Ortalama-varyans portföy optimizasyonunda genetik algoritma uygulamaları üzerine bir literatür araştırması

Mean-variance portfolio optimization model, introduced by Markowitz, provides a fundamental answer to the problem of portfolio management. This model seeks an efficient frontier with the best trade-offs between two conflicting objectives of maximizing return and minimizing risk. The problem of determining an efficient frontier is known to be NP-hard. Due to the complexity of the problem, genetic algorithms have been widely employed by a growing number of researchers to solve this problem. In this study, a literature review of genetic algorithms implementations on mean-variance portfolio optimization is examined from the recent published literature. Main specifications of the problems studied and the specifications of suggested genetic algorithms have been summarized

Portfolio selection problems in practice: a comparison between linear and quadratic optimization models

Several portfolio selection models take into account practical limitations on the number of assets to include and on their weights in the portfolio. We present here a study of the Limited Asset Markowitz (LAM), of the Limited Asset Mean Absolute Deviation (LAMAD) and of the Limited Asset Conditional Value-at-Risk (LACVaR) models, where the assets are limited with the introduction of quantity and cardinality constraints. We propose a completely new approach for solving the LAM model, based on reformulation as a Standard Quadratic Program and on some recent theoretical results. With this approach we obtain optimal solutions both for some well-known financial data sets used by several other authors, and for some unsolved large size portfolio problems. We also test our method on five new data sets involving real-world capital market indices from major stock markets. Our computational experience shows that, rather unexpectedly, it is easier to solve the quadratic LAM model with our algorithm, than to solve the linear LACVaR and LAMAD models with CPLEX, one of the best commercial codes for mixed integer linear programming (MILP) problems. Finally, on the new data sets we have also compared, using out-of-sample analysis, the performance of the portfolios obtained by the Limited Asset models with the performance provided by the unconstrained models and with that of the official capital market indices

Portfolio selection using neural networks

In this paper we apply a heuristic method based on artificial neural networks in order to trace out the efficient frontier associated to the portfolio selection problem. We consider a generalization of the standard Markowitz mean-variance model which includes cardinality and bounding constraints. These constraints ensure the investment in a given number of different assets and limit the amount of capital to be invested in each asset. We present some experimental results obtained with the neural network heuristic and we compare them to those obtained with three previous heuristic methods.Comment: 12 pages; submitted to "Computers & Operations Research

Differential Evolution for Multiobjective Portfolio Optimization

Financial portfolio optimization is a challenging problem. First, the problem is multiobjective (i.e.: minimize risk and maximize profit) and the objective functions are often multimodal and non smooth (e.g.: value at risk). Second, managers have often to face real-world constraints, which are typically non-linear. Hence, conventional optimization techniques, such as quadratic programming, cannot be used. Stochastic search heuristic can be an attractive alternative. In this paper, we propose a new multiobjective algorithm for portfolio optimization: DEMPO - Differential Evolution for Multiobjective Portfolio Optimization. The main advantage of this new algorithm is its generality, i.e., the ability to tackle a portfolio optimization task as it is, without simplifications. Our empirical results show the capability of our approach of obtaining highly accurate results in very reasonable runtime, in comparison with quadratic programming and another state-of-art search heuristic, the so-called NSGA II.Portfolio Optimization, Multiobjective, Real-world Constraints, Value at Risk, Expected Shortfall, Differential Evolution

Applying modern portfolio theory to the analysis of terrorism: computing the set of attack method combinations from which the rational terrorist group will choose in order to maximise injuries and fatalities

In this paper, terrorism is analysed using the tools of modern portfolio theory. This approach permits the analysis of the returns that a terrorist group can expect from their activities as well as the risk they face. The analysis sheds new light on the nature of the terrorist group’s (attack method) choice set and the efficiency properties of that set. If terrorist groups are, on average, more risk averse, the economist can expect the terrorist group to exhibit a bias towards bombing and armed attack. In addition, even the riskiest (from the terrorist group’s point of view) combinations of attack methods have maximum expected returns of less than 70 injuries and fatalities per attack per year

