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ACADEMY OF ECONOMIC STUDIES DOCTORAL SCHOOL OF FINANCE AND BANKING Causality in variance and volatility spillover effects between major European markets and East European countries MSc Student: Chiţu Irina Cristina Supervisor: Ph.D. Professor Moisă Altăr Bucharest 2008

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Introduction In this paper we examine the causality in variance and volatility spillovers between three developed equity markets (UK, France and Germany) and five selected East European equity markets (Poland, the Czech Republic, Hungary, Romania and Bulgaria) by applying the CCF testing procedure proposed by Cheung and Ng (1996) Cheung and Ng (1996) have implemented the cross-correlation testing procedure to study the causal relationships between the NIKKEI 225 and the S&P 500 stock price indices Inagaki (2007) studied the variance causality and spillovers between the British pound and the euro Wei et al. (1997) studied the variance causality and spillovers two developed markets (Japan and US) and four emerging markets in South China

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The Cross-Correlation Function (CCF) testing procedure and two stationary time series and two information sets is said to cause in variance if: where is the mean of conditioned on The concept of causality in the second moment can be viewed as a natural extension of the well-know Wiener-Granger causality in mean:,

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Suppose and are characterized by the following processes: where: - conditional mean ~ ARMA(m,n) - conditional variance ~ GARCH(p,q) Ifand are the squares of standardized innovations: then, the sample cross-correlation at lag k, will be: The Cross-Correlation Function (CCF) testing procedure where is the k-th lag sample cross covariance given by: k = 0, ±1, ±2,...,,,,

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Since both and are unobservable, their estimators will be used to test the hypothesis of no causality in variance Under the null hypothesis of no causality in variance, the sample cross-correlation is shown to have an asymptotic normal distribution Using Monte Carlo simulations, the two authors have also shown that the test is robust to non-normal errors The Cross-Correlation Function (CCF) testing procedure

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Tests for causality in variance (1) to test the causal relationship at a specific lag k, comparing with the standard normal distribution (2) a chi-square test: to test the hypothesis of no causality from lag j to lag k, comparing with a chi-square distribution with (k – j + 1) degrees of freedom,

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Data Indices from eight European equity markets for 2001-2008 period: Three major markets: London (FTSE 100), Frankfurt (DAX), Paris (CAC 40 ) Five selected East European markets: Warsaw (WIG 20), Prague (SP 50), Sofia (SOFIX), Budapest (BUX) and Bucharest (BET) Returns computed as log-differences: Augmented Dickey-Fuller test and the Phillips Perron test reject the null hypothesis of unit root Jarque-Bera statistic rejects the normality assumption for all returns series Kurtosis measure indicates that they exhibit clear signs of fat-tails Significant ARCH effects are confirmed by Ljung-Box test statistic

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First stage – estimating univariate models Conditional mean equation: Conditional variance equation: GARCH model EGARCH model where is assumed to follow a generalized error distribution (GED),,

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Finding the right model GARCH(1,1) AR(1) with GARCH(1,1) MA(1) with GARCH(1,1) ARMA(1,1) with GARCH(1,1) EGARCH(1,1) AR(1) with EGARCH(1,1) Tested models:

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Maximum-likelihood estimates of the selected models For each market, numbers in the first and second row are the estimated coefficients and p-values (in parentheses), respectively. D is the scale parameter for the GED

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Second stage – testing for causality in variance Chi-square test: to test the hypothesis of no causality from lag j to lag k we consider j =± 1 and k = ± 5 in order to examine whether there is any causal relationship for 5 lags jointly we consider k=0 in order to examine the contemporaneous relations t-test: to test the causal relationship at a specific lag k where k =1, 2, 3, 4, 5,

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Chi-square test statistics for the causality in variance test For each market, test statistic reported in the first row is for the null hypothesis of no causal relation from market A to B; test statistic reported in the second row is for the null hypothesis of no causal relation from market B to market A; test statistic reported in the third row is for the null hypothesis of no contemporaneous relation (i.e k=0) between two markets. (*) and (**) indicate significance at the 1% and 5% level respectively.

