International diversification: New evidence on market segmentation

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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 (see, e.g., Frankel, 1982, where CRRA is estimated to be no larger

    than zero, or Frankel 1983, where CRRA varies from 15 to 18). This combined evidence

    casts doubt on the conclusions of tests based on these simplified models, giving us a strong

    motive for avoiding the simplifying assumptions.

    The same approach used to test mean-variance optimization has been adapted to test for

    market segmentation, There is evidence that market segmentation has a large impact on

    optimal portfolios in the domestic context (see, e.g., the discussion in Merton 1987). Tests

    of international market segmentation in a mean-variance framework include Stehle 1977;

    Jorion and Schwartz 1986; Alexander, Eun, and Janakiramanan 1988; Hietala 1989; and

    Korajczyk and Viallet 1989. The majority of these tests find evidence of significant

    segmentation. However, they are based on the simplified models, and thus we ask whether

    the same conclusions would hold in a model without the simplifying assumptions.5*6

    There are many kinds of market-segmenting factors. They include transaction costs, taxes,

    short sale restrictions, investment prohibitions, incomplete information about some assets,

    or any other restriction on the list of assets held by investors (Levy 1978; Merton 1987;

    Markowitz 1990). There are two ways to incorporate these factors in the unrestricted

    mean-variance model. One approach, which allows the exact form of market segmentation

    to be modeled, is to add constraints to model (2.1). This is the approach in the domestic

    Generalized Capital Asset Pricing Model (GCAPM) of Levy (1978). Alternatively, the market-segmenting factors could be directly incorporated in the meas-

    urement of investors expected returns. For example, in the case of taxes or transaction costs,

    this would involve computing after-tax or net returns. Investment prohibitions would be

    equivalent to infinitely high transaction costs, Since we do not have sufficiently detailed

    information on either the forms or the magnitudes of the various international market-

    segmenting factors, we cannot apply either of these methods directly.

  • International Diversification 77

    Instead, we will draw conclusions about the existence of market segmentation by exam-

    ining the differences between the weights in an actual portfolio and the weights generated

    by the model without simplifying assumptions. We will also be able to infer the size of the

    market-segmenting factors by calculating the implied asset returns that would be required to generate the observed investment positions.

    III. DATA

    One of the contributions of this paper is the comparison of optimal portfolios to actual

    portfolio holdings. For this comparison to be meaningful, we need foreign holdings disag-

    gregated by country. Estimates of U.S. investors aggregate foreign holdings are available

    from several sources, but previous researchers have not had access to breakdowns of this

    aggregate into country-specific holdings.7 We were able to obtain a 1988 point estimate of

    foreign placements of managed pension funds (public and private) and mutual funds.8 These

    data were combined with information on domestic asset holdings from the Federal Reserve

    Boards Annual Statistical Digest and the Investment Company Institutes Mutual Fund Fact Book to arrive at the portfolio weights presented in Tables 1-A and 1-B.9*10

    Since institutional investors hold from 60 to 80% of the U.S. market, their behavior is a

    good proxy for investment patterns for U.S. investors as a group. We note also that the

    portfolios of pension and mutual funds are virtually identical. For the sake of brevity, we

    will therefore focus on the pension fund data in the remainder of the paper.

    Note that, in choosing the asset menu to examine, we have assumed that investors can

    diversify across stocks and long-term government bonds from 10 countries-Belgium,

    Country

    Table Z-A. Actual 1988 Portfolio Holdings of U.S. Pension Funds

    $ (Billions) Percent of Total

    Fixed Income $ Equity $ Total $ Fixed Income % Equity 96 Total %

    Belgium 0 0.7722 0.7722 0 0.0003 0.0003

    Canada 1.5443 2.3165 3.8608 0.0007 0.0010 0.0016

    FratXX 0.7722 5.4051 6.1773 0.0003 0.0023 0.0026

    GermanY 2.5095 8.1077 10.6172 0.0011 0.0034 0.0045

    I&Y 0 1.7374 1.7374 0 0.0007 0.0007

    Japan 4.4399 42.4689 46.9088 0.0019 0.0180 0.0199

    Netherlands 0.5791 4.2469 4.8260 0.0002 0.0018 0.0020

    Switzerland 0.1930 4.0538 4.2468 O.OQOl 0.0017 0.0018

    U.K. 2.5095 14.0919 16.6014 0.0011 0.0060 0.0070

    U.S. 885.8125 1378.9779 2264.7904 0.3753 0.5842 0.9594

    TOTAL 898.3600 1462.1783 2360.5383 0.3806 0.6194 l.OOQO

    Source: Inter&c Research Corp. and Federal Reserve Board Annual Statistical Digest

