ARTICOL PIETE Capital Market Europa Pieteas

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Int. Fin. Markets, Inst. and Money 20 (2010) 363375

Contents lists available at ScienceDirect

Journal of International Financial

Markets, Institutions & Moneyj ou r na l ho m e pa ge : w w w . e l s e v i e r . c o m / l o c a t e / i n t f i n

European capital market integration: An empirical study

based on a European asset pricing model

David Morelli

Kent Business School, University of Kent, Canterbury, Kent CT2 7PE, UK

a r t i c l e i n f o

Article history:

Received 4 December 2009

Accepted 25 March 2010

Available online 1 April 2010

JEL classification:

G12

G15

Keywords:

European capital markets

Integration

Factor analysis

Pricing model

a b s t r a c t

This paper investigates the integration between the capital mar-

kets of 15 European countries, all of which are members of the

European Union. Integration is tested under the joint hypothesis

of a European multifactor asset pricing model. A European portfo-

lio is constructed from which common factors are extracted using

maximum likelihood factor analysis.Empirical testsare undertaken

to determine whether these European factors are not only priced,but also equally priced across the European capital markets. The

results show that a number of common factors are extracted from

the European portfolio and a degree of capital market integration

is shown to exist across the European capital markets.

2010 Elsevier B.V. All rights reserved.

1. Introduction

This paper examines whether the capital markets of the European countries that form the European

Union are integrated. Over the years there has been a continuing process of integration within the

European Union. Events such as the harmonisation of monetary and fiscal policy, none more so than

the introduction of the Euro, have seen the capital markets of the countries of the European Union

become more integrated. From the point of view of investors, looking to create international portfolios

by investing in different European markets, so as to benefit primarily from international diversification

by reducing country specific systematic risk, greater capital market integration will reduce, and may

even eventually remove such benefits. Perfect integration across European capital markets would

imply that these capital markets share the same riskreturn relationship, thus securities would be

E-mail address: [email protected].

1042-4431/$ see front matter 2010 Elsevier B.V. All rights reserved.

doi:10.1016/j.intfin.2010.03.007
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364 D. Morelli / Int. Fin. Markets, Inst. and Money20 (2010) 363375

priced according to the same asset pricing model. To test for integration, in terms of examining the

riskreturn relationship between countries, an asset pricing model is required. The pricing model

adopted in this paper assumes that securities are priced according to a European multifactor asset

pricing model. Assuming this, then integration across the European capital markets would imply that

a securitys expected return should be directly related to its sensitivity to European risk factors.

Different methodologies have been adopted in studying capital market integration. One such

methodology is the use of multivariate cointegration techniques. Corhay et al. (1993) found evidence

of one cointegrating vector on examining five European capital markets. A study by Chung and Lui

(1994) found two cointegration vectors on examining the capital markets of the US, Japan, Taiwan,

Hong Kong, Singapore and South Korea. A more recent study by Chen et al. (2002) found evidence of

one integrating vector on examining the South American capital markets of Argentina, Brazil, Chile,

Columbia, Mexico and Venezuela. Pascal (2003) examining long-run comovements in the UK, French

and German capital markets found no evidence of an increasing number of cointegrating vectors.

Asset pricing models, both singleand multifactor, have been applied so as to examine capital market

integration. Single factor models such as the international CAPM examines whether security risk can

be explained by the covariance of national returns with an international portfolio. The results from

testing for integration using a singlerisk factor model have been somewhat mixed. Solnik (1977) foundevidence of a degree of integration between US and European countries, and Stehle (1977) showed

that the pricing of US securities was significantly related to a global market portfolio. Studies by Stulz

(1981) and Alder and Dumans (1983) provided evidence in support of an international CAPM, whereas

Jorion and Schwartz (1985) however found little evidence of integration between the Canadian and US

markets. Empirical studies to date adopting a multifactor asset pricing model to examine integration

across various capital markets have also produced mixed results. Studies by Gultekin et al. (1989)

examining the stock markets of the US and Japan, Korajczyk and Viallet (1989) examining the stock

markets of the US, Japan, France and the UK, and Vo and Daly (2005) on examining the European equity

markets, all failed to find any strong evidence of integration across these markets. Studies however

by Heston et al. (1995) on the capital markets of Europe and the USA, Cheng (1998) examining the

capital markets of the UK and USA, and Swanson (2003) examining Japan, Germany and the USA, allproduced evidence in support of integration across these markets.

