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Prospects for Portfolio Investments to Emerging European Stock Markets Dr. Theodore Syriopoulos Department of Business Administration, Technological Educational Institute, Larissa, and Department of Shipping and Entrepreneurial Services, University of Aegean, Chios, Greece Abstract The presence of short- and long-run linkages among major emerging Central European stock markets, namely Poland, Czech Republic, Hungary, and Slovakia, as well as developed markets, particularly Germany and the US, is investigated. An error correction vector autoregressive model is estimated to detect cointegration relationships and the empirical findings support the presence of one cointegration vector, indicating a stationary long-run relationship. Both domestic and external forces affect market behavior, leading to long-run equilibriu m but the individual Central European markets tend to display stronger lin kages with their mature counterparts rather than their neighbors. Long -run comovements imply that the potential for diversifying risk and attaining superior portfolio returns by investing in different Central European markets is rather limited for international investors. Paper Submitted for nd the 2 Annual Conference of the Hellenic Finance and Accounting Association Corresponding author: 12, Faid rou Str., 116 35 Athens, Greece. Tel.: 0030.210.75.15.567, 6944.911.787. e-mail: mourat@hellasnet.gr Paper Submitted for nd the 2 Annual Conference of the Hellenic Finance and Accounting Association November 8th , 2003 Athens Universtity of Economics and Business Prospects for Portfolio Investments to Emerging European Stock Markets Dr. Theodore Syriopoulos Department of Business Administration, Technological Educational Institute, Larissa, and Department of Shipping and Entrepreneurial Services, University of Aegean, Chios, Greece Corresponding author: 12, Faid rou Str., 116 35 Athens, Greece. Tel.: 0030.210.75.15.567, 6944.911.787. e-mail: mourat@hellasnet.gr 1 1. Introduction As stock markets have gained a dominant role in equity funding and portfolio allocation decisions, research examining possible stock market lin kages and interdependences has enriched recent literature. Significant long-run relationships among different stock markets could be related to a range of reasons. The presence of strong economic ties and policy coordination in various markets can indirectly link stock price behavior over time. W ith technological advances and financial innovations, advancement of international finance and trade, and regional and global cooperation, the geographical barriers among various national stock markets become less clear (Gelos and Sahay, 2000). Adoption of measures towards deregulation and market liberalizat ion, rapid development in communication s upport and computerized trading systems, and increasing activities by mu ltinational corporations are factors contributing to financial integration. The formation of co mmon trading blocks (e.g. EU, ASEA N, NAFTA), and the development of integrated economic s ystems (EMU, euro) also foster closer linkages of stock markets within the constituent states (Chen et al., 2002). These developments have in turn led to an increase in capital flows across markets, enhancing the globalizat ion and integration process, increasing accessibility, transparency and efficiency in t imely investment allocation decisions. Long-run comovements between stock markets have important regional and global implications, as a domestic economy cannot be insulated fro m external shocks and the scope for independent monetary policy appears then limited. Cointegration has emerged as a powerful technique for investigating common trends and long-run relationships and interdependencies among international stock markets, and provides a sound methodology for modeling both short- and long-run dynamics in a system of variables (e.g. Hamilton, 1994; Hendry, 1995; Enders, 1995; Campbell et al., 1997). If two or more variables are co integrated, then stationary linear co mbinations of these variables may exis t even though the variables themselves are individually non-stationary. Thus, variables that are cointegrated exhibit stable long-run behavior. In the short-run, financial time series across markets may deviate fro m each other, but market forces, investors ’ tastes and preferences, and government regulations will bring them back to their long-run equilibriu m. 2 A significant part of past research focuses on major European stock markets, such as Corhay et al. (1993), Choudhry (1996), Koutmos (1996), Serletis and King (1997), Steely and Steely (1999), Gerrits and Yuce (1999), Dickinson (2000), Ejara (2001), and Yang et al. (2003) among others. A number of studies investigate the Asian and Pacific stock markets, such as Hung and Cheug (1995), Cheug (1995), Chauhdri (1996), Corhay et al. (1995), Janakiramanan and Lamba (1998), Roca et al. (1998), Phylaktis and Ravazzolo (2001), Fan (2001), Sharma and Wongbangpo (2002), Yang et al. (2003), Shamsuddin and Kim (2003), among others. A body of research examines the relationships among international stock markets across regions, such as Eun and Shim (1989), Jeon and Chiang (1991), Kasa (1992), Chan et al. (1992, 1997), Masih and Masih (1997), Ghosh et al. (1999), Huang et al. (2000), Ratanapakorn and Sharma (2002), Chen et al. (2002), Swanson (2003), Chaudhuri and Wu (2003), Bessler and Yang (2003), among others. Few only studies focus on the CE stock markets, such as Jochum et