Size, value, and momentum in international stock returns

Abstract

In the four regions (North America, Europe, Japan, and Asia Pacific) we examine, there are value premiums in average stock returns that, except for Japan, decrease with size. Except for Japan, there is return momentum everywhere, and spreads in average momentum returns also decrease from smaller to bigger stocks. We test whether empirical asset pricing models capture the value and momentum patterns in international average returns and whether asset pricing seems to be integrated across the four regions. Integrated pricing across regions does not get strong support in our tests. For three regions (North America, Europe, and Japan), local models that use local explanatory returns provide passable descriptions of local average returns for portfolios formed on size and value versus growth. Even local models are less successful in tests on portfolios formed on size and momentum.

Introduction

Banz (1981) finds that stocks with lower market capitalization (small stocks) tend to have higher average returns. There is also evidence that value stocks, that is, stocks with high ratios of a fundamental like book value or cash flow to price, have higher average returns than growth stocks, which have low ratios of fundamentals to price (DeBondt and Thaler, 1985, Fama and French, 1992, Lakonishok et al., 1994). Jegadeesh and Titman (1993) show that U.S. stock returns also exhibit momentum: stocks that have done well over the past year tend to continue to do well. The value premium (higher average returns of value stocks relative to growth stocks) and momentum are also observed in international returns (Chan et al., 1991, Fama and French, 1998, Rouwenhorst, 1998, Griffin et al., 2003, Asness et al., 2009, Chui et al., 2010).

Fama and French (1993) propose a three-factor model to capture the patterns in U.S. average returns associated with size and value versus growth:

$$R_i(t)–RF(t)=a_i+b_i[RM(t)–RF(t)]+s_{i}SMB(t)+h_{i}HML(t)+e_i(t).$$

In this regression, R_i(t) is the return on asset i for month t, RF(t) is the riskfree rate, RM(t) is the market return, SMB(t) is the difference between the returns on diversified portfolios of small stocks and big stocks, and HML(t) is the difference between the returns on diversified portfolios of high book-to-market (value) stocks and low book-to-market (growth) stocks. In an attempt to also capture momentum returns, Carhart (1997) proposes a four-factor model for U.S. returns:

$$R_i(t)–RF(t)=a_i+b_i[RM(t)–RF(t)]+s_{i}SMB(t)+h_{i}HML(t)+w_{i}WML(t)+e_i(t),$$

which is (1) enhanced with a momentum return, WML(t), the difference between the month t returns on diversified portfolios of the winners and losers of the past year.

Regressions (1) and (2) are commonly used in applications, most notably to evaluate portfolio performance (Carhart, 1997, Kosowski et al., 2006, Fama and French, 2010). In the initial paper on the three-factor model, however, Fama and French (1993) find that, although it captures the size and value patterns in post-1962 U.S. average returns better than the capital asset pricing model (CAPM), the model's explanation of average returns is far from complete. Avramov and Chordia (2006) likewise find that the four-factor model fails to absorb all the momentum in U.S. average stock returns.

This paper examines international stock returns, with two goals. The first is to detail the size, value, and momentum patterns in average returns for developed markets. Our main contribution is evidence for size groups. Most prior work on international returns focuses on large stocks. Our sample covers all size groups, and tiny stocks (microcaps) produce challenging results. Our second goal is to examine how well (1) and (2) capture average returns for portfolios formed on size and value or size and momentum. We examine local versions of the models in which the explanatory returns (factors) and the returns to be explained are from the same region. For perspective on whether asset pricing is integrated across regions, we also examine models that use global factors to explain global and regional returns.

There is a literature on integrated international asset pricing, ably reviewed by Karolyi and Stulz (2003). The papers closest to ours are Griffin (2002) and Hou, Karolyi, and Kho (2011). We add to their work. For example, Griffin (2002) examines whether country-specific or aggregate versions of (1) better explain returns on portfolios and individual stocks in four countries, the U.S., the U.K., Canada, and Japan. We use 23 countries. Hou, Karolyi, and Kho (2011) do not examine how value premiums and momentum returns differ across size groups and whether the size patterns in average value premiums and momentum returns are captured by local and international asset pricing models—our main tasks.

Section 2 discusses the motivation for the tests. Section 3 describes the data and variables. Section 4 presents summary statistics for returns. 5 Asset pricing tests for size-B/M portfolios, 6 Asset pricing tests for size-momentum portfolios turn to tests of asset pricing models. Section 7 discusses robustness tests. A summary and conclusions are in Section 8.