Spillover effect: A study for major capital markets and Romanian capital market MSc Student: Cristina Belciuganu Coordinator Professor: Moisa Altar July 2008

Spillover Effect Study 12 July Topics Introduction Methodologies used and results Conclusion References-Annex

Spillover Effect Study 12 July Topics Introduction Methodologies used and results Conclusion References

Spillover Effect Study 12 July Introduction The scope of paper was to study how different capital markets are influencing each other The study is focused on the US market, major European countries and Romania, using the following indexes: – S&P 500, NASDAQ 100 and DJ INDUSTRIALS (US) – CAC 40, FTSE100 and DAX30 (Europe) – BET, Romanian index The period selected for the study was September 1997 – May 2008

Spillover Effect Study 12 July Introduction Instead of considering the risk in term of volatility to risk we reflected in term of extreme losses with low probability of being exceeded This means tail risk and we approach it through 1 day, 95% and 99% Value at Risk measure Our objective is to determine whether this kind of risk, presents spillover effects across the markets. Spillover effects being the influence of one market on others, is examined using the Granger causality, for daily changes of the VaR series

Spillover Effect Study 12 July Topics Introduction Methodologies used and results Conclusion References-Annex

Spillover Effect Study 12 July A five step process flow Moving average EWMA GARCH Daily log returns VolatilitySpilloverVaRBacktesting Historical Simulation Delta- Normal Extreme Value Theory Kupiec Test Unit Root Tests Granger Causality

Spillover Effect Study 12 July Standard deviations methods Moving average – Each day the forecast is updated by adding information from the preceding day and dropping information from (M+1) – We have calculated the moving average using a moving window of 10, 20 and 60 days

Spillover Effect Study 12 July Standard deviations methods EWMA – In order to capture the dynamic features of volatility it is use an exponential moving average of historical observations, where the latest observations carry the highest weight in volatility estimate – EWMA depends on the parameter- which is often referred to decay factor. This parameter determines the relative weight of past observations. – We have used a decay factor of 0.94

Spillover Effect Study 12 July Standard deviations methods - GARCH A general GARCH (p,q) model is given by Bollerslev, 1986, and the equations specified for this model are: – The conditional mean y (t/t-1) it is take as constant – Conditional variance equation – We have used Garch (1,1) with Normal and t distribution

Spillover Effect Study 12 July Value at Risk Methods Historical Simulation uses real historical data to build an empirical density for the portfolio P&L – It is the percentile of the empirical distribution corresponding to the confidence level of these distributions – We used two size of past observations of 100 and 250 days Delta-Normal is a parametric method based on the assumption that the return are normally distributed. – VaR is defined as Where Z is the alpha percentile of the standard normal density

Spillover Effect Study 12 July Value at Risk Methods EVT – used to model fat tails. In order to determine VaR the next steps have to be considered: – The standardized portfolio returns are given from the following formula – It is choose a threshold “u” to represent the 95th, 99th percentile – Let y = x + u. when x = z when z exceeds u; – The is estimated by the Hill estimator as defined bellow. When the tail parameter is positive then the return distributions is fat tailed – The VaR from the EVT combined with the variance model is calculated as

Spillover Effect Study 12 July Xi > 0 demonstrates the fat tail of series S&PDJINDUSNASDAQDAXFTSECACBET S&PDJINDUSNASDAQDAXFTSECACBET

Spillover Effect Study 12 July Backtesting VaR models must be accompanied by a validation. When the model is perfectly calibrated the number of observations falling outside VAR should be in line with the confidence level Kupiec (1995) develops approximate 95 percent confidence regions for such a test.. These regions are defined by the tail points of the log-likelihood ratio: The LR is asymptotically distributed chi-square with one degree of freedom under the null hypothesis that is the probability. It is reject the null hypothesis if LR> 3.84 (critical value)

Spillover Effect Study 12 July Backtesting results – 1 day 95% VaR 95% IndexMethodLR-UCAverage VaR BET Delta Normal HS (100) Delta Normal MA (10) Delta Normal MA (20) EVT MA(10) EVT MA(20) EVT MA(60) Delta Normal Garch CAC Delta Normal MA (10) Delta Normal MA (20) EVT MA(10) EVT MA(20) Delta Normal Garch DAX Delta Normal MA (10) Delta Normal MA (20) EVT MA(10) EVT MA(20) Delta Normal Garch

