Extreme value at risk: A scenario for risk management

This paper uses the generalised extreme value (GEV) distribution to model the extreme losses that are likely to occur during market crashes, in the case of an investor who has long positions in stocks and currencies. The null hypothesis - which tests for normality of asset returns - is rejected due to asymmetry of these returns. We assume that the asymmetric behaviour and volatility of the returns are captured by the shape and scale parameters, respectively, of a GEV distribution. The data set includes stock indices for the United States, Japan, the United Kingdom, Germany, France and South Africa, and the South African rand exchange rates against the US dollar observed from 3 January 2005 to 30 December 2009. In addition, we divide this sample period into two periods: the pre-crisis period, from 3 January 2005 to 31 December 2007 and the crisis period, from 1 January 2008 to 30 December 2009. We compared the estimates of value at risk (VaR) using an extreme value theory (EVT) model, with the estimates derived from the traditional variance-covariance method and found that during the crisis the 99% extreme VaR estimates are more reliable as they lie within the Basel II green zone. These results suggest that, at higher quintiles, the VaR estimates based on EVT are reliable and more accurate than estimates from the traditional method.