Estimation and Decomposition of Downside Risk for Portfolios with Non-Normal Returns

Journal of Risk, Vol. 11, No. 2, pp. 79-103, 2008

33 Pages Posted: 12 Nov 2007 Last revised: 4 Mar 2012

Kris Boudt

Vrije Universiteit Brussel (VUB); VU University Amsterdam

Brian G. Peterson

DV Trading

Christophe Croux

Université Libre de Bruxelles (ULB) - European Center for Advanced Research in Economics and Statistics (ECARES); Catholic University of Leuven (KUL) - Department of Applied Economics

Date Written: October 31, 2007

Abstract

Modied Value at Risk (VaR) is an estimator of VaR based on the Cornish-Fisher expansion. It is fast to compute and reliable for non-normal returns. In this paper, we introduce modified Expected Shortfall as a new analytical estimator for Expected Shortfall (ES), another popular measure of downside risk. We give all the necessary formulas for computing portfolio modified VaR and ES and for decomposing these risk measures into the contributions made by each of the portfolio holdings. This new methodology is shown to be very useful for analyzing the risk properties of portfolios of alternative investments.

Keywords: Customer lifetime value, Value, Companies, Order, Model, Product, Expected

JEL Classification: G1, G11, G14

Suggested Citation

Boudt, Kris and Peterson, Brian G. and Croux, Christophe, Estimation and Decomposition of Downside Risk for Portfolios with Non-Normal Returns (October 31, 2007). Journal of Risk, Vol. 11, No. 2, pp. 79-103, 2008. Available at SSRN: https://ssrn.com/abstract=1024151 or http://dx.doi.org/10.2139/ssrn.1024151

Kris Boudt

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
http://www.vub.ac.be/
Brussels, 1050
Belgium

VU University Amsterdam ( email )

De Boelelaan 1105
Amsterdam, ND North Holland 1081 HV
Netherlands

Brian G. Peterson (Contact Author)

DV Trading ( email )

216 W. Jackson, Suite 310
Chicago, IL 60605
United States
773-459-4973 (Phone)

Christophe Croux

Université Libre de Bruxelles (ULB) - European Center for Advanced Research in Economics and Statistics (ECARES) ( email )

Ave. Franklin D Roosevelt, 50 - C.P. 114
Brussels, B-1050
Belgium

Catholic University of Leuven (KUL) - Department of Applied Economics ( email )

Leuven, B-3000
Belgium

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