Chicago Booth’s Eugene F. Fama and Dartmouth’s Kenneth R. French pioneered the use of factors to explain average excess returns of stocks and other assets, and they have long maintained that stocks have only a few common sources of risk. Fama and French first proposed three and have since allowed for five, with the occasional appearance of a sixth factor—even as other researchers have investigated hundreds of potential factors affecting equity returns. (See “The 300 secrets to high stock returns,” Summer 2018.) In introducing their three-factor model, in 1993, Fama and French argued that market beta, size, and value can be used to explain average excess stock returns. In 2015, they added profitability and investment factors.

But what’s the best way to analyze factors and to determine whether these five—or others—really do explain average returns? Researchers use myriad statistical methods, but in a 2018 paper, Fama and French fix a problem embedded in previous factor models. And their innovation is likely to transform how academics and the investment industry work with factors.

Their new approach builds on the cross-section regressions that were pioneered in 1973 by Fama and James D. MacBeth. A regression is a statistical method used to isolate and establish the importance of a variable, functioning like a test that helps determine if an attribute such as leverage or industry performance could be helping to drive a stock’s average returns.

### The five factors driving returns

Market risk (beta): The riskiness of a stock compared with that of its benchmark. Stocks with less market risk have tended to outperform over time.

Size: The market capitalization of a stock. Small-cap stocks have tended to outperform large-cap ones.

Value: The measurement of a stock by its price-to-book ratio or other ratios.

Profitability: The operating profitability of a stock’s underlying company. Stocks of profitable companies tend to perform better.

Investment: The total asset growth of a stock’s underlying company. Stocks of companies with growing assets do worse.

*Momentum: The tendency of stocks that have outperformed in the past to post strong ongoing returns.

*Unofficial sixth factor, per Fama and French

A cross-section regression can explain the average impact of a variable on the returns of two or more stocks at a single point in time. Fama and MacBeth developed influential cross-section regressions that are still used by many researchers in asset pricing. Fama and French used these regressions in their three- and five-factor models to ascertain the importance of time-series factors, or risk factors that drive returns over time.

The problem Fama and French sought to solve was that previous factor models have an assumption baked in, that a factor’s contribution to explaining a security’s average excess returns is constant over time. To calculate a security’s monthly excess returns using a traditional factor model, for each month, you multiply each factor’s monthly return by a constant value, known as a constant slope, and then sum these values. However, over time, the contributions of each factor (the slopes) are likely to fluctuate, making constant slopes a crude approximation. For example, during the 2008–09 financial crisis, all stocks tended to move with the plunging market, changing the impact of the individual factors. Fama and French point out that, since a 1991 paper by University of Southern California’s Wayne Ferson and Duke University’s Campbell Harvey, people have known that slopes are likely to vary through time.

Many academics, understanding that they were missing something in their explanations of average returns, have sought to add or refine the factors used in factor models. Fama and French instead refined the model by taking on the long-known problem of constant slopes and developing a way to allow for more-realistic, time-varying slopes. Using the Fama-MacBeth cross-section regressions in a new way, Fama and French created an asset-pricing model that does a substantially better job of explaining average returns than do the traditional factor models or more recent variations, all of which use constant slopes.

The researchers’ work strongly suggests there may still be only a few factors, not dozens, that explain average stock returns. And by solving a longstanding, problematic assumption in the way people have been analyzing and using factors, Fama and French have paved the way for a change in how academics and market participants use and apply factors.