In this paper integration between the European capital markets is examined under the context of

a European multifactor asset pricing model. Applying a European pricing model itself implies that the

capital markets of Europe are integrated, thus the joint hypothesis problem exists. The application

of a European multifactor asset pricing model assumes that returns follow a k-factor structure.1 The

k-factor structure represents a number of common factors that explain the underlying correlations

between security returns across different markets. Clearly, the greater the correlation the greater

the integration. Various studies have examined correlations between different markets in an attempt

to identify integration across global markets. Studies by Daly (2003) found, on examining the Asian

markets, increased correlation after the stock market crash of 1997. Adjaoute and Danthine (2002)

and Hardouvelis et al. (1999) found evidence of correlation between the European markets.This paper examines capital market integration across 15 European countries all of which form part

of the European Union. The countries include: Austria, Belgium, Denmark, Finland, France, Germany,

Greece, Ireland, Italy, Luxembourg, Portugal, Spain, Sweden, The Netherlands and the UK. The question

of integration is examined by testing a European multifactor pricing model. The analysis involves

extracting common factors from a European portfolio which is made up of a combined subsample of

securities from each of the European countries. Thetechnique of maximum likelihood factor analysis is

adopted to extract common factors so as to determine the European factor structure. Once the factor

structure is known, factor scores are subsequently estimated based on the methods of; Thurston

(1935), Bartlett (1937) and Anderson and Rubin (1956), and are then adopted to test the validity of the

European multifactor asset pricing model. Are the European factors priced, in the sense that there is a

risk premium associated with them, and is this risk premium the same across all European countries.

1 Multifactor asset pricing models assume that the return on a security can be explained by common systematic risk factors

(see the Arbitrage Pricing Theory ofRoss (1976, 1977)).
http://dx.doi.org/10.1016/j.intfin.2010.03.007http://dx.doi.org/10.1016/j.intfin.2010.03.007http://dx.doi.org/10.1016/j.intfin.2010.03.007http://dx.doi.org/10.1016/j.intfin.2010.03.007http://dx.doi.org/10.1016/j.intfin.2010.03.007http://dx.doi.org/10.1016/j.intfin.2010.03.007http://dx.doi.org/10.1016/j.intfin.2010.03.007http://dx.doi.org/10.1016/j.intfin.2010.03.007http://dx.doi.org/10.1016/j.intfin.2010.03.007http://dx.doi.org/10.1016/j.intfin.2010.03.007


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D. Morelli / Int. Fin. Markets, Inst. and Money20 (2010) 363375 365

The same risk premium would indicate the same riskreturn relationship for all European countries,

implying full integration across the European capital markets.

Countries of the European Union have over recent years become more integrated primarily as a

result of economic and monetary union, and this paper contributes to the existing literature on capital

market integration by examining the European correlation structure, so as to investigate pricing in

order to test for integration across all 15 European countries. The main findings of this paper are that

common European factors do exist, some of which are priced, and priced equally across some of the

European countries. Full integration is not found, in that the risk premium associated with the factors

is not found to be the same for all countries, implying that diversification benefits exist for investors

looking to invest across the European capital markets.

2. Data

This study uses monthly security returns over a 13-year period, January 1995December 2007.

For each of the 15 European countries 100 securities are selected having continuous data over the

total time period. Returns are calculated in US Dollars.2 To convert the returns in to excess returns,

the one month US T-Bill rate is used to proxy for the risk-free rate. The need to select securities

having continuous data is a requirement of factor analysis, given the need to calculate correlations

which requires simultaneous observations. This clearly introduces a survival bias in to the sample as it

excludes those companies that have merged, been taken over, failed and those that are new listings.3

The European portfolio adopted in this study comprises of a combined subsample of 25 randomly

selected securities from each of the 15 European countries, thereby consisting of 375 securities. The

return on the European portfolio is a value-weighted average of all 375 securities. The selection of an

equal number of securities from each country ensures that no single country or group of countries

dominate the European portfolio, reducing the problem of extracting country specific factors from the

European portfolio. The data is obtained from Datastream.

