In their groundbreaking paper, “Digesting Anomalies: An Investment Approach,” Kewei Hou, Chen Xue and Lu Zhang proposed a new four-factor asset pricing model that goes a long way toward explaining many of the anomalies neither the Fama-French three-factor nor subsequent four-factor models could explain.
The study, which was published in the March 2015 issue of The Review of Financial Studies, covered the period 1972 through 2012.
The authors called their model the q-factor model. Specifically, their four factors are:
- The market excess return (beta)
- The difference between the return on a portfolio of small-cap stocks and the return on a portfolio of large-cap stocks
- The difference between the return on a portfolio of low-investment stocks and the return on a portfolio of high-investment stocks
- The difference between the return on a portfolio of high return-on-equity (ROE) stocks and the return on a portfolio of low ROE stocks
Profitability Predicts Stock Returns
In their study, Hou, Xue and Zhang provided the theoretical underpinnings for the investment and profitability factors. They write: “Intuitively, investment predicts stock returns because given expected cash flows, high costs of capital mean low net present values of new projects and low investment, and low costs of capital mean high net present values of new projects and high investment. Profitability predicts stock returns because high expected cash flows relative to low investment must mean high discount rates. The high discount rates are necessary to offset the high expected cash flows to induce low net present values of new projects and low investment.”
Among their important findings was that the investment and profitability (ROE) factors are almost totally uncorrelated, meaning they are independent, or unique. In addition, the authors found that the alphas of the value (HML) and momentum (UMD) factors in the q-factor model are small and insignificant.
These two factors, and the role they play, have been replaced by the investment and ROE factors. They also found that the q-factor model outperforms the Fama-French three-factor and four-factor models in its ability to explain most anomalies. In fact, most anomalies become insignificant at the 5 percent level of statistical significance. In other words, “many anomalies are basically different manifestations of the investment and ROE effects.”
Not A Perfect Model
The authors did acknowledge, however, that “the q-factor model is by no means perfect in capturing all the anomalies.” As with all models, even the q-factor model is flawed, or wrong. If a model were perfect, it would be called a law (like we have in physics).
But the fact that models are flawed doesn’t mean they’re absent of value. Think about it this way: Financial models aren’t cameras that provide us with a perfect picture of the way financial markets work; they are engines that advance our understanding of how markets operate and how prices are set.
And it certainly does seem that this new model has advanced our understanding of how markets set prices.
Fama & French Examine The Q-Model
Professors Eugene Fama and Kenneth French—in their paper, “A Five-Factor Asset Pricing Model,” which appears in the April 2015 issue of The Journal of Financial Economics—took a close look at a new five-factor model.
Their objective was to determine whether two new factors—profitability (RMW, or robust-minus-weak profitability) and investment (CMA, or conservative-minus-aggressive investment)—added explanatory power. In other words, if Fama and French knew in 1993 (when they constructed their original three-factor model) what they know today, which model would they have chosen? Following is a summary of their findings: