5/1/2008-866–JFQA #43:2 Eun, Huang, and Lai Page 489
JOURNAL OF FINANCIAL AND QUANTITATIVE ANALYSIS Vol. 43, No. 2, June 2008, pp. 489–524
COPYRIGHT 2008, MICHAEL G. FOSTER SCHOOL OF BUSINESS, UNIVERSITY OF WASHINGTON, SEATTLE, WA 98195
International Diversification with Large- and
Small-Cap Stocks
Cheol S. Eun, Wei Huang, and Sandy Lai
∗
Abstract
To the extent that investors diversify internationally, large-cap stocks receive the dominant
share of fund allocation. Increasingly, however, returns to large-cap stocks or stock market
indices tend to comove, mitigating the benefits from international div ersification. In con-
trast, stocks of locally oriented, small companies do not exhibit the same tendency. In this
paper, we assess the potential of small-cap stocks as a vehicle for international portfolio
diversification during the period 1980–1999. We show that the extra gains from the aug-
mented diversification with small-cap funds are statistically significant for both in-sample
and out-of-sample periods and remain robust to the consideration of market frictions.
I. Introduction
Since the classic studies of Grubel (1968), Levy and Sarnat (1970), and
Solnik (1974), numerous papers have documented the gains from international
portfolio diversification. They show that the g ains from international diversifi-
cation stem mostly from the relatively low correlation a mong international secu-
rities when compared to domestic securities. Further, previous studies, for ex-
ample, Heston and Rouwenhorst (1994) and Griffin and Karolyi (1998), show
that industrial structure explains relatively little of the cross-country difference in
stock market volatility, and that the low international correlation is mostly due
to country-specific sources of return variation. Also, they show that the domi-
nance of country factors in international returns is robust to differing definitions
of industry classifications. Relatively low international corr e lations, tog ether with
the gradual liberalization of capital markets, are indeed responsible for the rising
volume of cross-border investments and the proliferation of international mutual
funds both in the U.S. and abroad.
∗
Eun, cheol.eun@mgt.gatech.edu, College of Management, Georgia Institute of Technology, At-
lanta, GA 30332; Huang, weih@hawaii.edu, Shidler College of Business, University of Hawaii at
Manoa, Honolulu, HI 96822; Lai, sandylai@smu.edu.sg, Lee Kong Chian School of Business, Singa-
pore Management University, Singapore 259756. We thank Stephen Brown (the editor) and Andrew
Karolyi (the referee) for providing many helpful comments that significantly improved the paper. We
also benefited from the useful comments of participants at the 2003 BSI Gamma Foundation Con-
ference, 2004 Western Finance Association Meeting, and 2006 China International Conference in
Finance.
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As international capital markets become more integrated, however, stock
market correlations have risen, diminishing the potential gains from international
diversification. Longin and Solnik (1995), for example, document that interna-
tional correlations among stock market indices have indeed increased over the
30-year period 1960–1990. Goetzmann, Li, and Rouwenhorst (2005) also show
that international correlations tend to be higher during periods of higher economic
and financial integration. Higher international correlations observed in recent
years clearly cast doubt on the strength and validity of the case for international
diversification argued by the classic studies.
1
To the extent that investors diversify internationally, large-cap stocks have
received the dominant share of overseas investments. This large-cap bias is un-
derstandable as investors n aturally gravitate toward well-known, large fo reign
companies that are highly visible and often multinational.
2
The large-cap bias
is also reinforced by the fact that the majority of cross-listed stocks, a popular ve-
hicle for international investment, are large-cap stocks.
3
As discussed by Foerster
and Karolyi (1999) and others, companies often use the cross-listings of shares
to enhan ce the level of investor recognition and expand the sharehold er base.
The large-cap bias is also broadly consistent with Huberman’s (2001) proposition
that familiarity breeds investment. In addition, those investors, especially institu-
tional investors who track national stock market indices, may also contribute to the
large-cap bias as the (value-weighted) market indices are dominated by large-cap
stocks.