Spillover Effect Study 12 July Backtesting results – 1 day 95% VaR 95% IndexMethodLR-UCAverage VaR DJINDUS Delta Normal MA (10) Delta Normal MA (20) EVT MA(10) EVT MA(20) EVT MA(60) FTSE Delta Normal MA (10) Delta Normal MA (20) EVT MA(10) EVT MA(20) EVT MA(60) NASDAQ Delta Normal MA (10) Delta Normal MA (20) EVT MA(20) S&P Delta Normal MA (10) Delta Normal MA (20) EVT MA(10) EVT MA(20) EVT MA(60)

Spillover Effect Study 12 July Backtesting results – 1 day 99% VaR 99% IndexMethodLR-UCAverage VaR BET Delta Normal MA (20) EVT MA(60) Delta Normal Garch CAC Delta Normal MA (20) Delta Normal Garch DAX Delta Normal MA (10) Delta Normal Garch DJINDUS Delta Normal MA (20) EVT MA(60) FTSE EVT MA(60) Delta Student Garch NASDAQ Delta Normal MA (10) Delta Normal MA (20) S&P Delta Normal Garch

Spillover Effect Study 12 July Backtesting conclusion Extreme Value Theory estimates better the 95% VaR 99% VaR estimation is split between Delta Normal Garch, EVT and Delta Normal Moving Average

Spillover Effect Study 12 July Spillover (Unit Root tests) In order to proceed further we need to study the stationarity of the series Two methods used: – Augmented Dickey-Fuller (1981) test - takes care of the deterministic part – Philips-Perron - focuses on the stochastic part of the drift

Spillover Effect Study 12 July Spillover (Unit Root tests), 1 day 95% VaR Unit Root 1 day-95 % IndexADF(intercept) ADF(intercept & trend)PP(intercept)PP(intercept & trend) BET NASDAQ *0.0905* DJINDUS S&P CAC DAX FTSE BET, DJINDUS, S&P500, CAC40, DAX30 and FTSE100 present stationary NASDAQ100 are non-stationary since it has a unit root. Therefore the null hypothesis of the existence of a unit root is significant at 5% probability level.

Spillover Effect Study 12 July Spillover (Unit Root tests), 1 day 99% VaR BET, NASDAQ100, S&P500, CAC40 and DAX30 present stationary DJINDUS and FTSE100 are non-stationary since it has a unit root. Therefore the null hypothesis of the existence of a unit root is significant at 5% probability level Unit Root 1 day-99 % IndexADF(intercept) ADF(intercept & trend)PP(intercept) PP(intercept & trend) BET0000 NASDAQ DJINDUS0.8572*0.995*0.5873*0.986* S&P CAC DAX FTSE *0.9945*0.4048*0.9028*

Spillover Effect Study 12 July Spillover – Granger Causality In order to test for Granger causality across two variables X and Y we run bivariate regressions with a lag length set as k. These are called unrestricted regressions: Granger Causality is examined by testing the null hypothesis whether all are equal to zero

Spillover Effect Study 12 July Bivariate Granger causality between the daily changes of the 1 day, 95% VaR of the various indices

Spillover Effect Study 12 July Bivariate Granger causality between the daily changes of the 1 day, 95% VaR of the various indices

Spillover Effect Study 12 July Bivariate Granger causality between the daily changes of the 1 day, 95% VaR of the various indices at 1% probability level, there is a spillover effect from: – FTSE100 to CAC 40 DJINDUS NASDAQ100 S&P500 – CAC 40 to FTSE100 – DAX 30 to CAC40 – CAC40 to DAX30 – NASDAQ100 to CAC40

Spillover Effect Study 12 July Bivariate Granger causality between the daily changes of the 1 day, 95% VaR of the various indices at 5% probability level, there is a spillover effect from: – DAX30 to FTSE100 – NASADQ100 to DAX30, FTSE100 – DJINDUS to FTSE 100

Spillover Effect Study 12 July Bivariate Granger causality between the daily changes of the 1 day, 99% VaR of the various indices.

Spillover Effect Study 12 July Bivariate Granger causality between the daily changes of the 1 day, 99% VaR of the various indices.

