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http://ssrn.com/abstract=544742
 
 

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Drawdown Measure in Portfolio Optimization


Alexei Chekhlov


Columbia University - Department of Mathematics

Stanislav P. Uryasev


University of Florida

Michael Zabarankin


Stevens Institute of Technology - Department of Mathematical Sciences

June 25, 2003



Abstract:     
A new one-parameter family of risk measures called Conditional Drawdown (CDD) has been proposed. These measures of risk are functionals of the portfolio drawdown (underwater) curve considered in active portfolio management. For some value of the tolerance parameter Alpha, in the case of a single sample path, drawdown functional is defined as the mean of the worst (1 - Alpha) 100% drawdowns. The CDD measure generalizes the notion of the drawdown functional to a multi-scenario case and can be considered as a generalization of deviation measure to a dynamic case. The CDD measure includes the Maximal Drawdown and Average Drawdown as its limiting cases. Mathematical properties of the CDD measure have been studied and efficient optimization techniques for CDD computation and solving asset-allocation problems with a CDD measure have been developed. The CDD family of risk functionals is similar to Conditional Value-at-Risk (CVaR), which is also called Mean Shortfall, Mean Excess Loss, or Tail Value-at-Risk. Some recommendations on how to select the optimal risk functionals for getting practically stable portfolios have been provided. A real-life asset-allocation problem has been solved using the proposed measures. For this particular example, the optimal portfolios for cases of Maximal Drawdown, Average Drawdown, and several intermediate cases between these two have been found.

Number of Pages in PDF File: 41

JEL Classification: C15, C61, G11

working papers series





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Date posted: May 13, 2004  

Suggested Citation

Chekhlov, Alexei and Uryasev, Stanislav P. and Zabarankin, Michael, Drawdown Measure in Portfolio Optimization (June 25, 2003). Available at SSRN: http://ssrn.com/abstract=544742 or http://dx.doi.org/10.2139/ssrn.544742

Contact Information

Alexei Chekhlov
Columbia University - Department of Mathematics ( email )
New York, NY
United States
HOME PAGE: http://www.math.columbia.edu/~chekhlov/
Stanislav P. Uryasev (Contact Author)
University of Florida ( email )
303 Weil Hall
Gainesville, FL 32611-6595
United States
352-392-3091 (Phone)
352-392-3537 (Fax)
HOME PAGE: http://www.ise.ufl.edu/uryasev/
Michael Zabarankin
Stevens Institute of Technology - Department of Mathematical Sciences ( email )
Hoboken, NJ 07030
United States
HOME PAGE: http://personal.stevens.edu/~mzabaran/
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