Computing the Mean-Variance-Sustainability Nondominated Surface by ev-MOGA

[EN] Despite the widespread use of the classical bicriteria Markowitz mean-variance framework, a broad consensus is emerging on the need to include more criteria for complex portfolio selection problems. Sustainable investing, also called socially responsible investment, is becoming a mainstream investment practice. In recent years, some scholars have attempted to include sustainability as a third criterion to better reflect the individual preferences of those ethical or green investors who are willing to combine strong financial performance with social benefits. For this purpose, new computational methods for optimizing this complex multiobjective problem are needed. Multiobjective evolutionary algorithms (MOEAs) have been recently used for portfolio selection, thus extending the mean-variance methodology to obtain a mean-variance-sustainability nondominated surface. In this paper, we apply a recent multiobjective genetic algorithm based on the concept of epsilon-dominance called ev-MOGA. This algorithm tries to ensure convergence towards the Pareto set in a smart distributed manner with limited memory resources. It also adjusts the limits of the Pareto front dynamically and prevents solutions belonging to the ends of the front from being lost. Moreover, the individual preferences of socially responsible investors could be visualised using a novel tool, known as level diagrams, which helps investors better understand the range of values attainable and the tradeoff between return, risk, and sustainability.This work was funded by "Ministerio de Economia y Competitividad" (Spain), research project RTI2018-096904B-I00, and "Conselleria de Educacion, Cultura y DeporteGeneralitat Valenciana" (Spain), research project AICO/2019/055Garcia-Bernabeu, A.; Salcedo-Romero-De-Ávila, J.; Hilario Caballero, A.; Pla Santamaría, D.; Herrero Durá, JM. (2019). Computing the Mean-Variance-Sustainability Nondominated Surface by ev-MOGA. Complexity. 2019:1-12. https://doi.org/10.1155/2019/6095712S1122019Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77. doi:10.2307/2975974Hirschberger, M., Steuer, R. E., Utz, S., Wimmer, M., & Qi, Y. (2013). Computing the Nondominated Surface in Tri-Criterion Portfolio Selection. Operations Research, 61(1), 169-183. doi:10.1287/opre.1120.1140Utz, S., Wimmer, M., Hirschberger, M., & Steuer, R. E. (2014). Tri-criterion inverse portfolio optimization with application to socially responsible mutual funds. European Journal of Operational Research, 234(2), 491-498. doi:10.1016/j.ejor.2013.07.024Utz, S., Wimmer, M., & Steuer, R. E. (2015). Tri-criterion modeling for constructing more-sustainable mutual funds. European Journal of Operational Research, 246(1), 331-338. doi:10.1016/j.ejor.2015.04.035Qi, Y., Steuer, R. E., & Wimmer, M. (2015). An analytical derivation of the efficient surface in portfolio selection with three criteria. Annals of Operations Research, 251(1-2), 161-177. doi:10.1007/s10479-015-1900-yGasser, S. M., Rammerstorfer, M., & Weinmayer, K. (2017). Markowitz revisited: Social portfolio engineering. European Journal of Operational Research, 258(3), 1181-1190. doi:10.1016/j.ejor.2016.10.043Qi, Y. (2018). On outperforming social-screening-indexing by multiple-objective portfolio selection. Annals of Operations Research, 267(1-2), 493-513. doi:10.1007/s10479-018-2921-0Nathaphan, S., & Chunhachinda, P. (2010). Estimation Risk Modeling in Optimal Portfolio Selection: An Empirical Study from Emerging Markets. Economics Research International, 2010, 1-10. doi:10.1155/2010/340181DeMiguel, V., Garlappi, L., & Uppal, R. (2007). Optimal Versus Naive Diversification: How Inefficient is the 1/NPortfolio Strategy? Review of Financial Studies, 22(5), 1915-1953. doi:10.1093/rfs/hhm075Metaxiotis, K., & Liagkouras, K. (2012). Multiobjective Evolutionary Algorithms for Portfolio Management: A comprehensive literature review. Expert Systems with Applications, 39(14), 11685-11698. doi:10.1016/j.eswa.2012.04.053Bertsimas, D., & Shioda, R. (2007). Algorithm for cardinality-constrained quadratic optimization. Computational Optimization and Applications, 43(1), 1-22. doi:10.1007/s10589-007-9126-9Chang, T.-J., Yang, S.-C., & Chang, K.