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Academic Factor Models

It is relatively easy to look at a successful company like Amazon or Walmart and understand why their stocks have done so well. They are great companies that have transformed entire industries and transformed the U.S. economy. But what about the other 3,000+ stocks on the U.S. stock market? Without studying in detail all 3,000+ companies, is it possible to identify those companies that have been, or will be, successful stocks?

What factors contribute to a stock being successful over the long run? Does a company's stock do really well when the company grows really quickly? Or does a company's stock do really well when the company is really profitable, even if it doesn't grow very quickly? Or does a company's stock perform really well because the company's owners decide to pay out a high dividend to stockholders, which thus attracts a lot of investors? Why does one company's stock perform better than another company's stock? When looking at a small company, how do you know that it will become a really large company?

Because the U.S. stock market has been around for a 100+ years, and there is readily available data on the performance of over 3,000+ stocks, statisticians have started to perform academic research to determine if it is possible to identify which set of "factors" have generally caused one company's stock to outperform the market as a whole over long periods of time. This research is generally referred to as "factor research".

Researchers have identified hundreds of "potential factors" to look at, including factors about the company itself, such as :

  • How profitable was the company?
  • How fast was the company growing?
  • Was the company a small company or a big company?
  • Did the company pay a dividend?
  • Did the company spend a lot on capital improvements, such as for new plants and equipment?

Researchers have also identified factors related to the stock itself, such as:

  • Was the company's stock market price really volatile?
  • On average, was the company's stock market price really expensive (using measures like the price per share compared to the earnings per share of the company)?
The main limitation in this factor research is identifying those factors that have sufficient readily available information on, so that the researcher can systematically analyze the importance (or lack of importance) on the company's stock market performance.

The main goal of factor research is to build a "factor model" -- i.e. to identify a combination of factors that together do the best job of explaining, over long periods of time, why certain stocks outperform the stock market as a whole. No factor model is perfect, as the stock market is a complex thing, with hundreds of factors affecting the stock market on a daily basis. So the goal is to use some advanced statistical analysis to come up with best possible factor model, with the fewest limitations and flaws.

Factor research is generally performed by constructing sample portfolios. Using data on 3,000+ stocks, mostly from the last 30 years or so, researchers generally construct sample portfolios by sorting the data on the 3,000+ stocks using different criteria, or factors, like the size of the company, the profitability of the company, the price of the company's stock relative to earnings, etc... They then measure which of these sample portfolios performed better than the market as a whole.

For example, what happens if you construct a portfolio of the 100 stocks with the highest dividend yield? Does it perform better or worse than the market? If it performs better than the market, the researcher then applies advanced statistics to determine if the excess performance was statistically significant, or meaningful. Perhaps the excess performance was random luck.

The analysis gets more complicated because researchers have to form portfolios using multiple factors. What happens if you construct a portfolio of 100 stocks with the highest dividend yield and the lowest price to earnings ratio? What happens if you construct a portfolio of 100 stocks with the highest dividend yield, the lowest price to earnings ratio, and the lowest volatility? The number crunching and statistical calculations quickly get very complex.

Eventually, by running enough sample portfolios, you can eventually identify those investment factors that really are important.

Fama French three factor model

Perhaps the most famous factor investment research has been performed by two college professors, Kenneth R. French and Eugene F. Fama. Fama French originally published in 1993 an article stating that three factors can generally explain the performance of a stock over long periods of time:

  • The performance of the stock market as a whole
  • The size of the company (i.e. small caps generally outperform large caps)
  • Value stocks, defined as a low ratio between a company's book value (i.e. stockholder's equity on their balance sheet) and it's stock market value (market capitalization), generally outperform other stocks
This is referred to as their three factor model. View the paper.

The Fama French three factor model significantly advanced academic research concerning factors. Spurred on by Fama French, researchers began studying hundreds of potential factors, analyzing which ones could be significant. As a result, it became clear as time went by that the three factor model was incomplete.

Fama French five factor model

Fama French published in 2014 an updated article on their research in which they proposed that five factors can generally explain the performance of a stock over long periods of time:

  • The performance of the stock market as a whole
  • The size of the company (i.e. small caps generally outperform large caps) (SMB)
  • Value stocks, defined as a low ratio between a company's book value (i.e. stockholder's equity on their balance sheet) and it's stock market value (market capitalization), generally outperform other stocks (HML)
  • The stocks of companies that are more profitable (have higher operating earnings) generally outperform other stocks (RMW)
  • The stocks of companies that make fewer investments (measured using the growth in a company's total assets from year to year on their balance sheet) generally outperform the stocks of companies with higher investments (CMA)
This is referred to as their five factor model. View the paper. See Mr French's website for their ongoing research.

Some of the biggest questions about the Fama French five factor model have been that it is missing two widely accepted factors: low volatility and momentum. In a 2015 paper called Dissecting Anomalies, Fama French argue that the low volatility factor is captured by their five factor model using the combination of the profitability (RMW) and investment factors (CMA). They argue that companies with low volatility stocks tend to be highly profitable and invest conservatively.

Hou Xue and Zhang four factor q model

Hou, Xue and Zhang published in 2014 a four factor model that they call the "q model" to generally explain the performance of a stock over long periods of time:

  • The performance of the stock market as a whole
  • The size of the company (i.e. small caps generally outperform large caps)
  • The stocks of companies with a higher return on equity generally outperform other stocks
  • The stocks of companies that make fewer investments generally outperform the stocks of companies with higher investments
This is referred to as their four factor q model. View the paper. They also wrote a paper comparing their 4 factor model to the Fama French 5 factor model.View the comparison paper

Hou, Xue and Zhang measured investments as the growth in total assets on a company's balance sheet.

Asness six factor model

Cliff Asness of AQR Capital Management published in 2014 a six factor model that started with the Fama French Five Factor model but made several key changes. First, he adds the momentum factor to the model, based on research that the momentum factor is a well-established factor. Second, he adjusts the way that Fama French calculates the value factor (HML), using more recent pricing data compared to the Fama French calculation. See Asness Frazzini 2013 for details behind the value factor adjustment.

The resulting six factor model thus became:

  • The return of the market itself
  • Size
  • Earnings (quality)
  • Momentum
  • Value
  • Investment

The most important take away from this model is that this model resurrects the value factor. Even though Fama French included the value factor in their five factor model, they admitted that it was "redundant" - i.e. that it wasn't really necessary to improve the performance of the model. The Asness Six Factor model shows that value, as adjusted, can be significant.

Factor models in real life

There aren't any ETFs that are built on indexes that precisely follow the methodology of these academic factor models. However, there are currently 341 exchange traded products that are based on indexes that select securities using more than one investment factor. These "multi-factor" ETFs are essentially attempting to do the same thing as the academic factor models: identify the best combination of a few investment factors that are mostly likely to help build a portfolio of stocks that will outperform the stock market over long periods of time. You can read more about multi-factor ETFs in our article multi-factor ETFs.