al. (1999), Verchenko (2000), MacDonald (2001), Gilmo re and McManus (2003), and Vo ronkova (2003). The majority of past empirical work investigating long -term stock market linkages has concentrated main ly on mature rather than emerging stock markets, and has provided a range of amb iguous and inconsistent conclusions, as statistical evidence supports the presence of cointegration relationships in a number of markets whereas it rejects it in others. Further insight then is useful, especially in emerg ing stock markets that appear to have low correlations with mature markets. The conclusions have important imp licat ions for portfolio management decisions. If international stock markets share common trends, this would imp ly that there are no particular gains to be made fro m portfolio diversification, because the presence of common factors limits the amount o f independent variation. Imp licit ly, shocks to the stock prices in integrated markets are temporary rather than permanent, lead ing to predictable long-run stock prices. On the contrary, if financial markets do no appear interrelated, profitable opportunities fro m international portfolio d iversification can be exploited, lead ing to superior portfolio returns for long -term investors. It should be also noted, though, that a number of studies calls into question the violation of the weak form of market efficien cy, due to price predictability as implied by the presence of cointegration (Dwyer and Wallace, 1992; Cro wder, 1994, 1996; Engel, 1996; Caporalle and Pitt is, 1998). The purpose of this study is to enrich research in possible interdependencies between transitional and developed stock markets, exploring different market behaviors between emerging and mature 3 economies. The focus here is on long-run comovements of the emerging Central European (CE) markets, departing fro m past practice that focuses main ly on d eveloped European markets, the US, Asian-Pacific, and Latin A merican markets. The contribution of this study to the existing literature is related to a range of innovative and interesting conclusions. The major CE stock markets are analyzed in depth, in order to identify possible long-run comovements among the emerging markets of the region as well as international mature markets, namely Germany and the US. As the relevant empirical evidence appears to be thin and controversial, this effort intends to provide insight into the patterns of long-run relationships among the individual CE stock markets and mature markets, the degree of asset prices predictability and the prospects of a profitable portfolio diversificat ion to these markets. The dynamic structure of international market integration based on innovation accounting is also analyzed, as this topic has not been adequately investigated in relevant past studies. Central European markets are characterized by stable performance of the domestic economies, hig her growth rates compared to ‘old’ European economies and relat ively low valuations (Havlik, 2003). A mong the CE stock markets, Poland, the Czech Republic, Hungary, and Slovakia are considered the most developed, in terms of capitalizat ion, turnover and number of traded securities (Hanousek and Filer, 2000; Pajuste, 2001; Koke and Schroder, 2002). The efficient financial integration of the region with developed European markets has important implications for the accession of the CE economies in the European Union (EU), also affecting the long-term development prospects for Euroland as a whole. The reaction of these markets to internal and external shocks has also considerable impact on the potential gains fro m portfolio diversification to the region. If border effects still persist in the CE markets, portfolio managers have an interest in investing in these markets in order to diversify their risk; otherwise profitable opportunities for investor portfolios remain limited for such an allocation. The statistical data used in this study consist of the daily stock index closing prices (expressed in local currencies) of WIG (Po land), PX50 (the Czech Republic), BUX (Hungary), SAX (Slovakia), DAX (Germany), and S&P500 (the US), over January 1, 1997 to September 20, 2003, totaling 1,747 daily observations for each series. The rest of the paper is organized as follows. Section 2 outlines the emp irical methodology, Section 3 presents the empirical results, and Section 4 concludes. 4 2. Empirical Methodol ogy Two distinct types of links between stock markets (indices) can be seen; the first one is typically related to the ‘volatile behavior’ of stock indices and the second is related to the ‘trending behavior’ of the series. In the first case, models based on estimating time-varying volatilit ies to investigate stock price lin kages and the transmission of shocks from one market to another. In the latter case, emphasis is placed on joint tests of market integration and comovements in the long -run. Interrelations and linkages between the CE stock markets are studied here by estimat ion and testing for the presence and number of cointegrating vectors. As explained, cointegration relat ionships allow fo r the description of stable long-run stationary relationships among integrated variables, and are defined as independent linear combinations of these non-stationary variables achieving stationarity. When a meaningful interpretation can be attached to this linear combination, it imp lies that the series do not drift apart and are moving together by some long-run equilibriu m relationship. Individual