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Towards a Measurement Scale for Contagion Effect on Capital Market

Towards a Measurement Scale for Contagion Effect on Capital Market In the context of the recent financial crisis still seems to be the current theory of a specific system in the shape of the economies of the "center" and "peripheral countries". Also transmission of the contagion effect goes from more developed countries ­ the center to the less developed countries constituting the periphery. Is it possible feedbacks? Financial risk management in these conditions seems to be much more difficult. The aim of this study is to assess the risks arising from the contagion effect. In the analysis, author seeks answers to the questions: How is the interplay between changes in capital market indices of countries in Central and Eastern Europe, and selected indices of developed countries? How the contagion effect changes in time: before-, during and after the crisis 2008-2009? The survey was conducted for selected indices of capital markets in the period January 1995 - October 2012. The final results of GARCH model showed that during the recent crisis on the primary capital markets, the role of information coming from peripheral CEE markets. An estimated contagion effect between countries is greater from Europe to the U.S.A. than vice versa. Keywords: risk management, contagion effect, market volatility, capital index JEL Classification: G1, G11, G10, M21 1. Introduction Although theories about the causes of the contagion effect, a number, but it should be noted that in practice it is very difficult to determine their relative importance, due to the limited availability of information on the transmission channels and the fact that a significant relationship transmission channels. Contagion effect as the transmission of the crisis to the economy, resulting in real and financial relations with other countries, it is particularly important in the case of portfolio management on an international scale. Doubts may raise the financial risk diversification. To diversify effectively reduced the risk of an analysis of the correlation coefficients between the rows of funds. Particularly important is the knowledge of the development of the correlation coefficients over time. Instability correlation coefficients significantly impede portfolio management and estimating the probabilities of obtaining specific rates of return on investment. Undoubtedly we encouraged to undertake this research stage of integration processes in the capital markets. The paper is organized as follows: Section 2 gives a brief overview about market volatility and contagion effect literature; Section 3 presents the using data and methodology; Section 4 provides results of GARCH model on volatility on selected capital markets and Section 5 provides conclusion. 2. Literature review The problem of the risk management in economic crisis is the subject of numerous studies (Allen, Franklin, Gale, 2000 et al.), (Brylius, 2010). But the study on analyzing the correlation coefficients between the assets rates of return engaged only same of researchers Koch and Koch (1991). He tested the correlation coefficients stability on assets in eight markets in different years - 1972, 1980 and 1987. It showed the interdependence of financial markets. Similar conclusions were reached also in study of King and Wadhwani (1990). Bertero and Mayer (1987) found that periods of turbulence in the financial markets are characterized by increasing correlation, which explains the dominance of global over local factors. This phenomenon causes that minimization of risk, based on the diversification of the portfolio may not produce the desired effect, because due to the higher correlation during the crisis, a decline in the value of A assets will decline in value of an asset B. The most common feature of daily returns for stock market indices is the phenomenon of grouping variances and lack of randomness of these changes. Therefore, the modeling of financial processes is commonly used ARCH econometric models (Autoregressive Conditional Heteroscedastic). They are tools that make it easy to answer the question concerning the relationship between the various financial processes (e.g., the values of indices, exchange rates, the price of stocks, bonds, interest rates). Today, ARCH model began to be extended in various ways. Thanks to the models of the capital market began to take into account the variability of risk over time. The world study on the relationship between the variances of rates of return on the stock markets with the Journal of Advanced Research in Management use of single-equation or multi-equation models led Susmel and Engle (1993), and Ramchand and Susmel (1998). In particular the study focused on the analysis of the mutual impact of exchange of individual instruments from different segments of the financial market such as the foreign exchange market, money, capital, or the underlying markets in different geographical areas, the study on the impact of major global stock markets for smaller ones. The results of empirical studies are not conclusive. For example, French, Schwert, and Stambaugh (1987) and Engle, Lilien and Robins (1987) show a positive relationship between the expected rate of return and the conditional variance. On the other hand Glosten, Jagannathan and Runkle (1993) argue a negative relationship between the expected rate of return and variance. Backus and Gregory (1993) noted that the relationship between the risk premium and the conditional variance is usually the nature of any. In the works: Baillie and Bollerslev (1990) and Domowitz and Hakkio (1985) showed that the relationship between the expected rate of return and the risk was not statistically significant. Conducted observations confirm that the daily changes in trading stock indices of developing countries in Europe exhibit similar properties as data from highly developed markets (Brzeszczynski, 2002, 15). 3. Data and methodology Review of the literature and previously conducted research led author to deepen the earlier application for the capital market vulnerability to shocks coming from outside, and the so-called "contagion effect". The study was attempted, according to estimates, which take place between market indices of selected capital markets. For the study were selected two indices of developing country markets in Europe: Polish WIG index and the Hungarian BUX. However, the group of developed countries has been selected: the German DAX, the UK FTSE100 and the U.S. S&P500. The sample covered the period January 1995 - October 2012. Model estimation of rate of return and volatility indices for selected countries was based on GARCH (1,1) model. This choice was preceded by an analysis of the information criteria - Akaike, Hannan-Quinn, Schwarz and Shibata (Maddala, 2006, pp. 209-210). Analysis of the rates of return on some indices and their squares indicated that the period January 1995 - October 2012 should be separated into three sub-periods: from 02.01.2003 till 29.10.2007 