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The Journal of Alternative Investments

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Drawdown Control with a Risk Floor

Joe Zhou and James Shang
The Journal of Alternative Investments Spring 2015, 17 (4) 79-94; DOI: https://doi.org/10.3905/jai.2015.17.4.079
Joe Zhou
is a director and CIO at Ortus Capital Management Limited in Hong Kong.
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  • For correspondence: joe.zhou@ortuscapital.com
James Shang
is a director at Ortus Capital Management Limited in Hong Kong.
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  • For correspondence: james.shang@ortuscapital.com
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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.

TOPICS: Portfolio construction, risk management, statistical methods

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The Journal of Alternative Investments: 17 (4)
The Journal of Alternative Investments
Vol. 17, Issue 4
Spring 2015
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Drawdown Control with a Risk Floor
Joe Zhou, James Shang
The Journal of Alternative Investments Mar 2015, 17 (4) 79-94; DOI: 10.3905/jai.2015.17.4.079

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Drawdown Control with a Risk Floor
Joe Zhou, James Shang
The Journal of Alternative Investments Mar 2015, 17 (4) 79-94; DOI: 10.3905/jai.2015.17.4.079
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  • Article
    • Abstract
    • THE NOTION OF DECAYED DRAWDOWN
    • APPLICATION OF THE GROSSMAN–ZHOU POLICY IN DISCRETE TIMES WITH TRANSACTION COSTS
    • RATIONALE FOR RISK FLOOR
    • DRAWDOWN CONTROL WITH A RISK FLOOR (NO TRANSACTION COSTS)
    • OTHER RISK-TAKING RULES IN THE GROSSMAN–ZHOU FRAMEWORK
    • CONCLUSION
    • APPENDIX A
    • APPENDIX B
    • REFERENCES
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