Improved Constrained Portfolio Selection Model using Particle Swarm Optimization

Objective: The main objective of this study is to improve the extended Markowitz mean-variance portfolio selection model by introducing a new constraint known as expert opinion practicable for portfolio selection in real-life situation. Methods: This new extended model consists of four constraints namely: bounds on holdings, cardinality, minimum transaction lots, and expert opinion. The first three constraints have been presented in other researches in literature. The fourth constraint introduced in this study is an essential parameter in making and guiding a realistic portfolio selection. To solve this new extended model an efficient heuristic method of Particle Swarm Optimization (PSO) was engaged with existing benchmark data in the literature. Results: The outcome of the computational results obtained in this study with the new extended Markowitz mean-variance portfolio selection model proposed in this study and solved with PSO showed an improved performance over existing algorithm in particular GA in different instances of the data set used. Conclusion: The study evolves a new extended portfolio selection model and the findings

Portfolio Selection Problem Using Generalized Differential Evolution 3

This Portfolio selection Problem (PSP) remains an intractable research problem in finance and economics and often regarded as NP-hard problem in optimization and computational intelligence. This paper solved the extended Markowitz mean- variance portfolio selection model with an efficient Metaheuristics method of Generalized Differential Evolution 3 (GDE3). The extended Markowitz mean- variance portfolio selection model consists of four constraints: bounds on holdings, cardinality, minimum transaction lots, and expert opinion. There is no research in literature that had ever engaged the set of four constraints with GDE3 to solve PSP. This paper is the first to conduct the study in this direction. The first three sets of constraints have been presented in other researches in literatures. This paper introduced expert opinion constraint to existing portfolio selection models and solved with GDE3. The computational results obtained in this research study show improved performance when compared with other Metaheuristics methods of Genetic algorithm (GA), Simulated Annealing (SA), Tabu Search (TS) and Particle Swarm Optimization (PSO)

Machine learning asset allocation: Applications from FTSE, DAX AND BIST

Portföy optimizasyonu yarım yüzyılı aşkın süredir birçok araştırmacının ve yatırımcının test ettiği ve kullandığı bir teoridir. Ancak konu üzerine yapılan bazı çalışmalarda teoriye bir takım eleştiriler de getirilmektedir. Bu eleştirilerden bir tanesi de konsantrasyon problemidir. Temelinde çeşitlendirme olan bir teori ile elde edilen optimum portföylerin yatırım olanakları kümesindeki az sayıda varlığa yatırım yapılmasını önermesi önemli bir eleştiri noktasını oluşturmaktadır. Bu problemin çözümü üzerinde çalışan araştırmacılardan birisi olan Prado (2016; 2018), geliştirdiği Hiyerarşik Risk Paritesi (HRP) metodu ile makine öğrenmesi kullanılarak portföy optimizasyonu yapılabileceğini ifade etmektedir. Bu çalışmanın amacı HRP metodu kullanılarak BIST, FTSE ve DAX piyasalarında Temmuz 2005 - Haziran 2017 aralığında makine öğrenmesi algoritmalarının portföy performanslarını incelemektir. Analizler sonucunda, HRP metodunun BIST, FTSE piyasalarında başarılı olmamasına rağmen DAX piyasalarında başarılı performans sergilediğine ulaşılmıştır

