Chicago Booth’s Eugene F. Fama and Dartmouth’s Kenneth R. French pioneered the use of factors to explain 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 equities returns. (See “The 300 secrets to high stock returns,” Summer 2018.)
But what’s the best way to analyze factors and to determine whether these five—or others—really do explain returns? Researchers use myriad statistical methods, but Fama and French argue in favor of expanding on an earlier approach of describing returns across stocks, which they say could improve upon a widely used method that Fama helped develop.
Fama and French published their three-factor model in 1993, arguing that beta, size, and value can be used to explain stock returns. In 2015, they added profitability and investment as factors. To analyze the factor models, they relied largely on cross-section regressions that were pioneered in 1973 by Fama and James D. MacBeth.
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
Regressions are a statistical method used to isolate and determine the importance of a variable. Say you know of a couple measurable attributes of a stock—such as leverage and industry performance—that could be driving the stock’s returns. A regression functions like a test that helps determine if one of these attributes, which can be related to a factor, does indeed explain the returns. A cross-section regression can help explain differences between the returns of two stocks at a single point in time.
Fama and MacBeth’s influential cross-section regressions are used by many researchers in asset pricing. Fama and French used these regressions in their three- and five-factor models to identify time-series factors, or risk factors that drive returns over time.
Cross-section factors and models explain returns across stocks at a single point in time, time-series factors and models explain returns over time. Fama and French have traditionally used time-series factors and models—but now advocate using cross-section factors in time-series models.
“We contend that this perspective on [Fama-MacBeth] regressions can enhance the way they are viewed and applied,” write Fama and French.
The researchers follow the steps they lay out, plugging the results into their famous factor equations to produce five cross-section factors. They compare these cross-section factors to the five time-series factors they’d identified previously, as well as momentum, a kind of unofficial sixth factor for Fama and French. They find that when their models use the cross-section factors instead of the time-series ones, the cross-section ones do a better job of explaining returns.
The researchers’ work suggests there may be still only a few factors, not dozens, that explain stock returns. However, by revisiting and modifying well-established methods of analysis, Fama and French are tweaking the five factors they say best explain stock market changes.