イヌイ　コウジ   Inui Kouji   乾　孝治    所属   明治大学  総合数理学部    職種   専任教授
言語種別	英語
発行・発表の年月	2005/03
形態種別	学術雑誌
標題	VaR si subject to a significant positive bias
執筆形態	共著(筆頭者)
掲載誌名	Statistics & Probability Letters
巻・号・頁	72,pp.299-311
著者・共著者	Massaki Kijima, Atsushi Kitano
概要	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.