Rev Quant Finan Acc (2006) 27:27–46
Evaluating effects of excess kurtosis on VaR estimates:
Evidence for international stock indices
J. Samuel Baixauli · Susana Alvarez
Springer Science+ Business Media, LLC 2006
Abstract The calculus of VaR involves dealing with the conﬁdence level, the time horizon
and the true underlying conditional distribution function of asset returns. In this paper, we
shall examine the effects of using a speciﬁc distribution function that ﬁts well the low-
tail data of the observed distribution of asset returns on the accuracy of VaR estimates. In
our analysis, we consider some distributional forms characterized by capturing the excess
kurtosis characteristic of stock return distributions and we compare their performance using
some international stock indices.
Keywords Value at risk · Excess kurtosis · Low-tail behaviour · Nonparametric
goodness-of-ﬁt tests · Parametric bootstrap
JEL Classiﬁcation C15
Value-at-Risk (hereafter, VaR) is a popular measure of market risk, employed in the ﬁnancial
industry for both internal control and regulatory reporting. For instance, since 1998 U.S.
banks and bank holding companies with signiﬁcant amounts of trading activity are subject
to market risk requirements. They have been required to hold capital against their deﬁned
market risk exposures, and the capital charges are a function of banks’ own VaR estimates.
The evaluation of the accuracy of the models underlying VaR estimates is very important
Address for correspondence: J. Samuel Baixauli, Departamento de Organizacion de Empresas y Finanzas,
Facultad de Economia y Empresa, 30100 Campus de Espinardo, Murcia, (Spain). Tel: 0034968367819, Fax:
0034968367537, e-mail: firstname.lastname@example.org. Susana Alvarez, Departamento de Metodos Cuantitativos para la
Economia, Facultad de Economia y Empresa, 30100 Campus de Espinardo, Murcia (Spain).
Tel: 0034968367902, Fax: 0034968367905, email: email@example.com.
J. S. Baixauli (
Department of Management and Finance, University of Murcia (Spain)
Department of Quantitative Methods for the Economy, University of Murcia (Spain)