Evaluating Value-at-Risk Models before and after the Financial Crisis of 2008: International Evidence

Degiannakis, Stavros and Floros, Christos and Livada, Alexandra (2012): Evaluating Value-at-Risk Models before and after the Financial Crisis of 2008: International Evidence. Published in: Managerial Finance , Vol. 4, No. 38 (2012): pp. 436-452.

Abstract

Τhis paper focuses on the performance of three alternative Value-at-Risk (VaR) models to provide suitable estimates for measuring and forecasting market risk. The data sample consists of five international developed and emerging stock market indices over the time period from 2004 to 2008. The main research question is related to the performance of widely-accepted and simplified approaches to estimate VaR before and after the financial crisis. VaR is estimated using daily data from UK (FTSE 100), Germany (DAX30), USA (S&P500), Turkey (ISE National 100) and Greece (GRAGENL). Methods adopted to calculate VaR are: 1) EWMA of Riskmetrics, 2) classic GARCH(1,1) model of conditional variance assuming a conditional normally distributed returns and 3) asymmetric GARCH with skewed Student-t distributed standardized innovations. The results indicate that the widely accepted and simplified ARCH framework seems to provide satisfactory forecasts of VaR not only for the pre-2008 period of the financial crisis but also for the period of high volatility of stock market returns. Thus, the blame for financial crisis should not be cast upon quantitative techniques, used to measure and forecast market risk, alone.

• Item Type: MPRA Paper
• Language: English
• Keywords: ARCH, Value-at-Risk, Volatility, Forecasting, Financial Crisis
• Subjects: C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models; G - Financial Economics > G1 - General Financial Markets > G10 - General

References

Alexander, C. 2008a. Value-At-Risk Models. John Wiley & Sons, New York.

Alexander, C. 2008b. Practical Financial Econometrics. John Wiley & Sons, New York.

Alexander, G. J. 2009. From Markowitz to Modern Risk Management. European Journal of Finance 15: 451‐461.

Angelidis, T., and Benos A., 2008. Value-at-Risk for Greek Stocks. Multinational Finance Journal 12: 67-105.

Angelidis, T., and Degiannakis, S. 2005. Modelling Risk for Long and Short Trading Positions. Journal of Risk Finance 6(3): 226-238.

Angelidis, T., and Degiannakis, S. 2007. Backtesting VaR models: A Two-stage Procedure. Journal of Risk Model Validation 1(2): 1-22.

Angelidis, T., and Degiannakis, S. 2008a. Volatility Forecasting: Intra-day vs. Inter-day Models. Journal of International Financial Markets, Institutions and Money 18: 449-465.

Angelidis, T., and Degiannakis, S. 2008b. Forecasting One-day-ahead VaR and Intra-Day Realized Volatility in the Athens Stock Exchange Market. Managerial Finance 34(7): 489-497.

Artzner, P., Delbaen, F., Eber, J-M. and Heath, D. 1999. Coherent Measures of Risk. Mathematical Finance 9: 203‐228.

Assaf, A. 2009. Extreme observations and risk assessment in the equity markets of MENA region: Tail measures and Value-at-Risk. International Review of Financial Analysis 18: 109-116.

Bao Y., Le, T.H. and Saltoglu, B. 2006. Evaluating Predictive Performance of Value-at-Risk Models in Emerging Markets: A reality check. Journal of Forecasting 25: 101-128.

Bollerslev T. 1986. Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics 31: 307–327.

Bollerslev, T. and Wooldridge, J.M. (1992). Quasi-maximum Likelihood Estimation and Inference in Dynamic Models with Time-Varying Covariances. Econometric Reviews, 11, 143-172.

Byström H.N.E. 2004. Managing Extreme Risks in Tranquil and Volatile Markets Using Conditional Extreme Value Theory. International Review of Financial Analysis 13(2): 133-152.

Campbell J., Lo, A., and MacKinlay, A.C. 1997. The Econometrics of Financial Markets. Princeton University Press, New Jersey.

Cheong, C. W. 2008. Heavy-tailed Value-at-Risk Analysis for Malaysian Stock Exchange. Physica A 387: 4285-4298.

Christoffersen P. 1998. Evaluating Interval Forecasts. International Economic Review 39: 841-862.

