Robustness and Sensitivity Analysis of Risk Measurement Procedures

Columbia University Center for Financial Engineering, Financial Engineering Report No. 2007-06

33 Pages Posted: 24 Jan 2008 Last revised: 19 Apr 2010

See all articles by Rama Cont

Rama Cont

University of Oxford

Romain Deguest

Fundvisory

Giacomo Scandolo

University of Verona - Department of Economics

Date Written: January 1, 2008

Abstract

Measuring the risk of a financial portfolio involves two steps: estimating the loss distribution of the portfolio from available observations and computing a "risk measure" which summarizes the risk of the portfolio. We define the notion of "risk measurement procedure", which includes both of these steps, and study the robustness of risk measurement procedures and their sensitivity to a change in the data set. After introducing a rigorous definition of 'robustness' of a risk measurement procedure, we illustrate the presence of a conflict between subadditivity and robustness of risk measurement procedures. We propose a measure of sensitivity for risk measurement procedures and compute the sensitivity function of various examples of risk estimators used in financial risk management, showing that the same risk measure may exhibit quite different sensitivities depending on the estimation procedure used. Our results illustrate in particular that using historical Value at Risk leads to a more robust procedure for risk measurement than recently proposed alternatives like CVaR. We also propose other risk measurement procedures which possess the robustness property.

Keywords: risk measure, Value at Risk, statistical estimation, robustness

JEL Classification: C13, G10

Suggested Citation

Cont, Rama and Deguest, Romain and Scandolo, Giacomo, Robustness and Sensitivity Analysis of Risk Measurement Procedures (January 1, 2008). Columbia University Center for Financial Engineering, Financial Engineering Report No. 2007-06 . Available at SSRN: https://ssrn.com/abstract=1086698 or http://dx.doi.org/10.2139/ssrn.1086698

Rama Cont (Contact Author)

University of Oxford ( email )

Mathematical Institute
Oxford, OX2 6GG
United Kingdom

HOME PAGE: http://https://www.maths.ox.ac.uk/people/rama.cont

Romain Deguest

Fundvisory ( email )

112 rue la Boetie
Paris, 75008
France

HOME PAGE: http://www.fundvisory.com/

Giacomo Scandolo

University of Verona - Department of Economics ( email )

Via dell'Artigliere, 8
37129 Verona
Italy

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