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Risk minimization through portfolio replication

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  • S. Ciliberti
  • M. Mézard

Abstract

We use a replica approach to deal with portfolio optimization problems. A given risk measure is minimized using empirical estimates of asset values correlations. We study the phase transition which happens when the time series is too short with respect to the size of the portfolio. We also study the noise sensitivity of portfolio allocation when this transition is approached. We consider explicitely the cases where the absolute deviation and the conditional value-at-risk are chosen as a risk measure. We show how the replica method can study a wide range of risk measures, and deal with various types of time series correlations, including realistic ones with volatility clustering. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Suggested Citation

  • S. Ciliberti & M. Mézard, 2007. "Risk minimization through portfolio replication," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 57(2), pages 175-180, May.
    • Handle: RePEc:spr:eurphb:v:57:y:2007:i:2:p:175-180
    DOI: 10.1140/epjb/e2007-00130-7
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    References listed on IDEAS

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    1. 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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    Citations

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    Cited by:

    1. Takashi Shinzato, 2014. "Self-Averaging Property of Minimal Investment Risk of Mean-Variance Model," Papers 1404.5222, arXiv.org, revised Apr 2014.
    2. Fabio Caccioli & Imre Kondor & G'abor Papp, 2015. "Portfolio Optimization under Expected Shortfall: Contour Maps of Estimation Error," Papers 1510.04943, arXiv.org.
    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. Fabio Caccioli & Imre Kondor & G'abor Papp, 2015. "Portfolio Optimization under Expected Shortfall: Contour Maps of Estimation Error," Papers 1510.04943, arXiv.org.
    5. Jerome Garnier-Brun & Michael Benzaquen & Stefano Ciliberti & Jean-Philippe Bouchaud, 2021. "A new spin on optimal portfolios and ecological equilibria," Papers 2104.00668, arXiv.org, revised Oct 2021.
    6. Takashi Shinzato & Muneki Yasuda, 2015. "Belief Propagation Algorithm for Portfolio Optimization Problems," PLOS ONE, Public Library of Science, vol. 10(8), pages 1-10, August.
    7. 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.
    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. 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.
    11. Takashi Shinzato, 2015. "Self-Averaging Property of Minimal Investment Risk of Mean-Variance Model," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-24, July.
    12. 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.
    13. G'abor Papp & Imre Kondor & Fabio Caccioli, 2021. "Optimizing Expected Shortfall under an $\ell_1$ constraint -- an analytic approach," Papers 2103.04375, arXiv.org.
    14. Cerqueti, Roy & Giacalone, Massimiliano & Panarello, Demetrio, 2019. "A Generalized Error Distribution Copula-based method for portfolios risk assessment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 687-695.
    15. Jerome Garnier-Brun & Michael Benzaquen & Stefano Ciliberti & Jean-Philippe Bouchaud, 2021. "A new spin on optimal portfolios and ecological equilibria," Post-Print hal-03378915, HAL.
    16. 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.
    17. 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.

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