Data
I got the data from fama-french
data library. Then merged it with our locally created market
returns data set (from MBA land). This generated the following two
JMP data sets:
Paper
Bob and I are working on a paper. A very very preliminary version is
here.
Regression of excess return based on which decile number
Y = excess return for each of 100 portfolios
Size= decile number of size (0-9)
B/E = book to equity ratio decile number (0-9)
This is the raw JMP output. It basically shows the same thing that
the orginal Fama-French paper showed. Namely small stocks do
amazingly well. And high B/E ratio stocks to even better well.
Actual by Predicted Plot
![](fama-french-graphs/image1.PNG)
Summary of Fit
RSquare | 0.604354
|
RSquare Adj | 0.596196
|
Root Mean Square Error | 0.191787
|
Mean of Response | 0.916007
|
Observations (or Sum Wgts) | 100
|
Analysis of Variance
Source | DF | Sum of Squares | Mean Square | F Ratio
|
---|
Model | 2 | 5.4499712 | 2.72499 | 74.0843
|
Error | 97 | 3.5678765 | 0.03678 | Prob > F
|
C. Total | 99 | 9.0178477 | | <.0001
|
Parameter Estimates
Term | | Estimate | Std Error | t Ratio | Prob>|t|
|
---|
Intercept | | 0.772248 | 0.046621 | 16.56 | <.0001
|
size | | -0.039234 | 0.006677 | -5.88 | <.0001
|
B/E ratio | | 0.0711808 | 0.006677 | 10.66 | <.0001
|
Effect Tests
Source | Nparm | DF | Sum of Squares | F Ratio | Prob > F |
|
---|
size | 1 | 1 | 1.2699421 | 34.5260 | <.0001 |
|
B/E ratio | 1 | 1 | 4.1800291 | 113.6426 | <.0001 |
|
size
Leverage Plot
![](fama-french-graphs/image2.PNG)
B/E ratio
Leverage Plot
![](fama-french-graphs/image3.PNG)
Confidence intervals for each of the 100 portfolios
Inspite of the impressive performance we got above, none of them seem
to beat chance by very much. The following graph gives +/- 2*SE for
what CAPM would predict each of hte 100 portfolios should have for
its return. Only about 10 are outside this bound. We would expect
that 5 would be outside these bounds. But since the tests aren't
independent, it isn't clear if this is impressive or not.
![](fama-french-graphs/image4.PNG)
![](fama-french-graphs/image5.PNG)
Distribution of the z-statistics for the 100 portfolios
CAPM says that any portfolio you create should have an intercept which
is exactly zero. The following shows the z-statistcs for alpha for
these 100 portfolios.
CAPM along with independence would suggest that this should look like
100 normal zero-one random variables. Fama-French would suggest that
there are some serious outliers (namely those portfolios that are
either much better or much worse than expected.)
t(alpha)
![](fama-french-graphs/image6.PNG)
Quantiles
100.0% | maximum | 2.611
|
99.5% | | 2.611
|
97.5% | | 2.499
|
90.0% | | 2.030
|
75.0% | quartile | 1.614
|
50.0% | median | 0.763
|
25.0% | quartile | -0.329
|
10.0% | | -1.147
|
2.5% | | -1.753
|
0.5% | | -2.306
|
0.0% | minimum | -2.306
|
Moments
Mean | 0.5850628
|
Std Dev | 1.1989276
|
Std Err Mean | 0.1198928
|
upper 95% Mean | 0.822956
|
lower 95% Mean | 0.3471695
|
N | 100
|