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Equity portfolio management with cardinality constraints and risk parity control using multi-objective particle swarm optimization. (English) Zbl 1458.91195
Summary: The financial crisis and the market uncertainty of the last years have pointed out the shortcomings of traditional portfolio theory to adequately manage the different sources of risk of the investment process. This paper addresses the issue by developing an alternative portfolio design, that integrates risk parity into the cardinality constrained portfolio optimization model. The resulting mixed integer programming problem is handled by an improved multi-objective particle swarm optimization algorithm. Three hybrid approaches, based on a repair mechanism and different versions of the constrained-domination principle, are proposed to handle constraints. The efficiency of the algorithm and the effectiveness of the solution approaches are assessed through a set of numerical examples. Moreover, the benefits of adopting the proposed strategy instead of the cardinality constrained mean-variance approach are validated in an out-of-sample experiment.

MSC:
91G10 Portfolio theory
90C29 Multi-objective and goal programming
90C59 Approximation methods and heuristics in mathematical programming
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[1] Anagnostopoulos, K. P.; Mamanis, G., A portfolio optimization model with three objectives and discrete variables, Comput. Oper. Res., 37, 7, 1285-1297, (2010) · Zbl 1178.90299
[2] Anagnostopoulos, K. P.; Mamanis, G., The mean-variance cardinality constrained portfolio optimization problem: an experimental evaluation of five multiobjective evolutionary algorithms, Expert Syst. Appl., 38, 11, 14208-14217, (2011)
[3] Artzner, P.; Delbaen, F.; Eber, J.-M.; Heath, D., Coherent measures of risk, Math Financ., 9, 3, 203-228, (1999) · Zbl 0980.91042
[4] Auger, A.; Bader, J.; Brockhoff, D.; Zitzler, E., Theory of the hypervolume indicator: optimal μ-distributions and the choice of the reference point, Proceedings of the Tenth ACM SIGEVO Workshop on Foundations of Genetic Algorithms, 87-102, (2009), ACM · Zbl 1369.68293
[5] Bai, X.; Scheinberg, K.; Tutuncu, R., Least-squares approach to risk parity in portfolio selection, Quant. Financ., 16, 3, 357-376, (2016)
[6] Beasley, J. E., Portfolio optimisation: models and solution approaches, Theory Driven by Influential Applications, 201-221, (2013), INFORMS
[7] Bertsimas, D.; Shioda, R., Algorithm for cardinality-constrained quadratic optimization, Comput. Optim. Appl., 43, 1, 1-22, (2009) · Zbl 1178.90262
[8] Braga, M. D., Risk parity versus other μ-free strategies: a comparison in a triple view, Invest. Manag. Financ. Innov., 12, 2, 277-289, (2015)
[9] Bruni, R.; Cesarone, F.; Scozzari, A.; Tardella, F., Real-world datasets for portfolio selection and solutions of some stochastic dominance portfolio models, Data Brief, 8, 858-862, (2016)
[10] Cao, Y.; Smucker, B. J.; Robinson, T. J., On using the hypervolume indicator to compare pareto fronts: applications to multi-criteria optimal experimental design, J. Stat. Plan. Inference, 160, 60-74, (2015) · Zbl 1311.62115
[11] de Carvalho, R. L.; Lu, X.; Moulin, P., Demystifying equity risk-based strategies: a simple alpha plus beta description, J. Portf. Manag., 38, 3, 56-70, (2012)
[12] de Carvalho, R. L.; Lu, X.; Moulin, P., An integrated risk-budgeting approach for multi-strategy equity portfolios, J. Asset Manag., 15, 1, 24-47, (2014)
[13] Chang, T.-J.; Meade, N.; Beasley, J. E.; Sharaiha, Y. M., Heuristics for cardinality constrained portfolio optimisation, Comput. Oper. Res., 27, 13, 1271-1302, (2000) · Zbl 1032.91074
[14] Chaves, D.; Hsu, J.; Li, F.; Shakernia, O., Risk parity portfolio vs. other asset allocation heuristic portfolios, J. Invest., 20, 1, 108-118, (2011)
[15] Coello, C. A.C.; Pulido, G. T.; Lechuga, M. S., Handling multiple objectives with particle swarm optimization, IEEE Trans. Evol. Comput., 8, 3, 256-279, (2004)
[16] Crama, Y.; Schyns, M., Simulated annealing for complex portfolio selection problems, Eur. J. Oper. Res., 150, 3, 546-571, (2003) · Zbl 1046.91057
[17] Cura, T., Particle swarm optimization approach to portfolio optimization, Nonlinear Anal. Real World Appl., 10, 4, 2396-2406, (2009) · Zbl 1163.90669
