The Euro and international diversification benefits

Kpate ADJAOUTE*
(Corresponding author.)

and

Jean-Pierre DANTHINE

Ecole des HEC,
University of Lausanne

CH - 1015 Lausanne

Kpate.Adjaoute@hec.unil.ch

Jean-Pierre.Danthine@hec.unil.ch

 

The Euro and international diversification benefits

 

1. Introduction and outline

In this paper, we concentrate on equity investments and present evidence on the impact on risk diversification opportunities of the economic and monetary integration process at work in Euro-land in the 90’s. Portfolio theory tells us that diversification gains stem from the imperfect correlation between financial returns. In the context of Euro-land, international diversification is desirable to the extent that national stock markets are imperfectly correlated. The advent of the Euro has at least two possible implications in this respect: first, it corresponds mechanically to the disappearance of currency risks; second it is part of a broader set of structural changes likely to alter the traditional forces underlying asset returns and thus, the relevant correlations between stock indices.

To shed light on these issues and their implications for portfolio allocation decisions, we start by focusing on the characteristics of the variance-covariance matrix of returns within Euro-land. The question we address is the following: have we observed significant changes, over the recent past, as the monetary and economic convergence process develops and with the advent of the Euro, in the characteristics of returns and, if so, what are their implications for optimal portfolio allocations? In other words, we inquire how the advent of the Euro, preceded by the intensification of co-ordination between national policies, has affected the variance-covariance matrix of asset returns in the Euro zone (and to what extent can further changes be expected)?

A closely related issue is whether the evolution of return correlations at the country level would justify abandoning the traditional country allocation model in favour of an approach based on a diversification across industrial sectors. To get an insight into this question, we also study the time evolution of the variance- covariance matrices of sectoral returns. Two disaggregation levels are considered: at a first level, we consider four sectors per country, and at the second level 10 sectors are taken into account.

Given the persistence and the importance of the home bias in equity investments, we pursue our study with the following question: does the changing economic structures within Europe and the disappearance of currency risks tend to increase or decrease the cost of restricting one’s investment universe to home equities?

We start this inquiry by somewhat paradoxically abstracting from currency risk and concentrating on the implications for diversification benefits of the changes in economic structures. This is because our analysis is more transparent if we adopt the single viewpoint of the European investor which is appropriate post January 1, 1999. Accordingly, all our return data are expressed in Euro at single conversion rates: the official, permanent conversion rates of December 31st 1998. In a second step we check the robustness of this simplifying assumption and our initial conjectures that currency fluctuations have played a minor role for asset returns in the 1990’s (in Europe) by reconfiguring all our return series prior to that date at the effective exchange rates prevailing at the time.

For the purpose of comparison, we need pre-Euro and post-Euro periods. Given the limited time period since the formal introduction of the Euro, we make the assumption that January 1st 1999 was but the final consecration of a movement of convergence started in January 1995, the date of entry of the Maastricht treaty; the period from September 1990 to the end of 1994 is taken as representative of the ‘pre-convergence’ period.

2. Data

To conduct the study along the lines described above, we have collected weekly data on national stock market indices as well as sector indices for the Euro-land 11 countries. The indices used are the Datastream Global Equity indices. These indices are good representations of the national markets in the sense that they are broad and cover between 75% and 80% of the total capitalization of the respective markets. Moreover, they represent valid benchmarks for comparison with other indices used in current empirical studies and have the added advantage of being available for the set of countries that are of interest to us.(1). The whole sample runs from September 10, 1990 to April 19, 1999, which yields a total of 450 weekly return observations per index. (2).In a first approach, all series are expressed in Euros, pre-1999 prices being retrospectively converted at the December 31st (1998) permanent conversion rates. In a second pass at the question, we use national currency returns for pre-1999 indices.


(1). We used the FT Actuaries indices for eight countries and obtained outputs qualitatively similar to those reported here. We therefore decide to work with Datastream Global Equity indices which are available for all the Euro-land countries, in contrast to FT Actuaries.

(2). The total return observations is 380 for Luxembourg rather than 450.

 

Customarily, tests of asset pricing models are conducted using monthly frequency return observations because non-normality issues are less severe at sampling intervals greater than or equal to one month. However, if we elect to work with monthly data, the sample size becomes extremely small, particularly when it comes to comparing pre-Euro and post-Euro sub-periods. Our concern with non-normality is illustrated in Table 1A which contains summary statistics on national index returns for the whole sample. Based on the Jarque-Bera statistic (which is a chi square with two degrees of freedom), the normality assumption is rejected for all 11 countries. The normality is rejected both because of fat tails and asymmetry as indicated by the kurtosis and skewness coefficients. In fact, given that the kurtosis coefficient and the skewness , and that the Jarque-Bera is a combination of the latter two statistics, it is easy to see that asymmetry is present in all but three stock returns (Ireland, Italy and Spain). With no exception, index returns are characterized by fat tails. The essential question here is to figure out the likely consequences of this non-normality on the battery of tests that are going to be undertaken in this part of the study. Given the evidence of fat tails, the primary message is that sample second moments are unreliable estimates of the true population moments, which might not even exist. The very simple and conservative assumption that we are going to maintain is that the general form of the underlying return distribution (whatever it is) does not change significantly over the time period of our study, so that correlation and covariance matrices computed over two consecutive sub-periods can be viewed as coming from the same distribution.

We have partitioned the whole sample into two sub-samples of equal size. The first sub-sample runs from September 10, 1990 to December 26, 1994 and corresponds to the four years preceding the convergence period. The second sub-sample runs from January 2, 1995 to April 19,

Table 1A: Whole Sample Summary Statistics

AUSTR

BELG.

FINL

FRAN.

GERM

IRELA

ITALY

LUX

NETHE

PORTU

SPAIN

Mean

0.0023

0.1251

0.2218

0.1238

0.1033

0.17906

0.104

0.1921

0.1623

0.1001

0.1512

Median

0.0633

0.1493

0.1711

0.1852

0.148

0.14612

0.017

0.1716

0.1695

0.0284

0.2

Maximum

5.5086

3.8328

6.7605

4.457

4.9172

5.39144

5.169

6.3828

3.656

5.0664

6.3164

Minimum

-7.2925

-5.6564

-8.184

-5.53

-6.5061

-5.9338

-7.438

-5.244

-7.109

-6.502

-5.6296

Std. Dev.

1.2066

0.9995

1.8954

1.2774

1.1891

1.28925

1.769

0.9314

1.124

1.2256

1.5069

Skewness

-0.3167

-0.4174

-0.373

-0.37

-0.7052

-0.1542

-0.148

0.4579

-0.848

-0.3

-0.1923

Kurtosis

7.3416

6.2335

5.385

4.546

6.411

6.23011

3.949

10.966

9.6309

6.9529

4.7133

Jarque-Bera

360.95

209.11

117.11

55.07

255.45

197.413

18.52

1018.1

878.37

299.72

57.814

Probability

0

0

0

0

0

0

1E-04

0

0

0

0

Observation

450

450

450

450

450

450

450

380

450

450

450

This table gives the unconditional whole sample moments of the Euro-land index returns. The sample runs from September 10, 1990 to April 19, 1999 and observations are sampled weekly. Returns are continuously compounded and annualized. The Jarque-Bera is a chi square with two degrees of freedom and tests for both asymmetry and fat tails in the series.

