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Risk Management Performance of Alternative Distribution Functions January 2002

This paper compares the risk management performance of alternative distribution functions. The results indicate that the extreme value and skewed fat-tailed distributions, such as the skewed generalized t (SGT) and inverse hyperbolic sine (IHS) distributions, improve the standard VaR models that assume normality. This is because the SGT and IHS distributions put more emphasis on the tail areas of observed frequency distributions, and hence provide good predictions of catastrophic market risks during extraordinary periods. The empirical findings lead to a firm rejection of the hypothesis that one is obliged to use the distribution of extremes only (instead of the distribution of all returns) to obtain precise VaR measures. The results based on the actual and estimated VaR thresholds as well as the likelihood ratio tests point out that the maximum likely loss of financial institutions can be more accurately estimated using the generalized extreme value and skewed fat-tailed distributions. They perform surprisingly well in capturing both the rate of occurrence and the size of extreme observations in financial markets. In addition, this article proposes a conditional VaR approach that takes into account time-varying volatility, considers the non-normality of returns, and deals with extreme events. The results indicate that the actual VaR thresholds are time-varying to a degree not captured by the conditional normal density, but precisely estimated by the conditional SGT, IHS, and extreme value distributions.