bkmsol_ch13 - CHAPTER 13: EMPIRICAL EVIDENCE ON SECURITY...

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CHAPTER 13: EMPIRICAL EVIDENCE ON SECURITY RETURNS Note: For end-of-chapter problems in Chapter 13, the focus is on the estimation procedure . To keep the exercise feasible, the sample was limited to returns on nine stocks plus a market index and a second factor over a period of 12 years. The data were generated to conform to a two-factor CAPM so that actual rates of return equal CAPM expectations plus random noise, and the true intercept of the SCL is zero for all stocks. The exercise will provide a feel for the pitfalls of verifying social-science models. However, due to the small size of the sample, results are not always consistent with the findings of other studies are reported in the chapter. 1. Using the regression feature of Excel with the data presented in the text, the first- pass (SCL) estimation results are: Stock: A B C D E F G H I R Square 0.06 0.06 0.06 0.37 0.17 0.59 0.06 0.67 0.70 Observations 12 12 12 12 12 12 12 12 12 Alpha 9.00 -0.63 -0.64 -5.05 0.73 -4.53 5.94 -2.41 5.92 Beta -0.47 0.59 0.42 1.38 0.90 1.78 0.66 1.91 2.08 t-Alpha 0.73 -0.04 -0.06 -0.41 0.05 -0.45 0.33 -0.27 0.64 t-Beta -0.81 0.78 0.78 2.42 1.42 3.83 0.78 4.51 4.81 2. The hypotheses for the second-pass regression for the SML are: The intercept is zero; and, The slope is equal to the average return on the index portfolio. 3. The second-pass data from first-pass (SCL) estimates are: Average E x c e s s R e t u r n Beta A 5.18 -0.47 B 4.19 0.59 13-1
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C 2.75 0.42 D 6.15 1.38 E 8.05 0.90 F 9.90 1.78 G 11.32 0.66 H 13.11 1.91 I 22.83 2.08 M 8.12 The second-pass regression yields: Regression Statistics Multiple R 0.7074 R Square 0.5004 Adjusted R Square 0.4291 Standard Error 4.6234 Observations 9 Coefficients Standard Error t Statistic for β =0 t Statistic for =8.12 Intercept 3.92 2.54 1.54 Slope 5.21 1.97 2.65 -1.48 4. As we saw in the chapter, the intercept is too high (3.92% per year instead of 0) and the slope is too flat (5.21% instead of a predicted value equal to the sample-average risk premium: r M - r f = 8.12%). The intercept is not significantly greater than zero (the t-statistic is less than 2) and the slope is not significantly different from its theoretical value (the t-statistic for this hypothesis is - 1.48). This lack of statistical significance is probably due to the small size of the sample. 5. Arranging the securities in three portfolios based on betas from the SCL estimates, the first pass input data are: Year ABC DEG FHI 1 15.05 25.86 56.69 2 -16.76 -29.74 -50.85 3 19.67 -5.68 8.98 4 -15.83 -2.58 35.41 5 47.18 37.70 -3.25 6 -2.26 53.86 75.44 7 -18.67 15.32 12.50 8 -6.35 36.33 32.12 9 7.85 14.08 50.42 10 21.41 12.66 52.14 11 -2.53 -50.71 -66.12 13-2
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12 -0.30 -4.99 -20.10 Average 4.04 8.51 15.28 Std. Dev. 19.30 29.47 43.96 The first-pass (SCL) estimates are: ABC DEG FHI R Square 0.04 0.48 0.82 Observations 12 12 12 Alpha 2.58 0.54 -0.34 Beta 0.18 0.98 1.92 t-Alpha 0.42 0.08 -0.06 t-Beta 0.62 3.02 6.83 Grouping into portfolios has improved the SCL estimates as is evident from the
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bkmsol_ch13 - CHAPTER 13: EMPIRICAL EVIDENCE ON SECURITY...

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