Robust Portfolio Mean-Variance Optimization for Capital Allocation in Stock Investment Using the Genetic Algorithm: A Systematic Literature Review
Abstract
:1. Introduction
2. Materials and Methods
2.1. Selection Method
2.1.1. Identification Stage
- (i)
- Articles;
- (ii)
- Journal sources;
- (iii)
- Written in English;
- (iv)
- Published between 1995 and 2024;
- (v)
- Related to robust portfolios;
- (vi)
- MV or Markowitz;
- (vii)
- Stocks;
- (viii)
- GAs;
- (ix)
- Published in Scopus.
2.1.2. Screening Stage
2.1.3. Eligibility Stage
- (a)
- RQ1: This question assisted in identifying the primary objectives that the portfolio aims to achieve. Understanding these goals is essential as it guides the entire analysis and strategy formulation in portfolio management, ensuring that the research outcomes are aligned with the intended objectives.
- (b)
- RQ2: This question assisted in determining and evaluating the methods employed to maximize portfolio returns. By exploring the strategies used, this research can assess the effectiveness of different investment approaches within the context of this study.
- (c)
- RQ3: Given that uncertainty is a key factor in investment decisions, this question focuses on the methods used to address portfolio selection challenges under uncertain conditions. Understanding these methods is vital in analyzing how risks are managed and how investment decisions are made in unpredictable environments.
- (d)
- RQ4: This question aims to clarify the types of stocks included in the simulation. Knowing the stock types helps contextualize the research findings and ensures that the selected stocks are representative of relevant market conditions.
- (e)
- RQ5: This question explores the role of genetic algorithms (GAs) in solving portfolio problems involving uncertainty. By addressing this question, this research can evaluate the effectiveness of the GA as an optimization technique in complex and uncertain scenarios.
2.1.4. Inclusion Phase
2.2. Bibliometric Analysis
3. Results
3.1. Bibliometric Results
3.1.1. The Most Globally Cited Documents in Dataset 1
3.1.2. The Representation Network of Dataset 1
3.1.3. Mapping the Themes in Dataset 1
3.1.4. The Theme Evolution of Dataset 1
3.2. Results from SLR
3.2.1. RQ1: Study Objectives
3.2.2. RQ2: Study Methodologies Used to Obtain Maximum Portfolio Return
3.2.3. RQ3: Study Methodologies for Portfolios under Uncertainty
- Generate an initial population of multiple chromosomes.
- Assess the fitness of each chromosome in the population.
- Select “parents” from the population.
- Form the next generation by combining parents through crossover and mutation.
- Evaluate the fitness of the new generation.
- Replace part or all of the current population with the new generation.
- Repeat steps 3 to 6 until a satisfactory solution is achieved.
3.2.4. RQ4: Types of Stocks
3.2.5. RQ5: Role of GAs
4. Discussion
4.1. Limitations in Handling Uncertainty
4.2. Simple Assumptions on Robust Portfolio Parameters
4.3. Limited Empirical Validation
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Schottle, K.; Werner, R. Robustness Properties of Mean-Variance Portfolios. Optimization 2009, 58, 641–663. [Google Scholar] [CrossRef]
- Markowitz, H. Portfolio Selection. J. Financ. 1952, 7, 77–91. [Google Scholar]
- Markowitz, H. Portfolio Selection: Efficient Diversification of Investment; Yale University Press: New York, NY, USA, 1959. [Google Scholar]
- Hollad, J.H. Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence; University of Michigan Press: Ann Arbor, MI, USA, 1975. [Google Scholar]
- Arnone, S.; Loraschi, A.; Andrea, T. A Genetic Approach to Portfolio Selection. Neural Netw. World 1993, 6, 597–604. [Google Scholar]
- Chang, T.J.; Meade, N.; Beasly, Y.M.; Sharaina, Y.M. Heuristics for Cardinality Constrained Portfolio Optimisation. Comput. Oper. Res. 2000, 27, 1271–1302. [Google Scholar] [CrossRef]
- Soleimani, H.; Golmakani, H.R.; Salimi, M.H. Markowitz-based Portfolio Selection with Minimum Transaction Lots, Cardinality Constraints and Sector Capitalization Using Genetic Algorithm. Expert Syst. Appl. 2009, 36, 5058–5063. [Google Scholar] [CrossRef]
- Chang, T.J.; Yang, S.C.; Chang, K.J. Portfolio Optimization Problem in Different Risk Measures Using Genetic Algorithm. Expert Syst. Appl. 2009, 36, 10529–10537. [Google Scholar] [CrossRef]
- Mandal, P.K.; Thakur, M. Higher-Order Moments in Portfolio Selection Problems: A Comprehensive Literature Review. Expert Syst. Appl. 2024, 238, 121625. [Google Scholar] [CrossRef]
- Xidonas, P.; Steuer, R.; Hassapis, C. Robust Portfolio Optimization: A Categorical Bibliographic Review. Ann. Oper. Res. 2020, 292, 1. [Google Scholar] [CrossRef]
- Kalayci, C.B.; Ertenlice, O.; Akyer, H.A.H. A Review on the Current Applications of Genetic Algorithm in Mean-Variance Portfolio Optimization. Pamukkale Univ. J. Eng. Sci. 2017, 23, 470–476. [Google Scholar] [CrossRef]
- Kalayci, O.; Ertenlice, M.A.; Akbay, M.A. A Comprehensive Review of Deterministic Models and Applications for Mean-Variance Portfolio Optimization. Expert Syst. Appl. 2019, 129, 345–368. [Google Scholar] [CrossRef]
- Zhang, Y.; Li, X.; Guo, S. Portfolio Selection Problems with Markowitz’s Mean–Variance Framework: A Review of Literature. Fuzzy Optim. Decis. Mak. 2018, 17, 125–158. [Google Scholar] [CrossRef]
- Sadjadi, S.J.; Gharakhani, M.; Safari, E. Robust Optimization Framework for Cardinality Constrained Portfolio Problem. Appl. Soft Comput. 2012, 12, 91–99. [Google Scholar] [CrossRef]
- Chou, Y.-H.; Kuo, S.-y.; Lo, Y.-t. Portfolio Optimization Based on Funds Standardization and Genetic Algorithm. IEEE Access 2017, 5, 21885–21900. [Google Scholar] [CrossRef]
- Chen, C.; Zhou, Y.S. Robust Multiobjective Portfolio with Higher Moment. Expert Syst. Appl. 2018, 100, 165–181. [Google Scholar] [CrossRef]
- Caçador, S.; Dias, J.M.; Godinho, P. Portfolio Selection under Uncertainty: A New Methodology for Computing Relative-Robust Solutions. Int. Trans. Oper. Res. 2019, 28, 1296–1329. [Google Scholar] [CrossRef]
- Salehpoor, B.; Molla-Alizadeh, Z.S. A Constrained Portfolio Selection Model Considering Risk-Adjusted Measure by Using Hybrid Meta-Heuristic Algorithms. Appl. Soft Comput. J. 2019, 75, 233–253. [Google Scholar] [CrossRef]
- Lee, Y.; Kim, M.J.; Kim, J.H.; Jang, J.R.; Kim, W.C. Sparse and Robust Portfolio Selection via Semi-Definite Relaxation. J. Oper. Res. Soc. 2019, 71, 687–699. [Google Scholar] [CrossRef]
- Chen, C.; Lu, C.Y.; Lim, C.-B. An Intelligence Approach for Group Stock Portfolio Optimization with a Trading Mechanism. Knowl. Inf. Syst. 2019, 62, 287–316. [Google Scholar] [CrossRef]
- Caçador, S.; Dias, J.M.; Godinho, P. Global Minimum Variance Portfolios under Uncertainty: A Robust Optimization Approach. J. Glob. Optim. 2020, 76, 267–293. [Google Scholar] [CrossRef]
- Khodamoradi, T.; Salahi, M.; Najafi, A. Robust CCMV Model with Short Selling and Risk-Neutral Interest Rate. Physica A 2020, 547, 124429. [Google Scholar] [CrossRef]
- Xiaoa, H.; Renb, T.; Zhoub, Z.; Liu, W. Parameter Uncertainty in Estimation of Portfolio Efficiency: Evidence from an Interval Diversification-Consistent DEA Approach. Omega 2021, 103, 102357. [Google Scholar] [CrossRef]
- Quintana, D.; Moreno, D. Resampled Efficient Frontier Integration for MOEAs. Entropy 2021, 23, 422. [Google Scholar] [CrossRef] [PubMed]
- Farid, F.; Rosadi, D. Portfolio Optimization Based on Self-Organizing Maps Clustering and Genetics Algorithm. Int. J. Adv. Intell. Inform. 2022, 8, 33–44. [Google Scholar] [CrossRef]
- Min, L.; Han, Y.; Xiang, Y. A Two-Stage Robust Omega Portfolio Optimization with Cardinality Constraints. Int. J. Appl. Math. 2023, 53, 86–93. [Google Scholar]
- Rosadi, D.; Setiawan, E.P.; Templ, M.; Filzmoser, P. Robust Covariance Estimators for Mean-Variance Portfolio Optimization with Transaction Lots. Oper. Res. Perspect. 2020, 7, 1000154. [Google Scholar] [CrossRef]
- Ellegaard, O.; Wallin, J.A. The Bibliometric Analysis of: How Great is the Impact? Scientometrics 2015, 105, 1809–1831. [Google Scholar] [CrossRef]
- Van Eck, N.J.; Waltman, L. VOSviewer Manual; Leiden University: Leiden, The Netherlands, 2015; pp. 1–53. [Google Scholar]
- Aria, M.; Cuccurullo, C. Bibliometrix: An R-tool for Comprehensive Science Mapping Analysis. J. Informetr. 2017, 11, 959–975. [Google Scholar] [CrossRef]
- Markowitz, H. Portfolio Selection, 2nd ed.; Wiley: Cambridge, MA, USA, 1991. [Google Scholar]
- Bertsimas, D.; Sim, M. The Price of Robustness. Oper. Res. 2004, 52, 35–53. [Google Scholar] [CrossRef]
- Kim, W.C.; Fabozzi, F.J.; Cheridito, P.; Fox, C. Controlling Portfolio. Econ. Lett. 2014, 122, 1554–1558. [Google Scholar]
- Beasley, J.E. OR-library: Distributing Test Problems by Electronic Mail. J. Oper. Res. Soc. 1990, 41, 1069–1072. [Google Scholar] [CrossRef]
- Jegadeesh, N.; Titman, S. Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency. J. Financ. 1993, 48, 65–91. [Google Scholar] [CrossRef]
- Bondt, W.F.M.; Thaler, R. Does the Stock Market Overreact? J. Financ. 1985, 40, 793–805. [Google Scholar] [CrossRef]
- Faccini, D.; Maggioni, F.; Potra, F.A. Robust and Distributionally Robust Optimization Models for Linear Support Vector Machine. Comput. Oper. Res. 2022, 147, 105930. [Google Scholar] [CrossRef]
- Sehgal, R.; Jagadesh, P. Data-Driven Robust Portfolio Optimization with Semi Mean Absolute Deviation via Support Vector Clustering. Expert Syst. Appl. 2023, 224, 1200000. [Google Scholar] [CrossRef]
- Savaei, E.S.; Alinezhad, E.; Eghtesadifard, M. Stock Portfolio Optimization for Risk-Averse Investors: A Novel Hybrid Possibilistic and Flexible Robust Approach. Expert Syst. Appl. 2024, 250, 123754. [Google Scholar] [CrossRef]
No | Paper | Content Analysis? | Article Period | Robust Portfolio? | MV? | GA? |
---|---|---|---|---|---|---|
1 | [9] | ✔ | 1991–2021 | ✔ | - | - |
2 | [10] | ✔ | 1995–2019 | ✔ | - | - |
3 | [11] | ✔ | 1998–2016 | - | ✔ | ✔ |
4 | [12] | ✔ | 1998–2019 | - | ✔ | - |
5 | [13] | ✔ | 2002–2015 | ✔ | ✔ | - |
6 | Present study | ✔ | 1995–2024 | ✔ | ✔ | ✔ |
Code | Keyword | Number of Articles | Total | ||
---|---|---|---|---|---|
Scopus * | Science Direct ** | Dimensions *** | |||
A | (“robust portfolio”) | 2825 | 433 | 324 | 3582 |
B | (“robust portfolio”) AND (“mean-variance” OR “Markowitz”) | 1.338 | 226 | 66 | 1630 |
C | (“robust portfolio”) AND (“mean-variance” OR “Markowitz”) AND (“stocks”) | 814 | 142 | 20 | 976 |
D | (“robust portfolio”) AND (“mean-variance” OR “Markowitz”) AND (“stocks”) AND (“genetic algorithm”) | 137 | 13 | 0 | 150 |
Total | 5114 | 814 | 410 | 6338 |
No | RQ1 | RQ2 | RQ3 | RQ4 | RQ5 | Description | Ref |
---|---|---|---|---|---|---|---|
1 | Develop a novel portfolio modeling strategy considering data uncertainty using robust optimization methods. | New portfolio modeling with uncertain data and robust optimization methods. | GA. | Five indices from global capital markets (1992–1997). | To address the problem with a practical level of perturbation. | Reference Paper | [14] |
2 | Examine high- and low-return stocks, evaluate portfolio risk through fund standardization, and design a low-risk, stable-reward portfolio. | Fund standardization. | GA, Sharpe ratio. | Taiwan Economic Journal (2010–2016). | Precisely develop a portfolio that minimizes risk while maximizing rewards. | Not Suitable | [15] |
3 | Investigate portfolio problems with asymmetric distributions and uncertain parameters. | Robust multi-objective portfolio models with higher moments. | Multi-objective particle swarm optimization. | Ten Chinese stocks (2006–2010). | Not Suitable | [16] | |
4 | Introduce a novel method for calculating relative-robust portfolios. | Relative-robust portfolios based on minimax regret. | GA. | DAX index (1992–2016). | Calculation of the proposed robust portfolios for the minimax regret solutions. | Reference Paper | [17] |