4
Similarly, in documenting the gains from international diversification,
academic studies tend to use large-cap stocks or national stock market indices
dominated by the former. The potential role of small-cap stocks in international
diversification has received little attention in these studies.
As we show in this paper, the return-generating mechanisms for large- and
small-cap stocks are quite different. Specifically, returns on large-cap stocks are
substantially driven by common global factors. In contrast, returns on small-cap
stocks are primarily driven by local and idiosyncratic factors. This difference in
1
A fe w recent studies, for example, Cava glia, Brightman, and Aked (2000) and Baca, Garbe, and
Weiss (2000), suggest that the rising international correlations may be associated with the declining
importance of country factors relati ve to industry factors. This view, however, is not unanimously
held. Brooks and Del Negro (2004), for instance, argue that the rising importance of industry factors
relati ve to country factors does not reflect the ongoing financial integration, but rather a temporary
phenomenon associated with the recent stock market fluctuations. Although the relative importance
of country versus industry factors is an important, unsettled issue, we do not address this issue in our
paper. Rather, we focus on the merit of considering small-cap stocks in international diversification.
2
In their study of foreigners’ equity holdings in Japan, Kang and Stulz (1997) sho w that foreign
investors prefer large, export oriented, liquid, and U.S. cross-listed firms. Ferreira and Matos (2006)
also report that institutional investors strongly prefer large and liquid stocks with good governance
practices. In addition, institutional investors prefer those stocks that are cross-listed in the U.S. market
and members of the MSCI all-country world index.
3
At the end of 2003, for example, 40 of the French companies in our sample are traded as ADRs
in the U.S. Of these, 35 are from the top 20% largest companies in terms of market capitalization
and none is from the bottom 20%. Similarly, out of the 42 German companies with ADRs in our
sample, 35 are from the top 20% group and only one is from the bottom 20% group in terms of market
capitalization. In the case of Japan, 141 companies in our sample have ADRs, 127 of them are from
the top 20%, and none is from the bottom 20%.
4
In the case of MSCI market indices representing our 10 sample markets, large- (small-) cap stocks
from the top (bottom) 20% of the market capitalization account for 92.2% (0.2%) of the market value
of MSCI indices, on average, with mid-cap stocks accounting for the remaining 7.6%. As a result,
popular stock market indices, such as the MSCI indices, tend to be dominated by large-cap stocks.
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Eun, Huang, and Lai 491
the return-generating mechanism is understandable considering that many large-
cap stocks tend to be those of multinational companies with a substantial foreign
customer and investor base, whereas small-cap companies are likely to be m ore
locally oriented with a limited international exposure. As a result, the gains from
international diversification with large-cap stocks can be modest as their r eturns
are substantially driven by common global factors.
5
However, the same skepti-
cism may not be applicable to small-cap stocks as their returns are substantially
generated by local and idiosyncratic factors. Thus, small-cap stocks can poten-
tially be an effective vehicle for international diversification.
It is against this backdrop that investment companies in recent years have
introduced small-cap oriented international mutual funds, allowing investors to
diversify into foreign small-cap stocks without incurring excessive transaction
costs. Many investment companies such as Fid elity, ING, Lazard, Merrill Lynch,
Morgan Stanley, Oppenheimer, and Temp leton currently offer small-cap oriented
international mutual funds in the U.S. The recent advent of international small-
cap funds is thus highly instructive and also suggests the unique role that small-
cap stocks can play in global risk diversification.
6
Although there are currently
about 70 small-cap oriented international mutual funds in the U.S., little is known
about the potential o f small-cap stocks as a vehicle for international diversifica-
tion.
7
The current paper purports to fill this gap in the liter ature.
