Do Realistic Distribution Assumptions Improve Risk Estimates? A Long-Term Out-of-Sample Perspective on Risk Management

Abstract

Empirical studies suggest that the normal distribution is inadequate to describe the fat tails associated with returns from financial data series. However, using 26,115 daily out-of-sample observations from the Dow Jones Industrial Average over the period 1898-2002, we show that it is difficult to dismiss the normal distribution as an out-of-sample assumption. Contrary to popular belief, the findings suggest that powerful statistical methods such as the flexible multi-parameter Normal Inverse Gaussian (NIG) distribution function do not transfer their superior in-sample properties to out-of-sample observations. This indicates that there is a trade-off between realism and robustness, whereby realism in-sample may introduce instability out-of-sample.