Interpreting Average R-Squared in Fama–MacBeth Regressions

Summary

The document raises a model-evaluation question about a two-stage Fama–MacBeth analysis of Fama–French risk premia. The researcher first estimates company-level betas, then runs cross-sectional regressions over successive periods and averages the estimated premia. They ask whether averaging the regressions' R-squared values gives a defensible overall fit measure, especially for comparison with a CAPM estimate, or whether they should also run a conventional three-factor regression.

No answer or empirical results are included, so the document does not establish that average R-squared is technically appropriate or that adding factors improves explanatory power. Its value is in identifying that the meaning of a fit statistic depends on the regression setup and comparison being made. Any conclusion would need to specify which cross-sectional variation and periods the statistic summarizes, and use a comparison method aligned with the models being evaluated. The question alone does not resolve those methodological choices.

Key ideas

• The document describes a two-stage Fama–MacBeth procedure with estimated company betas and period-by-period cross-sectional regressions.
• The researcher asks whether the average of period-specific R-squared values can summarize overall model fit.
• The proposed comparison is between a multifactor specification and a CAPM estimate.
• No answer or results are provided, so the suitability of the average and the model comparison remain unresolved.

Tags

# Average of R squared correct/allowed/useful?


# Average of R squared correct/allowed/useful?












I just conducted a Fama-Macbeth analysis to estimate the risk premia of Fama/French.

In short, I estimated the betas on a company-individual basis first and then conducted a cross-section regression resulting in risk premia (t=1 to t=235). Subsequently a simple average of the risk premia was calculated.

Now I'm wondering if it's technically correct/allowed to calculate an average of the R2 of regression (t=1 to t=235) and make a statement about the "overall" R2 of the multifactor modell in comparison to the simple CAPM I calculated earlier.

Essentially I just want to say adding the factors (should've) increased the R2 of the model. Just not sure if I can do it with the Fama-Macbeth regressions or if I have to do a normal FF three-factor regression as well.

Thanks.

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.