The Evolution of Equity Market Integration on Sectoral Level A time-varying approach to analyzing the impact of EMU

Transcription

1 The Evolution of Equity Market Integration on Sectoral Level A time-varying approach to analyzing the impact of EMU Ralf Elfving Master Thesis Department of Economics Lund University 15 ECTS Spring 2011 Supervisor: Hossein Asgharian

2 Abstract This thesis analyzes the evolution of integration between equity markets based on a market index and six sector indices for four countries that adopted the EMU in 1999 as well as two countries that did not. The purpose is twofold; first to identify if the integration has increased and secondly try to determine if the EMU has played a part. The estimation window is set to January 1987 to December 2010 with daily frequency. The methods used are Johansen cointegration analysis and principal component analysis. To capture the time-variability in the integration that has been identified by previous research a rollingwindow technique is deployed. By estimating the methods over an event window of 1000 observations and rolling it forward one observation at a time while dropping one observation, keeping the window constant at 1000 observations, time-series of estimated results are generated. By plotting these the evolution of the estimates are presented and interpreted. Although the body of previous research is vast the author has not been able to find a study that utilize sectoral data and rolling-window techniques meaning that the results could potentially contribute with unique findings. The results and the subsequent interpretations from the two methods differ and are inconsistent. The Johansen cointegration method show little evidence of prolonged periods of significant cointegration or trends towards increased cointegration, even after the intensified stages of the EMU in the end of the 1990s. This is interpreted as if the EMU has had little impact on the market integration on the broader market index as well as the individual sectors for the four EMU adopters. It also shows that there still exists diversification opportunities for portfolio investors. The principal component analysis on the other hand show that the level of and convergence in participation of the first dominant component has increased since 1996 for the market index and most sectors, as has the explanatory power of the first component. The explanatory power is however largest for the market index and for financials indicating a lower degree of integration in other industries. The two non-emu member countries to a large extent share the level of participation in the first component meaning that role of EMU in the integration process is further questioned, although it s possible the findings could be explained by spill-over effects also to non-emu countries. Keywords: Integration, Cointegration, Time-varying Integration, Principal Component Analysis, Rolling windows, Sectoral Equity Indices, EMU

3 Contents 1 Introduction 5 2 Theory Portfolio theory Measures of Equity Market Integration Causes and Implications of Equity Market Integration Previous Research Econometric Theory Johansen Multivariate Cointegration Principal component analysis Method Rolling-window Johansen Cointegration Analysis Rolling-window Principal Component Analysis Data Data collection and transformation Data characteristics Unit Root Empirical Results Johansen Multivariate Cointegration Static analysis Rolling-window analysis Principal Component Analysis Static analysis Rolling-window analysis Conclusions 34 7 References 36 8 Appendix Tables Figures

4 List of Figures 5.1 Rolling-window Johansen Cointegration: Market Index Rolling-window Johansen Cointegration: Consumer Goods Rolling-window Johansen Cointegration: Financials Rolling-window Johansen Cointegration: Basic Materials Rolling-window PCA: Correlations to PC1 of Market Index Rolling-window PCA: Cum. expl. power of first two PCs of Market Index Rolling-window PCA: Correlations to PC1 of Financials Rolling-window PCA: Cum. expl. power of first two PCs of Industrials Rolling-window PCA: Correlations to PC1 of Health Care Rolling-window PCA: Cum. expl. power of first two PCs of Health Care Series of Market Index for all countries Series of Basic Materials for all countries Series of Consumer Goods for all countries Series of Consumer Services for all countries Series of Financials for all countries Series of Health Care for all countries Series of Industrials for all countries Rolling-window Johansen Cointegration: Market Index Rolling-window Johansen Cointegration: Basic Materials Rolling-window Johansen Cointegration: Consumer Goods Rolling-window Johansen Cointegration: Consumer Services Rolling-window Johansen Cointegration: Financials Rolling-window Johansen Cointegration: Health Care Rolling-window Johansen Cointegration: Industrials Rolling-window PCA: Correlations to PC1 of Market Index Rolling-window PCA: Cum. expl. power of first two PCs of Market Index Rolling-window PCA: Correlations to PC1 of Basic Materials Rolling-window PCA: Cum. expl. power of first two PCs of Basic Materials Rolling-window PCA: Correlations to PC1 of Consumer Goods Rolling-window PCA: Cum. expl. power of first two PCs of Consumer Goods Rolling-window PCA: Correlations to PC1 of Consumer Services Rolling-window PCA: Cum. expl. power of first two PCs of Consumer Services Rolling-window PCA: Correlations to PC1 of Financials Rolling-window PCA: Cum. expl. power of first two PCs of Financials Rolling-window PCA: Correlations to PC1 of Health Care Rolling-window PCA: Cum. expl. power of first two PCs of Health Care Rolling-window PCA: Correlations to PC1 of Industrials Rolling-window PCA: Cum. expl. power of first two PCs of Industrials

5 1 Introduction Despite the market turmoil that unfolded in the summer and fall of 2011 concentrated to Europe and specific European Monetary Union (EMU) member states the area is undergoing a major historic unification process. The region s long history of war and conflict over the past few centuries has been replaced with peace, co-operation and free movement. Although the common currency, the Euro, was introduced in the late 1990s the notion of European integration is not new, examples can be traced back to the Marshall Plan and the Economic Cooperation Act of 1948 that called on Europe to like USA create a continent-wide economic market. (Kindleberger 2006, p. 447) For Europe the case was and still is somewhat different compared to modern USA as integration takes place with regards to two components; an economic component and a political component. (Eichengreen 2004, p. 214f) This thesis focuses on a subcategory of the economic component; the equity markets. The integration of financial markets is of importance to many; e.g. for corporate managers that gain access to larger and more liquid markets that influence their cost of capital. Individual and institutional investors look for diversification by holding non-domestic assets in their portfolios can potentially lower their risk. As a result of the European Union as well as the European Monetary Union several integration processes between financial markets are under way. (see e.g. Fratzscher 2001, Rangvid 2001 and Voronkova 2004) Although integration open up for greater possibilities to diversify asset portfolios previous research has shown the diversification opportunities for portfolio managers have diminished as European markets have become more integrated. The purpose of this thesis is twofold. First and primarily it will estimate the evolution of equity market integration over time, measured as co-movement between six sectoral equity market indices and a broad market index, of the four European economies France, Germany, Italy and the Netherlands before and after their adoption of the Euro currency in January Secondly it will try to determine if and how the adoption of the Euro currency has impacted the integration of broad equity markets and individual sectors in the adopting countries. In order to better determine if and to what the extent the Euro currency has affected the change two European countries, Switzerland and United Kingdom, that did not adopt the new currency are included in parts of the study. These six countries constitute the ones with available data for the desired period, any extension to further countries would have decreased the length of the data severely. Much of the previous studies conducted on the topic have used static measures of integration where the integration is measured over a specific period, resulting in one single set of results indicating the level of integration. This does however not allow for any conclusions of the evolution of the integration, i.e. how it has changed over time. Fratzscher (2001, p. 9) notes that studies that compare the results of different sub-studies, such as Adjaouté & Danthine (2004), could miss much of the changes over time. The inherent time-variability of equity market integration has encouraged researchers to use rollingwindow techniques. Examples are Rangvid (2001) that test for increased convergence between three 5

6 Western European countries during and Gilmore et al (2008) that measure the evolution of integration between countries in the Eastern and Western Europe during the formers accession to the European Union (EU). These and other studies have found that there are indications of increased convergence over time, from 1980s or 1990s depending on the study, and cite the progression of EU and EMU as possible contributing factors. The implication of this increase in integration is that the diversification opportunities for portfolio managers have diminished. Although there have been encouraging recent steps in the sophistication of studies on the subject there are still a void that this study will fill as there are no to this author known studies that have used data that has a lower aggregation than broad equity market indices paired with rolling-window techniques. This leaves previous research potentially disconnected from the reality of portfolio investors; it is not improbable that investors look to diversify across national borders but only invest in specific industries as opposed to the broader markets. But it is improbable that the industrial or sectoral indices of these markets have the same characteristics as their market indices, thus the integration between these sectors are likely to differ from what has been presented in previous studies. To add relevance to the topic this study analyze sectoral equity indices using rolling-window methods to find out if diversification opportunities are still available. The remainder of this thesis is organized as follows. Chapter two presents the relevant theory on economic integration and econometrics followed by a summary of previous research conducted on the subject. Chapter three presents the methods used. Chapter four presents the data followed by the empirical results in chapter five. Finally, chapter six concludes. 6

7 2 Theory In this chapter the relevant theory and previous research is presented. Modern portfolio theory is reviewed to find out how integration plays an important role for the investment decisions of portfolio managers and how it effects portfolios. Different ways to measure equity market integration as well as the causes and implications of it are presented. A presentation of how previous studies have conducted their research is presented along with their main findings followed by the econometric theory that this thesis is built on. 2.1 Portfolio theory Although this study does not estimate or construct asset portfolios, the theory of portfolio selection is relevant in order to understand the effects that equity market integration have on asset portfolios. As been noted by previous research a higher degree of co-movement or integration between assets leads to lesser diversification possibilities for investors, ceteris paribus. As we will see this leads to higher risk for the investors. Portfolio theory revolves around the first two moments, the expected return and the variance of assets and ultimately of the portfolio of which they are included. The expected return of a portfolio of assets is the weighted average of the expected return of the individual assets, as depicted in (1), where X i is the proportion of asset i in the portfolio and R i is the return of asset i. The description of the variance of the portfolio, as depicted in (2), is somewhat analogue to (1) as the squared weights and the variance of the assets are summed together but the second term also accounts for the covariance between the each pair of assets in the portfolio. R p = N (X i Ri ) (1) i=1 N N σp 2 = (Xj 2 σj 2 ) + (X j X k σ jk ) (2) j=1 j=1 k=1 k j In the case of independence, i.e. zero correlation between assets, the second term on the right-hand side of (2) is equal to zero and drops out and the risk of the portfolio is a weighted sum of the individual assets risks. But with positive dependence between assets the risk of the portfolio is increased. In the case of intergration between assets there exist a degree of correlation between assets and the result is that the risk of a portfolio including these assets will be larger. It can also be proved that as the number of independent assets included in a portfolio goes to infinity the variance of the portfolio approaches zero. (Elton & Gruber 2007, 44ff) This is evident when you consider (3) below where a pro-forma allocation among the assets is assumed, with 1/N of the portfolio in each of N assets. Only the individual risk of the securities can be diversified away in this manner, but the contribution to the total risk that stem from 7