  • 78 DEBRA A. CLASSMAN and LEIGH A. RIDDICK

    Table Z-B. Actual 1988 Portfolio Holdings of U.S. Mutual Funds

    $ (Billions) Percent of Total

    Country Fixed Income $ Equity $ Total $ Fixed Income % Equity % Total %

    Belgium 0 0 0 0 0 0

    Canada 0.4050 2.0252 2.4302 0.0010 0.0049 0.0058

    France 0.4050 0.8101 1.2151 0.0010 0.0019 0.0029

    e-Y 0.2025 1.2151 1.4176 0.0005 0.0029 0.0034

    Italy 0.2025 0 0.2025 0.0005 0 0.0005

    Japan 0.2025 6.2782 6.4807 0.0005 0.0151 0.0155

    Netherlands 0.2025 0.8101 1.0126 0.0005 0.0019 0.0024

    Switzerland 0 0.8101 0.8101 0 0.0019 0.0019

    U.K. 0.6076 3.2403 3.8479 0.0015 0.0078 0.0092

    U.S. 158.7400 240.8600 399.6000 0.3807 0.5776 0.9582

    TOTAL 160.9676 256.0491 417.0167 0.3860 0.6140 1.0000

    Source: InterSec Research Corp. and the Mutual Fund Facr Book

    Canada, France, Germany, Italy, Japan, the Netherlands, Switzerland, the U.K., and the U.S.

    Together these countries represent 95% of world stock and world bond market capitalization.

    The key to the empirical specification of model (2.1) is the choice of a proxy for expected

    returns. We consider two proxies. The first proxy assumes that investors base their expec-

    tations of future real returns on the arithmetic means of past returns. We will refer to these

    as historical means. This proxy for expected future returns has been widely used in earlier

    work. Following previous authors, we assume that U.S. investors translate monthly returns

    into a common currency (the U.S. dollar), deflate by the U.S. price index, and estimate means

    and standard deviations from a 60-month sample period, July 1983-June 1988.

    The assumption that historical mean returns are the best predictors of future returns also

    implicitly assumes that investors have no uncertainty about their estimates for the means.

    However, Jorion (1985) notes that sample means can fluctuate substantially as the sample

    changes, imparting instability to predicted portfolios. He terms the problem estimation risk

    and argues that it accounts for the poor out-of-sample performance of estimated portfolios.

    Jorions response to estimation risk is to make the forecast of an assets future return a

    weighted average of its mean past return and the grand mean of past returns for all assets.

    This is a Bayes-Stein estimation procedure, with the grand mean serving as the prior and

    the weights being determined by the sample covariance matrix. l2 The procedure amounts to

    shrinking expected returns towards the grand mean. Jorions approach provides our second

    proxy for expected returns. We implement Bayes-Stein estimation separately for stocks and

    bonds, because it is well-accepted that the difference between stock and bond returns reflects

    differential risk.13

  • international Diversification 79

    Table 2. Means and Standard Deviations of Monthly Returns in Real U.S. Dollar Terms

    Asset Country Historical Mean Bayes-Stein Mean Standard Deviation

    Belgium

    FR3llCe

    Germany

    Italy

    Japan

    Netherlands

    Switzerland

    U.K.

    U.S.

    Belgium 0.011 0.011 0.0372

    Canada 0.006 0.007 0.0118

    France 0.010 0.010 0.0352

    GeWY O.OO!iJ 0.009 0.0379

    Italy 0.010 0.010 0.0327

    Japan 0.012 0.012 0.0332

    Netherlands 0.009 0.009 0.0382

    Switzerland 0.007 0.007 0.0407

    U.K. 0.008 0.008 0.0382

    U.S. 0.005 0.006 0.0024

    0.028 0.022 0.0706

    0.007 0.014 0.0550

    0.023 0.020 0.0761

    0.014 0.017 0.0714

    0.022 0.020 0.0826

    0.031 0.023 0.0673

    0.017 0.018 0.0548

    0.014 0.016 0.0563

    0.016 0.017 0.0656

    0.010 0.015 0.0513

    The stock returns were calculated from stock price indices that include dividends, and they

    were obtained from Morgan Stanleys Capital International Perspective. Long-term government bond returns, end-of-month exchange rates, and the U.S. price level (CPI) were

    drawn from International Financial Statistics. The values for the historical mean and Bayes-Stein proxies for expected monthly real

    returns are presented in Table 2. The historical covariance matrix, which is also calculated

    from the previous 60 months, yields the standard deviations in Table 2. When we estimate

    optimal portfolios in the next section, we will use this same covariance matrix in conjunction

    with both proxies for expected returns.

    We note two features of the proxies for expected returns. First, the real expected returns

    are quite high-as high as 37% per annum in one case for stocks and 15% per annum for

    bonds. Second, the Bayes-Stein estimates are fairly similar to the historical means, especially

    for the bonds. The remaining question is whether either proxy generates estimates that are

    consistent with observed investment positions.