 

Table 1B: Whole Sample Unconditional Correlations

Austria

1

Belgium

0.543

1

Finland

0.432

0.51

1

France

0.548

0.651

0.5261

1

Germany

0.582

0.69

0.5464

0.7505

1

Ireland

0.436

0.488

0.4402

0.4717

0.5252

1

Italy

0.374

0.488

0.4343

0.5633

0.5607

0.3296

1

Luxemb.

0.383

0.39

0.2585

0.3318

0.3929

0.3601

0.2403

1

Netherl.

0.599

0.735

0.5775

0.7453

0.7985

0.5617

0.5613

0.439

1

Portugal

0.368

0.529

0.3632

0.517

0.5324

0.4114

0.397

0.256

0.5433

1

Spain

0.49

0.6

0.4609

0.6521

0.6778

0.4535

0.5735

0.297

0.6818

0.508

1

This table gives the unconditional whole sample correlations of the Euro-land index returns. The sample runs from September 10, 1990 to April 19, 1999 and observations are sampled weekly. Returns are continuously compounded and annualized.

1999 and corresponds to the convergence period. We have further decomposed this second sub-sample into two sub-samples of equal length. Appendix A displays the relevant sub-sample summary statistics. In what follows, we focus on the analysis of the stability of correlation and variance-covariance matrices.

3. Statistical Analysis of Correlation and Variance-Covariance Matrices of Returns Based on Country Indices

To assess the extent to which the adoption of a common policy in the convergence phase has led to a significant modification of the investment opportunities within Euro-land, we partition the whole sample into two sub-samples of equal size. The modification of the investment opportunity set, if any, must manifest itself in the changing structure of the variance-covariance matrices of the pre convergence and convergence periods. In principle, a test of the stability of the covariance matrices can suffice. But given that correlation matrices are more appropriate to judge on the significance of international diversification benefits, we will consider tests of stability of both correlation and covariance matrices. The tests that we consider are the Jenrich [1970] and Box [1949] statistics which have been used to some extent by a number of authors including Longin and Solnik [1995] and Kaplanis [1985, 1988].

Operationally, we denote by and the variance-covariance matrices of the first sub-sample (pre-convergence) and second sub-sample (convergence), respectively. The corresponding correlation matrices are denoted by and respectively. For a test based on covariance matrices, the Box test is based on a ratio of determinants: , while the Jenrich uses as its principal input the quantity . The detailed computation of these test statistics are given in the technical note at the end of this section, and we just need to mention that they are asymptotically distributed as chi squares with degrees of freedom equal to where is the number of countries (assets). The small sample properties of both tests have been investigated by Kaplanis [1985]. It turns out that if the sample size is too small, the two tests can give conflicting conclusions. Hence, the use of both tests here can give guidance on possible sample issues.

For a test of stability of correlation matrices, the test statistic is a Jenrich test which is computed in exactly the same way as the test for stability of covariance matrices after making appropriate substitutions (replacing covariance matrices by correlation matrices) and adjusting for the number of degrees of freedom. That is, the Jenrich based on correlation matrices uses as its principal input the quantity . The adjustment in the number of degrees of freedom is necessary because the diagonal elements of the matrices are not an object of test, so that the relevant degrees of freedom is . To summarize, in the context of the present study involving 11 countries, the Box and Jenrich statistics based on covariance matrices have 66 degrees of freedom whereas the Jenrich statistic using correlation matrices has 55 degrees of freedom. The outputs of our calculations are reported in Table 2 below.

Table 2: Test of Stability of Covariance and Correlation Matrices

 

Test of Corr. Matrices

Test of Cov. Matrices

 

Jenrich

Jenrich Box

Sub-Samples Compared:

   

Pre Convergence vs Convergence

124.507

201.437 161.568

 

(0.0000)

(0.0000) (0.0000)

Two Sub-Periods of Convergence

83.642

250.002 114.107

 

(0.0076)

(0.0000) (0.0002)

When we focus on pre convergence vs convergence periods, the first sub-sample runs from September 10, 1990 to December 26, 1994 while the second sub-sample runs from January 2, 1995 to April 19, 1999. The first sub-period of convergence goes from December 26, 1994 to February 17, 1997 and the second sub-period runs from February 24, 1997 to April 19, 1999. The p-values are given in parentheses below each statistic.

Clearly, there is a strong evidence that both the correlation and variance-covariance matrices are unstable over time. The extremely low p-values given in parentheses reject the null hypothesis of equality of the two matrices, implying that the diversification benefits during the convergence period are different from those prevailing in the period before convergence. Additional information is presented in Figure 1 where we display the pre-convergence and convergence period country pair correlations. The corresponding numerical figures are reported in Tables B1 and B2 in Appendix B. The pre-convergence correlations are sorted in ascending order, and plotted along with the unsorted corresponding convergence period correlations. It is striking that every convergence period correlation is higher than its pre-convergence period counterpart. The formal Box and Jenrich tests confirm that these differences are statistically significant. In Figure 2, we provide similar evidence showing that the correlations of the last two years of convergence are higher than those of the first two years of convergence, indicating that the process appears to be continuing throughout the convergence period. The corresponding data can be found in Tables B3 and B4 (Appendix B).

Of course, it is a relevant question to inquire whether this pattern of increasing return correlations is specific to Euro-land countries and thus, presumably, associated with the process of economic and monetary unification, or whether it is merely a reflection of a broader world wide trend, possibly as a consequence of increasingly mobile international capital flows. Evidence on this question is provided in Figure 3 where we display the evolution of the return correlations between stock indices representing the major regions of the world. The regions that we consider here are: Americas (AM), Far East (FE), Pacific-Basin (PB), Australasia (AU), Non-European Union (NE), European Union (EE) and Asia (AS). While there is some increase in the level of correlations as the data in Appendix B (Table B5) suggest, the changes in correlations are significantly more pronounced in the case of Euro-land countries (the average of region pair correlations was 0.454 during the pre convergence period, and it moved to only 0.585 during the convergence period).(4). In addition, with the exception of the correlations involving the Far East and Pacific Basin regions, the level of correlations tend to be lower than those observed within Euro-land.


(4). Contrast this with an average pre convergence correlation of 0.333 and a convergence period average correlation of 0.585 for Euro-land countries.

Table 3 indicates that these changes in correlations were accompanied by an increase in the standard deviations of returns across Europe, with Italy being the sole exception and the Netherlands the extreme illustration. While it is easy to find some rationale for the increase in correlations (see section 2.3.1.7), it is not clear that the increase in the risk level has any causal relationship with EMU or the process of European economic integration, i.e., it is difficult to decide whether this increase in standard deviations is likely to be permanent or not. It is interesting to notice, however, that there is some presumptions that return correlations increase during periods of high volatility (see, e.g., ). The increase in the standard deviations in returns may in this sense explain part of the common increase in correlations both in Euro-land and elsewhere in the developed world.

