Interpreting Low R-Squared in European Equity Factor Regressions

Summary

The document describes a time-series analysis of European equity industry portfolio returns against Fama–French factor returns, with momentum included in one model. The portfolios include a value-weighted portfolio and equally weighted portfolios formed by size or value sorts. The researcher compares three factor-model specifications across the portfolios and reports that the resulting R-squared values are very low, with a stated maximum of 6.6%.

The text raises the issue of how to interpret those fit statistics, while observing that R-squared is not usually the central measure in factor-model analysis. It does not include replies, diagnostics, or a proposed explanation for the low values, so the setup alone cannot establish whether the result reflects portfolio construction, return data, model specification, or implementation. Its main value is as a concrete example of using time-series factor regressions and of treating explanatory fit as distinct from the broader purpose of a factor analysis.

Key ideas

• The analysis regresses European industry portfolio returns on standard equity factors and momentum.
• It compares three factor specifications across portfolios constructed with different weighting and sorting approaches.
• The reported R-squared values are low, and the maximum stated value is 6.6%.
• The document poses an interpretation question but provides no diagnostics or explanation for the fit results.
• R-squared alone is not presented as the most important criterion for evaluating a factor analysis.

Tags

# Fama-French 3, Carhart 4, Fama-French 5 Factor models return borderline 0% R2 (max. 6.6%). Time series regression


# Fama-French 3, Carhart 4, Fama-French 5 Factor models return borderline 0% R2 (max. 6.6%). Time series regression












I am currently working on an industry specific time series analysis of European Equities between 201001 and 201812. I use the European Fama French factor returns (plus the momentum factor return) that have been provided by Kenneth French on his website. I set up in total 7 portfolios for my industry returns. 1 value weighted. 3 sorted by size and 3 sorted value, which are all equally weighted. I run the returns for the portfolios against the factors. in total I end up with 21 outputs, given I run all three types of models for the 7 different portfolios. Anyone an idea why the R2 are so low?

Whereas R2 is of course not the most interesting or relevant component of my or any FF model analysis, I do wonder why it is as low as I have found.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.