Forecasting BET Index Volatility

1
Forecasting BET Index Volatility

• MSc. Razvan Ghelmeci
• Supervisor Prof. Moisa Altar

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.

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BET Index Return and Volatility

• We use BET index historical data between January
  3rd 2002 and May 31st 2007.
• The daily return for day n is
• The daily volatility for day n is

6
Data Series Statistics

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Data Series Statistics
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Models Definition

• GARCH type models are defined as follows
• ARCH(1)
• GARCH(1,1)
• EGARCH(1,1)
• TGARCH(1,1)

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Models Definition

• The rest of the models are defined as follows
• EWMA
• Moving Average
• Linear Regression
• Random Walk

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Forecasting and testing Methodology

• Rolling Window Method
• Classical tests
• Mean Error
• Root Mean Square Error
• Mean Absolute Error
• Mean Absolute Percent Error

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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

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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

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Empirical Results - Parameter Estimation
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Empirical Results Parameter Estimation

• Modified EGARCH(1,1)
• Modified TGARCH(1,1)

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Empirical Results Model Testing
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Empirical Results Tests Based on Value-at-Risk
Approach
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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.

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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.
• Brailsford, T.J. and R.W. Faff (1996), An
  Evaluation of Volatility Forecasting Techniques,
  Journal of Banking and Finance, 20, 419-438.
• Bollerslev, T. (1986), Generalized
  Autoregressive Conditional Heteroskedasticity,
  Journal of Econometrics, 31, 307-328.
• Brooks, C. (1998), Forecasting Stock Return
  Volatility Does Volume Help?, Journal of
  Forecasting, 17, 59-80.
• Brooks, C. and G. Persand (2000), Value at Risk
  and Market Crashes, Journal of Risk, 2, 5-26.
• Cheung, Y.W. and L.K. Ng (1992), Stock Price
  Dynamics and Firm Size An Empirical
  Investigation, Journal of Finance, 47,
  1985-1997.
• Day, T.E. and C.M. Lewis (1992), Stock Market
  Volatility and the Information Content of Stock
  Index Options, Journal of Econometrics, 52,
  267-287.
• Engle, R.F. (1982), Autoregressive Conditional
  Heteroskedasticity with Estimates of the Variance
  of U.K. Inflation, Econometrica, 50, 987-1008.
• Franses, P.H. and D. van Dijk (1996),
  Forecasting Stock Market Volatility Using
  Non-Linear GARCH Models, Journal of Forecasting,
  15, 229-235.

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References

• Granger, C.W.J. and S.H. Poon (2003),
  Forecasting Volatility in Financial Markets A
  Review, Journal of Economic Literature, 41,
  478-539.
• 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, 256-266.
• Johansen, A. and D. Sornette (1999), Critical
  Crashes, Journal of Risk, 12, 91-95.
• Klaassen, F. (2002), Improving GARCH Volatility
  Forecasts, Empirical Economics, 27, 363-394.
• Nelson, D.B. (1991), Conditional
  Heteroskedasticity in Asset Returns A New
  Approach, Econometrica, 59, 347-370.
• Pagan, A.R. and G.W. Schwert (1990), Alternative
  Models for Conditional Stock Volatilities,
  Journal of Econometrics, 45, 267-290.
• West, K.D. and D. Cho (1995),The Predictive
  Ability of Several Models of Exchange Rate
  Volatility, Journal of Econometrics, 69,
  367-391.
• Zumbach, G. (2002), Volatility Processes and
  Volatility Forecast with Long Memory, Working
  Paper, Olsen Associates.

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Thank you for your consideration!

• Bucharest, July 2007