Analysis of Canonical Heuristic Methods for the Optimization of an Investment Portfolio

Abstract

AbstractAn investment portfolio is a collection of financial assets in which an individual or a financial institution called an investor has decided to invest its capital based on criteria such as its risk aversion, the experience of a financial advisor or the formulation of an optimization problem. This last approach was the object of study of Harry Markowitz, an American economist who wrote the Theory of the optimal portfolio, in this, the amounts to be invested in the assets are determined in such a way that allows the maximum possible profit with the minimum possible risk. In this work it is proposed, as an optimization problem based on the Markowitz model, the obtaining of investment amounts of a six financial assets portfolio through the maximization of the profit ratio and the risk of loss. To determine the best possible solution, two genetic algorithms are compared with different percentage of cross, a clonal immunological algorithm and a differential evolution algorithm. The comparison criteria are the stability of the algorithm (obtainable with the coefficient of variability) and the hypothesis of normality and homoscedasticity obtainable from 60 executions of each of the proposed algorithms. It also determines the convergence of the algorithms used in this work. The results obtained allow to obtain a diversified portfolio, the first requirement of an investment portfolio according to Markowitz's theory.KeywordsInvestment portfolioTheory of the optimal portfolioOptimization problem