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Why Annual Fama–French Regressions Cannot Estimate Portfolio Factor Loadings

Article Quant Q&A · Author: T_K
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Summary

The document describes an attempt to estimate three-factor Fama–French regressions for annual stock portfolios sorted into ROIC quartiles. The proposed setup creates four portfolios per year and regresses each constituent company’s annual excess return on annual factor values. The reported obstacle is that every company in a given year receives the same SMB and HML observations, so the regression returns missing coefficients and reports singularities.

The account is a research question rather than a resolved analysis: it provides no alternative specification, empirical results, or code. Its central issue is the mismatch between company-level return observations and factor data that are constant across those observations within a year. The document does not establish whether the intended estimates are possible under a different sampling frequency or portfolio-return construction. Researchers should therefore treat it as a warning to check the variation and alignment of regressors before interpreting coefficients, not as evidence for a particular solution.

Key ideas

  • The proposed portfolios sort companies into annual ROIC quartiles.
  • Each annual portfolio regression uses company excess returns as observations.
  • Annual factor values are identical across companies within the same year in the described setup.
  • The reported singularities prevent estimation of the requested factor coefficients.
  • The document raises the specification problem but does not provide a tested remedy.

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Factor investingEquitiesStatistics
Full text
# Issues running Fama French regression for annual portfolios


# Issues running Fama French regression for annual portfolios












As part of my master thesis I am planning to do some analysis based on the 3-Factor Fama french model. I am not a quantitative finance person at all, so my question might be extremely basic and I might be missing something very basic.

My idea is, I have the list of companies from 2000-2023. For each year, I want to sort the companies into quartiles (top 25%, mid 25%, mid 25% and bottom 25%) based on their ROICs. These quartiles would be 1 portfolio. Which means the year 2000 will have 4 portfolios of random companies (which may or may not be repeated) the year 2001 will also have 4 portfolios of random companies. I want to then regress the excess returns of these companies within a portfolio (1 year company return - Riskfree rate) against the 3 factors of Fama-French. So, there should be ideally 4 regression equations for each year for each quartile. One equation for Quartile 1 in 2000, one equation for Quartile 2 in 2000, so on and so forth.

The problem I am facing is, whenever I run the regression, my coefficients for the 3 factors are returned as NA since my SMB, HML value from the dartmouth website are the same for each company as I am using annual SMB, HML values. So for eg, for Quartile 1 of the year 2000, the company based excess returns are different but the SMB and HML values are the same for each company, leading to an NA return and the r-code says that there are singularities, which I really do not understand.

Can anyone suggest another approach, help me out with the code, or tell me where the problem is? I am genuinely struggling with this. Any help is appreciated. I have a serious concern that what I am trying to do is actually not possible hence I would appreciate all the help

Thank you!

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