SAIPO-TAIPO and Genetic Algorithms for Investment Portfolios

Abstract

The classic model of Markowitz for designing investment portfolios is an optimization problem with two objectives: maximize returns and minimize risk. Various alternatives and improvements have been proposed by different authors, who have contributed to the theory of portfolio selection. One of the most important contributions is the Sharpe Ratio, which allows comparison of the expected return of portfolios. Another important concept for investors is diversification, measured through the average correlation. In this measure, a high correlation indicates a low level of diversification, while a low correlation represents a high degree of diversification. In this work, three algorithms developed to solve the portfolio problem are presented. These algorithms used the Sharpe Ratio as the main metric to solve the problem of the aforementioned two objectives into only one objective: maximization of the Sharpe Ratio. The first, GENPO, used a Genetic Algorithm (GA). In contrast, the second and third algorithms, SAIPO and TAIPO used Simulated Annealing and Threshold Accepting algorithms, respectively. We tested these algorithms using datasets taken from the Mexican Stock Exchange. The findings were compared with other mathematical models of related works, and obtained the best results with the proposed algorithms.