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Drawdown: From Practice to Theory and Back Again

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  • Lisa R. Goldberg
  • Ola Mahmoud

Abstract

Maximum drawdown, the largest cumulative loss from peak to trough, is one of the most widely used indicators of risk in the fund management industry, but one of the least developed in the context of measures of risk. We formalize drawdown risk as Conditional Expected Drawdown (CED), which is the tail mean of maximum drawdown distributions. We show that CED is a degree one positive homogenous risk measure, so that it can be linearly attributed to factors; and convex, so that it can be used in quantitative optimization. We empirically explore the differences in risk attributions based on CED, Expected Shortfall (ES) and volatility. An important feature of CED is its sensitivity to serial correlation. In an empirical study that fits AR(1) models to US Equity and US Bonds, we find substantially higher correlation between the autoregressive parameter and CED than with ES or with volatility.

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  • Lisa R. Goldberg & Ola Mahmoud, 2014. "Drawdown: From Practice to Theory and Back Again," Papers 1404.7493, arXiv.org, revised Sep 2016.
    • Handle: RePEc:arx:papers:1404.7493
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Korn, Olaf & Möller, Philipp M. & Schwehm, Christian, 2019. "Drawdown measures: Are they all the same?," CFR Working Papers 19-04, University of Cologne, Centre for Financial Research (CFR).
    2. Noureddine Kouaissah & Amin Hocine, 2021. "Forecasting systemic risk in portfolio selection: The role of technical trading rules," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(4), pages 708-729, July.
    3. Lisa R. Goldberg & Saad Mouti, 2019. "Sustainable Investing and the Cross-Section of Returns and Maximum Drawdown," Papers 1905.05237, arXiv.org, revised Dec 2023.
    4. Chung-Han Hsieh & B. Ross Barmish, 2017. "On Inefficiency of Markowitz-Style Investment Strategies When Drawdown is Important," Papers 1710.01501, arXiv.org, revised Aug 2018.
    5. Philipp M. Möller, 2018. "Drawdown Measures And Return Moments," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(07), pages 1-42, November.
    6. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078, December.
    7. C. A. Valle & J. E. Beasley, 2019. "A nonlinear optimisation model for constructing minimal drawdown portfolios," Papers 1908.08684, arXiv.org.
    8. Stanislaus Maier-Paape & Qiji Jim Zhu, 2018. "A General Framework for Portfolio Theory. Part II: Drawdown Risk Measures," Risks, MDPI, vol. 6(3), pages 1-31, August.
    9. Damiano Rossello & Silvestro Lo Cascio, 2021. "A refined measure of conditional maximum drawdown," Risk Management, Palgrave Macmillan, vol. 23(4), pages 301-321, December.
    10. Stanislaus Maier-Paape & Andreas Platen & Qiji Jim Zhu, 2019. "A General Framework for Portfolio Theory. Part III: Multi-Period Markets and Modular Approach," Risks, MDPI, vol. 7(2), pages 1-31, June.
    11. Chung-Han Hsieh & B. Ross Barmish, 2017. "On Drawdown-Modulated Feedback Control in Stock Trading," Papers 1710.01503, arXiv.org.

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