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On Drawdown-Modulated Feedback Control in Stock Trading

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  • Chung-Han Hsieh
  • B. Ross Barmish
Abstract
Control of drawdown, that is, the control of the drops in wealth over time from peaks to subsequent lows, is of great concern from a risk management perspective. With this motivation in mind, the focal point of this paper is to address the drawdown issue in a stock trading context. Although our analysis can be carried out without reference to control theory, to make the work accessible to this community, we use the language of feedback systems. The takeoff point for the results to follow, which we call the Drawdown Modulation Lemma, characterizes any investment which guarantees that the percentage drawdown is no greater than a prespecified level with probability one. With the aid of this lemma, we introduce a new scheme which we call the drawdown-modulated feedback control. To illustrate the power of the theory, we consider a drawdown-constrained version of the well-known Kelly Optimization Problem which involves maximizing the expected logarithmic growth of the trader's account value. As the drawdown parameter dmax in our new formulation tends to one, we recover existing results as a special case. This new theory leads to an optimal investment strategy whose application is illustrated via an example with historical stock-price data.

Suggested Citation

  • Chung-Han Hsieh & B. Ross Barmish, 2017. "On Drawdown-Modulated Feedback Control in Stock Trading," Papers 1710.01503, arXiv.org.
    • Handle: RePEc:arx:papers:1710.01503
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    References listed on IDEAS

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    1. Leonard Maclean & Edward Thorp & William Ziemba, 2010. "Long-term capital growth: the good and bad properties of the Kelly and fractional Kelly capital growth criteria," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 681-687.
    2. Klass, Michael J. & Nowicki, Krzysztof, 2005. "The Grossman and Zhou investment strategy is not always optimal," Statistics & Probability Letters, Elsevier, vol. 74(3), pages 245-252, October.
    3. 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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    5. Sanford J. Grossman & Zhongquan Zhou, 1993. "Optimal Investment Strategies For Controlling Drawdowns," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 241-276, July.
    6. Lisa R. Goldberg & Ola Mahmoud, 2014. "Drawdown: From Practice to Theory and Back Again," Papers 1404.7493, arXiv.org, revised Sep 2016.
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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. Chung-Han Hsieh, 2020. "Generalization of Affine Feedback Stock Trading Results to Include Stop-Loss Orders," Papers 2004.12848, arXiv.org.
    3. 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.
    4. Wu, Mu-En & Tsai, Hui-Huang & Chung, Wei-Ho & Chen, Chien-Ming, 2020. "Analysis of Kelly betting on finite repeated games," Applied Mathematics and Computation, Elsevier, vol. 373(C).

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