IDEAS home Printed from https://ideas.repec.org/a/bla/mathfi/v3y1993i3p241-276.html
   My bibliography  Save this article

Optimal Investment Strategies For Controlling Drawdowns

Author

Listed:
  • Sanford J. Grossman
  • Zhongquan Zhou

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 t α"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.

Suggested Citation

  • Sanford J. Grossman & Zhongquan Zhou, 1993. "Optimal Investment Strategies For Controlling Drawdowns," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 241-276.
  • Handle: RePEc:bla:mathfi:v:3:y:1993:i:3:p:241-276
    as

    Download full text from publisher

    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 search for a different version of it.

    More about this item

    Statistics

    Access and download statistics

    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:bla:mathfi:v:3:y:1993:i:3:p:241-276. See general information about how to correct material in RePEc.

    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). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0960-1627 .

    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.

    We have no references for this item. You can help adding them by using 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.