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Instability Of Portfolio Optimization Under Coherent Risk Measures

Author

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  • IMRE KONDOR

    (Collegium Budapest — Institute for Advanced Study, Szentháromság u. 2, H-1014 Budapest, Hungary;
    Department of Physics of Complex Systems, Eötvös University, Pázmány Péter Sétány 1/A, H-1117 Budapest, Hungary)

  • ISTVÁN VARGA-HASZONITS

    (Department of Physics of Complex Systems, Eötvös University, Pázmány Péter Sétány 1/A, H-1117 Budapest, Hungary;
    Analytics Department of Fixed Income Division, Morgan Stanley Hungary Analytics, Deák Ferenc u. 15, H-1052 Budapest, Hungary)

Abstract

It is shown that the axioms for coherent risk measures imply that whenever there is a pair of portfolios such that one of them dominates the other in a given sample (which happens with finite probability even for large samples), then there is no optimal portfolio under any coherent measure on that sample, and the risk measure diverges to minus infinity. This instability was first discovered in the special example of Expected Shortfall which is used here both as an illustration and as a springboard for generalization.

Suggested Citation

  • Imre Kondor & István Varga-Haszonits, 2010. "Instability Of Portfolio Optimization Under Coherent Risk Measures," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 425-437.
    • Handle: RePEc:wsi:acsxxx:v:13:y:2010:i:03:n:s0219525910002591
    DOI: 10.1142/S0219525910002591
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    References listed on IDEAS

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    1. Sverre Grepperud & Pål Andreas Pedersen, 2001. "The Crowding-out of Work Ethics," Studies in Economics 0102, School of Economics, University of Kent.
    2. Pål Andreas Pedersen, 2001. "A Game Theoretical Approach to Road Safety," Studies in Economics 0105, School of Economics, University of Kent.
    3. Carlo Acerbi & Claudio Nordio & Carlo Sirtori, 2001. "Expected Shortfall as a Tool for Financial Risk Management," Papers cond-mat/0102304, arXiv.org.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
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    Cited by:

    1. Fabio Caccioli & Imre Kondor & G'abor Papp, 2015. "Portfolio Optimization under Expected Shortfall: Contour Maps of Estimation Error," Papers 1510.04943, arXiv.org.
    2. Farkas, Walter & Fringuellotti, Fulvia & Tunaru, Radu, 2020. "A cost-benefit analysis of capital requirements adjusted for model risk," Journal of Corporate Finance, Elsevier, vol. 65(C).
    3. Caccioli, Fabio & Kondor, Imre & Papp, Gábor, 2015. "Portfolio optimization under expected shortfall: contour maps of estimation error," LSE Research Online Documents on Economics 119463, London School of Economics and Political Science, LSE Library.
    4. Imre Kondor & Fabio Caccioli & G'abor Papp & Matteo Marsili, 2015. "Contour map of estimation error for Expected Shortfall," Papers 1502.06217, arXiv.org.
    5. Fabio Caccioli & Imre Kondor & G'abor Papp, 2015. "Portfolio Optimization under Expected Shortfall: Contour Maps of Estimation Error," Papers 1510.04943, arXiv.org.
    6. Papp, Gábor & Caccioli, Fabio & Kondor, Imre, 2019. "Bias-variance trade-off in portfolio optimization under expected shortfall with ℓ 2 regularization," LSE Research Online Documents on Economics 100294, London School of Economics and Political Science, LSE Library.
    7. Fabio Caccioli & Imre Kondor & Matteo Marsili & Susanne Still, 2014. "$L_p$ regularized portfolio optimization," Papers 1404.4040, arXiv.org.
    8. Istvan Varga-Haszonits & Fabio Caccioli & Imre Kondor, 2016. "Replica approach to mean-variance portfolio optimization," Papers 1606.08679, arXiv.org.
    9. Papp, Gábor & Kondor, Imre & Caccioli, Fabio, 2021. "Optimizing expected shortfall under an ℓ1 constraint—an analytic approach," LSE Research Online Documents on Economics 111051, London School of Economics and Political Science, LSE Library.
    10. Imre Kondor, 2014. "Estimation Error of Expected Shortfall," Papers 1402.5534, arXiv.org.
    11. Varga-Haszonits, Istvan & Caccioli, Fabio & Kondor, Imre, 2016. "Replica approach to mean-variance portfolio optimization," LSE Research Online Documents on Economics 68955, London School of Economics and Political Science, LSE Library.
    12. Axel Pruser & Imre Kondor & Andreas Engel, 2021. "Aspects of a phase transition in high-dimensional random geometry," Papers 2105.04395, arXiv.org, revised Jun 2021.
    13. G'abor Papp & Fabio Caccioli & Imre Kondor, 2016. "Bias-variance trade-off in portfolio optimization under Expected Shortfall with $\ell_2$ regularization," Papers 1602.08297, arXiv.org, revised Jul 2018.
    14. Fabio Caccioli & Imre Kondor & Matteo Marsili & Susanne Still, 2016. "Liquidity Risk And Instabilities In Portfolio Optimization," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-28, August.

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    More about this item

    Keywords

    Coherent risk measures; portfolio optimization; expected shortfall; financial risk; estimation; 89.65.Gh; 89.75.-k; 02.60.Nm; G11; C13; D81;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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