Portfolio Optimization with Factors, Scenarios, and Realistic Short Positions

Operations Research, Vol. 53, No. 4, pp. 586-599, July/August 2005

Posted: 31 Mar 2017

See all articles by Bruce I. Jacobs, Ph.D.

Bruce I. Jacobs, Ph.D.

Jacobs Levy Equity Management

Kenneth N. Levy

Jacobs Levy Equity Management

Harry Markowitz

University of California at San Diego

Date Written: April 30, 2002

Abstract

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.

Keywords: portfolio optimization, factor models, scenario models, fast algorithms, long-short investing, short selling, mean-variance efficiency, covariance matrix, diagonalizable covariance matrix, feasible portfolios, efficient frontiers, critical line algorithm, CLA

JEL Classification: G11, C61

Suggested Citation

Jacobs, Bruce I. and Levy, Kenneth N. and Markowitz, Harry, Portfolio Optimization with Factors, Scenarios, and Realistic Short Positions (April 30, 2002). Operations Research, Vol. 53, No. 4, pp. 586-599, July/August 2005. Available at SSRN: https://ssrn.com/abstract=2447041

Bruce I. Jacobs (Contact Author)

Jacobs Levy Equity Management ( email )

100 Campus Drive
P.O. Box 650
Florham Park, NJ 07932-0650
United States
973-410-9222 (Phone)
973-410-9333 (Fax)

HOME PAGE: https://jlem.com/who-we-are#/nav/founders

Kenneth N. Levy

Jacobs Levy Equity Management ( email )

100 Campus Drive
P.O. Box 650
Florham Park, NJ 07932-0650
United States
973-410-9222 (Phone)
973-410-9333 (Fax)

HOME PAGE: https://jlem.com/who-we-are#/nav/founders

Harry Markowitz

University of California at San Diego ( email )

9500 Gilman Drive
La Jolla, CA 92093-0508
United States
(858) 534-3383 (Phone)

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