  • DEBRA A. GLASSMAN and LEIGH A. RIDDICK

    IV. ESTIMATES OF OPTIMAL PORTFOLIOS AND COMPARISON WITH ACTUAL HOLDINGS

    In this section we report optimal ex ante portfolio weights from the international portfolio

    model and compare them to the actual holdings of U.S. pension funds. Initially, the optimal

    portfolios are estimated using the historical mean proxy, both with and without a restriction

    on short sales. Then the Bayes-Stein mean proxy is used to generate a second set of optimal

    portfolios under the assumption of no short sales. Finally, both the aggregate portfolios and

    the individual assets in them are compared to the actual holdings of pension fund investors.

    Results Based on Historical Means

    We first compute the optimal portfolio shares allowing short sales and using historical

    means as a proxy for expected returns. The optimal shares are presented in Table 3 for various

    Table 3. Optimal Estimated Portfolio Weights for U.S. Investor Short Sales (Allowed; Unadjusted Historical Mean Returns; n = 60 )

    Coejjicient of Relative Risk Aversion

    Asset Country 1 2 5 10 20 30 Infinity

    STOCK WEIGHT

    Belgium 2.916 1.489 0.597 0.299 0.151 0.101 0.002

    Canada -10.837 -5.422 -2.172 -1.089 -0.548 -0.367 a.006

    Fmllce 3.507 1.156 0.706 0.356 0.181 0.122 0.006

    Germany -8.571 -4.287 -1.717 -0.860 -0.432 a.289 -0.003

    IdY -0.524 -0.270 -0.117 -0.066 -0.041 -0.032 -0.015

    Japan 5.338 2.672 1.072 0.539 0.272 0.183 0.005

    Ndl. 13.677 6.848 2.750 1.384 0.701 0.474 0.018

    Switz. 11.816 5.907 2.361 1.179 0.588 0.391 -0.003

    U.K. -6.901 -3.457 -1.390 -0.702 a.357 -0.242 -0.013

    U.S. -8.790 -4.394 -1.156 a.877 -0.437 XI.291 0.002

    LONG-TERM Belgium 197.075 98.551 39.435 19.731 9.879 BOND WEIGHT Canada 11.020 5.506 2.198 1.095 0.544

    France 44.292 22.183 8.917 4.495 2.285

    Germany -150.412 -75.192 -30.057 -15.015 -7.493

    Italy -5.388 -2.703 -1.091 a.554 -0.285

    Japan 17.823 8.906 3.555 1.172 0.880

    Neth. -52.464 -26.284 -10.575 -5.339 -2.721

    Switz. -43.616 -21.812 -8.731 -4.369 -2.189

    U.K. -2.151 -1.371 -0.539 -0.262 a.123

    us. -16.264 -7.627 -2.445 -0.718 0.146

    6.594 0.026

    0.360 -0.008

    1.548 0.074

    A.986 0.029

    a.196 -0.017

    0.583 a.012

    -1.848 -0.103

    -1.462 a.009

    4.071 0.016

    0.434 1.010

    MONTHLY PORTFOLIO 0.837 0.421 0.172 0.089 0.047 0.033 0.006

    RETURN

    MONTHLY PORTFOLIO 0.9118 0.4559 0.1824 0.0912 0.0456 0.0304 0.0016

    STANDARD DEVIATION

  • International Diversification 81

    0.08-

    0 I I I 1 I I I I 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

    Standard Deviation

    Figure 1. Historical Efficient Frontiers

    values of the CRRA. The last column, corresponding to infinite risk aversion, is the minimum

    variance portfolio.

    The most obvious feature of these portfolios is the presence of large short positions,

    sometimes amounting to many times the size of the portfolio. The short positions become

    somewhat less extreme as the CRRA increases, but they are clearly inconsistent with

    observed behavior. The last two rows of Table 3 give the ex ante portfolio return and standard

    deviation (both in per month terms) at each risk level. They clearly show the reduction in

    return corresponding to decreases in portfolio risk. These ex ante risk-return combinations

    are illustrated graphically in Figure 1 for CRRA = 2. The numbers in Table 3 correspond to

    the outer frontier in the graph.14,15

    The actual pension fund and mutual fund portfolios shown in Tables 1-A and 1-B have

    non-negative holdings of all assets. This is not unexpected, since short sales by these

    institutional investors are subject to legal limitations. For example, mutual funds are severely

    limited by the margin regulations in the Investment Company Act of 1940.16 Similarly, short

    sales by pension funds are limited in practice by the prohibition on borrowing from affiliated

    parties, since most short sales involve borrowing from the broker.

