Markowitz Model

Aproximación práctica a los métodos de selección de portafolios de inversión ArXiv ID: 2410.11070 “View on arXiv” Authors: Unknown Abstract This paper explores the practical approach to portfolio selection methods for investments. The study delves into portfolio theory, discussing concepts such as expected return, variance, asset correlation, and opportunity sets. It also presents the efficient frontier and its application in the Markowitz model, which employs mean-variance optimization techniques. An alternative approach based on the mean-semivariance model is introduced. This model accounts for the skewness and kurtosis of the asset return distribution, providing a more comprehensive view of risk and return. The study also addresses the practical implementation of these models, including the use of genetic algorithms to optimize portfolio selection. Additionally, transaction costs and integer constraints in portfolio optimization are considered, demonstrating the applicability of the Markowitz model. Este documento explorar la aproximación práctica a los métodos de selección de portafolios para inversiones. El estudio profundiza en la teoría de los portafolios, discutiendo conceptos como el rendimiento esperado, la varianza, la correlación entre activos y los conjuntos de oportunidades. También presenta la frontera eficiente y su aplicación en el modelo de Markowitz, que utiliza técnicas de optimización media-varianza. Se introduce un enfoque alternativo basado en el modelo media-semivarianza. Este modelo tiene en cuenta la asimetría y la curtosis de la distribución de retornos de los activos, proporcionando una visión más completa de riesgo y rendimiento. El estudio también aborda la implementación práctica de estos modelos, incluyendo el uso de algoritmos genéticos para optimizar la selección de portafolios. Además, se consideran los costos de transacción y las restricciones enteras en la optimización del portafolio. ...

Risk management in multi-objective portfolio optimization under uncertainty ArXiv ID: 2407.19936 “View on arXiv” Authors: Unknown Abstract In portfolio optimization, decision makers face difficulties from uncertainties inherent in real-world scenarios. These uncertainties significantly influence portfolio outcomes in both classical and multi-objective Markowitz models. To address these challenges, our research explores the power of robust multi-objective optimization. Since portfolio managers frequently measure their solutions against benchmarks, we enhance the multi-objective min-regret robustness concept by incorporating these benchmark comparisons. This approach bridges the gap between theoretical models and real-world investment scenarios, offering portfolio managers more reliable and adaptable strategies for navigating market uncertainties. Our framework provides a more nuanced and practical approach to portfolio optimization under real-world conditions. ...

Constrained Max Drawdown: a Fast and Robust Portfolio Optimization Approach ArXiv ID: 2401.02601 “View on arXiv” Authors: Unknown Abstract We propose an alternative linearization to the classical Markowitz quadratic portfolio optimization model, based on maximum drawdown. This model, which minimizes maximum portfolio drawdown, is particularly appealing during times of financial distress, like during the COVID-19 pandemic. In addition, we will present a Mixed-Integer Linear Programming variation of our new model that, based on our out-of-sample results and sensitivity analysis, delivers a more profitable and robust solution with a 200 times faster solving time compared to the standard Markowitz quadratic formulation. ...

Analysis of Optimal Portfolio Management Using Hierarchical Clustering ArXiv ID: 2308.11202 “View on arXiv” Authors: Unknown Abstract Portfolio optimization is a task that investors use to determine the best allocations for their investments, and fund managers implement computational models to help guide their decisions. While one of the most common portfolio optimization models in the industry is the Markowitz Model, practitioners recognize limitations in its framework that lead to suboptimal out-of-sample performance and unrealistic allocations. In this study, I refine the Markowitz Model by incorporating machine learning to improve portfolio performance. By using a hierarchical clustering-based approach, I am able to enhance portfolio performance on a risk-adjusted basis compared to the Markowitz Model, across various market factors. ...

A Simulation Package in VBA to Support Finance Students for Constructing Optimal Portfolios ArXiv ID: 2305.12826 “View on arXiv” Authors: Unknown Abstract This paper introduces a software component created in Visual Basic for Applications (VBA) that can be applied for creating an optimal portfolio using two different methods. The first method is the seminal approach of Markowitz that is based on finding budget shares via the minimization of the variance of the underlying portfolio. The second method is developed by El-Khatib and Hatemi-J, which combines risk and return directly in the optimization problem and yields budget shares that lead to maximizing the risk adjusted return of the portfolio. This approach is consistent with the expectation of rational investors since these investors consider both risk and return as the fundamental basis for selection of the investment assets. Our package offers another advantage that is usually neglected in the literature, which is the number of assets that should be included in the portfolio. The common practice is to assume that the number of assets is given exogenously when the portfolio is constructed. However, the current software component constructs all possible combinations and thus the investor can figure out empirically which portfolio is the best one among all portfolios considered. The software is consumer friendly via a graphical user interface. An application is also provided to demonstrate how the software can be used using real-time series data for several assets. ...