Drawdown Control with a Risk Floor

Abstract

With proportional transaction costs, this article shows that if the portfolio drawdown control policy introduced in 1993 by Grossman and Zhou is followed, the expected return of the portfolio can turn negative at a certain drawdown level, become more negative as drawdown deepens, and approach negative infinity as drawdown approaches its limit. This result suggests that a “no-action zone” should be in place around the drawdown limit to prevent the expected return from turning negative. By allowing a portfolio manager to take a small risk (a “risk floor”) regardless of drawdown, rather than cutting risk to zero as dictated by Grossman and Zhou when drawdown reaches its limit, the problem associated with negative expected return is eliminated. The proposed method would be suitable for open-ended fund management but may not be suitable for some managed accounts with absolute drawdown limits. The authors show that drawdown control with a risk floor can be solved in the Grossman–Zhou framework (no transaction costs). They also show that many well-known risk-taking rules in investment and/or betting are special cases of the more general Grossman–Zhou framework.