Specifically, the purpose of this paper is to assess the potential benefits from
international diversification with small- as well as large-cap stocks. We examine
the issue from the perspective of a U.S. (or dollar-based) investor who has diver-
sified internationally with MSCI country indices or large-cap stocks but desires to
augment her investment with small-cap funds from major foreign countries. Our
paper thus addresses the following question: Are there additional gains from inter-
national diversification with small-cap stocks? In this study, we consider 10 devel-
oped countries with relatively open capital markets—Australia, Canada, France,
Germany, Hong Kong, Italy, Japan, the Netherlands, the U.K., and the U.S. Our
sample comprises two countries from North America, three from Asia/Pacific, and
five from Europe. It is noted that international investors do not face formal barriers
to investing in stocks of these countries. For the sake of analytical tractability and
consistency with industry practices, we form three market capitalization-based
funds, i.e., large-, mid-, and small-cap funds, from each of our sample countries
and use the risk-return characteristics of cap-based funds computed over the 20-
year period 1980–1999. Our analysis in this paper comprises two parts. First,
we examine the different return-generating mechanisms for cap-based funds, the
5
A recent study by Brooks and Del Negro (2006) also shows that an increase in the interna-
tional component of a firm’s sales will increase (decrease) the exposure of the firm to global (country-
specific) shocks. This implies that multinational firms will be more susceptible to global shocks than
locally oriented firm s.
6
In terms of geographical cov e rage, some funds are global and international while others are re-
gional and national. Examples of the existing small-cap oriented international mutual funds include
Templeton Global Smaller Companies Fund, Merrill Lynch Global Small Cap Fund, Fidelity Inter-
national Small Cap Fund, Morgan Stanley International Small Cap Fund, AIM Europe Small Com-
pany Fund, FTI European Smaller Companies Fund, Fidelity Japan Smaller Companies Fund, DFA
Japanese Small Company Fund, and DFA United Kingdom Small Company Fund.
7
According to Morningstar, there are about 70 small-cap oriented international mutual funds in
the U.S. as of 2006.
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492 Journal of Financial and Quantitative Analysis
correlation structure of cap-based funds, and their implications for international
diversification. Second, we conduct the mean-variance analysis of international
portfolio investment with cap-based funds.
The key findings of our paper can be summarized as follows. First, our
mean-variance spanning tests show that international small-cap funds cannot be
spanned by country stock market indices. Small-cap fund returns are driven pri-
marily by local and idiosyncratic factors. As a result, small-cap funds have rela-
tively low correlations not only with large-cap funds but also with each other.In
contrast, large-cap funds tend to have relatively high correlations with each other,
reflecting their common exposure to global factors. During our sample period, for
instance, the correlation between the U.S. and the Netherlands large-cap funds is
0.61, whereas the correlation between small-cap funds from the two countries is
only 0.17. Further, the correlation b etween the U.S. large-cap and the Netherlands
small-cap funds is 0.21. This correlation structure suggests that large-cap funds
are relatively similar, but small-cap funds are distinct from each other. Our simu-
lations indeed show that a fully d iversified international large-cap stock portfolio
is about 9.2% as risky (measured by the portfolio variance) as a typical individual
stock, but a fully diversified international large- and small-cap stock portfolio can
further reduce the risk by about two-thirds. This result suggests that small-cap
stocks can play an effective and unique role in global risk diversification.
Second, to assess the potential mean-variance efficiency gains from diver-
sification with small-cap stocks, we solve fo r the optimal international po rtfolio
using the historical risk-return characteristics of cap-based funds during the pe-
riod 1980–1999. We consider the 10 MSCI country indices (proxies for large-cap
funds), small-cap funds, and mid-cap funds for portfolio holdings. Without short
sales for foreign stocks, a realistic restriction during much of our sample period,
the optimal (tangency) portfolio consists of i) the U.S. market index and ii) in-
ternational small-cap funds. It is noteworthy that neither foreign market indices
nor mid-cap funds receive a positive weight in the optimal international portfolio
during our sample period; neither does the U.S. small-cap fund. The optimal in-
ternational portfolio augmented with small-cap funds has a Sharpe performance
measure that is statistically significantly greater than that of the U.S. market in-
dex as well as that of the optimal portfolio only comprising MSCI country indices.
