Multifactor Explanations of Asset Pricing Anomalies

Source: Fama, E. F. & French, K. R. (1996). Journal of Finance 51(1), 55–84.

TL;DR

Shows that the Fama–French three-factor model (market, SMB, HML) absorbs most of the well-known

CAPM anomalies: long-term reversal, and sorts on E/P, C/P, BE/ME, and past sales growth all line up with

loadings on size and value, leaving near-zero alphas. The glaring exception is short-term momentum

(Jegadeesh–Titman continuation), which the three-factor model cannot explain and which stays an open

anomaly.

What anomaly it documents

Predictor: the paper is a factor paper — it tests whether many separate characteristic-based

return patterns (size, BE/ME, E/P, C/P, 5-year sales growth, De Bondt–Thaler long-term reversal,

Jegadeesh–Titman momentum) are manifestations of the same value (HML) and size (SMB) exposures.

Direction / shape: value-type firms (high BE/ME, high E/P, high C/P, low sales growth, prior

long-term losers) load positively on HML and earn high average returns; growth-type firms load

negatively and earn low returns. The common HML/SMB loading is what generates the cross-section.

OSAP predictors: the constituent legs map to BM (value), Size, EP, CFP, and

MRreversal; momentum (Mom12m) is the leg the model fails to absorb.

How to construct it

Factors: at end-June each year, sort NYSE/AMEX/NASDAQ stocks on size (2 groups) × BE/ME (3

groups) → 6 value-weight portfolios. SMB = small-minus-big average return; HML =

high-minus-low BE/ME average return; RM = value-weight return on all stocks; market factor =

RM − R_f.

Test assets: decile and double-sort portfolios formed on E/P, C/P, BE/ME, and 5-year sales rank

(LSV-style), reformed annually (some reformed monthly for the momentum/reversal tests).

Model: Rᵢₜ − R_fₜ = αᵢ + bᵢ(RMₜ − R_fₜ) + sᵢSMBₜ + hᵢHMLₜ + εᵢₜ (eqns 1–2).

Evidence and replication

Anomaly leg	Three-factor verdict	Source
Long-term reversal (De Bondt–Thaler)	Explained — losers get + SMB/+ HML loadings, winners −	this paper
E/P, C/P, BE/ME, sales growth (LSV)	Explained — spreads track HML loadings, alphas ≈ 0	this paper
Short-term momentum (Jegadeesh–Titman)	Not explained — HML predicts reversal, leaving continuation as a large alpha	this paper
International / OOS	Size, BE/ME, E/P, C/P relations recur out of sample	this paper (§ on data-snooping)

Headline regression results are reported as near-zero intercepts for the explained sorts (specific

alphas/t-stats are in the original tables, not the exposition on disk).

The authors note SMB and HML behave like mimicking portfolios for unspecified ICAPM/APT state

variables, but the theory does not pin down what those state variables are.

Why it might work

Risk story: HML and SMB proxy for distress / state-variable risk in an ICAPM/APT sense — value and

small firms are riskier in bad states, so their premia are compensation, not mispricing.

Behavioral story: investors overextrapolate (LSV), pushing distressed "value" prices too low; the

three-factor model then mechanically captures the resulting spread without settling the cause.

Limitations and risks

Momentum is unexplained — the model's HML loading predicts the wrong sign, motivating Carhart's

(1997) fourth factor and richer models.

Data-snooping critique (Black 1993; MacKinlay 1995): size/BE/ME effects could be sample-specific;

the authors rebut with international/out-of-sample evidence.

A successful description of average returns is not an explanation: the risk-vs-mispricing debate

over the value premium remains unresolved.

Key references

Fama, E. & French, K. (1996) — Multifactor Explanations of Asset Pricing Anomalies — Journal of Finance

Fama, E. & French, K. (1993) — Common Risk Factors in the Returns on Stocks and Bonds — Journal of Financial Economics

Jegadeesh, N. & Titman, S. (1993) — Returns to Buying Winners and Selling Losers — Journal of Finance

De Bondt, W. & Thaler, R. (1985) — Does the Stock Market Overreact? — Journal of Finance

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

Provenance: summarized from secondary material (slides), not the original paper's full text — figures indicative.