This paper compares the Hou, Xue, and Zhang (2014) q-factor model and the Fama and French (2014a) five-factor model on both conceptual and empirical grounds. It raises four concerns with the motivation of the five-factor model: The internal rate of return often correlates negatively with the one-period-ahead expected return; the value factor seems redundant in the data; the expected investment tends to correlate positively with the one-period-ahead expected return; and past investment is a poor

more »

... proxy for the expected investment. Empirically, the four-factor q-model outperforms the five-factor model, especially in capturing price and earnings momentum. Hou, Xue, and Zhang (HXZ, 2014) construct an empirical q-factor model that largely describes the cross section of average stock returns. Most (but not all) of the anomalies that plague the Fama-French (1993 , 1996 three-factor model can be captured. The q-factor model says that the expected return of an asset in excess of the risk-free rate is described by the sensitivities of its returns to the market factor, a size factor, an investment factor, and a profitability (return on equity, ROE) factor: in which E[R i ] − R f is the expected excess return, E[MKT], E[r ME ], E[r I/A ], and E[r ROE ] are expected factor premiums, and β i MKT , β i ME , β i I/A , and β i ROE are the corresponding factor loadings. Subsequent to our work, Fama and French (FF, 2014a) incorporate variables that resemble our investment and ROE factors into their three-factor model to form a five-factor model. 1 Motivating their new factors from valuation theory, FF show that the five-factor model outperforms their orig- inal three-factor model in a set of testing portfolios formed on size, book-to-market, investment, and profitability (the same variables underlying their new factors). FF (2014b) extend their set of testing portfolios to include accruals, net share issues, momentum, volatility, and the market beta, which are a small subset of the comprehensive universe of nearly 80 anomalies in HXZ (2014). 2 We provide a direct comparison between the q-factor model and the FF five-factor model on both conceptual and empirical grounds. The q-factors are constructed from a triple (2 × 3 × 3) sort on size, investment-to-assets, and ROE, whereas the new FF RMW (robust-minus-weak profitabil-