Better Five-factor Model of Stock Returns?

Which factor models of stock returns are currently best? In their June 2018 paper entitled “q⁵“,  Kewei Hou, Haitao Mo, Chen Xue and Lu Zhang, introduce the q⁵ model of stock returns, which adds a fifth factor (expected growth) to the previously developed q-factor model (market, size, asset growth, return on equity). They measure expected growth as 1-year, 2-year and 3-year ahead changes in investment-to-assets (this year total assets minus last year total assets, divided by last year total assets) as forecasted monthly via predictive regressions. They define an expected growth factor as average value-weighted returns for top 30% 1-year expected growth minus bottom 30% 1-year expected growth, calculated separately and further averaged for big and small stocks. They examine expected growth as a standalone factor and then conduct an empirical horse race of recently proposed 4-factor, 5-factor (including q⁵) and 6-factor models of stock returns based on their abilities to explain average return differences for value-weighted extreme tenth (decile) portfolios for 158 significant anomalies. Using monthly return and accounting data for a broad sample of non-financial U.S. common stocks during July 1963–December 2016, they find that:

• Over the full sample period, a portfolio that is each month long (short) the value-weighted decile of stocks with the highest (lowest) expected growth for the next one, two and three years generates average gross monthly returns 1.06%, 1.18% and 1.18%, respectively.
• The expected growth factor, as defined, earns 0.82% average gross monthly premium, translating to 0.63% monthly gross alpha relative to the old q-factor model. In other words, the information from the expected growth factor is largely new to the old model.
• The q⁵ model, incorporating the expected growth factor, is the best performing model with respect to explaining the test set of 158 anomalies. Specifically:
  • Average monthly gross alpha relative to the q⁵ model for these anomalies is just 0.18%.
  • Only 19 of the anomalies remain statistically significant relative to the q⁵ model (compared to 46 for the old q model), with improvements across all anomaly categories, including momentum, value, investment, profitability, intangibles and trading frictions, and especially investment and profitability.

In summary, evidence indicates that regression-based forecasts of firm asset growth may be a useful and unique predictor of U.S. stock returns.

Such factor model findings may inform investor choices of firm/return characteristics for stock screening. 

Cautions regarding findings include:

• As noted, return and alpha measurements are gross, not net. Accounting for monthly portfolio reformation frictions and shorting costs would reduce returns. Shorting may be problematic for some specified stocks due to lack of shares to borrow.
• Testing of an ever-growing number of potential factors and factor combinations on the same data elevates the role of luck (data snooping bias), such that the best-performing factor models overstate explanatory power. For additional perspective, see “Taming the Factor Zoo?”.
• Expected growth measurement and portfolio implementation are beyond the reach of many investors, who would bear fees for delegating to a fund manager.