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

A trust region algorithm for heterogeneous multiobjective optimization

This paper presents a new trust region method for multiobjective heterogeneous optimization problems. One of the objective functions is an expensive black-box function, for example given by a time-consuming simulation. For this function derivative information cannot be used and the computation of function values involves high computational effort. The other objective functions are given analytically and derivatives can easily be computed. The method uses the basic trust region approach by restricting the computations in every iteration to a local area and replacing the objective functions by suitable models. The search direction is generated in the image space by using local ideal points. It is proved that the presented algorithm converges to a Pareto critical point. Numerical results are presented and compared to another algorithm

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

Synergies, cooperation and syndication in venture capital game, portfolio optimization with genetic algorithms and asset auctions: essays in finance

This thesis looks at all scientific phenomenon of financial decision-making from both the empirical and theoretical side, with empirical trying to strengthen theoretical assumptions or even to expand it. In chapter 2, we propose a two-stage financing model with three players that consider the output elasticities of all parties using the Cobb-Douglas utility function. Theoretical findings in chapter 2 suggest that a higher complementary coefficient between players on both stages can lead to a higher level of effort from all three players, taking game dynamics away from the moral hazard problem and causing higher exit stage payoffs. Previous track record of the angel and VC and output elasticity of the entrepreneur, combined with the company’s shares offered the angel and VC, impact the three-player game dynamic, causing some players to reduce their efforts after specific funding rounds. Our empirical results show that VC syndication increases the average amount of funding offered to entrepreneurs as well as that syndicated ventures have a higher number of funding rounds, resulting in a higher number of possible entry-points provided by those start-ups. Our results in chapter 4 suggested that a two-point GA that minimized the risk for a given level of expected return slightly outperformed the results of the SPEA2. Compared with the previous industry standard for risk measure—Value-at-Risk, we show that both frontiers differed, especially at the low return side. The converted Value-at-Risk solutions were not evenly distributed along the efficient frontier and even inadequate for some ES values. In chapter 5, we use the game theory approach to examine the first-price package auction design for illiquid asset auctions. Our theoretical work suggests that every case that can be presented as a two or three asset game, as well as longer games that can be presented as two and three asset subgames, has a strong equilibrium if the bidders’ budgets and utilities for every asset are common knowledge

Otimização multiobjetivo utilizando algoritmos evolutivos em seleção de carteiras: uma abordagem envolvendo ômega, assimetria e antifragilidade