Machine Learning Asset Allocation

La optimización de portafolios de instrumentos financieros es una actividad que ocurre de manera diaria en el mundo financiero. En la mayoría de los casos se utiliza una metodología de optimización cuadrática que está diseñada para solucionar problemas de optimización de cartera con restricciones de desigualdad. El Critical Line Algorithm (CLA) es un algoritmo para este proposito que garantiza encontrar una solución exacta luego de varias iteraciones. A pesar de que la metodología matemática utilizada para la resolución del problema es correcta, el CLA puede presentar soluciones que no sean del todo confiables por la inestabilidad de las mismas, por su concentración en pocos activos de la cartera y por el bajo rendimiento fuera de la muestra. La razón de la inestabilidad se encuentra relacionada a que la optimización requiere una inversión en la matriz de covarianza. Por lo tanto, la matriz de covarianza es mas ante una mayor correlación en los activos es más inestable al calcular su inversa y la correlación lamentablemente es lo más habitual Marcos López de Prado (2016) nos presenta una solución alternativa a este problema de optimización llamado Hierarchical Risk Parity (HRP). El enfoque de HRP utiliza Machine Learning y teoría de grafos para construir un portafolio diversificado basado en la información contenida en la matriz de covarianza de los activos. El HRP se construye mediante la metodología de clustering jerárquico en donde las inversiones se intentan unir en grupos similares entre sí. En el trabajo propuesto se extraen datos de las acciones de las empresas que representan el índice S & P 500 del periodo 2015 – 2020. Seguidamente, se crea una cartera y se utilizan los distintos algoritmos de optimización en ella. Posteriormente, se hace un análisis comparativo de las ponderaciones y de la performance que tiene la cartera con los distintos algoritmos. También se generan 11 portafolios específicos de sectores en los que divide el S&P y se realiza el mismo análisis comparativo para cada uno de ellos. Además, se realiza una simulación de Monte Carlo con variables aleatorias para analizar la estabilidad de las soluciones de los distintos algoritmos de optimización utilizados. Los resultados más relevantes del analisis son que el CLA concentra sus asignaciones en 10 activos de un portafolio de 34 a diferencia del HRP que lo distribuye de forma más equitativa en todo el portafolio . Además, el HRP obtiene una mejor eficiencia de retorno ajustado en el riesgo en comparación al CLA (Sharpe Ratio). Lo mismo ocurre si se realiza una simulación de Monte Carlo en donde se utilizan variables aleatorias. Se puede concluir que ante shocks en el mercado se penaliza la concentración del CLA. En cambio, el HRP proporciona una mejor protección frente a los shocks al encontrar un compromiso entre la diversificación en todas las inversiones y la diversificación en grupos de inversiones en múltiples niveles jerárquicos

Portfolio allocation: a comparison between Hierarchical Risk Parity and Markowitz model in Python

The portfolio allocation is a predominant issue in the world of finance; everyday asset managers from all over the world have to elaborate financial portfolios coherent with the objectives of their clients. The most popular model implemented to solve the portfolio allocation problems derives from the Markowitz’s framework. Over the years, some limitations related to that model have emerged; contextually, new types of financial allocation have been developed, including the Hierarchical Risk Parity. This model aims to address the instability of the quadratic optimizers and it has its roots in the growing interest towards artificial intelligence. In this work a comparison between the Markowitz's framework and the Hierarchical Risk Parity is carried out via Python, through an empirical application on a portfolio of equity ETFs

An Open-Source Implementation of the Critical-Line Algorithm for Portfolio Optimization

Portfolio optimization is one of the problems most frequently encountered by financial practitioners. The main goal of this paper is to fill a gap in the literature by providing a well-documented, step-by-step open-source implementation of Critical Line Algorithm (CLA) in scientific language. The code is implemented as a Python class object, which allows it to be imported like any other Python module, and integrated seamlessly with pre-existing code. We discuss the logic behind CLA following the algorithm’s decision flow. In addition, we developed several utilities that support finding answers to recurrent practical problems. We believe this publication will offer a better alternative to financial practitioners, many of whom are currently relying on generic-purpose optimizers which often deliver suboptimal solutions. The source code discussed in this paper can be downloaded at the authors’ websites (see Appendix)

An Open-Source Implementation of the Critical-Line Algorithm for Portfolio Optimization

Portfolio optimization is one of the problems most frequently encountered by financial practitioners. The main goal of this paper is to fill a gap in the literature by providing a well-documented, step-by-step open-source implementation of Critical Line Algorithm (CLA) in scientific language. The code is implemented as a Python class object, which allows it to be imported like any other Python module, and integrated seamlessly with pre-existing code. We discuss the logic behind CLA following the algorithm’s decision flow. In addition, we developed several utilities that support finding answers to recurrent practical problems. We believe this publication will offer a better alternative to financial practitioners, many of whom are currently relying on generic-purpose optimizers which often deliver suboptimal solutions. The source code discussed in this paper can be downloaded at the authors’ websites (see Appendix)