non-stationary times series in a mu ltivariate system are driven by a reduced number of co mmon stochastic trends. A common stochastic trend in a system of stock price indices can be interpreted to mean that the stochastic trend in one individual stock price is related to the stochastic trend in some other individual stock price index. Testing for Unit Roots Cointegration tests require a certain stochastic structure of the individual time series involved. The focus here will be placed on first order non-stationary integrated processes, I(1), which require first differences to become weakly stationary. Thus, in order to test for the presence of stochastic non - stationarity in the data, the integration order of the individual time series is first investigated, using some well known unit root tests, such as the Augmented Dickey -Fuller (ADF) test (Dickey and Fuller, 1979, 1981), and the Ph illips and Perron (PP) non-parametric test (Perron, 1988; Phillips and Perron, 1988). These tests provide the appropriate tests statistics to determine whether a series contains a unit root, unit root plus a drift, and/or unit root plus drift plus a time t rend. The mo re general ADF test (including a d rift plus a time trend) is based on the following model: k Δyt = α + μ t + ρ yt-1 + i 1 ψi Δ yt-i + εt εt ~ i.i.d. (0, σ2 ) (1) which is estimated by ordinary least squares. The null hypothesis in the ADF test is a unit root, ρ=0. The normalized bias (T(ρ^ )), where T is the sample size, or the t-test for ρ=0 is computed. For yt to be stationary, ρ should be negative and significantly d ifferent fro m zero. Hypothesis tests concerning the coefficients of non-stationary variables cannot be conducted using traditional t-tests or F-tests. Under the null hypothesis of a unit root, the limit ing distributions of the test statistics are non -standard, since the empirical mo ments of unit processes generally converge to random variables instead of constants. Several assumptions concerning the determin istic components can also be tested using one-sided (F- type) tests (critical values in Fuller, 1976). The limit ing distribution crucially depends on the deterministic components of the univariate series. The optimal lag length for each of the autoreg ressive processes of the unit root tests is settled by the structure that minimizes various Information Criteria, such as the Akaike Informat ion Criterion (AIC) or the Shwarz Criterion (SC). Ph illips and Perron (1988) have modified the ADF test (based on Equation (1) without lagged differences), as the ADF tests are only valid under the crucial assumption of i.i.d. processes. In practice, it may be more realistic to allow for some dependence among the εt ’s. In that case, the asymptotic distribution changes. Phillips (1987), and Phillips and Perron (1988) have weakened the i.i.d. assumption by using a non -parametric correction to allo w for some serial correlation and heteroskedasticity: yt = α0 + a yt-1 + ut (2) Unit root tests can efficiently apply, in case the data generating process is quite general (Harris, 1995). The difference, then, between the two unit root tests (ADF vs. PP) lies in their treat ment of any ‘nuisance’ serial correlation. The PP test tends to be more robust to a wide range of serial correlations and time -dependent heteroskedasticity. In the PP test, the null hypothesis is that a series is non - stationary (i.e. difference stationary) if α = 1, hence, rejection of the unit root hypothesis is necessary to support stationarity. As with the ADF test, the PP test requests specifying whether to include a constant, a constant and a linear trend, or neither in the test regression. The asymptotic distribution of the PP t-statistic is the same as the ADF t-statistic. In the computation of these modified PP -statistics, the Newey and West (1987) non-negative long-run variance estimator is used and the truncation lag q needs to be specified, that is the number of periods of serial correlat ion to include. The asymptotic limit ing distribution is the same as that of the (τμ) tests tabulated by Fuller (1976). The sequential testing procedure proposed by Perron (1988) is to start from a quite general specification with both 6 trend and constant terms. The first hypothesis to be tested is that of a random walk (unit root) with drift against a trend stationary process. In case of non-rejection, the significance of the trend term is then tested and so on. The final hypothesis to be tested (provided all the previous less restrictive hypotheses have not been rejected) is the driftless random walk against the simple zero-mean stationary AR(1) process. The Johansen Procedure The implication that non-stationary variables can lead to spurious regressions, unless at least one cointegration vector is present, means that some form of testing for cointegration in the time series under study is mandatory. Recent empirical work departs fro m the earlier well known Engle -Granger (1987) framework towards incorporating the Johansen procedure (Johansen, 1988, 1991, 1992, 1995; Johansen and Juselius, 1990, 1992, 1994), in order to ease the consequences of the Engle-Granger approach, if mo re than one cointegration relationships exist. It is useful, consequently, to extend the single equation error-correct ion model (ECM ) to a mu ltivariate framework. A maximu m likelihood (ML) approach to mult ivariate autoregressive models is used for estimating and testing the number of cointegrating relationships and common stochastic trends among the components