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Comparison of Value at Risk (VaR) Multivariate Forecast Models

Author

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  • Fernanda Maria Müller

    (Business School, Federal University of Rio Grande do Sul)

  • Marcelo Brutti Righi

    (Business School, Federal University of Rio Grande do Sul)

Abstract

We investigate the performance of VaR (Value at Risk) forecasts, considering different multivariate models: HS (Historical Simulation), DCC-GARCH (Dynamic Conditional Correlation-Generalized Autoregressive Conditional Heteroskedasticity) with normal and Student’s t distribution, GO-GARCH (Generalized Orthogonal-Generalized Autoregressive Conditional Heteroskedasticity), and copulas Vine (C-Vine, D-Vine, and R-Vine). For copula models, we consider that marginal distribution follow normal, Student’s t and skewed Student’s t distribution. We assessed the performance of the models using stocks belonging to the Ibovespa index during the period from January 2012 to April 2022. We build portfolios with 6 and 12 stocks considering two strategies to form the portfolio weights. We use a rolling estimation window of 500 and 1000 observations and 1%, 2.5%, and 5% as significance levels for the risk estimation. To evaluate the quality of the risk forecasts, we compute the realized loss and cost. Our results show that the performance of the models is sensitive to the use of different significance levels, rolling windows, and strategies to determine portfolio weights. Furthermore, we find that the model that presents the best trade-off between the costs from risk overestimation and underestimation does not coincide with the model suggested by the realized loss.

