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Capital market integration: evidence from the G7

countriesDavid Morelli

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

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To cite this article: David Morelli (2009): Capital market integration: evidence from the G7 countries, Applied FinancialEconomics, 19:13, 1043-1057

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Applied Financial Economics, 2009, 19, 10431057

Capital market integration:

evidence from the G7 countries

David Morelli

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

E-mail: [email protected]

This article examines whether the capital markets of the G7 countries are

integrated. Capital market integration is examined under the joint

hypothesis of an international multifactor asset pricing model.

International factors are extracted from a world portfolio using both

maximum likelihood analysis and principal component analysis. Results

show that international common factors exist, some of which are priced

and equal across some countries, however, the international pricing model

does not hold for all G7 countries. The price of risk is not found to be the

same across all countries and the hypothesis of full capital market

integration is not supported.

I. Introduction

The extent of integration between the world capital

markets is clearly of importance in the finance world

with respect to investment selection and financingdecision. If the world capital markets are perfectly

integrated then the same asset pricing relationship

would exist for all countries, with the reward for risk

being the same irrespective of which market one

invests in. The absence of integration would imply

that the risk return relationship differs across

countries, which would lead to arbitrage opportu-

nities in that investors could simply adjust their

portfolio by investing in countries offering a greater

return whilst maintaining the same level of risk.

If the capital markets of different countries are

integrated, the expected return of a security orportfolio of a particular country should be deter-

mined solely by its exposure to the worlds risk factor

or factors, depending on whether one assumes a

single or multifactor pricing model. Failure to show

this would indicate that the relationship between risk

and return is explained by domestic and not world-

wide factors.

The existence of nonintegration across financial

markets is most likely to be due to factors such as,

market imperfections, the existence of differing ratesof taxation or restrictions imposed by the markets or

countries on the ownership of securities (Eun, 1985;

Eun and Janakiramanan, 1986). Studies by Divecha

et al. (1992), Michaud et al. (1996) and De Fusco

et al. (1996) found the lack of integration across

international markets was due primarily to barriers to

international trade and investment, insufficient infor-

mation on foreign securities and simply a bias by

investors to home securities.

Various studies have been conducted to test for

international integration across various financial

markets. Early studies focused on a single riskfactor as a proxy for the market portfolio in an

international capital asset pricing model. Solnik

(1974) found evidence in support of integration

between various European countries and the United

States. Jorion and Schwartz (1986) on examining the

Applied Financial Economics ISSN 09603107 print/ISSN 14664305 online 2009 Taylor & Francis 1043

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DOI: 10.1080/09603100802167262

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integration of the Canadian stock market relative to a

global North American market failed to find evidence

of integration. Campbell and Hamao (1992) found

evidence of common movement in expected excess

returns across the United States and Japan. Chou and

Lin (2002) found evidence in support of an interna-

tional pricing model across 17 developed countries,

which included all those within the G7. Empiricalstudies have also employed cointegration techniques

to examine the interdependence between the world

stock markets. Byers and Peel (1993) tested for

multivariate cointegration between the stock markets

of the US, UK, Japan, Germany and the

Netherlands, and found, with the exception of

the UK and Japan, no evidence to suggest that the

international stock markets were cointegrated. Kanas

(1998) found that the US stock market was not

pairwise cointegrated with any of the major

European stock markets. Empirical studies also

focused on multifactor asset pricing models.

Evidence against integration was found by Gultekin

et al. (1989) examining the USA and Japanese stock

markets, and also Korajczyk and Viallet (1989)

examining the capital markets of the United States,

Japan, France and the UK. Evidence supporting the

hypothesis of capital market integration was found

by Heston et al. (1995) examining the capital markets

of Europe and the USA, Cheng (1998) examining the

UK and US stock markets and also Swanson (2003)

examining three major financial markets, namely

Japan, Germany and the USA. A recent study by Vo

and Daly (2005) found little evidence of integration

between European equity markets and concluded thatdiversification benefits within Europe exist for US

investors.

This article examines whether the capital markets

of the G7 countries, namely, Canada, France,

Germany, Italy, Japan, the UK and the USA are

integrated. Empirical tests of integration require an

international asset pricing model. The use of an

international asset pricing model assumes that the

capital markets are integrated, for if they were not

integrated the pricing model would not hold. Thus,

the question of capital market integration is tested

under the joint hypothesis of an international asset

pricing model. In the empirical implementations in

this article it is assumed that returns follow a

k-factor structure, thus a multifactor international

asset pricing model is adopted.1 Pricing securities

on the basis of an international multifactor

pricing models implies that the only priced

risk should be the systematic risk relative to the

world factors. With an international pricingmodel domestic systematic factors should be

diversified away.

The extent to which countries of the G7 share

common factors is examined by extracting factors

from a world portfolio consisting of a combined

subsample of securities from each of the G7

countries. A global factor structure is obtained

using two well-known methods of factor extraction,

namely, principal component analysis and maximum

likelihood analysis. Factor scores are then con-

structed using three commonly used methods:

Thurston (1935) regression method, Bartlett (1937)

and AndersonRubin (1956). The factor scores can

then be used as proxies for the factors and used in

subsequent tests to determine whether the interna-

tional multifactor asset pricing model holds. Do the

factors command a risk premium? Is the risk

premium equal across countries thereby implying

that the reward for risk is the same irrespective of

which country one invests in? Such a finding is

essential in order to show that the G7 capital markets

are fully integrated.2 This article explicitly

differentiates between security returns being corre-

lated internationally, and financial integration. High

international correlations are at least as much aboutcorrelated fundamentals as they are about

integration, and this article investigates pricing in

response to these putative correlated international

factors. This article contributes to the existing

literature on capital market integration, and as far

as I am aware that the methodology adopted in this

article has not been attempted in any of the existing

literature.

