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A wide array of official capital controls across countries makes it difficult to perform cross-sectional analysis of the effects of market segmentation. This article constructs a measure of deviations from capital market integration that can be consistently applied across countries. It measures the deviations of asset returns from an equilibrium model of returns constructed assuming market integration. Applying the measure to stock returns from twenty-four national markets indicates that market segmentation tends to be much larger for emerging markets than for developed markets, and that the measure tends to decrease over time. Along several dimensions, the measure yields results that are consistent with reasonable priors about the relations between effective integration and explicit capital controls, capital market development, and economic growth.

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77118
THE WORLD BANK ECONOMIC REVIEW, VOL. 10, NO. 2. 267-289
A Measure of Stock Market Integration for
Developed and Emerging Markets
Robert A. Korajczyk
A wide array of official capital controls across countries makes it difficult to per-
form cross-sectional analysis of the effects of market segmentation. This article con-
structs a measure of deviations from capital market integration that can be consis-
tently applied across countries. It measures the deviations of asset returns from an
equilibrium model of returns constructed assuming market integration. Applying the
measure to stock returns from twenty-four national markets indicates that market
segmentation tends to be much larger for emerging markets than for developed mar-
kets, and that the measure tends to decrease over time. Along several dimensions,
the proposed measure yields results that are consistent with reasonable priors about
the relations between effective integration and explicit capital controls, capital mar-
ket development, and economic growth.
In financially integrated markets, capital should flow across borders in order to
ensure that the price of risk—the compensation investors receive for bearing
risk—is equalized across assets. Conversely, if capital controls or other forces
prevent free movement of capital across borders, then it is likely that different
economies will demand different levels of compensation for risk. In some mar-
kets, direct measures of the severity of capital controls are available. For ex-
ample, some countries have dual classes of common equity. Restricted equity
can be held only by domestic residents, but unrestricted equity can be held by
both domestic and foreign investors. The price differential between restricted
and unrestricted shares that have identical payoffs is a direct measure of the
effects of capital controls (Hietala 1989; Bailey and Jagtiani 1994). Similarly,
differences between official and black market exchange rates, between official
and offshore interest rates, or between the market price and the net asset value
of closed-end country mutual funds can be used to measure the effects of capital
controls (Bonser-Neal and others 1990).
A difficulty arises when attempting intercountry comparisons of the severity
of capital controls because different countries may have different mechanisms
Robert A. Korajczyk is with the Department of Finance at Northwestern University. This article was
originally prepared for the World Bank conference on Stock Markets, Corporate Finance, and Economic
Growth, held in Washington, D.C., February 16-17,1995. The author would like to thank Eric Chang,
Ash Demirgu£-Kunt, Ross Levine, Peter Montiel, participants at the conference, and two anonymous
referees for helpful comments.
C 1996 The International Bank for Reconstruction and Development/THE WORLD BANK
267
268 THE WORLD BANK ECONOMIC REVIEW, VOL. 10, NO. 2
for restricting capital movements. For example, a country that prohibits all for-
eign investment does not have unrestricted shares whose prices can be com-
pared to restricted shares. In addition, countries without any formal restrictions
against foreign investment will not have restricted shares trading. Although the
former case is ostensibly one of segmented markets and the latter case is one of
integrated markets, there may be methods by which investors circumvent the
restrictions in the former case, and there may be informal barriers that lead to
actual segmentation in the latter case (such as less stringent accounting stan-
dards or insider trading regulations).
Given the difficulty of directly comparing the effects of the wide array of
official capital controls across countries, a measure of deviations from capital
market integration that can be consistently applied across countries is impor-
tant for cross-sectional analyses of the effects of market segmentation. The ap-
proach taken here is to measure deviations from integration by measuring the
deviations of asset returns from an equilibrium model of returns constructed
assuming market integration.
Testing the law of one price (LOP) in financial markets requires a model
that identifies the type of risk that is important to investors. The model used
here is the International Arbitrage Pricing Theory (IAPT). An advantage of an
approach that relies on asset prices or returns is that effective barriers to
capital flows, regardless of their source, should lead to actual deviations from
LOP. Statutory barriers to capital flows that are ineffective should not lead to
pricing deviations. Ostensibly free markets with large nonstatutory barriers
(such as large differentials in information costs) should exhibit pricing de-
viations.
