A new set of improved value-at-risk backtests

Abstract

We propose a new set of formal backtests for VaR-forecasts that significantly improve upon existing backtesting procedures. Our new test of unconditional coverage can be used for both directional and non-directional testing and is thus able to test separately whether a VaR-model is too conservative or underestimates the actual risk exposure. Second, we stress the importance of testing the property of independent and identically distributed (i.i.d.) VaRexceedances and propose a simple approach that explicitly tests for the presence of clusters in VaR-violation processes. Results from a simulation study indicate that our tests significantly outperform competing backtests in several distinct settings. In addition, the empirical analysis of a unique data set consisting of asset returns of an asset manager’s portfolios underline the usefulness of our new backtests especially in times of market turmoil.