    These constraints would not have much impact on institutional investors if they were able

    to invest in contingent claims contracts, for it is well-accepted that it is possible to replicate

    short positions by investing in options, futures, etc. Indeed, firms dealing in foreign countries

  • 82 DEBRA A. CLASSMAN and LEIGH A. RIDDICK

    Table 4. Optimal Estimated Portfolio Weights for U.S. Investor No Short Sales (Unadjusted Historical Mean Returns; n = 60 )

    Coeflcient of Relative Risk Aversion

    Asset Country I 2 5 10 20 30 Infinity

    STOCK WEIGHT

    Belgium 0

    Canada 0

    France 0

    Germany 0

    IdY 0

    Japan 1.000

    Neth. 0

    Switz. 0

    U.K. 0

    U.S. 0

    LONG-TERM Belgium 0 BOND WEIGHT Canada 0

    France 0

    Germany 0

    Italy 0

    Japan 0

    Neth. 0

    Switz. 0

    U.K. 0

    U.S. 0

    MONTHLY PORTFOLIO RETURN

    MONTHLY PORTFOLIO STANDARD DEVIATION

    0.031

    0.0681

    0.1650 0.3341 0.2337 0.1150

    0 0 0 0

    0 0 0 0

    0 0 0 0

    0 0 0 0

    0.8350 0.6659 0.4221 0.2102

    0 0 0 0

    0 0 0 0

    0 0 0 0

    0 0 0 0

    0 0 0 0

    0 0 0.0465 0.0170

    0 0 0.0385 0.0191

    0 0 0 0

    0 0 0 0

    0 0 0 0

    0 0 0 0

    0 0 0 0

    0 0 0 0

    0 0 0.2592 0.6386

    0.031 0.030 0.022 0.013

    0.0635 0.0608 0.0405 0.0203

    0.0755

    0

    0

    0

    0

    0.1396

    0

    0

    0

    0

    0

    0.0072

    0.0126

    0

    0

    0

    0

    0

    0

    0.7651

    0.011

    0.0136

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    1.000

    0.005

    0.0021

    are known to hedge currency risk in this way. In practice, it is difficult to identify the extent

    of such activities by pension and mutual funds, because hedging activities typically are not

    shown on annual balance sheets.17

    Anecdotal evidence on hedging activity is mixed; while some pension and mutual funds

    claim to hedge, many say they do not. l8 Further, pension fund managers have told us that

    hedging in 1988 was minimal, because currency movements at that time were such that the

    costs of hedging outweighed the perceived benefits. For this reason, we are less concerned

    about the omission of hedging in our sample than we might be if we were examining a

    different time period.

    In the remainder of the analysis, we make the assumption that no short sales are possible.

    Table 4 presents the optimal portfolio shares with this constraint imposed. The effect of the

    short sale restriction is illustrated in Figure 1, again with CRRA = 2. As is usual, the

  • International Diversification 83

    imposition of the no-short-sales restriction generates a frontier that is interior to the one

    generated when short sales are allowed.

    The dominant feature of the portfolios in Table 4 is the small number of assets with

    non-zero holdings. This is a familiar result in the literature (see, e.g., the estimates in Solnik

    and Noetzlin, 1982, and the discussion in Merton 1987). As one might expect, diversification

    increases as the CRRA rises, but even highly risk-averse investors are predicted to hold only

    a handful of the 20 assets. Most strikingly, the model predicts no holdings of U.S. stocks,

    even though this is the largest category of assets actually held by investors. Moreover, the

    CRRA has to be very large in order for the asset allocation to include any U.S. bonds. Such

    high values are inconsistent with the widely-accepted belief that the CRRA is in the range

    of one to four (see, e.g., Friend and Blume, 1975, or Mehra and Prescott, 1985).

    Figure 1 also shows the ex ante risk-return combination achieved by the actual pension

    fund portfolio in Table l-A, given the same means and standard deviations as were used to

    generate the frontiers (i.e., historical values). l9 The actual portfolio is a sizable distance

    inside both frontiers. Note that even with respect to the interior frontier (the case with no

    short sales), the gap between actual and optimal portfolio returns is large: 1.08% in monthly

    terms.2o This would translate to more than 12% on an annual basis.

    The fact that the actual portfolio does not lie on, or even close to, the efficient frontier can

    be attributed to one of the three explanations discussed in the introduction to this paper.21

    Either investors fail to form mean-variance optimal (i.e., the most profitable) portfolios, or

    the model is mis-specified by virtue of relying on historical means to proxy expectations, or

    the assumption of perfectly integrated international markets is incorrect. Since we are

    unwilling to assume that investors are irrational, we consider the second and third explana-

    tions in turn.

    Portfolios Using the Bayes-Stein Proxy for Expected Returns

    Table 5 presents the optimal portfolio shares based on the model in equation (2.1), but

    using the Bayes-Stein proxy for expected returns. We again impose the restriction of no short

    sales. The portfolios based on the Bayes-Stein proxy differ in some notable ways from those

    based on historical means. First, there is somewhat more diversification in Table 5 than in

    Table 4. This is not surprising, since the Bayes-Stein procedure involves making returns

    more similar to each other. In addition, now U.S. stock holdings appear when the CRRA

    ranges from five to 30. However, the U.S. bonds do not enter the portfolios until the CRRA

    is 20 or higher.

