Coherent risk measures alone are ineffective in constraining portfolio losses
File(s)
Accepted version
Author(s)
Armstrong, John
Brigo, Damiano
Type
Journal Article
Abstract
We show that coherent risk measures alone are ineffective in curbing the behaviour of investors with
limited liability or excessive tail-risk seeking behaviour if the market admits statistical arbitrage opportunities which we term ρ-arbitrage for a risk measure ρ. We show how to determine analytically whether
such ρ-arbitrage portfolios exist in complete markets and in the Markowitz model. We also consider realistic numerical examples of incomplete markets and determine whether Expected-Shortfall arbitrage
exists in these markets. We find that the answer depends heavily upon the probability model selected by
the risk manager but that it is certainly possible for expected shortfall constraints to be ineffective in realistic markets. Since value at risk constraints are weaker than expected shortfall constraints, our results
can be applied to value at risk.
limited liability or excessive tail-risk seeking behaviour if the market admits statistical arbitrage opportunities which we term ρ-arbitrage for a risk measure ρ. We show how to determine analytically whether
such ρ-arbitrage portfolios exist in complete markets and in the Markowitz model. We also consider realistic numerical examples of incomplete markets and determine whether Expected-Shortfall arbitrage
exists in these markets. We find that the answer depends heavily upon the probability model selected by
the risk manager but that it is certainly possible for expected shortfall constraints to be ineffective in realistic markets. Since value at risk constraints are weaker than expected shortfall constraints, our results
can be applied to value at risk.
Date Issued
2022-07-01
Date Acceptance
2021-09-11
Citation
Journal of Banking & Finance, 2022, 140
ISSN
0378-4266
Publisher
Elsevier BV
Journal / Book Title
Journal of Banking & Finance
Volume
140
Copyright Statement
© 2021 Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/
Identifier
https://www.sciencedirect.com/science/article/pii/S0378426621002673?via%3Dihub
Subjects
Finance
0102 Applied Mathematics
1401 Economic Theory
1502 Banking, Finance and Investment
Publication Status
Published
Article Number
ARTN 106315
Date Publish Online
2021-09-13