Multi-attribute decision making applied to financial portfolio optimization problem

Abstract This paper proposes an integer multiobjective mean-CVaR portfolio optimization model with variable cardinality constraint and rebalancing and two different methods of decision-maker used to guide and select, according to the decision maker preferences, a solution comes from the non-dominated portfolios generated by a proposed evolutionary algorithm. The decision-making methods were used to approximate investor behavior according to three functions, chosen to represent different investor profiles (conservative, moderate and aggressive). The proposed methods are compared with those found in the literature. Additionally, computational simulations are performed using assets from the Brazilian stock exchange for the period between January 2011 and December 2015. The strategy is that each beginning of the month: the previous portfolio is sold, the optimization is performed, and the decision-making method selects the new portfolio to be purchased. Results of the simulations consider monthly maximum drawdown and cumulative return during the entire study period and show that the optimization model is robust, considering the three simulated profiles. The methods always present cumulative returns above safe investments for the analyzed period, and the aggressive profile obtained bigger gains with greater risk.

[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]  J. Narsoo.  Performance Analysis of Portfolio Optimisation Strategies: Evidence from the Exchange Market , 2017 .

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

[4]  D. A. Seaver,et al.  A comparison of weight approximation techniques in multiattribute utility decision making , 1981 .

[5]  Sylvia J. T. Jansen,et al.  The Multi-attribute Utility Method , 2011 .

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

[7]  J. Vasconcelos,et al.  The a posteriori decision in multiobjective optimization problems with smarts, promethee II, and a fuzzy algorithm , 2006, IEEE Transactions on Magnetics.

[8]  Massimiliano Kaucic,et al.  Portfolio optimization by improved NSGA-II and SPEA 2 based on different risk measures , 2019, Financial Innovation.

[9]  Kalyanmoy Deb,et al.  Simulated Binary Crossover for Continuous Search Space , 1995, Complex Syst..

[10]  Hamid Reza Golmakani,et al.  Markowitz-based portfolio selection with minimum transaction lots, cardinality constraints and regarding sector capitalization using genetic algorithm , 2009, Expert Syst. Appl..

[11]  Anand Subramanian,et al.  A multi-objective evolutionary algorithm for a class of mean-variance portfolio selection problems , 2019, Expert Syst. Appl..

[12]  D. Broomhead,et al.  Radial Basis Functions, Multi-Variable Functional Interpolation and Adaptive Networks , 1988 .

[13]  J. D. Bermúdez,et al.  Preference-based Evolutionary Multi-objective Optimization for Solving Fuzzy Portfolio Selection Problems , 2017 .

[14]  Ralph L. Keeney,et al.  Decisions with multiple objectives: preferences and value tradeoffs , 1976 .

[15]  M. Kendall.  A NEW MEASURE OF RANK CORRELATION , 1938 .

[16]  C. Zopounidis,et al.  Multicriteria decision systems for financial problems , 2013, TOP.

[17]  Yue Qi,et al.  Suitable-portfolio investors, nondominated frontier sensitivity, and the effect of multiple objectives on standard portfolio selection , 2007, Ann. Oper. Res..

[18]  Ricardo H. C. Takahashi,et al.  Modeling Decision-Maker Preferences through Utility Function Level Sets , 2011, EMO.

[19]  Ajay Kumar Bhurjee,et al.  Optimal Range of Sharpe Ratio of a Portfolio Model with Interval Parameters , 2015 .

[20]  Chelsea C. White,et al.  Question selection for multi-attribute decision-aiding , 2003, Eur. J. Oper. Res..

[21]  C. A. R. Hoare,et al.  Algorithm 64: Quicksort , 1961, Commun. ACM.

[22]  M. Ormos,et al.  Generalized Asset Pricing: Expected Downside Risk-Based Equilibrium Modelling , 2015, 1512.01806.

[23]  Renata Mansini,et al.  Linear and Mixed Integer Programming for Portfolio Optimization , 2015 .

[24]  Chen Chen,et al.  Robust multiobjective portfolio optimization: a set order relations approach , 2018, J. Comb. Optim..

[25]  S. Banihashemi,et al.  Portfolio performance evaluation in Mean-CVaR framework: A comparison with non-parametric methods value at risk in Mean-VaR analysis , 2017 .

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

[27]  Nikos E. Mastorakis,et al.  Multilayer perceptron and neural networks , 2009 .

[28]  Konstantinos Liagkouras,et al.  Efficient Portfolio Construction with the Use of Multiobjective Evolutionary Algorithms: Best Practices and Performance Metrics , 2015, Int. J. Inf. Technol. Decis. Mak..

[29]  Kalyanmoy Deb,et al.  Reference point based multi-objective optimization using evolutionary algorithms , 2006, GECCO.

[30]  Jean-Marc Martel,et al.  An Application of a Multicriteria Approach to Portfolio Comparisons , 1988 .

[31]  Geng Deng,et al.  Robust portfolio optimization with Value-at-Risk-adjusted Sharpe ratios , 2013 .

[32]  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).