    To illustrate the differences generated by the Bayes-Stein adjustment, Figure 2 presents

    both the efficient frontier based on the Bayes-Stein proxy and the efficient frontier that

    was generated by the historical means (in both cases with no short sales). As one might

    expect, the Bayes-Stein frontier is slightly interior to the historical frontier because the

    shrinkage towards the grand mean reduces the perceived opportunities to reap high returns.

  • 84 DEBRA A. GLASSMAN and LEIGH A. RIDDICK

    Figure 2 also shows two ex ante risk-return combinations for the actual pension fund

    portfolio. One is identical to that in Figure 1; i.e., it is based on unadjusted historical means.

    The other computes expected portfolio return using the Bayes-Stein values. The gap between

    the Bayes-Stein actual portfolio and the Bayes-Stein efficient frontier is 0.39 percent per

    month (approximately five percent on an annual basis).22 This is smaller than the gap

    between the Bayes-Stein actual portfolio and the historical means frontier (0.93 percent

    monthly), but is still a sizable difference in overall portfolio return between the predicted

    and actual portfolios.

    Furthermore, the asset weights in the predicted portfolios described above are strongly

    inconsistent with patterns of actual individual asset holdings. In particular they do not reflect

    the fact that U.S. investors hold relatively large amounts of domestic assets. As Tables 1-A

    Table 5. Optimal Estimated Portfolio Weights for U.S. Investor (No Short Sales Bayes-Stein Estimation of Mean Returns; n = 60)

    Coefficient of Relative Risk Aversion

    Asset Country 1 2 5 10 20 30 Infinity

    STOCK WEIGHT

    Belgium 0.2153 0.3310 0.1976 0.0470 0.0213 0.0134

    Callada 0 0 0 0 0 0

    France 0 0 0 0 0 0

    GetTtXitly 0 0 0 0 0 0

    Italy 0 0 0 0 0 0

    Japan 0.7847 0.6690 0.4656 0.1914 0.0943 0.0625

    Neth. 0 0 0.1404 0.0660 0.0356 0.0260

    Swim. 0 0 0.0133 0.0134 0.0036 0.0002

    U.K. 0 0 0 0 0 0

    U.S. 0 0 0.1314 0.2552 0.1293 0.0858

    LONG-TERM Belgium 0 0 0 0 0 0 0 BOND WEIGHT Cmada 0 0 0 0.0256 0.0341 0.0183 0

    France 0 0 0 0 0 0 0

    Germany 0 0 0 0 0 0 0

    ImlY 0 0 0 0 0 0 0

    Japan 0 0 0.0516 0.4013 0.2026 0.1330 0

    Neth. 0 0 0 0 0 0 0

    Switz. 0 0 0 0 0 0 0

    U.K. 0 0 0 0 0 0 0

    U.S. 0 0 0 0 0.4792 0.6608 1.000

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    MONTHLY PORTFOLIO 0.023 0.023 0.021 0.016 0.011 0.009 0.006

    RETURN

    MONTHLY PORTFOLIO 0.0625 0.0609 0.0495 0.0319 0.0162 0.0109 0.0021 STANDARD DEVIATION

  • international Diversification

    0.04

    85

    I I I I 1 I I I I 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

    Standard Deviation

    + Bayes-stein -!B- Historical X Aclual Hislc&al 0 Aclual Bayes-slein

    Figure 2. Historical and Bayes-Stein Frontiers

    and 1-B show, U.S. institutional investors hold small quantities of foreign equities and almost no foreign bonds. The only way to generate a preponderance of U.S. holdings in the

    mean-variance model is to increase the coefficient of risk aversion to levels that we believe

    to be unreasonably high. In the next section we report evidence supporting the interpretation

    that the remaining gap in return is reflective of market segmentation.

    V. MEASURES OF THE DEGREE OF MARKET SEGMENTATION

    We begin the examination of market segmentation by asking the following hypothetical

    question: What set of expected real asset returns would generate exactly the portfolio that

    we observe in Table 1-A (or I-B)? The calculations required to answer this question are

    straightforward. Let E(R*) represent the set of expected real returns that would make the

    optimal portfolio identical to the actual one. Substituting the actual portfolio shares (X*) for

    the vector X in equation (2.2):

    X* = (l/G)C-E(R*) + [ 1 - (1/6)1X-Au. (5.1)

    and solving for E(R*), we obtain:

    E(R*)=SCX*+(l-6)Aot. (5.2)

  • 86 DEBRA A. CLASSMAN and LEIGH A. RIDDICK

    Table 6. Comparison of Expected Annualized Returns

    Asset country Implied* Historical

    STOCKS Belgium

    Canada

    France

    Germany

    Italy

    Japan

    Netherlands

    Switzerland

    U.K.

    us.