-J. (2009). Portfolio optimization problems in different risk measures using genetic algorithm. Expert Systems with Applications, 36(7), 10529-10537. doi:10.1016/j.eswa.2009.02.062Woodside-Oriakhi, M., Lucas, C., & Beasley, J. E. (2011). Heuristic algorithms for the cardinality constrained efficient frontier. European Journal of Operational Research, 213(3), 538-550. doi:10.1016/j.ejor.2011.03.030Chen, B., Lin, Y., Zeng, W., Xu, H., & Zhang, D. (2017). The mean-variance cardinality constrained portfolio optimization problem using a local search-based multi-objective evolutionary algorithm. Applied Intelligence, 47(2), 505-525. doi:10.1007/s10489-017-0898-zLiagkouras, K. (2019). A new three-dimensional encoding multiobjective evolutionary algorithm with application to the portfolio optimization problem. Knowledge-Based Systems, 163, 186-203. doi:10.1016/j.knosys.2018.08.025Kaucic, M., Moradi, M., & Mirzazadeh, M. (2019). Portfolio optimization by improved NSGA-II and SPEA 2 based on different risk measures. Financial Innovation, 5(1). doi:10.1186/s40854-019-0140-6Silva, Y. L. T. V., Herthel, A. B., & Subramanian, A. (2019). A multi-objective evolutionary algorithm for a class of mean-variance portfolio selection problems. Expert Systems with Applications, 133, 225-241. doi:10.1016/j.eswa.2019.05.018Anagnostopoulos, K. P., & Mamanis, G. (2009). Multiobjective evolutionary algorithms for complex portfolio optimization problems. Computational Management Science, 8(3), 259-279. doi:10.1007/s10287-009-0113-8Ehrgott, M., Klamroth, K., & Schwehm, C. (2004). An MCDM approach to portfolio optimization. European Journal of Operational Research, 155(3), 752-770. doi:10.1016/s0377-2217(02)00881-0Steuer, R. E., Qi, Y., & Hirschberger, M. (2006). Suitable-portfolio investors, nondominated frontier sensitivity, and the effect of multiple objectives on standard portfolio selection. Annals of Operations Research, 152(1), 297-317. doi:10.1007/s10479-006-0137-1Anagnostopoulos, K. P., & Mamanis, G. (2010). A portfolio optimization model with three objectives and discrete variables. Computers & Operations Research, 37(7), 1285-1297. doi:10.1016/j.cor.2009.09.009Hallerbach, W. (2004). A framework for managing a portfolio of socially responsible investments. European Journal of Operational Research, 153(2), 517-529. doi:10.1016/s0377-2217(03)00172-3Ballestero, E., Bravo, M., Pérez-Gladish, B., Arenas-Parra, M., & Plà-Santamaria, D. (2012). Socially Responsible Investment: A multicriteria approach to portfolio selection combining ethical and financial objectives. European Journal of Operational Research, 216(2), 487-494. doi:10.1016/j.ejor.2011.07.011Cabello, J. M., Ruiz, F., Pérez-Gladish, B., & Méndez-Rodríguez, P. (2014). Synthetic indicators of mutual funds’ environmental responsibility: An application of the Reference Point Method. European Journal of Operational Research, 236(1), 313-325. doi:10.1016/j.ejor.2013.11.031Calvo, C., Ivorra, C., & Liern, V. (2014). Fuzzy portfolio selection with non-financial goals: exploring the efficient frontier. Annals of Operations Research, 245(1-2), 31-46. doi:10.1007/s10479-014-1561-2Laumanns, M., Thiele, L., Deb, K., & Zitzler, E. (2002). Combining Convergence and Diversity in Evolutionary Multiobjective Optimization. Evolutionary Computation, 10(3), 263-282. doi:10.1162/106365602760234108Blasco, X., Herrero, J. M., Sanchis, J., & Martínez, M. (2008). A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization. Information Sciences, 178(20), 3908-3924. doi:10.1016/j.ins.2008.06.01

Principal Portfolios: Recasting the Efficient Frontier

A new method of analyzing the efficient portfolio problem under the assumption that short sales are allowed is presented. It is based on the remarkable finding that the original asset set can be reorganized as a set of uncorrelated portfolios, here named principal portfolios. The original problem of portfolio selection from the existing, correlated assets is thereby traded for the reduced problem of choosing from a set of uncorrelated portfolios. These portfolios constitute a new investment environment of uncorrelated assets, thereby providing significant conceptual and practical simplification in any portfolio optimization process such as the determination of the efficient frontier. The principal portfolio analysis of the efficient frontier reveals new features of the volatility structure of the optimal portfolios.