The intermediary conclusions that we draw from the analysis of this section is that the process of economic and

monetary integration in place in Europe seems to be accompanied with an increase in the correlation of national stock indices indicating that the benefits of international diversification using country allocation models within Euro-land have diminished. A similar but less pronounced process of increasing correlations among country or regional indices seems to be at work elsewhere in the world, suggesting that EMU factors are not the only ones at work. It remains true that diversification opportunities on a purely geographical basis are better if extended outside the European region.

 

 

Table 3.

Return Volatilities in Euro-land

Country

Pre-Conv.

Converg.

Neth.

0.7306081

1.39186

Belg.

0.7774509

1.114882

Luxe.

0.8955599

0.953018

Germ.

0.9380667

1.286281

Port.

0.9956962

1.376585

Aust.

1.0016007

1.027208

Irel.

1.1253629

1.268636

Fran.

1.1486571

1.355324

Spai.

1.3931264

1.565336

Finl.

1.7876227

1.972845

Ital.

1.815288

1.796955

 

 

4 Countries or Sectors ?

In order to gain further insights on the process at work, we now repeat the same analysis as above, mutatis mutandis, using sector indices available for each of the 11 Euro-land economies. First we use a broad decomposition into 4 sectors per country distinguishing the ‘Resources’, ‘Financials’, ’Non-financials’, and ‘Non-financials excluding resources’ (partially overlapping) sectors. Figures 4.A to 4.D report the results when we pair country/sector returns, i.e., we look at the country to country correlations among ‘Financials’ returns, then ‘Non-financials’, etc. Although somewhat less so for the ‘Resources’ sector, the same pattern of increasing correlations over the period under review is observed. Note as well that the sector by sector return correlations tend to be lower than the corresponding correlations using aggregate country indices.

These results are confirmed at a finer level of disaggregation as indicated in Table 3 where a ten-sector decomposition is used. The average (across our 11 countries) pair-wise correlations increases in nine sectors out of ten, the UTILS sector being the single exception. The correlation increases range from 4.15 percentage points (from 29.44% to 33.59% for the CYSER sector) to 19 points ((from 20.875% to 39.883% for the NYCSR sector). Quite understandably, correlation levels are rather lower at this higher level of disaggregation.

Table 3: Average Correlations of Ten Industry Groups Within Euro-land

BASIC

CYSER

CYCGD

GENIN

ITECH

NYCG

NYCSR

RESOR

TOTLF

UTILS

Pre Convergence Period

Mean

0.197

0.2944

0.2046

0.2703

0.122

0.27

0.20875

0.1872

0.3707

0.2403

Median

0.159

0.2797

0.1687

0.2453

0.1449

0.2581

0.21266

0.1662

0.37901

0.2631

Maximum

0.536

0.5814

0.5783

0.5987

0.2213

0.5263

0.36925

0.5063

0.62549

0.4256

Minimum

-0.048

0.0763

0.0027

0.0352

-0.0479

0.081

-0.003

-0.002

0.06102

0.0388

Std. Dev.

0.157

0.1245

0.1486

0.121

0.0808

0.1079

0.11328

0.1057

0.15929

0.1093

Skewness

0.633

0.4142

0.973

0.4627

-1.0455

0.4416

-0.3622

0.9523

-0.0224

0.0453

Kurtosis

2.501

2.2264

3.2397

2.7709

3.1004

2.7591

1.933

4.3306

1.96855

2.4956

Convergence Period

Mean

0.285

0.3359

0.297

0.4035

0.2908

0.3339

0.39883

0.2747

0.5457

0.1889

Median

0.184

0.3079

0.2645

0.4023

0.2446

0.3258

0.4123

0.3117

0.54873

0.161

Maximum

0.689

0.6244

0.6624

0.6726

0.4708

0.6403

0.57649

0.5797

0.77234

0.5034

Minimum

-0.06

0.1152

0.0689

0.1857

0.1275

0.0708

0.2467

0.0317

0.31699

0.0393

Std. Dev.

0.222

0.1395

0.1562

0.1256

0.1291

0.1374

0.09471

0.1655

0.10549

0.1284

Skewness

0.078

0.347

0.8001

0.0884

0.5009

0.2541

-0.0358

0.1048

-0.0953

1.162

Kurtosis

1.483

2.0187

2.9309

2.0654

1.7085

2.2009

1.91191

1.657

2.54756

3.5651

The industry groups considered are: RESOR = resources, BASIC= basic industries, GENIN = general industrials, CYCGD = cyclical consumer goods, NCYCG = non-cyclical consumer goods, CYSER = cyclical services, NCYSR = non-cyclical services, UTILS = utilities, ITECH = information technology, TOTLF = financials. For each industry group, we compute the cross country correlation matrix of the returns and report the relevant statistics.

From this section, one can conclude that diversification opportunities are much better at the sector level than at the country level despite the fact that the European unification process appears manifest here as well in the form of an increase in the correlation among sectoral stock indices. On the face of it, it thus seems that allocating simultaneously across sectors and countries is a superior investment option. To make the case for such an assertion, we address next the question of whether the gains from diversification require investing internationally or whether they can be reaped by limiting one’s portfolio allocation to national equities.

5 The cost of the home bias

In this section, we look at the characteristics of the optimal portfolios of national investors constrained to investing in home equities only compared with those of optimally diversified portfolios across all Euro-land. The diversification in Euro-land can be achieved along two distinct lines: either across countries or across countries and sectors. We use the 10 sector disaggregation of Table 3. Tables 4.A to 4.D report the characteristics of the Minimum Variance Portfolio (MVP) and the Tangent Portfolio (TP) of a European investor selecting freely (without short-selling constraints) among the 10 sector indices either in his home country (French and German perspectives) or in the 11 Euro-land countries. Here, we consider the pre-convergence and convergence periods as well.

To provide relevant outputs, let denote the vector of expected returns for a chosen investment opportunity set "s" over a sample period . "s" refers to country indices when one diversifies by country, to sector indices in the case of an asset allocation by sectors within a given country, or to sector indices when we consider diversification by country and by sector in Euro-land. is the variance-covariance matrix associated with the expected returns of the selected investment opportunity set. If and are the vector of weights of the Minimum Variance Portfolio (MVP) and the Tangent Portfolio (TP) respectively, then:

Here, is a column vector of ones with the appropriate dimension, and given the portfolio weights , one can then easily compute the expected return, , and variance, , as well as the Sharpe ratio of the MVP or TP:

As is explicit from the computation of the optimal weights of the minimum variance and the tangent portfolios, we abstract from the existence of a riskless asset in our allocation problem. Also, short sales are permitted and the only constraint that we impose is that the portfolio be fully invested (sum of the weights equal to one: ).

As mentioned above, we provide portfolio characteristics by considering three leading diversification alternatives: 1) diversification by country within Euro-land, 2) diversification by sectors within a given country (France and Germany) and 3) diversification by sectors across Euro-land (focus on countries and sectors simultaneously). For each of these strategies, we provide output for both the pre-convergence and convergence periods.

