Why explaining stock returns remains so complex

Michael Maiello | Mar 23, 2018

Sections Finance

In the academic literature on predicting asset values, researchers have proposed hundreds of factors to explain an individual stock’s return.

Some researchers argue in favor of reducing the number of factors to a handful, the economic equivalent of searching for elementary particles in physics. But on the physics side, things did not get simpler as they got smaller, and they might not in finance either, suggest University of Michigan’s Serhiy Kozak, Chicago Booth’s Stefan Nagel, and University of Maryland’s Shrihari Santosh, who argue that the quest for simplification, while well-meaning, may be misguided.

“Our results suggest that the empirical asset-pricing literature’s multi-decade quest for a sparse characteristics-based factor model (e.g., with 3, 4, or 5 characteristics-based factors) is ultimately futile,” the researchers write.

Kozak, Nagel, and Santosh constructed a stochastic-discount-factor model, which pins down the factors that allow investors to earn a return premium—to analyze the predictive power of a large number of stock-return models. Factors in these models are attributes of companies or stocks that help explain a security’s performance. Size as a factor, for example, tells us that companies with small market capitalizations outperform large-cap companies. Stocks with low price-to-book ratios outperform stocks with high ratios, and so forth.

The five-factor model proposed in 2016 by Dartmouth’s Kenneth R. French and Chicago Booth’s Eugene F. Fama represents such a stochastic-discount-factor model, focusing on size, value, profitability, investment patterns, and market risk. But Kozak, Nagel, and Santosh argue that there is not enough redundancy to whittle things down to a handful of predictive factors.

The term “redundancy” has to do with factors that have different names but the same explanatory power. For example, a researcher might propose an “emerging markets factor” that shows stocks in emerging markets outperform those in developed markets. But the same effect might be better explained by the size factor, as emerging-markets companies tend to have lower market capitalizations than those in developed markets.

They test this and find that models based on a limited number of factors, including Fama-French from 2016, are not able to fully explain equity returns between 2005 and 2016. There must be something more at work, they suggest.

“Sparsity is elusive,” the researchers write. A model must include many factors to be complete. While they say they believe there is some redundancy out there within the world of factors, they suggest that models based on a half dozen or fewer factors will never fully explain stock returns. Complexity, they might say, is the most resilient factor of them all.