Which equity factors truly explain stock returns, and what group of them constitute the best model? In their November 2019 paper entitled “Bayesian Solutions for the Factor Zoo: We Just Ran Two Quadrillion Models”, Svetlana Bryzgalova, Jiantao Huang and Christian Julliard present a Bayesian estimation and model selection method for pricing of stock portfolios that allows simultaneous examination of the entire zoo of equity factors. They apply the method to 51 factors described in past papers, yielding a total of 2.25 quadrillion factor models of U.S. stock returns. They test abilities of these factors and models to price 25 portfolios of stocks sorted by market capitalization (size) and book-to-market ratio (value) and 30 industry portfolios. Using returns for factors available monthly during January 1970 through December 2017 and for factors available only quarterly during first quarter 1952 through third quarter 2017, and contemporaneous test portfolio returns, they find that:
- Only the conventional value factor, the conventional market factor, and adjusted versions of the size and market factors (hedging out unpriced risk) robustly explain returns across test portfolios.
- A model comprised of these four factors is much more likely to be correct than widely accepted multi-factor models of stock returns, including:
- 3-factor (market, size, book-to-market)
- 4-factor (market, size, book-to-market, momentum)
- 5-factor (market size, book-to-market, profitability, investment)
- q-factor (market, size, asset growth, return on equity)
- 2-factor (market, liquidity)
- 3-factor (profitability, growth, safety)
- About 25 factors are needed to achieve very high confidence in pricing test portfolios.
In summary, evidence suggests that widely used factor models are far from the best in explaining variations in returns across different kinds of stocks.
Cautions regarding findings include:
- Analyses are gross, not net. Since different factor and test portfolios have different turnovers, and therefore different levels of implementation frictions, net findings may differ from gross findings.
- Construction of the adjusted market and size factors is beyond the reach of most investors, who would bear fees for delegating exploitation of their power to predict stock returns.
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