Analysis of risk measures in multiobjective optimization portfolios with cardinality constraint

Portfolio selection has been the subject of extensive studies in order to obtain increased returns, minimizing the investment risk. However, the most appropriate risk measure to be considered is still an open problem. The aim of this work is to study different risk measures in the multiobjective portfolios optimization with cardinality constraint and rebalancing. The in-sample analysis compares the fronts of each algorithm, metric and range of cardinality, and out-of-sample analysis compares the results of each measure of risk with each other and with two benchmarks. The returns of portfolios are compared in terms of assets choice and assignment of weights. Statistical tests are performed to verify if any measure of risk shows some superiority. Results indicate that downside risk measures can reduce the cardinality and the risk of financial drawdown without reducing drawup, once they are able to reduce just the negative historical returns scenarios.

[1]  Rodrigo T. N. Cardoso,et al.  Composition of investment portfolios through a combinatorial multiobjective optimization model using CVaR , 2017, 2017 IEEE Congress on Evolutionary Computation (CEC).

[2]  Mei-Ling Tang,et al.  In search of robust methods for multi-currency portfolio construction by value at risk , 2018, Asia-Pacific Financial Markets.

[3]  Akiko Takeda,et al.  Optimizing over coherent risk measures and non-convexities: a robust mixed integer optimization approach , 2015, Comput. Optim. Appl..

[4]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .

[5]  Rodrigo T. N. Cardoso,et al.  Parallel MOEAs for Combinatorial Multiobjective Optimization Model of Financial Portfolio Selection , 2018, 2018 IEEE Congress on Evolutionary Computation (CEC).

[6]  Konstantinos Liagkouras,et al.  Multiobjective Evolutionary Algorithms for Portfolio Management: A comprehensive literature review , 2012, Expert Syst. Appl..

[7]  Jianjun Gao,et al.  On cardinality constrained mean-CVaR portfolio optimization , 2015, The 27th Chinese Control and Decision Conference (2015 CCDC).

[8]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[9]  Eva Alfaro-Cid,et al.  A naïve approach to speed up portfolio optimization problem using a multiobjective genetic algorithm , 2012 .

[10]  DIVERSIFICATION OF INVESTMENTS FOR THE BRAZILIAN EQUITY MARKET , 2014 .

[11]  Nico van der Wijst,et al.  Optimal portfolio selection and dynamic benchmark tracking , 2005, Eur. J. Oper. Res..

[12]  Marco Laumanns,et al.  SPEA2: Improving the strength pareto evolutionary algorithm , 2001 .

[13]  Lixing Zhu,et al.  Mean–variance, mean–VaR, and mean–CVaR models for portfolio selection with background risk , 2018, Risk Management.

[14]  R. Rockafellar,et al.  Optimization of conditional value-at risk , 2000 .

[15]  Christian Kanzow,et al.  Mathematical Programs with Cardinality Constraints: Reformulation by Complementarity-Type Conditions and a Regularization Method , 2016, SIAM J. Optim..

[16]  Kalyanmoy Deb,et al.  Bi-objective Portfolio Optimization Using a Customized Hybrid NSGA-II Procedure , 2011, EMO.

[17]  Rosario N. Mantegna,et al.  An Introduction to Econophysics: Contents , 1999 .

[18]  R. K. Ursem.  Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[19]  David N. Nawrocki.  A Brief History of Downside Risk Measures , 1999 .

[20]  R. Östermark,et al.  Portfolio optimization based on GARCH-EVT-Copula forecasting models , 2018, International Journal of Forecasting.

[21]  Javier Estrada,et al.  Mean-Semivariance Optimization: A Heuristic Approach , 2007 .

[22]  Martin Branda,et al.  Convergence of a Scholtes-type regularization method for cardinality-constrained optimization problems with an application in sparse robust portfolio optimization , 2017, Comput. Optim. Appl..

[23]  Konstantinos P. Anagnostopoulos,et al.  The mean-variance cardinality constrained portfolio optimization problem: An experimental evaluation of five multiobjective evolutionary algorithms , 2011, Expert Syst. Appl..

[24]  G. Mitra,et al.  Portfolio selection models: a review and new directions , 2009 .

[25]  Sandra Paterlini,et al.  Multiobjective optimization using differential evolution for real-world portfolio optimization , 2011, Comput. Manag. Sci..