prosperity trend, from 30.10.2007 till 17.02.2009, the downward trend associated with the global financial crisis, from 18.02.2009 till 31.10.2012, the - again an upward trend and the end of the financial crisis. This division also resulted in a prior study of correlation coefficients stability between the indexes and index changes before and after the crisis of 2007-2008. Also, the selection of variables in the study (indices: WIG, BUX, DAX, S & P500, FTSE100) results from the correlation analysis. Table 1. The correlation coefficients between the WIG index and selected indices, indicating delays of 1-4 days Delays (in days) BUX (Hungary) PX (Czech R.) CAC30 (Italy) DAX (Germany) FTSE100 (Britain) IBEX (Spain) Hang Seng (Shanghai) ATG (Greece) NIKKEI225 (Japan) -4 0,0274 * 0,0453 *** 0,0271 * 0,0207 0,0323 ** 0,0292 ** -0,0292 0,0477 *** 0,0188 -3 0,0232 0,0018 -0,0262 -0,0086 -0,0289 -0,0159 -0,0002 0,0126 -0,0093 -2 0,0217 0,0360 ** -0,0221 -0,0124 -0,0229 -0,0243 0,0003 0,0246 * 0,008 -1 0,0793 *** 0,1042 *** -0,0007 0,0133 -0,0075 -0,0023 0,1267 *** 0,0898 *** 0,1923 *** 0 0,4909 *** 0,4682 *** 0,4330 *** 0,4301 *** 0,4262 *** 0,4060 *** 0,3772 *** 0,3565 *** 0,2665 *** S&P500 (USA) 0,019 0,0081 -0,017 0,2957 *** 0,2535 *** Source: Calculation based on Thomson Reuters data. *, **, ***; determination of the statistical significance respectively 10%, 5%, 1%. The results of correlation between the WIG index and the selected indexes including delays from 1 to 4 days (Table1.) showed that for countries located in different time zones, this factor has a significant impact on the level of correlation between indexes. The strongest correlation (positive) occurred between the indices WIG, BUX and PX (0.49, 0.46). As it appears this is not a result of the business relationship between the developed economies of Hungary, the Czech Republic and Poland, but strong dependence under international speculative capital flows in the same risk basket countries of Central and Eastern Europe. The correlation coefficient drops significantly if we use a delay of 1-4 days in the comparable data. Another group, which according to the Warsaw WIG shows, are: Italy (CAC30), Germany (DAX), United Kingdom (FTSE100) and Spain (IBEX). The size of the correlation coefficient indicates a significant positive correlation row (in the level of 0,40-0,43), which confirms the impact of economic factors (Germany is the largest trading partner of Poland) and structural (large share of foreign capital present in the Polish market are investors from London). Reduced impact on the Warsaw market shows Asian markets (Nikkei225 and Hang Seng), but also the Greek economy (ATG- index). The situation on most of the stock markets in the world is shaped by information flowing from overseas. The NY stock market is considered to be a price-creative factor for other markets. Therefore, it may seem surprising that the correlation coefficient between the WIG index and the S&P500 reached its lowest level of the respondents (0.25). As an explanation for this situation may indicate that trading in New York ends after market close in Warsaw, hence the price of shares on the Stock Exchange adapt to events on the NYSE until the next day. The final part of the session has been held in Warsaw during trading in New York, because some of the market information is already discounted the day before. Therefore it can be assumed that the impact of the New York market on the Warsaw spread out over two days, so the relationship is weaker at the same time (the stronger relationship in the day before (0.29). Fiszeder (2009) conducted survey for more selected group of indexes, describe the relationship between WIG indices, the S&P500, BUX, DAX and FTSE250. He has received convergent results. The study of correlation between the WIG index and the selected indices including delays provided information on the development of the correlation coefficients for the entire study sample period 2 January 1995 - 31 October 2012. However, we have not information of changes in the relationship between the indices over the time. When the correlation was weakest, and when the strongest? When it was associated with the transmission of shock events - the so-called contagion effect? Studies have shown that short-term increase in the correlation coefficients is associated with an increase in the conditional variance of at least one of the studied indices. These conclusions were reached in the work of Kelm (2001), Engle et al. (1990), Diebold and Nerlove (1989). The model also introduces a first-order autoregression for the dependent variable index(t-1) and the independent S&P500(t-1). This has been carried out on the basis of earlier Quenouille'a autocorrelation coefficient test. Autocorrelation function (ACF) and partial autocorrelation (PACF), autocorrelation test Ljung-Box (Q) returns processes of individual indices: WIG, BUX, DAX, S&P500, FTSE100, with a significance level of = 0.05, indicated the autocorrelation first order AR (1). Test results indicated the presence of ARCH effect in the sample for each of the five countries. Testing helped determine that the observed correlation at random components is non-apparent. The verification was based on Lagrange multiplier test statistics (Maddala, 2006, p 213): LM = TR2 R2 (3.1) where: T-number of observations, - coefficient of determination of the estimated equations for the auxiliary chisquare distribution with m degrees of freedom. Table 2 contains the Lagrange multiplier test statistics based on the regression equation of squared residuals for their delay to the tenth. Table 2. The values of the Lagrange multiplier test statistics WIG LM = TR2 762,806 BUX 486 DAX 690,806 FTSE100 490,138 S&P500 738,392 Source: Calculated in GRETL The output of hypotheses test about the impact of external shocks from other countries in the n-th country is following regression equation: yn= (3.2) Testing how much a country is vulnerable to external influence is based on the verification of the hypothesis: H0 : n1 = ...