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.