[18] Deb, K., An efficient constraint handling method for genetic algorithms, Comput. Methods Appl. Mech. Eng., 186, 2, 311-338, (2000) · Zbl 1028.90533
[19] DeMiguel, V.; Garlappi, L.; Uppal, R., Optimal versus naive diversification: how inefficient is the 1/n portfolio strategy?, Rev. Financ. Stud., 22, 5, 1915-1953, (2007)
[20] Eakins, S. G.; Stansell, S., An examination of alternative portfolio rebalancing strategies applied to sector funds, J. Asset Manag., 8, 1, 1-8, (2007)
[21] Eberhart, R.; Kennedy, J., A new optimizer using particle swarm theory, Proceedings of the Sixth International Symposium on Micro Machine and Human Science, MHS’95, 39-43, (1995), IEEE
[22] Eiben, A. E.; Smit, S. K., Parameter tuning for configuring and analyzing evolutionary algorithms, Swarm Evol. Comput., 1, 1, 19-31, (2011)
[23] Ertenlice, O.; Kalayci, C. B., A survey of swarm intelligence for portfolio optimization: algorithms and applications, Swarm Evol. Comput., 39, 36-52, (2018)
[24] Feng, Y.; Palomar, D. P., SCRIP: successive convex optimization methods for risk parity portfolio design, IEEE Trans. Signal Process., 63, 19, 5285-5300, (2015) · Zbl 1394.94183
[25] Feng, Y.; Palomar, D. P., Portfolio optimization with asset selection and risk parity control, Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 6585-6589, (2016), IEEE
[26] Fonseca, C. M.; Knowles, J. D.; Thiele, L.; Zitzler, E., A tutorial on the performance assessment of stochastic multiobjective optimizers, Proceedings of the Third International Conference on Evolutionary Multi-Criterion Optimization (EMO), 216, 240, (2005)
[27] Griveau-Billion, T., Richard, J.-C., Roncalli, T., 2013. A fast algorithm for computing high-dimensional risk parity portfolios. available at SSRN: https://ssrn.com/abstract=2325255.
[28] Guerard Jr, J. B., Handbook of portfolio construction: contemporary applications of Markowitz techniques, (2009), Springer Science & Business Media
[29] Hochreiter, R., An evolutionary optimization approach to risk parity portfolio selection, Proceedings of the European Conference on the Applications of Evolutionary Computation, 279-288, (2015), Springer
[30] Ishibuchi, H.; Doi, K.; Nojima, Y., On the effect of normalization in MOEA/D for multi-objective and many-objective optimization, Complex Intell. Syst., 3, 4, 279-294, (2017)
[31] Jobst, N. J.; Horniman, M. D.; Lucas, C. A.; Mitra, G., Computational aspects of alternative portfolio selection models in the presence of discrete asset choice constraints, Quant. Financ., 1, 5, 489-501, (2001) · Zbl 1405.91559
[32] Kaya, H., Lee, W., 2012. Demystifying risk parity. available at SSRN: https://ssrn.com/abstract=1987770.
[33] Keating, C.; Shadwick, W. F., A universal performance measure, J. Perform. Meas., 6, 3, 59-84, (2002)
[34] Kolm, P. N.; Tütüncü, R.; Fabozzi, F. J., 60 years of portfolio optimization: practical challenges and current trends, Eur. J. Oper. Research, 234, 2, 356-371, (2014) · Zbl 1304.91200
[35] Li, D.; Sun, X.; Wang, J., Optimal lot solution to cardinality constrained mean-variance formulation for portfolio selection, Math. Financ., 16, 1, 83-101, (2006) · Zbl 1128.91028
[36] Li, M.; Yang, S.; Liu, X., A performance comparison indicator for pareto front approximations in many-objective optimization, Proceedings of the Annual Conference on Genetic and Evolutionary Computation, 703-710, (2015), ACM
[37] Liagkouras, K.; Metaxiotis, K., Efficient portfolio construction with the use of multiobjective evolutionary algorithms: best practices and performance metrics, Int. J. Inf. Technol. Decis. Mak., 14, 3, 535-564, (2015)
[38] Liagkouras, K.; Metaxiotis, K., Examining the effect of different configuration issues of the multiobjective evolutionary algorithms on the efficient frontier formulation for the constrained portfolio optimization problem, J. Oper. Res. Soc., 1-23, (2017)
[39] Liang, J. J.; Qu, B.-Y., Large-scale portfolio optimization using multiobjective dynamic mutli-swarm particle swarm optimizer, Proceedings of the IEEE Symposium on Swarm Intelligence (SIS), 1-6, (2013), IEEE
[40] Lizárraga, G. L., On the Evaluation of the Quality of Non-dominated Sets, (2009), Centro de Investigación en Matemáticas, AC (CIMAT), Ph. D. thesis