5 | Introduce a new decision-making framework for stock portfolio optimization using hybrid meta-heuristic algorithms. | The MV method has the followingrisk levels: mean absolute deviation (MAD), semi-variance (SV), and variance with skewness (VWS). | Electromagnetism-like Algorithm (EM), Particle Swarm Optimization (PSO), GA, Genetic Network Programming (GNP), and Simulated Annealing (SA). | Tehran Stock Exchange. | - | Not Suitable | [18] |
6 | Develop portfolio selection models offering limited assets to minimize costs and remain robust. | Sparse and robust portfolios. | L 2 -Norm regularization and worst-case optimization. | Kenneth French’s 49 industry portfolios (1975–2014). | - | Not Suitable | [19] |
7 | Enhance the efficiency of a diversified stock portfolio using a grouping GA. | MVPO with four fitness functions and a trading mechanism. | GA. | Taiwan Stock Exchange (2010–2014). | To address the GSP (Group Stok Portfolio) optimization problem. | Not Suitable | [20] |
8 | Introduce methods to optimize the variance and covariance of asset returns without expected return estimates. | Global minimum variance portfolio, robust optimization | - | Euro Stoxx50 index (1992–2016). | - | Not Suitable | [21] |
9 | Examine the MV portfolio optimization model under specific constraints in uncertain conditions. | Cardinality constraints mean-variance (CCMV) and robust counterpart. | - | S&P 500 Communication Service. | - | Not Suitable | [22] |
10 | Develop Data Envelopment Analysis (DEA) models consistent with diversification and study parameter uncertainty effects. | DEA under the MV framework; parameter uncertainty. | - | Thirty American industry portfolios. | - | Not Suitable | [23] |
11 | Address potential estimation inaccuracies in MVPO. | Conventional multi-objective evolutionary algorithms. | - | Comprehensive financial indices (2006–2020). | - | Not Suitable | [24] |
12 | Analyze clustering outcomes to select top-performing stocks using a GA for portfolio weighting. | Self-Organizing Maps (SOMs), MV. | GA. | LQ45 shares (2018–2019). | To obtain the best offspring to produce the optimal solution for the problems at hand. | Not Suitable | [25] |
13 | Develop a more aggressive robust Omega portfolio. | Robust Omega Portfolio. | GA. | The dataset of 30 U.S. industry portfolios was sourced from Kenneth R. French’s website. | To solve the mixed-integer programming problem suggested in the preselection. | Not Suitable | [26] |
14 | Improve MVPO considering integer transaction lots and robust covariance matrix estimators. | Markowitz portfolio, transaction lots, robust estimation | GA. | Six stocks in the Indonesia Stock Exchange. Distribution with contamination. | To complete integer optimization. | Reference Paper | [27] |
Database | Data Code D | Duplicate | Abstract and Title | Full Text | |||
---|---|---|---|---|---|---|---|
I | E | I | E | I | Ex | ||
Scopus | 137 | 137 | 0 | 13 | 124 | 2 | 13 |
ScienceDirect | 13 | 7 | 6 | 1 | 0 | 1 | 0 |
Dimensions | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Total | 150 | 144 | 6 | 14 * | 124 | 3 ** | 13 |
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Share and Cite
Fransisca, D.C.; Sukono; Chaerani, D.; Halim, N.A. Robust Portfolio Mean-Variance Optimization for Capital Allocation in Stock Investment Using the Genetic Algorithm: A Systematic Literature Review. Computation 2024, 12, 166. https://doi.org/10.3390/computation12080166
Fransisca DC, Sukono, Chaerani D, Halim NA. Robust Portfolio Mean-Variance Optimization for Capital Allocation in Stock Investment Using the Genetic Algorithm: A Systematic Literature Review. Computation. 2024; 12(8):166. https://doi.org/10.3390/computation12080166
Chicago/Turabian StyleFransisca, Diandra Chika, Sukono, Diah Chaerani, and Nurfadhlina Abdul Halim. 2024. "Robust Portfolio Mean-Variance Optimization for Capital Allocation in Stock Investment Using the Genetic Algorithm: A Systematic Literature Review" Computation 12, no. 8: 166. https://doi.org/10.3390/computation12080166