Portfolio Optimization with Factors, Scenarios, and Realistic Short Positions

• Published in: Operations research Vol. 53; no. 4; pp. 586 - 599
• Main Authors: Jacobs, Bruce I, Levy, Kenneth N, Markowitz, Harry M
• Format: Journal Article
• Language: English
• Published: Linthicum, MD INFORMS 01.07.2005; Institute for Operations Research and the Management Sciences
• Subjects: Algorithms; Applied sciences; Covariance; Covariance matrices; Exact sciences and technology; Expected returns; finance; Financial portfolios; Investors; Management; Margin requirements; Mathematical optimization; Methods; Modeling; Operational research and scientific management; Operational research. Management science; Portfolio management; Portfolio theory; portfolio:optimization with short sales; Security portfolios; Short sales; United States; portfolio: optimization with short sales; Covariance matrix; Portfolio management; Finance; Optimization
• DOI: 10.1287/opre.1050.0212
• ISSN: 0030-364X

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.