As a result, the new four-factor model—beta, size, value and momentum—became the standard tool used to analyze and explain the performance of investment managers and investment strategies.
However, there still remained a number of anomalies that the four-factor model could not adequately explain.
The Latest Research
Kewei Hou, Chen Xue and Lu Zhang—the authors of the 2012 study, “Digesting Anomalies: An Investment Approach”—proposed yet another four-factor model, one that went a long way toward explaining many of the anomalies that neither the Fama-French three-factor, nor the Carhart four-factor, models could.
The authors called their model the q-factor model. Its 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 size factor earned an average return of 0.31 percent per month with a t-stat of 2.12.
- The difference between the return on a portfolio of low-investment stocks and the return on a portfolio of high-investment stocks. The authors write: “Intuitively, investment predicts returns because given expected cash flows, high costs of capital imply low net present values of new capital and low investment, and low costs of capital imply high present values of new capital and high investment.” They noted that the investment factor is highly correlated (0.69) with the value premium, suggesting that it plays a similar role to that of the value factor. The investment factor earned an average return of 0.45 percent per month with a t-stat of 4.95.
- The difference between the return on a portfolio of high return-on-equity (ROE) stocks and the return on a portfolio of low return-on-equity stocks. They write: “ROE predicts returns because high expected ROE relative to low investment must imply high discount rates. The high discount rates are necessary to offset the high expected ROE to induce low net present values of new capital and low investment.” The profitability factor earned an average return of 0.58 percent per month with a t-stat of 4.81. The authors noted that the profitability factor has a high correlation (0.50) with the momentum factor, and it plays a similar role as the momentum factor in analyzing performance.