Inui Kouji
   Department   Undergraduate School  , School of Interdisciplinary Mathematical Sciences
   Position   Professor
Language English
Publication Date 2005/03
Type Academic Journal
Title VaR si subject to a significant positive bias
Contribution Type Co-authored (first author)
Journal Statistics & Probability Letters
Volume, Issue, Page 72,pp.299-311
Author and coauthor Massaki Kijima, Atsushi Kitano
Details 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 Harell-Davis quantile estimator and its simulation counterpart, called the bootstrap estimator, tend to have more significant positive bias for fat-tail distributions.