This article is organized as follows. The data and

corresponding statistics is discussed in Section II.

Section III discusses the international asset pricing

model. Section IV discusses the two methods used to

1 Asset pricing models explain the relationships between security returns and a common factor or factors. Asset pricingmodels, whether single or multifactor, are based on the notion that security returns can be explained by systematic riskfactors. The most well-known multifactor asset pricing model being the Arbitrage Pricing Theory of Ross (1976, 1977).2 Market integration could be determined by examining the returns on two portfolios of securities from two different countriesthat are perfectly correlated. If perfect market integration exists the price of such securities should be exactly the same, sinceany disequilibrium in the price would lead to arbitrage opportunities upon which equilibrium would be quickly restored.Theoretically this makes perfect sense; however, in practice it is almost impossible to construct these perfectly correlatedportfolios and thus virtually impossible to test.

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extract factors, maximum likelihood and principal

component analysis. Section V discusses the methods

by which the factor scores are estimated. Section VI

discusses the empirical tests. Empirical results arepresented in Section VII, and the conclusion is

presented in Section VIII.

II. Data

The data is collected from Datastream and consists

of monthly security returns from each of the G7

countries over the period January 1990 to December

2000.3 A total of 160 securities for each country were

selected with data covering the total period.4 All

returns are calculated in terms of US dollars, and themonthly return on a 3-month US Treasury Bill is

used as the risk free asset. The world portfolio used in

this article consists of a combined subsample of 50

randomly selected securities from each of the seven

countries (thus a value weighted average of 350

securities).5

Table 1 shows the monthly mean percentage return

for each country in addition to the world portfolio

calculated in terms of US dollars, along with the

SD, skewness, kurtosis and the Kolmogorov

Smirnov test for normality. The mean monthly

returns range from 0.794% for Canada to 1.117%

for the UK. With respect to the SD, which is a

measurement of volatility, its value ranges from

4.892% for the world portfolio to 8.932% for Italy.

Given that the world portfolio has the lowest SD this

clearly shows the benefit of risk reduction by

diversifying away unsystematic risk. With respect to

examining the risk return relationship it is shown that

the world portfolio offers a higher return than

Canada, France and Germany for a lower SD, thus

a rational investor would be advised to invest in theworld portfolio as apposed to either of these three

national markets given the better risk return

relationship.

With respect to skewness, with the exception of

France and the USA, all other countries in addition

to the world portfolio are positively skewed.

Table 1. Summary statisticsa

Countryb Mean (%) SD (%) Skewness Kurtosis KSc

Canada 0.794 5.103 0.138 1.12 0.476France 0.918 7.302 0.108 0.87 0.694Germany 0.942 7.930 0.082 1.33 0.401Italy 1.042 8.932 0.207 0.71 0.732Japan 1.101 6.619 0.361 1.16 0.431UK 1.117 7.036 0.219 0.68 0.703USA 1.081 5.729 0.349 0.95 0.657World 0.961 4.892 0.131 1.07 0.491

Notes: aStatistics provided over the total sample period.bStatistics for each country is based on a value weighted average of all 160 securities, and for the world portfolio avalue weighted average of 350 securities (50 from each country).cp-value of the KolmogorovSmirnov test for normality of returns.

3 The use of monthly returns, as opposes to say daily, avoids the problems associated with thin trading, primarily causingbiases when estimating the correlation matrices from which the factors are then extracted.4 The use of factor analysis requires the sample selected to have simultaneous observations given that this is required tocalculate the correlations. Given this requirement, only securities that have continuous data over the total period are selected.

This naturally introduces a survival bias into the sample given that a number of firms will be excluded, for example,companies that have failed, or are newly listed, or those that have simply merged or been taken over. Such a survival bias iscommon to all empirical tests requiring the use of factor analysis, and increases with the length of the sample period. Thesample size, 160 securities from each of the G7 countries, consists of securities from a number of different industry groups,thus representing a fair distribution of industries and should not be considered a sector specific sample. It is important for areasonable number of securities to be contained in the sample. The sample size adopted in this article is believed to satisfy thiscondition.5 Given the need to extract factors from the correlation matrix of security returns that constitutes the market portfolio, andalso the need to estimate factor scores, the market portfolio adopted cannot consist of an index, but must consist of a sampleof securities from all countries. The market portfolio consists of a subsample of securities from each country, for if the marketportfolio had consisted of all securities, this would have resulted in a 1120 1120 correlation matrix (160 securities 7 countries), well beyond the software capabilities with respect to computing factor loadings.

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Kurtosis levels are not large, and the Kolmogorov

Smirnov test for normality is not rejected for all G7

countries and the world portfolio.6

Table 2 shows the correlation matrix between all

seven countries and also the world portfolio. Two

important inferences can be made from Table 2, first

that linear relationships exist between the G7

countries given that the correlations are far from

zero, and secondly given that the correlations are also

far from unity, the possibility exists for international

diversification.7

III. International Asset Pricing Model

Testing for integration across the G7 capital

markets requires an international asset pricing

model, given that one needs to determine whether

the price of risk is the same across all countries.A valid international asset pricing model itself

implies integration across the international capital

markets. In this article, the international

asset pricing model used is a multifactor model

given by:

Rit i1F1t i2F2t ikFkt "it 1

Or in matrix notation:

Rt F0

t "t 2

where Rt is a 1 n row vector for n excess security

returns at time t, Ft i s a 1 k row vector of

observations on the common factors at time t

generated by using factor analysis, B is an n kmatrix of coefficients or loadings on the k factors for

each of the n securities, "t is an n 1 column vector of

idiosyncratic terms for each security at time t.

