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INTERNATIONAL DIVERSIFICATION:

NEW EVIDENCE ON MARKET

SEGMENTATION

DEBRA A. CLASSMAN and LEIGH A. RIDDICK

ABSTRACT

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.

I. INTRODUCTION

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.

73

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

expressed as:

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

inflation:

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