Variable neighborhood search heuristic for nonconvex portfolio optimization

Abstract

In this article we consider a portfolio optimization problem under multiple real-world constraints, such as: cardinality constraints, tracking error, active share, and turnover. We propose a heuristic based on variable neighborhood search (VNS) that effectively addresses additional constraints that introduce non-convexities. In the VNS-based heuristic, several neighborhood structures are introduced and fast local search is implemented. We develop a VNS portfolio rebalancing framework (VNS-PRF) with two rebalance strategies. Data sets provided by a financial investment firm are used to evaluate the validity and reliability of the proposed VNS-PRF. Computational experiments and different portfolio performance measures indicate that our approach is able to obtain solutions with competitive quality and can be applied on large-scale data sets.

Acknowledgment

The authors thank Principal for providing proprietary data sets as well as background information on the problem. The authors also thank Professors Dragana Makajić-Nikolić, Marija Kuzmanović, Gordana Savić and the editors and reviewers for improving the quality of this article through their valuable comments.

Additional information

Funding

This work is supported by the Serbian Ministry of Education and Science under Grant No. 174010.

Notes on contributors

Andrijana Bačević

Andrijana BaČeviĆ received a B.Sc. degree in operations management in 2016 and M.Sc. degree in business analytics from university of Belgrade, Faculty of Organizational Sciences, in 2017. Then, she joined the Department of Operations Research and Statistics, as a teaching assistant. Her current research interests include portfolio optimization, risk and reliability analysis, metaheuristics, and multi-criteria optimization methods.

Nemanja Vilimonović

Nemanja VilimonoviĆ received a B.Sc. degree in operations management in 2016. and M.Sc. degree in business analytics from university of Belgrade, Faculty of Organizational Sciences, in 2018. He worked in a medical institution in the Department of Finance and Controlling from November 2016 to May 2018. Since May 2018 he has been employed in the Customer Logistics, Procurement and Planning (CLP) Department of Robert Bosch GmbH. His future interests are in developing tools for faster planning and analysis.

Igor Dabić

Igor DabiĆ received a B.Sc. degree in operations management from the University of Belgrade, Faculty of Organizational Sciences, in 2016. Since 2016 he has been a master’s student in the Department of Business Analytics in the Faculty of Organizational Sciences. He works in the Customer Logistics, Procurement and Planning (CLP) Department of Robert Bosch GmbH. His future goal is to combine the knowledge of programming and operations research in developing simulations tools in spreadsheets program.

Jakov Petrović

Jakov PetroviĆ received a B.Sc. degree in information systems and technologies from the University of Belgrade, Faculty of Organizational Sciences, in 2017. Since 2017 he has been a masters student in the Department of Business Intelligence in the Faculty of Organizational Sciences. His current research interests include machine learning algorithms and methods for improvement of their performance.

Darko Damnjanović

Darko DamnjanoviĆ received a B.Sc. degree in operations management from the University of Belgrade, Faculty of Organizational Sciences, in 2018. Since 2018 he has been a master’s student in the Department of Business Analytics in the Faculty of Organizational Sciences. Darko has been a part of a few projects, including Coca-Cola HBC internship and a student competition at the INFORMS conference. His current plans consider further development through master, studies and more projects in logistics, business analytics and operations research.

Dušan Džamić

DuŠan DžamiĆ has been a teaching assistant at the University of Belgrade, Faculty of Organizational Sciences, Department for Mathematics since 2013. He is a Ph.D. student in computer science at the University of Belgrade, Faculty of Mathematics. His research is mainly focused on mathematical optimization methods and clustering in complex networks. His previously published research has appeared in Annals of Operations Research, International Transactions in Operational Research, Filomat, and other journals.