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Estimating Portfolio Value at Risk with GARCH and MGARCH models

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  • Restrepo E., María Isabel

Abstract

The aim of this paper is to estimate GARCH models, univariate and multivariate, for the daily returns of a portfolio consisting of five Colombian financial market assets, in order to evaluate which shows better performance in estimating the Value at Risk of the portfolio. To calculate VaR, with a confidence level of 95%, equal weight is assigned to the assets in the portfolio. The results show that the univariate GARCH models outperform the MGARCH in estimating the VaR of the portfolio. Resumen: El objetivo de este artículo es estimar algunos modelos GARCH, univariados y multivariados, para los retornos diarios de un portafolio compuesto por cinco activos del mercado financiero colombiano, con el fin de evaluar cual muestra mejor desempeno en el cálculo del Valor en Riesgo del portafolio. Para calcular el VaR, con un nivel de confianza del 95%, se le asigna igual peso a los activos en el portafolio. Los resultados muestran que los modelos GARCH univariados tienen mejor desempeno que los MGARCH en la estimación del VaR del portafolio.

Suggested Citation

  • Restrepo E., María Isabel, 2012. "Estimating Portfolio Value at Risk with GARCH and MGARCH models," Perfil de Coyuntura Económica, Universidad de Antioquia, CIE, issue 19, pages 77-92, July.
    • Handle: RePEc:col:000165:014799
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    File URL: https://revistas.udea.edu.co/index.php/coyuntura/article/view/15557/14227
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    References listed on IDEAS

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    1. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    2. M. Angeles Carnero, 2004. "Persistence and Kurtosis in GARCH and Stochastic Volatility Models," Journal of Financial Econometrics, Oxford University Press, vol. 2(2), pages 319-342.
    3. Luis Fernando Melo Velandia & Oscar reinaldo Becerra Camargo, 2005. "Medidas de Riesgo, Características y Técnicas de Medición: Una Aplicación del VAR y el ES a la Tasa Interbancaria de Colombia," Borradores de Economia 343, Banco de la Republica de Colombia.
    4. Daniel B. Nelson, 1994. "Asymptotically Optimal Smoothing with ARCH Models," NBER Technical Working Papers 0161, National Bureau of Economic Research, Inc.
    5. R. F. Engle & A. J. Patton, 2001. "What good is a volatility model?," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 237-245.
    6. Bera, Anil K. & Kim, Sangwhan, 2002. "Testing constancy of correlation and other specifications of the BGARCH model with an application to international equity returns," Journal of Empirical Finance, Elsevier, vol. 9(2), pages 171-195, March.
    7. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    More about this item

    Keywords

    Modelos GARCH; Modelos MGARCH; Valor en Riesgo;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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