Testing the Validity of Value-at-Risk Measures

Abstract

Value at Risk (<VaR >) is a notion meant to measure the risk linked to the holding of an asset or a portfolio of diverse assets. It is defined as the amount of money that one might lose with a certain confidence level and within a given time horizon. It is used by bankers because it allows them to measure, compare and consolidate “risk” that is linked to their trading activities. As it has recently been recommended to bankers by many financial institutions, it may increasingly become more and more widespread, with the possibility of becoming a market standard. Within a given time horizon, the portfolio return should not drop below a stated VaR number more often than predicted by the confidence interval. This paper aims to test this assertion under different methods of estimating VaR. Much of the current literature is devoted to the prediction of volatility, another measure of risk commonly used by bankers. However, the predictive power of Value-at-Risk has not been tested so far.

We show that “classical” ways of estimating VaR are valid only in reasonable ranges of confidence intervals. If bankers are looking at very low quantiles, then they might be advised to employ more sophisticated models.