Academy of Economic Studies Doctoral School of Finance and Banking - DOFIN

1. Academy of Economic StudiesDoctoral School of Finance and Banking - DOFIN VOLATILITY AND LONG TERM RELATIONS IN EQUITY MARKETS: Empirical Evidence from Romania, Germany and Poland MSc. Student: Mircia Ana-Maria Supervisor: PhD. Professor Moisa Altar July, 2009

2. GOALS • COMPARE SEVERAL GARCH MODELS for - modeling and forecasting conditional variance of Romania, Germany and Poland stock market indexes • LONG RUN RELATIONS BETWEEN THESE MARKETS

3. WHAT MOVES VOLATILITY? • NEWS • RESEARCH STRATEGIES • VOLATILITY MODELS • INTER-LINKAGES IN MARKET VOLATILITY

4. REVIEW OF PREVIOUS RESEARCH • Asymmetric effect to past information: Koutmos (1998) using TGARCH on 9 countries, Chen (2001) using EGARCH on 9 countries • Cointegration analysis, regarded as perhaps the most revolutionary development in econometrics since mid’80s, used by (Granger, 1986; Engle and Granger, 1987; Johansen, 1988; Johansen and Juselius, 1990)

5. VOLATILITY MODELS • GARCH • TGARCH: • EGARCH:

6. COMPONENT GARCH MODEL The conditional variance in the GARCH(1,1) model can be written as: => Allowing for the possibility that σ2 is not constant over time, but a time-varying trend qt, yields: Dt is a slope dummy variable that takes the value Dt = 1 for εt < 0 and Dt = 0 otherwise, in order to capture any asymmetric responses of volatility to shocks.

7. DECOMPOSITION IN PERMANENT AND TRANSITORY COMPONENTS • The long run component equation: • The short run component equation: • Stationarity of the CGARCH model and non-negativity of the conditional variance are ensured if the following inequality constraints are satisfied: 1 > ρ > (α+β), β > Φ > 0, α > 0, β > 0, Φ > 0, ω > 0.

8. DATA • DAILY DATA FROM 2000 THROUGH 2009 • FIRST 2200 observations for each stock market index were used for modeling • LAST 125 were kept out of sample to be used for forecasting volatility • Returns were computed using the prices log difference:

9. DATA STATISTICS FOR BET SERIES BET Index the main indicator on the progression of Bucharest Stock Exchange, is a free float weighted capitalization index of the most liquid 10 companies listed on the BSE regulated market. It was launched in September 19, 1997, when its value stood at 1,000 points.

10. DATA STATISTICS FOR DAX SERIES DAX Index, is the most commonly cited benchmark for measuring the returns posted by stocks on the Frankfurt Stock Exchange. Started in 1984 with a value of 1000, the index is comprised of the 30 largest and most liquid issues traded on the exchange.

11. DATA STATISTICS FOR WIG20 SERIES WIG20 Index, the main index of Warsaw Stock Exchange is calculated based on a portfolio comprised of shares in the 20 largest and most traded companies.. The index base date is April 16, 1994; and its base value is 1, 000 points.

12. CONDITIONAL VOLATILITY FOR GARCH MODELS BET Index

13. CONDITIONAL VOLATILITY FOR GARCH MODELS DAX Index

14. CONDITIONAL VOLATILITY FOR GARCH MODELS WIG20

15. CGARCH Components Chart BET Index

16. CGARCH Components Chart DAX Index

17. CGARCH Components Chart WIG20 Index

18. FORECASTING VOLATILITY • I used out-of-sample data in order to forecast volatility by using the last 125 observations • GARCH models are measured by the coefficient of determinations R2 coming from regressing squared returns on the volatility forecast: rt2=a + b σt2+ut • Trying to avoid the strongly influenced extreme values on rt2 , the following model is used: log rt2 =a + b log ht2 + ut l

