Multiobjective Financial Portfolio Design: A Hybrid Evolutionary Approach

Abstract

A principal challenge in modern computational finance is efficient portfolio designportfolio optimization followed by decision-making. Optimization based on even the widely used Markowitz two-objective mean-variance approach becomes computationally challenging for real-life portfolios. Practical portfolio design introduces further complexity as it requires the optimization of multiple return and risk measures subject to a variety of risk and regulatory constraints. Further, some of these measures may be nonlinear and nonconvex, presenting a daunting challenge to conventional optimization approaches. We introduce a powerful hybrid multiobjective optimization approach that combines evolutionary computation with linear programming to simultaneously maximize these return measures, minimize these risk measures, and identify the efficient frontier of portfolios that satisfy all constraints. We also present a novel interactive graphical decision-making method that allows the decision-maker to quickly down-select to a small subset of efficient portfolios. The approach has been tested on real-life portfolios with hundreds to thousands of assets, and is currently being used for investment decisionmaking in industry.

Multiobjective evolutionary algorithms for complex portfolio optimization problems

“…There are few studies that adopt a proper multiobjective approach to portfolio selection, most of them using a mean-variance formulation: MOEAs with local search for feasible solutions (Streichert et al 2003); a MOEA to solve the multi-objective quadratic programming problem (Ong et al 2005); greedy search, simulated annealing and ant colony optimization (Armananzas and Lozano 2005); NSGA-II, PESA and SPEA2 for solving the standard mean-variance portfolio optimization problem (Diosan 2005); a hybrid multiobjective optimization approach combining evolutionary computation with linear programming (Subbu et al 2005); a MOEA with an ordered based representation (Chiam et al 2008); a hybrid algorithm combining NSGA-II with the critical line algorithm (Branke et al 2009); a differential evolution algorithm for multiobjective portfolio optimization (Krink and Paterlini 2009).…”

2-Phase NSGA II: An Optimized Reward and Risk Measurements Algorithm in Portfolio Optimization

“…Besides, the paper [25] applied greedy search, simulated annealing and ant colony optimization for portfolio problem. On the other hand, [26] used NSGA II, PESA and SPEA 2 for solving mean-variance portfolio optimization problem and [27] integrated evolutionary computations and linear programming to suggest a hybrid multi-objective optimization approach. Moreover, authors in [12] used multi-objective evolutionary algorithm presentation on an ordered basis.…”

“…Reference [28] suggested a hybrid algorithm that integrated critical line algorithm and NSGA II. Furthermore, NSGA II, PESA and SPEA 2 in portfolio optimization problem was compared by [27]. Reference [11] considered third objective function of the number of securities in the portfolio except two other common objectives of risk and return.…”

Natural Computing in Finance – A Review

“…The formulation of the portfolio problem includes cardinality and buy-in constraints, and a repair mechanism was applied in order to ensure that generated solutions were feasible. The utility of differing crossover operators and differing genotypic representations for the portfolio selection problem was examined by [103,104], and the application of EC hybrids was examined by [106] and [105]. The impact of cardinality constraints was examined in [46] and [82] (the latter also adopted an EC hybrid approach).…”