Using Fama–French Regression Alpha and R-Squared to Assess Returns

Summary

The note describes evaluating a portfolio against the Fama–French three-factor model by regressing portfolio excess returns on the factor returns. It proposes removing the factor contributions from the portfolio return series and asks whether the resulting cumulative performance can indicate sources of return beyond those factors. The response frames the regression intercept, or alpha, as the portfolio’s expected return not explained by the model, while R-squared measures the share of return variation explained by the factors.

These statistics address different aspects of performance: alpha concerns the average return left unexplained, whereas R-squared concerns fit to variation in the sample. The note provides no regression output, statistical significance, or tests of model assumptions. A positive cumulative residual series alone does not establish a reliable or persistent source of excess performance; interpreting alpha calls for uncertainty estimates and careful model specification. The answer is a concise conceptual explanation, not a full performance evaluation procedure.

Key ideas

• Regress portfolio excess returns on the Fama–French factors to assess factor exposure.
• The regression intercept estimates average return not explained by the included factors.
• R-squared summarizes how much return variation the factors explain in the fitted sample.
• Positive cumulative residual returns alone do not establish statistically reliable excess performance.

Tags

# Fama French Factor adjusted returns


# Fama French Factor adjusted returns












I want to understand the extent to which portfolio performance can be explained by the three Fama French Factor model. I use the following approach:

- Regress the portfolio's excess returns against the factors.

- Subtract the resulting coefficients multiplied by the factor values from the portfolio's excess returns.

This essentially gives me a time series for the regression constant + residual.

I have 2 questions:

- Is this a viable method for understanding the extent to which portfolio performance can be explained by the three Fama French Factor model?

- If I see positive cumulative returns from the resultant time series, can I make the claim that there are sources of performance beyond the three fama french Factors?

## Answer by phdstudent (score 3)

https://quant.stackexchange.com/a/76276

Yes. In a nutshell, the alpha of that regression will tell you how much of the portfolio expected return is not explained by the Fama-French 3-factor model and the $R^2$ of the regression will tell you how much of the variation in your portfolio return is explained by the variation of the three factors.

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.