Table 1 reports the mean, standard deviation, skewness, kurtosis and KolmogorovSmirnov test

for normality for the monthly returns for all 15 countries and the European portfolio over the totaltime period. It can be seen that Sweden and The Netherlands have the highest return whilst Greece

and Portugal offer the lowest. Greece has the highest volatility as measured by the standard deviation

and Austria the lowest. The volatility of the European portfolio is lower than any of the 15 European

countries. The European portfolio can be seen as a more efficient portfolio for any risk averse investor

compared to an investment in country portfolios; Austria, Finland, Greece, Ireland, Italy, Portugal and

Spain, given that it offers a superior riskreturn trade off.

The skewness statistic shows that for all countries apart from Germany and Sweden the returns

tend to be positively skewed, and that the kurtosis levels are not high. The KolmogorovSmirnov test

for normality clearly shows that for all countries, including the European portfolio, the returns do

not depart from normality. One of the requirements in order to use factor analysis is for the security

returns to be multivariate normally distributed. Maximum likelihood factor analysis can be adopted ifthe data is normally distributed, for the assumption regarding normality is required in order to apply

significance tests when attempting to determine the number of factors in the k-factor model. To test

for multivariate normality is complex due to the infinite number of linear combinations of variables

for normality, however given that univariate normality is required for multivariate normality, one can

test for the former. The requirement for normality does introduce an additional bias in the selection

of securities given that those securities with extreme observations are excluded.4

2 Of the 15 European countries, as of yet only 3 have not adopted the Euro as their currency; Denmark, Sweden and United

Kingdom, furthermore for the remaining countries the Euro was only introduced in 1999. The sample thus contains a degree of

exchange rate risk. Due to different currencies throughout the time period of this study all returns are calculated in US Dollars.3 Such a survival bias is common to all empirical studies adopting factor analysis. The greater the time period of the study

the greater the bias. The time period of this paper extends over a period of 13 years and resultantly the survival bias is not as

strong as those studies which extend over greater time periods.4 Table 1 reports the results from the KolmogorovSmirnov test for normality for the average returns for each country over

the total time period. Test are conducted on each security (due to the large sample size the results are not reported for each


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Table 1

Summary statistics over the total time period.

Mean S.D. Skewness Kurtosis KS

Austria 0.976 5.143 0.231 0.33 0.892

Belgium 1.165 5.781 0.416 1.73 0.185

Denmark 1.196 5.821 0.38 1.42 0.454

Finland 0.967 6.835 0.43 1.31 0.521

France 1.078 7.214 0.21 0.72 0.663

Germany 1.097 6.821 -0.18 0.41 0.741

Greece 0.912 7.983 0.43 1.31 0.583

Ireland 0.982 6.023 0.34 0.64 0.412

Italy 0.994 7.832 0.278 0.79 0.257

Luxembourg 1.065 5.724 0.243 0.53 0.512

Portugal 0.914 6.012 0.40 1.21 0.246

Spain 0.945 5.945 0.372 0.97 0.378

Sweden 1.243 6.876 -0.412 1.19 0.312

The Netherlands 1.214 5.723 0.12 0.35 0.892

UK 1.095 6.893 0.253 0.71 0.713

Europe 1.03 4.472 0.217 1.15 0.602

Summary statistics for each European country are based on a value-weighted portfolio returnof all 100 securities in thesample,

and for the European portfolio on a value-weighted average of the 375 securities.

The correlation between the returns of all 15 European countries and also the European portfolio is

shown in Table 2. What is evident to see from Table 2 is that the European countries exhibit a degree of

integration given that the correlations are far from zero, implying a linear relationship between these

countries. Furthermore it can be seen that perfect correlation does not exist, implying that benefits

may exist for international diversification.