    0.0269 0.3352

    0.0323 0.0870

    0.0304 0.2743

    0.0219 0.1708

    0.0218 0.2678

    0.0139 0.3689

    0.0269 0.2036

    0.0244 0.1663

    0.0312 0.1952

    0.0377 0.1192

    LONG-TERM BONDS

    Belgium 4X026 0.1284 0.1271

    Canada 0.0019 0.0777 0.0795

    France -0.0017 0.1229 0.1219

    Germany -0.0035 0.1085 0.1083

    Italy a.0023 0.1194 0.1186

    Japan Al.0030 0.1483 0.1457

    Netherlands -0.0030 0.1122 0.1119

    Switzerland -0.0040 0.0867 0.0880

    U.K. Xl.0039 0.0979 0.0984

    U.S. 0.0002 0.0648 0.0674

    Bayes-Stein

    0.2666

    0.1646

    0.2416

    0.1991

    0.2389

    0.2805

    0.2126

    0.1973

    0.2091

    0.1779

    Note: *Expected returns required to generate actual pension fund portfolio, assuming CRRA = 2.

    We compute E(R*) by setting X* equal to the pension fund shares and assuming a relative risk aversion coefficient of two. We will refer to the computed values as implied returns.

    The annualized values of these implied returns are shown in the first column of Table 6.23,24

    For purposes of comparison, the annualized values of the historical and Bayes-Stein means

    are presented in the second and third columns, respectively.

    Two patterns in Table 6 support our conclusion of market segmentation. First, the most

    striking feature of the implied returns is that they are substantially smaller than the two

    proxies for expected returns. Whereas the historical and Bayes-Stein means suggest annual-

    ized returns in the range of 9-37% for stocks, the implied real returns are in the range of

    14% per annum. Many of the implied bond returns are negative, as a result of the very small actual weights in X* for those assets. The observation that the implied returns are smaller

    than the proxies is consistent with the presence of costs associated with investment, since

    costs drive down net returns. The second pattern we observe is that the difference between the implied returns and the

    proxies is almost always larger for foreign than for domestic assets. This is indicative of

    international market segmentation. For example, the difference between the implied return

    and the historical mean return for U.S. stocks is 8.15% per annum. However, the difference

    between implied and historical returns for almost all the remaining stocks is much larger,

  • International Diversification 87

    varying from a low of 14.19% for Switzerland to a high of 35.50% for Japan. The one

    exception is Canada, where the difference between implied and proxied returns is similar in

    size to the U.S. This is consistent with the high degree of integration between the Canadian

    and U.S. markets, which makes investment in either one approximately equal in cost. The

    patterns are similar if we instead use Bayes-Stein estimates for the comparisons among stock

    returns, and the same patterns are present in the bond returns, as well.

    We view these differences in returns as indicative of the type of market segmentation

    present. If the segmentation were due to transaction costs, we would expect the gap between

    implied and proxied returns to be rather small. At the opposite extreme, if the segmentation

    were due to outright and severe investment prohibitions, then the gap would be very large.

    We argue that the gaps we measure-which range from 5.47-35.5 percent-are too large

    to be accounted for by transaction costs alone. Some transaction costs, such as taxes,

    brokerage fees and spreads, are quantifiable, and the evidence suggests that such costs are

    higher for foreign assets than for domestic ones. However, these transaction costs are still

    relatively small in magnitude. For example, Glassman (1987) estimates the bid-ask spread

    for foreign exchange transaction to be a fraction of a percent. French and Poterba (1990)

    argue that taxes are unlikely to account for more than 0.50-0.75 percentage points of return.

    Altogether, differences in transaction costs and tax assessments probably do not explain more

    than one percentage point of annual return. Other causes must be considered.

    At this juncture it is important to discuss a limitation in our data. It is common knowledge

    that U.S. investors have means of international diversification other than direct purchase of

    foreign assets, one being the purchase of a foreign stock in the form of an American

    Depository Receipt. Another is the purchase of shares in a country fund listed on a U.S.

    exchange. Our measure of U.S. equity holdings incorrectly includes these U.S.-listed foreign

    assets in the category of U.S. assets. However, as they are less than 1% of the total market,

    we do not believe this data error explains the large gap in returns we observe.

    Another, more indirect, means of international diversification is to buy shares in a

    company with multinational activities. Agmon and Lessard (1977) and Yang, Wansley, and

    Lane (1985) provide evidence that purchase of shares in multinational corporations substi-

    tutes for investing in foreign assets, while Jacquillat and Solnik (1978) report evidence to

    the contrary. Regardless of which conclusion is correct, we do not think it fully explains our

    results, again because the divergence between predicted and actual holdings is so large.