While our results have to be taken with a grain of salt because we did not impose any restriction on the ability to sell short, with the result that in some instances the considered portfolios would have included unusually large short positions, our results display the impressive superiority, both in terms of Sharpe ratios or in terms of the risk level of the Minimum Variance portfolio, of the ‘theoretically’ optimal strategy consisting in a diversifying by sectors across all of Euro-land. Such a strategy would also have permitted a minimal loss of performance between the pre-convergence and the convergence periods despite the increase in correlation of returns noted above.

The home bias – leading to a strategy of diversifying ‘at home’ across industry would have been very costly in terms of both our measures of performance, but so is the pure country allocation strategy across Euro-land. On the other hand, limiting one’s investment horizon to home would have entailed a minimal loss of performance for either the French or the German investors (the two types of investors we have considered) if the alternative is a pure country allocation strategy. Said differently, if the international investment alternative is based on a pure country allocation, the ‘home bias’ is not very costly in terms of performance (Sharpe ratio) or in terms of risk (for the investor interested in the minimum variance portfolio). In fact for the French investor a ‘home biased’ would have outperformed the international ‘country allocation’ strategy during the first ‘pre-convergence’ period.

These results underline the sub-optimality of the traditional two-step allocation procedures consisting first in a country allocation decision, then in a ‘value oriented’ stock selection procedure within each country. They also suggest that this frequent practice of the investment advising industry may have a causal relationship with the home bias.

Table 4.A: International Diversification by Country

MVP1

MVP2

TP1

TP2

Austria

-0.06933255

0.570661882

-0.62271807

-1.16619701

Belgium

0.308530748

0.470652149

-0.12049101

1.236503643

Finland

-0.00208894

-0.11074957

0.192321883

0.318590949

France

-0.08367694

-0.03404844

-0.11085488

0.154834482

Germa.

0.068656228

0.083483691

0.143535964

-0.92480574

Ireland

-0.0321054

0.256168385

0.281323804

0.939672073

Italy

-0.01034946

-0.01726868

-0.2063736

-0.25492938

Netherl.

0.65309373

-0.27128428

1.463967615

0.327838054

Portugal

0.260021694

0.119516657

-0.00957495

-0.01655405

Spain

-0.09274911

-0.06713179

-0.01113675

0.385046983

E(Rp)

0.0663

0.10435

0.20462

0.545432

V(Rp)

0.408247

0.738017

1.259972

3.857566

Sharpe

0.103765272

0.12146727

0.18229201

0.277705148

The previous table gives the weights of country indices in the Minimum Variance Portfolio (MVP) and the Tangent Portfolio (TP). MVP1 and MVP2 stand for pre convergence and convergence Minimum Variance Portfolios respectively, while TP1 and TP2 are the corresponding Tangent Portfolios.

 

Table 4.B: Diversification by Industry: German Case

MVP1

MVP2

TP1

TP2

Basic

0.037579682

0.062220805

0.528788734

0.045000088

Cyclical CG

-0.03401575

-0.0075316

-0.72729458

0.120363192

Cyclical Serv.

0.028285357

0.024787093

-0.12361212

0.095861844

General Ind.

-0.00740825

-0.08798103

-0.18703055

-0.29005986

Inform. Tech

-0.00647038

-0.0289989

0.371687999

0.071076729

Non-cyclical CG

-0.06471365

0.01297134

0.168466113

0.189494875

Non-cyclical serv.

0.21049095

0.255489085

0.396243799

0.177823157

Resources

0.097105103

0.070845689

-0.36753543

-0.27940601

Financials

-0.01234226

-0.05028437

-0.1778627

-0.042295

Utilities

0.751489187

0.748481884

1.11814874

0.912140978

E(Rp)

0.054796823

0.099563835

0.233041347

0.244106326

V(Rp)

0.370899277

0.394250433

1.577370059

0.966606252

Sharpe

0.089976146

0.158567992

0.185552233

0.248287145

This table gives the weights of German sector indices in the Minimum Variance Portfolio (MVP) and the Tangent Portfolio (TP) in an allocation by sector within Germany. MVP1 and MVP2 stand for pre convergence and convergence Minimum Variance Portfolios respectively, while TP1 and TP2 are the corresponding Tangent Portfolios.

 

 

Table 4.C: Diversification by Industry: the French Case

MVP1

MVP2

TP1

TP2

Basic

0.36208588

0.332294768

0.259203949

0.183930167

Cyclical CG

0.0543102

-0.22635855

0.710216008

-0.44067269

Cyclical Serv.

0.112585812

0.605366994

-1.08417612

0.700872994

General Ind.

-0.08256922

-0.16604577

-0.38574462

-0.11781442

Non-cyclic. CG

0.170272377

0.114348042

1.006522077

0.475409974

Non-cycli. Serv.

0.202783421

0.078369438

0.48664666

0.011633146

Resources

0.118992511

0.12393848

-0.03512431

0.176207984

Financials

-0.0368079

0.01797704

-0.53585876

-0.02223691

Utilities

0.098346925

0.120109556

0.578315111

0.032669748

E(Rp)

0.108841419

0.189244698

0.434585734

0.286764745

V(Rp)

0.744838624

0.711841471

2.974017101

1.07866186

Sharpe

0.126113942

0.224301448

0.252001853

0.276110611

This table gives the weights of French sector indices in the Minimum Variance Portfolio (MVP) and the Tangent Portfolio (TP) in an allocation by sector within France. MVP1 and MVP2 stand for pre convergence and convergence Minimum Variance Portfolios respectively, while TP1 and TP2 are the corresponding Tangent Portfolios.

 

 

Table 4.D: Euro-land Wide Diversification by Sectors

MVP1

MVP2

TP1

TP2

E(Rp)

0.072706294

0.070393514

0.892045234

0.967017345

V(Rp)

0.104725897

0.115190696

1.284898912

1.58241002

Sharpe

0.224669937

0.207407255

0.786959526

0.768731632

This table gives the weights of sector indices in the Minimum Variance Portfolio (MVP) and the Tangent Portfolio (TP) in an allocation by country and sector. MVP1 and MVP2 stand for pre convergence and convergence Minimum Variance Portfolios respectively, while TP1 and TP2 are the corresponding Tangent Portfolios. The industry groups considered in each Euro-land country are : RESOR = resources (8 indices), BASIC= basic industries(10 indices), GENIN = general industrials(10 indices), CYCGD = cyclical consumer goods(7 indices), NCYCG = non-cyclical consumer goods(10 indices), CYSER = cyclical services(10 indices), NCYSR = non-cyclical services(8 indices), UTILS = utilities(6 indices), ITECH = information technology(5 indices), TOTLF = financials(10 indices). In principle, if each industry group is available in each of the participating countries, then we should have a total of 11 x 10 = 110 investable indices. However, some sectors are not available in some countries so that the number of investable indices is reduced to 84.

 

6 Re-introducing currency risk

So far, we have used return data on the basis of indices expressed in Euro, that is, converting all national and sector indices in Euro at the December 31st 1998 conversion rates, also for index values preceding the formal advent of EMU. The implicit underlying hypothesis was that the currency exchange rates movements since 1990 have been mostly neutral to stock returns and that the main measurable effect of the advent of the Euro is not so much the result of the disappearance of currency risks but rather follows the changes in economic structure that the process of economic and monetary unification has provoked. This hypothesis finds its roots in the observation that, since the beginning of the 1990’s, currency movements have been confined within narrowly defined fluctuations bands (see Table). We now test the robustness of our results to this simplification by using return series computed on the basis of indices converted in Euro at market exchange rates until December 31, 1998 and at the official permanent conversion rates since that date.

