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Empirical tests of parametric and non-parametric Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) measures for the Brazilian stock market index

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  • Rostagno, Luciano Martin

Abstract

This study aims to verify empirically the accuracy of parametric and non-parametric approaches in estimating Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) measures of the Brazilian stock market index (Ibovespa). The period of analysis goes from the first day of trade of 1995 to the last day of trade of 2004, which is used for estimation and test of the risk parameters. Parametric approaches assume that daily returns follow a normal and a t-distribution. Non-parametric approaches are the historical simulation and the volatility-weighted historical simulation technique. The binomial test is applied to verify if the failure rates predicted by VaR measures given by the models are acceptable and the sample differences paired test is used to evaluate the accuracy of the CVaR measures in forecasting tail losses. The results point out that the volatility-weighted historical simulation approach gives better estimates of both measures of risk. The rates of losses exceeding volatility-weighted historical simulation VaRs (VWHS-VaRs) ranged between 4.7-6.0%, at the 95% cl, and between 0.9-1.2%, at the 99% cl. For all periods of estimation used (1, 2, 3, 4, and 5 years), at the 95% cl, the sample differences paired test indicated no statistically significant differences between the VWHS-CVaR estimates and the losses beyond its VaR estimates. Risk lines for the normal and historical simulation VaR (HS-VaR) estimates presented flatness, or excessive smoothness, for large periods of estimation, and the student t VaR (T-VaR) estimates were sometimes too low or too high. For these models, short periods of estimation gave more accurate VaR estimates. For the CVaR estimates, the normal and t-distribution assumptions caused overestimation of the value of the tail losses. Finally, the HS-CVaR had similar performance of HS-VaR providing, at the 95% cl, good estimates of tail losses when short periods of estimation were used.

Suggested Citation

  • Rostagno, Luciano Martin, 2005. "Empirical tests of parametric and non-parametric Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) measures for the Brazilian stock market index," ISU General Staff Papers 2005010108000021878, Iowa State University, Department of Economics.
    • Handle: RePEc:isu:genstf:2005010108000021878
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