Suggested Citation

  • Fernanda Maria Müller & Marcelo Brutti Righi, 2024. "Comparison of Value at Risk (VaR) Multivariate Forecast Models," Computational Economics, Springer;Society for Computational Economics, vol. 63(1), pages 75-110, January.
    • Handle: RePEc:kap:compec:v:63:y:2024:i:1:d:10.1007_s10614-022-10330-x
    DOI: 10.1007/s10614-022-10330-x
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    1. Victor DeMiguel & Lorenzo Garlappi & Raman Uppal, 2009. "Optimal Versus Naive Diversification: How Inefficient is the 1-N Portfolio Strategy?," The Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1915-1953, May.
    2. Tiwari, Aviral Kumar & Trabelsi, Nader & Alqahtani, Faisal & Raheem, Ibrahim D., 2020. "Systemic risk spillovers between crude oil and stock index returns of G7 economies: Conditional value-at-risk and marginal expected shortfall approaches," Energy Economics, Elsevier, vol. 86(C).
    3. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    4. Righi, Marcelo Brutti & Ceretta, Paulo Sergio, 2015. "A comparison of Expected Shortfall estimation models," Journal of Economics and Business, Elsevier, vol. 78(C), pages 14-47.
    5. Patton, Andrew J. & Ziegel, Johanna F. & Chen, Rui, 2019. "Dynamic semiparametric models for expected shortfall (and Value-at-Risk)," Journal of Econometrics, Elsevier, vol. 211(2), pages 388-413.
    6. Rouatbi, Wael & Demir, Ender & Kizys, Renatas & Zaremba, Adam, 2021. "Immunizing markets against the pandemic: COVID-19 vaccinations and stock volatility around the world," International Review of Financial Analysis, Elsevier, vol. 77(C).
    7. Evangelos Vasileiou & Aristeidis Samitas & Maria Karagiannaki & Jagadish Dandu, 2021. "Health risk and the efficient market hypothesis in the time of COVID-19," International Review of Applied Economics, Taylor & Francis Journals, vol. 35(2), pages 210-223, March.
    8. Pérignon, Christophe & Smith, Daniel R., 2010. "The level and quality of Value-at-Risk disclosure by commercial banks," Journal of Banking & Finance, Elsevier, vol. 34(2), pages 362-377, February.
    9. Hartz, Christoph & Mittnik, Stefan & Paolella, Marc, 2006. "Accurate value-at-risk forecasting based on the normal-GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2295-2312, December.
    10. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    11. Steven Kou & Xianhua Peng, 2016. "On the Measurement of Economic Tail Risk," Operations Research, INFORMS, vol. 64(5), pages 1056-1072, October.
    12. Gregor Weiß, 2013. "Copula-GARCH versus dynamic conditional correlation: an empirical study on VaR and ES forecasting accuracy," Review of Quantitative Finance and Accounting, Springer, vol. 41(2), pages 179-202, August.
    13. Laura Garcia‐Jorcano & Alfonso Novales, 2021. "Volatility specifications versus probability distributions in VaR forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(2), pages 189-212, March.
    14. Tse, Y K & Tsui, Albert K C, 2002. "A Multivariate Generalized Autoregressive Conditional Heteroscedasticity Model with Time-Varying Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 351-362, July.
    15. Lanne, Markku & Saikkonen, Pentti, 2007. "A Multivariate Generalized Orthogonal Factor GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 61-75, January.
    16. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    17. Marco Geidosch & Matthias Fischer, 2016. "Application of Vine Copulas to Credit Portfolio Risk Modeling," JRFM, MDPI, vol. 9(2), pages 1-15, June.
    18. Keith Kuester & Stefan Mittnik & Marc S. Paolella, 2006. "Value-at-Risk Prediction: A Comparison of Alternative Strategies," Journal of Financial Econometrics, Oxford University Press, vol. 4(1), pages 53-89.
    19. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    20. Johanna F. Ziegel, 2016. "Coherence And Elicitability," Mathematical Finance, Wiley Blackwell, vol. 26(4), pages 901-918, October.
    21. Müller, Fernanda Maria & Santos, Samuel Solgon & Gössling, Thalles Weber & Righi, Marcelo Brutti, 2022. "Comparison of risk forecasts for cryptocurrencies: A focus on Range Value at Risk," Finance Research Letters, Elsevier, vol. 48(C).
    22. Kole, Erik & Koedijk, Kees & Verbeek, Marno, 2007. "Selecting copulas for risk management," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2405-2423, August.
    23. Fernanda Maria Müller & Marcelo Brutti Righi, 2018. "Numerical comparison of multivariate models to forecasting risk measures," Risk Management, Palgrave Macmillan, vol. 20(1), pages 29-50, February.
    24. Marcelo Brutti Righi & Paulo Sergio Ceretta, 2013. "Pair Copula Construction based Expected Shortfall estimation," Economics Bulletin, AccessEcon, vol. 33(2), pages 1067-1072.
    25. Pritsker, Matthew, 2006. "The hidden dangers of historical simulation," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 561-582, February.
    26. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    27. Righi, Marcelo Brutti & Borenstein, Denis, 2018. "A simulation comparison of risk measures for portfolio optimization," Finance Research Letters, Elsevier, vol. 24(C), pages 105-112.
    28. Roy van der Weide, 2002. "GO-GARCH: a multivariate generalized orthogonal GARCH model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 549-564.
    29. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    30. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    31. Carlo Marinelli & Stefano D'Addona & Svetlozar T. Rachev, 2007. "A Comparison Of Some Univariate Models For Value-At-Risk And Expected Shortfall," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(06), pages 1043-1075.
    32. Steven Kou & Xianhua Peng & Chris C. Heyde, 2013. "External Risk Measures and Basel Accords," Mathematics of Operations Research, INFORMS, vol. 38(3), pages 393-417, August.
    33. Fedya Telmoudi & Mohamed EL Ghourabi & Mohamed Limam, 2016. "On conditional risk estimation considering model risk," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(8), pages 1386-1399, June.
    34. Carlos Trucíos & Aviral K. Tiwari & Faisal Alqahtani, 2020. "Value-at-risk and expected shortfall in cryptocurrencies’ portfolio: a vine copula–based approach," Applied Economics, Taylor & Francis Journals, vol. 52(24), pages 2580-2593, May.
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