3. European multifactor asset pricing model

As previously mentioned, testing for capital market integration across the Europeancapital markets

is performed under the joint hypothesis of a European asset pricing model. The multifactor European

asset pricing model adopted and tested in this paper is given by:

Rt = Ft+ t (1)

where Rt represents 1n row vector of excess security returns at time t, n represents the number of

securities, is a nk matrix of coefficients on the k-factors for each of the n securities, Ft is a 1krow vector of common factors at time t generated from factor analysis, t is a n1 column vectorof idiosyncratic terms for each of the n securities at time t. The idiosyncratic terms are assumed to

be independent of the factors, cov(Ftt) = 0, and identically distributed as a joint multivariate normaldistribution with mean zero E(t) = 0, and covariance matrix D over time, cov(t

t) = 2I = D. The

covariance matrix D is assumed to be diagonal and proportional to the identity matrix, I.

The factors as shown in Eq. (1) represent Europeanfactors extracted and estimated from a European

portfolio adopting maximum likelihood factor analysis. Factor analysis simply involves attempting to

extract a small number of common factors from a large number of interrelated variables, namely the

excess security returns. The relationship between the excess security returns is shown by a correlation

matrix and factor analysis explains this matrix using underlying common factors. A key advantage of

adopting maximum likelihood analysis is that it allows the variance of the excess security returns to

be separated out into their common and unique components resulting in the extraction of common

factors. Maximum likelihood factor analysis not only provides a theoretical reasoning for the estima-

tion process but also allows the use of statistical tests, namely the Chi-square goodness of fit statistic,

security though are available upon request), and for each European country the securities selected comply with the assumption

of normality.


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Table 2

Correlation matrix between portfolio returns of European countriesa .

Austria Belgium Denmark Finland France Germany Greece Ireland Italy Luxembourg Portuga

Belgium 0.315

Denmark 0.189 0.301

Finland 0.303 0.231 0.328

France 0.266 0.287 0.216 0.227

Germany 0.284 0.319 0.305 0.313 0.314

Greece 0.187 0.327 0.275 0.214 0.323 0.201

Ireland 0.243 0.216 0.187 0.228 0.311 0.235 0.251Italy 0.318 0.187 0.218 0.327 0.328 0.342 0.217 0.258

Luxembourg 0.327 0.325 0.264 0.338 0.331 0.318 0.186 0.275 0.162

Portugal 0.203 0.213 0.327 0.187 0.216 0.238 0.198 0.253 0.189 0.231

Spain 0.168 0.276 0.175 0.221 0.238 0.227 0.230 0.289 0.231 0.301 0.301

Sweden 0.269 0.219 0.194 0.285 0.304 0.197 0.218 0.301 0.210 0.175 0.234

The Netherlands 0.176 0.308 0.215 0.319 0.227 0.314 0.206 0.286 0.231 0.198 0.208

UK 0.216 0.317 0.228 0.169 0.318 0.332 0.278 0.341 0.279 0.205 0.271

Europe 0.206 0.275 0.217 0.221 0.297 0.301 0.197 0.261 0.172 0.221 0.238

a Portfolio returns for each European country is a value-weighted average of all 100 securities, and the European portfolio a value-w

country).


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to determine the number of factors to extract.5 Having extracted the common factors a structure then

exists for the k-factor European pricing model.

The use of factor analysis on large samples can cause problems given that a positive relationship

exists between the number of factors extracted and the size of the sample. Extracting many fac-

tors would be of little use when testing for capital market integration as a large factor model would

concentrate more on risk premia associated with country specific factors as opposed to risk premia

associated with common factors between the European countries. To overcome this problem, a restric-

tion is placed on the total number of factors that can be extracted from the European portfolio. The

restriction is based upon the average number of factors extracted from each European country, and

also on the eigenvalue of the average number of factors +1. The eigenvalue represents the total amount

of variance of the excess security returns within each of the portfolios that is explained by the common

factors extracted.