Profitability in investments has always been the desire of any investor, whether an individual or a company. In periods of declining interest rates in world economies, as well as the existence of an unstable performance of stock exchange assets due to recurringfinancial crises, such as the recent one caused by COVID-19, the profitability of Fixed and Variable Income assets is increasingly threatened.This context causes investors to increasingly search for assets that manage toreconcile profitability and a minimum of security in the composition of their portfolios. Itmakes the selection of asset portfolios undoubtedly one of the most challenging topics inthe Finance area.Since Markowitz’s initial contribution, several researchers have sought to studymethods, techniques, and models applicable to the topic. A crucial theoretical landmarkwas the proposal in the 1960s of the CAPM model, which has severe empirical flaws,although robust and consistent. Its empirical limitation is pointed out by the fact that themarket portfolio proxy idealized by the model does not take effect in practice. In additionto this, some premises as normal distribution and the quadratic utility function make theCAPM model less and less likely to succeed when implemented in practice.Therefore, new approaches have been presented, with a recent highlight for theOCAPM model, in which the Omega measure allows us to relax these CAPM premisesand represent the investor’s preference more effectively. Thus, new attributes that notonly mean and variance become relevant in the process of building new approaches to themodel, transforming the problem into a multiobjective approach.As OCAPM does not yet have a full empirical application, this research splits intothree parts: the first works with mono-objective optimization and seeks to empirically knowif the OCAPM model performs better than the CAPM model in the studied markets. Thesecond part works with the optimization of purely convex attributes. It aims to ratify theview that the mean and variance may not be sufficient to represent the entire distributionof return on assets and, therefore, investors’ decisions. The third part, the central part ofthe research, deals with the optimization of multiobjective portfolios involving convex andnon-convex attributes through the use of evolutionary algorithms.In this experiment, there are three multiobjective portfolios: i) Global, involvingthe optimization of the omega, mean, asymmetry, kurtosis, drawdown, and antifragilityattributes; ii) Antifragile, involving drawdown and antifragility and iii) Asymmetric,involving omega, skewness, and kurtosis.The results of the research show that the antifragile portfolio brought higher averagereturns than CAPM and OCAPM models, and the American market showed better riskconditions. Valuing assets that have a low drawdown and have relative resilience in times of turbulence becomes advantageous in investment management. Losing little in crisistimes seems to be more significant than winning in periods of calm and stability. Amongthe evolutionary algorithms used, the highlight is the NSGA3, which presented the bestperformance out of the sample in the optimization of multiobjective portfolios.A rentabilidade em investimentos sempre foi desejo de qualquer investidor, seja pessoa física ou jurídica. Em períodos de quedas das taxas de juros das economias mundiais,bem como a existência de um desempenho instável dos ativos das bolsas de valores devido a recorrentes crises financeiras, como a recente ocasionada pelo COVID-19, a rentabilidade de ativos de Renda Fixa e Variável está cada vez mais ameaçada.Esse contexto suscita nos investidores uma busca cada vez maior por ativos que consigam conciliar rentabilidade e um mínimo de segurança na composição de seus portfólios.Isso faz com que a seleção de carteiras de ativos seja, sem dúvida, um dos temas mais desafiadores da área de Finanças.Desde a contribuição inicial de Markowitz, diversos pesquisadores têm busca do estudar métodos, técnicas e modelos aplicáveis ao tema. Um marco teórico importante foi a proposição nos anos 60 do modelo CAPM que, embora robusto e consistente, apresenta falhas severas empíricas. Sua limitação empírica é apontada pelo fato da proxy da carteira de mercado idealizada pelo modelo não se efetivar na prática. Aliado a isso, algumas premissas como a normalidade da distribuição e a função utilidade quadrática tornam o modelo CAPM cada vez menos propenso ao sucesso quando implementado na prática.Diante disso, novas abordagens têm sido apresentadas, com destaque recente para o modelo OCAPM, em que a medida Ômega permite relaxar essas premissas do CAPM e pode representar com maior efetividade a preferência do investidor. Novos atributos que não somente a média e variância passam a ser relevantes no processo de tomada dedecisão do investidor, transformando o problema em uma abordagem multi objetiva.Como o OCAPM ainda não tem ampla aplicação empírica, esta pesquisa se divide em três partes: a primeira, trabalha com otimização mono-objetivo e busca conhecer empiricamente se o modelo OCAPM apresenta desempenho superior ao modelo CAPMnos mercados estudados; a segunda parte trabalha com uma otimização de atributos puramente convexos e visa ratificar a visão de que a média e variância podem não ser,por si só, suficientes para representar toda a distribuição de retorno dos ativos e, por conseguinte, da decisão dos investidores. A terceira parte, a principal da pesquisa, tratada otimização de carteiras multi objetivas que envolvam atributos convexos e não-convexosatravés do emprego de algoritmos evolutivos.Neste experimento, são propostas 03 carteiras multi objetivas:i) Global, envolvendo a otimização dos atributos ômega, média, assimetria, curtose, drawdowne antifragilidade;ii) Antifrágil, envolvendo drawdowne antifragilidade e iii) Assimétrica, envolvendo ômega,assimetria e curtose.Os resultados da pesquisa mostram que a carteira Antifrágil trouxe ganhos superiores em relação à média de retornos dos demais modelos e sobretudo no mercado americano apresentou melhores condições de risco. Valorizar ativos que apresentem baixo drawdowne possuam relativa resiliência em períodos de turbulência se torna vantajoso na gestão de investimentos. Perder pouco em momentos de crise parece ser mais significativo que ganharem períodos de bonança e estabilidade. Dentre os algoritmos evolutivos empregados, o destaque fica com o NSGA3, que apresentou o melhor desempenho fora da amostra na otimização de carteiras multi objetivas

Multiobjective evolutionary algorithms for complex portfolio optimization problems

Multiobjective optimization, NSGA-II, PESA, Portfolio selection, SPEA2,

OPTIMIZACIÓN MULTIOBJETIVO PARA LA SELECCIÓN DE CARTERAS A LA LUZ DE LA TEORÍA DE LA CREDIBILIDAD: UNA APLICACIÓN EN EL MERCADO INTEGRADO LATINOAMERICANO

