Skip to content
All library documents

Evaluating Factor Models Beyond Regression Significance

Article Quant Q&A · Author: Borun Chowdhury
Read the original

Summary

The document asks how to verify a factor model across many stocks after estimating each asset’s factor loadings by regression. The response cautions that statistically significant coefficients alone do not establish that a factor is useful: factors can explain or decompose returns without offering a premium for bearing their associated risks. It distinguishes explanatory risk factors from factors that may support an investment return premium.

For a candidate factor intended to earn a premium, the suggested evaluation is a high-minus-low portfolio that buys assets with high factor exposure and sells those with low exposure. The response recommends checking whether the result persists across markets, since a backtest may work by chance in a particular sample. Economic intuition and prior factor research are presented as important guides, especially when computational methods generate candidates. The guidance is qualitative: it supplies no formal multiple-testing correction, statistical threshold, or specific validation protocol, so those would be needed for a rigorous empirical assessment.

Key ideas

  • Statistical significance of regression loadings alone does not validate a factor as an investment strategy.
  • Some factors help explain or decompose returns without offering a risk premium.
  • A high-minus-low long-short portfolio can test whether exposure to a proposed factor is associated with returns.
  • Check candidate factors across markets to reduce the chance that an apparent result is specific to one sample.
  • Economic reasoning and careful validation matter when searching computationally for factors.

Tags

Factor investingEquitiesBacktestingStatistics
Full text
# How would one go about verifying a factor model


# How would one go about verifying a factor model












Suppose I have a factor model

$$ \rho_i = \sum_J \beta_{iJ} \rho_J + \epsilon_i $$

where $\rho_i$ is the excess return of asset i over the risk free rate and $\rho_J$ is the excess return of the factor J portfolio. My J's are fixed and i's are all the possible stocks.

How would I go about verifying the model? Concretely, it is a linear regression problem and I can find out the $\beta_{iJ}$ and their statistical significance. If it were just one stock I were regressing against the statistical significance would tell me if the model is good. However, for multiple stocks what is the criteria? I am sure this can be answered using stats but I want to know if this is a well known result or should I sit down and compute it.

The motivation for this is that CAPM and Fama-French were based on some intuition for the factors (and that is how it should be) but in the age of cheap computation and AI one might find a factor and it will be useful to verify it across a large universe of stocks.

## Answer by Dhruv Mahajan (score 4, accepted)

https://quant.stackexchange.com/a/46008

Just finding factors based on regression is a poor idea. A statistically significant factor in all honesty may mean nothing. Read the fama French original paper, they were not just trying to find factors which explained risk( like in CAPM, beta is a measure of systematic risk), but they were trying to find out factors that provided a "risk premia". There are a ton of factors in the BARRA risk models which don't have any premia attached to them ( no profits for taking those risks) but they just act as a simple factor to decompose returns. If you want to find factors on your own, you'll have to backtest them using a high-low bucket long-short strategy and see if it works, but again it may only work by chance in your specific case, so you'll have to check in markets all over the world for consistency. Finding factors with risk premia is a hard task, but you can read tons of papers on already existing factors and modify them according to your specific need.

And don't get swayed by the idea of using machine learning to fit factors, mostly those factors will be shit and unless you can explain the economic intuition behind them, it'll mean nothing

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.