The return generating process is composed of two

components, a common component and an idiosyn-

cratic one. It is assumed that the idiosyncratic terms

are independent and identically distributed as a joint

multivariate normal distribution with mean zero

E("t) 0, and covariance matrix D over time,

cov("t"t0) 2I D, which is diagonal and propor-

tional to the identity matrix.8 In addition, it is

assumed that the idiosyncratic terms and the factors

are independent of each other, cov(Ft"t) 0. Theassumption relating to the covariance matrix D of

idiosyncratic terms implies that the idiosyncratic

variances equate to one another thereby allowing

the use of principal component analysis to estimate

the return generating factor model shown by

Equation 2. This assumption is not required when

using maximum likelihood analysis, thus the

Table 2. Correlation matrix between all G7 countries portfolios and also the world portfolioa

Canada France Germany Italy Japan UK USA

France 0.201Germany 0.354 0.374Italy 0.168 0.291 0.363Japan 0.182 0.206 0.154 0.148UK 0.254 0.282 0.308 0.325 0.176USA 0.337 0.261 0.274 0.334 0.263 0.392World 0.244 0.287 0.271 0.257 0.221 0.284 0.331

Note: aSee footnote b from Table 1.

6 Factor analysis requires multivariate normal distribution of the security returns. Maximum likelihood factor analysis can beused when one assumes the data to be normally distributed, thereby allowing the use of significance tests on the factorsextracted. It is difficult to test for multivariate normal distribution given the numbers involved; however, one can test forunivariate normality given that this is required for multivariate normality. Table 1 reports the results for average returns for

each country. (For individual securities the results are not reported due to large amounts of data though are available uponrequest). The requirement of multivariate normal distribution itself creates an additional bias in the sample to that alreadydiscussed in footnote 4. Those companies that have abnormally high or low returns during periods within the data period willnot be included. Clearly by using monthly returns, any extremities in returns will tend to be smoothed out, though if daily orweekly data has been used the results with respect to the requirement of normality may not have been so favourable.7 Table 2 reports, in some cases, low correlations between the returns of various countries. The correlation coefficient is ameasure of linear association or linear dependence only and has no meaning for describing nonlinear relations. It is possiblethat low correlations, such as those shown for some countries in Table 2, may originate as a result of the hypothesis of linearcorrelation being false; however, tests performed to determine whether this could be the case clearly indicate that no nonlinearrelationships exists. (The results from this test are available upon request).8 The assumption with respect to the diagonal matrix implies that the idiosyncratic terms across the different securities are, onaverage, uncorrelated over time.

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idiosyncratic variances can differ from each other;

however the assumption that returns follow a multi-

variate normal distribution is required instead.

The pricing relationship as shown by Equation 2 is

examined. The factors represent world factors, and

given that they are unobservable, they are extracted

and estimated from the world portfolio using the

statistical technique of factor analysis. Factor analy-sis begins with a T n matrix of excess security

returns, the relationship between these returns is

shown by the correlation matrix, and factor

analysis attempts to simplify this matrix such that it

can be explained in terms of a small number of

underlying common factors (factor analysis is

discussed in more detail in the next section). Tests

are conducted, as discussed in Section VI, testing the

validity of the k-factor international pricing model

and integration of the capital markets across the

G7 countries.

IV. Factor Analysis

Factor analysis has been around for many years, first

developed by Spearman (1904) using mathematical

models in a study of human ability. Factor analysis is

simply a statistical technique that can be used to

identify a small number of common factors that

explain the relationship between a number of inter-

related variables, in this case security returns. The

correlation matrix shows the relationship between the

security returns, thus the objective is simply to

reproduce the correlation matrix with a small

number of common factors. There are two commonly

used methods of extracting factors from a sample

correlation matrix, namely principal component

analysis and maximum likelihood analysis (Lawley

and Maxwell, 1971). Their difference lies with the

amount of variance of the variable that is to be

explained. In this article, both methods are used to

extract factors from the correlation matrix of returns

from each of the G7 countries and also the world

portfolio.

Principal component analysis and maximum like-

lihood analysis differ with respect to the assumption

that is made regarding the amount of the unit

variance of each variable (security return) which is

to appear in the common factors, referred to as the

communality. It is the figure placed in the diagonal of

the correlation matrix that determines this, given that

the diagonal value in the correlation matrix repre-sents the total amount of variance of a variable

distributed among the common factors. With princi-

pal component analysis, unity (the number one) is

entered in the diagonal of the matrix, thus all the

variance of the variable is explained by the factors.

There is no unique factor in the model as all the

variance of a variable is treated as being common.

Given this, if the number of factors extracted equalled

the number of variables, 100% of the variance of all

the variables would be accounted for.9 Clearly a

criteria needs to be selected so as to determine how

many factors to extract that represent the correlation

matrix. The Kaisers criterion is a method that isoften adopted. When applying the Kaisers criterion

the eigenvalue is examined given that this represents

the total variance explained by each factor. Given

that factors with eigenvalues less than one are no

better than individual variables, only those factors

with eigenvalues greater than one are extracted, as

they are looked upon as common factors.10

Clearly it would be beneficial if one could separate

the common from the unique variance given the

importance of the common variance. In order to do

this, one would require, before commencing, some

knowledge regarding the communality of a variable,

and place this value in the diagonal of the correlation

matrix, thus allowing for unique variance to be built

into the model. This is the principle underlying

maximum likelihood factor analysis and represents

the fundamental difference between the two methods.

