The authors found, importantly, that the investment and profitability factors are almost totally uncorrelated, meaning they are independent, or unique, factors. They also found the alphas of the value (high minus low (HML)) and momentum (up minus down) factors in the q-factor model are small and insignificant, their roles having been replaced by the investment and profitability factors.
Finally, the authors found that the q-factor model outperforms the Fama-French three-factor and four-factor models in its ability to explain the majority of anomalies. Most of the 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.”
Given the importance of the issue of data mining, the investment and profitability factors had t-stats of close to five—they’re highly significant. And while the t-stat of the size factor was lower at just more than 2, including it helps the q-factor model fit average returns across the size deciles.
Finally, the authors acknowledge that “the q-factor model is by no means perfect in capturing all the anomalies.” Like all models, even the q-factor model is “flawed.” But it does seem that this new model has advanced our understanding of how markets set prices.
Fama And French Examine The Q-Model
Professors Fama and French—in a November 2013 paper, “A Five-Factor Asset Pricing Model”—closely examined the q-factor model to determine whether its two new factors (investment and profitability) added explanatory power.
In other words, if Fama and French knew in 1993 what they know today, which model would they have chosen? The following is a summary of their findings: