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CHAPTER 13: EMPIRICAL EVIDENCE ON SECURITY RETURNSCHAPTER 13: EMPIRICAL EVIDENCE ON SECURITY RETURNS
PROBLEM SETS
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.
• The slope is equal to the average return on the index portfolio.
3. The second-pass data from first-pass (SCL) estimates are:
Average
Excess
Return Beta
A 5.18 -0.47
B 4.19 0.59
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
13-1
Copyright © 2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
, CHAPTER 13: EMPIRICAL EVIDENCE ON SECURITY RETURNS
S second-pass regression yields:
The
Regression Statistics
Multiple R 0.7074
R-square 0.5004
Adjusted R-square 0.4291
Standard error 4.6234
Observations 9
Standard t Statistic t Statistic
Coefficients Error for β=0 for β=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: rM − rf = 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
12 -0.30 -4.99 -20.10
Average 4.04 8.51 15.28
Std. Dev. 19.30 29.47 43.96
13-2
Copyright © 2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
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