One needs to determine what value to enter in the

diagonal of the correlation matrix. Unlike with

principal component analysis the initial communal-

ities have to be less than one, given that we are

concerned only with the common variance. The

multiple R2 from the regression equation that predicts

9

It would be fruitless to extract as many factors as there are variables given the aim of factor analysis is to explain acorrelation matrix in terms of a few underlying factors.10 There do exist other criteria, in addition to eigenvalues greater than one, to determine how many factors to correctly retain.These include, the criteria of substantive importance, the Scree-test, and also the criteria of interpretability and invariance.The criteria of substantive importance simply sets a criteria at which one would consider a factor to be substantivelyimportant. So if one considers important factors as those that explain a minimum of 5% of the variance of the variables, thecriteria set would be 5%. The percentage of the variance of the variables explained by the factors is simply a percentageversion of the eigenvalue. The Scree-test involves plotting the eigenvalue against each corresponding factor. The number offactors to retain is represented by the point where the eigenvalues begin to level off (so-called Scree as it represents the rubbleat the foot of a mountain). This criterion is very subjective as one can find more than one break in the graph. The criteria ofinterpretability and invariance attempts to combine various rules and accepts decisions that are supported by a number ofcriteria. This method is extremely illusive. Given the above, it is for these reasons why the eigenvalue criteria is adopted.

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that variable from all other variables is used as the

initial estimate of the communality of a variable. The

Chi-square goodness-of-fit statistics for the adequacy

of the model is used to determine the number of

factors to extract. Factors are simply added one at a

time until the Chi-square statistics no longer shows

significance at the 10% level.11

The main difference between principal componentanalysis and maximum likelihood analysis, in terms of

the extracted factors, is that, because with principal

component analysis the communality (the diagonal

element in the correlation matrix) is equal to one,

common and unique variance is not separated out.

The extracted factors therefore capture all the variance

of the variables, because it is the variables that

determine the factors, and that the variables consist

of both common and unique variance. With maximum

likelihood analysis, because the communality is not

equal to one, common and unique variance is

separated out, thereby resulting in common factors.12

When dealing with large samples, such as the world

portfolio, the methods used to extract factors can

result in the extraction of a large number of factors.13

With principal component analysis, using the Keiser

criterion can result in many factors having eigenva-

lues that are greater than one, though at the same

time being very close to one, which is not ideal. With

respect to maximum likelihood factor analysis, with

large sample sizes the goodness-of-fit statistics can

cause small discrepancies in fit to be statistically

significant which in turn will result in a larger number

of factors then is required being extracted. A large

factor model would be of no benefit when examiningcapital market integration given that it would not

focus on risk premia for the common factors between

countries. Given these problems with large sample

sizes, the number of factors extracted from the world

portfolio is restricted to a fixed number based on two

criteria, firstly the average number of factors

extracted from each of the G7 countries, and

secondly, examination of the eigenvalue of the

average number of factors 1, so as to determinehow much additional variance of the variables is

being explained by this additional factor (this is

discussed further in Section VII). With respect to the

first of these criteria, the factors extracted from each

of the G7 countries are not extracted from a single

portfolio consisting of all 160 securities, due to the

problem discussed earlier relating to the extraction of

factors from large samples, instead the securities of

each country are randomly divided into four equal

portfolios of 40 securities and factor analysis

conducted on each group. The average of the

number of factors extracted, across all the portfolios

of all the G7 countries, is adopted with respect to

these criteria in terms of determining the number of

factors to be used to explain the world portfolio.

Restricting the number of factors is necessary due to

this positive relationship that exists between the

number of factors and portfolio size.

V. Factor Scores

Having estimated the factor structure for the world

portfolio, the next step is to estimate the factorscores.14 Factor scores are constructed from a linear

11 Other methods of extracting risk factors do exists, such as, principal factor analysis, minimum residual factor analysis,image analysis and alpha factor analysis. These are different methods of common factor analysis. These methods are similarto the maximum likelihood analysis in that they separate the common from unique variance. Given this family of techniquesthat extract common factors, this article only adopts maximum likelihood analysis given its key advantage in that it adoptsstatistical tests for the significance of the factors extracted, which is the most satisfactory solution from solely a statisticalviewpoint.12 Given that with principal component analysis the factors are derived from the actual correlation matrix of the variables,the factors extracted are termed real factors, also referred to as components. With maximum likelihood analysis, because thecommunalities are estimated (is

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combination of the observed variables (excess

security returns R) as shown by Equation 3.

Fj wj1R1 wj2R2 wjnRn 3

where Fj represents the j-th factor, wji represents the

factor score coefficient for the j-th factor and

the i-th variable, where i 1,. . .

, n (n representingthe number of securities in the world portfolio,

namely 350).

When maximum likelihood analysis is used to

extract factors, it is not possible to exactly identify the

common factors from the variables due to the fact

that each variable consists of a factor component, as

given by its communality, and an idiosyncratic

component, which represents its uniqueness. In

terms of common and unique factors, this can be

expressed as shown by Equation 4.

Ri i1F1 i2F2 ikFk Ui 4

where F represents the common factors, U represents

the unique factor, unique to the i-th variable. Given

that the factor scores are a linear combination of the

observed variables, as shown by Equation 3, there

thus exists a degree of indeterminacy when construct-

ing the factor scores.

The problem with constructing factor scores is

that there does not exist a unique method. Given

the indeterminacy problem that exists when con-

structing factor scores, three criteria are applied to

the estimated factor scores. First, the estimated

factors should be highly correlated with the true

factors. Second, the estimated factors should beunivocal, in that they should be highly correlated

with the corresponding true factors and no other

factors, and finally, the estimated factors should be

orthogonal. Given that there does not exist one

estimator that can satisfy all the above criteria,

three well-known estimating methods are adopted,

namely: AndersonRubin (1956), Bartlett (1937)

and Thurstons (1935) regression method.15

AndersonRubin is orthogonal but not univocal,

the Bartlett method is univocal but not orthogonal

and the Thurston method does not meet the

orthogonal nor univocal criteria though is superior

with respect to the estimated factors correlatinghighly with the true factors. For each of the

three methods, the factor scores are estimated as

follows:

Anderson Rubin F R0U2

BB0U2

SU2B1=2

5

Bartlett F R0U2

BB0U2

B1 6

Thurston F R0S1B 7

where F represents a T k matrix of factor scores, R

is a T n matrix of observed variables (excess

security returns for the world portfolio), B is an

n k factor loading matrix, U is an n n diagonal

matrix of unique variances, S is an n n sample

correlation matrix of observed variables, Trepresents

the time period, n and k the number of variables and

factors, respectively.