The eigenvalue of the average number of factors + 1 is examined in order to determine whether

the amount of additional variance of the excess security returns within the portfolio explained by this

additional factor is significant. In order to determine the average number of factors extracted from

each European country, given the problems associated with using large samples in factor analysis,

factor analysis is conducted on four randomly divided equal size portfolios of 25 securities for eachEuropean country. From each of these portfolios factors are extracted, and it is the average number of

factors extracted from each of these portfolios, from each of the European countries, that determines

the factor structure that will be applied to the European multifactor pricing model.6

Once the factor structure for the European portfolio has been determined, the factor scores are then

estimated. Due to the indeterminacy problem associated with constructing factor scores, the factor

scores are estimated according to three different criteria.7 The criteria are that the estimated factors

and the true factors should display a high degree of correlation, they should also be univocal, and also

orthogonal. Unfortunately, not one estimator satisfies all three criteria, resultantly three commonly

adopted methods are used, namely; Anderson and Rubin (1956), Bartlett (1937) and Thurstons (1935)

regression method, as shown by Eqs. (2), (3) and (4), respectively.

F = RU2B(BU2SU2B)1/2

(2)

F = RU2B(BU2B)1

(3)

F = R(S1B) (4)

where F is the Tk matrix of factor scores, R is a Tn matrix of excess security returns for theEuropean

portfolio, n represents the number of variables, k the number of factors, B is a nk matrix of factor

loadings, T is the time period, U is a nn diagonal matrix of unique variances, S is a nn sample

correlation matrix of excess security returns.

5 Other methods of factor extraction exist such as, minimum residual factor analysis, image analysis, alpha factor analysis.

These common factoranalysis methods separate thecommon from uniquevariance of thevariablesand in that sense aresimilar

to maximum likelihood analysis,however the methodof determining thenumber of factors to extract is more subjective, unlike

maximum likelihood analysis which adopts statistical tests. It is for this reason why maximum likelihood analysis is adopted

in favour of these other methods of factor extraction. An alternative to these common factor analysis methods used to extract

factor is principal component analysis. Principal component analysis is simply a mathematical transformation of the data. The

factors extracted do not separate out the common from unique variance, and given that it is the common variance that is of

interest, for this reason this method of factor extraction is not applied.6 This approach is necessary given the problems with using large data samples when using factor analysis. Given that max-

imum likelihood analysis adopts the Chi-square goodness of fit test statistic to determine the number of factors to extract,

applying such a test to large sample can result in small discrepancies in fit showing significance, which in turn would result in

a larger factor model. The European market portfolio consists of 375 securities, the application of factor analysis to such a large

data sample would clearly result in such problems. This is overcome by restricting the numbers of factors extracted from theEuropean portfolio based on the criteria discussed.7 This indeterminacy problem exists because factor scores are not unique, primarily due to the fact that each excess security

return contains a factor component and idiosyncratic (unique) component. Factor scores are constructed from a linear combi-

nation of the excess security returns, thus the factor scores will consist of two components; a deterministic linear combination

of the excess security returns and a random vector orthogonal to the excess security returns.


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4. Empirical tests

The pricing model shown by Eq. (1) implies a linear pricing relationship between the expected

excess returns and the k European factors. To test the validity of this pricing relationship, a time-

series regression is undertaken on a country by country basis of all individual security returns from

each European country on the European factors extracted from the European portfolio.

Rt = +Ft+ t (5)

The time-series regression results in estimates of a n1 vector ofs, a nk matrix ofs, and D,a nn unbiased matrix of the covariance matrix of idiosyncratic terms.

Having estimateds from time-series regression given by Eq.(5), for eachcountry a cross-sectionalregression is then performed of excess security return against the s as follows:

R = X (6)

where R represents a n1 vector of monthly excess security returns, n representing the number of

securities, X represents a n (k + 1) matrix, the first column being a vector of ones and the subsequent

k columns a n1 vector ofs estimated from Eq. (5), i s a (k + 1)1 vector of risk premia estimatedfrom a generalised least square regression, where = (XD1X)1XD1R.

