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Choosing SMB Factors in Fama–French Performance Regressions

Article Quant Q&A · Author: Mads
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Summary

The document considers which size factor to use when estimating three-, four-, and five-factor performance regressions: the SMB series associated with the three-factor model or the version used in the five-factor model. It describes the regressions as including market, size, and value factors, with momentum added in the four-factor specification and profitability and investment factors in the five-factor specification.

The response argues that additional factors may improve fit in some settings, but their relevance can vary by sector and type of company. It raises possible collinearity among SMB, profitability, and investment factors, which could contribute to overfitting, particularly for small-cap or innovation-focused portfolios. It suggests the five-factor model may suit some large-cap portfolios better, while emphasizing that the appropriate choice depends on the target holdings. No tests or comparative results are provided, so the practical recommendation is to evaluate both choices through backtesting on the intended portfolio.

Key ideas

  • The choice of SMB series depends on the factor model and portfolio being analyzed.
  • Profitability and investment factors may have different relevance across sectors.
  • Collinearity among factors can increase overfitting risk.
  • Backtesting on the target portfolio can help compare model specifications.

Tags

EquitiesFactor investingStatisticsBacktesting
Full text
# Correct choice of SMB factor for regression models


# Correct choice of SMB factor for regression models












I am currently conducting a performance analysis, where I use the 3-, 4-, and 5-factor models, hence

$R_{it}-R_{Ft}=\alpha+b_{i}RMRF+s_{i}SMB+h_{i}HML$

$R_{it}-R_{Ft}=\alpha+b_{i}RMRF+s_{i}SMB+h_{i}HML+w_{i}WML$

$R_{it}-R_{Ft}=\alpha+b_{i}RMRF+s_{i}SMB+h_{i}HML+r_{i}RMW+c_{i}CMA$

where $WML$ is the Fama/French/Carhart momentum factor.

I download the factor returns from Kenneth French's webpage, but I am unsure as to whether I should use the three-factor $SMB$ or the five-factor $SMB$ when using the three-, and four-factor model. Does anyone have an idea?

What are the pros and cons of both factors?

## Answer by Hui (score 0, accepted)

https://quant.stackexchange.com/a/39917

In general, 5 factors should perform better than 3 and 4 as farma-french should have performed their fundamental and statistical tests. However, it definitely has drawbacks. Fundamentally, RMW (return spread of most profitable minus least profitable) varies from different sectors. For example, on the bio-tech small caps, most of them are burning money while many of them performed strongly. Also for CMA, there is no common significance on different sectors. Amazon and tesla stock price will drop if they say they will reduce the investments while it will be totally different stories for traditional business or high dividend yield stocks. I will think the old 3 factors show more common significance for the entire stock market.

From statistical perspective, I belive there are collineraity issues between SMB and RMW, as well as between RMW and CMA on a lot of stocks. This might cause problems of overfitting and as a result, the performance could be way worse than 3-factor on some stocks.

Overall, 5-factor might perform better on large-cap stocks but will have many overfitting issues on small caps and innovation-driven stocks. So really depends on what your target portfolio is. However, my final answer to you is you should do back-testing to eventually pick which model you would like to use

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.