8 the covariance term cannot be diversified away if there exist a dependence. Thus, a larger degree of positive correlation between the assets implies a higher portfolio risk, ceteris paribus. (Elton & Gruber 2007) σ 2 p = 1 N σ2 j + N 1 N σ jk = 1 N (σ2 j σ jk ) + σ jk (3) This relationship can easily be extended to international assets when taking into account exchange rates between the investor s domestic country and the country or countries of the international assets. For a monetary union such as the EMU post January 1999 the exchange rate variations have been eliminated due to the adaption of a common currency. 1 As we will see in the section on previous research it has been generally found that the degree of market linkage has increased over the past three decades; possibly as a result of the EU and EMU. As this section has showed this increased integration leads to higher, nondiversifiable portfolio risk for investors that invest in equities across the EU/EMU member countries. This of course a broad group of people, e.g. all those that has invested money in pension funds that allocate capital to equities in this geographical area. But how does one measure integration? That will be answered in the next section. 2.2 Measures of Equity Market Integration Kearney & Lucey (2004) provides a frequently cited survey on the theory and research of international equity market integration. As explained by the authors there are three basic approaches to defining the extent of financial market integration and these are further divided into two broad categories; direct and indirect measures. The latter having two subcategories. The direct measure builds on the law of one price and to which extent the rates of return on financial assets with similar characteristics, in e.g. risk and maturity, are equal across national borders. The two indirect measures are based on measures of international capital market completeness on the one hand, and to what proportions the domestic investment are financed from world savings as opposed to domestic on the other. A high degree of investments financed by world savings would indicate a relatively high degree of integration as supply and demand would not only be driven by domestic decisions or shocks. It could help to think of this as in an extreme case: a country that is completely closed and does not permit capital flows over its borders will not be integrated with other markets and is thus only subject to domestic supply, demand and shocks. One of the methods within the direct measure is to evaluate the evolution of equity market cointegration; to measure the emergence of common stochastic trends in the returns of equity markets and the specification of dynamic paths towards an increase or decrease in integration in them. This is however not unproblematic as markets subject to the same exogenous chocks may show evidence of comovement 1 It is also noted by Elton & Gruber (2007, p. 258) that: This [increased correlation primarily] is due to the increased correlation among countries within the European Monetary Union because of the elimination of exchange rate changes and greater integration of the economies. 8

9 although there is no underlying integration. A recent example is the financial crisis of 2008 that originally begun in the US housing market but eventually spread and caused stock markets, commodities, house prices and the prices of other financial assets to tumble across the world. Although all of these declined at the same time, and sometimes at similar rates, does not mean that they re integrated; not even assets of the same class in the same market that move together, e.g. as a reaction to a crisis, need to be integrated. An important question one should ask is if there are any underlying long-run causal relations or if prices are moving in tune simply because of a shock that stretches across markets or assets. Three main approaches are typically used in the literature to test direct measures: testing segmentation of equity markets via the international CAPM, examination of the determinants of changes in correlation or cointegration structure of markets and its extent and finally testing time-varying measures of integration. The argument for correlation and cointegration studies is that if the correlation structure demonstrates instability over time the degree of correlation is changing with a trend to or from increased integration. When used on fixed research windows there is however a risk of gaining only partial results as risk premium on equities is time-varying. 2.3 Causes and Implications of Equity Market Integration We briefly touched on the subject of markets that move together in one direction at the same time without necessarily being integrated, noting that a causal relation could clarify if cointegration exists. The comovements of equity markets can arise from different causes. International trade, increasing capital mobility, relaxation of controls on international capital movements and political and policy alignment associated with economic unions. Of course the numerous agreements put in place after the second world war by European states, culminating in the relatively recent formation of EU and EMU, would be a likely platform for increased integration as these enable many of the above mentioned causes. (Gilmore et al 2008, p. 605) Kearney & Lucey (2004, p. 572) explain that linkages of financial assets arise as national and overseas residents, individuals and organizations, increasingly decide to hold a greater mix of non-domestic assets. Although the so-called home-bias exists, where households hold a greater share of domestic assets compared to what portfolio theory suggests is optimal, it is decreasing as they look for investments in markets abroad which spur these linkages. As explained by Kearney & Lucey (2004, p. 576f) there are three broad sets of implications if integration drives developments in the financial sector (also see Pagano, 1993). First it weakens the opportunities for international portfolio diversification as returns are equalized across countries. Secondly, more complete global capital markets will lead to more robust economic conditions of the individual states. Thirdly, household savings rates will change over time. As noted by Aggarwal et al (2010, p. 643) the former two are thought to have a positive impact on the economic growth but the implications of the latter is uncertain. In a theoretical framework by Martin & Rey (2000) the authors demonstrate and provide evidence 9

10 from other studies supporting the notion that financial integration leads to a reduction in the cost of capital. It also leads to an increase in the average price of financial assets (due to greater demand). Further, evidence show that there is a positive relation between increased financial development and economic development, the former being a major cause of the later. Drivers behind this are typically seen to be related to changes in legal practices, increased of capital supply and an increase in competition on local financial intermediaries in the developing countries. (Kearney & Lucey 2004, p. 577) 2.4 Previous Research With the knowledge of the causes, implications and how to measure integration now reviewed, what evidence is there of integration based on previous research? There exist an extensive body of research on integration between different regions or countries, including different setups with European countries, and these studies have varying focus in terms of their measures and methods of finding integration. Due to the amount of research that has been conducted this review mainly focus on research that have used the methods that will be applied in this thesis and that are outlined in the next section. The majority of studies performed have found equity markets of developed European countries to be well integrated, citing that political agreements beginning in the 1980s have led to a more unified Europe in terms of politics and economics. This has had the implication that the opportunity for portfolio diversification has been lowered. As reported by De Nicolo & Tieman (2006, p. 4) the literature however exhibits mixed results. While Fratzscher (2001, p. 4) note that numerous studies have shown that the degree of real integration has a strong impact on financial integration De Nicolo & Tieman (2006, p. 4) explain that equity market integration does not necessarily follow mechanically from cross-country convergence in macro economic factors such as interest rates. They base this on their findings that there is an increase in real activity synchronization beginning in the 1980s but evidence of equity market integration is not seen until the 1990s. (ibid) Many studies have studied integration over a fixed estimation window or over multiple sub-windows. Fratzscher (2001, p. 9) notes that although comparing different sub-periods may be a good rough proxy for changes happening in the long-term it could also mask much of the underlying time variation as the degree of integration may change frequently as well as exhibit high volatility. Aggarwal et al (2010, p ) and Voronkova (2004, p. 634) note that previous studies have highlighted the time-varying nature of comovements between markets and explain that this behavior may distort the results that static cointegration analysis give. Although some studies have examined the dynamics by deploying static cointegration methods on sub-periods, according to Aggarwal et al (2010, p. 644) few have used dynamic cointegration techniques. But with a higher degree of sophistication in recent studies, dynamic methods have been deployed which better take into account the time variability that has been found to exist in the data. Aggarawal et al (2003, p. 2) notes that given the non-stationary stock prices and the stationary nature of the 10

11 first differences, the returns, dynamic cointegration techniques can be very useful in examining market integration. Voronkova (2004) finds some pairwise cointegration relations between two central European and three developed equity markets between September 1993 and April She also finds that the Gregory-Hansen (1996) procedure, that allows for one structural break in the data, detects cointegration relationships not detected by the Engle-Granger and Johansen tests and that long-run relations do not cease after the structural breaks. Kearney et al (2004, p. 576), presenting a literature review, however note that studies that have used the more sophisticated Johansen multivariate approach generally find stronger evidence of cointegration which is a conflicting finding. Rangvid (2001) tests if the stock markets of France, United Kingdom and Germany have become increasingly converged as time has passed using recursive cointegration tests on a sample ranging from 1960 to The findings are that no clear cut evidence of increased convergence can be found until 1982, but after this period a more clear tendency for the markets to be driven by the same few common stochastic trends is seen. Arshanapalli & Doukas (1993, p. 206) find evidence that the degree of international co-movements in stock markets has changed significantly since the market crash in October Also Kearney & Lucey (2004, p. 571) come to similar conclusions as they note that the level and pace of international financial integration have increased over time. Gilmore et al (2008) use dynamic cointegration metods and rolling-window principal component analysis to analyze short and long-term co-movements between three central European and two western European countries and find that the static approach indicate a low level of long-run co-movement where the dynamic methods show periods of higher level of cointegration. They state that the EU accession process may have played some small role in the increase of correlations. (Gilmore et al 2008, p. 608). Adjaouté & Danthine (2004, p. 1227) similarly note that the results of their study, a long and slow structural evolution over their sample period ( ), could be credited economic and monetary integration within the EU and EMU. As previously explained this study will focus on equity market integration, a sub-category of the economic component of integration between markets. However, as noted by Eichengreen (2004, ch. 8) it can be hard to interpret the economic component without taking into account the political component and vice versa. Both are likely to be nested or intertwined; political decisions have economic consequences just as economic events have political consequences and the chain of effects can be complex. The results from any quantitative study of either are thus highly contextual. This study will not go into greater detail of presenting a broad historical background of the political decisions taken before or during the event window but highlight possible important contemporary events or findings that could be reflected in the results. Readers that are looking for a more detailed background to, and history of, the European financial integration are encouraged to turn to Kindleberger (2006) and Eichengreen (2004, 2007 & 2008). 11

