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On the feasibility of portfolio optimization under expected shortfall

Author

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  • Stefano Ciliberti
  • Imre Kondor
  • Marc Mezard

Abstract

We address the problem of portfolio optimization under the simplest coherent risk measure, i.e. the expected shortfall. As is well known, one can map this problem into a linear programming setting. For some values of the external parameters, when the available time series is too short, portfolio optimization is ill-posed because it leads to unbounded positions, infinitely short on some assets and infinitely long on others. As first observed by Kondor and coworkers, this phenomenon is actually a phase transition. We investigate the nature of this transition by means of a replica approach.

Suggested Citation

  • Stefano Ciliberti & Imre Kondor & Marc Mezard, 2007. "On the feasibility of portfolio optimization under expected shortfall," Quantitative Finance, Taylor & Francis Journals, vol. 7(4), pages 389-396.
    • Handle: RePEc:taf:quantf:v:7:y:2007:i:4:p:389-396
    DOI: 10.1080/14697680701422089
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    1. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    2. Frey, Rudiger & McNeil, Alexander J., 2002. "VaR and expected shortfall in portfolios of dependent credit risks: Conceptual and practical insights," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1317-1334, July.
    3. Kondor, Imre & Pafka, Szilard & Nagy, Gabor, 2007. "Noise sensitivity of portfolio selection under various risk measures," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1545-1573, May.
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    Cited by:

    1. 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.
    2. Giovanni Bonaccolto & Massimiliano Caporin & Sandra Paterlini, 2018. "Asset allocation strategies based on penalized quantile regression," Computational Management Science, Springer, vol. 15(1), pages 1-32, January.
    3. Fabio Caccioli & Imre Kondor & G'abor Papp, 2015. "Portfolio Optimization under Expected Shortfall: Contour Maps of Estimation Error," Papers 1510.04943, arXiv.org.
    4. 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.
    5. Fabio Caccioli & Imre Kondor & Matteo Marsili & Susanne Still, 2014. "$L_p$ regularized portfolio optimization," Papers 1404.4040, arXiv.org.
    6. Martin Herdegen & Nazem Khan, 2020. "Mean-$\rho$ portfolio selection and $\rho$-arbitrage for coherent risk measures," Papers 2009.05498, arXiv.org, revised Jul 2021.
    7. Anastasis Kratsios, 2019. "Partial Uncertainty and Applications to Risk-Averse Valuation," Papers 1909.13610, arXiv.org, revised Oct 2019.
    8. 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.
    9. Imre Kondor, 2014. "Estimation Error of Expected Shortfall," Papers 1402.5534, arXiv.org.
    10. Joel Bun & Jean-Philippe Bouchaud & Marc Potters, 2016. "Cleaning large correlation matrices: tools from random matrix theory," Papers 1610.08104, arXiv.org.
    11. Shinzato, Takashi, 2018. "Maximizing and minimizing investment concentration with constraints of budget and investment risk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 986-993.
    12. 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.
    13. Giovanni Bonaccolto, 2021. "Quantile– based portfolios: post– model– selection estimation with alternative specifications," Computational Management Science, Springer, vol. 18(3), pages 355-383, July.
    14. Imre Kondor & Fabio Caccioli & G'abor Papp & Matteo Marsili, 2015. "Contour map of estimation error for Expected Shortfall," Papers 1502.06217, arXiv.org.
    15. Jean-Philippe Bouchaud & Matteo Marsili & Jean-Pierre Nadal, 2023. "Application of spin glass ideas in social sciences, economics and finance," Papers 2306.16165, arXiv.org.
    16. Istvan Varga-Haszonits & Fabio Caccioli & Imre Kondor, 2016. "Replica approach to mean-variance portfolio optimization," Papers 1606.08679, arXiv.org.
    17. Kristoffer Andersson & Cornelis W. Oosterlee, 2023. "D-TIPO: Deep time-inconsistent portfolio optimization with stocks and options," Papers 2308.10556, arXiv.org, revised Sep 2023.
    18. Martin Herdegen & Nazem Khan, 2022. "Mean‐ρ$\rho$ portfolio selection and ρ$\rho$‐arbitrage for coherent risk measures," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 226-272, January.
    19. 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.
    20. 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.
    21. Giovanni Bonaccolto, 2019. "Critical Decisions for Asset Allocation via Penalized Quantile Regression," Papers 1908.04697, arXiv.org.
    22. G'abor Papp & Imre Kondor & Fabio Caccioli, 2021. "Optimizing Expected Shortfall under an $\ell_1$ constraint -- an analytic approach," Papers 2103.04375, arXiv.org.
    23. 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.
    24. Imre Kondor & G'abor Papp & Fabio Caccioli, 2016. "Analytic solution to variance optimization with no short-selling," Papers 1612.07067, arXiv.org, revised Jan 2017.
    25. Thapar, Rishi & Minsky, Bernard & Obradovic, M & Tang, Qi, 2009. "Applying a global optimisation algorithm to Fund of Hedge Funds portfolio optimisation," MPRA Paper 17099, University Library of Munich, Germany.

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