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Using Financial Ratios as Factors in Cross-Sectional Models

Article Quant Q&A · Author: silencer
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Summary

The document clarifies how security-specific fundamental ratios such as price-to-earnings fit into factor modeling. In a cross-sectional regression, a ratio can serve as a security’s explanatory variable or loading, while the model estimates its relationship to returns; it does not need to be a common factor return shared by all securities. Transformations may help make ratios better behaved before they are used.

A second approach is to construct a factor-mimicking portfolio: go long securities with high ratio values and short those with low values, potentially adjusting the portfolio to reduce exposure to other variables. The resulting portfolio return series can then serve as a factor return. These are conceptual alternatives rather than a worked empirical comparison, and the document gives no evidence about which ratio treatment performs better or how to choose transformations or portfolio weights.

Key ideas

  • A security-specific ratio can be used as an explanatory variable in a cross-sectional return model.
  • A fundamental ratio does not need to be treated as a common return series for every security.
  • Transforming ratios may improve their behavior in a regression.
  • A long-short portfolio sorted on a ratio can create a factor-mimicking return series.
  • Factor-mimicking portfolios may be adjusted to reduce exposure to other variables.

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Factor investingEquitiesStatistics
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# How to use financial ratios in a factor model?


# How to use financial ratios in a factor model?












I am trying to understand how factor loadings in a general factor model are computed. For simplicity sake, lets assume a simple model:

$$ R = B \times F + \epsilon $$

$$ R = N \times 1 $$ $$ B = N \times K $$ $$ F = K \times 1 $$

where $B$ are the factor loadings and $F$ is the factor return and $N$ is the number of securities.

The way this equation is setup, a factor that is common to all $N$ assets, like GDP, inflation, or market index, can easily be plugged in as a factor return ($F$) into the above equation. But how about financial ratios? Let's say for example the PE ratio. The PE ratio is different for each security, which would in turn give us a different factor loading for each security. But how can we plugin a factor return for PE ratio into $F$; its different for each security.

Or is my understanding of using fundamental ratios in a factor model totally off?

## Answer by Black Diamond (score 2)

https://quant.stackexchange.com/a/8627

If you are doing something cross-sectional (like Fama-Macbeth regressions) you can just use the ratios where you would put the factor loadings (i.e. betas from the time series regs). You probably want to do some kind of transformation on the ratio to make it well-behaved first though. If you want an actual factor based on the ratio, you can use "factor mimicking portfolios", which are basically portfolios that are long stocks with high values of the ratio and short stocks with low values, with some attempt to orthogonalize them to other variables. See Ken French's website. The return time series from this portfolio is your factor.

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.