IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v74y2005i3p245-252.html
   My bibliography  Save this article

The Grossman and Zhou investment strategy is not always optimal

Author

Listed:
  • Klass, Michael J.
  • Nowicki, Krzysztof

Abstract

Grossman and Zhou [1993. Optimal investment strategies for controlling drawdowns. Math. Finance 3, 241-276] proposed a strategy to maximize the asymptotic long-run growth rate of one's fortune Ft subject to its never falling below , where 0[less-than-or-equals, slant][lambda][less-than-or-equals, slant]1 is a fixed constant chosen by the investor and r is a fixed, known, non-negative, continuously compounded interest rate on invested capital. In this paper we show that the strategy proposed in Grossman and Zhou does not retain its optimal long-run growth property when generalized to the discrete-time setting.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:74:y:2005:i:3:p:245-252
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(05)00164-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sanford J. Grossman & Zhongquan Zhou, 1993. "Optimal Investment Strategies For Controlling Drawdowns," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 241-276, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Steven D. Moffitt, 2018. "Why Markets are Inefficient: A Gambling "Theory" of Financial Markets For Practitioners and Theorists," Papers 1801.01948, arXiv.org.
    2. Chung-Han Hsieh & B. Ross Barmish, 2017. "On Drawdown-Modulated Feedback Control in Stock Trading," Papers 1710.01503, arXiv.org.
    3. Vladimir Cherny & Jan Obłój, 2013. "Portfolio optimisation under non-linear drawdown constraints in a semimartingale financial model," Finance and Stochastics, Springer, vol. 17(4), pages 771-800, October.
    4. Michael J. Klass & Krzysztof Nowicki, 2010. "On The Consumption/Distribution Theorem Under The Long-Run Growth Criterion Subject To A Drawdown Constraint," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(06), pages 931-957.
    5. Chen, Xinfu & Landriault, David & Li, Bin & Li, Dongchen, 2015. "On minimizing drawdown risks of lifetime investments," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 46-54.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Neofytos Rodosthenous & Hongzhong Zhang, 2020. "When to sell an asset amid anxiety about drawdowns," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1422-1460, October.
    2. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078, October.
    3. Zbigniew Palmowski & Joanna Tumilewicz, 2017. "Fair valuation of L\'evy-type drawdown-drawup contracts with general insured and penalty functions," Papers 1712.04418, arXiv.org, revised Feb 2018.
    4. Alexander, Gordon J. & Baptista, Alexandre M., 2006. "Portfolio selection with a drawdown constraint," Journal of Banking & Finance, Elsevier, vol. 30(11), pages 3171-3189, November.
    5. Kentaro Imajo & Kentaro Minami & Katsuya Ito & Kei Nakagawa, 2020. "Deep Portfolio Optimization via Distributional Prediction of Residual Factors," Papers 2012.07245, arXiv.org.
    6. Drenovak, Mikica & Ranković, Vladimir & Urošević, Branko & Jelic, Ranko, 2022. "Mean-Maximum Drawdown Optimization of Buy-and-Hold Portfolios Using a Multi-objective Evolutionary Algorithm," Finance Research Letters, Elsevier, vol. 46(PA).
    7. Vladimir Cherny & Jan Obłój, 2013. "Portfolio optimisation under non-linear drawdown constraints in a semimartingale financial model," Finance and Stochastics, Springer, vol. 17(4), pages 771-800, October.
    8. Sami Attaoui & Vincent Lacoste, 2013. "A scenario-based description of optimal American capital guaranteed strategies," Finance, Presses universitaires de Grenoble, vol. 34(2), pages 65-119.
    9. David Landriault & Bin Li & Hongzhong Zhang, 2014. "On the Frequency of Drawdowns for Brownian Motion Processes," Papers 1403.1183, arXiv.org.
    10. Hongzhong Zhang & Olympia Hadjiliadis, 2012. "Drawdowns and the Speed of Market Crash," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 739-752, September.
    11. Koichi Matsumoto, 2007. "Portfolio Insurance with Liquidity Risk," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 14(4), pages 363-386, December.
    12. Auh, Jun Kyung & Cho, Wonho, 2023. "Factor-based portfolio optimization," Economics Letters, Elsevier, vol. 228(C).
    13. Laurent Carraro & Nicole El Karoui & Jan Ob{l}'oj, 2009. "On Az\'ema-Yor processes, their optimal properties and the Bachelier-drawdown equation," Papers 0902.1328, arXiv.org, revised Sep 2012.
    14. Steven D. Moffitt, 2018. "Why Markets are Inefficient: A Gambling "Theory" of Financial Markets For Practitioners and Theorists," Papers 1801.01948, arXiv.org.
    15. Hanauer, Matthias X. & Lauterbach, Jochim G., 2019. "The cross-section of emerging market stock returns," Emerging Markets Review, Elsevier, vol. 38(C), pages 265-286.
    16. Zhang, Hongzhong & Leung, Tim & Hadjiliadis, Olympia, 2013. "Stochastic modeling and fair valuation of drawdown insurance," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 840-850.
    17. Dangl, Thomas & Randl, Otto & Zechner, Josef, 2016. "Risk control in asset management: Motives and concepts," CFS Working Paper Series 546, Center for Financial Studies (CFS).
    18. Mendes, Beatriz Vaz de Melo & Lavrado, Rafael Coelho, 2017. "Implementing and testing the Maximum Drawdown at Risk," Finance Research Letters, Elsevier, vol. 22(C), pages 95-100.
    19. Anna Ananova & Rama Cont & Renyuan Xu, 2020. "Model-free Analysis of Dynamic Trading Strategies," Papers 2011.02870, arXiv.org, revised Aug 2023.
    20. Ren Liu & Johannes Muhle-Karbe & Marko H. Weber, 2014. "Rebalancing with Linear and Quadratic Costs," Papers 1402.5306, arXiv.org, revised Sep 2017.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:74:y:2005:i:3:p:245-252. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.