19. BET stock market forecasted volatility

20. DAX stock market forecasted volatility

21. WIG20 stock market forecasted volatility

22. COINTEGRATION ANALYSIS Cointegration requires the variables to be integrated of the same order. Unit root tests are performed on each of the price index series in log first differences through the ADF test and the Phillips-Peron test:

23. COINTEGRATION ANALYSIS • Further we estimatea VAR and the lag length using AIC and SC: Yt = c + ∑Δyt-1 + εt The information criteria selects a VAR(2) • Next step is the determination of the number of cointegrating relations in VAR

24. COINTEGRATION ANALYSIS Primary finding is that a stationary long-run relationship exists between the three equity markets. Further a VECM is created and the parsimonious model according to AIC and SC was found to be a VECM (4) with the cointegration rank =1. VECM estimated results:

25. CONCLUDING REMARKS • GARCH models showed evidence of asymmetric effect for DAX and WIG20, but not for BET • The autoregressive parameters in the trend equations, ρ, is very close to one for all indices, so the series are very close to being integrated • Error correction parameter is not significant for BET Index, Romania market will be the first one to react to the external shocks, while Germany is the one who impose shocks • It could be interesting to detect how much the exchange rate is important for investors who operate in this markets and how stock market and economic variables react

26. BIBLIOGRAPHY • Anderssen, T & T. Bollerslev (1997). Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-run in High Frequency Returns. Journal of Finance. 52, 975 – 1005 • Alexander, C. (2001). Market Models. A Guide to Financial Data Analysis. 1st ed. Chichester: John Wiley & Sons Ltd. 494 • Bekaert, Geert & Campbell R. Harvey (1997). Emerging equity market volatility. Journal of Financial Economics. 43: 29-77 • Bekaert, Geert & Guojun Wu. (2000). Asymmetric volatility and risk in equity markets. The Review of Financial Studies. 13: 1, 1-42. • Bollerslev, T., R.Y. Chou & Kroner K. F. (1992). ARCH-Modeling in Finance: A review of the theory and empirical evidence. Journal of Econometrics. 52: 5-59. • Brooks, C. (2002). Introductory Econometrics for Finance. 1st ed. Cambridge: Cambridge University Press. 701 • Campbell John Y. (1990). Measuring the persistence of expected returns. The American Economic Review. 80: 2, 43-47. • Dickey, D. & W. Fuller(1979) Distribution of the estimators for the autoregressive Time series with a unit root. Journal of the American Statistical Association 74. 427 – 431. • Ding, Z., Granger C. W. & Engle R. F. (1996). A long memory property of stock returns and a new model. Journal of Empirical Finance. 1: 83-106

27. BIBLIOGRAPHY • Fama, E. (1970). Efficient capital markets: A review of theory and empirical work. The Journal of Finance. 25: 383-432.  • Glosten, L., Jagannathan, R & D. Runkle (1993). On the relation between expected value and the volatility of the nominal excess returns on stocks. The Journal of Finance 48. 1779 – 1801. • Granger, C.W.J., and Joyeaux, R. (1980), An introduction to long memory time series models and fractional diferencing., Journal of Time Series Analysis, 1, 15-39. • Johansen, S (1988). Statistical Analysis of Co-integration Vectors, Journal of Economic Dynamics and Control, 12, 231-254. • Johansen, S. & J. Katarina (1990). Maximum Likelihood Estimation and Inference on Co integration with Application to the Demand for Money, Oxford Bulletin of Economics and Statistics, 52, 169 210. • Mandelbrot, B. (1963). The variation of certain speculative prices. Journal of Business. 36: 394 – 419.  • Nelson, D (1990). ARCH models as diffusion approximations. Journal of Econometrics 45. 7 – 38. • Porteba, James M. (1990). Linkages between equity markets. The Review of Financial Studies. 3: 1, 34-35.  • Zakoian, J-M (1994). Threshold heteroskedastic models. Journal of Economic Dynamics and Control 18. 931 – 955.

28. Thank you for your consideration!