When to Use Individual Stocks Instead of Portfolios in Fama–French Regressions

Summary

The document considers whether stocks must be sorted into portfolios when estimating Fama–French factor models. With only three companies available, the accepted answer recommends running separate regressions on each stock’s excess returns using the factor time series, rather than forming portfolios from such a small sample. This directly addresses a comparison of how three-factor and five-factor specifications describe those stocks.

Portfolio formation is useful in broader asset-pricing research because averaging across companies can reduce company-specific return noise while preserving systematic patterns, provided the stocks grouped together have similar factor characteristics. Sorting is therefore tied to the research design and available cross-section, not an automatic requirement for every regression. The document gives a qualitative rationale and practical guidance for a tiny stock universe, but it does not discuss regression diagnostics, statistical power, or criteria for deciding which factor model fits best.

Key ideas

• A small set of three stocks can be analyzed with separate regressions rather than portfolio sorting.
• Portfolio averaging can reduce the influence of company-specific return patterns.
• Stocks should be grouped by similar systematic characteristics if portfolio averages are meant to preserve factor patterns.
• The choice between three-factor and five-factor models still requires an appropriate comparison of fit and evidence.

Tags

# Is sorting stocks into portfolio mandatory in Fama-French model?


# Is sorting stocks into portfolio mandatory in Fama-French model?












I am currently doing a report regarding Fama and French 3 and 5 factors model. I was provided 3 companies with each of its daily stock return from 2015-2020, and the values of all 5 factors during that period (Mkt-RF, SMB, HML, RMW, CMA, RF). I will be using Excel to compute a regression analysis. But is it mandatory to sort the stocks into portfolios as how Fama and French did? Or can I do regression on the three companies separately and analyze it? The final approach will be deciding which between three-factor and five-factor model best describe excess stock returns of the 3 companies.

## Answer by Richard Hardy (score 3, accepted)

https://quant.stackexchange.com/a/77475

When you only have three stocks in your data set, trying to form portfolios will not be helpful. Run the analysis on the individual stocks' data as is.

Using portfolios instead of individual assets in estimating and testing asset pricing models makes sense because we expect idiosyncratic (company-specific) patterns in returns to become less pronounced in averages across companies (that is, portfolios). Meanwhile, we expect deterministic patterns to stay about as strong as they were, as long as the companies within a portfolio contain similar deterministic patterns. That is why we do not put just any stocks in a given portfolio but look for ones that have similar deterministic patterns – such as a similar level of systematic risk, similar sensitivity to size or value factors and such.

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.