Coherent risk measures under filtered historical simulation Kostas Giannopoulos a, * , Radu Tunaru b a UAE University, CBE P.O. Box 17555 A1 Ain, AD, United Arab Emirates b London Metropolitan University, 31 Jewry Street, London EC3N 2EY, UK Available online 29 September 2004 Abstract Recent studies have strongly criticised conventional VaR models for not providing a coher- ent risk measure. Acerbi provides the intuition for an entire family of coherent measures of risk known as ‘‘spectral risk measures’’ [Spectral measures of risk: A coherent representation of subjective risk aversion. Journal of Banking and Finance 26 (7) (2002) 1505–1518]. In this study we illustrate how the Filtered Historical Simulation [Barone-Adesi, G., Bourgoin, F., Giannopoulos, K., 1998. DonÕt look back. Risk 11, 100–104; Barone-Adesi, Giannopoulos, K., Vosper, L., 1999. VaR without correlations for non-linear portfolios. Journal of Futures Markets 19, 583–602], can provide an improved methodology for calculating the Expected Shortfall. Thereafter, we prove that these new risk measures are spectral and are coherent as well, following Acerbi. Furthermore, we provide the statistical error formula that allows to calculate the error for our model. Ó 2004 Elsevier B.V. All rights reserved. JEL classification: D81; C13 Keywords: Expected shortfall; Filtered historical simulation; Ordered statistics; Coherent measure; Spectral risk measure; Generalised extreme value distribution 0378-4266/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jbankfin.2004.08.009 * Corresponding author. E-mail address: kgiannopoulos@uaeu.ac.ae (K. Giannopoulos). Journal of Banking & Finance 29 (2005) 979–996 www.elsevier.com/locate/econbase