Table 5A and 5B display the characteristics of the pure currency returns obtained during the period by German and French investors, respectively, while Tables 6A and 6B look at the total equity returns inclusive of currency returns for the similarly based investors. Note that the currency returns series are shorter than those used for asset returns as they terminate on Jan 1, 1999 .for obvious reasons.(5). The similarity between the mean return series expressed in DMK, in FRF or in Euro (Table 1A) permits anticipating most of the results to follow.


(5). Note as well that we insert a shorter currency series for Luxemburg (which as a result differs from the BEF series) to be used in conjunction with the (shorter) equity return series for that country.

 

Table 7 confirms the results of Table 2. Taking account of currency fluctuations in fact reinforces the view that, as far as asset returns are concerned, the pre-convergence and the convergence periods have significantly different statistical properties and Figures 5A and 5B similarly confirm that the difference correspond to a visible increase in the degree of correlation among asset returns also when currency returns are included. The corresponding results are presented in Tables C1 to C4 in Appendix C.

Finally we look at the properties of the Minimum Variance and Tangent portfolios with these new series of returns. The results are presented in Tables 8A and 8B. Our hypothesis of the relative irrelevance of currency returns finds a confirmation in the almost identical Sharpe ratios and very similar characteristics of the MVP and TP of German and French investors, respectively.

Table 5A: DMK Returns Against Other Euro-land Currencies

ATS

BEF

ESP

FMK

FRF

IRP

ITL

LUF

NLG

PSC

Mean

0.002639

0.0008

-0.03305

-0.02625

0.003885

-0.007

-0.0339

0.00262

0.00303

-0.0169

Median

0.005454

0.003028

-0.00514

-0.00397

0.016873

0.02536

-0.0074

0.004578

0.00464

-0.0017

Maximum

1.887337

1.962902

1.647928

2.131592

1.391829

1.84225

2.62635

0.896092

1.74339

1.55771

Minimum

-1.799913

-1.652677

-4.13025

-5.91884

-1.440927

-4.96291

-5.07

-0.84166

-1.56207

-2.644

Std. Dev.

0.365714

0.345744

0.491112

0.642571

0.349599

0.57194

0.59892

0.215935

0.39249

0.35759

Skewness

-0.115094

0.369364

-1.72232

-2.85751

-0.248029

-1.70805

-1.9056

-0.03205

0.00547

-1.8214

Kurtosis

7.240137

11.99241

15.63636

26.84328

5.326523

16.5303

18.9053

5.362552

6.57419

16.0694

Jarque-Bera

314.0529

1417.876

2987.712

10470.26

98.55711

3391.69

4659.01

60.51241

222.497

3206.04

Probability

0

0

0

0

0

0

0

0

0

0

Observations

418

418

418

418

418

418

418

260

418

418

 

Table 5B: FRF Returns Against Other Euro-land Currencies

ATS

BEF

DMK

ESP

FMK

IRP

ITL

LUF

NLG

Mean

-0.001247

-0.003085

-0.00389

-0.03694

-0.030132

-0.01089

-0.0378

-0.00065

-0.00086

Median

-0.012703

-0.01966

-0.01687

-0.03089

-0.005045

-0.0012

-0.0209

-0.00804

-0.01152

Maximum

2.146706

1.661731

1.440927

1.419961

1.581367

1.65214

2.07542

1.222448

2.00276

Minimum

-1.497532

-1.608361

-1.39183

-4.39867

-5.707171

-4.50164

-3.6291

-1.13835

-1.54803

Std. Dev.

0.353941

0.400917

0.349599

0.415293

0.577941

0.49808

0.5685

0.243176

0.34025

Skewness

0.472881

0.270928

0.248029

-3.05414

-3.319134

-1.74103

-0.991

0.1087

0.62903

Kurtosis

9.207642

6.207924

5.326523

34.07393

33.20284

19.1469

9.73712

8.801958

9.61644

Jarque-Bera

686.7267

184.3447

98.55711

17467.18

16655.18

4752.06

858.944

365.1914

790.02

Probability

0

0

0

0

0

0

0

0

0

Observation

418

418

418

418

418

418

418

260

418

 

Table 6A: Euro-land Country Index Returns Expressed in DMK

Aust

Belg

Germ

Spai

Finl

Fran

Irel

Ital

Luxe

Neth

Port

Mean

0.006683

0.152334

0.119917

0.142675

0.227939

0.13043

0.18674

0.09262

0.12745

0.17795

0.12409

Median

0.039258

0.164229

0.162868

0.241499

0.194118

0.20265

0.163

0.173671

0.15412

0.20724

0.06831

Maximum

5.45129

3.822995

4.917269

6.11959

8.027822

4.09096

4.63247

7.64595

2.78089

3.81916

5.1023

Minimum

-4.100769

-5.602373

-6.50709

-5.85532

-8.226608

-5.61873

-6.1001

-7.45092

-5.18211

-7.198

-6.3702

Std. Dev.

1.154506

1.043792

1.171001

1.611388

2.019024

1.34975

1.35494

2.034777

0.89676

1.21888

1.25712

Skewness

0.093372

-0.348473

-0.70753

-0.42946

-0.187792

-0.45904

-0.3415

-0.1542

-0.79187

-0.8438

-0.299

Kurtosis

4.87744

5.455887

6.64091

4.714514

4.795005

4.6387

5.58872

3.791316

7.44067

8.77074

6.41768

Jarque-Bera

61.9973

113.5064

265.7541

64.0461

58.57412

61.4499

124.842

12.56244

240.801

629.604

209.664

Probability

0

0

0

0

0

0

0

0.001871

0

0

0

Observ.

418

418

418

418

418

418

418

418

260

418

418

 

 

Table 6B : Euro-land Country Index Returns Expressed in FRF)

Aust

Belg

Germ

Spai

Finl

Fran

Irel

Ital

Luxe

Neth

Port

Mean

0.002797

0.148449

0.116032

0.13879

0.224054

0.12654

0.18286

0.088735

0.12418

0.17407

0.12021

Median

-0.001154

0.14253

0.130832

0.197105

0.151529

0.18546

0.17483

0.152552

0.1707

0.15952

0.0943

Maximum

5.81735

3.963525

5.283329

6.393852

7.785446

4.45702

4.873

6.71786

2.79443

3.59612

5.37656

Minimum

-4.52516

-5.578945

-6.48366

-5.66917

-8.257244

-5.53013

-5.9949

-7.31701

-5.15868

-7.1746

-6.3468

Std. Dev.

