Drawdown Measure in Portfolio Optimization

41 Pages Posted: 13 May 2004

See all articles by Alexei Chekhlov

Alexei Chekhlov

Dassault Systemes; Columbia University, Mathematics Department

Stanislav P. Uryasev

University of Florida

Michael Zabarankin

Stevens Institute of Technology - Department of Mathematical Sciences

Date Written: 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.

JEL Classification: C15, C61, G11

Suggested Citation

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

Alexei Chekhlov

Dassault Systemes ( email )

175 Wyman St
Waltham, MA 02451
United States
7745563822 (Phone)

HOME PAGE: http://www.3ds.com

Columbia University, Mathematics Department ( email )

RM 427A, MC 4437
2990 Broadway
New York, NY 10027
United States
2128544303 (Phone)

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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