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Have your cake and eat it too: increasing returns while lowering large risks!

Author

Listed:
  • J. V. Andersen

    (NORDITA, Denmark)

  • D. Sornette

    (CNRS/Univ. Nice France and UCLA)

Abstract

Based on a faithful representation of the heavy tail multivariate distribution of asset returns introduced previously (Sornette et al., 1998, 1999) that we extend to the case of asymmetric return distributions, we generalize the return-risk efficient frontier concept to incorporate the dimensions of large risks embedded in the tail of the asset distributions. We demonstrate that it is often possible to increase the portfolio return while decreasing the large risks as quantified by the fourth and higher order cumulants. Exact theoretical formulas are validated by empirical tests.

Suggested Citation

  • J. V. Andersen & D. Sornette, 1999. "Have your cake and eat it too: increasing returns while lowering large risks!," Papers cond-mat/9907217, arXiv.org.
    • Handle: RePEc:arx:papers:cond-mat/9907217
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    References listed on IDEAS

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    1. Jean-Philippe Bouchaud & Didier Sornette & Christian Walter & Jean-Pierre Aguilar, 1998. "Taming large events: portfolio selection for strongly fluctuating assets," Science & Finance (CFM) working paper archive 500044, Science & Finance, Capital Fund Management.
    2. Didier Sornette, 1998. "Large deviations and portfolio optimization," Papers cond-mat/9802059, arXiv.org, revised Jun 1998.
    3. J. P. Bouchaud & D. Sornette & C. Walter & J. P. Aguilar, 1998. "Taming Large Events: Optimal Portfolio Theory for Strongly Fluctuating Assets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 25-41.
    4. D. Sornette & P. Simonetti & J. V. Andersen, 1999. ""Nonlinear" covariance matrix and portfolio theory for non-Gaussian multivariate distributions," Papers cond-mat/9903203, arXiv.org.
    5. D. Sornette & J. V. Andersen & P. Simonetti, 1998. "Minimizing volatility increases large risks," Papers cond-mat/9811292, arXiv.org.
    6. Sornette, Didier, 1998. "Large deviations and portfolio optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 256(1), pages 251-283.
    7. D. Sornette & P. Simonetti & J.V. Andersen, 1999. ""Nonlinear" covariance matrix and portfolio theory for non-Gaussian multivariate distributions," Finance 9902004, University Library of Munich, Germany.
    8. Thomas Lux & Michele Marchesi, 1999. "Scaling and criticality in a stochastic multi-agent model of a financial market," Nature, Nature, vol. 397(6719), pages 498-500, February.
    9. P. Gopikrishnan & M. Meyer & L.A.N. Amaral & H.E. Stanley, 1998. "Inverse cubic law for the distribution of stock price variations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 3(2), pages 139-140, July.
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    Cited by:

    1. Sancetta, A., 2005. "Copula Based Monte Carlo Integration in Financial Problems," Cambridge Working Papers in Economics 0506, Faculty of Economics, University of Cambridge.
    2. Alessio Sancetta & Steve E. Satchell, 2007. "Changing Correlation and Equity Portfolio Diversification Failure for Linear Factor Models during Market Declines," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(3), pages 227-242.
    3. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.

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