of a vector zt of non-stationary variables, incorporating different short- and long-run dynamics. The Johansen approach relies on the relat ionship between the rank of a matrix and its characteristic roots, provides more robust results when more than two variables are included, circu mvents the use of two - step estimators, has the advantage of taking into account the error structure of the underlying process, and provides relatively powerfu l tests when the model is correct ly specified. Defining a vector zt of n potentially endogenous variables, it is possible to specify the following data generating process (d.g.p.) and model zt as an unrestricted vector autoregression (VAR) involving up to k-lags of zt : zt = A1 zt-1 + A2 zt-2 + … + Ak zt-k + u t u t ~ IN (0, Σ) (3) 7 where zt is a (n x 1) matrix, and each of Ai is a (n x n) matrix of parameters. This type of VA R models has been advocated most notably by Sims (1980), as a way to estimate dynamic relationships among jointly endogenous variables without imposing strong a priori restrictions, such as particular structural relationships and / or the exogeneity of some of the variables (Harris, 1995). The system is in reduced form with each variable in zt regressed on only lagged values of both itself and all the other variables in the system. Equation (3) can be reformu lated into a vector error -correction (VECM ) form: Δzt = Γ1 Δzt-1 + Γ2 Δzt-2 + …+ Γk-1 Δzt-k+1 + Π zt-k + u t or k 1 Δzt = i 1 Γi Δzt-i + Π zt-k + u t (4) where Γi = -(I - A1 - … - Ai ), (i = 1,…, k -1), Γi are interim mu ltipliers, and Π = -(I - A1 - … - Ak). This way, the system contains information on both the short- and long-run adjustment to changes in zt , via the estimates of Γi ^ and Π^ respectively; the Π matrix, specifically, contains information on the long-run relationships. Granger’s representation theorem asserts that if the coefficient mat rix Π has reduced rank r < n, there exist (n x r) matrices α and β each with ran k r such that Π = α β´, and β´zt is stationary. It is assumed in fact that Π can be deco mposed into Π = α β´, where α and β can both be reduced in dimension to (n x r). The short-run structure of stock market integration involves two parts, α, and Γi . The matrix α defines the error correction (speed of) adjustment through which the system is pulled back to its long-run equilibriu m. The matrix ( Γi … Γk-1 ) defines the short-run adjustment to changes in the variables, while β is a matrix of long-run coefficients, such that the term β´zt-1 (embedded in Equation (4)), represents up to (n - 1) cointegration vectors in the multivariate model (wh ich ensure that the zt converge to their long-run steady state solutions). It has been recognized, however, that like in a standard VA R model, the indiv idual coefficients of the ECM are hard to interpret, and innovation accounting may be a better description of the short-run dynamic structure (e.g. Sims, 1980; Lutkephol and Reimers, 1992). 8 Assuming zt is a vector of non-stationary I(1) variables, then all the terms in (4) which involve Δzt-i are I(0), while Πzt-k must also be stationary for u t ~ I(0) to be ‘white noise’. There are three instances when this requirement, that Πzt-k ~ I(0), is met : (i) when all the variables in zt are in fact stationary, zt ~ I(0) (Π has full rank), wh ich imp lies that there is no problem of spurious regression and the appropriate modeling strategy is to estimate the standard Sims -type VA R in levels (i.e. Equation (3)); (ii) when there is no cointegration at all, imply ing that there are no linear comb inations of the zt that are I(0), and consequently Π is an (n x n) matrix of zeros (rank Π = 0, the matrix is null) - the appropriate model then is a VAR in first differences involving no long -run elements; (iii) when there exist up to (n - 1) cointegration relationships: β´zt-k ~ I(0). In this case, r < (n - 1) cointegration vectors exist in β (i.e. r columns of β form r linearly independent combinations of the variables in zt , each of which is stationary), together with (n - r) non-stationary vectors (i.e. (n – r) columns of β form I(1) common stochastic trends). Only the cointegration vectors in β enter (4), otherwise Πzt-k would not be I(0), which implies that the last (n - r) colu mns of α are insignificantly s mall (i.e. effect ively zero). Thus, the typical problem of determining how many r < (n - 1) cointegration vectors exist in β, is equivalent to testing which columns of α are zero. Testing, then, for cointegration amounts to consideration of the rank of Π, that is, finding the number of r linearly independent columns in Π (cointegrating vectors). The Johansen approach provides estimates of α and β using the ‘reduced rank regression’ procedure (Harris, 1995). The ML estimate of a basis of the cointegrating space is given by the empirical canonical variates of zt-k with respect to Δzt corrected for the short-run dynamics and possible deterministic co mponents. The number of significant canonical correlations gives the number of cointegrating relationships. Their significance can be tested by means of a sequence of likelihood ratio (LR) tests whose limit ing distribution is expressed in terms of vector Brownian motions (Johansen, 1988, 1991). Two test statistics can be used for the hypothesis of the existence of r cointegrating vectors. First, the so-called ‘trace test’, i.e. the LR test statistic for the hypothesis that there are at most r distinct cointegrating vectors against a general alternative, given by: n λtrace (r) = -2 log (Q) = -T i r 1 log (1 – λ^i ) 9 where i = r+1,…,n, are the (n - r) s mallest squared canonical correlations , r = 0, 1, 2,…, n - 1, and λtrace (r) = 0, when all λi = 0. Asymptotic critical values are provided by Osterwald -Lenu m (1992). Alternatively, the ‘maximum eigenvalue’ test can be used to compare the null hypothesis of r cointegrating vectors against the alternative of (r + 1) cointegrating vectors. The LR test statistic for this hypothesis is given by: λmax (r, r+1) = -2 log (Q) = -T log (1 - λ ^r+1) where r = 0, 1, 2,…, n - 1, and if the estimated value of the characteristic root is close to zero, λmax will be small. The limiting distribution of 2log(Q), which is a function of a (n - r) dimensional vector Bro wnian mot ion, is not independent of the unknown drift term. Critical values have been tabulated for various hypotheses concerning the behavior of the deterministic co mponents (Johansen and Juselius, 1990). The distributions of both the trace and the eigenvalue tests in the case without drift have broader tails than in the case with drift. Emp irical applications should therefore carefully investigate t he presence or absence of trends in the long run. To test for the presence of an intercept in the cointegrating vector as opposed to the unrestricted drift, a likelihood ratio test can be implemented. Asymptotically the statistic: n -T i r 1 [ log (1 - λi* ) – log (1 - λi) ] has a χ2 distribution with (n - r) degrees of freedom, and λi * and λi denote the ordered characteristic roots of the restricted and unrestricted Π matrix respectively. If the restriction is not binding, all values of log(1- λi *) and log(1-λ i) should be equivalent. As a result, small values of the test statistic imp ly that it is ad missible to include the intercept in the cointegrating vector. However, the presence of the intercept in the cointegrating vector increases the likelihood of finding a stationary linear comb ination of the n variables. Thus, a large value of λ* r+1 , implies that the restriction artificially inflates the number of cointegrating vectors (Enders, 1995). Once the number of co integrating relationships has been determined, it is possible to test particular hypotheses concerning α and β using standard χ2 distributed LR tests. 10 It should be noted that cointegrating vectors are obtained from the reduced form of a system where all of the variables are assumed to be jointly endogenous (Dickey et al., 1991). Thus, cointegrating vectors cannot be interpreted as representing structural equations. However, cointegrating vectors may be due to constraints that an economic structure imposes on the long -run relationship between the jointly endogenous variables 3. Empirical Results Contemporaneous Correlations Regressing non-stationary variables on each other can lead to potentially misleading inferences about the estimated parameters resulting to the problem of spurious regressions . Before testing for cointegration, therefore, the order of integration of stock prices must be determined. As a preliminary step, the CE stock prices were transformed into natural logs, their integrated properties were investigated and their graphical representations were inspected. Most of the CE stock markets (indices) under study appear to possess some deterministic trend co mponent or might even be characterized as trend-stationary processes (Figure 1). A range of descriptive statistics of the CE stock markets is analyzed (Table 1). The negative skewness apparent in some stock markets imp lies that the distribution of the series (around the mean) has a long left tail, whereas the relevant Jarque -Bera statistics indicate rejection of the normality hypothes is. Table 1: Stock Market Descripti ve Statistics S&P500 DAX WIG PX50 BUX SAX Mean 7.010 8.465 9.656 6.157 8.891 4.736 Median 7.018 8.518 9.646 6.167 8.917 4.709 Maximu m 7.331 8.995 10.038 6.538 9.256 5.341 Minimu m 6.603 7.698 9.257 5.756 8.236 4.251 Std. Deviat ion 0.186 0.287 0.139 0.148 0.167 0.299 Skewness -0.152 -0.330 0.218 -0.118 -0.781 0.347 Kurtosis 1.957 2.266 2.940 2.706 4.009 1.883 Jarque-Bera 95.913 70.812 14.125 10.363 252.024 125.833 Probability 0.0000 0.0000 0.0009 0.0056 0.00000 0.00000 Observations 1,747 1,747 1,747 1,747 1,747 1,747 The following indices correspond to the respective stock market: S&P500: US; DAX: Germany; WIG: Poland; PX50: Czech Republic; BUX: Hungary; SAX: Slovakia. 11 The contemporaneous correlations matrix of the four CE stock indices as well as the German and the US stock indices is also studied (Table 2). The stock indices of Poland, Hungary, and the Czech Republic indicate relat ively high and positive pairwise correlat ions (WIG / PX50: 0.82, WIG / BUX: 0.63, PX50 / BUX: 0.52), and the same holds for Germany and the US (S&P500 / DAX: 0.91). The SAX Index, however, shows high negative correlation with the mature markets (SAX / S&P500: -0.87, SAX / DAX: -0.78) and low correlation with most of the neighboring CE markets. Overall, the correlation coefficients appear rather low, indicating weak (short-term) contemporaneous interactions between these markets. These findings may be associated to the relatively short active life of the CE stock markets since their reopening (early 1990s), and the absence of substantial market depth, in terms of number of listed companies, capitalization and turnover. Table 2: Contemporaneous Correlations Matrix S&P500 DAX WIG PX50 BUX SAX S&P500 1.000 DAX 0.908 1.000 WIG 0.369 0.405 1.000 PX50 -0.002 0.010 0.818 1.000 BUX 0.331 0.318 0.629 0.521 1.000 SAX -0.874 -0.776 -0.096 0.210 -0.137 1.000 Unit Roots In order to test for the presence of stochastic non-stationarity in the data, the integration order of the individual time series is investigated using the ADF and PP tests for the presence of unit roots. The selection of optimal lags is determined by minimizing AIC, and is set at four lags for the ADF test and at seven lags for the PP test. Both the ADF and PP tests are considered with and without trend. The null hypothesis in each test is that each of the price series contains a unit root (i.e., testing the series as I(1) against I(0)); it should be rejected if the test s tatistics are less than the critical value. The results from the ADF and PP tests indicate that, for every stock price index series, the null hypothesis of a unit root is not rejected at the 5% significance level by both tests (Table 3). To verify that the order of integration is I(1), the presence of a unit root in the first difference of the stock price indices was also tested but no unit roots in first differenced series was found. 12 Table 3: Uni t Root Tests ADF Test PP Test Without With Without With Trend Trend Trend Trend S&P500 -2.153 -2.115 -2.216 -2.166 DAX -1.668 -2.004 -1.699 -2.030 WIG -2.280 -2.222 -2.390 -2.352 PX50 -1.877 -1.729 -1.696 -1.541 BUX -3.110 -3.155 -3.299 -3.316 SAX -1.059 -0.702 -1.022 -0.676 Critical values - without trend: -3.437 at the 1% level; -2.864 at the 5% level; -2.568 at the10% level. Critical values - with trend: -3.969 at the 1% level; -3.415 at the 5% level; -3.129 at the 10% level. MacKinnon (1991) critical values for rejection of hypothesis of a unit root. Cointegration Vectors As the null hypothesis of unit roots cannot be rejected, multivariate models can be built to enable investigation of the presence or absence of cointegrating relationships in the data set. Departing fro m the bivariate cointegration regressions in the Engle-Granger framewo rk, a vector error cointegration model (VECM ) such as in Equation (4) is estimated to consider the six series jo intly, according to the procedure advanced by Johansen (1989, 1991). The six stock markets are modeled as in Equation (4) and the order the stock indices are entered into the VAR model is based on their market capitalizat ion (all other orderings are also analyzed in supplementary models). The choice of optimal lags is given by consideration of minimizing the AIC and absence of autocorrelation in the VA R residuals; four lags for the levels of variables are included. Three alternative models are compared and contrasted: (a) a model with a constant restricted to the cointegrating space; (b) a model with unrestricted constant; and (c) a model with a linear trend in the cointegration vector. Table 4: Model S pecification Null Eigenvalues λtrace test critical values at 95% Model 1 Model 2 Model 3 Model 1 Model 2 Model 3 Model 1 Model 2 Model 3 r= 0 0.0242 0.0242 0.0243 105.42 104.13 117.10 102.14 94.15 114.90 r< 1 0.0133 0.0130 0.0148 62.81 61.53 74.23 76.07 68.52 87.31 r< 2 0.0120 0.0117 0.0118 39.41 38.76 48.28 53.12 47.21 62.99 r< 3 0.0055 0.0054 0.0064 18.33 18.17 27.59 34.91 29.68 42.44 r< 4 0.0046 0.0045 0.0049 8.86 8.72 16.49 19.96 15.41 25.32 r< 5 0.0005 0.0006 0.0045 0.82 0.81 7.88 9.24 3.76 12.25 H1(r) against H 1(n) Model 1: model with a constant restricted to the cointegrating space Model 2: model with unrestricted constant Model 3: model with a linear trend in the cointegration vector 13 Table 5: Tests for the Number of Cointegrating Vectors Null λmax test critical values at 95% n -r Model 1 Model 2 Model 3 Model 1 Model 2 Model 3 r= 0 42.61 42.60 42.87 40.30 39.37 43.97 r= 1 23.41 22.77 25.95 34.40 33.46 37.52 r= 2 21.08 20.59 20.68 28.14 27.07 31.46 r= 3 9.47 9.45 11.10 22.00 20.97 25.54 r= 4 8.04 7.90 8.61 15.67 14.07 18.96 r= 5 0.82 0.81 7.88 9.24 3.76 12.25 H 1(r) against H 1(r+1) Model 1: model with a constant restricted to the cointegrating space Model 2: model with unrestricted constant Model 3: model with a linear trend in the cointegration vector Critical values are obtained from Ostenwald-Lemum (1992). The results of the λmax and λtrace tests are reported in Tables 4, and 5 respectively. The empirical findings indicate the presence of one cointegrating vector in the markets under study, in all three versions of the model. The null hypothesis that the four CE stock markets, Germany, and the US are not cointegrated (r = 0) against the alternative of one or more cointegrating vectors (r > 0) is rejected, since the λmax(0) statistic exceeds the critical value at the 5% significance level. However, the λmax and λtrace statistics suggest no more than one cointegrating vector, since H0 of r < 1 is not rejected, as λ max(1) is less than the critical value at the 5% significance level. The normalized cointegration vector fro m the three versions of the model is included in Table 6. The relative magnitude of the coefficients of the cointegrating vector is informat ive on the respective role of the individual stock markets in the group. The results indicate positive long-run relationship for Germany, Czech Republic, and Slovakia and negative long-run linkages for Hungary and Poland. The comovements in these subgroups may be related to their extensive trade and financial linkages respectively. Stock price fluctuations in the mature markets, especially in the US, appear to have a significant impact on the emerging CE stock markets. 