12 2.5 Econometric Theory Johansen Multivariate Cointegration As the Engle-Granger approach, a common bivariate test to see if two series are cointegrated, is vulnerable to model specification which require the researcher to test the underlying hypothesis both ways (see e.g. Voronkova 2004, p. 639) the Johansen multivariate cointegration method is used. Although this selection of method leads to some loss of information of which countries that share the integration it is easier to present as the Engle-Granger method would generate 10 results per industry between the 4 countries included in the study; i.e. 70 in total. The base for Johansen s method is a Vector Autoregression (VAR) model which includes all variables of interest. Methods to find cointegration between variables integrated of different order exist, but these are more complex than for variables of the same order of integration. (Harris & Sollis, 2005, p.112) In the representation below it is therefore assumed that all variables are integrated of order one. The VAR, of order p, is written as Y t = δ + Θ 1 Y t Θ p Y t p + ɛ t, (4) If cointegration exists, this equation can be rewritten in the form of a vector error correction by differentiation, Y t = δ + Γ 1 Y t Γ p 1 Y t p+1 + ΠY t 1 + e t, (5) where Γ i = (Θ i + +Θ p ) and Π = (Θ 1 + +Θ p I n ), I n denoting the n-dimensional identity matrix and δ denoting a vector of constants, not necessarily equal to δ in (4). The intuition with this separation is that, if all variables in Y t are integrated of order one, their first differences will be stationary. In (5), all variables except the last part, Y t 1, are thus stationary. And so if all residuals from (5) are stationary, the matrix Π must contain the cointergration relationships. Π is thus called the cointegration matrix, and there are three possible setups of this matrix which yield stationary residuals. If the matrix is of full rank, meaning the matrix span the entire n-dimensional space, all different linear combinations give stationary residuals. This imply that all variables are stationary and cointegration analysis is not applicable. In the second setup the matrix have rank zero, implying that Π is the zero matrix and that no cointegrating vector exists. The last possibility is 0 < rank(π) < (n 1) meaning that at least one cointegration relationship exists. Further, the cointegration matrix can be separated into two matrices, Π = αβ where α and β are both of size (n p), α represents the speed of adjustment to equilibrium and β represents the long-run relationship. Johansen (1991) proposed a method to estimate Π = αβ by running two auxiliary VAR-models as given below. Y t = ˆδ + ˆP 1 Y t ˆP p 1 Y t p+1 + u t (6) Y t 1 = ˆδ + ˆζ 1 Y t ˆζ p 1 Y t p+1 + v t (7) 12

13 Equation (6) consists only of variables in their first difference and will thus give stationary residuals by definition. Equation (7) contains the variables in level, and so the residuals will no necessarily be stationary. The basis for the cointegration space is found by finding a basis in which the residual sets show a high correlation, this because both sets of residuals need to be stationary to be able to show significant correlation and this can only happen if ΠY t 1 give stationary, and thus cointegrated, combinations. This basis is found by calculating the eigenvectors of the block covariance matrix from the residual series u t and v t as given below. [ ] Σ = Σ uu Σ vu Σ uv Σ vv (8) Where Σ i,j, {i, j} = {u, v} denotes the covariance matrix between residual sets i and j. The eigenvalue to this matrix contains information regarding the significance of the cointegration vector, and testing for cointegration thus is about testing the significance of the eigenvalue of this matrix. The number of cointegrating vectors, i.e. the number of cointegrating relations, equal the number of significant eigenvalues of the matrix. A more detailed presentation is available in Johansen (1991) and Hamilton (1994) Principal component analysis There are several methods to estimate common components in time series. This study uses Principal Component Analysis (PCA), a method that converts a matrix of the asset returns into linear combinations of unobserved factors called principal components as described in Campbell et al (1997, p ). The components explain the variance of the returns of the series included and thus function as a dimensionality reduction. Further, the components are constructed so that the first component explains the greatest amount of variation in the data, with any incremental component explaining less than the previous. There are as many components as there are variables included and the approach is modelindependent, i.e. there is no necessity for regression specification. The method however require that the underlying variables are stationary. (see e.g. Lansangan & Barrios, 2009) and the results are sensitive to how the original data is represented in the method. Where PCA is used with a variance-covariance matrix it is sensitive to the units of measurement which is not an issue when using the correlation matrix. (Focardi & Fabozzi 2004, p. 337) The first principal component is the normalized linear combination of asset return that has the largest variance. The first component is created by a line going through the (T x N) matrix space, where T is the number of observations in time and N the number of variables. The squared deviations from this line will yield the coordinates for the component. Further, the total variance of the series can be divided into that which can be explained by the component and that which cannot. Every new subsequent component is also a linear combination of asset returns with the largest possible variance, although subject to the constraint that it is orthogonal to all previous components. Thus, it explains as much as possible of the variance that was unexplained by earlier components. The first principal component is 13

14 x 1 R where x 1, a (N 1) vector, is the solution to the maximization problem in (9) subject to the aforementioned restriction in (10). Max x 1 x 1 ˆΣx 1 (9) x 1x 1 = 1 (10) ˆΣ is the sample correlation matrix of returns and x 1 is the eigenvector associated with the largest eigenvalue of ˆΣ. PCA works either on the variance-covariance matrix or on the correlation matrix where the technique is the same but the results can differ. This study uses the correlation matrix in line with Gilmore et al (2008). 14

15 3 Method Although the econometric methods used in this thesis were presented in the previous chapter there are specific details that warrant explanation, clarification and discussion. This is done in the sections below for each of the two methods separately Rolling-window Johansen Cointegration Analysis The Johansen cointegration method presented in the previous chapter is normally used in static analysis, i.e. over an event window spanning all observations in a sample and that yield one set of test statistics representing the entire sample. As explained earlier the level of cointegration is however time-varying and that results based on a fixed-window analysis can be misleading. Even static cointegration analysis over many subperiods is not unproblematic in finding a correct representation of the evolution of integration, as explained by Fratzscher (2001, p. 9). Researchers have thus turned to a rolling-window approach which this thesis will apply and is explained below. The rolling-window Johansen cointegration analysis is based on deploying the method, as explained in chapter 2, on an event window of fixed size representing a subset of the sample and then roll it forward. As it is rolled forward it takes in a new segment of observations into the event window while leaving a segment with the equal amount of observations behind, making the window overlap the data as it s rolled across the sample. This thesis uses an event window of 1000 observations, meaning that the analysis starts with the first 1000 observations. It moves the window one observation, corresponding to one day, forward at a time until the estimation window covers the last 1000 observations of the sample. For each step the window is moved the cointegration analysis is performed, thus there is a set of test statistics for each event window in time. This results in (T W + 1) N test statisticas and critical values, where T is the number of observations, W is the size of the estimation window and N is the number of hypotheses tested. The number of hypotheses tested will equal the number of series included in the test as the Johansen method test the null of r = i against r i + 1 for i = 0, 1,..., k 1 where k is the number of variables in the system (four in this thesis). As performing such analysis using e.g. EViews graphical user interface would be unpractical and time-consuming I have for this thesis programmed a Matlab script that performs the Johansen method, available in the Matlab Econometrics Toolbox, with the desired settings and the specified event window and rolls it over the entire sample. This generates time series of statisticas and 95 % critical values for each event window and for each of the cointegrating vectors. Although results from static cointegration analysis is usually presented in tables such presentation is not possible with the amount of data the rolling-window technique method generates. Instead the resulting time-series of test statistics and critical values will be plotted in graphs so that their evolution over time is easier to grasp. For ease 2 I would here like to point out that a recursive Johansen method was also estimated and evaluated but left out of the final version due to restrictions on the length of the thesis. Had they been included they would not have changed the general conclusions. 15

16 of interpretation the time-series of test statistics for each of the cointegration vectors have been scaled (divided) by their 95 % critical values. Thus any series (representing cointegration vectors) that have a value greater than one indicate that it is statistically significant at the 95 %-level for that observation in time; remember that an observation in these figures is based on a window of the previous 1000 days of underlying data. This critical level of one is represented in the graphs by a dashed "critical line". The nature of the hypotheses tests will typically see the level of each subsequent series to be lower than the previous, thus the first cointegrating vector will be at the top of the figures followed by the second, third and so on. This is easy to understand when you consider this: If the test accepts the null r = 0, i.e. no significant cointegrating vectors, it is unlikely that it will reject the null of any subsequent test for a higher number of vectors and the test statistics are expected to fall compared to the corresponding critical value for each of these subsequent hypotheses. To exemplify how to interpret the results I present an example. If for a given day the upper line (representing the first cointegration vector) is at a level above the critical line and the second line has a value less than one this means that we i) cannot reject the alternative hypothesis of the first series that there are at least one significant cointegrating vector (r 1) and, ii) that we reject the alternative hypothesis of r 2 in favor of the null hypothesis of the second series meaning that there are at most one significant cointegrating vectors (r = 1). As noted by e.g. Rangvid (2001, p. 386) an upward (downward) trend of the series is interpreted as as a movement to increased (decreased) cointegration as the level of significance of that cointegrating vector is increasing (decreasing). This idea behind this is straightforward, as the measured level of cointegration increases so should the test values which result in a higher level of the generated series above the critical level (the numerator increases while the denominator is constant). And like De Nicolo & Tieman (2006, p. 8) this thesis will not focus only on looking at the existence of integration per se, but the changes in integration; i.e. the trends of the generated series. Although the rolling-window approach have positive sides, such as portraying how the level of cointegration varies over time, it is not unproblematic. One potential problem has to do with the size of the event window; a too small event window might fail to identify cointegration and a too large eats up observations. This thesis uses 1000 observations, double that of Lucey et al (2004) that concede that "... the number of data points, at 500, is relatively small given the complexity of the system being investigated, and accordingly dropping the confidence level to 90 %." (Lucey et al 2004, p. 20). The amount of observations used for every event window should thus be sufficient to a greater extent that previous studies and has also allowed to set the confidence level to 95 % which increases the validity of the results. Adjaoute & Danthine (2004, p. 1228) explain that tests based on a rolling correlation matrix would make little sense as virtually no change would be observed based on conventional testing procedures because of overlapping data. This criticism is however unfounded as previous research has showed that the cointegration process is time-varying, even with windows that largely overlap. There is however warranted criticism not raised in any previous studies that I would like to point 16