    Even if transaction costs and indirect means of international investment accounted for a

    5 or 10% difference between implied and historical returns, we would still be left with a

    large gap to explain. Therefore we next consider explicit investment restrictions and other

    barriers to international investment as possible explanations of the remaining gap.

    A variety of legal and regulatory restrictions form explicit barriers to foreign investment.

    The restrictions on U.S. investment in foreign equity markets generally take the form of

    ownership restrictions (Eun and Janakiramanan, 1986). Many countries limit sales of

    government bonds to specified large investors or financial institutions. Some have no secondary markets for these bonds.25 In a few countries (e.g., France and Italy), foreign investors must open special bank accounts to trade securities, and some have a separate class of shares for foreign purchasers.26

  • 88 DEBRA A. CLASSMAN and LEIGH A. RIDDICK

    While such barriers existed during our sample period, the mid-1980s was a period of

    decreasing restrictions on foreign investments. Indeed, French and Poterba (1990) conclude

    that the restrictions were not binding during this time period. Eun and Janakiramanan (1986)

    provide simulation results for a two-country, eight-asset model that suggest that binding

    ownership restrictions would reduce asset returns by approximately 40 to 60%. Since our

    gap between implied and proxied returns averages roughly 15%, it is likely that ownership

    constraints are not binding here.27

    Given the evidence that the low level of foreign investment is explained by something

    bigger than typical transaction costs and smaller than outright prohibitions, we turn to a final

    category of market-segmenting factors: information costs. It is generally acknowledged that

    information costs are greater for foreign than for domestic investment (Merton, 1987).

    Investors are unfamiliar with foreign market institutions and practices, and they face

    significant difficulties in obtaining information about the determinants of a foreign assets

    value. Furthermore, there is extensive indirect evidence of the importance of information

    costs. For example, the presence of such costs accounts for the fact that most individuals

    invest in foreign stocks through mutual funds (country funds) rather than directly. Informa-

    tion costs thus could explain a large portion of the apparent market segmentation.

    In summary, we assert that quantifiable transaction costs, such as tax differences and

    spreads, alone cannot explain the implied costs of market segmentation. Similarly, indirect

    opportunities to invest internationally are such a small fraction of the market that they cannot

    account for the entire gap between implied and proxied returns. Other factors must be at

    work, including explicit investment barriers and information costs. Our estimates of the

    degree of market segmentation suggest that information costs are of more importance than

    outright barriers to investment.

    VI. CONCLUSIONS

    Prior research on international portfolio diversification has relied on models that invoke

    unrealistic simplifying assumptions. These assumptions may have influenced their results regarding both the validity of mean-variance optimization and related conclusions about

    market segmentation.

    The analysis in this paper takes three steps in extending this research:

    1. We generate predicted portfolio holdings with a mean-variance model that does not

    impose the simplifying assumptions that have been widely used in earlier studies.

    2. A unique set of data on institutional portfolios enables us to compare country-specific

    predicted holdings to actual holdings at a point in time.

    3. We use these results to calculate an estimate of the degree of international market

    segmentation. As in the earlier work with restricted asset pricing models, we find that the international

    mean-variance model based on perfect market integration cannot explain observed invest-

    ment behavior. When historical returns are used as predictors of future returns, short sales

    are prohibited, and the CRRA is below 10, investors are predicted to hold no domestic assets.

  • International Diversification 89

    When historical returns are adjusted for estimation risk with a Bayes-Stein procedure, the

    model predicts U.S. holdings amounting to 13%. But even this latter prediction contrasts

    sharply with the evidence that institutional investors actually hold over 96% of their

    portfolios in domestic assets.

    We also confirm the conclusions of earlier studies regarding the presence of international

    market segmentation. We then go one step further and provide a measure of the extent of

    the segmentation. We find that more than simple transaction costs and taxes are at work.

    However, the degree of segmentation is not large enough to indicate that outright restrictions

    on international investment are binding. We therefore attribute most of the segmentation to

    information costs associated with foreign investment.

    ACKNOWLEDGMENT

    This work was supported by a faculty development grant from the American University. We are indebted to Morgan Stanley, the Investment Company Institute, and, particularly, Mr. Duncan Fordyce of Inter&c Research Corporation for providing data. We wish to acknowledge the useful comments of Bernard Dumas, Ted Jaditz and two anonymous referees. The paper also benefitted from discussions during presentations for the American Finance Association, the Foundation for Research in Intema- tional Banking and Finance, the Securities and Exchange Commission and Georgetown University. Rajesh Agarwal provided capable research assistance. The usual caveat applies.

