Analysis of new approaches used in portfolio optimization: a systematic literature review

Milhomem, Danilo Alcantara; Dantas, Maria José Pereira

doi:10.1590/0103-6513.20190144

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Systematic Review • Prod. 30 • 2020 • https://doi.org/10.1590/0103-6513.20190144 linkcopy

Analysis of new approaches used in portfolio optimization: a systematic literature review

Authorship SCIMAGO INSTITUTIONS RANKINGS

Paper aims To do a comprehensive review of the exact and heuristic methods, software/programming languages, constraints, and types of analysis (technical and fundamental) used to solve the portfolio optimization problem.

Originality The paper presents a useful discussion on aspects of portfolio optimization, both for researchers and investors and for finance professionals.

Research method A systematic literature review was performed, and the articles were compiled according to pre-established criteria/filters.

Main findings A point of attention should be given to the input data of optimization models. Depending on the degree of the estimation error of these input parameters, the optimization results may be lower than the results of the 1/N trading strategy.

Implications for theory and practice Robust optimization, Fuzzy logic, and prediction are examples of techniques used to reduce estimation errors. At the end of the article are pointed out trends and some gaps for future work.

Keywords:
Portfolio selection; Heuristics; Constraints; Stock market

PROTOCOL FOR SYSTEMATIC LITERATURE REVIEW: SEARCH STRATEGY
Central Theme: The Central Theme is Portfolio Optimization. This theme will be approached in an open manner with the objective of finding the greatest number of academic and scientific publications.
Conceptual Framework: Portfolio Optimization is a very important topic in the stock market area. Since the creation of the Mean-Variance Model by Markowitz (1952), several studies have been developed in order to improve the model/create more robust analysis methods through the insertion of realistic constraints in the model. This review has the purpose of identifying the studies that include the theme, the tools, and methods for optimizing Portfolio.
Background:	Diversification and optimization of an investment portfolio.
Scope:	The Search period will be between 2014 and 2018, with the intention of finding the most relevant publications published in the last five years.
Theoretical currents:	Portfolio Optimization.
Languages:	Both the search terms and the papers will be in English.
Research Questions:	Question 1 - Which key methods, tools, or techniques are used in portfolio optimization?
	Question 2 - Which realistic constraints are used?
	Question 3 - What type of analysis is done regarding the stock: fundamental, technical, or mixed (fundamental and technical)?
	Question 4 - Which software/programming language are used?
Review Strategy:	(X) Configurative () Aggregative
Inclusion Criteria	The papers should contain the latest discoveries about portfolio optimization models as well as realistic constraints, analysis types, and algorithms.
Exclusion Criteria	Duplicate papers
Search terms:	1st search: “Optimization” AND “portfolio” AND “algorithms” AND “return” AND “risk”;
	2nd search: “Optimization” AND “portfolio” AND “algorithms” AND “return” AND “risk”;
	3rt search: “Portfolio Optimization” AND “stock market” AND “Markowitz”;
	4th search: “stock market” AND “Portfolio selection” AND “portfolio optimization”;
	5th search: “Portfolio Optimization” AND “stock market” AND “financial”.
Search Sources	Web of Science database.

Journal	Impact factor	Papers
Journal	(5 years)	Papers
IEEE TRANSACTIONS ON FUZZY SYSTEMS	9.340	1
MANAGEMENT SCIENCE	4.927	2
SWARM AND EVOLUTIONARY COMPUTATION	4.607	4
APPLIED SOFT COMPUTING (PRINT)	4.004	2
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH	3.960	4
EXPERT SYSTEMS WITH APPLICATIONS	3.711	6
PLOS ONE	3.352	1
OPERATIONS RESEARCH	3.047	1
ELECTRIC POWER SYSTEMS RESEARCH	2.859	1
NEURAL COMPUTING & APPLICATIONS	2.697	1
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING	2.504	1
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT	2.228	1
OR-SPEKTRUM	2.227	1
PHYSICA. A (PRINT)	2.076	2
ANNALS OF OPERATION RESEARCH	1.943	2
ECONOMIC MODELLING	1.844	3
INTERNATIONAL JOURNAL OF INFORMATION TECHNOLOGY & DECISION MAKING	1.670	1
JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY	1.634	1
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS	1.412	1
QUANTITATIVE FINANCE (PRINT)	1.190	2
MATHEMATICAL PROBLEMS IN ENGINEERING (PRINT)	1.156	1
CENTRAL EUROPEAN JOURNAL OF OPERATIONS RESEARCH	0.948	1
INTELLIGENT SYSTEMS IN ACCOUNTING, FINANCE & MANAGEMENT	N/D	1

References	Technique: Exact
Al Janabi (2014)	LVaR
Ayub et al. (2015)	DR framework
Ackermann et al. (2016)	MV
Ali et al. (2016)	MINLP
Algarvio et al. (2017)	MV
Ban et al. (2016)	PBR
Benati (2015)	MedMAD
Bensaïda et al. (2018)	Markov chains
Ceren & Köksalan (2014)	MILP
Ji et al. (2017)	MinG
Levy & Kaplanski (2015)	SSDMN
Marzban et al. (2015)	IMPRO
Ren et al. (2017)	MST
Sharma & Banerjee (2015)	Mean-variance-asymmetry-kurtosis
Sun & Liu (2016)	DCCA
Le Thi & Moeini (2014)	MAD
Zhao et al. (2018a)	q-dependent
Zhao et al. (2018b)	Temporal network structure