1.161068

1.070855

1.206177

1.576226

1.997849

1.27124

1.31963

2.019268

0.88358

1.18859

1.27752

Skewness

0.265701

-0.222488

-0.61948

-0.29749

-0.202972

-0.40396

-0.2617

-0.10622

-0.91575

-0.7891

-0.2169

Kurtosis

5.229234

5.300714

6.480786

4.616246

4.860617

4.69561

5.64081

3.561202

7.82736

9.41663

6.09074

Jarque-Ber

91.47014

95.63994

237.7532

51.66226

63.1648

61.4425

126.232

6.271359

288.793

760.48

169.654

Probability

0

0

0

0

0

0

0

0.04347

0

0

0

Observ.

418

418

418

418

418

418

418

418

260

418

418

 

 

Table 7 : Test of Stability of Covariance and Correlation Matrices
When Returns Are Expressed in DMK and in FRF

 

Test of Corr. Matrices

Test of Cov. Matrices

Jenrich

Jenrich

Returns in DMK

171.752

231.681

(0.0000)

(0.0000)

Returns in FRF

172.259

230.489

(0.0000)

(0.0000)

When we focus on pre convergence vs convergence periods, the first sub-sample runs from December 31, 1990 to December 26, 1994 while the second sub-sample runs from January 2, 1995 to December 26, 1998. The p-values are given in parentheses below each statistic.

 

 

 

Table 8A: Optimal Portfolio Characteristics : Returns in DMK

MVP1

MVP2

TP1

TP2

Aust

-0.0584431

0.603254171

-0.8616618

-1.63855576

Belg

0.357381948

0.446868376

0.167546264

1.73530373

Germ

0.22755863

0.194830687

0.594285647

-0.92147177

Spai

-0.06739715

-0.06574296

-0.31932487

0.464742103

Finl

-0.00491299

-0.13610718

0.179085317

0.33532885

Fran

-0.06793962

-0.01413403

-0.0782107

-0.15614312

Irel

-0.06640605

0.194958076

0.125387425

1.060925402

Ital

-0.00775681

-0.02878118

-0.22683473

-0.39981433

Neth

0.419229773

-0.31959028

1.452442094

0.059660429

Port

0.268685373

0.124444325

-0.03271465

0.460024468

E(Rp)

0.083259196

0.092237386

0.269982202

0.717010311

V(Rp)

0.509568609

0.752369398

1.652363484

5.848567915

Sharpe

0.116635534

0.106338719

0.210030488

0.296483571

 

Table 8B: Optimal Portfolio Characteristics : Returns in FRF

MVP1

MVP2

TP1

TP2

Aust

-0.03633469

0.565958382

-0.82632755

-1.7340071

Belg

0.309997066

0.377153798

0.123287225

1.699012891

Germ

0.04836573

0.080396638

0.409054205

-1.0648642

Spai

-0.04907381

-0.04086897

-0.29685328

0.50337759

Finl

0.001055102

-0.13766284

0.182023682

0.346002875

Fran

0.094228182

0.107848283

0.084126221

-0.03784471

Irel

-0.08347784

0.253576433

0.105157555

1.142008111

Ital

-0.02005085

-0.02165421

-0.23552142

-0.40231246

Neth

0.494270533

-0.28410584

1.510469935

0.104983134

Port

0.24102058

0.09935833

-0.05541658

0.443643872

E(Rp)

0.08942705

0.094726549

0.273075468

0.735706921

V(Rp)

0.538305377

0.792717379

1.643775477

6.156749837

Sharpe

0.121886203

0.10639287

0.212991091

0.296502997

 

7 What do our results suggest as to the impact of EMU on the underlying economic structures

It is helpful at this stage to conceptualize the environment in which the individual investor operates. Variations in firm profitability as reflected in country-wide stock indices result from the interaction of shocks affecting economies, economic structures themselves and their evolution through time, and macro-economic policies.

To see this interaction one may start by wondering whether the nature of shocks affecting economic agents are affected by the economic integration process. Let us think of supply shocks first. It is unlikely that the process of economic and monetary integration would result into an increase in the commonness of supply shocks. It may however affect the structure of national economies in a way that technology disturbances will increasingly show up at the country level. This is the case if economic integration increases the degree of specialization of national economies. At the limit in a one-sector economy, sectoral shock and economy-wide shocks fully coincide. If, however, EMU is accompanied with a higher degree of diversification in national economic structures, supply shocks will become less important macro-economically in the sense that either they wash out (if the number of sectors is large enough and under the plausible assumption that sectoral shocks are little correlated) or they show up as EU-wide risk factor if all the national economies part of Euro-land represent the same portfolio of economic sectors.

Thinking of demand shocks now, it is clear that policy shocks within EMU – be they associated with monetary policy (interest rate shocks, foreign exchange shocks) or fiscal policy are fully or increasingly common in nature. If one believe in the importance of animal spirits one can argue similarly that the impact of EMU, if any, must be to make European consumers and investors more alike and subject to the same sort of psychological factors. Finally demand shocks associated with foreign demand are bound to get more similar under a common currency, besides being influenced by the same structural factors as those discussed above (more common if economies are getting to be more diversified and thus more alike, less so if specialization is increasing).

In a sense the above discussion illustrating the interactions between shocks, policies and structures suggest the possibility of two polar outcomes from the process of economic and monetary integration. In the unfavourable case, European economies are getting more specialized, foreign demand shocks translate more and more into differential country shocks calling for differentiated stabilization policies (at variance with the constraints of a monetary union). The other polar case is one where economic structures become more diversified, countries represent better diversified and also more homogenous portfolios of sectors and common macroeconomic policies are increasingly appropriate.

Our results seem to clearly support the latter interpretation of what has been and is currently happening within Euro-land. They appear to accord with a large portion of the recent macro literature. Fatas (1997), for one, looking at the correlation between employment growth rates finds that European countries represent increasingly better diversified portfolios of regions. Imbs (1999) also finds that developed, increasingly service related, economies are getting more and more alike.

 

APPENDIX A

Table A1: Unconditional Sample1 Summary Statistics

AUSTR

BELG.

FINL

FRAN.

GERM

IRELA

ITALY

LUXEM

NETHE

PORTU

SPAIN

Mean

-0.0401

0.0319

0.1191

0.0557

0.0301

0.10346

0.006

0.2121

0.0924

0.0161

0.05

Median

-0.0705

0.0724

-0.008

0.1291

0.0554

-0.0749

-0.104

0.1084

0.0991

0

-0.0175

Maximum

5.5086

2.5657

6.7605

4.457

4.9172

5.39144

5.084

3.3797

2.3794

2.8432

4.7624

Minimum

-7.2925

-3.4116

-6.46

-4.177

-4.5389

-4.4701

-4.879

-1.957

-2.039

-5.291

-4.5158

Std. Dev.

1.3618

0.8583

1.8083

1.19

1.0778

1.30524

1.734

0.8985

0.7593

1.0455

1.4388

Skewness

-0.2504

-0.1002

0.4039

0.0657

-0.1896

0.55686

0.149

0.7486

0.067

-0.431

-0.0371

Kurtosis

7.648

4.0832

4.1495

3.864

6.1948

4.93809

3.1

4.1553

2.9708

5.8544

4.0929

Jarque-Bera

204.89

11.377

18.506

7.1605

97.038

46.8431

0.926

23.097

0.1763

83.352

11.248

Probability

0

0.0034

1E-04

0.0279

0

0

0.629

1E-05

0.9156

0

0.0036

Observation

225

225

225

225

225

225

225

155

225

225

225

 

Table A2: Unconditional Sample2 Summary Statistics

AUSTR

BELG.

