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Stock market convergence and investment

diversification in the European Union

Jaap Willems*

Supervisor: A.J. Meesters

23 January 2009

MScBA Finance

University of Groningen

Faculty of Economics and Business

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ABSTRACT

Recent literature (e.g. Carrieri, Errunza and Sarkissian, 2004) has emphasized the growing relative importance of sector-level asset diversification strategies in comparison to country-level diversification strategies, as country-level stock returns have converged while sector-level returns remained stable. In this thesis, I investigate the structure and stability of sector and country equity returns in the European Union between 1987 and 2006 to assess whether this trend is also present in Europe. This is done by performing hierarchical cluster analysis on equity returns from 26 European Union stock indices and 10 pan-European sector indices. Results show that country-level equity returns are indeed converging fast in Europe, while sector-level equity returns remain relatively stable. However, since sector-level equity returns are systematically highly correlated, for the moment country-level diversification strategies still provide the highest diversification benefits.

1. Introduction

Due to political, economic, financial and regulatory forces, European stock markets have, according to recent literature, converged towards full integration in the past two decades (Hardouvelis, Malliaropulos and Priestley, 2006; Licht, 1998). In light of this development, investors in Europe have gradually seen the benefits of country-level investment diversification strategies diminish (Carrieri, Errunza and Sarkissian, 2004). Several publications (e.g. Roll, 1992; Carrieri et al., 2004) have therefore come to emphasize the increasing relative importance of sector-level diversification in comparison to country-level diversification. So far, the existence of increasing integration of European stock markets has been proven statistically using more advanced methods such as Vector Auto Regression (VAR), and the increasing relative importance of sector-level diversification has been shown by simple correlational studies. Yet a clear and recent study visualizing the structure of the European capital market, and the stability of that structure, has not been performed. This information, however, is crucial for investors who want to know across which countries or industries in Europe they should spread their investments to achieve the best diversification results. Information about the structure is needed to determine how to diversify investments in Europe, while the stability of the structure is of interest because it gives an indication of continuity and possible future trends of financial market structures. Combined they paint a picture of the degree and speed of integration of Europe’s financial markets.

One tested method of visually depicting the structure and stability of international financial markets was presented three decades ago by Panton, Lessig and Joy (1976). In their paper, a method called

hierarchical cluster analysis based on correlation analysis was introduced to financial research.

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results about the capital market structure of that time. Although the original publication by Panton et al. is dated, the methodology itself remains highly applicable to this area of financial research, as Modern Portfolio Theory, which uses correlations as one of its criteria for selecting an investment portfolio, remains popular and broadly used. Therefore, I will revisit the methodology in this thesis, applying it to sector-level and country-level equity returns in Europe. This allows me to make a clear comparison and draw definite conclusions about the state of capital market integration, and the state of investment diversification opportunities in Europe. This approach also enables me to take a micro-perspective on the developments, putting focus on single objects (sectors or countries) and developments in their characteristics over time.

This thesis broadly has two objectives. First, using national stock market data, and sector stock price data, over the years 1987-2006, I will clearly map both the current and historical intra-European equity market structure, aiming to investigate the characteristics and development of this structure in both the geographic and sectoral sense. Second, combining these results, I will come to conclusions about intra-European asset diversification opportunities. In summary, the research question can be formulated as follows:

Has stock market convergence in the European Union led to geographic investment diversification strategies becoming relatively less attractive than sectoral investment diversification strategies?

The rest of this thesis is organized as follows. Section 2 reviews past literature deemed relevant to the research topic to build a theoretical framework. Based on this, a set of three main hypotheses is defined. These hypotheses are presented throughout section 2 in tables 2, 3 and 4. In section 3, a description of the used data and its sources is presented. Section 4 carefully describes the methodology and some issues related to it. Finally, in section 5 the results are presented and discussed, after which section 6 comes to some final conclusions.

2. Literature review

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return, or maximizing return for a given amount of risk. Key to this theory was that as long as assets could be found which had a less than perfect correlation to each other, risk could be reduced through diversification. Initially, the focus of such risk diversification was domestic, but in the decade which followed Markowitz’ publication, the post-Second World War process of globalization in many areas had gained momentum, and research began to focus on the benefits of international diversification. Sixteen years later, Grubel (1968) wrote a paper on international equity diversification in which he acknowledged that Modern Portfolio Theory had now become, according to him, “basic economic orthodoxy.” He examined the risk and return characteristics of 11 industrialized countries over the years 1959-1966 and came to the conclusion that diversifying investments across these countries would have given investors higher rates of return or lower variance of their portfolios than investing domestically. Keeping portfolio variance constant, in those years an American investor could have seen a return of 12.6 percent on an international portfolio, as opposed to merely 7.5 percent on a purely domestic (United States) portfolio. The benefits of international diversification were now clear.

Levy and Sarnat (1970) came to the same conclusion, and noted that “the existence of a relatively high degree of positive correlation within an economy suggests the possibility that risk reduction might be facilitated by diversifying securities portfolios internationally.” To examine the potential gains of international diversification, Levy and Sarnat gathered the mean rate of return and standard deviation of common stocks in 28 countries – both developed and developing countries – over the years 1951 to 1967. From this data they constructed mean-variance optimal portfolios, and found that only 9 out of the 28 countries were included in any one of the optimal portfolios. The largest part of most of these portfolios was to be invested in countries with such diverse backgrounds as the United States, Japan, Venezuela and New Zealand. Strikingly missing from any of the portfolios were developed countries such as Canada and the countries of Western Europe. All of this is not very surprising if one looks at the characteristics of the individual countries. For instance, return on investment in Japan had a negative correlation with 5 other countries, including the United States, and had both high risk and return. Canada on the other hand, had a positive correlation of .81 with the United States, while its return was relatively lower, and risk relatively higher.

