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Portfolio Optimization with Factors, Scenarios, and Realistic Short Positions

Jacobs Levy Equity Management, 100 Campus Drive, P.O. Box 650, Florham Park, New Jersey 07932-0650
Jacobs Levy Equity Management, 100 Campus Drive, P.O. Box 650, Florham Park, New Jersey 07932-0650
Harry Markowitz Company, 1010 Turquoise Street, Suite 245, San Diego, California 92109
bruce.jacobs{at}jlem.com
ken.levy{at}jlem.com
harryhmm{at}aol.com

This paper presents fast algorithms for calculating mean-variance efficient frontiers when the investor can sell securities short as well as buy long, and when a factor and/or scenario model of covariance is assumed. Currently, fast algorithms for factor, scenario, or mixed (factor and scenario) models exist, but (except for a special case of the results reported here) apply only to portfolios of long positions. Factor and scenario models are used widely in applied portfolio analysis, and short sales have been used increasingly as part of large institutional portfolios. Generally, the critical line algorithm (CLA) traces out mean-variance efficient sets when the investor’s choice is subject to any system of linear equality or inequality constraints. Versions of CLA that take advantage of factor and/or scenario models of covariance gain speed by greatly simplifying the equations for segments of the efficient set. These same algorithms can be used, unchanged, for the long-short portfolio selection problem provided a certain condition on the constraint set holds. This condition usually holds in practice.

Subject classifications: finance; portfolio:optimization with short sales.
History: Received April 2002; revision received June 2003; revision received May 2004; accepted July 2004.