=: nn-1 = nn+1 = ... = n = 0 H1 : H0 Hypothesis (3.3) has been tested using the likelihood ratio statistics for GARCH and Schwarz Bayesian criterion. In the table 3-5 were estimated parameters of basic model (3.2) for selected index and was verified hypothesis (3.3). In any case, null hypothesis H0 was rejected (the lack of ARCH effect) in favor of alternative hypothesis of variable variance of the random component. For each of five cases the best model was GARCH (1,1). (3.3) Journal of Advanced Research in Management 4. Empirical results Model GARCH (1,1) estimates the Polish capital market vulnerable to shocks coming from Hungary, USA, Germany, Great Britain: RtWIG = 0 + 11Rt-1WIG + 21 RtBUX + 31Rt-1S&P500 + 41RtDAX + 51RtFTSE100 + t (4.1) D(0,htWIG), htWIG = 0 + (4.2) + RtWIG ­ daily logarithmic WIG rate of return, Rt-1WIG ­ 1-day lagged variable RtWIG RtBUX ­ daily logarithmic BUX rate of return, Rt-1S&P500 ­ 1-day lagged variable RtS&P500 RtDAX ­ daily logarithmic DAX rate of return, RtFTSE100 ­ daily logarithmic FTSE rate of return. Table 3. Estimates of GARCH (1,1) model parameters showing the shocks transmission from selected capital markets into Polish market Full sample: 2003/01/02-2012/10/31 (N = 2557), Std. dev. the dependent variable = 0.013, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 456.761 The mean equation The variance equation Const Coefficient p- value 0,0003 0,0458 Rt-1WIG 0,0320 0,0388 RtBUX 0,30327 <0,001 Rt-1S&P 0,0468 0,0045 RtDAX 0,13937 <0,001 RtFTSE 0,2204 <0,001 0 0,0000 0,0017 (WIGt-1)2 0,05864 <0,001 hWIGt-1 0,93162 <0,0001 Test A: 2003/01/02-2007/10/29 (N = 1258), Std. dev. dependent variable = 0.011, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 87.1291 Coefficient p- value 0,0006 0,00712 0,01637 0,45882 0,37134 <0,00001 0,03797 0,15232 0,07543 0,00223 0,15238 0,00009 0,00000 0,05276 0,03793 0,00001 0,95092 <0,00001 Test B: 2007/10/30-2009/02/17 (N = 341), Std. dev. dependent variable = 0.019, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 65.2059 Coefficient p- value -0,0016 0,66324 0,05033 0,07272 0,25676 <0,00001 0,05072 0,07782 0,29542 <0,00001 0,18968 0,001 0,00000 0,13908 0,07450 0,00031 0,91746 <0,00001 Test C: 2009/02/18-2012/10/31 (N = 958) Std. dev. dependent variable = 0.013, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 171.407 Coefficient p- value 0,00002 0,95188 0,00067 0,98408 0,17550 <0,00001 0,05112 0,09499 0,30168 <0,00001 0,16121 0,00077 0,00000 0,05799 0,08985 0,00086 0,86844 <0,00001 Similarly, to examine the vulnerability of other countries to shocks from the outside, the following parameters were estimated GARCH models. Below GARCH (1.1) model estimated the vulnerability of the Hungarian capital market shocks coming from Poland, USA, Germany, Great Britain: RtBUX = 0 + 11* Rt-1BUX + 21* RtWIG + 31* Rt-1S&P500 + 41* RtDAX + 51* RtFTSE100 + t D(0,htBUX), (4.3) htBUX = 0 + + (4.4) Table 4. Estimates of GARCH (1,1) model parameters showing the shocks transmission from selected capital markets into Hungarian market Full sample: 2003/01/02-2012/10/31 (N = 2557), Std. dev. the dependent variable = 0,017, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 466,579 The mean equation The variance equation Const Rt-1BUX RtWIG Rt-1S&P RtDAX RtFTSE 0 (BUXt-1)2 hBUXt-1 Coefficient p- value 0,0001 0,5835 0,0235 0,1617 0,50990 <0,0001 0,0637 0,0075 0,0987 0,0013 0,2149 <0,001 0,0000 0,0028 0,06608 <0,0001 0,90913 <0,0001 Test A: 2003/01/02-2007/10/29 (N = 1258), Std. dev. dependent variable = 0.012, The likelihood ratio test for the (G) ARCH: Chi-square (2) =24,4674 Coefficient p- value 0,00023 0,43517 0,04698 0,05209 0,48540 <0,00001 0,15880 0,00002 0,01648 0,64765 0,16771 0,00117 0,00000 0,13452 0,04191 0,00565 0,91259 <0,00001 Test B: 2007/10/30-2009/02/17 (N = 341), Std. dev. dependent variable = 0,025, The likelihood ratio test for the (G) ARCH: Chi-square (2) =127,541 Coefficient p- value 0,00070 0,27286 0,03714 0,37418 0,32659 <0,00001 0,10029 0,03492 0,23584 0,00902 0,20509 0,02127 0,00001 0,16161 0,17115 0,00382 0,82666 <0,00001 Test C: 2009/02/18-2012/10/31 (N = 958) Std. dev. dependent variable = 0,018, The likelihood ratio test for the (G) ARCH: Chi-square (2) =152,579 Coefficient p- value -0,00018 0,62888 -0,0130 0,64415 0,59483 <0,00001 -0,0123 0,75384 0,20656 0,00052 0,19446 0,00722 0,00001 0,0209 0,08457 0,00018 0,87558 <0,00001 Model GARCH (1,1) estimates the German capital market vulnerability to shocks coming from Poland, Hungary, USA, UK: RtDAX = 0 + 11* Rt-1DAX + 21* RtWIG + 31* RtBUX + 41* Rt-1 S&P500 + 51* RtFTSE100 + t D(0,htDAX), htDAX = 0 + + (4.5) (4.6) Table 5. Estimates of GARCH (1,1) model parameters showing the shocks transmission from selected capital markets into German market Full sample: 2003/01/02-2012/10/31 (N = 2557), Std. dev. the dependent variable = 0,015, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 851,478 Const Coefficient p- value 0,00027 0,02337 Rt-1DAX 0,01593 0,22318 The mean equation RtWIG Rt-1BUX 0,10329 <0,00001 0,05087 <0,00001 Rt-1S&P -0,02115 0,17137 RtFTSE 0,90564 <0,00001 0 The variance equation (DAXt-1)2 hDAXt-1 0,10000 <0,00001 0,88174 <0,00001 0,00000 0,0001 Test A: 2003/01/02-2007/10/29 (N = 1258), Std. dev. dependent variable = 0,012, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 510,971 Coefficient p- value 0,00030 0,05415 -0,02012 0,3182 0,06037 0,00123 0,02164 0,16649 0,04272 0,12934 0,96448 0,00000 0,05699 0,00004 0,92918 <0,00001 <0,00001 0,01231 Test B: 2007/10/30-2009/02/17 (N = 341), Std. dev. dependent variable = 0,022, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 141,786 Coefficient 7,84E-05 -0,016535 0,0911007 0,108932 0,000633 0,776155 1,03E-5 0,460475 0,504187 Journal of Advanced Research in Management Full sample: 2003/01/02-2012/10/31 (N = 2557), Std. dev. the dependent variable = 0,015, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 851,478 p- value 0,83357 0,60585 0,03771 <0,00001 0,98327 <0,00001 0,02019 0,00013 0,00001 Test C: 2009/02/18-2012/10/31 (N = 958) Std. dev. dependent variable =0,015, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 105,95 Coefficient p- value 0,000192 0,33751 0,0339286 0,1088 0,2151 <0,00001 0,049596 0,00129 -0,04263 0,0849 0,874305 1,29E-6 0,08515 0,0008 0,887199 <0,00001 <0,00001 0,04224 GARCH (1.1) model estimating the vulnerability of the U.S. capital markets to shocks coming from Poland, Hungary, Germany, Great Britain: RtS&P500 = 0 + 11* Rt-1S&P500 + 21* RtWIG + 31* RtBUX + 41* RtDAX + 51* RtFTSE100 + t D(0,htS&P500) htS&P500 = 0 + + Table 6. Estimates of GARCH (1,1) model parameters showing the shocks transmission from selected capital markets into USA market Full sample: 2003/01/02-2012/10/31 (N = 2557), Std. dev. the dependent variable = 0,013, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 1165,79 Const Coefficient p- value 0,000215 0,09739 Rt-1S&P -0,15540 <0,00001 The mean equation RtWIG RtBUX 0,0360385 0,02158 -0,00388 0,74957 RtDAX 0,33751 RtFTSE 0,193416 The variance equation 0 (S&Pt-1)2 hS&Pt-1 1,16E-6 0,0922896 <0,00001 0,892092 <0,00001 (4.7) (4.8) <0,00001 <0,00001 0,00004 Test A: 2003/01/02-2007/10/29 (N = 1258), Std. dev. dependent variable = 0,008 The likelihood ratio test for the (G) ARCH: Chi-square (2) = 84,1475 Coefficient p- value 0,000214 0,20247 -0,15592 <0,00001 0,04284 0,02526 -0,03726 0,021 0,295731 <0,00001 0,142987 0,00009 1,04E-6 0,02214 0,0518579 0,00002 0,922735 <0,00001 Test B: 2007/10/30-2009/02/17 (N = 341), Std. dev. dependent variable =0,024 The likelihood ratio test for the (G) ARCH: Chi-square (2) = 87,3623 Coefficient p- value -0,00099 0,13472 -0,31257 <0,00001 -0,00951 0,8757 0,150572 0,00408 0,611575 <0,00001 0,259491 0,75705 1,29E-5 0,05988 0,208349 0,00059 0,752676 <0,00001 Test C: 2009/02/18-2012/10/31 (N = 958) Std. dev. dependent variable = 0,013 The likelihood ratio test for the (G) ARCH: Chi-square (2) = 268,589 Coefficient p- value 0,00044 0,03535 -0,10700 0,00002 0,01232 0,68756 0,005199 0,79132 0,40113 0,222099 2,23E-6 0,120172 <0,00001 0,847908 <0,00001 <0,00001 <0,00001 0,00524 GARCH (1.1) model is estimating the vulnerability of the British capital market shocks coming from