NEW EVIDENCE ON MARKET
DEBRA A. CLASSMAN and LEIGH A. RIDDICK
This paper examines the mean-variance optimality of international portfolio allocations using both a less restrictive model of international investor behavior and more detailed data than have been used in previous empirical studies. The estimated optimal portfolios are compared to point estimates of the actual holdings of U.S. pension funds and mutual funds. There is a substantial divergence between actual and predicted holdings, which we attribute to the presence of international market segmentation. The comparison of predicted and actual portfolios enables us to estimate the degree of market segmentation and to determine that it is caused by more than simple transaction costs.
A variety of empirical studies have failed to support the mean-variance paradigm as a
description of international portfolio behavior. Three kinds of explanations have been
proposed for these results. Some researchers suggest that investors may fail to exploit
Direct all correspondence to: Leigh A. Riddick, Department of Finance & Real Estate, Kogod College of Business Administration, The American University, Washington, DC 20016; Debra A. Glassman, School of Business Administration, University of Washington, DJ-10, Seattle, WA 98195.
International Review of Economics and Finance, 3(l): 73-92 Copyright 0 1994 by JAI Press, Inc. ISSN: 1059-0560 All rights of remoduction in anv form reserved.
74 DEBRA A. GLASSMAN and LEIGH A. RIDDICK
profitable investment opportunities (e.g., Frankel and Engel, 1984; Levy and Lerman, 1988).
Others interpret the results as evidence of international capital market segmentation (e.g.,
Solnik, 1974b; Grauer and Hakansson, 1987). The third possible explanation, recognized by
all authors, is that all tests are joint tests of the hypothesis of mean-variance optimization
and a particular model specification.
This papers starting point is the observation that virtually all tests of international
mean-variance optimization-and extensions of those tests for market segmentation-have
been based on simplified versions of the portfolio choice model. The simplifications, such
as assuming purchasing power parity, facilitate aggregation of asset demands across coun-
tries. This aggregation is necessary for the derivation of tractable international asset pricing
solutions, such as the International Capital Asset Pricing Model (ICAPM).
It has been shown (Glassman and Riddick 1994) that the simplifying restrictions have the
potential to systematically alter the estimates of portfolio shares. Thus, it is reasonable to
ask whether the conclusions regarding mean-variance optimality and market segmentation
are dependent upon the model restrictions that have been used. To address that issue, we
estimate a mean-variance model of international portfolio choice that does not impose the
widely-used simplifying assumptions. This unrestricted mean-variance model is estimated
with two different proxies for expected returns- historical mean returns and Bayes-Stein
estimates of mean returns.
Since, the unrestricted mean-variance model does not generate a tractable asset pricing
expression for use in comparisons, we instead compare the optimal portfolio weights to
actual portfolio weights. Prior papers have been unable to make such comparisons
because of the lack of country-specific data on actual portfolio holdings. To overcome
that obstacle, we introduce data on the international portfolio holdings of U.S. institu-
tional investors which are disaggregated by country. We have only a point estimate, so
formal hypothesis tests are not possible. However, the simple comparison of actual and
predicted weights reveals a wide divergence between them, a finding that is consistent
with market segmentation.
We next provide quantitative measures of the degree of international market segmentation
by deriving the expected asset returns that would be consistent with the actual portfolio
holdings. These implied returns are considerably lower than the conventional proxies for
expected returns, and, thus, they suggest that transaction costs alone cannot explain interna-
tional investment patterns. We conclude that other forms of international market segmenta-
tion must be present. In the next section we outline the general model of international portfolio choice. Section
III describes the data on the actual international portfolios of U.S. institutional investors. It
also discusses the estimation of the model of portfolio choice. In Section IV we present the
model estimates based on the two different proxies for expected returns, and then we compare
the actual and predicted holdings. Measures of market segmentation are estimated in Section
V, and a summary section concludes.
International Diversification 75
II. SOLUTION OF THE INTERNATIONAL PORTFOLIO CHOICE MODEL
The specification of the model of international portfolio choice is well-known. It is a
straightforward extension of Markowitz mean-variance optimization to an asset menu that
includes foreign as well as domestic assets. In this section we discuss the interpretation of
the model to highlight the importance of the simplifying assumptions widely used in the
literature and to motivate the analysis of portfolio weights in this paper.
A standard formulation of the mean-variance portfolio model assumes that investors are
risk-averse, that they maximize the expected utility of end-of-period real wealth, and that
asset markets are perfectly integrated. The maximization problem for D assets can be
Max E(u) = xE(r) - 0.5 6(x Cx), (2.1) x
s.t. xe = 1
where x is a Dxl vector of portfolio weights, E(r) is a vector of expected real asset returns,
6 is the coefficient of relative risk aversion (CRRA), Z is the covariance matrix of real asset
returns, and e is a vector of ones. In the international case, real returns are obtained by
expressing nominal returns on both domestic and foreign assets in a common currency and
then deflating them by the investors price index. Thus, the international investor has three
sources of potential risk: nominal asset returns, exchange rates, and inflation.
Substituting in the adding-up constraint, the solution of model (2.1) for the first D-1
portfolio weights (X) can be written in a form that decomposes the effects of returns and
X = (1 /G)Z-E(R) + [ 1 - (1 /G)]CAa, (2.2)
where E(R) is the (D-1)x1 vector of expected nominal asset returns measured relative to a reference asset, A is a matrix of covariances between nominal asset returns and goods prices, a is a vector of expenditure shares for the goods, and all values are measured in a
common currency. We note that the solution to the international portfolio optimization
model can be represented graphically by the familiar efficient frontier.
The model solution in (2.2) allows us to see clearly the key difference between domestic and international asset pricing models. The optimal portfolio in (2.2) is a linear combination
of two portfolios: ZE(R) and E-Ao!. The former is sometimes called the logarithmic portfolio; it depends on nominal asset returns and therefore is the same for all investors.3
The latter is the minimum variance portfolio. It serves as the investors hedge against
purchasing power changes, and thus it varies with the price index each investor uses to deflate expected returns.
If all investors use the same price indices (i.e., have the same consumption bundle CZ), then
they will have the same perceptions of expected real returns. In this case of homogeneous
expectations, it is easy to aggregate asset demands and solve for a standard asset pricing
76 DEBRA A. CLASSMAN and LEIGH A. RIDDICK
expression. For example, in the domestic case this would be the CAPM, and in the
international case this would be the ICAPM.
In the domestic setting, it may be reasonable to assume that all investors use the same price
indices. However, when consumption bundles differ across countries and purchasing power
parity does not hold, investors from different countries have heterogeneous expectations, because they deflate nominal returns by different price indices. In this case, optimal
portfolios must differ across countries.4 Thus, as Adler and Dumas (1983) show, heteroge-
neity results in an aggregate asset demand function that includes country-specific measures
of risk aversion and wealth. This makes international asset pricing expressions much less
tractable than domestic ones.
Virtually all researchers engaged in the empirical analysis of international asset pricing
have tried to circumvent the heterogeneity problem by invoking simplifying-and umealis-
tic-assumptions, such as no inflation or purchasing power parity. A recent paper (Glassman
and Riddick 1994) shows that, while these simplifying assumptions are necessary to derive
an international asset pricing model such as the ICAPM, the same restrictions systematically
alter estimates of optimal portfolios weights. Further, the tests of the simplified models that
reject the hypothesis of mean-variance optimization produce implausible estimates of the
degree of risk aversion