Are the returns from individual European countries explained by the k-factor generating model?

Various tests canbe applied to test thevalidityof thepricing relationshipshownby Eq.(6). Withrespect

to the intercept term, given that excess security returns are used, this should equal zero. A simple t-test

can be adopted to test, for each country, the hypothesis Ho: 0 = 0 against the alternative H1: 1 /= 0.Furthermore, one can apply the exact F-test ofGibbons et al. (1989) to test the joint restriction that the

intercept term is equal to zero across all the 15 European countries, which one would expect to find if

these markets were integrated. The Chi-square test is adopted for each European country to test if the

vector of risk premia is statistically significant.8 The hypothesis tested is simply, Ho:1 =2 = =k = 0against the alternative H1: 1 =2 = =k /= 0. With respect to the significance of individual risk

premia, the hypothesis tested is simply, Ho: 1 = 0, 2 = 0, . . . k = 0 against the alternative H1: 1 /= 0,2 /= 0 . . . k /= 0. The hypothesis is tested using the simple t-test. Such tests establish whether theEuropean pricing model is a valid pricing model, in that the tests determine whether the European risk

factors price European countries security returns, which would imply integration across the European

countries. This would not necessarily imply full integration between the European capital markets,

as full integration requires the same price of risk across all the European countries. It is therefore

necessary to test whether the risk premia for corresponding factors equate across all the European

countries. This is tested across all European countries using a paired t-test. A paired t-test is performed

between the time-series estimates of risk premia for corresponding factors between the groups of two

countries.

5. Results

As discussed in Section 3 the number of factors extracted from the European portfolio is determined

by the average number of factors across the European countries and examination of the eigenvalue

of the k + 1 factor extracted from the European portfolio. Table 3 reports, for each European country,

the number of factors extracted from each of the 4 portfolios each consisting of 25 securities, in

addition to the eigenvalue given as a percentage of the total factor model. It can be seen that for each

country the number of factors extracted is not the same, implying that the k-factor return generating

model is not the same across all the European countries. Some of the factors extracted will clearly be

country specific factors, which inturn explains why the k-factor model is not unique across countries.

The finding of country specific factors is expected, however given that country specific factors are

not common to all countries, as the name suggests, they will most probably not be captured by the

8 The test statistic is TkW1

k = 2 where k is simply a vector of average risk premia, W represents a covariance matrix

of time-series estimates of risk premia. The test statistic is 2 distributed with k degrees of freedom.


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Table 3

Number of factors extracted from the European countries.

Austria Belgium Denmark Finland France Germany Greece Ireland

Portfolio 1 5 (52.6%) 7 (58.6%) 6 (60.3%) 5 (47.2%) 5 (47.3%) 6 (61.2%) 5 (48.2%) 6 (40.5%)

Portfolio 2 5 (54.8%) 6 (55.9%) 5 (58.1%) 6 (45.6%) 4 (45.6%) 5 (59.3%) 5 (50.6%) 7 (43.7%)

Portfolio 3 6 (55.2%) 6 (52.1%) 5 (62.1%) 6 (52.2%) 6 (48.2%) 5 (63.6%) 6 (46.4%) 7 (46.4%)

Portfolio 4 5 (51.4%) 7 (57.8%) 4 (60.3%) 6 (50.1%) 6 (53.1%) 6 (60.4%) 7 (53.4%) 6 (44.7%)

Italy Luxembourg Portugal Spain Sweden The Netherlands UK

Portfolio 1 6 (58.3%) 6 (53.4%) 6 (49.5%) 6 (43.2%) 7 (47.5%) 7 (54.8%) 7 (51.2%)

Portfolio 2 6 (55.9%) 7 (57.3%) 7 (47.2%) 7 (46.8%) 7 (49.2%) 7 (51.9%) 6 (54.7%)

Portfolio 3 5 (57.2%) 6 (51.9%) 7 (44.6%) 7 (50.7%) 6 (44.7%) 6 (48.6%) 7 (50.2%)

Portfolio 4 7 (60.3%) 7 (53.8%) 5 (43.8%) 6 (48.4%) 6 (46.3%) 6 (46.2%) 6 (56.7%)

Table reports the number of factors extracted using maximum likelihood analysis from each of the 4 portfolios consist of 25

securities for each of the European countries. The eigenvalue, expressed as a percentage, of the factor model is also shown in

parenthesis.