14 Table 6: Normalized Cointegrating Vector Model 1 S&P500 DAX WIG PX50 BUX SAX C TREND 1.000 0.939 -4.075 3.163 -0.102 0.817 1.953 - (0.828) (0.574) (0.058) (0.278) (0.383) (0.955) Model 2 S&P500 DAX WIG PX50 BUX SAX C TREND 1.000 0.936 -4.064 3.152 -0.098 0.815 1.907 - (0.823) (0.559) (0.045) (0.277) (0.381) Model 3 S&P500 DAX WIG PX50 BUX SAX C TREND 1.000 1.273 -4.800 3.861 -0.314 0.972 2.909 0.00008 (0.824) (0.623) (0.014) (0.504) (0.599) (0.0002) Model 1: model with a constant restricted to the cointegrating space Model 2: model with unrestricted constant Model 3: model with a linear trend in the cointegration vector Asymptotic standard errors in parentheses. The presence of one cointegrating vector implies that the stock indices of the six markets under study share a long-run equilibriu m. An important aspect of international financial globalization is that market prices are interrelated and price movements in one national stock market are expected to affect stock prices in other international markets, through efficient informat ion, easy accessibility and timely portfolio management. The CE (Poland, the Czech Republic, Hungary, Slovakia) s tock markets, as well as the German, and the US stock markets share a common stochastic trend with long -run movements of national stock prices. The presence of equilibriu m relationships could be attributed to the growing inflow of foreign portfolio investments in the CE markets and the common economic path of their economies. Both domestic and external forces affect the CE stock markets, leading to their long-run equilibriu m. This outcome, however, imp lies that investors with long holding periods, who diversify their portfolios across the CE stock markets, should expect only modest portfolio gains from such an investment allocation. Innovation Accounting Analysis The decomposition of forecast error variance of each market provides an alternative view of t he system dynamics and gives a quantitative measure of the interdependences among the CE, German, and US stock markets. Variance decomposition breaks down variation in an endogenous variable into the component shocks to the endogenous variables in the VA R model and gives information about the relative importance of each random innovation to the variables in the model. In other words, this 15 method indicates the magnitude of a movement in one market that can be explained by other markets, in terms of the percentage of the forecast error variance of that market. The variance decomposition results of 1-day, 5-day, 10-day, and 20-day horizon ahead forecast error variances of each stock index into fractions that are attributable to innovations in each of the six ma rkets under study, based on the estimated ECM, are summarized in Table 7. These findings provide further support to the presence of long-run stock market linkages. At a 20-day horizon, for instance, the proportion of domestic stock index variance that can be collectively attributable to the CE neighboring index innovations ranges fro m 1.03% for Slovakia, to 3.25%, 15.20%, and 21.57% for Poland, Hungary, and the Czech Republic, respectively. The proportion of domestic stock index variance that can be attribu table to the mature market innovations ranges from 0.84% for Slovakia, to 14.67%, 24.99%, and 25.81% for the Czech Republic, Hungary, and Poland, respectively. With the exception of Slovakia, a significant part of the international shocks to the CE markets , and to Germany as well, is attributable to the US stock market; this impact is stronger especially for Po land (21.74%), and Hungary (16.39%). Hence, statistical evidence indicates that stock movements in the US predo minantly (and in Germany, to a lesser extent) drive fluctuations in the Central European markets. The influential ro le of the US market is also depicted by the fact that no individual market can exp lain any significant part of the US error variance, a conclusion in line with previous studies (e.g. Ratanapakorn and Sharma, 2002). Overall, the emp irical findings suggest that both domestic and external forces affect CE markets, leading them to equilibriu m in the long-run. The individual CE stock markets appear relatively closer lin ked and more influenced by movements in the developed markets of the US and Germany rather than by their other CE neighbors in the group. The reaction of the CE markets to international shocks may be related to the fact that, according to recent estimates, foreign investors are involved in approximately 70% of trading in Budapest Stock Exchange, 30% in Warsaw Stock Exchange, and a lower percentage in Prague Stock Exchange (Hanousek and Filer, 2000). 16 Table 7: Decomposition of Index Innovations Stock Index Horizon Percentage of forecast error variance by innovations in: (days) S&P500 DAX WIG PX50 BUX SAX S&P500 1 100.000 0.000 0.000 0.000 0.000 0.000 5 99.431 0.371 0.033 0.014 0.058 0.093 10 99.356 0.390 0.020 0.032 0.069 0.133 20 99.279 0.380 0.023 0.074 0.069 0.174 DAX 1 29.002 70.998 0.000 0.000 0.000 0.000 5 47.528 52.306 0.035 0.030 0.027 0.075 10 49.347 50.482 0.021 0.022 0.021 0.108 20 50.260 49.532 0.032 0.012 0.016 0.148 WIG 1 3.350 2.449 94.201 0.000 0.000 0.000 5 17.323 2.913 78.542 0.925 0.289 0.009 10 19.246 3.390 75.379 1.630 0.339 0.016 20 21.741 4.070 70.938 2.841 0.347 0.062 PX50 1 3.617 5.764 5.037 85.582 0.000 0.000 5 9.952 5.569 7.481 76.530 0.410 0.057 10 10.232 5.421 11.693 71.995 0.625 0.034 20 9.792 4.866 20.679 63.772 0.844 0.048 BUX 1 3.844 9.453 9.293 4.346 73.064 0.000 5 15.464 8.693 8.089 5.940 61.689 0.126 10 16.222 8.735 8.324 6.127 60.455 0.137 20 16.387 8.603 9.229 5.851 59.809 0.121 SAX 1 0.100 