[41] Lwin, K.; Qu, R.; Kendall, G., A learning-guided multi-objective evolutionary algorithm for constrained portfolio optimization, Appl. Soft Comput., 24, 757-772, (2014)
[42] Maillard, S.; Roncalli, T.; Teïletche, J., The properties of equally weighted risk contribution portfolios, J. Portf. Manag., 36, 4, 60-70, (2010)
[43] Markowitz, H., Portfolio selection, J. Financ., 7, 1, 77-91, (1952)
[44] Meghwani, S. S.; Thakur, M., Multi-criteria algorithms for portfolio optimization under practical constraints, Swarm Evol. Comput., 37, 104-125, (2017)
[45] Mishra, S. K.; Panda, G.; Majhi, R., A comparative performance assessment of a set of multiobjective algorithms for constrained portfolio assets selection, Swarm Evol. Comput., 16, 38-51, (2014)
[46] Moral-Escudero, R.; Ruiz-Torrubiano, R.; Suárez, A., Selection of optimal investment portfolios with cardinality constraints, Proceedings of the IEEE Congress on Evolutionary Computation, CEC, 2382-2388, (2006), IEEE
[47] Mutunge, P.; Haugland, D., Minimizing the tracking error of cardinality constrained portfolios, Comput. Oper. Res., 90, 33-41, (2018) · Zbl 1391.90434
[48] Qian, E., On the financial interpretation of risk contribution: risk budgets do add up, J. Invest. Manag., 4, 4, 41-51, (2006)
[49] Rockafellar, R. T.; Uryasev, S., Optimization of conditional value-at-risk, J. Risk, 2, 21-42, (2000)
[50] Roncalli, T., Introduction to Risk Parity and Budgeting, (2013), CRC Press · Zbl 1278.91001
[51] Roncalli, T., 2014. Introducing expected returns into risk parity portfolios: a new framework for asset allocation. available at SSRN: https://ssrn.com/abstract=2321309.
[52] Sharpe, W. F., Mutual fund performance, J. Bus., 39, 1, 119-138, (1966)
[53] Shaw, D. X.; Liu, S.; Kopman, L., Lagrangian relaxation procedure for cardinality-constrained portfolio optimization, Optim. Methods Softw., 23, 3, 411-420, (2008) · Zbl 1162.90531
[54] Siu, F., Risk parity strategies for equity portfolio management: can an asset-class strategy translate to equities?, J. Indexes, 18-25, (2014)
[55] Spinu, F., 2013. An algorithm for computing risk parity weights. available at SSRN: https://ssrn.com/abstract=2297383.
[56] Streichert, F.; Ulmer, H.; Zell, A., Evaluating a hybrid encoding and three crossover operators on the constrained portfolio selection problem, Proceedings of the Congress on Evolutionary Computation, CEC, 1, 932-939, (2004), IEEE
[57] Tseng, P., Convergence of a block coordinate descent method for nondifferentiable minimization, J. Optim. Theory Appl., 109, 3, 475-494, (2001) · Zbl 1006.65062
[58] Vijayalakshmi Pai, G.; Michel, T., Metaheuristic optimization of marginal risk constrained long-short portfolios, J. Artif. Intell. Soft Comput. Res., 2, 3, 259-274, (2012)
[59] Woerheide, W.; Persson, D., An index of portfolio diversification, Financ. Serv. Rev., 2, 2, 73-85, (1993)
[60] Woldesenbet, Y. G.; Yen, G. G.; Tessema, B. G., Constraint handling in multiobjective evolutionary optimization, IEEE Trans. Evol. Comput., 13, 3, 514-525, (2009)
[61] Woodside-Oriakhi, M.; Lucas, C.; Beasley, J. E., Heuristic algorithms for the cardinality constrained efficient frontier, Eur. J. Oper. Res., 213, 3, 538-550, (2011) · Zbl 1218.91151
[62] Xu, F.; Chen, W., Stochastic portfolio selection based on velocity limited particle swarm optimization, Proceedings of the Sixth World Congress on Intelligent Control and Automation, WCICA, 1, 3599-3603, (2006), IEEE
[63] Yaakob, S. B.; Watada, J., A hybrid particle swarm optimization approach to mixed integer quadratic programming for portfolio selection problems, Int. J. Simul. Syst. Sci. Technol., 11, 5, (2010)
[64] Zhang, H.; Rangaiah, G., An efficient constraint handling method with integrated differential evolution for numerical and engineering optimization, Comput. Chem. Eng., 37, 74-88, (2012)
[65] Zitzler, E.; Brockhoff, D.; Thiele, L., The hypervolume indicator revisited: on the design of pareto-compliant indicators via weighted integration, Proceedings of the International Conference on Evolutionary Multi-Criterion Optimization, 862-876, (2007), Springer
[66] Zitzler, E.; Thiele, L., Multiobjective optimization using evolutionary algorithms a comparative case study, Proceedings of the International Conference on Parallel Problem Solving from Nature, 292-301, (1998), Springer
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