A disadvantage of the IAPT approach is that it relies on a particular specifica-
tion of the asset pricing model. If the asset pricing model is incorrect, then pric-
ing errors will be observed even when markets are integrated. Also, regime shifts,
such as those that would occur when an economy moves from being segmented
to integrated, will lead to changes in the asset pricing relation and to large short-
term measured deviations from LOP.
The next section contains a brief description of the asset pricing model. Sec-
tion II relates pricing errors to the existence of deviations from the law of one
price induced by market segmentation. Section HI discusses estimation of pric-
ing errors. Section IV addresses the effects of regime shifts. Section V describes
the data. The techniques used to construct factor-mimicking portfolios are de-
scribed in section VI. The empirical measures of deviations from the law of one
price are described in section VII. Section VIII presents conclusions and sugges-
tions for future work.
I. THE MULTIFACTOR ASSET PRICING MODEL
The logic behind the Arbitrage Pricing Theory (APT; Ross 1976) and interna-
tional extensions (Ross and Walsh 1983; Solnik 1983; Levine 1989; and Clyman,
Korajczyk 269
Edelson, and Hiller 1991) is that there are a small number of risks that are
common to most assets, for which investors command risk premiums. Risk that
is specific to one asset (or a small set of assets) is diversifiable and, therefore,
investors do not demand compensation for this risk.
The Case without Diversifiable Risk
The arbitrage argument can be most easily illustrated in the case where there
is no diversifiable, or idiosyncratic, risk. Assume that the realized returns on
securities are given by the following linear factor model:
(1) riwt = \ih,
h
where r/ ( denotes realized returns on asset / at time t, b^ is the sensitivity of asset/' to
the ith common source of risk, 8 a is the realization of risk factor i in period t, and
Hu = E,_i(rlrt) is the expected return on asset /'. In this case where there is no asset-
specific risk, there could be a riskless, costless arbitrage opportunity unless:1
(2) H,,, = h,t + bjAXu + . ã ã + bukXk-t
where XQ t is the return on a riskless asset and \ t is the risk premium on the z'th
source of risk. More generally, expected returns could be expressed as
(3) \L,,t = a, + Xoi( + bjAXu + . . . + bhkXkit
where a ; represents the pricing error, or deviation of expected returns from the
predictions of the multifactor asset pricing model.
In this case, a, must equal zero for all / so that no arbitrage opportunities are
possible. Letp' = (u1 (, u 2 j ,,... u n / ),a' = (a l5 a 2 , . . .,an),X' = (Xo,Xy,.. .,Xk), and
B = (l, b) where i is an w-vector of ones and b is an n x k matrix whose (/', /)
element is blti. In matrix notation, equation 3 can be expressed as:
u. = a + BX.
The value of A, that minimizes the pricing error (in terms of minimizing the sum
of squared pricing errors) is X = (B'B^B'p and a = [/ - B(B' B) 1 B']p, where / is
an n x n identity matrix. Note that a'B = 0, so that a portfolio formed by choos-
ing the portfolio weight on asset i to be a, is costless (since a'l = 0) and riskless
(since a'b = 0, which implies that the portfolio has no exposure to the risk fac-
tors). The expected return on the portfolio is
a'n=o'a + a'BX = a'a + 0 0.
1. This requires the assumptions that there are more assets than sources of risk (n k) and that the
n x k matrix of sensitivities, b—where the (/,/) element of b is bw—has rank k.
270 THE WORLD BANK ECONOMIC REVIEW, VOL. 10, NO. 2
Thus, this portfolio is riskless and costless and has a strictly positive return. This
is an arbitrage opportunity that will be exploited. In order to avoid arbitrage
opportunities, the pricing relation given by equation 2 must hold. That is, a, = 0
for all / in equation 3.
