Do Realistic Distribution Assumptions Improve Risk Estimates? A Long-Term Out-of-Sample Perspective on Risk Management
34 Pages Posted: 19 May 2003
Date Written: February 11, 2003
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.
Keywords: VaR back-test, Normal Inverse Gaussian distribution, GARCH
JEL Classification: C16, C52
Suggested Citation: Suggested Citation