17 out. When testing for cointegration there are some underlying assumptions that have to be made, such as the model specification and lag length in the auxiliary regressions. When performing a static cointegration analysis these are quite easily determined as the researcher can examine the data and determine the appropriate settings as well as use e.g. lag length selection tests. With a rolling-window approach this is however not unproblematic. As the event window changes, so does the appropriate underlying assumptions. A set of settings appropriate for one event window is unlikely appropriate for another, just as the appropriate settings for the entire sample is not necessarily appropriate for the subsets. Although it is practically possible to test for the lag length that score best according to an information criteria for each event window and let the lag length vary over time according to this, it would lead to lesser transparency about what underlying assumptions that lie behind each observation. It s also a possibility to in a similar fashion run the tests with different fixed settings and cumulate the measure, e.g. an information ratio, and chose the setting that on average has proved to be the best. However, as this entails a large degree of experimentation and is time consuming this thesis builds on constant assumptions, not due to belief that it is the case but out of necessity. The regression specification is set to stochastic cointegration (H ) and lag length to zero throughout the entire study. For greater comparison also the initial static cointegration analysis presented in chapter 5 is based on the same assumptions. Optimal lag-length selection was evaluated for the full sample which gave a wide variety of optimal lag lengths ranging from 0 to 25 depending on which information criteria that was used. For sake of robustness different lag length have been tested also for the rolling-window method which mostly resulted in changes in the levels rather than change in trends. Although the underlying assumptions used in this thesis could differ from that of previous research, or from what could be deemed "optimal" based on a more thorough specification method, any deviation from such settings is systematic through this study which means that comparison across industries is still valid to a large extent. 3.2 Rolling-window Principal Component Analysis Principal component analysis (PCA) is generally applied as a static model with a fixed event window spanning over the entire sample. This results in a single set of principal components, their explanatory power and loadings by the series included that mirror the co-movements of the entire sample. Examples of such studies are Selover (1999) that study international transmissions of business cycles among countries in the ASEAN and Fratzscher (2001) that study the role of EMU in the integration process of European equity markets. But similar to the discussion on cointegration above it is also possible to apply PCA using rolling-window techniques. The method allows to estimate and analyze the evolution of the principal components over time, detecting changing levels of linkage. An example of a study that utilize the rolling-window PCA technique on equity markets is Gilmore et al (2008) which analyze the financial linkage between eastern and western European countries, in- 17

18 terpreting the first component as a measure of the extent of equity market co-movements. They also interpret the proportion of the total variance that the first principal component can explain, suggesting that a dominant first principal component indicate that all underlying series participate in the relationship. They however explain that the series need to have have a similar level of correlation between their returns and the component for them to share the relationship and outline a method of how to extract this information. This thesis thus follows the method of Gilmore et al (2008). Similar to the rolling-window cointegration method explained above it is estimated over a window of 1000 observations, starting with the first 1000 observations and moving one observation forward until it covers the last 1000 observations of the sample. For each estimation window the eigenvalues corresponding to the first and second principal components are collected as well as the corresponding explanatory power and the loadings of each country to the components. The calculations are based on the correlation matrix of mean-centered returns of the underlying series. The participation of the countries in the first component is presented in graphs, as is the cumulative explanatory power of the two first components. As explained by Gilmore et al (2008, p. 621) the participation is calculated by multiplying the individual series loading with the square root of the corresponding eigenvalue. This is what they and and subsequently this thesis refers to as the correlation between the returns and the first component. A difference compared to the cointegration analysis also performed in this study is that the PCA analysis includes two non-emu countries, Switzerland and United Kingdom. The reason for this is to see if the evolution of these two countries are different to that of the EMU-countries, a feature not possible with the Johansen cointegration method. This could give insight if the EMU project has had an influence on the first component that is specific to the EMU-countries. To exemplify: If the EMU-countries increasingly move upwards together and converge towards a similar level but Switzerland and United Kingdom don t it could point towards a relatively greater convergence between EMU-countries possibly due to their participation in the monetary union. But if there is no noticeable distinction between the levels and evolution of the two groups of countries the importance of EMU only on the EMU countries would be doubtful. Although this could be interpreted as rejecting the influence of EMU on the market integration one should be cautious about jumping to such conclusions. It could just as well be that the EMU has had a great importance on integration but that it also has spilled over on non-emu countries that are geographically or economically connected. This is also warrants the inclusion of the EU-country United Kingdom as well as Switzerland that stands outside both unions, creating a potential larger divide between the country and the EMU member countries. This caution over interpretation should be considered a flaw, and there are more issues that needs to be discussed about the method itself. As PCA is model-independent the criticism leveled towards the Johansen cointegration in terms of how one models the test is not applicable here. But there are however other points of criticism that are valid. As PCA transforms the information in the data into unobservable components there s no certainty about what the components actually represent. Previous research has 18

19 interpreted the first component as an indicator of the degree of integration (see e.g. Gilmore et al 2008, p. 621), thus a larger explanatory power of the first component paired with a larger participation in it would be interpreted as the returns of the market being affected by a common component to a larger extent. This discussion is linked to a weakness of PCA, the fact that the method doesn t test a certain hypothesis. Because of this there is no hypothesis that can be accepted or rejected with a certain statistical level of confidence, inference based on the results is open to criticism. We can not test the importance of the EMU, only draw possible conclusions based on the findings. The method is however still widely used across disciplines showing a confidence in it and as explained earlier, if the first component can explain a large degree of the variation it does represent dominant underlying factors. 19

20 4 Data In this chapter the underlying data of the empirical tests is presented. The data collection process is described together with how the data has been transformed as well as a discussion revolving around the advantages of this data compared to other. We also explore statistical properties of the full sample, including tests if the series exhibit a unit root. 4.1 Data collection and transformation The data used in this study was collected from Thomson Reuters Datastream and covers daily observations of a broad market index and six sector indices for a total of six countries. Four of these countries; France, Holland, Italy and Germany joined the realization of the European Monetary Union in January The two remaining, Switzerland and United Kingdom, did not but is included in the study as a control group in the principal component analysis as the method results in country-specific output. Other than the broader market index the study is performed on the second-level sectors basic materials, consumer goods, consumer services, financials, health care and industrials. There are further industries available to analyze, but those included in the study were the only with data for all countries over the entire period and inclusion of these have cut short the data by several years. For a complete presentation of the different sub-groups of all sectors analyzed in this study as well as those excluded please consult the Datastream Global Equity Indices User Guide (Thomson Financial, 2008). All series are presented in daily frequency as chained series with base value 100 on January 1st 1986, the earliest date for which the series had observations for all sectors and countries. In total each series consists of 6262 observations; in total. The reason behind the choice of daily data is, as noted by Voronkova (2004, p. 635), that it exhibits information on market interactions that lower frequency series might exclude. I concede that it is also likely to include what can be termed "noise" which could distort results. The reason behind the choice of analyzing sector indices rather than just broad indices is that these series are likely to exhibit information that would be lost in the aggregate. Further, there are no to this author known studies that analyze sectoral data in combination with rolling-window methods meaning that any conclusions based on the findings in this thesis can potentially shed new light on the topic. This however also has the implication that the empirical presentation in this thesis is more extensive as the results of seven different setups of data has to be presented as compared to one (market index). The series for the Euro-countries were stated in euros upon retrieval from Datastream, whereas those for the two other countries have been translated to euros using daily exchange rates over the entire period, also obtained from Datastream. This is to reflect the actual returns a portfolio manager based in Euro-land would have got from investing in the different countries including profits and losses due to currency fluctuations. Worth noting here is that the exchange rate of the Swiss Franc to the Euro was not available for the entire period, but the exchange rate of the Swiss Franc to the British Pound was. Thus, the Franc/Euro exchange rate series has been constructed based on the Franc/Pound and Pound/Euro exchange rate series and the assumption of no exchange rate arbitrage (i.e. exchanging 20