Spillover Effect Study 12 July Bivariate Granger causality between the daily changes of the 1 day, 99% VaR of the various indices. at 1% probability level there is a spillover effect from: – NASDAQ100 to DAX 30, – DJINDUS to BET – FTSE100 to BET

Spillover Effect Study 12 July Bivariate Granger causality between the daily changes of the 1 day, 99% VaR of the various indices. at 5% probability level there is a spillover effect from: – DAX30 to FTSE100 – FTSE100 to DJINDUS S&P 500 – DJINDUS to FTSE100

Spillover Effect Study 12 July Topics Introduction Methodologies used and results Conclusion References-Annex

Spillover Effect Study 12 July Conclusion (1) There is are spillover effects from US and European market to Romanian market, especially from DJINDUS and FTSE 100. Comparing the two different levels of risk (95 % and 99%) we observe that for the 95% VaR there are more spillover effects across the markets But, as per 99% VaR calculations, the US and European markets influence the Romanian capital market

Spillover Effect Study 12 July Conclusion (2) US indexes have the greatest effect across the indexes, in particular DJ INDUSTRIALS and NASDAQ100 Another interesting result is that FTSE100 plays a significant role since it leads many other markets. Also we have found a causal relationship between DAC30 and CAC 40 to European market.

Spillover Effect Study 12 July Conclusions beyond formulas Globalisation has an important role in the correlations between markets. Big players have access to all the markets and usually they have a unitary strategy that will influence accordingly all the markets on which they are active Investors expectations triggers also the correlations between markets. If they see an upward or downward move on other important markets they will expect the same move on the their market. Hence they will buy or sell accordingly

Spillover Effect Study 12 July Topics Introduction Methodologies used and results Conclusion References-Annex

Spillover Effect Study 12 July References-Annex Fama, E., 1965, The Behavior of Stock Market Prices, Journal of Business, vol 38. nr 1, page Engle R., 2004, Risk and Volatility, Econometric Models and Financial Practice, vol 94, nr. 3, page Hamao, Y., Masulis, R. W., Ng, V., 1990, Correlations in Price Changes and Volatility Across International Stock Markets, Review of Financial Studies 3., nr 2, page Martens, M., Poon, S. H., 2000, Returns Synchronization and Daily Correlation Dynamics, Journal of Banking and Finance Wen- Ling-Lin, Robert F. Engle, Takatoski, 1994, Do bulls and bears move across borders? International transmission of Stock returns and Volatility, The Review of Financial Studies, vol. 7, nr. 3, page Bollerslev T., 1987, A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return, The Review of Economics and Statistics, vol 69, nr.3, page Poon s. H., M. Rockinger, J. Tawn, 2004, Extreme Value dependence in Financial Market- Diagnostics, Models and Financial Implications, Review of Financial Studies, vol. 17. nr. 2., page Stanley J.K., 1984, Models of Stock Returns – A Comparison, the Journal of Finance, vol. 39., nr 1, page Lee S.J, 2006, Volatility spillover among Six Asian Countries and US, Financial Supervisory Service South Korea

Spillover Effect Study 12 July References-Annex Nylud S., 2001, Value at Risk Analysis for Heavy- Tailed Financial Returns, Helsinki University of Technology, Department of Engineering Physics and Mathematics Granger, C. J., 1969, "Investigating Causal Relationships by Econometrics Models and Cross Spectral Methods." Econometrica, Vol. 37. Hiemstra C., D.J. Jonathan, 1994, Testing for linear and non-linear Granger causality in Stock Prices – The Journal of Finance, vol. 49. Nr. 5. Page Engle R., 2001, The use of ARCH/GARCH Models in Applied econometrics, The Journal of Economic Perspectives, vol. 15, nr 4, page Thomas S.Y. Ho, S.B. Lee (2004), The Oxford Guide to financial Modeling- Applications for Capital Markets, Corporate Finance, Risk Management and Financial Institution Hull, J., Options, Futures and Other Derivatives, 6th edition. Morgan J. P., December 1996, Risk Metrics - Technical Document, 4th edition Alexander C. (2001), A Guide to Financial Data Analysis Jorion P. (2002), Managing Financial Risk- Value at Risk

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