1 Forecasting BET Index Volatility MSc.: Răzvan Ghelmeci Supervisor: Prof. Moisă Altăr

2 Introduction Into this paper we try to combine volatility forecasting and risk management, analyzing if the intensely used predicting models can be calibrated on data from Romanian stock exchange and if the realized predictions can be employed as risk management instruments using several test based on computing Value-at- Risk. The literature on forecasting volatility is significant and still growing at a high rate. The techniques of measuring and managing financial risk have developed rapidly as a result of financial disasters and legal requirements.

3 Literature Review Akgiray (1989) showed that GARCH model is superior to ARCH model, EWMA and models based on historical mean in predicting monthly US stock index volatility. A similar result was observed by West and Cho (1995) regarding daily forecast of US Dollar exchange rate using root mean square error test (RMSE). Nevertheless, for longer time horizons GARCH model did not gave better results than Long Term Mean, IGARCH or autoregressive models. Franses and van Dijk (1996) compared three types of GARCH models (standard GARCH, QGARCH and TGARCH) in predicting the weekly volatility of different European stock exchange indexes, nonlinear GARCH models bringing no better results than the standard model.

4 Literature Review Other papers tried to combine stock index volatility forecast derived from traded options prices with those generated by econometric models – Day and Lewis (1992). Alexander and Leigh (1997) present an evaluation of relative accuracy of some GARCH models, equally weighted and exponentially weighted moving average, using statistic criterions. GARCH model was considered better than exponentially weighted moving average (EWMA) in terms of minimizing the number of failures although the simple mean was superior to both. Jackson et al. (1998) assessed the empirical performance of different VaR models using historical returns from the actual portfolio of a large investment bank.

5 BET Index Return and Volatility We use BET index historical data between January 3rd 2002 and May 31st The daily return for day n is: The daily volatility for day n is:

6 Data Series Statistics

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8 Models Definition GARCH type models are defined as follows: 1. ARCH(1) 2. GARCH(1,1) 3. EGARCH(1,1) 4. TGARCH(1,1)

9 Models Definition The rest of the models are defined as follows: 1. EWMA 2. Moving Average 3. Linear Regression 4. Random Walk

10 Forecasting and testing Methodology “Rolling Window” Method Classical tests 1. Mean Error 2. Root Mean Square Error 3. Mean Absolute Error 4. Mean Absolute Percent Error

11 Forecasting and testing Methodology Value-at-Risk Approach The money-loss in a portfolio that is expected to occur over a pre- determined horizon and a pre-determined degree of confidence as a result of assets price changes. The VaR computing equation is:

12 Forecasting and testing Methodology Time Until First Failure The first day in the testing period where the capital held is insufficient to absorb the loss of that day. Failure Rate The percentage level of the times the computed value of VaR is insufficient to cover the real losses during the testing period

13 Empirical Results - Parameter Estimation

14 Empirical Results – Parameter Estimation Modified EGARCH(1,1) Modified TGARCH(1,1)

15 Empirical Results – Model Testing

16 Empirical Results – Tests Based on Value-at-Risk Approach

17 Conclusions The results we obtained revealed that, although they can be easily calibrated on Romanian stock exchange index, the models used for predicting the volatility have a low performance, even unsatisfactory compared with the results obtained using simpler methods. The tests performed using a financial risk management framework rejected all the models employed and showed that they could not be successfully used in establishing a minimum capital requirement based on the risk assumed by investing in portfolios that replicate the Bucharest Stock Exchange index – BET. The explanation for this failure is that the volatility on the Romanian market is generally high, existing periods of accentuated turbulences that make hard to use the classic econometric volatility forecasting models.

18 References Akgiray, V. (1989), “Conditional Heteroskedasticity in Time Series of Stock Returns: Evidence and Forecasts”, Journal of Business, 62, Brailsford, T.J. and R.W. Faff (1996), “An Evaluation of Volatility Forecasting Techniques”, Journal of Banking and Finance, 20, Bollerslev, T. (1986), “Generalized Autoregressive Conditional Heteroskedasticity”, Journal of Econometrics, 31, Brooks, C. (1998), “Forecasting Stock Return Volatility: Does Volume Help?”, Journal of Forecasting, 17, Brooks, C. and G. Persand (2000), “Value at Risk and Market Crashes”, Journal of Risk, 2, Cheung, Y.W. and L.K. Ng (1992), “Stock Price Dynamics and Firm Size: An Empirical Investigation”, Journal of Finance, 47, Day, T.E. and C.M. Lewis (1992), “Stock Market Volatility and the Information Content of Stock Index Options”, Journal of Econometrics, 52, Engle, R.F. (1982), “Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of U.K. Inflation”, Econometrica, 50, Franses, P.H. and D. van Dijk (1996), “Forecasting Stock Market Volatility Using Non-Linear GARCH Models”, Journal of Forecasting, 15,

19 References Granger, C.W.J. and S.H. Poon (2003), “Forecasting Volatility in Financial Markets: A Review”, Journal of Economic Literature, 41, J.P. Morgan (1996), “RiskMetrics – Technical Document”, 4th Edition. Jackson, P., D.J. Maude, and W. Perraudin (1998), “Testing Value at Risk Approaches to Capital Adequacy”, Bank of England Quarterly Bulletin, 38, Johansen, A. and D. Sornette (1999), “Critical Crashes”, Journal of Risk, 12, Klaassen, F. (2002), “Improving GARCH Volatility Forecasts”, Empirical Economics, 27, Nelson, D.B. (1991), “Conditional Heteroskedasticity in Asset Returns: A New Approach”, Econometrica, 59, Pagan, A.R. and G.W. Schwert (1990), “Alternative Models for Conditional Stock Volatilities”, Journal of Econometrics, 45, West, K.D. and D. Cho (1995),”The Predictive Ability of Several Models of Exchange Rate Volatility”, Journal of Econometrics, 69, Zumbach, G. (2002), “Volatility Processes and Volatility Forecast with Long Memory”, Working Paper, Olsen Associates.

20 Thank you for your consideration! Bucharest, July 2007