2.1 International capital market structure

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market which nonetheless influenced, and was influenced by, other capital markets, some authors had started to wonder whether one should not just consider the world as one large single integrated capital market. Defining what constitutes such an integrated capital market however, is no easy task, as was noted by Furstenberg (1998), who stated that no clear and accepted definition of an integrated capital market exists. According to his paper, there were however certain preconditions which had to be met in order for financial integration to take place, such as no discrimination between markets in regulatory, tax and legal areas. Emiris (2002) put forward the point that if there is full capital market integration, investors in all markets use only common risk factors to price assets, as the country-specific risk is fully diversifiable to them. If markets are only partially integrated however, investors price both common and country-specific risk and assets with the same risk will have different prices in different markets.

According to Agmon (1972), who argued for the existence of a single international capital market, most academics took the existence of different political systems, currencies and trade barriers as proof of a segmented international capital market, but they should reconsider that idea. After examining the behavior of international asset prices in the United States, United Kingdom, Germany and Japan, he found that the price behavior in these markets was consistent with his so-called one market hypothesis. His results showed that a great amount of German stocks could not be differentiated from their American counterparts. Furthermore, he found that the stocks in the United Kingdom and Japan behaved as a type of “specialized low-beta stocks” within the presumed single international market. Solnik (1974) however, argued that Agmon’s method lacked “conceptual justification” and had statistical shortcomings. In his paper, Solnik developed an “international market structure of asset prices” and showed that a single international capital market is unrealistic due to precisely the national factors which influence stock prices. Based on the results of Solnik’s investigation and testing, the most realistic situation of international stock prices turned out to be a multi-index specification which considered both international as well as domestic factors.

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“the more open the [nation’s] stock market is to capital flows, the higher will be the covariance between that market and the markets in other countries.”

Panton, Parker and Joy (1976) also noted the importance of these comovements for investors, and performed a similar study as Ripley into their structure, with the notable difference being that they also wanted to find out if the international equity market structure (of comovements) remained stable over time. This information is important for investors, as a stable structure in equity markets implies that they are able to diversify without the need for forecasting. Panton et al. used a data set of 12 countries, and using a method called cluster analysis,1 examined stock market returns over the years 1963-1972. They used tree-like figures called dendrograms to visually display the development of the international capital market structure over time. The results showed that a distinct “core” group of worldwide equity markets (the United States, Canada, and some Western European markets) could be identified which had high similarity with each other. All of these markets were situated in highly developed western countries. Furthermore, besides this core group of highly similar markets, four separate pairs of countries with especially high similarity to each other could be identified. These were the United States and Canada, France and Belgium, Germany and the Netherlands and England and Australia. Investigating the stability over time of their results, Panton et al. noted that results were more stable in the short-term (when comparing year-on-year structures) than in the long-term (when comparing for example three-, five- and ten-year steps).

Hilliard (1979) acknowledged all of the previously discussed papers, but was more interested in what would happen to the international equity market structure during the time of a financial crisis. To investigate this, he took daily stock market closing prices of 10 worldwide stock markets (6 European markets and the United States, Australia, Japan and Canada) from July 1973 until April 1974. This period included the oil crisis of 1973, which started in October 1973 and ended in March 1974. Hilliard expected this crisis to operate as a common external variable to all the 10 stock markets and thus introduce comovements. He furthermore hypothesized that there should be no lag in real time reactions of the different stock markets to the oil shock. Using spectral analysis,2 Hilliard investigated the coherence between the 10 markets. Results showed that during this period there was not a particularly strong link between the American and European stock markets, with exception of The Netherlands’ and the United States’ stock markets. Markets with a high coherence

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with other markets in general were The Netherlands, Germany, United States and France. On the other hand, Australia, Japan and Italy displayed low coherence with other markets. Not much appeared to be different from previous findings. Table 1 lists the main findings relating to European countries of the period in financial research lasting from the late 1960’s to late 1970’s, when there was a lot of emphasis on the international capital market structure.

Table 1: Summary of relevant early literature about the international capital market structure

Author and year Period European countries in data Results on European countries

Grubel (1968) 1959-1966 6 out of 11:* Belgium, France, Germany, Italy, Netherlands, UK

Correlations of 6 European countries to US range from .11 (Belgium) to .30

(Germany). Intra-European correlations not given.

Levy and Sarnat (1970) 1951-1967 14 out of 28: Austria, Belgium, Denmark, Finland, France, Germany, Italy, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, UK

High correlations between founding EEC members excluding Luxembourg, from .31 (Italy-Belgium) to .76

(Germany-Netherlands). Given correlations of

non-EEC European countries range from .10 (Austria-Denmark) to .38 (Austria-UK). Ripley (1973) 1960-1970 13 out of 19: Austria,

Belgium, Denmark, Finland, France, Germany, Ireland, Italy, Netherlands, Norway, Sweden, Switzerland, UK

On average, half of the movement of a country's stock market is unique to that country. Inside Europe, this uniqueness reaches as high as 70% for Denmark and

Finland, and as low as 30% for Switzerland and the Netherlands.

Panton, Lessig and Joy (1976)

1963-1972 8 out of 12: Austria, Belgium, France, Germany, Italy, Netherlands,

Switzerland, UK

Of the European countries, three distinct clusters of countries can be identified.

Austria and Italy cluster together, as do the UK and Belgium. Both clusters have low

similarity to each other, and are also largely dissimilar to other countries in the data.

Germany, the Netherlands and

Switzerland also cluster together and have

a relatively high degree of similarity. Hilliard (1979) 1973-1974 6 out of 10: France,

Germany, Italy, Netherlands, Switzerland, UK

The Netherlands, Germany and France

have high “coherence” with the other countries. Italy displays low coherence. Highest coherence between The

Netherlands and Germany (.362), lowest

between Italy and Switzerland (.095).

