An application of Markowitz theorem on Tehran Stock Exchange

During the past 65 years, there have been tremendous efforts on portfolio selection problem. The standard Markowitz mean–variance model to portfolio selection includes tracing out an efficient frontier, a continuous curve demonstrating the tradeoff between return and risk. This frontier can be often detected via standard quadratic programming, categorized in convex optimization. Traditional Markowitz problem has been recently extended into a new form of mixed integer nonlinear problems by considering various constraints such as cardinality constraints, industry limitation, etc. This paper proposes a mixed integer nonlinear programming to determine optimal asset allocation on Tehran Stock Exchange. The results have indicated that a petrochemical firm named Farabi has gained 44% of the portfolio followed by a drug firm named Kosar Pharmacy gaining 28%. In addition, banking sector was the third winning firm where Eghtesad Novin bank gained nearly 10% of the portfolio. Minerals and mining firms were the next sector in our portfolio where Gol Gohar Iron Ore and Tehran Cement collected 0.73% and 0.57% of the portfolio, respectively. In our survey, auto industry gained only 0.26% of the portfolio, which belonged to Saipa group

Incorporating Electrical Distribution Network Structure into Energy Portfolio Optimization for an Isolated Grid

AbstractIn large scale electricity grids, the goal to reduce fossil fuel dependence can be addressed in multiple ways: generation, storage technologies, demand response, etc. In an isolated grid not connected to a transmission infrastructure, such as a military base or isolated resort, the problem is more difficult to address because of space and funding limitations, less efficient supply chains, and reliability concerns. Design for zero fossil fuel reliance in an isolated grid should combine these solutions in a portfolio while accounting for the limitations of isolation. In this paper, a methodology is formulated to optimize energy portfolios for small scale independently operated grids. Previous studies have achieved this but do not include the structure and constraints imposed by the isolated distribution grid. To address this need, the standard optimization tool, NREL's HOMER, has been linked with a grid analysis tool, PowerWorld, to take into account the design variables arising from the structure of the distribution grid, such as the need for replacement or extension of lines, extra construction space, or transformers. These added optimization factors modify HOMER's ranking of optimized portfolios as well as the economic analysis. A discussion of implications of the results to larger grid systems modeling is provided

A superior active portfolio optimization model for stock exchange

Due to the vast number of stocks and the multiple appearances of developing investment portfolios, investors in the financial market face multiple investment opportunities. In this regard, the investor task becomes extremely difficult as investors define their preferences for expected return and the amount to which they want to avoid potential investment risks. This research attempts to design active portfolios that outperform the performance of the appropriate market index. To achieve this aim, technical analysis and optimization procedures were used based on a hybrid model. It combines the strong features of the Markowitz model with the General Reduced Gradient (GRG) algorithm to maintain a good compromise between diversification and exploitation. The proposed model is used to construct an active portfolio optimization model for the Iraq Stock Exchange (ISX) for the period from January 2010 to February 2020. This is applied to all 132 companies registered on the exchange. In addition to the market portfolio, two methods, namely, Equal Weight (EW) and Markowitz were used to generate active portfolios to compare the research findings. After a thorough review based on the Sharpe ratio criterion, the suggested model demonstrated its robustness, resulting in maximizing earnings with low risks

Resampled efficient frontier integration for MOEAs

This article belongs to the Section Multidisciplinary Applications.Mean-variance portfolio optimization is subject to estimation errors for asset returns and covariances. The search for robust solutions has been traditionally tackled using resampling strategies that offer alternatives to reference sets of returns or risk aversion parameters, which are subsequently combined. The issue with the standard method of averaging the composition of the portfolios for the same risk aversion is that, under real-world conditions, the approach might result in unfeasible solutions. In case the efficient frontiers for the different scenarios are identified using multiobjective evolutionary algorithms, it is often the case that the approach to averaging the portfolio composition cannot be used, due to differences in the number of portfolios or their spacing along the Pareto front. In this study, we introduce three alternatives to solving this problem, making resampling with standard multiobjective evolutionary algorithms under real-world constraints possible. The robustness of these approaches is experimentally tested on 15 years of market data.This research was funded by Spanish Ministry of Education under grant number CAS15/0025

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