VaR is subject to a significant positive bias

This article shows that value-at-risk (VaR), the most popular risk measure in financial practice, has a considerable positive bias when used for a portfolio with fat-tail distribution. The bias increases with higher confidence level, heavier tails, and smaller sample size. Also, the Harrell-Davis quantile estimator and its simulation counterpart, called the bootstrap estimator, tend to have a more significant positive bias for fattail distributions. (c) 2005 Elsevier B.V. All rights reserved.