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Portfolio Theory For "Fat Tails"

Author

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  • D. SORNETTE

    (Institute of Geophysics and Planetary Physics and Department of Earth and Space Science, University of California, Los Angeles, California 90095, USA;
    Laboratoire de Physique de la Matière Condensée, CNRS UMR6622 and Université des Sciences, B.P. 70, Parc Valrose, 06108 Nice Cedex 2, France)

  • J. V. ANDERSEN

    (Nordic Institute for Theoretical Physics, Blegdamsvej 17, DK-2100 Copenhagen, Denmark)

  • P. SIMONETTI

    (Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089-0484, USA)

Abstract

We introduce a faithful representation of the heavy tail multivariate distribution of asset returns, as parsimonious as the Gaussian framework. Using calculation techniques of functional integration and Feynman diagrams borrowed from particle physics, we characterize precisely, through its cumulants of high order, the distribution of wealth variations of a portfolio composed of an arbitrary mixture of assets. This approach makes quantitative and rigorous the well-known fact that minimizing the variance, i.e. the relatively "small" risks, often increases larger risks as measured by higher normalized cumulants and the Value-at-Risk.

Suggested Citation

  • D. Sornette & J. V. Andersen & P. Simonetti, 2000. "Portfolio Theory For "Fat Tails"," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 523-535.
    • Handle: RePEc:wsi:ijtafx:v:03:y:2000:i:03:n:s0219024900000504
    DOI: 10.1142/S0219024900000504
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    Citations

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    Cited by:

    1. Y. Malevergne & V. Pisarenko & D. Sornette, 2006. "The modified weibull distribution for asset returns: reply," Quantitative Finance, Taylor & Francis Journals, vol. 6(6), pages 451-451.
    2. Y. Malevergne & D. Sornette, 2001. "General framework for a portfolio theory with non-Gaussian risks and non-linear correlations," Papers cond-mat/0103020, arXiv.org.
    3. Y. Malevergne & D. Sornette, 2003. "Testing the Gaussian copula hypothesis for financial assets dependences," Quantitative Finance, Taylor & Francis Journals, vol. 3(4), pages 231-250.
    4. Gzyl, Henryk & ter Horst, Enrique & Molina, Germán, 2019. "A model-free, non-parametric method for density determination, with application to asset returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 210-221.
    5. Chen, Qian & Gerlach, Richard H., 2013. "The two-sided Weibull distribution and forecasting financial tail risk," International Journal of Forecasting, Elsevier, vol. 29(4), pages 527-540.
    6. Roberta Fiori & Simonetta Iannotti, 2006. "Scenario Based Principal Component Value-at-Risk: an Application to Italian Banks' Interest Rate Risk Exposure," Temi di discussione (Economic working papers) 602, Bank of Italy, Economic Research and International Relations Area.
    7. repec:dau:papers:123456789/9298 is not listed on IDEAS
    8. Davies, G.B. & Satchell, S.E., 2004. "Continuous Cumulative Prospect Theory and Individual Asset Allocation," Cambridge Working Papers in Economics 0467, Faculty of Economics, University of Cambridge.
    9. Jorge M. Uribe, 2018. "“Scaling Down Downside Risk with Inter-Quantile Semivariances”," IREA Working Papers 201826, University of Barcelona, Research Institute of Applied Economics, revised Oct 2018.
    10. Christian Bongiorno & Marco Berritta, 2023. "Optimal Covariance Cleaning for Heavy-Tailed Distributions: Insights from Information Theory," Papers 2304.14098, arXiv.org, revised Apr 2023.
    11. Y. Malevergne & D. Sornette, 2002. "Investigating Extreme Dependences: Concepts and Tools," Papers cond-mat/0203166, arXiv.org.
    12. Marie Brière & Jean-David Fermanian & Hassan Malongo & Ombretta Signori, 2012. "Volatility Strategies for Global and Country Specific European Investors," Post-Print hal-01494509, HAL.

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