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Probability distribution of drawdowns in risky investments

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  • Maslov, Sergei
  • Zhang, Yi-Cheng

Abstract

We study the risk criterion for investments based on the drawdown from the maximal value of the capital in the past. Depending on investor's risk attitude, thus his risk exposure, we find that the distribution of these drawdowns follows a general power law. In particular, if the risk exposure is Kelly-optimal, the exponent of this power law has the borderline value of 2, i.e. the average drawdown is just about to diverge.

Suggested Citation

  • Maslov, Sergei & Zhang, Yi-Cheng, 1999. "Probability distribution of drawdowns in risky investments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 262(1), pages 232-241.
    • Handle: RePEc:eee:phsmap:v:262:y:1999:i:1:p:232-241
    DOI: 10.1016/S0378-4371(98)00416-6
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    Cited by:

    1. Ren, Fei & Zhong, Li-Xin, 2012. "The price impact asymmetry of institutional trading in the Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2667-2677.
    2. Ingve Simonsen & Mogens H. Jensen & Anders Johansen, 2002. "Optimal Investment Horizons," Papers cond-mat/0202352, arXiv.org.
    3. Fei Ren & Li-Xin Zhong, 2011. "Price impact asymmetry of institutional trading in Chinese stock market," Papers 1110.3133, arXiv.org.
    4. Hendrik J. Blok, 2000. "On the nature of the stock market: Simulations and experiments," Papers cond-mat/0010211, arXiv.org.

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