Our findings remain robust to a realistic range of additional costs for investing in
small-cap funds. Also, our findings remain robust so long as the accessibility of
small-cap stocks is not severely constrained. By contrast, the optimal interna-
tional portfolio only comprising MSCI country indices has a Sharpe measure that
is insignificantly different from that of the U.S. market index during our sample
period. Our key findings hold for in-sample as well as out-of-sample periods,
regardless of whether we consider conditioning information.
The rest of the paper is organized as follows. Section II describes the data,
fund design, and the risk-return characteristics o f cap-based funds. Section III
tests if small-cap funds can be spanned by country market indices or large-cap
funds, investigates the return-generating mechanism for market cap-based funds,
and assesses via simulations the capacity of small-cap stocks for global risk di-
versification. Section IV discusses optimal international allocation strategies with
small-cap funds and evaluates the gains from employing such strategies. Sec-
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Eun, Huang, and Lai 493
tion V provides robustness checks of our key findings. Lastly, Section VI offers
concluding remarks.
II. Data, Fund Design, and Preliminary Analysis
Our dataset includes monthly stock prices and returns, the number of shares
outstanding for exchange-listed companies, and MSCI stock market indices from
the 10 major countries during the period January 1980–December 1999. There is
a consensus among researchers that investors would not have faced major barri-
ers to international investments during this period in the 10 developed countries
we study. We obtain the firm level data from CRSP for U.S. firms and from
Datastream for international firms. We obtain MSCI stock market indices from
Datastream. In addition, we obtain the U.S. T-bill rate from CRSP and use it as a
proxy for the risk-free interest rate. Our sample includes all U.S. firms listed on
the NYSE, ASE, and Nasdaq and all foreign firms from each of the 10 countries
for which Datastream provides the necessary data during our sample period.
We exclude non-common stocks, such as preferred stocks, REITs, and closed-
end funds, from our sample. In addition, we exclude those firms that are incor-
porated outside their home countries and those that are indicated by Datastream
as duplicates. To filter out the recording errors embedded in Datastream, we treat
the monthly holding period returns greater than 400% as missing values. Datas-
tream maintains the historical data of delisted stock s in a separate inactive file.
We consolidate both active and inactive stock files to avoid a survivorship bias in
our data. In view of the practice that Datastream sets the return to a constant af-
ter a stock ceases trading, we accordingly change the constant value to a missing
value in the inactive file.
8
For the sake of both analytical tractability and consistency with industry
practices, we form three market cap-based funds (CBFs), i.e., large-, mid-, and
small-cap funds, from each of our sample countries. To form the CBFs, we rank
all our sample firms in each country based o n their market capitalization at the
end of each year. We then form a large-cap fund with the top 20% of the largest-
cap stocks, a small-cap fund with the bottom 20% of the smallest-cap stocks, and
a mid-cap fund with the rest of stocks in each country. Further, we use the rel-
ative market value for each stock to determine its weight in the fund. We thus
form three cap-based, value-weighted index funds from each country. We then
calculate the monthly (value-weighted) returns for each fund in terms of U.S. dol-
lars. Because there are three funds from each of the 10 countries, we generate
8
Ince and Porter (2006) also find data problems in the Datastream U.S. dataset similar to what
we find in our Datastream international dataset. Specifically, they compare the individual U.S. equity
return data obtained from Datastream with those obtained from CRSP. They find that Datastream
often mixes non-common stocks with common stocks, and firms incorporated inside the U.S. with
those outside the U.S. Furthermore, Datastream maintains a constant return index value for delisted
U.S. stocks e ven after they cease trading. Also, there are instances of data errors. They propose to
drop delisted stocks from the sample following their delisting and screen out the non-common stocks
and firms incorporated outside the U.S. when studying U.S. common equity returns. In addition, they
suggest using 300% as the threshold for monthly return data and set any return above the threshold
that is rev e rsed within one month to missing. However, they caution that the threshold they selected is
somewhat arbitrary and can be higher or lower in other markets. In general, our data screening process
is in spirit similar to what Ince and Porter propose in their paper.
