -.01 = .05 CN75 2. Next, compute the standard deviation for Stock A. The standard deviations for Stocks B and C have been provided for you. State Probability Ret. Stock A Ret. Stock B Ret. Stock C Boom .20 .15 .40 –.10 Normal .60 .05 .10 .03 Bust .20 –.05 –.20 .15 ?A = .05 ?B = .10 ?C = .028 Std. Dev. A: _____________ Std. Dev. B: 0Std. Dev. C: 0 ?2A = .2 x (.15 - .05)2 + .6 x (.05 - .05)2 + .2 x (-.05 - .05)2 = .002 + 0 + .002 = .004 (Variance of A) ? = .063245553 (Std. Dev. A) CN75 Now, compute the covariance and correlation coefficient of each pair of stocks (A/B, A/C, B/C). State Probability Ret. Stock A Ret. Stock B Ret. Stock C Boom .20 .15 .40 –.10 Normal .60 .05 .10 .03 Bust .20 –.05 –.20 .15 ?A = .05 ?B = .10 ?C = .028 Std. Dev. A: 0.063245553 Std. Dev. B: 0Std. Dev. C: 0.07909488
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