El presente trabajo de investigación doctoral tiene como fin optimizar carteras multiobjetivo a la luz de la teoría de la credibilidad. Con el fin de cumplir con este propósito, se propone un novedoso modelo difuso de optimización denominado "Modelo Credibilístico Multiobjetivo de Media-Semivarianza-Liquidez para la Selección de Carteras". La incertidumbre de la liquidez y el rendimiento futuro de cada activo se modela por medio de números difusos L-R con funciones de referencia tipo potencia. Con el objetivo de conseguir un modelo más realista se considera la restricción de cardinalidad que limita el número de activos que participan en las carteras y las restricciones de cotas superiores e inferiores que permiten combinaciones de activos que respetan las preferencias del inversor. Con el propósito de seleccionar la cartera óptima, esta investigación define por primera vez el ratio de Sortino en un entorno credibilístico. El problema de optimización multiobjetivo resultante es lineal y convexo, y la introducción de restricciones realistas convierte el modelo de un problema de optimización cuadrática clásica (classical quadratic optimization problem) a un problema de programación cuadrática de enteros mixtos (quadratic mixed-integer problem) que es NP-hard. Para superar este inconveniente se aplica el Non-dominated Sorting Genetic Algorithm (NSGAII), MOEA que ha sido utilizado con éxito en la generación de soluciones eficientes en varios modelos multiobjetivos de selección de carteras. Finalmente, se demuestra la efectividad y eficiencia del modelo en aplicaciones prácticas, asumiendo por primera vez la toma de decisiones de inversión en el Mercado Integrado Latinoamericano (MILA), que integra los mercados bursátiles de Chile, Colombia, México y Perú.The present doctoral dissertation aims to optimize multiobjective portfolio in the light of credibility theory. In order to meet this purpose, a novel fuzzy optimization model called "Multiobjective Credibilistic Mean-Semivariance-Liquidity Portfolio Selection Model" is proposed. The uncertainty of the future return and liquidity of each asset are modeled by means of LR-fuzzy numbers belonging to the power family. In order to make a more realistic model, it is considered the cardinality constraint limiting the number of assets participating in the portfolios, and upper and lower bound constraints allowing assets combinations which respect the investor's wishes. In the interest of selecting the optimal portfolio, this research defines for the first time, the Sortino ratio under a credibilistic environment. The resulting multiobjective optimization problem is linear and convex, and the introduction of realistic constraints into the portfolio optimization problem convert the model from a classical quadratic optimization problem to a quadratic mixed-integer problem (QMIP) that is NP-hard. To overcome this drawback, it is applied the Non-dominated Sorting Genetic Algorithm (NSGAII), MOEA that has been used successfully in the generation of efficient solutions in several multi-objective portfolio selection models. Finally, an empirical study is included to demonstrate the effectiveness and efficiency of the model in practical applications using for the first time a dataset of assets from the Latin American Integrated Market (MILA by its Spanish acronym), which integrates the stock exchange markets of Chile, Colombia, Mexico, and Peru.El present treball d'investigació doctoral té com a finalitat optimitzar carteres multiobjectiu a la llum de la teoria de la credibilitat. Per tal de complir amb aquest propòsit, es proposa un nou model difús d'optimització denominat "Model Credibilístic multiobjectiu de Mitjana-Semivarianza-Liquiditat per a la Selecció de Carteres". La incertesa de la liquiditat i el rendiment futur de cada actiu es modela per mitjà de nombres difusos L-R amb funcions de referència tipus potència. Amb l'objectiu d'aconseguir un model més realista es considera la restricció de cardinalitat que limita el nombre d'actius que participen en les carteres i les restriccions de cotes superiors i inferiors que permeten combinacions d'actius que respecten les preferències de l'inversor. Amb el propòsit de seleccionar la cartera òptima, aquesta investigació defineix per primera vegada la ràtio de Sortino en un entorn credibilístic. El problema d'optimització multiobjectiu resultant és lineal i convex, la introducció de restriccions realistes converteix el model d'un problema d'optimització quadràtica clàssica (classical quadratic optimization problem), a un problema de programació quadràtica d'enters mixtes (quadratic mixed-integer problem) que és NP-hard. Per superar aquest inconvenient s'aplica el Non-dominated Sorting Genetic Algorithm (NSGAII), MOEA que ha estat utilitzat amb èxit en la generació de solucions eficients en diversos models multiobjectiu de selecció de carteres. Finalment, es demostra l'efectivitat i eficiència del model en aplicacions pràctiques, assumint per primera vegada la presa de decisions d'inversió al Mercat Integrat Llatinoamericà (MILA), que integra els mercats borsaris de Xile, Colòmbia, Mèxic i Perú.González Bueno, JA. (2018). OPTIMIZACIÓN MULTIOBJETIVO PARA LA SELECCIÓN DE CARTERAS A LA LUZ DE LA TEORÍA DE LA CREDIBILIDAD: UNA APLICACIÓN EN EL MERCADO INTEGRADO LATINOAMERICANO [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/102362TESI