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 (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.
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,
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
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 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
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
MONTHLY PORTFOLIO 0.837 0.421 0.172 0.089 0.047 0.033 0.006
MONTHLY PORTFOLIO 0.9118 0.4559 0.1824 0.0912 0.0456 0.0304 0.0016
International Diversification 81
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
Figure 1. Historical Efficient Frontiers
values of the CRRA. The last column, corresponding to infinite risk aversion, is the minimum
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
LONG-TERM Belgium 0 BOND WEIGHT Canada 0
MONTHLY PORTFOLIO RETURN
MONTHLY PORTFOLIO STANDARD DEVIATION
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
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
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
MONTHLY PORTFOLIO 0.023 0.023 0.021 0.016 0.011 0.009 0.006
MONTHLY PORTFOLIO 0.0625 0.0609 0.0495 0.0319 0.0162 0.0109 0.0021 STANDARD DEVIATION
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
+ 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:
86 DEBRA A. CLASSMAN and LEIGH A. RIDDICK
Table 6. Comparison of Expected Annualized Returns
Asset country Implied* Historical
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
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.
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
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.
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.
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
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