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HW5_sol - Cov(Apex Bpex = 0.91*1.32*0.04 = 0.0480 b You...

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Purdue University Krannert School of Management MGMT 411: INVESTMENTS Assignment #5 Solutions You have information about two stocks: Apex and Bpex. Namely, the output from regressing the monthly returns of Apex and Bpex on the S&P 500 Index monthly return for the period 1946- 2009 is: R apex = 0.0012 + 0.91*R S&P + ε apex (0.0010) (0.31) R bpex = 0.0044 + 1.32*R S&P + ε bpex (0.0020) (0.23) The output above shows that the alpha of Apex is 0.0012, the beta of Apex is 0.91, etc. The numbers below the coefficients represent the corresponding standard errors: e.g., the standard error of the alpha of Apex is 0.0010, etc. You also know that the standard deviation of ε apex is 0.0450, while the standard deviation of ε bpex is 0.0530. The variance of the return of the S&P 500 index is 0.04. a) What is the covariance between the two stocks? Cov(Apex, Bpex) = 0.91*1.32*Var(S&P)
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Unformatted text preview: Cov(Apex, Bpex) = 0.91*1.32*0.04 = 0.0480 b) You want to test the hypothesis that the alpha of Bpex is equal to 0. Based on the regression output from above, what is the conclusion from your test? The t-stat associated with the null hypothesis that the alpha of Bpex is zero is: 0.0044/0.0020 = 2.2. This is greater than 2 in absolute value, so we reject the null. c) Based on the regression output, which company has higher idiosyncratic risk? The standard deviation of the residual term for Apex is 0.045. The standard deviation of the residual term for Bpex is 0.053. Therefore, Bpex has higher idiosyncratic risk. d) What is the total variance of Bpex stock return according to the index model? V(Bpex) = (beta) 2 *Var(S&P) + (SD( ε apex )) 2 V(Bpex) = (1.32) 2 *0.04 + (0.0530) 2...
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