There’s a substantial body of research demonstrating that measures of company proﬁtability and investment have explanatory power for the cross section of stock returns. High-proﬁt ﬁrms tend to outperform low-proﬁt ﬁrms, and high-investment ﬁrms tend to underperform low-investment ﬁrms.

For example, Kewei Hou, Chen Xue and Lu Zhang, authors of the 2015 paper “Digesting Anomalies: An Investment Approach,” proposed replacing the Fama-French three-factor (market beta, size and value) model with a new four-factor model that went a long way toward accounting for many of the anomalies that neither the Fama-French three-factor model nor the Carhart four-factor model (which added momentum as the fourth factor) could explain.

**Q-Factor Model**

In their model, which Hou, Xue and Zhang call the q-factor model, an asset’s expected return in excess of the riskless rate is described by the sensitivity of its return to the returns of four factors: market beta, size, investment (the difference between the return on a portfolio of low-investment stocks and the return on a portfolio of high-investment stocks) and profitability (the difference between the return on a portfolio of high return-on-equity stocks and the return on a portfolio of low return-on-equity stocks).

In an analysis of the q-factor model, Eugene Fama and Kenneth French (developers of the aforementioned three-factor model) agreed that a four-factor model that excludes the value factor (HML, or high minus low) captures average returns as well as any other four-factor model they considered, and that a five-factor model (including HML) doesn’t improve the description of average returns over that of the four-factor models. This occurs because the average HML return is captured by HML’s exposure to other factors. Thus, in the five-factor model, HML is redundant in explaining average returns.

However, Fama and French did note that “while the five-factor model doesn’t improve the description of average returns of the four-factor model that drops HML, the five-factor model may be a better choice in applications. For example, though captured by exposures to other factors, there is a large value premium in average returns that is often targeted by money managers.”

Thus, “in evaluating how investment performance relates to known premiums,” investors “probably want to know the tilts of the portfolios toward each of the factors.”

They add that, “for explaining average returns, nothing is lost in using a redundant factor.” Fama and French further found that the five-factor model performs well. They write: “Unexplained average returns for individual portfolios are almost all close to zero.”

**Q Factors & Bonds**

Benedikt Franke, Sebastian Muller and Sonja Muller contribute to the literature on the profitability and investment factors with their study “The Q-Factors and Expected Bond Returns,” published in the October 2017 issue of the Journal of Banking & Finance. They used a sample of U.S. corporate bonds from 1995 to 2011 to examine how exposure to the q-factors is priced by corporate bond investors.

Corporate bonds are an important segment of ﬁnancial markets with outstanding assets of more than $8 trillion. In addition, the corporate bond market is dominated by institutional investors who are likely to be more sophisticated than individuals. And, most importantly, the bond market allowed the authors to offer new insight into the debate on whether factor premiums are risk-based or behavioral-based.