Portfolio Optimization with Factors, Scenarios, and Realistic Short Positions

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) mod...

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Bibliographic Details
Published inOperations research Vol. 53; no. 4; pp. 586 - 599
Main Authors Jacobs, Bruce I, Levy, Kenneth N, Markowitz, Harry M
Format Journal Article
LanguageEnglish
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
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Summary: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.
ISSN:0030-364X
1526-5463
DOI:10.1287/opre.1050.0212