Size, Value, and Momentum in International Stock Returns
Source: Fama, E. F. & French, K. R. (2012). Journal of Financial Economics 105(3), 457–472. DOI: 10.1016/j.jfineco.2012.05.011
TL;DR
Documents size, value (book-to-market), and momentum patterns in average returns across four developed-market regions — North America, Europe, Japan, and Asia Pacific (23 countries) — over November 1990–March 2011 ("1991–2010"). Value premiums exist in all four regions and, except in Japan, decrease with size (are larger for small stocks); momentum is strong everywhere except Japan, also larger for small stocks. Tests of whether asset pricing is integrated across regions find weak support: local (regional) factor models describe local returns better than global models, and even local four-factor models struggle on size-momentum portfolios.
What anomaly it documents
Predictor(s): market capitalization (size), book-to-market (value), and prior-year return (momentum).
Direction: small > big (size); high B/M (value) > low B/M (growth); past winners > losers (momentum).
Shape: value and momentum premiums are both monotonically larger for smaller stocks (interaction with size) in all regions except Japan, where value is roughly flat across size and momentum is essentially zero.
This is an international-robustness study of established U.S. anomalies, extended to small-cap stocks across many markets.
How to construct it
For each region, sort stocks into size × value and size × momentum portfolios and build factor returns: SMB (small minus big), HML (high minus low B/M), and WML (winners minus losers, prior 2–12 month return), plus the market premium RM−RF.
Estimate the Fama–French three-factor model (1) and the Carhart four-factor model (2), Ri−RF = a + b(RM−RF) + s·SMB + h·HML + w·WML + e, using local regional explanatory returns vs. global factors.
Data from Bloomberg/Datastream/Worldscope; sample assembled with Dimensional Fund Advisors.
Evidence and replication (IS/OOS)
Equity premiums (1991–2010) range from 0.56%/mo (Europe) to 0.86%/mo (Asia Pacific); Japan is negative at −0.12%/mo.
Global HML = 0.45%/mo (t = 2.85); the value premium is larger for small stocks 0.66% (t = 3.78) than big stocks 0.24% (t = 1.36), difference 0.42% (2.76 SE). Japan is the exception: similar for small 0.47% (t = 2.38) and big 0.50% (t = 2.02).
Global WML = 0.62%/mo (t = 2.30), with 0.82% (t = 3.14) for small vs. 0.41% (t = 1.38) for big stocks. Regional WML ranges from 0.64% (t = 1.91, North America) to 0.92% (t = 3.38, Europe); Japan's WML is near zero.
Integrated (global) pricing is not strongly supported; local models give "passable" descriptions of size-value portfolios for North America, Europe, and Japan, but are less successful on size-momentum portfolios.
Why it might work
Common risk and/or behavioral drivers of value and momentum span developed markets, but segmented pricing means regional factors capture local risks/sentiment better than global ones.
Japan's missing momentum is a long-standing puzzle; the authors are skeptical of the individualism-culture explanation (Chui–Titman–Wei) and note a Hotelling T² test fails to reject equal expected WML across regions at the 90% level — so chance is a serious contender.
Limitations and risks
Short sample (~20 years) reduces statistical power, especially for integration tests and Japan.
Implementation costs, currency effects, and data quality vary across regions; results are sensitive to the test assets and sample period.
Even the best (local four-factor) models leave substantial unexplained variation in size-momentum portfolios.
Key references
Fama, E. & French, K. (2012) — Size, Value, and Momentum in International Stock Returns — Journal of Financial Economics
Fama, E. & French, K. (1993) — Common Risk Factors in the Returns on Stocks and Bonds — JFE (three-factor model)
Carhart, M. (1997) — On Persistence in Mutual Fund Performance — Journal of Finance (four-factor model)
Asness, C., Moskowitz, T. & Pedersen, L. (2013) — Value and Momentum Everywhere — Journal of Finance
Provenance: verified/generated from the paper's full text.