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1993, they came to the conclusion that the correlation matrix changed significantly over the years. They found that this instability was present in both the short-term (quarter on quarter results) as in the long term (6 months to 11 years results). This is a result quite opposed to Panton et al, who found that especially in the short-term, stock returns were stable. More recently, the direction of research has shifted towards trying to explain the drivers of international capital market structure and comovements of stock prices (e.g. Cheung and Lai 1999; Connolly and Wang, 2003), and to explaining through what mechanism changes in one stock market are transmitted to another (e.g. Eun and Shim, 1989). These topics are largely beyond the scope of this thesis.

2.2 Economic integration and financial market integration

Chen, Roll and Ross (1986) noted that there are several macroeconomic variables which systematically influenced the stock market, for instance the spread between long and short interest rates, expected and unexpected inflation, industrial production, and the spread between high- and low-grade bonds. Asprem (1989) further investigated the effect of macroeconomic events in 10 European countries over the years 1968 to 1984. He found that the stock market was positively correlated to exports and, as also found by Chen et al. 3 years before, to industrial production. Furthermore, he found that the stock market was negatively correlated to employment, exchange rate, imports, inflation and the interest rate. Jorion (1990) furthermore found that there is a relationship between the value of multinationals and the exchange rate. Finally, according to Emiris (2002) there are several reasons why economic integration leads to integration of financial markets. As monetary and fiscal policies converge, inflation, short-term interest rates and real expected cash flows converge as well. This then leads to increased synchronization of business cycles, and consequently to higher correlations of stock returns.

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around three crises (the 1987 market crash, the East Asian financial crisis of 1997, and the Mexican peso devaluation of 1994). They concluded that there was no evidence for contagion, but that instead there was interdependence between stock markets in all periods. Their results however are largely refuted by Corsetti, Pericoli and Sbracia (2005) who criticize the methodology – which they say implicitly assumes the market volatility of the country where a shock to the stock markets originates to be the common market volatility for all countries under study, and after altering it find that there are several countries where evidence of contagion can indeed be found.

2.3 Developments in the European Union

Integration of European capital markets should be seen in the greater context of ever increasing regional integration in Europe on economic, political and regulatory levels. The three most groundbreaking economic developments in the post-Second World War era have been the formation of the European Economic Community (EEC) in 1957, the creation of the Economic and Monetary Union (EMU) of the European Union in 1990, and finally the evolvement of the EEC into the European Union in 1993 due to the Maastricht Treaty. The latter event was followed by the complete liberalization of capital movements, converging European policies (whether forced or not) on prominent economic indicators such as inflation, government debt, government spending and interest rates, the creation of the European Central Bank (ECB), and the introduction of the euro in light of the EMU as common currency in the late 1990's. Currently the European Union totals 27 member states, and the euro is in use by 15 countries. Both the EU and the eurozone look set to expand further in the future.

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to join the eurozone or not.

The third influence, catastrophes or other purely domestic events, still have the ability to affect a single country’s stock market in unequal terms. Finally, the business cycle is the only area in which there is no full certainty about whether convergence is taking place or not. Although popular opinion based on anecdotal evidence seems to be that there is a certain degree of convergence in the business cycle – e.g. as of 2008, the larger countries of the European Union are collectively entering a recession due to the fallout of the current financial crisis, scientific research has not reached a conclusion. To illustrate the contrasting opinions, Camacho, Perez-Quiros and Saiz (2006) and Artis (2003) argued strongly that a common business cycle does not exist, whereas Artis, Krolzig and Toro (2004) found that “there is clear evidence of comovements in output growth among European countries.”

Furstenberg (1998) stated that the preconditions which have to be in place for financial integration are that there is no discrimination between markets in the areas of regulation, tax and other legal matters. In the area of regulation, a distinction has to be made between the European-wide legal system, and the national legal systems which obviously are still in place. The European Union has the power to introduce regulation which then becomes law in all member countries, but the national laws still remain in place. Discrimination between markets in this area has thus decreased, but nevertheless still exists and this situation is not likely to change in the immediate future. In the area of tax, clearly there is discrimination between markets, as each member country maintains its own tax system. To illustrate the point, while fully realizing that there are many exceptions to every tax system, capital gains tax in the Netherlands is effectively 1.2%, while in France it is 29%.3 Finally, in the area of legal matters, there is convergence in the European Union due to regulation which is enforced by the European Court of Justice.

Hilliard (1979) summarized two main reasons for the comovements and interdependence of equity markets. Firstly, when the GDP of countries moves together, expectations about the economy become more similar, indirectly linking stock prices between countries. Secondly, when large multinational firms are represented in two indices, this creates a situation where the stock of one company in two markets creates “nearly identical price behavior”, albeit still limited by capital flow

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http://www.belastingdienst.nl/particulier/aangifte2007/boxen_en_tarieven/boxen_en_tarieven-limitations. These capital flow limitations are not present anymore in the European Union. Yang, Min and Li (2003) noted that the faster transmission and processing of information across countries pushes European stock markets closer together. They furthermore pointed out that in recent years there has been a series of mergers and consolidations of European stock markets, leading to convergence because of various reasons. Examples of such mergers are the OMX exchanges, the Euronext-NYSE exchanges, or the merger between the London Stock Exchange and Borsa Italiana. 4

Hardouvelis, Malliaropulos and Priestley (2002) found that many investment barriers in Europe have been lifted through recent developments, and the euro has effectively standardized European equity prices. It has furthermore reduced investors' transaction and information costs. Institutional investors saw barriers on European non-domestic holdings disappear, and private European investors are now also more easily able to invest across borders than ever before. All of this implies that intra-European trading has become easier. It can be expected that due to this, when new information hits the market, it is quickly implemented and equally distributed across European markets.

