Index fund optimization using a hybrid model: genetic algorithm and mixed-integer nonlinear programming

Abstract

Index funds consist of a subset of stocks, an index tracking portfolio, included in the market index. The index tracking portfolio aims to match the performance of the benchmark index. In this paper, we propose a hybrid model for solving the multiperiod index tracking problem, which includes rebalancing concerns, transaction costs, limits on the number of stocks, and diversification by sector, market capitalization, and stock weight. Our hybrid model combines the genetic algorithm (GA) to select stocks of the index tracking portfolio and mixed-integer nonlinear programming (MINLP) to estimate its weights. Finally, we apply our proposed hybrid model to the S&P500 to find an index tracking portfolio that includes those constraints. The results show that our hybrid model is able to create an index fund whose return rate is similar to the market index with significantly lower risk.

Keywords:

• Index fund
• Portfolio optimization
• Genetic algorithm
• Mixed-integer nonlinear programming

Additional information

Notes on contributors

Juan Díaz

Juan Díaz holds a M.Sc. in engineering from the University of los Andes. His interests are visual Analytics, optimization, and data science.

María Cortés

Maria Cortes holds a M.Sc. in engineering from University de los Andes. Her interests include the stochastic modelling of systems, machine learning and statistical data analysis for decision-making.

Juan Hernández

Juan Hernández holds a M.Sc. in engineering from the University of Los Andes. His research interests are data science, machine learning and metaheuristics.

Óscar Clavijo

Óscar Clavijo holds a B.S. in engineering and physics from the University of Los Andes. His research interests are data science, machine learning and statistics inference.

Carlos Ardila

Carlos Ardila holds a M.Sc. in engineering from the University of Los Andes. He is interested in statistics and data analysis, as well as its applications in simulation, overall operation improvement and public policy issues.

Sergio Cabrales

Dr. Sergio Cabrales received his Ph.D. in Management from the University of los Andes, and M.Sc. degrees in engineering. His research interests are financial engineering, analytics, game theory, decision theory and applications in the energy sector and financial systems.