Poland, Hungary, USA, Germany: RtFTSE100 = 0 + 11* Rt-1FTSE100 + 21* RtWIG + 31* RtBUX + 41* Rt-1S&P500 + 51* RtDAX + t D(0,htFTSE100) htFTSE100 = 0 + + (4.9) (4.10) Table 7. Estimates of GARCH (1,1) model parameters showing the shocks transmission from selected capital markets into British market Full sample: 2003/01/02-2012/10/31 (N = 2557), Std. dev. the dependent variable = 0,012, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 827,704 const Coefficient p- value -0,0011 Rt-1FTSE -0,072 The mean equation RtWIG RtBUX 0,07278 <0,00001 0,0387936 <0,00001 Rt-1S&P 0,079895 <0,00001 RtDAX 0,5831 0 The variance equation (FTSEt-1)2 hFTSEt-1 0,101348 0,883171 <0,00001 6,45E-7 0,21156 <0,00001 <0,00001 0,00127 <0,00001 Test A: 2003/01/02-2007/10/29 (N = 1258), Std. dev. dependent variable = 0,008, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 379,593 Coefficient p- value -9,6E-5 0,40817 -0,07591 0,00008 0,059316 0,00001 0,0318283 0,00355 0,0914527 <0,00001 0,498302 7,69E-7 0,120791 0,00003 0,848395 <0,00001 <0,00001 0,00809 Test B: 2007/10/30-2009/02/17 (N = 341), Std. dev. dependent variable = 0,021, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 102,102 Coefficient p- value 0,00019 -0,10954 0,157898 <0,00001 0,04027 0,16759 0,101405 0,00002 0,742606 5,84E-6 0,327653 0,00161 0,643739 <0,00001 0,60624 <0,00001 <0,00001 0,05334 Test C: 2009/02/18-2012/10/31 (N = 958) Std. dev. dependent variable = 0,012, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 124,099 Coefficient p- value -5,7E-6 0,97284 -0,04959 0,01731 0,0632809 0,00302 0,0311115 0,02159 0,0525012 0,0102 0,632664 2,10E-6 0,120258 0,0004 0,819822 <0,00001 <0,00001 0,02027 Conclusion The results of model parameters estimated by GARCH (1,1) are presented in Tables 3-7. Verification of the hypothesis (3.3) for each of the capital markets in the study showed that the value of the likelihood ratio test statistic is high, which suggests that it is necessary to reject the null hypothesis stating that the capital markets: Poland, Hungary, Germany, Britain, the United States are not vulnerable to shocks coming from outside. At the begging Poland and Hungary (the capital markets of countries representing the developing countries of Europe) were subjected of the study. Based on the estimated parameters presented in Table 3 and 4 we can concluded that the Polish market is subject to the greatest influence of the Hungarian market, but the observations of individual research trials, before-during and after the crisis, suggest that this effect tends to decrease, however, it is a significant variable. The growing importance of the German capital market effects - before the crisis, this estimate was (0.075), while after the crisis (0.30). It confirms the trend observed in the market to greater interdependence of the Polish market to the Western Europe markets than in Central and Eastern Europe. During last crisis short-term capital flows also showed that investors distinguish the Polish capital market from the current group of developing countries in Europe. Impact of the U.S. market was a slight and significant, but only in times of crisis (at 10% significance level). The impact of shocks coming from London were stable at (0,15-0,18). The WIG lagged variable had no significant meaning to the value of the expected return rate. For comparison, it could observe a greater impact from the Polish to Hungarian market, so we can speak of infection between Warsaw and Budapest (see Table 4.). Table 4 shows the Hungarian market more susceptible to shocks coming from Poland, Britain and Germany. Influence from the U.S. market on the stock exchange in Budapest proved to be the most important in a time of crisis. In total, it can be concluded that the capital market in Hungary has been and continues to be more vulnerable to negative shocks coming from other markets. Interesting findings come from the study of the German market. The results presented in Table 5 show that the greatest impact on pricing has the London Stock Exchange (which is not surprising given the economic and capital ties of the country), but this effect was less during the crisis than outside. During the crisis the increased importance of influences is coming from the Hungarian and Polish markets (respectively 0.10 and 0.9). In the case of interactions between Warsaw - Frankfurt this trend is constant also for the period after the crisis (Table 5, the sample C). Estimation of Rt-1S&P variable turned out to be statistically insignificant in the pre- and during the Journal of Advanced Research in Management crisis, while the last attempt took negative values. This may suggest a lack of impact of negative shocks from the U.S. market on the German market. Looking at study of American market (S&P500) can be seen that during the crisis the stock exchange in New York had the greatest impact information from the German and British markets (see Table 6). It is also typical for developed countries, that significant influence on the rate of return was lagged variable Rt-1 S&P. The UK market was dominated by influences coming from the German stock market, especially in times of crisis. However, during crisis, the very important variable was WIG, compared with the S&P500 parameters were estimated - WIG (0.15), S&P500 (0.10) (see Table 7). Undoubtedly, this is a confirmation of the structure of the dominant investors in these markets and confirms earlier guesses that emerging markets are also a source of contagion. The study also showed that the estimated effect of contagion between countries is greater from Europe to the U.S. than vice versa. However it should take into consideration the impact of time zones, the European market opens at 8 hours in advance, so the information is received from Europe in the United States of late and have a greater impact on them. References [1] Backus D.K., A.W. Gregory. 1993. Theoretical Relations between Risk Premiums and Conditional Variances. Journal of Business & Economic Statistics. Vol. 11. No. 2 pp. 177-185. [2] Baillie R. T., Bollerslev T. 1990. A Multivariate Generalized ARCH Approach to Modeling Risk Premia in Foreign Exchange Markets. Journal of International Money and Finance. 9. 309-324. [3] Bertero E., Mayer C. 1987. Structure and Performance. Global Interdependence of Stock Markets around the Crash of October. European Economic Review. Vol. 34. [4] Brylius P. 2010. Economic crisis and SMEs sustainability policies: application of emotional well-being function for analysis. Journal of Advanced Research in Management. Vol I (1): 18-29. [5] Brzeszczyski J., Kelm R. 2002. 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Wadhwani. 1990. Transmission of Volatility between Stock Markets, Review of Financial Studies. Vol. 3. [13] Koch P. D., Koch T.W. 1991. Evolution in dynamic linkages across National Stock Indexes. Journal of International Money and Finance. Vol. 10. 2. 231­251. [14] Maddala G. S. 2008. Econometrics. Publisher PWN. Warsaw. [15] Ramchand L., Susmel R. 1998. Volatility and Cross Correlation cross Major Stock Markets. Journal of Empirical Finance. 5. 397-416. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Advanced Research in Management de Gruyter