Koutmos (1996) found clear integration among stock markets of large European countries. He investigated so-called first and second moment interactions among four large European stock markets. First moment interactions are defined as a lead-lag relationship in both directions, whereas second moment interactions are defined as interactions of volatility between markets. Koutmos’ findings showed that European stock markets were interdependent and “integrated in the sense that they react not only to local news but also to news originating in the other markets, especially when the news is adverse.” Emiris (2002) also investigated whether European monetary and economic convergence also led to stock market integration by investigating stock returns from 8 European countries. She studied whether European-wide risk gradually started to affect stock prices more than country-specific risk, a sign of integration. Results showed that the European stock markets were not perfectly integrated, but that the biggest convergence towards integration was noticeable in the smaller countries of the European Union.

Galati and Tsatsaronis (2003) noted that after the introduction of the euro, the macroeconomic

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environment in Europe became more homogeneous, and as a result of this the influence of country-factors in the pricing of stocks decreased. Yang, Min and Li (2003) discovered that EMU countries with more prominent stock markets were converging faster after the introduction of the euro, but the EMU countries together became less integrated with the stock market of the UK, a non-EMU country. Kim, Moshirian and Wu (2005) performed a study on recent evidence of financial integration, using data from EMU countries as well as Japan and the United States, over the years 1989 to 2003. They showed that in the 1990’s, stock market integration in Europe was highly volatile, but that in the two years leading up to the introduction of the euro integration increased rapidly. Since 1999, the movement towards integration became both stronger and more stable as volatility and return spillovers increased.

Corhay, Tourani Rad and Urbain (1993) performed a cointegration analysis on 5 major European stock indices, and used the actual prices instead of the returns to be able to investigate the long-term behavior of these markets. Their results show evidence of cointegration between European stock markets, which prove “the existence of common long-run stochastic trends.” Hardouvelis, Malliaropulos and Priestley (2002) found that European stock markets – at least those of eurozone countries – have converged and tended towards full integration in the past two decades. They note that this was already the case for money and bond markets, but now can also be shown to be the case in stock markets.

Past literature would thus suggest that economic convergence leads to stock market convergence (e.g. Emiris, 2002), and that this is a development which has also been taking place in the European Union (e.g. Corhay et al., 1993; Koutmos, 1996; Hardouvelis et al., 2002; Galati and Tsatsaronis, 2003). Based on this, the first hypothesis (and sub hypothesis) can be formulated:

Table 2: Research hypotheses 1 and 1a (H1 form)

Hypothesis 1: Correlations of stock market returns of the current members of the European Union have converged between 1987 and 2006

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2.4 Sectoral diversification

So far, all the papers discussed in this thesis prior to this point, have emphasized the geographic differences between markets and stock returns, and the opportunities for investment diversification created by these differences. However, as financial market integration has continued, diversification opportunities have decreased as well, and the focus has now shifted to portfolio diversification among sectors. This is deemed by many to be a more beneficial diversification strategy, as the interaction of “sector returns” with the business cycle is different for each sector. For instance, common wisdom says that in a recession, the food sector provides a safe haven, whereas investing in the car industry at such a moment might not be a good idea.

Roll (1992) found that in fact country-factors and sector-factors should not be seen separately, and could in fact be combined. He argued that national stock price behavior could be explained by the industrial composition of a country, and concluded that “countries with similar industries tend to be more correlated than countries with dissimilar industries.” Adjaouté, Danthine and Isakov (2003) later came to a similar result, as they found that in fact the country factors of equity returns in Europe are now “dominated by the factors associated with the industry or sector.” This implies that when comparing equity returns of countries, it is important to take into consideration which industries are relatively large in those countries. They also found that this effect is more visible in Europe than it is elsewhere, indicating that it is in fact a European trend. This shares some common ground with Roll’s finding that the effect takes mostly place in developed countries.

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come as a surprise as “in the [United States], no portfolio manager would think of allocation across states.”

Finally, Galati and Tsatsaronis (2003) quoted a survey by Merrill Lynch about diversification strategies among market participants in Europe. Of those questioned, 75% said that they now based their portfolio allocation on sector diversification, while only 10% still did so among geographic lines. In the past these results had been far less pronounced in favor of sectoral diversification. There thus seems to be a trend towards sectoral diversification in Europe, and away from country diversification. To investigate whether this matches the actual developments of European stock returns, and to put a contra-hypothesis opposite hypothesis 1 and 1a, I formulate the following hypothesis and sub hypothesis:

Table 3: Research hypotheses 2 and 2a (H1 form)

Hypothesis 2: Correlations of sectoral stock returns inside the European Union have remained stable between 1987 and 2006

Hypothesis 2a: In the European Union, groups of sectors can be identified whose stock returns consistently clustered together between 1987 and 2006

Finally, hypothesis 3 summarizes the findings of hypothesis 1 and 2 and allows me to answer the research question presented in the introduction:

Table 4: Research hypothesis 3 (H1 form)

Hypothesis 3: Investors into Europe should diversify their investments among sectors, instead of countries, to achieve the maximum diversification benefits

3. Data

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In 1958 six countries formed the European Economic Community: Belgium, France, (West) Germany, Italy, Luxembourg and The Netherlands. Before the transition to the European Union there were three rounds of enlargement, in 1973, 1981 and 1986. In these years Denmark, Ireland, the United Kingdom, Greece, Portugal and Spain respectively entered the EEC. Since the European Union came into existence in 1993, there have been two further rounds of enlargement. First in 1995 when Austria, Finland and Sweden acceded, and then in 2004 when a total of twelve countries joined the European Union. As of 2008, the Union totals 27 countries. Lithuania is excluded, for no data was available from its stock market OMX Vilnius. The dataset includes monthly returns in domestic currency on the most prominent national stock markets of 26 of the 27 current European Union countries. All data is taken from Thomson Datastream. Monthly returns are calculated in the typical way:

Returni,t = (Pricei,t – Pricei,t-1) / Pricei,t-1 (1)

Where i is defined as the country, and t is the time period. This thesis therefore employs returns unadjusted for exchange rate fluctuations. Returns of 16 out of the 26 countries are denoted in euro, but the 10 other countries all use different currencies. The choice for using unadjusted returns is discussed further in section 3.3.

