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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?

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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

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