FINL

FRAN.

GERM

IRELA

ITALY

LUXEM

NETHE

PORTU

SPAIN

Mean

0.0448

0.2183

0.3246

0.192

0.1766

0.25467

0.203

0.1783

0.2323

0.1842

0.2523

Median

0.1237

0.3023

0.3181

0.2492

0.2368

0.26826

0.145

0.2323

0.2456

0.1149

0.3044

Maximum

3.4464

3.8328

5.8755

3.9867

2.7848

3.93614

5.169

6.3828

3.656

5.0664

6.3164

Minimum

-3.6196

-5.6564

-8.184

-5.53

-6.5061

-5.9338

-7.438

-5.244

-7.109

-6.502

-5.6296

Std. Dev.

1.0295

1.1174

1.9772

1.3583

1.2891

1.27147

1.801

0.9551

1.395

1.3797

1.5688

Skewness

-0.3505

-0.657

-0.994

-0.696

-1.0512

-0.9153

-0.426

0.2961

-1.007

-0.312

-0.3442

Kurtosis

4.3426

6.7352

6.4728

4.9877

6.4779

8.06502

4.802

14.553

8.0789

6.762

5.2008

Jarque-Bera

21.505

146.98

150.15

55.225

154.83

271.93

37.23

1254.5

279.89

136.33

49.852

Probability

2E-05

0

0

0

0

0

0

0

0

0

0

Observation

225

225

225

225

225

225

225

225

225

225

225


 

Table A3 : First period of convergence

AUSTR

BELG.

FINL

FRAN.

GERM

IRELA

ITALY

LUXEM

NETHE

PORTU

SPAIN

Mean

0.0609

0.1891

0.208

0.1722

0.158

0.23914

0.096

0.2186

0.272

0.1667

0.2325

Median

0.1869

0.3023

0.1969

0.1895

0.2308

0.26826

-0.066

0.2327

0.2387

0.1429

0.2216

Maximum

2.3337

1.8597

3.2338

2.1277

1.786

2.14804

5.169

2.9227

2.5084

3.7646

2.5714

Minimum

-2.0918

-1.5585

-8.184

-2.697

-1.81

-1.9323

-3.017

-1.389

-1.313

-1.659

-2.634

Std. Dev.

0.6998

0.6586

1.583

0.9469

0.699

0.72711

1.484

0.7456

0.7021

0.7331

0.9957

Skewness

-0.3686

-0.2145

-1.741

-0.627

-0.4142

-0.1089

0.502

0.3162

0.3074

1.2028

-0.2552

Kurtosis

3.9602

2.9006

10.2

3.2553

3.3127

3.07797

3.586

3.9741

3.2671

8.2501

3.1017

Jarque-Bera

6.8996

0.9133

301.17

7.7083

3.6921

0.25194

6.367

6.3501

2.1154

157.02

1.2757

Probability

0.0318

0.6334

0

0.0212

0.1579

0.88164

0.041

0.0418

0.3473

0

0.5284

Observation

113

113

113

113

113

113

113

113

113

113

113

 

Table A4 : Summary Statistics for Second period of convergence

AUSTR

BELG.

FINL

FRAN.

GERM

IRELA

ITALY

LUXEM

NETHE

PORTU

SPAIN

Mean

0.0331

0.2495

0.4371

0.2182

0.1974

0.28184

0.325

0.1352

0.1934

0.1996

0.2656

Median

0.0493

0.3251

0.4588

0.3253

0.2567

0.30655

0.446

0.226

0.2747

0.0122

0.4453

Maximum

3.4464

3.8328

5.8755

3.9867

2.7848

3.93614

4.925

6.3828

3.656

5.0664

6.3164

Minimum

-3.6196

-5.6564

-8.095

-5.53

-6.5061

-5.9338

-7.438

-5.244

-7.109

-6.502

-5.6296

Std. Dev.

1.2775

1.4359

2.2997

1.6724

1.6838

1.64895

2.07

1.1252

1.8428

1.8081

1.9837

Skewness

-0.2905

-0.6524

-0.774

-0.669

-0.9475

-0.8714

-0.84

0.3389

-0.839

-0.379

-0.322

Kurtosis

3.3147

4.8846

4.8304

4.061

4.4181

5.67022

4.789

14.439

5.1844

4.397

3.8971

Jarque-Bera

2.0554

24.739

27.069

13.731

26.376

47.8712

28.34

618.26

35.713

11.894

5.7424

Probability

0.3578

4E-06

1E-06

0.001

2E-06

0

1E-06

0

0

0.0026

0.0566

Observation

113

113

113

113

113

113

113

113

113

113

113

 

APPENDIX B

Table B1: Pre Convergence Correlation Matrix

Austria

1

Belgium

0.493

1

Finland

0.252

0.342

1

France

0.400

0.424

0.3323

1

Germany

0.499

0.491

0.2569

0.6219

1

Ireland

0.357

0.44

0.2601

0.3603

0.324

1

Italy

0.218

0.213

0.2456

0.3543

0.4228

0.1539

1

Luxemb.

0.287

0.307

0.1361

0.1731

0.3087

0.3196

0.0593

1

Netherl.

0.499

0.562

0.3291

0.6522

0.6305

0.4895

0.4102

0.332

1

Portugal

0.171

0.257

0.0763

0.2643

0.2414

0.2451

0.1052

0.091

0.2254

1

Spain

0.371

0.413

0.2237

0.5388

0.5076

0.2975

0.3692

0.178

0.5388

0.271

1

This table gives the unconditional correlations of the first sub-sample (pre convergence period) of the Euro-land index returns. The sub-sample runs from September 10, 1990 to December 26, 1994 and observations are sampled weekly. Returns are continuously compounded and annualized.

Table B2: Convergence Period Correlation Matrix

Austria

1

Belgium

0.577

1

Finland

0.542

0.591

1

France

0.635

0.745

0.6308

1

Germany

0.632

0.759

0.6835

0.8069

1

Ireland

0.483

0.509

0.5417

0.5271

0.6162

1

Italy

0.479

0.631

0.5551

0.6886

0.6397

0.437

1

Luxemb.

0.445

0.438

0.3303

0.4218

0.4388

0.3863

0.3604

1

Netherl.

0.666

0.784

0.6819

0.7931

0.8512

0.602

0.6481

0.497

1

Portugal

0.47

0.624

0.4961

0.6249

0.6375

0.4864

0.5504

0.337

0.6316

1

Spain

0.561

0.683

0.5946

0.7097

0.7569

0.5356

0.7006

0.368

0.75

0.616

1

This table gives the unconditional correlations of the second sub-sample (convergence period) of the Euro-land index returns. The sub-sample runs from January 2, 1995 to April 19, 1999 and observations are sampled weekly. Returns are continuously compounded and annualized.

 

Table B3 : Unconditional correlations: Subsample1 of Convergence

Austria

1

Belgium

0.52

1

Finland

0.322

0.363

1

France

0.501

0.6

0.3596

1

Germany

0.542

0.528

0.4386

0.6226

1

Ireland

0.363

0.473

0.2489

0.4802

0.5138

1

Italy

0.353

0.552

0.3274

0.5173

0.4479

0.332

1

Luxemb.

