Chapter 13 – Empirical Evidence on Security Returns
13-1
CHAPTER 13: EMPIRICAL EVIDENCE ON SECURITY RETURNS
PROBLEM SETS
1. Even if the single-factor CCAPM (with a consumption-tracking portfolio used as
the index) performs better than the CAPM, it is still quite possible that the
2. Wealth and consumption should be positively correlated and, therefore, market
volatility and consumption volatility should also be positively correlated. Periods of
high market volatility might coincide with periods of high consumption volatility.
The conventional CAPM focuses on the covariance of security returns with returns
for the market portfolio (which in turn tracks aggregate wealth), while the
Chapter 13 – Empirical Evidence on Security Returns
13-2
Note: For the following problems, the focus is on the estimation procedure. To keep
the exercise feasible, the sample was limited to returns on nine stocks plus a market
3. 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
12
12
12
12
12
12
12
12
12
9.00
0.73
5.94
5.92
0.59
0.42
1.38
0.90
1.78
0.66
1.91
2.08
0.73
0.05
0.33
0.64
0.78
0.78
2.42
1.42
3.83
0.78
4.51
4.81
4. The hypotheses for the second-pass regression for the SML are:
5. 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
0.66
H
1.91
2.08
8.12
Chapter 13 – Empirical Evidence on Security Returns
13-3
S
The second-pass regression yields:
Multiple R
0.7074
0.5004
Standard error
4.6234
Intercept
3.92
2.54
1.54
6. 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
7. 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
21.41
12.66
52.14
-2.53
-50.71
-66.12
-0.30
-4.99
-20.10
Average
4.04
15.28
Std. Dev.
19.30
29.47
43.96
Chapter 13 – Empirical Evidence on Security Returns
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
0.42
0.08
-0.06
0.62
3.02
6.83
The inputs for the second pass regression are:
Average
Excess
Return
Beta
ABC
4.04
0.18
DEH
8.51
0.98
15.28
1.92
M
8.12
The second-pass estimates are:
Regression Statistics
Multiple R
0.9975
Adjusted R-square
0.9899
Standard error
0.5693
Intercept
F
H
FHI
Chapter 13 – Empirical Evidence on Security Returns
13-5
8. Roll’s critique suggests that the problem begins with the market index, which is
not the theoretical portfolio against which the second pass regression should hold.
9.
10. The first-pass (SCL) regression results are summarized below:
A
B
C
D
E
F
G
H
I
R-square
0.07
0.36
0.11
0.44
0.24
0.84
0.12
0.68
0.71
Observations
12
12
12
12
12
12
12
12
12
Intercept
9.19
-1.89
-1.00
-4.48
0.17
-3.47
5.32
-2.64
5.66
Beta M
-0.47
0.58
0.41
1.39
0.89
1.79
0.65
1.91
2.08
0.71
-0.13
-0.08
-0.37
0.01
-0.52
0.29
-0.28
0.59
CAPITAL MARKET LINE FROM SAMPLE DATA
I
20
25
CML
Chapter 13 – Empirical Evidence on Security Returns
13-6
11. The hypotheses for the second-pass regression for the two-factor SML are:
• The intercept is zero.
12. The inputs for the second pass regression are:
Average
Excess
Return
Beta M
Beta F
A
5.18
-0.47
-0.35
B
4.19
0.58
2.33
C
2.75
0.41
0.67
D
6.15
1.39
-1.05
E
8.05
0.89
1.03
F
9.90
1.79
-1.95
G
0.65
1.15
H
1.91
0.43
I
2.08
0.48
F
0.60
The second-pass regression yields:
Regression Statistics
Multiple R
0.7234
R-square
0.5233
Adjusted R-square
0.3644
Standard error
4.8786
Coefficients
Standard
Error
t Statistic
for β =0
t Statistic
for β =8.12
t Statistic
for β =0.6
Intercept
3.35
2.88
1.16
Beta M
5.53
2.16
2.56
Beta F
0.80
1.42
0.56
0.14
These results are slightly better than those for the single factor test; that is, the
intercept is smaller and the slope of M is slightly greater. We cannot expect a great
to the average excess return and the difference is less than one standard error.
Chapter 13 – Empirical Evidence on Security Returns
13-7
13. When we use the actual factor, we implicitly assume that investors can perfectly
replicate it, that is, they can invest in a portfolio that is perfectly correlated with the
factor. When this is not possible, one cannot expect the CAPM equation (the second
pass regression) to hold. Investors can use a replicating portfolio (a proxy for the
period returns are:
This proxy (PF) has an R-square
with the actual factor of 0.80.
We next perform the first pass
regressions for the two factor
model using PF instead of P:
A
B
C
D
E
F
G
H
I
R-square
0.08
0.55
0.20
0.43
0.33
0.88
0.16
0.71
0.72
Observations
12
12
12
12
12
12
12
12
12
Intercept
9.28
-2.53
-1.35
-4.45
-0.23
-3.20
4.99
-2.92
5.54
Beta M
-0.50
0.80
0.49
1.32
1.00
1.64
0.76
1.97
2.12
Beta PF
-0.06
0.42
0.16
-0.13
0.21
-0.29
0.21
0.11
0.08
0.72
-0.21
-0.12
-0.36
-0.02
-0.55
0.27
-0.33
0.58
-0.83
1.43
0.94
2.29
1.66
6.00
0.90
4.67
4.77
Proxy Portfolio for Factor F (PF)
Weights on
Universe
Stocks
Year
PF Holding
Period
Returns
A
-0.14
1
-33.51
B
1.00
2
62.78
C
0.95
3
D
-0.35
4
-153.56
E
0.16
5
200.76
F
-1.00
6
-36.62
G
0.13
7
-74.34
H
0.19
8
-10.84
I
0.06
9
28.11
59.51
-59.15
14.22
Chapter 13 – Empirical Evidence on Security Returns
13-8
Average
Excess
Return
Beta M
Beta PF
A
5.18
-0.50
-0.06
B
4.19
0.80
0.42
C
2.75
0.49
0.16
D
6.15
1.32
-0.13
E
8.05
1.00
0.21
9.90
1.64
-0.29
G
0.76
0.21
H
1.97
0.11
I
2.12
0.08
8.12
0.6
The second-pass regression yields:
Regression Statistics
Multiple R
0.71
0.51
Adjusted R-square
0.35
Standard error
4.95
Coefficients
Standard
Error
t Statistic
for β =0
t Statistic
for β =8.12
t Statistic
for β =0.6
Intercept
3.50
2.99
1.17
Beta M
5.39
2.18
2.48
Chapter 13 – Empirical Evidence on Security Returns
13-9
14. We assume that the value of your labor is incorporated in the calculation of the rate
of return for your business. It would likely make sense to commission a valuation of
your business at least once each year. The resultant sequence of figures for
CFA PROBLEMS
1. (i) Betas are estimated with respect to market indexes that are proxies for the true
market portfolio, which is inherently unobservable.
2. a. The basic procedure in portfolio evaluation is to compare the returns on a
managed portfolio to the return expected on an unmanaged portfolio having
the same risk, using the SML. That is, expected return is calculated from:
Chapter 13 – Empirical Evidence on Security Returns
c. Your graph should show an efficient frontier obtained from actual returns, and
a different one that represents (unobserved) ex-ante expectations. The CML
e. The question is really whether the CAPM is at all testable. The problem is that
3. The effect of an incorrectly specified market proxy is that the beta of Black’s
portfolio is likely to be underestimated (i.e., too low) relative to the beta calculated
based on the true market portfolio. This is because the Dow Jones Industrial
Average (DJIA) and other market proxies are likely to have less diversification and