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Time-Inconsistency of VaR and Time-Consistent Alternatives

8 Pages Posted: 5 Mar 2008  

Patrick Cheridito

ETH Zurich; Swiss Finance Institute

Mitja Stadje

Tilburg University - Department of Econometrics & Operations Research

Date Written: November 2007

Abstract

We show that VaR (value-at-risk) is not time-consistent and discuss examples where this leads to dynamically inconsistent behavior. Then we propose two time-consistent alternatives to VaR. The first one is a composition of one-period VaR's. It has some of the theoretical drawbacks of static VaR and should be used with care in situations where financial positions are not normally distributed or in models with complex dependence structures. The second one is a composition of average VaR's. It is a time-consistent coherent risk measure and provides good results in any situation.

Keywords: time-consistency, value at risk, composed value at risk, composed average value at risk

JEL Classification: D81, G18

Suggested Citation

Cheridito, Patrick and Stadje, Mitja, Time-Inconsistency of VaR and Time-Consistent Alternatives (November 2007). Available at SSRN: https://ssrn.com/abstract=1098863 or http://dx.doi.org/10.2139/ssrn.1098863

Patrick Cheridito (Contact Author)

ETH Zurich ( email )

Department of Mathematics
8092 Zurich
Switzerland

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Mitja Stadje

Tilburg University - Department of Econometrics & Operations Research ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

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