When principal component analysis is used,

because it is an exact mathematical transformation

of the variables, and as a result the problem ofindeterminacy discussed earlier does not apply, all

three methods, AndersonRubin, Bartlett and

Thurstons regression method will result in identical

exact factor scores and not estimates.16 With max-

imum likelihood analysis, all three methods result in

different factor scores.

VI. Tests for Integration of the G7Capital Markets

Once the factor scores are estimated for the world

portfolio tests can be carried out to determine

whether individual country security returns are

correctly priced by the world factors. The pricing

model as given by Equation 1 states that there exists a

linear pricing relationship between the expected

excess return and the k world factors. In order to

test this, firstly a time-series regression of all

individual security returns from each country on the

world factors is performed. This is carried out on a

country-by-country basis.

Rit i i1F1t i2F2t ikFkt "it 8

15 There is another method that can be adopted to construct factor scores, namely, least square criterion. As the least squarecriterion is similar to Thurstons (1935) regression method, it is not adopted in this article. One could also construct factor-based scores, which involves the simple summation of variables having large factor loadings. This method considers onlyvariables with a factor loading above a given value, and a factor-based score is created from these chosen variables. Thisapproach utilizes information from factor analysis, namely the factor loadings, to create the factor-based scores. As thismethod creates more factor-based scores than factor scores, it is not adopted in this article.16 Recall that with principal component analysis, the factors account for all the variance in the correlation matrix, there is noseparate unique variance, thus Equation 4 would not include the unique factor U.

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where Rit represents security is excess return at time t

(i 1, . . . , n, where n 160 securities), Fjt represent

the factor scores at time t (j 1, . . . , k factors), i and

ik represents the parameters to be estimated with ijrepresenting the sensitivity of the i-th security to the

j-th factor where j 1, . . . , k, "it, the idiosyncratic

term for i-th security. The resulting time series

regression results in estimates of an n 1 vector ofIs, an n k matrix ofijs, and D which is simply an

n n unbiased matrix of the covariance matrix of

idiosyncratic terms.

One then performs, for each country, a cross-

sectional regression of excess security return against

the s estimated from the time series regression.

Given that the data sample used consists of monthly

observations spanning 11 years, a total of 132 cross-

sectional regressions are conducted for each country

(one cross-sectional regression for each month t). The

cross-sectional regression is shown as follows:

Ri 0 1i1 2i2 kik 9

Or in matrix notation;

R X& 10

where R is an n 1 vector of monthly excess security

returns for n securities, X is an n (k 1) matrix, the

first column of which is a vector of ones and the next

k columns representing an n 1 vector of systematic

risks estimated previously from the time series

regression given by Equation 8, & i s a (k 1) 1

vector of risk premia to be estimated. Estimation of

& is obtained by employing a generalized least square

regression procedure, where & (X0D1

X)1

X0D1

R.The above regressions are carried out for each

country. Thus for each country, 160 time-series

regressions are performed and 132 cross-sectional

regressions, resulting in the estimation of 132 k risk

premia, the mean of these risk premia is then

calculated upon which test are conducted. Does the

k-world factor generating model explain the returns

from individual G7 countries? In order to determine

whether the pricing relationship as given by

Equation 10 holds, for each individual country the

Chi-square test is employed to determine the signifi-

cance of the vector of risk premia.17 The t-test is

employed to determine the significance of individual

risk premia, and also to test whether the intercept term

is zero.

As previously discussed, integration of the capital

markets requires an international pricing model to

price risk. The above tests would determine if the

international pricing model holds, in that individual

country security returns are properly priced by theworld risk factors. This itself would imply integra-

tion; however, it does not automatically imply that

the capital markets of the G7 are fully integrated. For

full integration to exist the price of risk must be the

same across all countries. With respect to determining

whether capital markets are fully integrated, an

additional hypothesis is tested, namely, the hypoth-

esis that the risk premia for corresponding factors are

the same across all the G7 countries, thereby

indicating that risks are priced equally across

countries. To test this a paired t-test is conducted

between time series estimates of risk premia for

corresponding factors between groups of two coun-

tries. This is performed across all countries.18

A further test can be performed with respect to the

intercept term. As previously discussed, the intercept

term is tested to determine whether it equals zero for

each individual country. Additionally, one can test a

joint hypothesis that the intercept terms across all G7

countries are zero. The exact F-test of Gibbons et al.

(1989) is employed to test this hypothesis.

VII. Results

Table 3 shows the number of factors extracted from

each of the four portfolios (each consisting of 40

securities as explained in Section IV) for each

individual country, and also the eigenvalue expressed

as a percentage of the total factor model, using both

maximum likelihood and principal component ana-

lysis.19 Depending on the method used to extract the

factors, the number of factors extracted differs for

each of the G7 countries. If one accepts a k factor

return generating model, then the existence of

differing number of factors indicates that this

return generating model is not unique across the

17 The test involves testing the null hypothesis that l1 l2 lk 0 against the alternative 60. The test statistic is given asTlk W

1l

0k

2, where W is the covariance matrix of the time series estimates of risk premia, lk is a vector of mean riskpremia. The test statistic is 2 with k degrees of freedom.18 Testing, for example, whether the price of risk in the UK is the same as for the USA for international factor 1,l1UK l1USA, is tested adopting a paired t-test with null hypothesis l1UK l1USA 0 against the alternative 6 0. Clearly forfull integration the price of risk must be the same across all countries.19 The purpose of this is to compare the factor structure across the G7 countries and to use this information to impose a globalfactor structure based on the world portfolio. One could have conducted inter-battery factor analysis between two countriesfor all countries in an attempt to extract common factors, or also canonical correlation to determine whether countries sharecommon factors; however, both of these methods have been conducted in previous research and thus are not attempted here.

