Multiobjective Model Predictive Control for portfolio optimization with cardinality constraint - de Melo, Maísa Kely; Cardoso, Rodrigo Tomás Nogueira; Jesus, Tales Argolo (Expert systems with applications, 2022)
Model Predictive Control has been shown to be adequate to solve portfolio optimization problems because of its ability to perform the dynamic readjustment of the portfolio considering the market expectations. To consider both wealth and risk and real issues imposed by the financial market, this work proposes a Multiobjective Model Predictive Control strategy with cardinality constraints, besides transaction costs, self-financing, and upper and lower limits. The objective functions are the expected portfolio wealth and the expected Variance and Conditional Value at Risk as the portfolio risk measures. The optimization is performed by a multiobjective genetic algorithm, with operators proposed to control the number of assets in each portfolio and respect the prediction horizon perspective. Finally, an insightful case study is designed using the Brazilian Stock Exchange data in 2019 and 2020. An in-sample analysis explores the relationship between prediction horizon length, cardinality, optimal portfolio composition, risk-free asset, and objective functions on performance. An out-of-sample analysis considers the cumulative wealth, Sharpe ratio, maximum Drawdown, and the monthly accumulated return. Numerical experiments indicate that the proposed strategy outperforms the myopic portfolio selection, beats the primary Brazilian benchmark, a modified Markowitz model, and some top Brazilian investment funds even in crisis times like during the COVID-19 pandemic. •The cardinality constraint for multiobjective model predictive control is proposed.•Adaptation in the NSGA2 to deal with the prediction horizon perspective is proposed.•Analysis matching free risk allocation, cardinality, prediction horizon is proposed.