TY - JOUR
T1 - VaR is subject to a significant positive bias
AU - Inui, Koji
AU - Kijima, Masaaki
AU - Kitano, Atsushi
N1 - Funding Information:
This research is supported in part by Daiwa Securities Group Inc.
PY - 2005/5/15
Y1 - 2005/5/15
N2 - 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 fat-tail distributions.
AB - 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 fat-tail distributions.
KW - Concave ordering
KW - Harrell-Davis estimator
KW - Historical simulation
KW - Value-at-risk
UR - http://www.scopus.com/inward/record.url?scp=17444424205&partnerID=8YFLogxK
U2 - 10.1016/j.spl.2005.02.001
DO - 10.1016/j.spl.2005.02.001
M3 - Article
AN - SCOPUS:17444424205
VL - 72
SP - 299
EP - 311
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
SN - 0167-7152
IS - 4
ER -