Performance and conservatism of monthly FHS VaR: An international investigation

This study examines 16 models of monthly Value-at-Risk (VaR) for three equity indices with an emphasis on the filtered historical simulation (FHS) technique. We investigate the importance of historical simulation versus a parametrized approach, the presence of filter versus a static modeling of the return distribution, the choice of GARCH versus RiskMetrics conditional variances and the use of monthly versus daily data sampling frequencies. Tests for unconditional and conditional coverage and for independence show that two daily GARCH-type FHS models perform the best. The most conservative daily FHS model, an asymmetric GARCH specification, indicates that the CRSP value-weighted index, the DAX index and the NIKKEI 225 index have a 5% probability of a respective loss averaging at least 6.9%, 8.7% and 9.3% of their value over one month.