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t-statistics for the causality in variance test

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t-statistics for the causality in variance test (continuation)

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(*) and (**) indicate significance at the 1% and 5% level respectively.

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Remarks We find that contemporaneous relation across the studied countries is considerably higher for the group of developed markets compared to the selected East European markets This is hardly surprising as more developed financial markets are likely to share information more intensively, as they are, on average, more liquid and more diversified The absence of volatility spillover can also be regarded as evidence of rapid and efficient information transmission We find evidence of causality in variance from the developed markets to smaller markets (Romania and Bulgaria): For Bulgaria (SOFIX), we find evidence of causality at lag 1 from both France (CAC 40) and Czech Republic (SP 50) The volatilities of all three developed markets UK, France and Germany at lag 1 have a significant influence on the Romanian market Geographical proximity is also likely to be a factor in volatility spillovers as we find evidence of causality in variance from BET index to SOFIX index and vice-versa at different lags

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Conclusions Exponential GARCH (EGARCH) processes satisfactorily characterize the daily stock returns of the equity markets studied. For five of the markets studied significant asymmetric effects were observed, while for the two of the cases (Romania and Poland) the asymmetry coefficients were negative but not statistically significant at the 5% level Using the CCF testing procedure proposed by Cheung and Ng (1996) we bring new evidence on the causality in variance and volatility spillover effects across eight European markets Our results are useful to domestic and foreign portfolio managers that are considering in their portfolios equity from European markets Studies (see Thorp and Milunovich, 2006) have pointed out that accounting for volatility spillovers in mean-variance portfolio models results in small but significant improvements in portfolio efficiency, relative to benchmark

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References Akgiray, V., (1989). Conditional heteroskedasticity in time series of stock returns: Evidence and forecasts, Journal of Business 62, 55-80. Baele, L., (2003). Volatility spillover effects in European equity markets, Ghent University working paper, Ghent. Baillie, R.T. and T. Bollerslev, (1991). Intra-day and inter-market volatility in foreign exchange rates, Review of Economic Studies, 58, 565-585. Bollerslev, T., (1986). Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 31, 307-327. Cheung Y-W and L.K. Ng, (1996). A causality-in-variance test and its application to financial market prices, Journal of Econometrics, 72, 33-48. Engle, R.F. (1982), Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of U.K. Inflation, Econometrica, 50, 987-1008. Egert, B. and Koubaa, Y. (2004). Modelling Stock Returns in the G-7 and in Selected CEE Economies: A Non- linear GARCH Approach, William Davidson Institute Working Paper, 663 Granger, C.W. (1969). Investigating Causal Relations by Econometric Models and Cross-spectral Methods, Econometrica, 37, 424-438 Hong, Y., 2001. A test for volatility spillover with application to exchange rates. J. Econ. 103, 183–224. Inagaki, K. (2007). Testing for volatility spillover between the British pound and the euro, Research in International Business and Finance, 21, 161–174. Milunovich, G. and Thorp, S. (2006). Valuing volatility spillovers, Global Finance Journal, 17, 1–22. Martens, M., & Poon, S. -H. (2001). Returns synchronization and daily correlation dynamics between international stock markets, Journal of Banking and Finance, 25, 18051827. Nelson, D. (1991). Conditional heteroskedasticity in asset returns: A new approach, Econometrica, 59, 347370. Ross, S.A., 1989. Information and volatility: The no-arbitrage martingale approach to timing and resolution irrelevancy, Journal of Finance 44, 1-17. Wei-Shan Hu J., Chen, M-Y. and Fok, R, Bwo-Nung Huang b, (1997). Causality in volatility and volatility spillover effects between US, Japan and four equity markets in the South China Growth Triangular, Journal of International Financial Markets, Institutions and Money, 7, 35 l-367.

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Thank you!

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