Risk²: Measuring the Risk in Value at Risk

Abstract

The recent derivatives disasters have focused the attention of the finance industry on the need to control financial risks better. This search has led to a uniform measure of risk called value at risk (VAR), which is the expected worst loss over a given horizon at a given confidence level. VAR numbers, however, are themselves affected by sampling variation, or “estimation risk”—thus, the risk in value at risk itself. Nevertheless, given these limitations, VAR is an indispensable tool to control financial risks. This article lays out the statistical methodology for analyzing estimation error in VAR and shows how to improve the accuracy of VAR estimates.