Towards a Measurement Scale for Contagion Effect on Capital Market

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de Gruyter
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2068-7532
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10.2478/v10258-012-0009-3
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Abstract

In the context of the recent financial crisis still seems to be the current theory of a specific system in the shape of the economies of the "center" and "peripheral countries". Also transmission of the contagion effect goes from more developed countries ­ the center to the less developed countries constituting the periphery. Is it possible feedbacks? Financial risk management in these conditions seems to be much more difficult. The aim of this study is to assess the risks arising from the contagion effect. In the analysis, author seeks answers to the questions: How is the interplay between changes in capital market indices of countries in Central and Eastern Europe, and selected indices of developed countries? How the contagion effect changes in time: before-, during and after the crisis 2008-2009? The survey was conducted for selected indices of capital markets in the period January 1995 - October 2012. The final results of GARCH model showed that during the recent crisis on the primary capital markets, the role of information coming from peripheral CEE markets. An estimated contagion effect between countries is greater from Europe to the U.S.A. than vice versa. Keywords: risk management, contagion effect, market volatility, capital index JEL Classification: G1, G11, G10, M21 1. Introduction Although theories about the causes of the contagion effect, a number, but it should be noted that in practice it is very difficult to determine their relative importance, due to the limited availability of information on the transmission channels and the fact that a significant relationship transmission channels. Contagion effect as the transmission of the crisis to the economy, resulting in real and financial relations with other countries, it is particularly important in the case of portfolio management on an international scale. Doubts may raise the financial risk diversification. To diversify effectively reduced the risk of an analysis of the correlation coefficients between the rows of funds. Particularly important is the knowledge of the development of the correlation coefficients over time. Instability correlation coefficients significantly impede portfolio management and estimating the probabilities of obtaining specific rates of return on investment. Undoubtedly we encouraged to undertake this research stage of integration processes in the capital markets. The paper is organized as follows: Section 2 gives a brief overview about market volatility and contagion effect literature; Section 3 presents the using data and methodology; Section 4 provides results of GARCH model on volatility on selected capital markets and Section 5 provides conclusion. 2. Literature review The problem of the risk management in economic crisis is the subject of numerous studies (Allen, Franklin, Gale, 2000 et al.), (Brylius, 2010). But the study on analyzing the correlation coefficients between the assets rates of return engaged only same of researchers Koch and Koch (1991). He tested the correlation coefficients stability on assets in eight markets in different years - 1972, 1980 and 1987. It showed the interdependence of financial markets. Similar conclusions were reached also in study of King and Wadhwani (1990). Bertero and Mayer (1987) found that periods of turbulence in the financial markets are characterized by increasing correlation, which explains the dominance of global over local factors. This phenomenon causes that minimization of risk, based on the diversification of the portfolio may not produce the desired effect, because due to the higher correlation during the crisis, a decline in the value of A assets will decline in value of an asset B. The most common feature of daily returns for stock market indices is the phenomenon of grouping variances and lack of randomness of these changes. Therefore, the modeling of financial processes is commonly used ARCH econometric models (Autoregressive Conditional Heteroscedastic). They are tools that make it easy to answer the question concerning the relationship between the various financial processes (e.g., the values of indices, exchange rates, the price of stocks, bonds, interest rates). Today, ARCH model began to be extended in various ways. Thanks to the models of the capital market began to take into account the variability of risk over time. The world study on the relationship between the variances of rates of return on the stock markets with the Journal of Advanced Research in Management use of single-equation or multi-equation models led Susmel and Engle (1993), and Ramchand and Susmel (1998). In particular the study focused on the analysis of the mutual impact of exchange of individual instruments from different segments of the financial market such as the foreign exchange market, money, capital, or the underlying markets in different geographical areas, the study on the impact of major global stock markets for smaller ones. The results of empirical studies are not conclusive. For example, French, Schwert, and Stambaugh (1987) and Engle, Lilien and Robins (1987) show a positive relationship between the expected rate of return and the conditional variance. On the other hand Glosten, Jagannathan and Runkle (1993) argue a negative relationship between the expected rate of return and variance. Backus and Gregory (1993) noted that the relationship between the risk premium and the conditional variance is usually the nature of any. In the works: Baillie and Bollerslev (1990) and Domowitz and Hakkio (1985) showed that the relationship between the expected rate of return and the risk was not statistically significant. Conducted observations confirm that the daily changes in trading stock indices of developing countries in Europe exhibit similar properties as data from highly developed markets (Brzeszczynski, 2002, 15). 