    NOTES

    1. Early empirical applications of international mean-variance optimization were provided by Grubel(l968) and Levy and Sarnat (1970). Solnik (1974a) derived an international asset pricing model which was later generalized by Stulz (198 1 a) and others.

    2. The derivation of the solution to the optimization problem in (2.1) can be found in a number of sources. This particular decomposition is emphasized in Adler and Dumas (1983) and Macedo (1983). Note that if short sales are excluded, it is not possible to explicitly solve for the optimal portfolio weights, as in equation (2.2). Instead, the weights can be estimated by quadratic programming.

    3. The term logarithmic portfolio derives from the fact that this is the portfolio that would be held by an investor with logarithmic utility (CRRA = 1). See, for example, Macedo (1983).

    4. Note that the heterogeneity appears in expectations of real returns; nothing in the argument precludes investors having homogeneous expectations regarding nominal returns.

    5. An exception is Wheatley (1988), who uses a consumption-based asset pricing model, and finds evidence of a lack of market segmentation.

    6. An alternative to mean-variance CAPM-type models is to base tests on multi-factor APT models. Using this approach, Cho, Eun, and Senbet (1986), Gultekin, Gultekin, and Penati (1989), and Korajcyzk and Viallet (1989) also find evidence of market segmentation.

    7. Government agencies, investment houses and some authors (e.g., French and Poterba, 1990, 1991) construct estimates of country-specific holdings by cumulating net cross-border equity flows. However, it is generally acknowledged that cumulative flow measures can be unreliable proxies for stocks of assets.

    8. These data were made available to us by InterSec Research Corporation of Stamford, London and Tokyo.

  • 90 DEBRA A. CLASSMAN and LEIGH A. RIDDICK

    9. There was an unavoidable mismatch in timing in the data. The Federal Reserve data are for December 1987, the Mutual Fund Fact Book data are for December 1988, and pension and mutual fund holdings are for June 30, 1988.

    10. The relative magnitudes of domestic and foreign holdings in these tables have been confirmed by a variety of other sources. See, for example, Morgan Guaranty Trust Company (1989).

    11. In practice, of course, the menu of assets is much larger. For example, one might include both short-term bonds and cash instruments for all countries. In response to the suggestion of an anonymous reviewer, we included money market assets in the model estimation. We found that these assets never entered efficient portfolios, as they were dominated by long-term bonds in our sample period. Since our data on actual portfolio holdings do not include foreign short-term assets, we could not have compared the estimates to an actual measure in any event.

    12. The formula for calculating weights is given in Jorion (1985). A similar approach is followed in Eun and Resnick (1987) in the context of comparing portfolios with Sharpe measures.

    13. Pooling these returns would effectively remove part of the risk differential. Jorion (1985) alludes to this issue in his footnote 1.

    14. It is also noteworthy that the frontier in the unrestricted case is very nearly linear, and that it very nearly (but not quite) intersects the vertical axis; it seems to be almost achieving the linear relationship (and two fund separation) of the familiar Capital Market Line. This is not surprising since our government bond approximates the U.S. riskfree asset.

    15. Recall that our focus is on an unrestricted model, since this allows us to consider the effects of all sources of risk on portfolio diversification. One important source of risk is inflation, and thus, it is necessary for us to use real returns. Therefore, there is no truly riskfree asset here. This means we cannot derive the Capital Market Line, and we instead compare our actual portfolios to the efficient frontier.

    16. See T. Frankel(l980) for a discussion of the SEC interpretation of the Act. 17. It is unclear whether the absence of hedging activities on annual accounting statements-even

    for those institutional investors who claim to hedge-is due to the closing out of open positions at year-end or to some accounting convention.

    18. For example, while the annual report for the TIAA-CREF funds clearly states that such hedging is allowed, we were told that the funds were not hedging in 1988.

    19. The actual mutual fund portfolio is virtually identical, and is not shown separately. 20. This difference arises from comparing two portfolios with the same standard deviation: one

    for the efficient frontier with an expected return of 1.95 percent and the actual portfolio expected return of 0.87 percent.

    21. The actual portfolio is not required to lie precisely on the efficient frontier, because a portfolio which is a combination of efficient portfolios is not, in theory, necessarily efficient when short sales are restricted.

    22. This difference arises from comparing two portfolios with the same standard deviation: one with the expected return of 1.54 percent for the efficient portfolio, and the actual portfolio with an expected return of 1.15 percent.

    23. The implied returns calculated from mutual fund shares are virtually identical and therefore are not reported here.

    24. This method of calculating implied returns, which we first used in an earlier version of this paper, was also independently developed by French and Poterba (1990).

    25. See OECD (1983) for details. 26. Swiss bearer shares are a historical example. See Eun and Janakiramanan (1986) and Directory

    of World Stock Exchanges (1988) for additional information. 27. This finding supports the model of mild segmentation developed by Errunza and Losq

    (1985).

  • International Diversification 91

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