21 Francs to Euros or Francs to Punds and then Pounds to Euros are thought to be equivalent). The impact of any deviation from this assumption is expected to be negligible as correlation between the estimated exchange rate and the real rate was sufficiently high for the period where the latter was available. All series have been transformed by taking the logarithm of them. Thus, any statistics, graphs and results are measured in the log of the series unless else stated. Whenever returns are used it describes the log returns. 4.2 Data characteristics The equity indices used are constructed by Datastream and are homogenous which allows greater comparison across countries, as indices have a higher degree of comparability. The series are of fixed index datatypes, meaning that they are not recalculated historically when the constituents change meaning that stocks that are delisted from an exchange are not excluded from earlier index calculations. Further, these indices also include firms with smaller capitalization and thus represent a more accurate representation of the whole market. (Fratzscher 2001, p. 15) Thus the data avoid a source of criticism of differences in construction and inclusion patterns, as noted by e.g. Aggarawal et al (2003). For a full review of the method of the indices composition please see the Datastream Global Equity Indices User Guide (Thomson Financial, 2008). Market Index Basic Materials E(R i ) σ Skew. Kurt. JB JB prob. E(R i ) σ Skew. Kurt. JB JB prob. France 0.02 % 1.23 % % 1.40 % Germany 0.02 % 1.20 % % 1.32 % Italy 0.01 % 1.29 % % 1.66 % Netherl % 1.19 % % 1.74 % Switzerl % 1.16 % % 1.31 % U.K % 1.19 % % 1.70 % Consumer Goods Consumer Services E(R i ) σ Skew. Kurt. JB JB prob. E(R i ) σ Skew. Kurt. JB JB prob. France 0.02 % 1.45 % % 1.25 % Germany 0.02 % 1.70 % % 1.26 % Italy -0.00% 1.53 % % 1.30 % Netherl % 1.49 % % 1.17 % Switzerl % 1.90 % % 1.46 % U.K % 1.42 % % 1.19 % Financials Health Care E(R i ) σ Skew. Kurt. JB JB prob. E(R i ) σ Skew. Kurt. JB JB prob. France 0.01 % 1.49 % % 1.29 % Germany 0.01 % 1.38 % % 0.93 % Italy 0.00 % 1.42 % % 1.42 % Netherl % 1.43 % % 1.49 % Switzerl % 1.53 % % 1.18 % U.K % 1.51 % % 1.25 % Industrials E(R i ) σ Skew. Kurt. JB JB prob. France 0.02 % 1.37 % Germany 0.02 % 1.41 % Italy % 1.44 % Netherl % 2.06 % Switzerl % 1.48 % U.K % 1.27 % Table 1: Statistical properties of data Selected statistical properties for full sample of daily logarithmic returns January December E(R i) is the mean of returns, σ is the standard deviation of returns, Skew. is the skewness and kurt. is the Kurtosis. JB is the computed statistics for the Jarque-Bera normality test, JB probability values below 0.05 indicate non-normality. 21

22 Although this study will analyze the evolution of integration between European equity markets key statistics will for brevity reason only be presented for the entire period. Table 1 summarizes key statistical measures of the daily logarithmic returns for the six countries over the full period, grouped by industry. Full-size figures of the indices, grouped by industry, are available in appendix: Figure 8.1 through to Figure 8.7. As we can tell from the statistics in Table 1 above only two series have showed negative average returns over the sample; consumer goods and industrials in Italy. All series are leptokurtic and with only three exceptions exhibit negative skewness; the distribution of most series thus exhibit a relatively larger left tail and fewer observations around the mean compared to that of a normal distribution. As we can see from the Jarque-Bera statistics we reject the null of a normal distribution for all series. 4.3 Unit Root As a cointegration relationship requires the series to be non-stationary it is necessary to conduct unit root tests of all series included in the analysis. This is performed using conventional methods and these will therefore not be described in further detail. For rigidity reasons three different tests are used; the Augmented Dickey-Fuller (ADF) test, the Phillips-Perron (PP) test and the KPSS test that has an inverted null hypothesis compared to the previous two. Due to the amount of test statistics the results are presented in Tables 4 to 6 in the appendix. As is evident from the results the tests indicate the presence of a unit root in all series for all tests no matter if a constant, constant and linear trend or no exogenous component is included in the tests. This is a strong indication that all series exhibit a unit root, qualifying them for inclusion in the cointegration analysis. It s however worth noting that although they exhibit a unit root based on the entire sample it s possible that there will be sub-periods where they don t. It has however been deemed to lie outside of the scope of this thesis to research the time-variability of the unit root of the series, setting the bar of inclusion in the study only to evidence of an unit root for the entire sample period. Any periodically deviations from the presence of a unit root will result in fewer significant vectors in the cointegration analysis as an unit root for at least two series is a prerequisite for a cointegrating relation to exist. 22

23 5 Empirical Results In this chapter the results of the empirical tests are presented, based on the methods presented in chapter 2 and 3. We begin with the results based on the Johansen cointegration method followed by the principal component analysis. For ease of comparison the sections of each method is divided into two parts; one that presents the results based on the full sample and one that presents the equivalent of the rolling-window technique. In the latter only the results of the market index is presented in detail followed by examples and comments from the other industries. Due to space restrictions figures for all industries can not be presented but are available in the appendix, Figures 8.8 to Johansen Multivariate Cointegration Static analysis Table 2 below presents the results of the Johansen cointegration analysis for the market index and the sector indices over the entire sample. For brevity reasons only the first two null hypothesies are presented as a rejection of a given hypothesis was followed by a rejection of all consecutive null hypotheses. According to this there is only evidence of cointegration in the industrials at a 5 %-level and consumer goods industries at the 1 %-level among the four Euro-countries; health care also coming close with a p-value of The failure to accept the null of r = 0 means that we can not reject the alternative of r 1, meaning that there is at least one significant cointegrating vector. As noted above, the subsequent tests of r = 1 to the alternative r 2 fails to reject the null for both consumer goods and industrials indicating that there is one significant cointegrating vector for these industries over the entire sample. H 0 H 1 Stat. C. val. P. val. Market Index r = 0 r r = 1 r Basic Materials r = 0 r r = 1 r Cons. Goods r = 0 r r = 1 r Cons. Services r = 0 r r = 1 r Financials r = 0 r r = 1 r Health Care r = 0 r r = 1 r Industrials r = 0 r r = 1 r Table 2: Johansen Multivariate Cointegration test for series of France, Germany, Italy and Netherlands. Series are in logarithms and cover daily prices from January 1987 to end of December Stat. stand for test statistic, C. val for critical value and P. val. for probability value - all based on a 95 % significance level with zero lags. A probability value above 0.05 indicate a failure to reject the null of r number of significant cointegration vectors. 23

24 Given the absence of previous research on industry indices it is hard to know what to expect, although it could be thought as surprising that the market index was not among those series that exhibited or being close to exhibiting significant cointegration. It is however not unlikely that although many series show no sign of cointegration over the entire sample they could exhibit it over parts of the sample. That s why we turn to the rolling window analysis below Rolling-window analysis As the previous research has utilized data on broad market indices it is appropriate to begin our analysis with looking at what results this thesis find on comparative data and briefly compare it to previous findings. We then move on to a presentation of various findings in the results of individual industry indices. As a detailed presentation of each industry would have low marginal value and be repetitive a general presentation will be made combined with highlights of key findings. Market Index Figure 5.1 below presents the results of the rolling-window Johansen cointegration analysis for the market index based on the methods outlined in chapter 2 & 3. As we can see the study begins with one significant cointegration vector which spikes in 1991 where also the second vector becomes significant, if only for a few observations. Although this could be interpreted that events unfolded in 1991 raised the level of integration, a look at the underlying indices (Figure 8.1 in appendix) give some merit to the possibility that the crash of 1987 in combination of the recession of early 1990s dominated the estimation window. With the exception of two brief peaks above the critical line in the series stay in statistically insignificant territory until mid At this stage the first series begin to hover around the critical line and from mid-1997 until early 1998 the first series stay well above the critical line. Also the second series move above, as does the third for a very short period, indicating two more significant cointegration vectors. At this stage, around , the EMU project is well under way and the countries that will be part of the first phase of EMU has been announced; Adjaouté Danthine (2004, p. 1230) cite information that by August 1997 a poll showed that the overwhelming majority of 200 financial and economic forecasters predicted that the 10 to-be member countries were to be part of the EMU. Aggarwal et al (2010, p. 650) also point out that on 25 March 1998 it was officially announced which countries that were to join, leaving little room for further speculation. If this would lead to an increase in convergence there is little evidence that such was the case based on the cointegration after this event as the series stay below the critical line from this date until Similar to the peak in the series during , the rise in integration during 2001 is not sustained and eventually decline below the critical line before the end of the year; the second series this time having given little indication to rise as it did before. In 2002 a positive trend begins ending for the first series with a plateau above the critical line in After a hovering around the critical line over 24

25 Figure 5.1: Rolling-window Johansen Cointegration test: Market Index Series of Market Index for France, Germany, Italy and Netherlands. The test statistics have been scaled to their critical value for ease of interpretation, thus any series above 1 indicate a rejection the number of significant cointegration vectors. the next year it shoots up above again in 2006 and then decline with high volatility once again ending up below in It stays there until the recent financial crisis which has an adverse impact as the first series shoot up to extreme levels. Although even the second series reaching above levels seen by any series until this date it quickly reverts below, as does the first series eventually in According to the results found here cointegration between the market indices of the four EMU member countries have been episodic and frail and there are no evident long-lasting trends towards increased or decreased cointegration over time. This is a surprising result given that the findings of most previous studies have showed trends of increased integration over time; both from the 1980s as well as 1990s depending on the study. Although it could be argued that some of them used 90 % critical values this does not change the underlying trends, only the levels relative to the critical line. Industries We begin by looking at consumer goods and industrials, the industries that showed a significant cointegrating relationship over the entire sample. The first series of consumer goods, as presented in Figure 5.2 stays above the critical line for large parts of the first half of 1990s and similar to the market index again in After this there s a prolonged period of consolidation below the critical line lasting until 2004, although a positive trend begun already in It fails to establish itself above, although a peak in 2006 also seen in the market index see the second series become significant. The financial crisis has the same effect as for the market index but with also the fourth vector becoming significant indicating that all underlying indices are stationary. For industrials there is significant cointegration in the early 1990s, and then only sporadically until the early 2000s, similar to previously described series. In 2001 there is a trend upward for the first series, 25

