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Drawdown Measure In Portfolio Optimization

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  • ALEXEI CHEKHLOV

    (Thor Asset Management, Inc., 551 Fifth Ave., Suite 601, 6th Floor, New York, NY 10017, USA)

  • STANISLAV URYASEV

    (Department of Industrial and Systems Engineering, University of Florida, P.O. Box 116595, 303 Weil Hall, Gainesville, FL 32611-6595, USA)

  • MICHAEL ZABARANKIN

    (Department of Industrial and Systems Engineering, University of Florida, P.O. Box 116595, 303 Weil Hall, Gainesville, FL 32611-6595, USA)

Abstract

A new one-parameter family of risk measures called Conditional Drawdown (CDD) has been proposed. These measures of risk are functionals of the portfolio drawdown (underwater) curve considered in active portfolio management. For some value of the tolerance parameter α, in the case of a single sample path, drawdown functional is defined as the mean of the worst (1 - α) * 100% drawdowns. The CDD measure generalizes the notion of the drawdown functional to a multi-scenario case and can be considered as a generalization of deviation measure to a dynamic case. The CDD measure includes the Maximal Drawdown and Average Drawdown as its limiting cases. Mathematical properties of the CDD measure have been studied and efficient optimization techniques for CDD computation and solving asset-allocation problems with a CDD measure have been developed. The CDD family of risk functionals is similar to Conditional Value-at-Risk (CVaR), which is also called Mean Shortfall, Mean Excess Loss, or Tail Value-at-Risk. Some recommendations on how to select the optimal risk functionals for getting practically stable portfolios have been provided. A real-life asset-allocation problem has been solved using the proposed measures. For this particular example, the optimal portfolios for cases of Maximal Drawdown, Average Drawdown, and several intermediate cases between these two have been found.

Suggested Citation

  • Alexei Chekhlov & Stanislav Uryasev & Michael Zabarankin, 2005. "Drawdown Measure In Portfolio Optimization," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 13-58.
    • Handle: RePEc:wsi:ijtafx:v:08:y:2005:i:01:n:s0219024905002767
    DOI: 10.1142/S0219024905002767
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    References listed on IDEAS

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    1. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
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