0.382

0.41

0.2333

0.2842

0.3261

0.2386

0.3417

1

Netherl.

0.511

0.611

0.4081

0.6369

0.6835

0.4911

0.4259

0.372

1

Portugal

0.24

0.294

0.1949

0.2749

0.2577

0.1621

0.2308

0.227

0.1839

1

Spain

0.404

0.492

0.3519

0.5459

0.5796

0.4232

0.468

0.349

0.5584

0.188

1

Table B4 : Unconditional correlations: Subsample2 of convergence

Austria

1

Belgium

0.595

1

Finland

0.63

0.674

1

France

0.677

0.786

0.7387

1

Germany

0.657

0.804

0.7731

0.8575

1

Ireland

0.516

0.516

0.64

0.5431

0.6343

1

Italy

0.537

0.672

0.6616

0.7648

0.7186

0.486

1

Luxemb.

0.468

0.455

0.3799

0.475

0.4811

0.4349

0.3718

1

Netherl.

0.705

0.818

0.7826

0.8386

0.8791

0.6212

0.74

0.543

1

Portugal

0.524

0.685

0.5958

0.7107

0.7011

0.5423

0.6615

0.376

0.7015

1

Spain

0.603

0.727

0.6869

0.7549

0.7951

0.5567

0.7916

0.38

0.7913

0.705

1

 

Table B5 :

AMERICAS

1

ASIA

0.1676907

1

AUSTRALASIA

0.3420364

0.304517

1

EEC

0.4502127

0.489253

0.3411

1

FAR_EAST01

0.1626266

0.9985

0.295

0.47406

1

NON_EEC01

0.3653845

0.378988

0.2942

0.73584

0.36538

1

PACIFIC_BASIN01

0.1784735

0.999236

0.3265

0.49204

0.99842

0.38137

1

First Period

 

AMERICAS

1

ASIA

0.340735

1

AUSTRALASIA

0.53693

0.581872

1

EEC

0.609744

0.520372

0.5587

1

FAR_EAST01

0.314605

0.992436

0.5446

0.49291

1

NON_EEC01

0.48334

0.510832

0.4704

0.84359

0.48922

1

PACIFIC_BASIN01

0.358277

0.998625

0.6164

0.53208

0.99059

0.51753

1

Convergence Period

 

APPENDIX C

Table C1: Pre Convergence Unconditional Correlations (Returns in DMK)

Aust

1

Belg

0.536608

1

Germ

0.425486

0.6140054

1

Spai

0.346622

0.5370041

0.51013

1

Finl

0.225583

0.4332429

0.325159

0.446083

1

Fran

0.441650

0.6416965

0.648244

0.585069

0.444588

1

Irel

0.567841

0.564794

0.397879

0.327831

0.475666

0.51901

1

Ital

0.132183

0.2748599

0.487553

0.393289

0.320581

0.34015

0.11781

1

Luxe

0.511735

0.4431805

0.158073

0.087085

0.211855

0.25836

0.48336

-0.13151

1

Neth

0.553393

0.6623321

0.684734

0.604305

0.533637

0.66263

0.67351

0.385714

0.39562

1

Port

0.323554

0.3278389

0.275881

0.368323

0.363155

0.38654

0.35719

0.352297

0.0611

0.30888

1


 

Table C2 : Convergence Period Unconditional Correlations (Returns in DMK)

Aust

1

Belg

0.544152

1

Germ

0.617712

0.7607735

1

Spai

0.532614

0.6759345

0.757912

1

Finl

0.575650

0.5852378

0.717167

0.625061

1

Fran

0.593456

0.7141319

0.798548

0.717504

0.633936

1

Irel

0.541650

0.5069203

0.619058

0.552389

0.588759

0.58972

1

Ital

0.409448

0.5887661

0.615592

0.687867

0.558657

0.67154

0.49391

1

Luxe

0.451677

0.4939711

0.471677

0.429566

0.382867

0.4831

0.4794

0.381578

1

Neth

0.659134

0.7610128

0.849728

0.733016

0.713691

0.78063

0.664

0.591278

0.50459

1

Port

0.500014

0.6300251

0.68002

0.640248

0.514352

0.66129

0.4643

0.554109

0.43519

0.66403

1

 

Table C3: Pre Convergence Unconditional Correlations (Returns in FRF)

Aust

1

Belg

0.5447598

1

Germ

0.4476294

0.6481

1

Spai

0.3207278

0.5097272

0.498967

1

Finl

0.2126732

0.4236046

0.328026

0.434376

1

Fran

0.4076219

0.6134069

0.642244

0.565868

0.430297

1

Irel

0.5717239

0.5709035

0.416427

0.316983

0.472877

0.5115

1

Ital

0.1114942

0.259148

0.474276

0.379893

0.310484

0.3208

0.10909

1

Luxe

0.5055674

0.4660494

0.198738

0.057181

0.201352

0.21796

0.48936

-0.15256

1

Neth

0.5457135

0.6656702

0.69838

0.58657

0.526131

0.64176

0.67745

0.370514

0.39072

1

Port

0.3155767

0.3370664

0.293186

0.352135

0.35614

0.36513

0.35905

0.340906

0.05604

0.30239

1



Table C4: Convergence Period Unconditional Correlations (Returns in FRF)

Aust

1

Belg

0.5600959

1

Germ

0.6248145

0.7661507

1

Spai

0.5152307

0.6635441

0.748983

1

Finl

0.5627252

0.5748288

0.70905

0.616594

1

Fran

0.565067

0.6974459

0.788574

0.703901

0.625031

1

Irel

0.5115109

0.4856093

0.602793

0.528779

0.577513

0.55472

1

Ital

0.3798789

0.5654461

0.596645

0.674697

0.546171

0.65496

0.46622

1

Luxe

0.453979

0.5055889

0.475346

0.402333

0.365478

0.43564

0.43143

0.342414

1

Neth

0.6490894

0.7548857

0.846137

0.723602

0.707772

0.76933

0.64593

0.573079

0.48603

1

Port

0.5079499

0.6372548

0.684133

0.63195

0.50716

0.64995

0.44571

0.536932

0.43821

0.66036

1

 

Technical Note

For the sack of completeness, we provide in this technical note provides computational details of the Jenrich test statistics reported in section 2.3.1.3. Let and be the sample correlation matrices of pre-convergence and convergence periods, respectively. The two matrices are based on samples of size and , and the null hypothesis we are testing through the Jenrich statistic is . Define:

= "average" correlation matrix.

= Kronecker delta = identity matrix of the same dimension as .

The Jenrich test statistic can then finally be computed as:

As discussed in the body of this section, this test statistic is a chi square with degrees of freedom equal to where n is the number of assets (or countries). If we replace the correlation matrices with the corresponding covariance matrices, then the appropriate test statistic becomes:

Hence, the second term in the statistic for testing the equality of correlation matrices can be viewed as a correction term, since comparison of covariance matrices involves a higher degree of freedom ( ).