3. Data and methodology Review of the literature and previously conducted research led author to deepen the earlier application for the capital market vulnerability to shocks coming from outside, and the so-called "contagion effect". The study was attempted, according to estimates, which take place between market indices of selected capital markets. For the study were selected two indices of developing country markets in Europe: Polish WIG index and the Hungarian BUX. However, the group of developed countries has been selected: the German DAX, the UK FTSE100 and the U.S. S&P500. The sample covered the period January 1995 - October 2012. Model estimation of rate of return and volatility indices for selected countries was based on GARCH (1,1) model. This choice was preceded by an analysis of the information criteria - Akaike, Hannan-Quinn, Schwarz and Shibata (Maddala, 2006, pp. 209-210). Analysis of the rates of return on some indices and their squares indicated that the period January 1995 - October 2012 should be separated into three sub-periods: from 02.01.2003 till 29.10.2007 prosperity trend, from 30.10.2007 till 17.02.2009, the downward trend associated with the global financial crisis, from 18.02.2009 till 31.10.2012, the - again an upward trend and the end of the financial crisis. This division also resulted in a prior study of correlation coefficients stability between the indexes and index changes before and after the crisis of 2007-2008. Also, the selection of variables in the study (indices: WIG, BUX, DAX, S & P500, FTSE100) results from the correlation analysis. Table 1. The correlation coefficients between the WIG index and selected indices, indicating delays of 1-4 days Delays (in days) BUX (Hungary) PX (Czech R.) CAC30 (Italy) DAX (Germany) FTSE100 (Britain) IBEX (Spain) Hang Seng (Shanghai) ATG (Greece) NIKKEI225 (Japan) -4 0,0274 * 0,0453 *** 0,0271 * 0,0207 0,0323 ** 0,0292 ** -0,0292 0,0477 *** 0,0188 -3 0,0232 0,0018 -0,0262 -0,0086 -0,0289 -0,0159 -0,0002 0,0126 -0,0093 -2 0,0217 0,0360 ** -0,0221 -0,0124 -0,0229 -0,0243 0,0003 0,0246 * 0,008 -1 0,0793 *** 0,1042 *** -0,0007 0,0133 -0,0075 -0,0023 0,1267 *** 0,0898 *** 0,1923 *** 0 0,4909 *** 0,4682 *** 0,4330 *** 0,4301 *** 0,4262 *** 0,4060 *** 0,3772 *** 0,3565 *** 0,2665 *** S&P500 (USA) 0,019 0,0081 -0,017 0,2957 *** 0,2535 *** Source: Calculation based on Thomson Reuters data. *, **, ***; determination of the statistical significance respectively 10%, 5%, 1%. The results of correlation between the WIG index and the selected indexes including delays from 1 to 4 days (Table1.) showed that for countries located in different time zones, this factor has a significant impact on the level of correlation between indexes. The strongest correlation (positive) occurred between the indices WIG, BUX and PX (0.49, 0.46). As it appears this is not a result of the business relationship between the developed economies of Hungary, the Czech Republic and Poland, but strong dependence under international speculative capital flows in the same risk basket countries of Central and Eastern Europe. The correlation coefficient drops significantly if we use a delay of 1-4 days in the comparable data. Another group, which according to the Warsaw WIG shows, are: Italy (CAC30), Germany (DAX), United Kingdom (FTSE100) and Spain (IBEX). The size of the correlation coefficient indicates a significant positive correlation row (in the level of 0,40-0,43), which confirms the impact of economic factors (Germany is the largest trading partner of Poland) and structural (large share of foreign capital present in the Polish market are investors from London). Reduced impact on the Warsaw market shows Asian markets (Nikkei225 and Hang Seng), but also the Greek economy (ATG- index). The situation on most of the stock markets in the world is shaped by information flowing from overseas. The NY stock market is considered to be a price-creative factor for other markets. Therefore, it may seem surprising that the correlation coefficient between the WIG index and the S&P500 reached its lowest level of the respondents (0.25). As an explanation for this situation may indicate that trading in New York ends after market close in Warsaw, hence the price of shares on the Stock Exchange adapt to events on the NYSE until the next day. The final part of the session has been held in Warsaw during trading in New York, because some of the market information is already discounted the day before. Therefore it can be assumed that the impact of the New York market on the Warsaw spread out over two days, so the relationship is weaker at the same time (the stronger relationship in the day before (0.29). Fiszeder (2009) conducted survey for more selected group of indexes, describe the relationship between WIG indices, the S&P500, BUX, DAX and FTSE250. He has received convergent results. The study of correlation between the WIG index and the selected indices including delays provided information on the development of the correlation coefficients for the entire study sample period 2 January 1995 - 31 October 2012. However, we have not information of changes in the relationship between the indices over the time. When the correlation was weakest, and when the strongest? When it was associated with the transmission of shock events - the so-called contagion effect? Studies have shown that short-term increase in the correlation coefficients is associated with an increase in the conditional variance of at least one of the studied indices. These conclusions were reached in the work of Kelm (2001), Engle et al. (1990), Diebold and Nerlove (1989). The model also introduces a first-order autoregression for the dependent variable index(t-1) and the independent S&P500(t-1). This has been carried out on the basis of earlier Quenouille'a autocorrelation coefficient test. Autocorrelation function (ACF) and partial autocorrelation (PACF), autocorrelation test Ljung-Box (Q) returns processes of individual indices: WIG, BUX, DAX, S&P500, FTSE100, with a significance level of = 0.05, indicated the autocorrelation first order AR (1). Test results indicated the presence of ARCH effect in the sample for each of the five countries. Testing helped determine that the observed correlation at random components is non-apparent. The verification was based on Lagrange multiplier test statistics (Maddala, 2006, p 213): LM = TR2 R2 (3.1) where: T-number of observations, - coefficient of determination of the estimated equations for the auxiliary chisquare distribution with m degrees of freedom. Table 2 contains the Lagrange multiplier test statistics based on the regression equation of squared residuals for their delay to the tenth. Table 2. The values of the Lagrange multiplier test statistics WIG LM = TR2 762,806 BUX 486 DAX 690,806 FTSE100 490,138 S&P500 738,392 Source: Calculated in GRETL The output of hypotheses test about the impact of external shocks from other countries in the n-th country is following regression equation: yn= (3.2) Testing how much a country is vulnerable to external influence is based on the verification of the hypothesis: H0 : n1 = ...