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observations, the mean, standard deviation, minimum and maximum.

Included in the dataset are also monthly index returns of 10 artificial sector indices over the years 1987-2006 (20 years). The indices are taken from and composed by Thomson Datastream and are universally used and relied upon in financial publications. Returns are again calculated as in equation 1, with the difference that now i is defined as the sectoral index. Appendix 8.2.1 briefly names the sectors, their Thomson Datastream codes, and currencies. Appendix 8.2.2 displays descriptive statistics for each sector, listing observations, mean, standard deviation, minimum and maximum.

3.1 Data visualization

In section 4 and 5 I will respectively discuss the methodology and its results, using the data as described earlier in this section. Before getting to that part of the thesis, it is interesting to briefly visualize some of the differences which persist in correlations between different countries, and between different industries. This will not yield any new information, but it presents a clearer image of some of the developments than only correlations can. Consider graph 1, which on the left plots the returns of France and the Netherlands against each other, and on the right plots the returns of Austria and the Netherlands against each other. This confirms what one would expect based on previous literature and empirical research; the stock markets of two long-standing EU members (the Netherlands and France) move in a much more similar way to each other than the stock market of one long-standing member (the Netherlands) and one relatively new EU member (Austria).

Graph 1: scatter plots of four European Union countries, monthly returns (1987-2007)

-0,200 0,00 0 0,20 0

France (CAC m onthly ret., 1987-2007)

-0,300 -0,200 -0,100 0,00 0 0,10 0 N e th e rl a n d s (A EX m o n th ly r e t. , 1 9 8 7 -2 0 0 7 )                                                                                                                                                                                                                                           -0,200 0,00 0 0,20 0

Austria (ATX m onthly ret., 1987-2007)

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Similar differences can be shown to exist in European sectoral equity returns. In the left of graph 2, the returns of the EU’s basic materials sector vis-à-vis the returns of the EU’s industrials sector are shown over the years 1987 to 2007. The right side of graph 2 shows the returns of the EU’s telecom sector against those of the EU’s oil and gas sector. Clearly, basic materials and industrials move closely together, while there is no such strong relation at all between telecom and oil and gas. This is an intuitively logical result, considering the dependence of industrial companies on basic materials

Graph 2: scatter plots of four European sectors, monthly returns (1987-2007)

-0,200 -0,100 0,00 0 0,10 0

Industrials (m onthly ret., 1987-2007)

-0,200 -0,100 0,00 0 0,10 0 B a s ic M a te ri a ls (m o n th ly r e t. , 1 9 8 7 -2 0 0 7 )                                                                                                                                                                                                                                             -0,200 0 -0,100 0 0,00 00 0,10 00

Oil and Gas (m onthly ret., 1987-2007)

-0,200 0,00 0 0,20 0 T e le c o m (m o n th ly r e t. , 1 9 8 7 -2 0 0 7 )                                                                                                                                                                                                                                                 

3.2 The case for unadjusted returns

In this thesis I employ monthly stock market and sector index returns which have not been adjusted for exchange rate fluctuations. Of the country-level data, 16 out of 26 countries indices are denominated in euro, with the remaining 10 denominated in other currencies. The sector-level data is all based on indices denominated in U.S. dollar. Therefore exchange rate changes of the currency in which the underlying European stocks are denominated to the U.S. dollar affect each return in a systematic way and do not influence calculated correlations.

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variance. They attributed this to idiosyncratic shocks which domestic stock prices face. In an earlier paper which employed a similar technique as the one used in this thesis, Panton, Lessig and Joy (1976) also struggled with the same issue. After performing their research both with returns adjusted and unadjusted for exchange rates, they came to the conclusion that “the resulting correlation matrices [of exchange rate adjusted returns] were nearly identical to those calculated without the exchange rate adjustment.” Based on these results, I have decided to employ unadjusted returns in this thesis as well.

4. Methodology

4.1 Hierarchical cluster analysis

In this thesis, I employ a methodology called hierarchical cluster analysis and consequently dendrograms to respectively calculate, and graphically map, the structure of national and sectoral equity returns in Europe.5 It is a technique which previously has been mainly used in marketing, biological sciences and medical studies, but which was already used on a similar topic by Panton et al. (1976). Since then, other arguably more advanced graphical methods such as MultiDimensional Scaling techniques (MDS) have been applied to show linkages between stock markets (e.g. Groenen and Franses, 2000). However, for the topic at hand, cluster analysis is more suitable, as the focus of MDS is fully on the graphical output, whereas hierarchical cluster analysis puts emphasis on the statistical output. Moreover, the focus comes to lie on correlations between equity returns, which are the driver for diversification decisions by rational investors. I choose dendrograms to graphically picture this output. Dendrograms are discussed in section 4.2.

In essence, cluster analysis is a technique which investigates different cases or variables and their relation to each other based on a certain measure of distance and similarity, such as for example correlations or Euclidean distance. When employed on a dataset of several variables, it starts out with all variables as a separate group, and then goes on to group them together step by step – based on the closeness of variables to each other – until all variables form one big group. It thus starts with n clusters which at that point are n variables. The two variables which are most similar are then merged into one large cluster, and (n-1) clusters are left. From these (n-1) clusters, the two most similar clusters are found and merged, so that in the end there are only (n-2) clusters left. And so on, until one big group remains.

