## 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

SourceDFSum of SquaresMean SquareF Ratio
Model25.44997122.7249974.0843
Error973.56787650.03678Prob > F
C. Total999.0178477<.0001

#### Parameter Estimates

TermEstimateStd Errort RatioProb>|t|
Intercept0.7722480.04662116.56<.0001
size-0.0392340.006677-5.88<.0001
B/E ratio0.07118080.00667710.66<.0001

#### Effect Tests

SourceNparmDFSum of SquaresF RatioProb > F
size111.269942134.5260<.0001
B/E ratio114.1800291113.6426<.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% 2.03 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 0.585063 Std Dev 1.19893 Std Err Mean 0.119893 upper 95% Mean 0.822956 lower 95% Mean 0.34717 N 100