Advanced Search
MyIDEAS: Login

Optimal Investment Strategies For Controlling Drawdowns

Contents:

Author Info

  • Sanford J. Grossman
  • Zhongquan Zhou
Registered author(s):

    Abstract

    We analyze the optimal risky investment policy for an investor who, at each point in time, wants to lose no more than a fixed percentage of the maximum value his wealth has achieved up to that time. In particular, if "M" t is the maximum level of wealth W attained on or before time "t", then the constraint imposed on his portfolio choice is that W tα"M" t, where α is an exogenous number betweenα O and 1. We show that, for constant relative risk aversion utility functions, the optimal policy involves an investment in risky assets at time "t" in proportion to the "surplus""W" t - α"M" t. the optimal policy may appear similar to the constant-proportion portfolio insurance policy analyzed in Black and Perold (1987) and Grossman and Vila (1989). However, in those papers, the investor keeps his wealth above a "nonstochastic" floor "F" instead of a stochastic floor α"M" t. the "stochastic" character of the floor studied here has interesting effects on the investment policy in states of nature when wealth is at an all-time high; i.e., when Wt ="M" t. It can be shown that at "W" t="M" t, α"M" t is expected to grow at a faster rate than "W" t, and therefore the investment in the risky asset can be expected to fall. We also show that the investment in the risky asset can be expected to rise when "W" t is close to α"M" t. We conjecture that in an equilibrium model the stochastic character of the floor creates "resistance" levels as the market approaches an all-time high (because of the reluctance of investors to take more risk when "W" t="M" t). Copyright 1993 Blackwell Publishers.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9965.1993.tb00044.x
    File Function: link to full text
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Wiley Blackwell in its journal Mathematical Finance.

    Volume (Year): 3 (1993)
    Issue (Month): 3 ()
    Pages: 241-276

    as in new window
    Handle: RePEc:bla:mathfi:v:3:y:1993:i:3:p:241-276

    Contact details of provider:
    Web page: http://www.blackwellpublishing.com/journal.asp?ref=0960-1627

    Order Information:
    Web: http://www.blackwellpublishing.com/subs.asp?ref=0960-1627

    Related research

    Keywords:

    References

    No references listed on IDEAS
    You can help add them by filling out this form.

    Citations

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

    Cited by:
    1. Romuald Elie & Nizar Touzi, 2008. "Optimal lifetime consumption and investment under a drawdown constraint," Finance and Stochastics, Springer, vol. 12(3), pages 299-330, July.
    2. Vladimir Cherny & Jan Obloj, 2011. "Portfolio optimisation under non-linear drawdown constraints in a semimartingale financial model," Papers 1110.6289, arXiv.org, revised Apr 2013.
    3. Wolff, Dominik & Bessler, Wolfgang & Opfer, Heiko, 2012. "Multi-Asset Portfolio Optimization and Out-of-Sample Performance: An Evaluation of Black-Litterman, Mean Variance and Naïve Diversification Approaches," Annual Conference 2012 (Goettingen): New Approaches and Challenges for the Labor Market of the 21st Century 62020, Verein für Socialpolitik / German Economic Association.
    4. El Karoui, Nicole & Jeanblanc, Monique & Lacoste, Vincent, 2005. "Optimal portfolio management with American capital guarantee," Journal of Economic Dynamics and Control, Elsevier, vol. 29(3), pages 449-468, March.
    5. T. Arun, 2012. "The Merton Problem with a Drawdown Constraint on Consumption," Papers 1210.5205, arXiv.org.
    6. Luisa Corrado & Marcus Miller & Lei Zhang, 2007. "Bulls, bears and excess volatility: can currency intervention help?," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 12(2), pages 261-272.
    7. Pospisil, Libor & Vecer, Jan & Hadjiliadis, Olympia, 2009. "Formulas for stopped diffusion processes with stopping times based on drawdowns and drawups," Stochastic Processes and their Applications, Elsevier, vol. 119(8), pages 2563-2578, August.
    8. Jiang Wang, 2002. "Trading Volume and Asset Prices," Annals of Economics and Finance, Society for AEF, vol. 3(2), pages 299-359, November.
    9. 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.
    10. Balder, Sven & Brandl, Michael & Mahayni, Antje, 2009. "Effectiveness of CPPI strategies under discrete-time trading," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 204-220, January.
    11. Alexander, Gordon J. & Baptista, Alexandre M., 2009. "Stress testing by financial intermediaries: Implications for portfolio selection and asset pricing," Journal of Financial Intermediation, Elsevier, vol. 18(1), pages 65-92, January.
    12. Schuhmacher, Frank & Eling, Martin, 2011. "Sufficient conditions for expected utility to imply drawdown-based performance rankings," Journal of Banking & Finance, Elsevier, vol. 35(9), pages 2311-2318, September.
    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. Vladimir Cherny & Jan Obloj, 2013. "Optimal portfolios of a long-term investor with floor or drawdown constraints," Papers 1305.6831, arXiv.org.
    15. Paolo Guasoni & Scott Robertson, 2012. "Portfolios and risk premia for the long run," Papers 1203.1399, arXiv.org.
    16. Koichi Matsumoto, 2007. "Portfolio Insurance with Liquidity Risk," Asia-Pacific Financial Markets, Springer, vol. 14(4), pages 363-386, December.
    17. Bielecki, Tomasz R. & Pliska, Stanley R. & Sherris, Michael, 2000. "Risk sensitive asset allocation," Journal of Economic Dynamics and Control, Elsevier, vol. 24(8), pages 1145-1177, July.
    18. A. Johansen & D. Sornette, 2002. "Endogenous versus Exogenous Crashes in Financial Markets," Papers cond-mat/0210509, arXiv.org.
    19. MacLean, Leonard C. & Sanegre, Rafael & Zhao, Yonggan & Ziemba, William T., 2004. "Capital growth with security," Journal of Economic Dynamics and Control, Elsevier, vol. 28(5), pages 937-954, February.
    20. 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.
    21. Traian A. Pirvu & Gordan Zitkovic, 2007. "Maximizing the Growth Rate under Risk Constraints," Papers 0706.0480, arXiv.org.

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:bla:mathfi:v:3:y:1993:i:3:p:241-276

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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