In this note it is argued that the estimation error in Value-at-Risk predictors gives rise to underestimation of portfolio risk. We propose a simple correction and end in an empirical illustration that it is economically relevant

The estimation of risk at extreme levels of significance (such as 0.1%) can be crucial to capture the losses during market downturns, such as the global financial crisis and the COVID-19 market crash. For many existing models, it is challenging to estimate risk at extreme levels of significance....