• Ivica Terzić Singidunum University
  • Marko Milojević Singidunum University


The purpose of this paper is to evaluate performance of value-at-risk (VaR) produced by two risk models: historical simulation and Risk Metrics. We perform three backtest: unconditional coverage, independence and conditional coverage. We present results on both VaR 1% and VaR 5% on a one-day horizon for the following indices: S&P 500, DAX, SAX, PX and Belex 15. Our results show that Historical simulation 500 days rolling window approach satisfies unconditional coverage for all tested indices, while Risk Metrics has many rejection cases. On the other hand Risk Metrics model satisfies independence backtest for three indices, while Historical simulation has rejected more times. Based on our strong criteria to accept accuracy of VaR models only if both unconditional coverage and independence properties are satisfied, results indicate that during the crisis period all tested VaR models underestimate the true level of market risk exposure.


Anatolyev, S. (2006). Nonparametric retrospection and monitoring of predictability of financial returns. Moscow, Russia: Centre for Economic and Financial Research at New Economic School.

Campbell, S. (2005). A review of backtesting and backtesting procedures. Washington, D.C.: Finance and Economics Discussion Series, Federal Reserve Board.

Carol, A. (2008). Value at Risk Models. Chichester, England: John Wiley & Sons.

Dowd, K. (2002). Measuring Market Risk. Chichester, England: John Wiley & Sons.

Esch, L., Kieffer, R. & Lopez, T. (2005). Asset and Risk Managment. New York, NY: The Wiley Finance.

Jorion, P. (2002). Value at Risk : the new benchmark for managing financial risk. New York, NY: McGraw-Hill. PMid:12050528

Jurun, E., Pivac, S. & Arnerić, J. (2007). Historical and Prognostic Risk Measuring Across Stocks and Markets. Journal of WSEAS Transactions on Business and Economic, Vol. 4., No. 8, 126-134.

Khindanova, I. & Rachev, S. (2000). Value at risk: Recent Advances. In Anastassiou, G. (Ed.), Handbook of Analytic Computational Methods in Applied Mathematics (p. 801 – 858). Boca Raton, FL: Chapman and Hall/CRC Press LLC. http://dx.doi.org/10.1201/9781420036053.ch18

Kovačić, Z. (2007). Forecasting volatility: Evidence from the Macedonian stock exchange. MPRA Paper No. 5319. Munich, Germany: University Library of Munich. Retrieved from http://mpra.ub.uni-muenchen.de

Kupiec, P. (1995). Techniques for verifying the accuracy of risk managment models. Journal of Derivates, Vol. 3, No. 2, 73-84. http://dx.doi.org/10.3905/jod.1995.407942

Milojević, M. (2008). Impact macroeconomic factors on Belgrade Stock Exchange. Belgrade, Serbia: Singidunum University.

Radivojević, N., Milojković, D. & Stojković, D. (2010). Testiranje aplikativnosti parametarske i neparametarske metode vrednosti pri riziku na trzhishtu kapitala Srbije [Testing the Applicability of parametric and nonparametric methods of Value at Risk at the Serbian Capital Market]. Bankarstvo, Vol. 2010, No.11/12, 46-61.

Terzić, I. & Milojević, M. (in press). Kvalitet metoda merenja trzhishnog rizika na trzhishtu kapitala srbije i nemaczke [Quality of Market Risk Measures on Serbian and German Capital Market]. Proceedings of International science conference Quality leads to Europe held in Bijeljina, Bosnia and Herzegovina April 1, 2013. PMid:19461241

Živković, S. (2006). Applying Hybrid Approach to calculating VaR in Croatia. Proceedings of the International Conference „From Transition to Sustainable Development: The Path to European Integration“ held in Sarajevo, Bosnia and Herzegovina, October 12-13, 2006. (p. 50-71). Sarajevo, Bosnia: Faculty of Economics in Sarajevo.

Živković, S. (2006). Implications of Measuring VaR using Historical simulation; an Example of

Zagreb Stock Exchange index – CROBEX. In Roufagalas, J. (Ed.), Resource Allocation and Institutions: Explorations in Economics, Finance and Law (p. 367-389). Athens, Greece: Athens Institute for Education and Research.

Živković, S. (2007). Testing Popular VaR Models in EU New Member and Candidate States. Journal of Economics and Business, Vol. 25, No. 2, 325-346. Rijeka, Croatia: Rijeka Faculty of Economics.