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G7 countries. A possible reason for this is due to the

existence of country-specific factors. Such factors are

unlikely to be captured by the world portfolio as they

are not common to all countries.20 The average

number of factors extracted across the G7 countries is

seven, based on maximum likelihood factor analysis

and eight based on principal component analysis.

Thus, maximum likelihood analysis and principal

component analysis is performed on the world

portfolio, restricting the number of factors to this

amount.21 Based on the maximum likelihood analy-

sis, the eigenvalue of the factor structure of the world

portfolio is found to be 43.61% and with principal

component analysis, 46.28%. The existence of

common factors extracted from the world portfoliodoes not indicate that the markets are integrated;

however, it is of importance given that one can only

test whether the price of risk is the same across

countries if common sources of risk exists.

Table 4 shows the results from testing the pricing

relationship as given by Equation 10, where the

factors are extracted using principal component

analysis. The table reports, with respect to each

country, the average coefficients and corresponding

t-statistics testing whether the intercept is zero and

whether the risk premium for each factor is priced,

and also the results of the joint 2 test for the vector

of risk premia. When examining individual risk

premia associated with the factors for each country,

we can see that even though the majority of the

factors are not priced, a number of factors are priced.

Factor 1 is priced across four countries, namely

Canada, Japan, Germany and the USA. Factor 2 is

priced across the UK and USA, and factor 4 across

Canada, Italy, Japan and the USA. What is clear to

see, however, is that the same factors are not priced

across all countries. With respect to the 2 test, the

results show that for three countries, Canada, Japan

and the USA, the hypothesis that the risk premiavector is not statistically significant is rejected. It is

important to recognize that this test is biased in

favour of the null hypothesis (Type II error) given

that all the factors are included in this test, the

majority of which are not significant. One could

simply repeat the test with a reduced number of

factors, however, this would create a bias against the

null hypothesis. By incorporating all the factors the

power of the test is clearly reduced. Table 4 also

Table 3. Number of factors extracted from G7 countries and world portfolioa

Canada France Germany Italy Japan UK USA

Panal A: Based on maximum likelihood analysisPortfolio 1 6 (48.32%) 6 (53.45%) 5 (49.72%) 6 (48.04%) 6 (48.37%) 8 (61.03%) 5 (54.72%)Portfolio 2 7 (49.04%) 8 (56.93%) 7 (55.75%) 5 (47.21%) 5 (43.54%) 9 (62.84%) 7 (56.03%)Portfolio 3 5 (46.08%) 7 (56.52%) 6 (54.93%) 7 (52.82%) 5 (45.47%) 9 (59.23%) 6 (52.05%)Portfolio 4 5 (47.91%) 7 (55.61%) 7 (55.98%) 6 (53.84%) 7 (51.52%) 8 (58.31%) 6 (57.83%)

Panal A: Based on principal component analysisPortfolio 1 7 (52.37%) 8 (61.32%) 7 (56.21%) 8 (57.42%) 6 (52.07%) 9 (63.43%) 6 (58.21%)Portfolio 2 7 (51.03%) 9 (63.81%) 9 (60.37%) 6 (52.05%) 6 (48.56%) 10 (66.2%) 8 (62.73%)Portfolio 3 6 (49.21%) 9 (60.52%) 6 (57.64%) 9 (55.41%) 6 (50.53%) 10 (63.72%) 6 (55.48%)Portfolio 4 6 (48.21%) 8 (58.71%) 8 (58.96%) 8 (56.92%) 7 (53.98%) 9 (60.62%) 7 (61.38%)

Notes: aThis table shows the number of factors extracted and also the eigenvalue of the factor model expressed as a percentagein parenthesis. For each of the G7 countries, factor analysis is conducted on each of their four portfolios each consisting of40 securities.

20 It is possible that some of the factors extracted from the world portfolio may turn out to be common to a particular countrywithin that portfolio, given that the factors attempt to explain the correlation matrix which itself contains correlationsbetween security returns from the same country. This would be more likely with a large factor structure, which has beenavoided in this article (see discussions in Section IV).21 The restriction is due to the problems discussed in Section IV relating to large samples. On examining the eigenvalue of theK 1 factor for the world portfolio, in other words the 8th and 9th factor, this is found to be 1.28 and 1.19 for maximumlikelihood and principal component analysis, respectively, which in percentage terms represents 0.37 and 0.34% of thevariation in the returns of the world portfolio, thus is of minor importance. As the number of factors increase, the estimatedfactor loadings of high-order models will contain more noise than information. Given this, the SEs may well be of the samemagnitude as the actual coefficients, which, if one was attempting to predict the price of risk, may result in very unstablepredictions.

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Table4.