The Case with Diversifiable Risk
The expression for asset returns in equation 1 assumes that there are only k
worldwide factors that influence all asset returns. To generalize this specifica-
tion to include uncertainty that is asset specific, or diversifiable, returns will be
expressed as:
where zut is the uncertainty in asset /'s returns that is not explained by the
worldwide factors. Ross (1976) assumes that there are an infinite number of
assets and that the asset-specific risks are uncorrelated across assets, that is,
corr(e /( , em /) = 0 for/ * m. Ross notes that weaker conditions also imply that
the risk embodied in the term ziit is diversifiable (Chamberlain and Rothschild
1983; Connor and Korajczyk 1993).
Because each asset has its own unique, or asset-specific, risk, it will not be
possible to form riskless portfolios from a finite set of risky assets. However, an
asymptotic arbitrage opportunity can be defined as one in which it is possible to
construct a sequence of portfolios whose expected returns approach infinity and
whose variance approaches zero as the number of assets, n, approaches infinity.
The absence of such arbitrage opportunities implies that the sum of squared
pricing deviations (a? + af + .. . + ctjj) must remain finite as n approaches infinity
(Ross 1976; Huberman 1982).
The fact that the sum of squared pricing deviations must remain finite implies
(in an economy with an infinite number of assets) that most of the pricing errors
must be small and that equation 2 holds as an approximation for most assets:
(5) \ij,t = XQ' + b/.iX,, + . . . + blkXkl.
Further restrictions can be placed on the economy to get the pricing model to
hold as an equality (Connor 1984; Constantinides 1989). I will assume that,
under the null hypothesis of financial market integration, either such restric-
tions hold or the approximation is good enough to ignore the approximation
error in equation 5.
II. MARKET SEGMENTATION AND PRICING ERRORS
Although the method of estimating the risk factors is described more fully
later, it is useful at this juncture to point out that capital market segmentation
prevents cross-market arbitrage and, therefore, prevents the prices of risk (vec-
Korajczyk 271
tor X) from being equated across markets. Capital market segmentation will lead
to pricing errors relative to risk factors constructed assuming capital market
integration. This is illustrated by a hypothetical world consisting of two markets
(a and b) that are influenced by the same single-world factor. That is, assets in
each economy satisfy a one-factor pricing model. However, because the markets
are segmented, the parameters of the asset pricing model are different across
markets. The expected returns on asset / in the two markets are given by
]ibhl = Xg + bbhXX\
with X# * A$and Xf * Xb. However, the implied riskless return and world factor
risk premium estimated by pooling the two markets together and assuming (in-
correctly) that they are integrated will be (assuming the markets are of equiva-
lent size and have the same distribution of sensitivities) XQ = (Xg + X$)/2 and
A.j = (k\ + X\) 12. That is, estimating an integrated model when the null is incor-
rect will lead to estimated risk premiums that are weighted averages of the true
segmented risk premiums. This implies that for economy a, the measured pric-
ing deviation (relative to a model estimated assuming integration) of asset / is
(6) cHj=(Xi- Xo) + ^,i(A,1- X,)
and for economy b, the measured pricing deviation of asset / is
(7) a* = (A.fc-Xo) + ^ . i M - * i ) -
Thus, the mispricing parameters, a, provide a direct measure of deviations from
the LOP.
Although the example assumes a single common factor, the results extend to
any number of common factors, under the assumption that the IAPT would be
the appropriate pricing model in an integrated world. That is, different prices of
risk for common factors will lead to nonzero alphas relative to the IAPT.
Under certain conditions, the pricing errors relative to a factor model might
actually miss market segmentation. This could occur if there are local factors in
one or more countries that are priced locally (because of segmentation) but not
priced in other countries. In addition, market segmentation could be missed if
(1) the local factors are unrelated to asset returns in the other countries (that is,
the factors are not common in that the sensitivities of nonlocal assets to the
local factors are zero) and (2) the local factors are included in the asset pricing
model. To illustrate this situation, consider a hypothetical world consisting of
two markets (a and b) that are influenced by the same single-world factor. Coun-
try b's assets are sensitive to a local factor that is priced in b but not in a. That is,
assets in each economy satisfy the factor pricing models
272 THE WORLD BANK ECONOMIC REVIEW, VOL. 10, NO. 2
where W and L stand for world and local factors. Here I have assumed that the
two economies have the same price of risk for the world factor but different
prices for the local factor. Applying a two-factor model to these economies us-
ing the world and local factors will not reveal a pricing deviation even though
the nonzero price of the local factor in country b is due to market segmentation.
