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
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
B/E ratio
Leverage Plot
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.
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)
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
|