Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
1 PORTFOLIO OPTIMIZATION WITH DRAWDOWN CONSTRAINTS Alexei Chekhlov 1 , Stanislav Uryasev 2 , Michael Zabarankin 2 Risk Management and Financial Engineering Lab Center for Applied Optimization Department of Industrial and Systems Engineering University of Florida, Gainesville, FL 32611 Date: January 13, 2003 Correspondence should be addressed to: Stanislav Uryasev Abstract We propose a new one-parameter family of risk functions defined on portfolio return sample-paths, which is called conditional drawdown-at-risk (CDaR). These risk functions depend on the portfolio drawdown (underwater) curve considered in active portfolio management. For some value of the tolerance parameter a , the CDaR is defined as the mean of the worst % 100 ) 1 ( - a drawdowns. The CDaR risk function contains the maximal drawdown and average drawdown as its limiting cases. For a particular example, we find optimal portfolios with constraints on the maximal drawdown, average drawdown and several intermediate cases between these two. The CDaR family of risk functions originates from the conditional value-at-risk (CVaR) measure. Some recommendations on how to select the optimal risk measure for getting practically stable portfolios are provided. We solved a real life portfolio allocation problem using the proposed risk functions. 1. Introduction Optimal portfolio allocation is a longstanding issue in both practical portfolio management and academic research on portfolio theory. Various methods have been proposed and studied (for a review, see, for example, Grinold and Kahn, 1999). All of them, as a starting point, assume some measure of portfolio risk. From a standpoint of a fund manager, who trades clients' or bank’s proprietary capital, and for whom the clients' accounts are the only source of income coming in the form of management and incentive fees, losing these accounts is equivalent to the death of his business. This is true with no regard to whether the employed strategy is long-term valid and has very attractive expected 1 Thor Asset Management, Inc., 551 Fifth Ave., Suite 601, 6th Floor, New York, NY 10017; e-mail: a_chekhlov@thorcapital.com 2 University of Florida, ISE, P.O. Box 116595, 303 Weil Hall Gainesville, FL 32611-6595; e-mail: uryasev@ise.ufl.edu , zabarank@ufl.edu
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 return characteristics. Such fund manager's primary concern is to keep the existing accounts and to attract the new ones in order to increase his revenues. A particular client who was persuaded into opening an account with the manager through reading the disclosure document, listening to the manager's attractive story, knowing his previous returns, etc., will decide on firing the manager based, most likely, on his account's drawdown magnitude and duration. In particular, it is highly uncommon, for a Commodity Trading Advisor (CTA) to still hold a client whose account was in a drawdown, even of small size, for longer than 2 years. By the same token, it is unlikely that a particular client will tolerate a 50% drawdown in an account with an average- or small-risk CTA. Similarly, in an investment bank setup, a proprietary system trader will be
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/08/2011 for the course CIS 625 taught by Professor Michaelkearns during the Spring '12 term at Pennsylvania State University, University Park.

Page1 / 17


This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online