26 Figure 5.2: Rolling-window Johansen Cointegration test: Consumer Goods Series of Consumer Goods for France, Germany, Italy and Netherlands. The test statistics have been scaled to their critical value for ease of interpretation, thus any series above 1 indicate a significant number of cointegration vectors. which see significant cointegration in after which there is a large downturn. The recent financial crisis has a lesser aggressive effect compared to previous series as the first relation already in early 2008 begin to rise and later that year become significant to stay above the critical line until end of Figure 5.3: Rolling-window Johansen Cointegration test: Financials Series of Financials for France, Germany, Italy and Netherlands. The test statistics have been scaled to their critical value for ease of interpretation, thus any series above 1 indicate a significant number of cointegration vectors. Looking across the industries there are some similarities; all begin the study with the first series above or close to the critical line and show evidence of significant cointegration in the first years. But all move back below the critical line around 1992 or 1993, some already in late Consumer services does not recover until 1997, but then fall back almost immediately. Apart from some spikes along the way, the first series only establish itself comfortably over the critical line after the financial crisis. 26

27 Although oscillating around the critical line in the financials then move well below, as we can see in Figure 5.3. But in 2000 there seem to be a trend starting to move upward and with the exceptions of some drops along the way it spans until 2006 at which stage it reaches the value of two; the second and even the third vectors becoming significant at the 95 %-level indicating strong cointegration in the system. Similar to industrials the series then rapidly move back below the critical level only to shoot up in the financial crisis, doing so to a level not seen in any other industry in this study. These very strong reactions to the financial crisis can be interpreted as evidence for the seemingly increased cointegration that a strong negative shock can create. This is related to the discussion provided in chapter 2 where it was explained that market can move together although they are not integrated; financial panics lead to large and broad sell-offs of risky assets and most equities move downward together. Figure 5.4: Rolling-window Johansen Cointegration test: Basic Materials Series of Basic Materials for France, Germany, Italy and Netherlands. The test statistics have been scaled to their critical value for ease of interpretation, thus any series above 1 indicate a significant number of cointegration vectors. The industry that show the strongest cointegration is basic materials, presented in in Figure 5.4. It does not only have the strongest level of cointegration in the early 1990s, it also has it during during which the second relation remain high for an extended period compared to other industries. Also in basic materials show reassuring signs of cointegration, including the second vector in , but fall and stay below from mid An interesting note is that the effect of the financial crisis is mild compared to other industries. 5.2 Principal Component Analysis Static analysis We begin with providing an overview of what results a static principal component analysis (PCA) provides when calculated over the entire sample. Table 3 present the explanatory power and correlation of each country s return to the first component for each of the industries. As explained in Gilmore 27

28 et al (2008, p. 621) the correlation is interpreted as the level of participation of individual series in the component, with interests also taken in if series are grouped at different levels of correlation which provide information about linkages. The explanatory power is how much of the total variation the first component can explain. France Germany Italy Netherl. Switzerl. UK Avg. (ind.) Expl. Power Market Index Basic Materials Cons. Goods Cons. Services Financials Health Care Industrials Avg. (country) Table 3: Explanatory power of and correlation between the returns and the first principal component for full sample from January 1987 to December As is evident the correlation of the countries returns to the first principal component of the market index dominates the equivalent of all other industries with only two exceptions: financials for Switzerland and Italy. That financials is the exception in both cases seem to be no coincidence. Because when excluding the market index, financials is the industry that has the highest explanatory power and the highest correlation across all countries and sectors with just one exception: Germany where instead industrials is the dominant industry. It is somewhat surprising that the explanatory power and almost all correlation coefficients for consumer services are higher than those of consumer goods. The results indicate that the comovements of stocks in the consumer service sector in the different countries is higher than that of consumer goods although we based on basic macroeconomics would expect the reversed to be true as goods are easier to export than services. Although the first component is believed to be a measure of the level of integration it is not possible to deduce how large the impact is on portfolio diversification opportunities. But if the first component measures the integration well it is evident that at least in relative terms there should exist greater diversification opportunities in the industries than in the market index based on the entire sample. Further, there is no clear divide between the group of Euro-countries and the two other which could cast some doubt on the importance of the EMU on the level of integration based on PCA. It is however of interest to see if and how the levels of participation to the first component as well as its explanatory power have changed over time which is why we turn to the results of the rolling-window approach. 28

29 5.2.2 Rolling-window analysis Market indices have been the focal series of previous studies, but how does its evolution compare to that of the other industries? We saw previously from the summarized statistics for the entire sample that there seem to be evident differences for the industries which we will analyze further below. A more thorough analysis is first provided for the market index followed by some examples of overall differences and similarities for the industries. Market Index As can be seen from the explanatory power of the first loading for the market index, presented in Figure 5.6, there has been clear trends over the past two decades. An upward trend from around 61 to 65 % in is abruptly ended with a large drop in late As noted in the presentation of the Johansen cointegration analysis this is possibly due to the dominance of the crisis of 1987 and the 1990 recession in the early sample. Although there is a tendency of recovery in the following years a negative trend reasserts itself and the explanatory power of the first component reaches its lowest level in mid As is evident from Figure 5.6 the drop and eventual negative trend is due to the lesser participation in the first component of Italy, Germany, Switzerland and some extent France during the period; although United Kingdom continues a steady upward trend, as is Netherlands. The trend-reversal in 1996 is evident as Italy, Switzerland and France reverse their negative trends in tune, Germany showing hints of a slight lag of a few months. Figure 5.5: Rolling-window Principal Component Analysis: Market Index Correlation of logarithmic returns to first component of Market Index for France, Germany, Italy, Netherlands, Switzerland and United Kingdom. Estimation window set to 1000 observations, moving 1 observation at a time From mid-1996 until late 1997 there is a clear upward trend for the explanatory power of the first component. The stability is however interrupted as the trend gets a sudden upward shift from 59 to 64 29

30 Figure 5.6: Rolling-window PCA: Cum. expl. power of first two PCs of Market Index Cumulative explanatory power of the first two principal components for logarithmic returns of series of Market Index for France, Germany, Italy, Netherlands, Switzerland and United Kingdom. Thus, PC2 represent the cumulative explanatory power of PC1 & PC2. % in late 1997 at a time corresponding to the development of the Asia crisis. The reason is that the participation of all countries in the component take a similar discrete shift upward, Italy then being the only country which se a rapid increase directly following this jump while Netherlands, United Kingdom and Germany make an inverted u-shaped move which is also evident in the explanatory power. In 1998 a new shock propels the participation and explanatory power upward; the latter moving from 64 to 73 %. It is possible that this move is related to the Russian debt crisis. Italy s level of participation in the first component having previously moved far below that of most other countries has now almost made up all ground. This means that the gap of almost 30 percentage points that existed between Italy in the bottom and Netherlands in the top in the beginning of 1996 has by 1999 been narrowed by two thirds. Starting in 1999 the four Euro-countries begin to converge in terms of participation while Switzerland, the only non-eu country of the six, is starting to build up some distance as it moves sideward or slightly downward until United Kingdom has joined the Euro-countries in levels and is moving very closely to Italy and Germany while France and Netherlands seem to form a close link at a higher level. There is however only approximately 5 percentage points between the groups. During this convergence period the explanatory power moves from 75 % in 2001 to a peak of 85 % in Although the deterioration and eventual regain in the explanatory power over the next two years, leading up to the financial crisis of 2008, could largely be attributed to a further detachment of Switzerland from the other countries a tendency for the others to make a u-shape is also evident for all countries except Germany. As the recent financial crisis hits in 2008 Germany is the only country with a significant change in participation, plummeting from 91 to 78 %. Although some ground is made up over the next two years Germany and Switzerland are clearly grouped together at around 85 % at the end of the study. Italy, Netherlands and United Kingdom are closely aligned at 95 % and France at close to 100 %. The 30

31 explanatory power exhibits a spike and levels out at just below 85 %. Although this is 20 percentage points above the early peak in 1991 and 30 percentage points above the lows of 1996, the jumps of 1997 and 1998 together account for 14 percentage points; almost half of the increase from the bottom to the end of the sample. Industries The industry that has most in common with the evolution of the market indices is financials, a confirmation of the hint that the full-sample estimations gave us. Both the levels and the evolution during the 1990s is to a large extent identical with some exception for France. From the late 1990s, after 1998, and during the 2000s there are however some dissimilarities; there is a greater convergence across the board as also Switzerland and United Kingdom have levels of correlations similar to the Euro-countries and Germany stays close to the rest even after the financial crisis leading to a 7 percentage points gap between France in the top and Switzerland in the bottom at the end of The similarities in the explanatory power of the first component is also striking with the overall increase for financials even being approximately 5 percentage points greater when comparing values at the beginning and the end; beginning at a lower level but similarly to the market index ending up at just below 85 %. Figure 5.7: Rolling-window Principal Component Analysis: Financials Correlation of logarithmic returns to first component of Financials for France, Germany, Italy, Netherlands, Switzerland and United Kingdom. Estimation window set to 1000 observations, moving 1 observation at a time In terms of the explanatory power of the first component at the end of 2010 it is only industrials, presented in Figure 5.8, with 78 % that can compare to the market index and financials. A contributing factor to this is the absence of a slump in and that the recent financial crisis seem to have a positive impact on the explanatory power; prior to the crisis industrials had 70 % compared to the market index s 83 %. The correlation of the underlying series see some similarities of the market index throughout the 1990s but consistently at a lower level; Netherlands the most deviating country as it has 31