=: nn-1 = nn+1 = ... = n = 0 H1 : H0 Hypothesis (3.3) has been tested using the likelihood ratio statistics for GARCH and Schwarz Bayesian criterion. In the table 3-5 were estimated parameters of basic model (3.2) for selected index and was verified hypothesis (3.3). In any case, null hypothesis H0 was rejected (the lack of ARCH effect) in favor of alternative hypothesis of variable variance of the random component. For each of five cases the best model was GARCH (1,1). (3.3) Journal of Advanced Research in Management 4. Empirical results Model GARCH (1,1) estimates the Polish capital market vulnerable to shocks coming from Hungary, USA, Germany, Great Britain: RtWIG = 0 + 11Rt-1WIG + 21 RtBUX + 31Rt-1S&P500 + 41RtDAX + 51RtFTSE100 + t (4.1) D(0,htWIG), htWIG = 0 + (4.2) + RtWIG ­ daily logarithmic WIG rate of return, Rt-1WIG ­ 1-day lagged variable RtWIG RtBUX ­ daily logarithmic BUX rate of return, Rt-1S&P500 ­ 1-day lagged variable RtS&P500 RtDAX ­ daily logarithmic DAX rate of return, RtFTSE100 ­ daily logarithmic FTSE rate of return. Table 3. Estimates of GARCH (1,1) model parameters showing the shocks transmission from selected capital markets into Polish market Full sample: 2003/01/02-2012/10/31 (N = 2557), Std. dev. the dependent variable = 0.013, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 456.761 The mean equation The variance equation Const Coefficient p- value 0,0003 0,0458 Rt-1WIG 0,0320 0,0388 RtBUX 0,30327 <0,001 Rt-1S&P 0,0468 0,0045 RtDAX 0,13937 <0,001 RtFTSE 0,2204 <0,001 0 0,0000 0,0017 (WIGt-1)2 0,05864 <0,001 hWIGt-1 0,93162 <0,0001 Test A: 2003/01/02-2007/10/29 (N = 1258), Std. dev. dependent variable = 0.011, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 87.1291 Coefficient p- value 0,0006 0,00712 0,01637 0,45882 0,37134 <0,00001 0,03797 0,15232 0,07543 0,00223 0,15238 0,00009 0,00000 0,05276 0,03793 0,00001 0,95092 <0,00001 Test B: 2007/10/30-2009/02/17 (N = 341), Std. dev. dependent variable = 0.019, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 65.2059 Coefficient p- value -0,0016 0,66324 0,05033 0,07272 0,25676 <0,00001 0,05072 0,07782 0,29542 <0,00001 0,18968 0,001 0,00000 0,13908 0,07450 0,00031 0,91746 <0,00001 Test C: 2009/02/18-2012/10/31 (N = 958) Std. dev. dependent variable = 0.013, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 171.407 Coefficient p- value 0,00002 0,95188 0,00067 0,98408 0,17550 <0,00001 0,05112 0,09499 0,30168 <0,00001 0,16121 0,00077 0,00000 0,05799 0,08985 0,00086 0,86844 <0,00001 Similarly, to examine the vulnerability of other countries to shocks from the outside, the following parameters were estimated GARCH models. Below GARCH (1.1) model estimated the vulnerability of the Hungarian capital market shocks coming from Poland, USA, Germany, Great Britain: RtBUX = 0 + 11* Rt-1BUX + 21* RtWIG + 31* Rt-1S&P500 + 41* RtDAX + 51* RtFTSE100 + t D(0,htBUX), (4.3) htBUX = 0 + + (4.4) Table 4. Estimates of GARCH (1,1) model parameters showing the shocks transmission from selected capital markets into Hungarian market Full sample: 2003/01/02-2012/10/31 (N = 2557), Std. dev. the dependent variable = 0,017, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 466,579 The mean equation The variance equation Const Rt-1BUX RtWIG Rt-1S&P RtDAX RtFTSE 0 (BUXt-1)2 hBUXt-1 Coefficient p- value 0,0001 0,5835 0,0235 0,1617 0,50990 <0,0001 0,0637 0,0075 0,0987 0,0013 0,2149 <0,001 0,0000 0,0028 0,06608 <0,0001 0,90913 <0,0001 Test A: 2003/01/02-2007/10/29 (N = 1258), Std. dev. dependent variable = 0.012, The likelihood ratio test for the (G) ARCH: Chi-square (2) =24,4674 Coefficient p- value 0,00023 0,43517 0,04698 0,05209 0,48540 <0,00001 0,15880 0,00002 0,01648 0,64765 0,16771 0,00117 0,00000 0,13452 0,04191 0,00565 0,91259 <0,00001 Test B: 2007/10/30-2009/02/17 (N = 341), Std. dev. dependent variable = 0,025, The likelihood ratio test for the (G) ARCH: Chi-square (2) =127,541 Coefficient p- value 0,00070 0,27286 0,03714 0,37418 0,32659 <0,00001 0,10029 0,03492 0,23584 0,00902 0,20509 0,02127 0,00001 0,16161 0,17115 0,00382 0,82666 <0,00001 Test C: 2009/02/18-2012/10/31 (N = 958) Std. dev. dependent variable = 0,018, The likelihood ratio test for the (G) ARCH: Chi-square (2) =152,579 Coefficient p- value -0,00018 0,62888 -0,0130 0,64415 0,59483 <0,00001 -0,0123 0,75384 0,20656 0,00052 0,19446 0,00722 0,00001 0,0209 0,08457 0,00018 0,87558 <0,00001 Model GARCH (1,1) estimates the German capital market vulnerability to shocks coming from Poland, Hungary, USA, UK: RtDAX = 0 + 11* Rt-1DAX + 21* RtWIG + 31* RtBUX + 41* Rt-1 S&P500 + 51* RtFTSE100 + t D(0,htDAX), htDAX = 0 + + (4.5) (4.6) Table 5. Estimates of GARCH (1,1) model parameters showing the shocks transmission from selected capital markets into German market Full sample: 2003/01/02-2012/10/31 (N = 2557), Std. dev. the dependent variable = 0,015, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 851,478 Const Coefficient p- value 0,00027 0,02337 Rt-1DAX 0,01593 0,22318 The mean equation RtWIG Rt-1BUX 0,10329 <0,00001 0,05087 <0,00001 Rt-1S&P -0,02115 0,17137 RtFTSE 0,90564 <0,00001 0 The variance equation (DAXt-1)2 hDAXt-1 0,10000 <0,00001 0,88174 <0,00001 0,00000 0,0001 Test A: 2003/01/02-2007/10/29 (N = 1258), Std. dev. dependent variable = 0,012, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 510,971 Coefficient p- value 0,00030 0,05415 -0,02012 0,3182 0,06037 0,00123 0,02164 0,16649 0,04272 0,12934 0,96448 0,00000 0,05699 0,00004 0,92918 <0,00001 <0,00001 0,01231 Test B: 2007/10/30-2009/02/17 (N = 341), Std. dev. dependent variable = 0,022, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 141,786 Coefficient 7,84E-05 -0,016535 0,0911007 0,108932 0,000633 0,776155 1,03E-5 0,460475 0,504187 Journal of Advanced Research in Management Full sample: 2003/01/02-2012/10/31 (N = 2557), Std. dev. the dependent variable = 0,015, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 851,478 p- value 0,83357 0,60585 0,03771 <0,00001 0,98327 <0,00001 0,02019 0,00013 0,00001 Test C: 2009/02/18-2012/10/31 (N = 958) Std. dev. dependent variable =0,015, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 105,95 Coefficient p- value 0,000192 0,33751 0,0339286 0,1088 0,2151 <0,00001 0,049596 0,00129 -0,04263 0,0849 0,874305 1,29E-6 0,08515 0,0008 0,887199 <0,00001 <0,00001 0,04224 GARCH (1.1) model estimating the vulnerability of the U.S. capital markets to shocks coming from Poland, Hungary, Germany, Great Britain: RtS&P500 = 0 + 11* Rt-1S&P500 + 21* RtWIG + 31* RtBUX + 41* RtDAX + 51* RtFTSE100 + t D(0,htS&P500) htS&P500 = 0 + + Table 6. Estimates of GARCH (1,1) model parameters showing the shocks transmission from selected capital markets into USA market Full sample: 2003/01/02-2012/10/31 (N = 2557), Std. dev. the dependent variable = 0,013, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 1165,79 Const Coefficient p- value 0,000215 0,09739 Rt-1S&P -0,15540 <0,00001 The mean equation RtWIG RtBUX 0,0360385 0,02158 -0,00388 0,74957 RtDAX 0,33751 RtFTSE 0,193416 The variance equation 0 (S&Pt-1)2 hS&Pt-1 1,16E-6 0,0922896 <0,00001 0,892092 <0,00001 (4.7) (4.8) <0,00001 <0,00001 0,00004 Test A: 2003/01/02-2007/10/29 (N = 1258), Std. dev. dependent variable = 0,008 The likelihood ratio test for the (G) ARCH: Chi-square (2) = 84,1475 Coefficient p- value 0,000214 0,20247 -0,15592 <0,00001 0,04284 0,02526 -0,03726 0,021 0,295731 <0,00001 0,142987 0,00009 1,04E-6 0,02214 0,0518579 0,00002 0,922735 <0,00001 Test B: 2007/10/30-2009/02/17 (N = 341), Std. dev. dependent variable =0,024 The likelihood ratio test for the (G) ARCH: Chi-square (2) = 87,3623 Coefficient p- value -0,00099 0,13472 -0,31257 <0,00001 -0,00951 0,8757 0,150572 0,00408 0,611575 <0,00001 0,259491 0,75705 1,29E-5 0,05988 0,208349 0,00059 0,752676 <0,00001 Test C: 2009/02/18-2012/10/31 (N = 958) Std. dev. dependent variable = 0,013 The likelihood ratio test for the (G) ARCH: Chi-square (2) = 268,589 Coefficient p- value 