The q-factor model, proposed by Hou, Xue, and Zhang (2015), is a four-factor asset pricing model grounded in investment-based (production-side) asset pricing theory. It is the primary competitor to the Fama-French five-factor model.
Model specification
The four factors:
- MKT: market excess return
- r_ME: size factor (small minus big)
- r_I/A: investment factor (low investment-to-assets minus high)
- r_ROE: profitability factor (high ROE minus low ROE)
Factors constructed from triple 2x3x3 sorts on size, investment-to-assets, and ROE. Sample period 1972-2012: size 0.31%/mo (t=2.12), investment 0.45%/mo (t=4.95), ROE 0.58%/mo (t=4.81).
Theoretical foundation
From a two-period q-theory model, the stock return equals profitability divided by the marginal cost of investment:
This yields two channels:
- Investment channel: given expected profitability, high investment implies low expected returns (low discount rates justify high NPV projects). Explains value, asset growth, net issuance, accruals, and long-term reversal anomalies.
- Profitability channel: given investment, high expected profitability implies high expected returns (high discount rates are needed to offset high profitability and keep investment low). Explains momentum, post-earnings-announcement drift, and financial distress effects.
Performance vs. Fama-French and Carhart
Across 35 significant anomalies (from ~80 tested):
- q-factor model: average |alpha| = 0.20%/mo, 5 significant alphas, GRS rejected in 20/35
- Carhart 4-factor: average |alpha| = 0.33%/mo, 19 significant alphas, GRS rejected in 24/35
- FF 3-factor: average |alpha| = 0.55%/mo, 27 significant alphas, GRS rejected in 28/35
The q-factor model particularly outperforms on momentum: price momentum high-minus-low has a q-alpha of 0.24%/mo (t=0.71) vs. Fama-French alpha of 1.12%/mo (t=4.47). HML and UMD alphas are small and insignificant in the q-factor model, suggesting they are “noisy versions” of the q-factors.
Relationship to Fama-French five-factor model
The investment factor (r_I/A) correlates 0.69 with HML, and the ROE factor correlates 0.50 with UMD. The q-factor model and FF5 share investment and profitability as core factors but differ in:
- Construction: q uses ROE (quarterly, timely); FF5 uses operating profitability (annual)
- Theoretical basis: q derives from production-side first principles; FF5 is motivated by dividend discount model decomposition
- Momentum: q-model captures momentum through the ROE factor; FF5 explicitly omits momentum
The q-factor model was circulated (NBER WP 18435, October 2012) before the FF5 paper, and the authors note that FF subsequently incorporated similar factors.
Subsequent development: q5
Hou, Mo, Xue, and Zhang (2021) extended the model to q5, adding an expected growth factor. This further improves performance on anomalies related to expected earnings growth.