Análise da Coerência de Medidas de Risco no Mercado Brasileiro de Ações e Desenvolvimento de uma Metodologia Híbrida para o Expected Shortfall

This work seeks to analyze empirically the coherence of the VaR and the Expected Shortfall by the definition of Artzner et al. (1997) at the Brazilian Stock Market (Bovespa), calculated with three methodologies: the historical simulation, the analytical approach with EWMA volatility from RiskMetricsTM and the hybrid approach developed by Boudoukh et al. (1998). The sample includes the ten most traded stocks of Bovespa in November 2003 with prices covering the period from July 4th 1994 through October 31st 2003. For the purpose of backtesting, we use the test developed in Kupiec (1995) for the VaR, and the tail test elaborated in Berkowitz (2001) for the Expected Shortfall. The values of the Expected Shortfall, calculated with the three methodologies, are compared using the following criteria: the test developed in Pitman (1937), the simple mean error and the mean square error. The results show that the hybrid approach gives the closest Expected Shortfall to the loss that occurs when the VaR is violated.