Digesting Anomalies: An Investment Approach

Source: Hou, K., Xue, C. & Zhang, L. (2015) · Review of Financial Studies 28(3), 650–705 · DOI: 10.1093/rfs/hhu068

TL;DR

Proposes the q-factor model — market, size (rME), investment (rI/A), and profitability/ROE (rROE) — motivated by the neoclassical q-theory of investment. Across nearly 80 anomalies (about half of which are insignificant in the broad cross-section), the four-factor model's performance is at least comparable to, and often better than, the Fama-French (1993) 3-factor and Carhart (1997) 4-factor models. It frames the cross-section through firms' real investment and expected-profitability decisions rather than risk factors per se.

The question

The Fama-French 3-factor model fails to price a wide array of anomalies (momentum, profitability, net issues, distress, earnings surprises). Can a small, theory-grounded set of factors derived from the firm's investment first-order conditions instead summarize the cross-section of average returns?

The model

The expected excess return is described by sensitivities to four factors:

E[rᵢ]−r_f = β_MKT·E[MKT] + β_ME·E[rME] + β_I/A·E[rI/A] + β_ROE·E[rROE] (eq. 1)

Economic logic from investment-based pricing: the investment Euler equation implies that, holding expected profitability fixed, firms that invest more have lower expected returns (the discount rate is in the denominator of the NPV rule), and holding investment fixed, firms with higher expected profitability have higher expected returns. Factors are built from a triple 2×3×3 sort on size, investment-to-assets (I/A), and ROE; ROE uses the most recent quarterly earnings, giving it monthly rebalancing that helps capture momentum.

Key predictions

A negative investment–return relation and a positive profitability–return relation, jointly pricing the cross-section.

Value (HML) and momentum (UMD) are "noisy versions" of the q-factors: their q-alphas should be small.

Empirical status

Factor premiums, Jan 1972–Dec 2012: size 0.31%/mo (t=2.12), investment rI/A 0.45% (t=4.95), ROE rROE 0.58% (t=4.81).

Correlations: rI/A correlates 0.69 with HML; rROE correlates 0.50 with UMD. In the q-model, HML and UMD alphas are small/insignificant, but rI/A and rROE retain large significant alphas in the Carhart model.

Anomalies: of ~80 variables, about one-half are insignificant in the broad cross-section; for high-minus-low deciles the average alpha magnitude is 0.20%/mo in the q-model, passing the GRS test in 20 of the decile sets.

Momentum: price-momentum decile has a Fama-French alpha of 1.12%/mo (t=4.47) but a q-alpha of 0.24% (t=0.71); earnings-momentum FF alpha 0.55% vs q-alpha 0.16% (t=1.12) — both subsumed.

Limitations

The FF5-vs-q "winner" depends on factor construction (annual double-sort HML vs monthly ROE; triple sort); the debate is unresolved.

ROE's monthly construction blurs the line between a risk factor and a momentum-capturing characteristic.

Like all factor models, exposed to multiple-testing and replication critiques (addressed in the authors' 2020 "Replicating Anomalies").

Key references

Fama, E. & French, K. (2015) — A Five-Factor Asset Pricing Model — Journal of Financial Economics

Hou, K., Xue, C. & Zhang, L. (2020) — Replicating Anomalies — Review of Financial Studies

Carhart, M. (1997) — On Persistence in Mutual Fund Performance — Journal of Finance

Provenance: verified/generated from the paper's full text.