The pricing deviation will be undetected because assets in economy a have zero
sensitivity to the local factor.
Failure to reject integration in this case hinges on including the local factor in
the model. If only the world factor, and not the local factor, is included in the
model, then the pricing errors for country fc's assets will be nonzero and should
lead to a rejection of the market integration hypothesis.
An alternative approach to testing the law of one price is to estimate the price
of risk for different subsets of securities and test the hypothesis that the price of
risk is equal across subsets. This is done within a single country in Roll and Ross
(1980), who test for the equality of the zero-beta return, XQ, across subsets, and
in Brown and Weinstein (1983), who test for the equality of all risk premiums.
In an international setting, subsetting by country allows an estimate of country-
specific prices of risk. This is done by Cho, Eun, and Senbet (1986); Gultekin,
Gultekin, and Penati (1989); and Harvey (1991).
III. ESTIMATION OF PRICING ERRORS
The pricing deviations discussed in sections I and II were expressed as dis-
crepancies between an asset's true expected return and the expected return im-
plied by the asset pricing model. However, the ex post return on the asset is
observed, not the true expected returns on the asset. From equation 4, the asset's
ex post return deviates from its expected return because of shocks from the
common factors and asset-specific shocks.
Let T be the number of time periods for observed asset returns; n the number
of securities; f the n x T matrix of excess returns on the assets; F the k x T
matrix of realized factors plus risk premiums F( r = 8,, + A^, where Fit is the
excess return on the portfolio that mimics factor i in period t; b then x k matrix
of sensitivities, or factor loadings; and e the n x k matrix of idiosyncratic (asset
specific) returns. Equations 2 and 4 imply that
(8) rn = b F + en
with E(Fe ') = 0, £(e ) = 0, and £(e en'/T) = V.
The assumption of a factor structure and the asset pricing theory (equations 2
and 4) imply that there is a restriction on a multivariate regression of asset
Korajczyk 273
returns on a constant and the excess returns on factor-mimicking portfolios,
which is embodied in equation 8. The restriction is that the intercepts are jointly
equal to zero. That is, in the multivariate regression
(9) r = a + b F + e
the vector of intercept terms, a , contains the pricing deviations. If markets are
integrated and the multifactor asset pricing model describes asset expected re-
turns, a should be equal to zero. However, if risks are priced differently across
economies, these pricing differences will lead to nonzero values of a . Thus, one
measure of financial integration is the size of the intercept terms in the multi-
variate regression (equation 9).
IV. ASSET PRICING DYNAMICS AND REGIME SHIFTS
The theoretical pricing errors in equations 6 and 7 are derived assuming
that each economy is in a steady-state segmented equilibrium each period.
However, the recent trend in most markets is movement from segmented
markets toward integrated markets. This trend implies that the asset pricing
regimes will shift from segmented to integrated regimes and that the param-
eters in equation 9 are likely to change through time. In the long run, in-
creasing integration should lead to smaller pricing errors (zero pricing errors
in the limit approaching complete integration). However, in the short run,
measured pricing errors might be larger as asset prices change because of the
changes in asset pricing regimes. Since the movement from a completely seg-
mented market to a completely integrated market is rarely smooth, the asset
pricing dynamics during the transition phase are difficult to characterize. In
particular, if market participants anticipate the liberalization from a seg-
mented to integrated market, asset expected returns in the transition period
are not likely to be set according to models that assume complete segmenta-
tion or complete integration.
The appendix contains a simple numerical example of an unanticipated
regime shift. Although the numerical results are clearly dependent on the
numbers picked for the example, the fact still remains that shifts across pric-
ing regimes are likely to cause changes in the parameters (a and b) and cause
large measures of mispricing in the short run. Also, these shifts in pricing
should occur as shifts in regimes become anticipated. Thus, the effects of
regime shifts could be spread over a longer period as th

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