Backtesting Aggregate Risk

This paper proposes the implementation of a VaR backtesting procedure able to overcome the subadditivity property failure of value‐at‐risk (VaR). More precisely, we propose the implementation of a multivariate portmanteau test statistic of Ljung–Box type applied to hits collected from several trading desks or divisions at once. Simulation \exercises illustrate that this method is testing for aggregate risk, accurately accounting both for diversification (negative hit cross‐correlation) and contagion/risk spillovers (positive hit cross‐correlation). An application using profit and loss and VaR data collected for two international major banks illustrates how our proposed backtesting procedure performs in a realistic environment. Copyright 2015 John Wiley & Sons, Ltd.