Resultsfrom

testing

thepricingrelationshipasgivenbyEqu

ation10wherefactorsareextractedusingprincipalcomponentanalysis

l0

l1

l2

l

3

l4

l5

l6

l7

l8

2

Canada

0.0072

0.0325**

0.0069

0.0114

0.0254**

0.00

89

0.0014

0.00218

0.0011

15.91**

(1.02)

(4.17)

(0.85)

(1.41)

(2.29)

(1.12

)

(0.39)

(0.45)

(0.32)

France

0.0033

0.0063

0.0051

0.0194*

0.0069

0.01

32

0.0022

0.0015

0.004

10.32

(0.79)

(0.84)

(0.72))

(1.82)

(0.85)

(1.56

)

(0.58)

(0.47)

(0.68)

Germany

0.0109*

0.0288**

0.0013

0.0029

0.0016

0.00

72

0.0049

0.0018

0.0027

10.23

(1.98)

(3.46)

(0.22)

(0.32)

(0.24)

(1.09

)

(0.56)

(0.25)

(0.31)

Italy

0.0064

0.0019

0.0015

0.0032

0.0198*

0.00

21

0.001

0.0009

0.0016

8.64

(0.57)

(0.37)

(0.27)

(0.51)

(1.84)

(0.43

)

(0.25)

(0.17)

(0.30)

Japan

0.0028

0.0216**

0.0021

0.0013

0.0308**

0.00

09

0.0039

0.0016

0.0025

13.92*

(1.03)

(3.03)

(0.93)

(0.62)

(3.91)

(0.59

)

(1.27)

(0.69)

(0.97)

UK

0.0041

0.0080

0.039**

0.001

0.0017

0.00

92

0.0030

0.0023

0.0017

9.02

(0.63)

(1.07)

(3.37)

(0.38)

(0.42)

(1.16

)

(0.56)

(0.0.47)

(0.38)

USA

0.0015

0.0421**

0.0237**

0.0032

0.0181*

0.00

41

0.0021

0.0019

0.0015

16.03**

(0.52)

(4.92)

(3.21)

(0.63)

(1.71)

(0.83

)

(0.51)

(0.47)

(0.32)

AllG7

0.0027

0.0357**

0.0105

0.00371

0.0217**

0.00

81

0.0032

0.0017

0.0024

13.51*

countries

(0.71)

(3.57)

(1.21)

(0.53)

(2.36)

(1.02

)

(0.51)

(0.32)

(0.46)

Notes:Averageinterceptand

riskpremiumforeachcountryisshownalongwithcorrespondingt-statisticin

parenthesis.The

2

testattheendofeachrowtestingwhether

thevectorofriskpremiaiss

ignificantlydifferentfromzero.Thecritical

2

valuewith8d.f.isgivenas15.507atthe5%

leveland13.361atthe1

0%

level.

*and**indicatesignificanceatthe10and5%

levels,respectively.

1052 D. Morelli

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shows that when the cross-sectional regression is

performed across all G7 countries, as opposed to each

individual country, two factors are found to be

significant and the risk premia vector is found to be

statistically significant, though only at the 10% level.

With respect to the intercept term, it is found that for

all countries except Germany, the null hypothesis that

the intercept is zero is not rejected.Table 5 reports the results from the same pricing

relationship as shown by Equation 10, but where the

factors are extracted using maximum likelihood

analysis and the factor scores estimated using

AndersonRubin, Bartlett and Thurstons regression

method. The results are very similar across all three

methods of factor score estimation. Again factor 1

shows significance across Canada, Germany, Japan

and the USA, with factor 2 being priced across

France, UK and USA, and factor 3 priced across

Canada and Italy. All countries have at least one

priced factor, though again this is not the same

factor. The 2 test results are similar to those found inTable 4 in that the same three countries, Canada,

Japan and the USA, reject the hypothesis that the risk

premia vector is not statistically significant. When the

cross-sectional regression is performed across all G7

countries, two factors are found to be significant and

the risk premia vector is found to be statistically

significant, again only at the 10% level. The 2

statistic is the same irrespective as to which method is

used given that the total amount of variance of the

variables explained by the common factors stays the

same across all three methods. The amount of

variance explained by individual common factorscan change, though overall the total variance

explained stays the same. The coefficient with respect

to the intercept term stays the same across all three

methods as this is not affected by the method of

factor score estimation, and for all countries one fails

to reject the hypothesis that the intercept term is zero.

Irrespective as to which method is used to

extract the factors or estimate the factor scores, it

can be seen that the international asset pricing

model does not hold for all the G7 countries. For

four out of the seven countries, France, Germany,

Italy and the UK, the model does not hold. This

itself implies the absence of integration throughoutall the G7 countries. Only when the cross-sectional

tests are performed across all G7 countries, as

opposed to individually, is the risk premia vector

found to be statistically significant, thus implying

a degree of integration existing between these

markets, though clearly this is influenced by the

strong cross-sectional results for Canada, Japan

and the USA.

Table 6 reports the F-statistic testing the joint

restriction that all intercept terms across the G7

countries are zero. The results clearly show that

irrespective as to which method is adopted regarding

factor extraction and factor score estimates, the

hypothesis that the intercept of all G7 countries iszero cannot be rejected.

Table 7 summarizes the results from testing

whether the risk premia are the same across all

seven countries.22 Results are shown for both

principal component and maximum likelihood

analysis. Factor 1 is found to have the same risk

premia across Canada, Germany and the USA,

and thus the price of risk is the same for this

factor across these countries, implying a degree of

integration between these three stock markets.

Factor 1 is the most important factor given it

explains the highest proportion of the totalvariance of the world portfolio. The summarized

results show that some countries clearly have the

same price of risk, but this cannot be said across

all countries. The results are not surprising

following the results shown in Tables 4 and 5,

given that capital market integration can only be

tested under the joint hypothesis of an interna-

tional asset pricing model, which clearly does not

hold across all G7 countries. Where factors are

extracted using maximum likelihood analysis, those

countries having the same risk premia are very

similar, and in many cases the same, across the

three different methods of factor score estimation.For example, for factor 2, which accounts for the

second largest proportion of total variance of the

world portfolio, the UK and USA have the same

risk premia across all three methods of factor

score estimation, thus implying a degree of

integration. The integration that exists between

some of the G7 countries is dependant upon the

technique used to extract the factors, for again,

using factor 2 as an example, when using principal

component analysis, Canada, France, Germany

and Italy were found to have the same price of

risk, and not the UK and USA which was thecase with maximum likelihood analysis. However,

irrespective as to the technique adopted, Table 7

clearly shows that the price of risk is not the same

across all the G7 countries and thereby implying

that the capital markets of the G7 are not fully

internationally integrated.