European portfolio.9 From Table 3 one can determine that the average number of factors extracted

across all the European countries is six. In terms of examining the eigenvalue of the k + 1 factor, namely

the 7th factor, maximum likelihood analysis is performed on the European portfolio and analysis of

the eigenvalue of the 7th factor if found to show no statistical significance. Resultantly, factor analysis

is performed on the European portfolio where the number of factors extracted is restricted to six. 10

For the European portfolio, the eigenvalue of the factor structure is 48.23%, thus almost half of the

variance of the excess security returns that constitute the European portfolio can be explained by

the six common factors. The finding of common factors imply that sources of common risk exist,

however in order to be able to show that the European capital markets are integrated, these common

sources of risk must be priced across the individual European countries, and priced equally to show

full integration.Table 4 shows the results from the cross-section regression equation (6). The results show a strong

similarity across all three methods of factor score estimation. Factor 1 shows significance across Bel-

gium, Denmark, Finland, France, Greece, Italy, Spain, Sweden, and the UK. Factor 2 is priced across

Austria, Belgium, Germany, Ireland, Luxembourg, Portugal, Spain, The Netherlands and the UK. Factor

3 is priced across Austria and Germany and Factor 4 is priced across France and Sweden. Thus, for

these factors for these countries the null hypothesis of no riskreturn relationship is rejected, imply-

ing priced European factors. What is evidently clear is that for all countries a minimum of at least

one factor is priced, though not always the same factor. The Chi-square test shows that for, Belgium,

Finland, Germany, Spain, Sweden and the UK, the null hypothesis that the risk premia vector is not

statistically significant is rejected. The cross-sectional regression across all the European countries

results in factors one and two showing statistical significance, along with a statistically significantrisk premia vector. The results also show that the Chi-square statistic does not change according to

the method of factor score estimation (Thurston, 1935; Bartlett, 1937; Anderson and Rubin, 1956).

Dependent upon the method used to estimate the factor scores, the amount of variance of the security

returns explained by individual factors can change, however the total amount of variance explained

by all the common factors does not change.

The results with respect to testing the hypothesis relating to the intercept term show that for all

European countries, with the exception of Germany (at the 10% significance level), one fails to reject

9 Clearly the possibility doesexist that country specific factors may be extracted froma European portfolio. The factors capture

the correlations between the security returns, and if strong correlations exist between the returns within specific countries thismay be captured by a factor. Such occurrences would be more probable with large factor structures, a problem that has been

avoided in this study given the restrictions applied when determining the factor structure of the European portfolio.10 Restricting the factor model to six factors is due to the problems associated with large samples. The eigenvalue of the K+ 1

factor (7th factor) for the European portfolio is 1.16, which equates to only 0.31% of the variation in the returns of the European

portfolio.


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Table 5

European countries having the same price of risk.

