Exercise
The Eviews file capm.wf1 contains Belgian monthly financial data over the 19881996 period. The dataset includes:
rpet: return on the “Petrofina” firm,
rm: return on the market,
rf: risk-free interest rate.
The file also contains UK’s FTSE-100 stock index.
a) Construct the long-run trend of the FTSE-100 index using the HodrickPrescott trend and plot the % deviations from this trend.
b) Construct the excess return variables exretpet=rpet-rf and exretmar=rm-rf.
Plot the two variables together. Note: I have already constructed the variables.
Alternatively, on the command window, you type:
genr exretpet=rpet-rf
genr exretmar=rm-rf
This generates the excess return variables. Once you do that, click on the
“View” button to calculate the mean and standard deviation of each variable.
c) Test the validity of the CAPM model by regressing rpet-rf on rm-rf.
d) Re-estimate the CAPM model allowing for a January effect generated (in
Eviews) as genr jandum=@seas(1). [Note: The financial literature suggests
that returns might be higher in January. This is typically the case for small
firms and for firms whose price has already declined during the year. Hence,
an investor can make money by buying in December and selling in January.
The most likely cause of the year-end effect is tax selling; for ordinary
investors, the relevant consideration is whether to realise enough of their
losses to get some benefit on their taxes. Capital losses are fully deductible
against gains, and in the US, up to $3,000 of losses can also be deducted from
ordinary income. This last can save an investor in the 28 percent tax bracket
$840 on his tax return in April.].
e) Test for autocorrelation of order 12, heteroskedasticity, and normality. Test for
parameter instability by splitting the sample in 1992:02. What do you infer
from these tests?
Answer to part a): Click on the ftse100 series, then choose “proc”, then choose
Hodrick-Prescott filter. Then, accept the setting of the package (what the package
suggests). The smoothed series hptrend01 gives you the smoothed trend. To calculate
%
deviations
from
the
trend,
type
in
deviation=100*(ftse100-hptrend01)/hptrend01.
the
command
window:
genr
I have already done this for you.
Then click on deviation and get the plot of the series:
DEVIATION
15
10
5
0
-5
-10
-15
1988
1989
1990
1991
1992
1993
1994
1995
What the plot is telling you is that the UK stock market was 12%-15% below its longrun trend in 1990 (UK recession) and in 1992 (when the UK exited the Exchange Rate
Mechanism; see for instance: http://en.wikipedia.org/wiki/Black_Wednesday) and
some 15% above its long-run trend in early 1994.
Brief answer to part b):
.3
.2
.1
.0
-.1
-.2
-.3
1988
1989
1990
1991
EXRETPET
1992
1993
1994
1995
EXRETMAR
From the above graph, the two excess return variables move very close to each other.
This seems to suggest a beta coefficient which is close to 1. To get a summary of
statistics for each variable, open the two variables as a group. Then click on the
“Descriptive Stats” option:
EXRETPET
EXRETMAR
Mean
-0.003764
0.001300
Median
-0.005510
-0.002904
Maximum
0.165594
0.220758
Minimum
-0.231116
-0.116153
Std. Dev.
0.058685
0.047400
Skewness
-0.079797
0.876733
Kurtosis
5.096003
7.160984
Jarque-Bera
18.04303
83.25273
Probability
0.000121
0.000000
The excess return on Petrofina has a lower mean return (and a higher volatility) than
the excess return on the market portfolio.
Brief answer to part c):
Note: I have already saved the regression in the icon
“part_c”. Click on the icon “part_c”.
Dependent Variable: EXRETPET
Method: Least Squares
Date: 05/20/04 Time: 10:07
Sample: 1988:01 1996:02
Included observations: 98
Variable
Coefficient Std. Error
t-Statistic
Prob.
C
EXRETMAR
-0.004991
0.942958
-1.291955
11.51591
0.1995
0.0000
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.580082
0.575708
0.038226
0.140278
181.8498
1.959643
0.003863
0.081883
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
-0.003764
0.058685
-3.670404
-3.617649
132.6162
0.000000
Brief answer to part d):
Check the icon “part_d”, where the coefficient on the January dummy variable is
equal to -0.002519 with a t-ratio of -0.185159.
e) Autocorrelation (serial correlation) test of order 12: The model does not fail the
test.
Breusch-Godfrey Serial Correlation LM Test:
F-statistic 0.690664
Prob. F(12,84)
0.7560
Heteroskedasticity test: The model fails the test at 5% (but not at 1%) since the pvalue is between 0.01 and 0.05.
Heteroskedasticity Test: White
F-statistic 3.448676
Prob. F(2,95)
0.0358
Normality test: The model fails badly the test as the p-value is equal to 0.
20
Series: Residuals
Sample 1988M01 1996M02
Observations 98
16
12
8
4
0
-0.15
-0.10
-0.05
0.00
0.05
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
3.68e-18
0.005173
0.127032
-0.149042
0.038028
-0.483391
5.261202
Jarque-Bera
Probability
24.69478
0.000004
0.10
Parameter stability test: In Eviews, choose: Stability tests, then Chow Forecast test
and enter 1992:02. The model does not fail the test as the p-value=0.1125.
Chow Forecast Test: Forecast from 1992M02 to 1996M02
F-statistic 1.424959
Prob. F(49,47)
0.1125