Why Factor Regression Can Reduce a Benchmark’s Estimated Beta
Summary
The discussion examines why a portfolio’s benchmark beta can fall and lose statistical significance when size, value, and momentum factors are added to a regression. In the example, the benchmark-only model reports a larger, significant loading, while the four-factor model assigns explanatory power to SMB and MOM and estimates a smaller, nonsignificant benchmark loading.
The proposed explanations are overlap among the benchmark and added factors, which can make coefficients unstable, and the benchmark’s narrow industry composition. SMB may partly proxy for market exposure omitted by a narrowly defined index. The answer recommends checking the result with a broader or otherwise different benchmark. The reported regressions illustrate the issue but do not establish which explanation applies; the example alone cannot prove the portfolio is market neutral. Model specification and benchmark choice affect how exposure is attributed.
Key ideas
- Adding correlated factors can change a regression’s estimated benchmark beta and its significance.
- A narrow benchmark may fail to capture broader market exposure.
- Size, value, or momentum factors may overlap with the benchmark and complicate interpretation.
- Compare results across benchmarks before concluding that a portfolio is market neutral.
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Full text
# Factor Model Regression Market Factor Statistically Insignificant After Adding Extra Factors
# Factor Model Regression Market Factor Statistically Insignificant After Adding Extra Factors
I am running a simple 4 factor model which includes the factors: Benchmark (Market - FortyConsumerSixtyHealthcare), SMB, HML and MOM.
When I simply apply the regression to the portfolio returns and the benchmark I get a statistically significant result and a fairly strong Beta of 0.4262:
```
================================================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------------------------
Intercept 0.0192 0.006 2.973 0.004 0.006 0.032
FortyConsumerSixtyHealthcare(BM) 0.4262 0.178 2.398 0.018 0.073 0.779
```
However when I run the model with the other factors included the significance is lost and the loading is also reduced significantly to 0.1809:
```
================================================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------------------------
Intercept 0.0233 0.006 3.902 0.000 0.011 0.035
FortyConsumerSixtyHealthcare(BM) 0.1809 0.171 1.060 0.292 -0.158 0.520
SMB 0.0085 0.003 3.374 0.001 0.003 0.013
HML -0.0017 0.002 -0.706 0.482 -0.007 0.003
MOM -0.0055 0.002 -2.589 0.011 -0.010 -0.001
```
The only statistically significant factors now seem to be size and momentum both of which have tiny loadings.
I am not sure why the loading on the benchmark has changed so significantly by adding other factors and why it is now not statistically significant, surely this would lead someone to think that the portfolio is market neutral when in fact it has a beta 0.4262?
## Answer by kurtosis (score 0, accepted)
https://quant.stackexchange.com/a/57190
A lot has been written on the Fama-French and Carhart factors -- including that SMB may help proxy for the market index being too narrowly-defined. Here you may also be facing that problem. Why else might your coefficient estimates have changed so much? Perhaps HML, SMB, or MOM is multicollinear with your benchmark index.
However, your benchmark index is likely a problem: it is even more narrow than the S&P 500 and has a strong industry bias. I would try using a different benchmark to see how that affects your results.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.