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Optimal Investment Strategies For Controlling Drawdowns


  • Sanford J. Grossman
  • Zhongquan Zhou


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

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