For about three decades, the working asset pricing model was the capital asset pricing model (CAPM), with beta—specifically market beta—being its sole factor. Then, in 1993, the Fama-French three-factor model—which added size and value—replaced the CAPM as the workhorse model.
By eliminating two major anomalies (the outperformance of small stocks and of value stocks), it improved the model’s explanatory power from about two-thirds of the differences in returns of diversified portfolios to more than 90%. Thus, it was a major advance.
In 1997, momentum was added as a fourth factor. It too improved the explanatory power of the asset pricing model by eliminating another large anomaly. The next major advance came from Robert Novy-Marx in 2012.
In his paper, “The Other Side of Value: The Gross Profitability Premium,” he proposed a fifth factor, which also improved the model’s explanatory power while eliminating another important anomaly—the outperformance of stocks with higher profitability.
Since then, what might be called the “battle of the factor models” has occurred, with parsimony considered a major virtue—the fewer factors needed, the better. Kewei Hou, Chen Xue and Lu Zhang—authors of the October 2012 study, “Digesting Anomalies: An Investment Approach”—proposed a new four-factor model, the q-factor model. It included market beta, size, investment and profitability, and went a long way to explaining many anomalies.
In 2015, Eugene Fama and Kenneth French proposed a new five-factor model, using their original three factors and adding somewhat different definitions of investment and profitability.
Robert Stambaugh and Yu Yuan, authors of the January 2016 paper “Mispricing Factors,” add to the literature by proposing another four-factor model that includes two “mispricing” factors in addition to the factors of market beta and size. The authors note: “Factor models can be useful whether expected returns reflect risk or mispricing.”
By incorporating these mispricing factors, they are better able to accommodate 11 well-known anomalies. These anomalies, which represent violations of the Fama-French three-factor model, are: