An Empirical Evaluation of GARCH Models in Value-at-Risk Estimation: Evidence from the Macedonian Stock Exchange

• Authors: Vesna Bucevska
• Languages of publication: EN

Abstracts

EN

Background: In light of the latest global financial crisis and the ongoing sovereign debt crisis, accurate measuring of market losses has become a very current issue. One of the most popular risk measures is Value-at-Risk (VaR). Objectives: Our paper has two main purposes. The first is to test the relative performance of selected GARCH-type models in terms of their ability of delivering volatility estimates. The second one is to contribute to extend the very scarce empirical research on VaR estimation in emerging financial markets. Methods/Approach: Using the daily returns of the Macedonian stock exchange index-MBI 10, we have tested the performance of the symmetric GARCH (1,1) and the GARCH-M model as well as of the asymmetric EGARCH (1,1) model, the GARCH-GJR model and the APARCH (1,1) model with different residual distributions. Results: The most adequate GARCH family models for estimating volatility in the Macedonian stock market are the asymmetric EGARCH model with Student’s t-distribution, the EGARCH model with normal distribution and the GARCH-GJR model. Conclusion: The econometric estimation of VaR is related to the chosen GARCH model. The obtained findings bear important implications regarding VaR estimation in turbulent times that have to be addressed by investors in emerging capital markets

Keywords

EN

Value-at-Risk; GARCH models; forecasting volatility; financial crisis; Macedonia

• Publisher: Sciendo
• Journal: Business Systems Research Journal
• Year: 2013
• Volume: 4
• Issue: 1
• Pages: 49-64

Dates

published

2013-03-01

online

2013-05-14

Contributors

author

Vesna Bucevska

• Faculty of Economics, University “Ss. Cyril and Methodius”, Skopje, Republic of Macedonia

References

• 1. Andjelić, G., Djaković, V., Radišić, S. (2010), “Application of VaR in Emerging markets: A Case of Selected Central and Eastern European Countries”, African Journal of Business Management, Vol. 4, No. 17, pp. 3666-3680.
• 2. Angabini, A., Wasiuzzaman, S. (2011), “GARCH Models and the Financial Crisis-A Study of the Malaysian Stock Market”, The International Journal of Applied Economics and Finance, Vol. 5, No. 3, pp. 226-236.
• 3. Angelidis, T., Degiannakis, S. (2005), "Modeling Risk for Long and Short Trading Positions", The Journal of Risk Finance, Vol. 6, No. 3, pp. 226 - 238. [Crossref]
• 4. Bae, K., Karolyi, G. A. (1994), “Good News, Bad News and International Spillovers of Stock Return Volatility between Japan and the U.S.”, Pacific-Basin Finance Journal, Vol. 2, No. 4, pp. 405-438.
• 5. Balaban, E. (2002), “Comparative Forecasting Performance of Symmetric and Asymmetric Conditional Volatility Models of an Exchange Rate”, Working Paper, University of Edinburgh Center for Financial Markets Research, Edinburgh, pp. 1-14.
• 6. Bao, Y., Lee, T., Saltoglu, B. (2006), “Evaluating Predictive Performance of Value-at-Risk Models in Emerging Markets: A Reality Check”, Journal of Forecasting, Vol. 25, No. 2, pp. 101-128. [Crossref]
• 7. Batten, J. A., Szilagyi, P. G. (2011), “The Impact of the Global Financial Crisis on Emerging Financial Markets: An Introduction”, in Batten, J. A., Szilagyi P. G. (eds.), The Impact of the Global Financial Crisis on Emerging Financial Markets (Contemporary Studies in Economic and Financial Analysis 93), Emerald Group Publishing Limited, Bingley, pp. 3-17. [Crossref]
• 8. Bekaert, G., Harvey, C. R. (1995), “Time-Varying World Market Integration”, Journal of Finance, Vol. 50, No. 2, pp. 403-444. [Crossref]
• 9. Bekaert, G., Guojun, W. (2000), “Asymmetric Volatility and Risk in Equity Markets”, The Review of Financial Studies, Vol. 13, No. 1, pp. 1-42. [Crossref]
• 10. Benaković, D., Posedel, P. (2010), "Do Macroeconomic Factors Matter for Stock Returns? Evidence from Estimating a Multifactor Model on the Croatian Market", Business Systems Research Journal, Vol. 1, No.1-2, pp. 39-46.
• 11. Berndt, E., Hall, B., Hall, R., Hausman, J. (1974), “Estimation and Inference in Nonlinear Structural Models”, Annals of Economic and Social Measurement, Vol. 3, pp. 653-665.
• 12. Black, F. (1976), “Studies of Stock Price Volatility Changes”, in Proceeding of the 1976 Meetings of the Business and Economic Statistics Section, American Statistical Association, pp. 177-181.
• 13. Braun, P. A., Nelson, D. B., Sunier, A. M. (1995), “Good News, Bad News, Volatility, and Betas”, Journal of Finance, Vol. 50, No. 5, pp. 1575-1603. [Crossref]
• 14. Bollerslev, T. (1987), “Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return”, Review of Economics and Statistics, Vol. 69, No. 3, pp. 542-547. [Crossref]
• 15. Brooks, C. (2008). Introductory Econometrics for Finance, 2nd ed., Cambridge, Cambridge University Press.
• 16. Bollerslev, T., Chou, R. Y., Kroner, K. F. (1992), “ARCH Modeling in Finance: A Review of the Theory and Empirical Evidence”, Journal of Econometrics, Vol. 52, No. 1-2, pp. 5-59.
• 17. Brooks, C., Persand G. (2000), “A Word of Caution on Calculating Market Based Minimum Capital Risk Requirements”, Journal of Banking and Finance, Vol. 24, No. 10, pp. 1557-1574.
• 18. Campbell, J. Y., Hentshel, L. (1992), “No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns”, Journal of Financial Economics, Vol. 31, No. 3, pp. 281-318. [Crossref]
• 19. Cheung, Y., Ng, L. (1992), “Stock Price Dynamics and Firm Size: An Empirical Investigation”, Journal of Finance, Vol. 47, No. 5, pp. 1985-1997. [Crossref]
• 20. Christie, A. A. (1982), “The Stochastic Behavior of Common Stock Variances - Value, Leverage and Interest Rate Effects” , Journal of Financial Economics, Vol. 10, No. 4, pp. 407-432. [Crossref]
• 21. Curto, J. D., Pinto, J. C., Tavares, G. N. (2009), “Modelling Stock Markets’ Volatility Using GARCH Models with Normal, Student’s t and Stable Paretian Distributions”, Statistical Papers, Vol. 50, No. 2, pp. 311-321. [Crossref]
• 22. Da Silva, A., Beatriz, V., de Melo Mendes, B. (2003), “Value-at-Risk and Extreme Returns in Asian Stock markets”, International Journal of Business, Vol. 8, No. 1, pp. 17-40.
• 23. Dimitrakopoulos, D. N., Kavussanos M. G. and Spyrou, S. I. (2010), “Value at Risk Models for Volatile Emerging Markets Equity Portfolios”, The Quarterly Review of Economics and Finance, Vol. 50, No. 4, pp. 515-526. [Crossref]
• 24. Ding, Z., Engle, R., Granger C. (1993), “A Long Memory Property of Stock Market Returns and A New Model”, Journal of Empirical Finance, Vol. 1, No. 1, pp. 83-106.
• 25. Dufee, G. R. (1995), “Stock Returns and Volatility: A Firm Level Analysis”, Journal of Financial Economics, Vol. 37, No. 3, pp. 399-420. [Crossref]
• 26. Engle, R. F. (1982), “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of UK Inflation”, Econometrica, Vol. 50, No. 4, pp. 987-1008. [Crossref]
• 27. Engle, R. F. (2001), “GARCH 101: The Use of ARCH/GARCH Models in Applied Econometrics”, Journal of Economic Perspectives, Vol. 15, No. 4, pp. 157-168. [Crossref]
• 28. Engle, R. F., Lilien, D. M., Robbins, R. P. (1987), “Estimating Time Varying Risk Premia in the Term Structure: The ARCH-M Model”, Econometrica, Vol. 55, No. 2, pp. 391-407. [Crossref]
• 29. Engle, R. F., Ng, V. K. (1993), “Measuring and Testing the Impact of News on Volatility”, Journal of Finance, Vol. 48, No. 5, pp. 1749-1778. [Crossref]
• 30. Franses, P. H., Van Dijk, D. (1996), “Forecasting Stock Market Volatility Using (Non-Linear) GARCH Models”, Journal of Forecasting, Vol. 15, No. 3, pp. 229-235. [Crossref]
• 31. French, K., Schwert, G., Stambaugh, R. (1987), “Expected Stock Returns and Volatility”, Journal of Financial Economics, Vol. 19, No. 1, pp. 3-29. [Crossref]
• 32. Glosten, L. R., Jagannathan, R., Runkle, D. E. (1993), “On the Relation Between the Expected Value and the Volatility of the Nominal Excess Return on Stocks”, Journal of Finance, Vol. 48, No. 5, pp. 1779-1801. [Crossref]
• 33. Gokcan, S. (2000), “Forecasting Volatility of Emerging Stock Markets: Linear Versus Non- Linear GARCH Models”, Journal of Forecasting, Vol. 19, No. 6, pp. 499-504. [Crossref]
• 34. Hagerud, G. E. (1997), “Modelling Nordic Stock Returns with Asymmetric GARCH models”, Working Paper Series in Economics and Finance, Vol. 164, Stockholm School of Economics, Stockholm, pp. 1-26.
• 35. Hien, M. T. T. (2008), “Modelling and Forecasting Volatility by GARCH-Type Models: The Case of Vietnam Stock Exchange”, A Dissertation Presented in Part Consideration for the Degree of MA. Finance and Investment, pp. 1-97, available at: http://edissertations.nottingham.ac.uk/2017/1/08MAlixhm7.pdf (9 April 2012).
• 36. Jorion, P. (2007). Value at Risk: The New Benchmark for Managing Financial Risk, 3rd ed., New York, McGraw-Hill.
• 37. Kovacic, Z. (2007), “Forecasting Volatility: Evidence from the Macedonian Stock Exchange” Unpublished MPRA Paper No. 5319, pp. 1-44, available at: http://mpra.ub.unimuenchen. de/5319/1/MPRA_paper_5319.pdf (15 January 2012).
• 38. Macedonian stock exchange, available at: http://www.mse.org.mk (5 December 2011).
• 39. Magnusson, G., Andonov, S. (2002), “Basel Capital Adequacy Ratio and the Iceland Banking Sector: Quantitative Impact, Structural Changes and Optimality Considerations”, IOES Working Paper Series, W02:05, pp. 1-51, Institute of Economic Studies, Reykjavik, May 2002.
• 40. Mandelbrot, B. (1963), “The Variation of Certain Speculative Prices”, Journal of Business, Vol. 36, No. 4, pp. 349-419.
• 41. McMillan, D. G., Speight, A. E. H. (2007), “Value-at-Risk in Emerging Equity Markets: Comparative Evidence for Symmetric, Asymmetric and Long-Memory GARCH Models”, International Review of Finance, Vol. 7, No. 1-2, pp. 1-19.
• 42. Nelson, D. B. (1991), “Conditional Heteroskedasticity in Asset Returns: A New Approach”, Econometrica, Vol. 59, No. 2, pp. 347-370. [Crossref]
• 43. Ng, A. (2000), “Volatility Spillover Effects from Japan and the US to the Pacific-Basin”, Journal of Monetary Economics, Vol. 19, No. 2, pp. 207-233.
• 44. Pagan, A. R., Schwert, G. W. (1990), “Alternative Models for Conditional Stock Volatility”, Journal of Econometrics, Vol. 45, No. 1-2, pp. 267-290.
• 45. Parrondo, J. M. R. (1997), “Calculation of the Value at Risk in Emerging Markets”, Working Paper, Universidad Complutense de Madrid, Madrid, pp. 1-38.
• 46. Poon, S., Granger, C. W. J. (2003), “Forecasting Volatility in Financial Markets, A Review”, Journal of Economic Literature, Vol. 41, No. 2, pp. 478-539. [Crossref]
• 47. Schwert, G. W. (1990), “Stock Volatility and the Crash of ’87”, Review of Financial Studies, Vol. 3, No. 1, pp. 77-102.
• 48. Valentinyi-Endresz, M. (2004), “Structural Breaks and Financial Risk Management”, Magyar Nemzeti Bank, Working paper, No. 2004/11, Budapest, pp. 1-60,
• 49. Vilasuso, J. (2002), “Forecasting Exchange Rate Volatility”, Economics Letters, Vol. 76, No. 1, pp. 59-64. [Crossref]
• 50. Zikovic, S. (2007), “Measuring Market Risk in EU New Member States”, available at: http://www.hnb.hr/dub-konf/13-konferencija/zivkovic.pdf (12 December 2011).
• 51. Zikovic, S., Aktan, B. (2009), “Global Financial Crisis and VAR Performance in Emerging Markets: A Case of EU Candidate States - Turkey and Croatia”, Journal of Economics and Business - Proceedings of Rijeka Faculty of Economics, Vol. 27, No. 1, pp. 149-170.
• 52. Zikovic, S., Bezic, H. (2006), “Is Historical Simulation Appropriate for Measuring Market Risk? A Case of Countries Candidates for EU accession”, in Proceedings of the CEDIMES conference, Ohrid, Macedonia, 23-27th March, pp. 1-20.
• 53. Zikovic, S., Filler, R. K. (2009), “Hybrid Historical Simulation VAR and ES: Performance in Developed and Emerging Markets”, CESifo Working paper Series, No. 2820, pp. 1-39, available at: http://www.cesifo-group.de/portal/page/portal/DocBase_Content/WP/WPCESifo_Working_Papers/wp-cesifo-2009/wp-cesifo-2009-10/cesifo1_wp2820.pdf (14 December 2011).

Identifiers

DOI

10.2478/bsrj-2013-0005