5

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There are two important choices which have to be made when applying cluster analysis to interval data as in this thesis. The first choice pertains to the criterion with which similarity or distance between the variables is measured. I will employ Pearson’s (standard) correlations, as it is the commonly used measure of relations between objects in financial research, and moreover is the standard measure of similarity on which asset diversification decisions are based. It is, of course, also easy to interpret. The second choice which has to be made is the criterion based on which variables are clustered together at successive steps. In this thesis I employ a method called UPGMA (“Unweighted Pair-Group Method using Arithmetic averages”), which sometimes is also termed the average-linkage-between-groups method. In this method, the distance between two clusters is defined as the arithmetic average of the distance between all possible pairs of variables. For instance, picture a situation with two clusters. The first cluster consists of variables A and B, and the second cluster consists of variables C, D and E. The UPGMA distance would then be calculated by taking the arithmetic average of the following distances: (A, C), (A, D), (A, E) and (B, C), (B, D), (B,

E).

Using an example from Panton et al. (1976) and letting Ri,j represent correlation between variables I and J, the average correlation of cluster (A, B) with cluster (C, D, E) as above can be calculated as

R(A,B), (C,D,E) = (RA,C + RA,D + RA,E + RB,C + RB,D + RB,E) / 6 (2)

This example can of course be extended or simplified to apply to other cases.

4.2 Dendrograms

After going through the steps as described in the previous section, you end up with information about clustering and the proximity of variables to clusters and clusters to each other. This information is summarized in a so-called agglomeration schedule. It is now necessary to make a graphical front for this information. This can be done through a dendrogram. A dendrogram is a sort of tree diagram which graphically shows at which point clusters merge with each other, and at what level of similarity.

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of clustering and the correlational coefficients which go along with it. Before the dendrogram, the name of the variable (in this case A, B, C, D, or E) is given, followed by its identification number, which is simply the number it is assigned in the dataset. Above the dendrogram, the highest and lowest correlation of the clusters is shown. Shown is that variables C and D cluster together at a correlation of .810 (which is thus higher than the correlation of any of the other variables with each other). Variables A and B cluster together at a lower correlation of .744 (which is not displayed above the table, but can be looked up in the agglomeration schedule). After variable E has attached itself to cluster (C, D) at an average correlation of .727, the cluster consisting of A and B clusters together with the cluster consisting of C, D and E at a correlation of .165. It should be noted that the distance in the dendrogram is relative: it ranges from the highest to the lowest clustering correlation and everything in between is scaled in the right proportion. In the case of an extreme outlier in the data, all the other variables are going to appear to be located much closer together, but inspection of the agglomeration schedule is necessary to see if this is in fact true.

Graph 3: Example of a dendrogram and agglomeration schedule (below)

Correlation: .810 .165 +---+---+---+---+---+ C 3  D 4   E 5   A 1  B 2 

Stage Cluster 1 Cluster 2 Coefficient Stage Cluster 1 Cluster 2 Coefficient

1 C D .810 3 C E .727

2 A B .744 4 A C .165

One final note ought to be made about the table below the dendrogram. At every stage of clustering, there is a “cluster 1” and “cluster 2”. In each instance, every cluster is represented by the variable in that cluster with the lowest identification number (i.e. cluster A-B is represented by A since 1 is lower than 2, the identification number attached to B). If two clusters are merged, “cluster 1” is represented by the cluster with the lowest identification number. This has no further implications for the results.

4.3. Issues concerning hierarchical cluster analysis

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which need to be addressed. The first issue, the fact that selecting the final amount of clusters is a rather subjective activity, is well-known and well-documented. The second issue, that results of hierarchical cluster analysis can become instable due to the order in which data is put into the model, is a bit more obscure and often ignored, but was recently well documented by Kloot, Spaans and Heiser (2005).

Perhaps the most obvious downside of cluster analysis which needs to be pointed out is the fact that it is not clear how to determine the stage of clustering at which the desired amount of clusters are produced. In other words: at the beginning there are N clusters, and in the end there is 1 cluster, but at how many clusters does one assume the result to be final? At which stage can one claim that the data consists of X sufficiently different clusters? Of graph 3 in the previous section, one could say, for instance that there are either 5 clusters (A, B, C, D and E), that there are 3 clusters (C-D, A-B and E), that there are two clusters (C-D-E and A-B), or simply that the data is so close that it all forms one group (A-B-C-D-E). This is open to debate, and although there are some statistical ways to come to a “desired” level of clustering depending on the data, it normally is decided in a subjective way (e.g. in Panton et al., the authors at one point take a correlation of .3 as a cutoff point for clustering). In this thesis as well, the final clustering result is more or less subjectively decided. I shall use the following subjective measure to determine when a cluster is formed, and use it throughout the thesis:

A definitive cluster is formed when there is an absolute difference of .100 or more between the correlation to the existing cluster of the last country added to that cluster and the correlation of a new country to the existing cluster (including the last country added).

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A more serious problem which directly affects the outcome is the problem of a slight instability in the results when the order of data input is changed, as described by Kloot, Spaans and Heiser (2005). When calculating the distances between variables, hierarchical cluster analysis employs a proximity matrix, showing the distance of each variable to each other. In this thesis these proximities are based on Pearson’s (standard) correlations. A procedure then starts to discover which entities are closest together, and merges these entities into a cluster at a level called the “fusion coefficient”. The problem shows up when, in the proximity matrix or at any stage in the clustering process, there are two pairs of entities (variables or clusters) which share the same fusion coefficient. If, for instance, the correlation of A-B to C is .750, whereas the distance between D and E is also .750, distances are tied and the procedure of hierarchical cluster analysis goes on to make a random choice about which pair to cluster first. This then has implications for the rest of the dendrogram, although it has to be stressed again that the effect is only limited. As stated by Kloot et al., “a common approach to data order instability is to ignore the fact that tied distances may produce multiple [hierarchical cluster analysis] solutions. This is default in SPSS and many other statistical analysis packages.”6 Other ways of dealing with this issue might be to run many cluster analyses with random order of input, and then to “report, compare and interpret” all the different outcomes.