Risk

premia

Price of risk the

same across all

seven countries

Countries showing the same price of risk

Factor scores estimated using

Anderson-Rubin Bartlett Thurston

1 No Belgium and Denmark and

Greece, Italy and France

and Spain

Belgium and German,

Finland and France and

Spain and Sweden, Greece

and UK

Belgium and Denmark and

Greece and Spain and

Sweden, German and

Austria

2 No Austria and Belgium and

The Netherlands, Finland

and Italy, Ireland and

Portugal

Austria and Germany and

The Netherlands, Ireland

and Portugal, Spain and UK

Austria and Belgium and

Germany, Italy and Finland,

Ireland and Luxembourg

and Spain and UK

3 No Denmark and Finland,

Belgium and Greece and

Luxembourg and UK

Austria and Denmark,

Spain and Sweden,

Belgium and France and UK

Denmark and Finland and

Greece, Ireland and Italy,

Greece and Luxemburg4 No Finland and Italy and

Luxembourg and Portugal

and UK

Belgium and Denmark,

Austria and Germany,

Finland, and Luxembourg

and Portugal

Belgium and Greece,

Denmark and Italy and

Luxembourg and UK

5 No France and Greece and

Sweden, German and Italy

and The Netherlands

Denmark and Germany

and Portugal, Belgium and

Greece and Ireland and

Portugal and UK

Austria and Belgium,

Finland and Ireland,

Luxembourg and Sweden

and UK

6 No Denmark and Finland and

France and Greece and

Italy and Portugal and UK

Belgium and France and

Italy and Sweden and UK

Denmark and Germany

and Ireland andThe

Netherlands

The table reports those European countries in which the price of risk (risk premia) is found to be the same. Results are shown

for all three methods of factor score estimation; Anderson-Rubin, Bartlett or Thurstons methodology.

the null hypothesis that 0 = 0. In terms of testing the joint restriction that the intercept term acrossall countries are zero, application of the exact F-test ofGibbons et al. (1989) produces a F-statistic of

1.03, thus failing to reject the null hypothesis that the intercept term is zero across all countries. 11

Despite that fact that some of the factors are priced, and for some countries the vector of risk

premia is statistically significant, the European pricing model is not found to be a valid model across

all the European countries. This is the case irrespective of whether the Anderson and Rubin (1956),

Bartlett (1937) and Thurstons (1935) regression method is used to estimate the factor scores. The

results from Table 4 show that for 9 out of the 15 countries the European multifactor asset pricing

model does not hold, thus integration across all the 15 European countries is not evident to see.

On performing cross-sectional tests across all European countries, rather than individually, the nullhypothesis of an insignificant risk premia vector is rejected, from which one can conclude a degree

of European market integration. However the rejection of the null hypothesis of an insignificant risk

premia vector is influenced by the strong cross-sectional results for Belgium, Finland, Germany, Spain,

Sweden and the UK.

In terms of determining whether the price of risk is the same across all 15 European countries,

summarised results are reported in Table 5. It is clear to see that some factors have the same risk

premia across a number of countries, implying a degree of integration between these capital markets.

From analysing Factor 1, given that this out of all the factors is the most important factor, as it explains

the largest proportion of the total variance of the European portfolio, it can be seen that a number of

European countries do have the same price of risk. Although it is found that a degree of integration is

11 The coefficients of the intercepts are not sensitive to the method of factor score estimations. The method of factor score

estimation only effects the proportion of variance of the variables explained by the factors and as a result will not influence the

intercept term.


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evident across some of the European countries, given the same price of risk, this is clearly not the case

across all countries. Such findings indicate the absence of full European capital market integration.

The results are not surprising given that capital market integration can only be tested under the joint

hypothesis of an European asset pricing model, which clearly does not hold across all 15 European

countries.

6. Conclusion

Countries of the European Union have, over the years, become more integrated as a result of growth

in international trade, in services and financial assets, and for a number of countries as a result of mon-

etary union. Capital market integration implies that individual capital markets move in a similar way,

and as a result of this have high correlations, which in turn implies reduced benefits from international

portfolio diversification. This paper examines the covariance structure of a European portfolio made

up from a subset of securities from each of the 15 European countries, in an attempt to determine

whether these capital markets are integrated. Integration of the capital markets is tested under the

joint hypothesis of a European multifactor asset pricing model.Results show that common factors exist, some of which are priced. For some countries the price

of risk is found to be the same, implying that their capital markets are closely related, however this

is not the case for all 15 European countries of the European Union. A degree of integration is found

to exist between some European countries, however based on the empirical analysis from testing a

European multifactor asset pricing model it is evident that the hypothesis of full integration across

all the European countries is not shown to hold. Such findings imply that to an international portfo-

lio investor there are benefits of diversification from investing across the European capital markets,

though between some of the European countries this benefit has been slightly reduced due to the

integration of the these capital markets.

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