0.034 0.246 0.018 0.054 99.549 5 0.683 0.013 0.180 0.046 0.056 99.021 10 0.803 0.011 0.318 0.094 0.064 98.708 20 0.823 0.018 0.733 0.219 0.079 98.128 Impulse responses trace out the responsiveness of the dependent variable in the VAR to shocks to each of the variables. For each variab le fro m each equation separately, a unit shock is applied to the error, and the persistence of the effects upon the VAR system over time is noted. Provided that the system is stable, the shock should gradually die away (Brooks, 2002). If the effect of a shock in one of the variables does not die out in the long-run (even if no further shocks occur), it shifts the system to a new equilibriu m, and it is called the permanent effect. If, on the other hand, the system returns to its previous equilibriu m value after some time, it is called the transitory effect. A fast adjustment to the previous equilibriu m indicates strong cointegration relationships in the long -run, as deviations from equilibriu m are short lived (Ratanapakorn and Sharma, 2002). Hence, the pattern of the impulse response of each CE stock market index to a shock in the US and German stock markets (which appear to be the most influential markets for the CE region) is examined, in order to obtain additional insight into the structure of the CE stock market linkages. For that, the impulse responses based on the simu lated responses of the estimated VAR system are produced. The plots of the time path of impulse responses of each stock index to one standard deviation shock of the US and German stock indices are inspected for a range of time horizons (not shown). The findings from the impulse response analysis indicate a rather slow response of the CE stock markets to a shock induced by the US or German markets, imp lying that the CE markets react in a rather stable pattern. The contemporaneous impact of shocks on the CE markets appears rather weak. The mature stock markets appear more integrated with each other, as deviations from equilibriu m are restored relat ively fast. 4. Conclusions This study investigates the short- and long-run linkages among stock indices of major transitional Central European markets, namely Po land, Czech Republic, Hungary, Slovakia, and developed markets, particu larly Germany, and the US. The emp irical findings enrich the thin body of the literature focusing on emerg ing economies and the CE markets in particu lar. As Central European states are on the way to join the European Union, the examination of possible long -run interdependencies and comovements of these markets with major international stock markets remains a crucial issue. An error correction vector autoregressive model is estimated to detect cointegration relationships, and the emp irical findings support the presence of one cointegration vector, indicating a stationary long -run relationship. Both domestic and external forces affect the CE stock markets, leading to their long -run equilibriu m. The CE markets tend to display stronger linkages with their mature counterparts, whereas the interdependencies between the individual CE markets and the other CE neighbors appear rather weak. These findings may be related to the relatively short active life of the CE stock markets since their reopening in the early 1990s, and the absence of substantial market depth, in terms of number of listed companies, capitalization and turnover. There is, on the other hand, growing inflow of foreign portfolio investments and international investors have increased trading activity in the CE stock markets. The Czech market, followed by Hungary, and Poland, exhib its the h ighest proportion of domestic stock index variance that can be collectively attributable to the CE neighboring index innovations. The Polish and Hungarian stock markets are more sensitive to shocks stemming fro m mature markets. The US market holds a leading role, as it can induce strong movements in the CE markets but is not influenced by them. The Slovakian stock market appears to exhibit a more autonomous behavior relative to its CE 18 peers. A rather slow response of the CE markets to a shock in the mature markets is indicated, and the contemporaneous impact of shocks on the CE markets appears rather weak. The US and German markets appear more integrated, as deviations from equilibriu m are restored relatively fast. The presence of cointegrating relationships , however, has important implications for portfolio management. Long-run comovements imp ly that the potential for diversify ing risk and attaining superior portfolio returns by investing in different CE markets is rather limited fo r international investors. To conclude, the Central European markets follow a co mmon path of development and become gradually more integrated with the international mature markets. 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Yang, J.J., Min, I., Li, Q., 2003. European stock market integration: Does EMU matter?. Journal of Business Finance and Accounting 30, forthcoming. 23 Figure 1: Central European, US, German Stock Indices 9.4 9.2 9.0 9.2 8.8 9.0 8.6 8.8 8.4 8.2 8.6 8.0 8.4 7.8 8.2 7.6 1/02/97 12/03/98 11/02/00 10/03/02 1/02/97 12/03/98 11/02/00 10/03/02 LB U X LD A X 6.6 5.4 5.2 6.4 5.0 6.2 4.8 6.0 4.6 5.8 4.4 5.6 4.2 1/02/97 12/03/98 11/02/00 10/03/02 1/02/97 12/03/98 11/02/00 10/03/02 LP X 50 LS A X 7.4 10.2 7.2 10.0 7.0 9.8 6.8 9.6 6.6 9.4 6.4 9.2 1/02/97 12/03/98 11/02/00 10/03/02 1/02/97 12/03/98 11/02/00 10/03/02 LS P 500 LW IG 24

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