In this thesis I choose the former option, while bluntly acknowledging that this will – slightly – influence the outcome. However, the outcomes are not radically different. At most, correlations might be slightly over- or understated, or an entity might merge into a different cluster one step too early. The big picture however, remains largely the same and there is barely any room for false conclusions. It should be pointed out that large amounts of previous research (Panton, Lessig and Joy, 1976 is such an example) have been conducted employing this methodology, and entirely ignoring this issue – which was already known at that time. The reason why I so clearly need to point it out here is that in my results, I first investigate a core group of countries in each period (section 5.1.1), and then investigate the countries when adding new ones in every period (section 5.1.2). Because of this, it is easy to compare clustering results when certain countries are present or not, and it is obvious that there are slight differences in correlation and clustering activity.7

6

In my thesis, I employed SPSS 15.0 and thus originally was oblivious to this problem. 7

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5. Results

This section presents the results of the country-level and sector-level equity returns structure. In section 5.1 the results on country-level equity returns will be discussed. Section 5.1.1 presents the results on the “core” group of countries – the group for which data was available over all periods. These results are not used to investigate any of the hypotheses, but are included to create a full picture, i.e. what happens to the structure if no countries are added to the group at any moment. Section 5.1.2 presents the results on all the countries which are available for each given time interval. Results in this section are used to investigate hypotheses 1 and 1a. Section 5.2 discusses the results of the sector-level equity returns. Results of this section are used to investigate hypothesis 2 and 2a. Combining the findings of section 5.1 and 5.2 and the results on both hypotheses, section 5.3 discusses the state of diversification opportunities in the European Union to come to a conclusion about hypothesis 3.

5.1 Geographic structure of equity returns

In this section I present the results of the evolution of clustering among 26 national equity markets in 4 steps of 5 years: 1987-1991, 1992-1996, 1997-2001 and 2002-2006. In the first step (1987-1991), there is information of only 12 countries. These are the “core” group of countries which have data available from the beginning, and only miss a maximum of 1.5 years worth of data – or 18 observations – in this time span. In the second step (1992-1996) 5 countries are added, under the same condition of missing out a maximum of 18 observations, to make a total of 17. In the third step (1997-2001) another 8 countries are added to create a nearly complete group. In the final step (2002-2006), the final country is added to the group. This approach enables me to at least analyze two steps (1997-2001 and 2002-2006) in which the group is nearly complete. However, in order to investigate the stability of the structure without considering new countries at every step, I will in addition analyze the changes in the structure of only the “core” group (the 12 countries for which data is available for the entire period from 1987 to 2006). This is an important prelude to the full analysis, and its results are presented in section 5.1.1. Section 5.1.2 then continues to analyze all the countries.

5.1.1 Clustering activity of the core group

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until the closing values in 2006. The remaining countries all miss a few months, but never more than 13 observations (e.g. Greece and Germany each only have 227 observations, which is 13 observations less than the total of 240). Graph 4 and 5 show the evolvement of the clustering between these countries from 1987 to 2006. The graphs of the periods in between from 1992-1996 and 1997-2001 can be found in the appendix, in section 8.3.1 and 8.3.2 respectively.

Graph 4: Dendrogram of the core group, 1987-1991

Correlation: .751 .144 +---+---+---+---+---+ Belgium 2  France 3   Netherlands 1    Italy 5    Germany 4   UK 7    Sweden 12     Ireland 6     Spain 9    Austria 10   Finland 11   Greece 8  

Stage Cluster 1 Cluster 2 Coefficient Stage Cluster 1 Cluster 2 Coefficient

1 Belgium France .751 7 Ireland Spain .559

2 Netherlands Italy .731 8 Netherlands Ireland .513

3 Netherlands Germany .709 9 Austria Finland .429

4 Netherlands Belgium .686 10 Netherlands Austria .371

5 UK Sweden .652 11 Netherlands Greece .144

6 Ireland UK .593

Graph 5: Dendrogram of the core group, 2002-2006

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Stage Cluster 1 Cluster 2 Coefficient Stage Cluster 1 Cluster 2 Coefficient

1 France Germany .959 7 Netherlands Belgium .818

2 Netherlands France .944 8 Netherlands Ireland .774

3 Netherlands Sweden .882 9 Netherlands Finland .703

4 Netherlands Spain .865 10 Netherlands Greece .628

5 Netherlands Italy .864 11 Netherlands Austria .582

6 Netherlands UK .822

Upon reviewing these results, a few obvious observations can immediately be made. First and foremost, the trend from 1987 to 2006 is one of increasingly smaller distance between the group of countries as a whole, indicating convergence and integration. The correlation of the two most highly correlated countries goes up throughout each period (from .751 between Belgium and France in the first period, to .959 between France and Germany in the last period), while the correlation of the cluster furthest away from the other countries also goes up in each period (from .144 for outlier Greece in the first period, to .582 for outlier Austria in the last period). This implies that the stock returns of these 12 countries are clearly converging.

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clustering takes place. Greece is the country which is consistently least similar to the rest of the group, but does attach itself to the main group in the final period, as absolute distances decreased.

5.1.2 Clustering activity of all the countries

The entire group of countries starts out as a group of 12 countries (the core group), but in the following periods increases to a group of respectively 17, 25 and 26 countries. There are thus two periods in which the group is (almost) fully complete. Graph 4 in the preceding section shows the clustering of these countries between 1987 and 1991. Graphs 6, 7 and 8 in this section show the development of clustering in these countries from 1992 to 2006. Below each graph it is shown which countries are left out at each point. The names of the countries in the core group have been printed in bold to follow their developments in comparison to the newly added countries.

