An empirical evaluation of Value at Risk

Abstract: In light of the recent financial crisis, risk management has become a very current issue. One of the most intuitive and comprehendible risk measures is Value at Risk (VaR). VaR puts a monetary value on the risk that arises from holding an asset and is defined as the “the worst loss over a target horizon with a given level of confidence”. There are currently numerous techniques for calculating VaR on the market and no standard is set on how it should be done. This can make the field of VaR hard to overlook for someone not initiated in the world of econometrics. In this paper we examine three basic widely used approaches used to calculate VaR. The approaches examined are the non Historical Simulation approach, the GARCH approach and the Moving Average approach. This paper has two main purposes, the first is to test the different approaches and compare them to each other in terms of accuracy. The second is to analyze the results and see if any conclusions can be drawn from the accuracy of the approach with respect to the return characteristics of the underlying assets. The accuracy of a VaR approach is tested by the number of VaR breaks that it produces i.e. the number of times that the observed asset return exceeds the predicted VaR. The number of VaR breaks is evaluated with the Kupiec test which defines an interval of VaR breaks in which the approach must perform to be accepted. By the term “asset return characteristics” we mean the statistical properties of the returns of the assets such as volatility, kurtosis and skewness. The study is conducted on three fundamentally different assets, Brent crude oil, OMXs 30 and Swedish three months treasury bills. Daily return data has been collected starting from January 1st 1987 to September 30th 2008 for all the assets. Observations spanning from 1987 to 1995 will be used as historical input for the approaches and observations spanning from 1996 to September 30th 2008 will be the comparative period in which the approaches performance will be measured. The results of the study show that none of the three approaches are superior to the others and that more complex approaches do not guarantee more accurate results. Instead it seems that the characteristics of the asset returns in combination with the desired confidence level determine how well a certain approach performs on a certain asset. We show that the choice of VaR approach should be evaluated individually depending on the assets to which it is to be applied.