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Estimating Fama–French Factor Betas with Linear Regression

Article Quant Q&A · Author: Thomas Johnson
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Summary

The document explains how to estimate a stock’s exposure to the Fama–French SMB and HML factors. The proposed method is a linear regression of the stock’s returns on the relevant factor returns; the resulting coefficients are the estimated factor betas. Factor return data can be obtained from published datasets, with coverage varying by country. Standard regression tools can also report associated statistics such as standard errors and fit measures.

The responses caution that the Fama–French framework is primarily intended for portfolios, where factor exposures may be more economically interpretable. A regression can still be run for an individual stock, but its coefficients may be noisy or difficult to interpret. The document does not specify a return frequency, sample period, factor model specification, or empirical results, so those choices would need to be made for a particular analysis.

Key ideas

  • Estimate SMB and HML exposures by regressing stock returns on factor returns.
  • The regression coefficients provide the estimated factor betas.
  • Published factor datasets exist for multiple markets, though country coverage differs.
  • Individual-stock estimates may be less stable or interpretable than portfolio-level estimates.

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Factor investingEquitiesStatistics
Full text
# How can I calculate Fama-French betas for a particular stock?


# How can I calculate Fama-French betas for a particular stock?












For a particular stock, what's the simplest way to calculate betas for the Fama-French factors SMB and HML?

## Answer by Richi Wa (score 3)

https://quant.stackexchange.com/a/11362

Not sure what the question is. As John points out: the method is linear regression.

For the data you could look at Kenneth French's wegpage for US stocks. In the wikipedia article you find the links to factors for other countries (UK, Germny, Switzerland) - though I have not checked these links.

Note however that the Fama-French model works better for portfolios than for individual stocks.

## Answer by Quantopik (score 0)

https://quant.stackexchange.com/a/14091

First of all, the only one way to compute factor betas is to use the linear regression model, as suggested by John in the 1st comment. There is not other way to get them. You can get it by simply using excel through the Data Analysis package or using the relative command/code in other statistical command; in Stata, for instance, the command regress gives as output all statistics you need for(betas, st. dev., R^2,...).

Secondly, the Fama-French model is portfolio-based. So, following their model you can compute beta factors on stock portfolios, built ranking stocks on their characteristics (the most used is the size or mkt cap); it would have been no sense to compute betas for each stock in the market you're analyzing, since you did not conclude anything.

Indeed, all regression-based model in financial economics, as the one you cited in the question, are portfolio-based and not stock-based.

Anyway, you can compute betas for each stock theoretically, but you'll not get economically explicable output.

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.