Risk Management and VaR: Comparison of the accuracy of risk measurement for different assets

Abstract

This paper investigates the performance of VaR models for seven categories of assets traded in Brazilian market. Six different VaR methodologies are tested: Normal Delta, EWMA, GARCH, Historical Simulation (HS), Monte Carlo Simulation (MC) and CVaR, which have as main differences the treatment given to volatility and the inference about the returns distribution. For the statistical results validation, are applied the Kupiec test, to evaluate the proportion of violations, and the Christoffersen test, to verify the adjustment speed of the model against market oscillations. Two analyses are made; the first one considerate an estimation window of 1000 days and the second one 252 days. For both, GARCH and CVaR have the highest number of accurately violation ratio (VR) having the good performance validated by backtesting tests. Among the assets, IFIX and IMA-B have the best performance for first analyse and Ibov for the second one. The models have low accurately loss forecast for private bond and commodities indices, which indicates that methodologies focused on market risk are not appropriate for these assets categories. The results also suggest that a smaller estimation window tends to favour the estimation of loss for high volatility assets.