Graph 6: Clustering of European equity market returns, years 1992-1996

Correlation: .785 -.030 +---+---+---+---+---+ Netherlands 1  Germany 4   Austria 10   Belgium 2   France 3    UK 7    Spain 9   Denmark 14   Ireland 6  Finland 11  Sweden 12    Luxembourg 13    Italy 5   Greece 8    Portugal 16    Hungary 15   Cyprus 17 

Stage Cluster 1 Cluster 2 Coefficient Stage Cluster 1 Cluster 2 Coefficient

1 Netherlands Germany .785 9 Greece Portugal .557

2 Finland Sweden .719 10 Greece Hungary .521

3 Netherlands Austria .702 11 Netherlands Ireland .516

4 Spain Denmark .680 12 Netherlands Finland .502

5 Belgium France .676 13 Netherlands Lux. .492

6 Netherlands Belgium .649 14 Netherlands Italy .398

7 Netherlands UK .614 15 Netherlands Greece .383

8 Netherlands Spain .566 16 Netherlands Cyprus -.030

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Graph 7: Clustering of European equity market returns, years 1997-2001 Correlation: .911 -.061 +---+---+---+---+---+ France 3  Germany 4   Sweden 12  Netherlands 1   UK 7   Italy 5  Spain 9   Portugal 15    Denmark 14    Belgium 2   Austria 10    Ireland 6    Luxembourg 13   Czech Rep. 17   Hungary 19    Finland 11    Poland 22    Greece 8   Slovenia 24    Estonia 18    Latvia 20     Malta 21    Romania 25    Cyprus 16   Slovakia 23 

Stage Cluster 1 Cluster 2 Coefficient Stage Cluster 1 Cluster 2 Coefficient

1 France Germany .911 13 Netherlands Ireland .593

2 France Sweden .872 14 Netherlands Lux. .550

3 Netherlands France .850 15 Finland Czech Rep. .518

4 Spain Portugal .815 16 Netherlands Finland .488

5 Netherlands UK .791 17 Greece Slovenia .421

6 Netherlands Italy .746 18 Estonia Latvia .298

7 Netherlands Spain .725 19 Netherlands Greece .270

8 Czech Rep. Hungary .717 20 Estonia Malta .256

9 Belgium Austria .699 21 Netherlands Estonia .237

10 Netherlands Denmark .691 22 Netherlands Romania .143

11 Finland Poland .653 23 Netherlands Cyprus .126

12 Netherlands Belgium .601 24 Netherlands Slovakia -.061

(28)

Graph 8: Clustering of European equity market returns, years 2002-2006 Correlation: .959 .044 +---+---+---+---+---+ France 3  Germany 4  Netherlands 1   Sweden 11  Spain 9  Italy 5   UK 7  Belgium 2   Ireland 6   Denmark 15  Portugal 14   Finland 10   Greece 8   Luxembourg 12    Austria 13    Cyprus 16   Hungary 19    Poland 22     Czech Rep. 17     Estonia 18    Malta 21    Latvia 20    Slovakia 23   Bulgaria 25   Slovenia 24  Romania 26 

Stage Cluster 1 Cluster 2 Coefficient Stage Cluster 1 Cluster 2 Coefficient

1 France Germany .959 14 Netherlands Greece .642

2 Netherlands France .944 15 Czech Rep. Hungary .588

3 Netherlands Sweden .882 16 Netherlands Austria .575

4 Netherlands Spain .865 17 Czech Rep. Estonia .501

5 Netherlands Italy .864 18 Slovakia Bulgaria .473

6 Netherlands UK .822 19 Netherlands Cyprus .454

7 Netherlands Belgium .818 20 Netherlands Czech Rep. .427

8 Netherlands Ireland .774 21 Slovenia Romania .252

9 Greece Lux. .739 22 Netherlands Malta .248

10 Netherlands Denmark .726 23 Netherlands Latvia .200

11 Netherlands Portugal .704 24 Netherlands Slovakia .134

12 Netherlands Finland .696 25 Netherlands Slovenia .044

(29)

When studying all the countries together, the development of the countries as a whole converging towards each other is less pronounced, due to the fact that new countries are added in every period. Therefore the analysis has to be slightly different from the analysis of a consistent group of countries such as in the preceding section. If I only focus on the distance between the first countries to be clustered together and the last country to be added to the cluster, the conclusions might become skewed, as new countries – which for the biggest part are all countries with recently opened and relatively underdeveloped stock and capital markets – are added at every step. Consider the absolute distance of the entire group. In the first period, the correlation of the first cluster is .751, whereas the correlation of the last country to be added to the whole cluster is .144. In the last periods these correlations were .959 and .044 respectively, indicating that whereas the center of the core group kept getting closer, the addition of new countries meant a larger absolute distance between all countries.

When one tracks the developments of the core group (which has its names printed in bold) over all the four periods in comparison to the newly added countries, it can be seen that only Portugal, Denmark and Luxembourg really manage to fit in with the core group, and the other countries stay rather far away. This is easily explained, as these three countries are all developed countries and their absence in the core group was only due to data restrictions in the first place. Appendix 8.4.1 displays the clusters and their contents as they are formed in each period, according to the definition given in section 4.3. Clearly visible are two developments. First it can be seen that in the latter two periods, almost the entire core group, plus Portugal, Denmark and Luxembourg, form the first cluster. This cluster has in effect become the center of equity markets in Europe, and developments inside of it have largely been discussed in section 5.1.1. The first cluster gradually increases in size, as in the first period it contains only 5 countries whereas in the last it contains 15 countries.

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