22 The results are summarized due to the vast amounts of data. Full statistical results are available upon request.

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VIII. Conclusion

Over the years, the economic and financial systems of

the G7 countries have increasingly become more

integrated due to the expansion in areas such as trade,

services and financial assets. This article distinguishes

between financial integration and security returns

being correlated internationally, focusing on thelatter in testing for capital market integration.

This article provides empirical investigation of an

international asset pricing model in an attempt to

determine whether the capital markets of the G7

countries are integrated. Capital market integration is

tested using a multifactor pricing model, where

common factors are extracted from a world portfolio

made up from a combined subset of securities from

each of the G7 countries. Two well-known methods

are adopted to extract factors, namely, maximum

likelihood factor analysis and principal component

analysis, where the number of factors extracted is

based upon the chi-square goodness-of-fit statistics

and Kaisers criterion, respectively.

In order to imply that the capital markets of the G7

are fully integrated, the price of risk must be the same

across all countries and thus the same factor must

have the same risk premium for all countries. The

cross-sectional results as shown in Tables 4 and 5

show that in terms of the international asset pricing

model, for each country at least one, and in some

cases more than one, risk premia is found to be

priced, however this does not relate to the same factor

across all countries. On examining the price of risk, as

shown in Table 7, it is found to be the same for somefactors for some of the countries, thereby implying a

degree of integration, however, is not found to be the

same for all countries.

Clearly, the results obtained and conclusions

drawn are based upon the methodology adopted,

specifically in terms of the techniques and criteria

adopted to extract factors and estimate the factor

scores. Given the two different techniques adopted

in this article to extract factors, namely, principal

component analysis and maximum likelihood factor

analysis, the results obtained do not differ signifi-

cantly upon the technique adopted. The number of

factors extracted from the world portfolio differed

only slightly, seven based on Maximum likelihood

and eight for principal component analysis. Of the

various criteria to adopt to determine the number of

factors to extract (see footnote 10), the chi-squaregoodness-of-fit statistics and Kaisers criterion were

applied. Clearly, different criteria can result in

different numbers of factors extracted, however,

what is important is not so much the number of

factors extracted but whether the factors are priced,

and more importantly, in terms of integration,

whether they are priced equally across all G7

countries. Although the results show different

numbers of priced factors (Tables 4 and 5) and

different countries having a similar price of risk

according to the technique used to extract the

factors (Table 7), irrespective of the techniqueadopted that the price of risk is not found to be

the same across all the G7 countries. The factor

scores proxy for the true risk factors. The use of

proxies can have an influence on the overall results

depending upon the accuracy of the proxy. Three

different methods were adopted to estimate the

factor scores AndersonRubin, Bartlett and

Thurston. Of these methods, Thurstons method is

superior in terms of producing estimated factors

which correlate highly with the true factors. Given

this, the results are found to be similar across all

three methods. Clearly, when extracting factors

using maximum likelihood analysis the factorscores are estimates, unlike principal component

analysis which produces exact factor scores, how-

ever, the results are still similar in that the price of

risk is still found not to be the same across all G7

countries. Thus the conclusion from this article in

terms of the question of full integration is similar

irrespective of the technique adopted to extract the

factors and estimate factor scores and thus implying

that the conclusion drawn is not sensitive to the

different methods and techniques adopted.

To test for integration requires a valid interna-

tional asset pricing model, which in turn is only avalid model if the markets are integrated, thereby

resulting in a joint hypothesis problem. The results

provide evidence against this joint hypothesis.

Although a degree of integration is shown to exist

between some of the G7 countries, one would have

to conclude that based on an international

multifactor asset pricing model, the hypothesis of

full integration between all the G7 countries does

not hold.

Table 6. The F-statistic testing the joint restriction that allthe intercepts across the G7 countries are zero

F-test

Factors extracted using principalcomponent analysis

0.826

Factors extracted using maximumlikelihood analysisAndersonRubin 0.747Bartlett 0.747Thurston 0.747

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Table7.

Summaryofresults

from

testingwhethertheriskpremiaarethesameacrossallG7countries

Countrieswhereriskpremiawerefoundtobethesame

Factorsextractedusing

Risk

premia

Riskpremia

the

sameacross

all

sevencountriesa

Principalcomponentanalysis

Maximumlikelihoodana

lysis

AndersonRubin

Bartlett

Thurston

l1

No

USAandCanada,

GermanyandJapan

Canada,Germany

andUSA

Canada,Germany

andUSA

Canada,Germany

andUSA

l2

No

CanadaandFrance,

GermanyandItaly

UKandUSA

UKandUSA

UKandUSA

l3

No

Germany,ItalyandUSA

CanadaandItaly,

GermanyandUSA

CanadaandItaly,

GermanyandUSA

CanadaandItaly,

GermanyandUSA

l4

No

ItalyandUSA

l5

No

CanadaandUK

ItalyandFrance

ItalyandFrance

l6

No

CanadaandFrance,

UKandUSA

CanadaandFrance,

UKandUSA

Canada,UKandUSA

l7

No

GermanyandUSA

Canada,GermanyandIt

aly

ItalyandGermany

Canada,Germany

andItaly

l8

No

Italy,UKandUSA

Notes:aTheresultsreportedshowthatnoindividualriskpremiawasfoundtobethesameacrossallseven

countries.Thiswasthecaseirrespectiveofwhetherthefactorswere

extractedusingmaximumlik

elihoodorprincipalcomponentanalysis,orwhetherAndersonRubin,BartlettorThurstonsmethodologywasusedtoestimatethefactorscores.

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