32 a pronounced downward trend. The trend reversion is similar to the market index in 1996 and most of the gap has been closed by early 1999 at which a more pronounced upward trend is evident. The trend will continue for all Euro-countries until the end of the sample, United Kingdom and Switzerland here deviating to a large extent during the beginning of the 2000s but eventually joining the group in 2008; France in the top with some distance to Germany and Netherlands around 90 % and the rest at 85 %. Figure 5.8: Rolling-window PCA: Cum. expl. power of first two PCs of Industrials Cumulative explanatory power of the first two principal components for logarithmic returns of series of Industrials for France, Germany, Italy, Netherlands, Switzerland and United Kingdom. Thus, PC2 represent the cumulative explanatory power of PC1 & PC2. An interesting finding is that only for consumer goods does the correlation of Germany see a large drop as the financial crisis of 2008 hit the series just as it did for the market index; it does however jump up for basic materials. Germany s drop is substantial too, from above 80 to below 30 %. The overall evolution of the correlations in the consumer goods sector is somewhat different to that of the market index; e.g. Netherlands have a pronounced negative trend over the first half of the 1990s and Italy isn t the series that move at the bottom. Although there is an upward trend for most countries the convergence in levels is not as pronounced as for the market index. But when excluding Germany the gap between the series at the end of the study is still substantial, 15 percentage points between France in the top and Switzerland in the bottom. This is mirrored in the explanatory power that end at a level of 65 %, down from a peak of 70 % just before the crisis. As seen in the results presented in the table of the static analysis consumer services seemed to have fared better over the entire sample. The explanatory power ends at 70 %, also dropping from a higher level of 74 % prior to the crisis. Although the overall convergence during the 2000s is greater for consumer services, there is still a gap of approximately 13 percentage points in the top group at the end of the study with Switzerland another 20 percentage points below Netherlands which is the lowest of those. 32

33 Figure 5.9: Rolling-window Principal Component Analysis: Health Care Correlation of logarithmic returns to first component of Health Care for France, Germany, Italy, Netherlands, Switzerland and United Kingdom. Estimation window set to 1000 observations, moving 1 observation at a time The industry that stands out is health care, presented in Figures 5.9 & 5.10, that is the only that have an explanatory power that is smaller in the end of the study at 54 % compared to in the beginning at 55 %, although episodically moving above it. Looking at the correlations the largest degree of convergence is found in as France, Netherlands, Switzerland and United Kingdom move together at almost identical levels; but in a weakly negative trend. Although Italy and Germany are largely detached from the others at this stage Germany does make up this ground from 2003 onwards while Netherlands join Italy at depressed levels in Figure 5.10: Rolling-window PCA: Cum. expl. power of first two PCs of Health Care Cumulative explanatory power of the first two principal components for logarithmic returns of series of Health Care for France, Germany, Italy, Netherlands, Switzerland and United Kingdom. Thus, PC2 represent the cumulative explanatory power of PC1 & PC2. 33

34 6 Conclusions A majority of previous studies have found equity markets of Europe to be well integrated. Studies that have analyzed the evolution of the integration have also found that they are increasingly so since the European unification process intensified during the 1990s. This has to some extent merited the possibility that the EU and EMU projects has influenced the integration. The results of this study over the period 1986 to 2010 however show mixed results as the findings of the Johansen cointegration analysis show little evidence of any integration and the principal component analysis pointing towards an increased integration as measured by the first component. The previous studies have analyzed the integration of market indices and the results in this thesis based on the Johansen method show only episodical periods of significant cointegration at the 95 %-level with no clear trends of an increase over time. The results of the individual industries studied show similar evidence, although the length and number of periods of significant cointegration vary. Although financials and basic materials exhibit a trend towards increased cointegration during the early 2000s until 2006 the level is not sustained. The overall results have two implications; on one hand it casts the effect of the EMU on equity market integration in doubt and on the other show that there still exists diversification opportunities for portfolio investors across the four countries studied; no matter if measured over the market index or individual industries. It is evident from the principal component analysis that the market index as well as certain industries, most notably financials and industrials, saw an increased explanatory power of the first component paired with a higher degree of correlation of their returns with the component starting in the late 1990s. This evolution could very well be a result of the intensified work of launching the EMU, starting with the Madrid Declaration II in late 1995 that set the date of the Euro launch to January An observation that however cast some doubt on the EMUs importance in this is that United Kingdom and Switzerland often share the level of correlation as well as some Euro-countries sometimes being detached from the others also during the 2000s. A possible explanation to this could be that the integration that the EMU has brought to the equity markets of its member countries is transmitted also to other countries; the fact that Switzerland, not in either union, never has a correlation with the first component that is higher than that of United Kingdom could indicate that this integration is transmitted to other EUcountries to a larger extent. At the same time however, many industries show a less positive evolution which indicates that whatever integration that the first principal component can be translated into it is substantially lower at industry level for a set of industries, such as health care, relative the market index. Based on the findings in this thesis there is evidence both supporting and undermining that equity market integration among the four EMU-countries has increased over the past decades, meaning that the two methods are not interchangeable. The Johansen cointegration method show very little evidence of an increase in integration and based on this there still exist diversification opportunities for portfolio investors. Even if the PCA analysis show tendencies towards greater convergence from 1996 the EMUs 34

35 role in this evolution is doubtful. The reason for this conclusion is twofold. For one is that although there is a gradual increase in the explanatory power of the first component over the late 1990s and 2000s a large part of the overall increase over the period is due to shocks in 1997 and Secondly the non-emu countries in the study to a large extent share the level of correlation with the first component as the EMU-countries when it could be expected that latter would be grouped together at a higher level. A possible explanation to this could however be that there are spill-over effects of integration to other developed European countries. With the results from this study being conflicting and also to some extent different to previous studies based on market indices further research is warranted. More studies that make use of sectoral data would shed light on the differences and similarities of these compared to market indices. Combined with rolling-window techniques, as done in this thesis, would create a body of empirical studies that to a larger extent mirror to the realities of portfolio investors that invest in industries rather than broad market indices in different countries. It would also be of interest to include further countries in and outside the EMU as well as countries that joined the project at a later date in PCA to find if the potential spill-over effect is evident to different extents and over different windows in time, possibly indicating that the EMU has played a role in the integration process after all. This and other studies into PCA could also help shed light on what the first component actually stands for. As the rolling-window cointegration method is open criticism, as explained for the Johansen method in chapter 3, research into the impact on results depending on differences in specification could also increase the validity of future studies. 35

36 7 References Adjaouté, K. & Danthine, J-P. (2004). Portfolio diversification: alive and well in Euro-land! Applied Financial Economics No. 14: Aggarwal, R., Lucey, B. & Muckley, C. (2010). Dynamics of Equity Market Integration in Europe: Impact of political events. Journal of Common Market Studies, Vol. 48, No. 3: Arshanapalli, B. & Doukas, J. (1993). International Stock Market Linkages: Evidence from the pre- and post-october 1987 period. Journal of Banking and Finance. Vol. 17, No. 1: Campbell, J.Y., Lo, A.W. & MacKinley, A.C. (1997). The Econometrics of Financial Markets. United States: Princeton University Press. De Nicolò, G. & Tieman, A. (2006). Economic Integration and Financial Stability: A European perspective. IMF Working Paper, 06/296. Eichengreen, B. (2004). Capital Flows and Crisis. United States: MIT Press. Eichengreen, B (2007). The European Economy Since 1945: Coordinated capitalism and beyond. United States: Princeton University Press. Eichengreen, B. (2008). Globalizing Capital. New Jersey: Princeton University Press. Elton, E.J., Gruber, M.J., Brown, S.J. & Goetzmann, W.N. (2007). Investment Analysis. United States: John Wiley & Sons. Modern Portfolio Theory and Focardi, S.F. & Fabozzi, F.J. (2004). The Mathematics of Financial Modeling and Investment Management United States: John Wiley & Sons. Fratzscher, M. (2001). Financial Market Integration in Europe: On The Effects of EMU on Stock Markets. European Central Bank Working Paper Series, No. 48. Gilmore, C.G., Lucey, B.M. & McManus, G.M. (2008). The Dynamics of Central European Equity Market Comovements. The Quarterly Review of Economic and Finance, No. 48: Gregory, A. W. & Hansen, B. E. (1996). Residual-based Tests for Cointegration in the Models With Regime Shifts. Journal of Econometrics, Vol. 70: Hamilton, J. (1994). Time Series Analysis. USA: Princeton University Press. 36

37 Harris, S. & Sollis, R. (2003). Applied Time Series Modeling. England: John Wiley & Sons Ltd. Johansen, S. (1991). Cointegration and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models. Econometrica, Vol. 59, No. 6: Kearney, C. & Brian, M.L. (2004). International Equity Market Integration: Theory, Evidence and Implications. International Review of Financial Analysis. No. 13: Kindleberger, C.P. (2006). A Financial History of Western Europe. Oxon: Routhledge. Lansangan, J.R.G. & Barrios, E.B. (2009). Principal Component Analysis of Nonstationary Time Series Data. Statistics and Computing, Vol. 19, No. 2: Martin, P., & Rey, H. (2000). Financial integration and asset returns. No. 44: European Economic Review, Pagano, M. (1993). Financial markets and growth: An overview. European Economic Review. No. 37: Rangvid, J. (2001). Increasing Convergence Among European Stock Markets? A Recursive Common Stochastic Trends Analysis. Economic Letters No. 71: Selover, D.D. (1999). International Interdependence and Business Cycles Transmission in ASEAN. Journal of the Japanese and International Economies 13: Thomson Financial (2008). Datastream Global Equity Indices User Guide: Issue 5. Voronkova, S. (2004). Equity Market Integration in Central European Emerging Markets: A cointegration analysis with shifting regimes. International Review of Financial Analysis No. 13:

38 8 Appendix 8.1 Tables None Constant Constant & trend Market Index Lags t-stat C.val P.val Lags t-stat C. val P. val Lags t-stat. C. val. P. val. France Germany Italy Netherlands Basic Materials France Germany Italy Netherlands Consumer goods France Germany Italy Netherlands Consumer Services France Germany Italy Netherlands Financials France Germany Italy Netherlands Health Care France Germany Italy Netherlands Industrials France Germany Italy Netherlands Table 4: Augmented Dickey-Fuller Unit Root Test ADF-test with null of a unit root performed on full sample; January 1987 to December Lag length selected automatically based on SIC with maximum value of 33. t-stat is the test statistic, C. val is the 5 %-level critical values and P.val is the MacKinnon (1996) one-sided p-values. P-values equal or below 0.05 indicate a rejection of the null of a unit root. 38

39 Constant Constant & trend Market Index BW LM-stat C. val BW LM-stat. C. val. France Germany Italy Netherlands Basic Materials France Germany Italy Netherlands Consumer goods France Germany Italy Netherlands Consumer Services France Germany Italy Netherlands Financials France Germany Italy Netherlands Health Care France Germany Italy Netherlands Industrials France Germany Italy Netherlands Table 5: KPSS Unit Root Test KPSS-test with null of stationarity performed on full sample; January 1987 to December BW is the bandwidth automatically selected by Newey-West/Bartlett kernel. LM-stat is the KPSS Lagrange multiplier test statistic and C. val is the 5 %-level asymptotic critical values. A LM-statistic greater than the critical value indicates a failure to accept the null of stationarity. 39

40 Constant Constant & trend Market Index BW t-stat C. val P.val BW t-stat C. val P. val BW t-stat. C. val. P. val. France Germany Italy Netherlands Basic Materials France Germany Italy Netherlands Consumer goods France Germany Italy Netherlands Consumer Services France Germany Italy Netherlands Financials France Germany Italy Netherlands Health Care France Germany Italy Netherlands Industrials France Germany Italy Netherlands Table 6: Phillips-Perron Unit Root Test PP-test with null of a unit root performed on full sample; January 1987 to December BW is the bandwidth automatically selected by Newey-West/Bartlett kernel. t-stat is the adjusted test statistic, C. val is the 5 %-level critical value and the p.value is the one-sided p-value from MacKinnon (1996). A p-value greater than 0.05 indicate a failure to accept the null of a unit root.. 40

41 8.2 Figures 41

42 42 Figure 8.1: Series of Market Index for all countries; France, Germany, Netherlands, Italy, Switzerland and United Kingdom. The series represent the logarithm of original indices rebased to 100 on January

43 43 Figure 8.2: Series of Basic Materials for all countries; France, Germany, Netherlands, Italy, Switzerland and United Kingdom. The series represent the logarithm of original indices rebased to 100 on January

44 44 Figure 8.3: Series of Consumer Goods for all countries; France, Germany, Netherlands, Italy, Switzerland and United Kingdom. The series represent the logarithm of original indices rebased to 100 on January

45 45 Figure 8.4: Series of Consumer Services for all countries; France, Germany, Netherlands, Italy, Switzerland and United Kingdom. The series represent the logarithm of original indices rebased to 100 on January

46 46 Figure 8.5: Series of Financials for all countries; France, Germany, Netherlands, Italy, Switzerland and United Kingdom. The series represent the logarithm of original indices rebased to 100 on January

47 47 Figure 8.6: Series of Health Care for all countries; France, Germany, Netherlands, Italy, Switzerland and United Kingdom. The series represent the logarithm of original indices rebased to 100 on January

48 48 Figure 8.7: Series of Industrials for all countries; France, Germany, Netherlands, Italy, Switzerland and United Kingdom. The series represent the logarithm of original indices rebased to 100 on January

49 Figure 8.8: Rolling-window Johansen Cointegration test: Market Index Series of Market Index for France, Germany, Italy and Netherlands. The test statistics have been scaled to their critical value for ease of interpretation, thus any series above 1 indicate a significant number of cointegration vectors. Figure 8.9: Rolling-window Johansen Cointegration test: Basic Materials Series of Basic Materials for France, Germany, Italy and Netherlands. The test statistics have been scaled to their critical value for ease of interpretation, thus any series above 1 indicate a significant number of cointegration vectors. 49

50 Figure 8.10: Rolling-window Johansen Cointegration test: Consumer Goods Series of Consumer Goods for France, Germany, Italy and Netherlands. The test statistics have been scaled to their critical value for ease of interpretation, thus any series above 1 indicate a significant number of cointegration vectors. Figure 8.11: Rolling-window Johansen Cointegration test: Consumer Services Series of Consumer Services for France, Germany, Italy and Netherlands. The test statistics have been scaled to their critical value for ease of interpretation, thus any series above 1 indicate a significant number of cointegration vectors. 50

51 Figure 8.12: Rolling-window Johansen Cointegration test: Financials Series of Financials for France, Germany, Italy and Netherlands. The test statistics have been scaled to their critical value for ease of interpretation, thus any series above 1 indicate a significant number of cointegration vectors. Figure 8.13: Rolling-window Johansen Cointegration test: Health Care Series of Health Care for France, Germany, Italy and Netherlands. The test statistics have been scaled to their critical value for ease of interpretation, thus any series above 1 indicate a significant number of cointegration vectors. 51

52 Figure 8.14: Rolling-window Johansen Cointegration test: Industrials Series of Industrials for France, Germany, Italy and Netherlands. The test statistics have been scaled to their critical value for ease of interpretation, thus any series above 1 indicate a significant number of cointegration vectors. x 52

53 Figure 8.15: Rolling-window Principal Component Analysis: Market Index Correlation of logarithmic returns to first component of Market Index for France, Germany, Italy, Netherlands, Switzerland and United Kingdom. Estimation window set to 1000 observations, moving 1 observation at a time Figure 8.16: Rolling-window PCA: Cum. expl. power of first two PCs of Market Index Cumulative explanatory power of the first two principal components for logarithmic returns of series of Market Index for France, Germany, Italy, Netherlands, Switzerland and United Kingdom. Thus, PC2 represent the cumulative explanatory power of PC1 & PC2. 53

54 Figure 8.17: Rolling-window Principal Component Analysis: Basic Materials Correlation of logarithmic returns to first component of Basic Materials for France, Germany, Italy, Netherlands, Switzerland and United Kingdom. Estimation window set to 1000 observations, moving 1 observation at a time x 54

55 Figure 8.18: Rolling-window PCA: Cum. expl. power of first two PCs of Basic Materials Cumulative explanatory power of the first two principal components for logarithmic returns of series of Basic Materials for France, Germany, Italy, Netherlands, Switzerland and United Kingdom. Thus, PC2 represent the cumulative explanatory power of PC1 & PC2. x 55

56 Figure 8.19: Rolling-window Principal Component Analysis: Consumer Goods Correlation of logarithmic returns to first component of Consumer Goods for France, Germany, Italy, Netherlands, Switzerland and United Kingdom. Estimation window set to 1000 observations, moving 1 observation at a time Figure 8.20: Rolling-window PCA: Cum. expl. power of first two PCs of Consumer Goods Cumulative explanatory power of the first two principal components for logarithmic returns of series of Consumer Goods for France, Germany, Italy, Netherlands, Switzerland and United Kingdom. Thus, PC2 represent the cumulative explanatory power of PC1 & PC2. 56

57 Figure 8.21: Rolling-window Principal Component Analysis: Consumer Services Correlation of logarithmic returns to first component of Consumer Services for France, Germany, Italy, Netherlands, Switzerland and United Kingdom. Estimation window set to 1000 observations, moving 1 observation at a time x 57

58 Figure 8.22: Rolling-window PCA: Cum. expl. power of first two PCs of Consumer Services Cumulative explanatory power of the first two principal components for logarithmic returns of series of Consumer Services for France, Germany, Italy, Netherlands, Switzerland and United Kingdom. Thus, PC2 represent the cumulative explanatory power of PC1 & PC2. x 58

59 Figure 8.23: Rolling-window Principal Component Analysis: Financials Correlation of logarithmic returns to first component of Financials for France, Germany, Italy, Netherlands, Switzerland and United Kingdom. Estimation window set to 1000 observations, moving 1 observation at a time Figure 8.24: Rolling-window PCA: Cum. expl. power of first two PCs of Financials Cumulative explanatory power of the first two principal components for logarithmic returns of series of Financials for France, Germany, Italy, Netherlands, Switzerland and United Kingdom. Thus, PC2 represent the cumulative explanatory power of PC1 & PC2. 59

60 Figure 8.25: Rolling-window Principal Component Analysis: Health Care Correlation of logarithmic returns to first component of Health Care for France, Germany, Italy, Netherlands, Switzerland and United Kingdom. Estimation window set to 1000 observations, moving 1 observation at a time x 60

61 Figure 8.26: Rolling-window PCA: Cum. expl. power of first two PCs of Health Care Cumulative explanatory power of the first two principal components for logarithmic returns of series of Health Care for France, Germany, Italy, Netherlands, Switzerland and United Kingdom. Thus, PC2 represent the cumulative explanatory power of PC1 & PC2. Figure 8.27: Rolling-window Principal Component Analysis: Industrials Correlation of logarithmic returns to first component of Industrials for France, Germany, Italy, Netherlands, Switzerland and United Kingdom. Estimation window set to 1000 observations, moving 1 observation at a time 61