References	Technique: Exact/Heuristic	Heuristic	Hybrid heuristic	Single-period	Multi-period	Single-objective	Multi-objective
Babaei et al. (2015)	MOPSO	X		X			X
Berutich et al. (2016)	GP	X			X		X
Chen & Zhou (2018)	MOPSO	X			X		X
García et al. (2018)	GA and TS	X			X	X
Kumar & Mishra (2017)	M-CABC	X		X			X
Li & Bao (2014)	Immunological algorithm	X		X			X
Liu & Zhang (2015)	GA with Fuzzy		X		X		X
Macedo et al. (2017)	NSGA II and SPEA 2	X			X		X
Meghwani & Thakur (2018)	NSGA II; MOEA/D and GWASF-GA	X			X		X
Mishra et al. (2016)	SR-MOPSO	X		X			X
Pai (2017)	MODE/Fuzzy and MOES/Fuzzy)		X		X		X
Pekár et al. (2016)	Algorithm of differential evolution	X		X		X
Qu et al. (2017)	(NMOEA/D)	X			X		X
Reveiz-Herault (2016)	GA	X		N/D	N/D	X
Rezaei Pouya et al. (2016)	IWO and PSO	X		X		X
Rubio et al. (2016)	FTS	X
Rubio, et al. (2017)	FLR	X
Saborido et al. (2016)	MDRS		X	X			X
Silva et al. (2015)	GA	X			X		X
Vercher & Bermúdez (2015)	GA with Fuzzy		X	X			X
Zhang & Liu (2014)	GA with Fuzzy		X		X		X

Author(s)	Heuristic method	Realistic constraints	Database
Babaei et al. (2015)	MOPSO	threshold constraints; Cardinality constraints;	S&P500
Berutich et al. (2016)	GP	N/D	Stock Market Espanha (índice IBEX35)
Chen & Zhou (2018)	MOPSO, NSGA II and SPEA 2	Long-only constraint	Stock Market China
García et al. (2018)	GA and TS	Cardinality constraints	OR-Library
Kumar & Mishra (2017)	M-CABC	Cardinality constraints; threshold constraints; Long only constraint;	OR-Library
Li & Bao (2014)	Immunological algorithm	Cardinality constraints; threshold constraints; Transaction cost;	Indices: Hang Seng 33, DAX 200, FTSE 100, S & P 100 e Nikkei 225.
Liu & Zhang (2015)	GA with Fuzzy	Cardinality constraints; Transaction cost; Transaction lots;	Stock market China
Macedo et al. (2017)	NSGA II and SPEA 2	Cardinality constraints; Transaction cost; Transaction lots;	Thompson-Reuters Datastream (agora Eikon)
Meghwani & Thakur (2018)	NSGA II, MOEA/D, and GWASF-GA	Cardinality constraints; Quantity constraint; self-financing constraint; Transaction cost.	Fama and French Data Library
Mishra et al. (2016)	SR-MOPSO	Cardinality constraints; threshold constraints;	OR-Library
Pai (2017)	MODE/Fuzzy and MOES/Fuzzy	Long-only constraint	Índice BSE (Bombaim Stock Exchange, Índia)
Pekár et al. (2016)	Algorithm of differential evolution	Non-constrained problem with continuous variables	Indice Dow Jones
Rezaei Pouya et al. (2016)	IWO and PSO	Sector Capitalization; Transaction lots; Cardinality constraints; threshold constraints;	Tehran Stock Exchange Market in 2013
Qu et al. (2017)	NMOEA/D	N/D	Stock Market China
Reveiz-Herault (2016)	GA	Tracking Error Constraints.	Índice de títulos dos EUA
Saborido et al. (2016)	MDRS	Cardinality constraints	Stock Market Espanha (índice IBEX35)
Silva et al. (2015)	GA	Cardinality constraint; Quantity constraint; Long only constraint; Transaction costs.	S&P500
Vercher & Bermúdez (2015)	GA with Fuzzy	Cardinality Constraints	Stock Market Espanha (índice IBEX35)
Zhang & Liu (2014)	GA with Fuzzy	self-financing constraint; the Long only constraint	Stock market Shangai

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[1] MAD: Mean-Absolute Deviation Model; PBR: Performance-based Regularization-Combinatorial optimization; MV: Mean-Variance; MINLP: Mixed-integer nonlinear programming; MedMAD: Median Mean Absolute Deviation (MAD); MILP: Mixed-integer linear programming; IMPRO: Insured Multi-period Portfolio Robust Optimization - linear model; MinG: Minimal Gini model; LVar: Liquidity adjusted value at risk; DR Framework: Extension of the Markowitz model where the proxy variance was substituted for the downside risk as asymmetric lower partial moments (ALPM); SSDMN: Stochastic Domain for mixed normal distributions; DCCA: Method for Cross‐Correlation Analysis; q-dependent: q-dependent cross-correlation coefficient; MST: Dynamic portfolio Strategy based on network structures (minimum spanning tree).