Diamandis, P.F., Kouretas, G.P.. and Zarangas, L. 2006. Value-at-Risk for Long and Short Trading Positions: The Case of the Athens Stock Exchange. University of Crete, Department of Economics, Working Papers, 0601.

Ding, Z., Granger, C.W.J., and Engle, R.F. 1993. A Long Memory Property of Stock Market Returns and a New Model. Journal of Empirical Finance 1: 83-106.

Engle, R.F. 2002. Dynamic Conditional Correlation: A Simple class of Multivariate GARCH Models. Journal of Business and Economic Statistics 20: 339-350.

Engle, R.F. and Manganelli, S. 2004. CAViaR: Conditional autoregressive Value at Risk by Regression Quantiles. Journal of Business and Economic Statistics 22(4): 367-381.

Fernandez, C., and Steel., M. 1998. On Bayesian Modeling of Fat Tails and Skewness. Journal of the American Statistical Association 93: 359-371.

Gençay, R., and Selçuk, F. 2004. Extreme Value Theory and Value-at-Risk: Relative Performance in Emerging Markets. International Journal of Forecasting 20(2): 287-303.

Glosten, L., Jaganathan, R., and Runkle, D. 1993. Relationship Between the Expected Value and the Volatility of the Nominal Excess Returns on Stocks. Journal of Finance 48: 1779-1802.

Hansen, P.R., 2005. A Test for Superior Predictive Ability. Journal of Business and Economic Statistics 23: 365-380.

Hansen, P.R., and Lunde, A. 2005. A Forecast Comparison of Volatility Models: Does Anything Beat a GARCH(1,1)?. Journal of Applied Econometrics 20(7): 873-889.

Huang, A.Y-H., and Tseng, T-W. 2009. Forecast of value at risk for equity indices: an analysis from developed and emerging markets. Journal of Risk Finance 10(4): 393-409.

Hull, J., and White, A. 1998. Incorporating Volatility Updating into the Historical Simulation Method for VaR. Journal of Risk 1: 5-19.

Iglesias, E.M., and Linton, O.B. 2009. Estimation of Tail Thickness Parameters from GJR-GARCH Models, Working paper 09-47 Economic Series (26), Universidad Carlos III de Madrid.

Kupiec, P.H., 1995. Techniques for Verifying the Accuracy of Risk Measurement Models. Journal of Derivatives 3: 73-84.

Lambert, P. and Laurent, S. 2000. Modeling Skewness Dynamics in Series of Financial Data. Discussion Paper, Institut de Statistique, Louvain-la-Neuve.

Lambert, P., and Laurent, S. 2001. Modeling Financial Time Series Using GARCH-type Models and a Skewed Student Density. Universite de Liege, Mimeo.

Linton, O. and Mammen, E. 2005. Estimating Semiparametric ARCH(∞) Models by Kernel Smoothing Methods. Econometrica 73(3): 771-836.

Longstaff, F.A., 2010. The subprime credit crisis and contagion in financial markets. Journal of Financial Economics 97(3): 436-450.

Lopez, J.A., 1999. Methods for Evaluating Value-at-risk Estimates, Economic Policy Review. Federal Reserve Bank of New York 2, 3-17.

Morgan, J.P., 1996. RiskmetricsTM. Technical Document, 4th Edition, New York.

Ozun, A., Cifter, A., and Yilmazer, S. 2010. Filtered extreme-value theory for value-at-risk estimation: evidence from Turkey. Journal of Risk Finance 11(2): 164-179.

Pafka, S., and Kondor, I. 2001. Evaluating the RiskMetrics methodology in measuring volatility and Value-at-Risk in financial markets. Physica A 299: 305-310.

Sarma, M., Thomas, S., and Shah, A. 2003. Selection of VaR Models. Journal of Forecasting 22(4): 337-358.

Stulz, R.M., 2008. Risk Management Failures: What are they and when doe they happen?. Journal of Applied Corporate Finance 20(4): 58-67.

Winker, P. and Maringer, D., 2007. The Hidden Risks of Optimizing Bond Portfolios under Value at Risk. Journal of Risk 9: 1‐19.

Xekalaki, E., and Degiannakis, S. 2010. ARCH Models for Financial Applications. John Wiley & Sons, New York.