A Relaxed Optimization Approach for Cardinality-Constrained Portfolios

European Control Conference, Italy 2019

8 Pages Posted: 16 Nov 2018 Last revised: 23 Mar 2019

See all articles by Jize Zhang

Jize Zhang

University of Washington, Department of Applied Mathematics, Students

Tim Leung

University of Washington - Department of Applied Math

Aleksandr Aravkin

University of Washington - Department of Applied Mathematics

Date Written: October 25, 2018

Abstract

A cardinality-constrained portfolio caps the number of stocks to be traded across and within groups or sectors. These limitations arise from real-world scenarios faced by fund managers, who are constrained by transaction costs and client preferences as they seek to maximize return and limit risk. We develop a new approach to solve cardinality-constrained portfolio optimization problems, extending both Markowitz and conditional value at risk (CVaR) optimization models with cardinality constraints. We derive a continuous relaxation method for the NP-hard objective, which allows for very efficient algorithms with standard convergence guarantees for nonconvex problems. For smaller cases, where brute force search is feasible to compute the globally optimal cardinality-constrained portfolio, the new approach finds the best portfolio for the cardinality-constrained Markowitz model and a very good local minimum for the cardinality-constrained CVaR model. For higher dimensions, where brute-force search is prohibitively expensive, we find feasible portfolios that are nearly as efficient as their non-cardinality constrained counterparts.

Keywords: portfolio optimization, conditional value at risk, mean variance portfolio, cardinality constraints

JEL Classification: C58, C61, C63

Suggested Citation

Zhang, Jize and Leung, Tim and Aravkin, Aleksandr, A Relaxed Optimization Approach for Cardinality-Constrained Portfolios (October 25, 2018). European Control Conference, Italy 2019, Available at SSRN: https://ssrn.com/abstract=3272588 or http://dx.doi.org/10.2139/ssrn.3272588

Jize Zhang

University of Washington, Department of Applied Mathematics, Students ( email )

Seattle, WA
United States

Tim Leung (Contact Author)

University of Washington - Department of Applied Math ( email )

Lewis Hall 217
Department of Applied Math
Seattle, WA 98195
United States

HOME PAGE: http://faculty.washington.edu/timleung/

Aleksandr Aravkin

University of Washington - Department of Applied Mathematics ( email )

Box 352420
Seattle, WA 98195-2420
United States

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
257
Abstract Views
1,133
Rank
180,737
PlumX Metrics