0,00044 0,03535 -0,10700 0,00002 0,01232 0,68756 0,005199 0,79132 0,40113 0,222099 2,23E-6 0,120172 <0,00001 0,847908 <0,00001 <0,00001 <0,00001 0,00524 GARCH (1.1) model is estimating the vulnerability of the British capital market shocks coming from Poland, Hungary, USA, Germany: RtFTSE100 = 0 + 11* Rt-1FTSE100 + 21* RtWIG + 31* RtBUX + 41* Rt-1S&P500 + 51* RtDAX + t D(0,htFTSE100) htFTSE100 = 0 + + (4.9) (4.10) Table 7. Estimates of GARCH (1,1) model parameters showing the shocks transmission from selected capital markets into British market Full sample: 2003/01/02-2012/10/31 (N = 2557), Std. dev. the dependent variable = 0,012, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 827,704 const Coefficient p- value -0,0011 Rt-1FTSE -0,072 The mean equation RtWIG RtBUX 0,07278 <0,00001 0,0387936 <0,00001 Rt-1S&P 0,079895 <0,00001 RtDAX 0,5831 0 The variance equation (FTSEt-1)2 hFTSEt-1 0,101348 0,883171 <0,00001 6,45E-7 0,21156 <0,00001 <0,00001 0,00127 <0,00001 Test A: 2003/01/02-2007/10/29 (N = 1258), Std. dev. dependent variable = 0,008, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 379,593 Coefficient p- value -9,6E-5 0,40817 -0,07591 0,00008 0,059316 0,00001 0,0318283 0,00355 0,0914527 <0,00001 0,498302 7,69E-7 0,120791 0,00003 0,848395 <0,00001 <0,00001 0,00809 Test B: 2007/10/30-2009/02/17 (N = 341), Std. dev. dependent variable = 0,021, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 102,102 Coefficient p- value 0,00019 -0,10954 0,157898 <0,00001 0,04027 0,16759 0,101405 0,00002 0,742606 5,84E-6 0,327653 0,00161 0,643739 <0,00001 0,60624 <0,00001 <0,00001 0,05334 Test C: 2009/02/18-2012/10/31 (N = 958) Std. dev. dependent variable = 0,012, The likelihood ratio test for the (G) ARCH: Chi-square (2) = 124,099 Coefficient p- value -5,7E-6 0,97284 -0,04959 0,01731 0,0632809 0,00302 0,0311115 0,02159 0,0525012 0,0102 0,632664 2,10E-6 0,120258 0,0004 0,819822 <0,00001 <0,00001 0,02027 Conclusion The results of model parameters estimated by GARCH (1,1) are presented in Tables 3-7. Verification of the hypothesis (3.3) for each of the capital markets in the study showed that the value of the likelihood ratio test statistic is high, which suggests that it is necessary to reject the null hypothesis stating that the capital markets: Poland, Hungary, Germany, Britain, the United States are not vulnerable to shocks coming from outside. At the begging Poland and Hungary (the capital markets of countries representing the developing countries of Europe) were subjected of the study. Based on the estimated parameters presented in Table 3 and 4 we can concluded that the Polish market is subject to the greatest influence of the Hungarian market, but the observations of individual research trials, before-during and after the crisis, suggest that this effect tends to decrease, however, it is a significant variable. The growing importance of the German capital market effects - before the crisis, this estimate was (0.075), while after the crisis (0.30). It confirms the trend observed in the market to greater interdependence of the Polish market to the Western Europe markets than in Central and Eastern Europe. During last crisis short-term capital flows also showed that investors distinguish the Polish capital market from the current group of developing countries in Europe. Impact of the U.S. market was a slight and significant, but only in times of crisis (at 10% significance level). The impact of shocks coming from London were stable at (0,15-0,18). The WIG lagged variable had no significant meaning to the value of the expected return rate. For comparison, it could observe a greater impact from the Polish to Hungarian market, so we can speak of infection between Warsaw and Budapest (see Table 4.). Table 4 shows the Hungarian market more susceptible to shocks coming from Poland, Britain and Germany. Influence from the U.S. market on the stock exchange in Budapest proved to be the most important in a time of crisis. In total, it can be concluded that the capital market in Hungary has been and continues to be more vulnerable to negative shocks coming from other markets. Interesting findings come from the study of the German market. The results presented in Table 5 show that the greatest impact on pricing has the London Stock Exchange (which is not surprising given the economic and capital ties of the country), but this effect was less during the crisis than outside. During the crisis the increased importance of influences is coming from the Hungarian and Polish markets (respectively 0.10 and 0.9). In the case of interactions between Warsaw - Frankfurt this trend is constant also for the period after the crisis (Table 5, the sample C). Estimation of Rt-1S&P variable turned out to be statistically insignificant in the pre- and during the Journal of Advanced Research in Management crisis, while the last attempt took negative values. This may suggest a lack of impact of negative shocks from the U.S. market on the German market. Looking at study of American market (S&P500) can be seen that during the crisis the stock exchange in New York had the greatest impact information from the German and British markets (see Table 6). It is also typical for developed countries, that significant influence on the rate of return was lagged variable Rt-1 S&P. The UK market was dominated by influences coming from the German stock market, especially in times of crisis. However, during crisis, the very important variable was WIG, compared with the S&P500 parameters were estimated - WIG (0.15), S&P500 (0.10) (see Table 7). Undoubtedly, this is a confirmation of the structure of the dominant investors in these markets and confirms earlier guesses that emerging markets are also a source of contagion. The study also showed that the estimated effect of contagion between countries is greater from Europe to the U.S. than vice versa. 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Econometric models of financial markets. WIG-Press. Warsaw. [6] Domowitz I., Hakkio C. S. 1985. Conditional variance and the risk premium in the foreign exchange market. Journal of International Economics. Elsevier, vol. 19(1-2), pp. 47-66. [7] Engle R., Susmel R. 1993. Common Volatility in International Equity Markets, Journal of Business & Economic Statistic. Vol. 11. 167-176. [8] Engle R.F., D. M. Lilien, R.P. Robins. 1987. Estimating time varying risk premia in the term structure. The ARCH-M Model, Econometrica. vol. 55. 391-407. [9] Franklin A., Gale D. 2000. Financial contagion. The Journal of Political Economy 108, no. 1: 1-33. [10] French K. R., Schwert G. W., Stambaugh R. 1987. Expected Stock Return and Volatility. Journal of Financial Economics. 19. pp. 3-29. [11] Glosten L. R., Jagannathan R., Runkle D. E. 1993. On the Relation Between the Expected Value and the Volatility of the Nominal Excess Return on Stocks. Journal of Finance. 48. 1779-1801. [12] King M., and S. 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Journal of Advanced Research in Managementde Gruyter

Published: Dec 1, 2012

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