Seleção de carteiras ótimas pelo método de markowitz: análise do Índice de Sharpe, Índice de Treynor e Alfa de Jensen no Microsoft Excel

Abstract

The Portfolio Selection Model emerged in 1952, created by the economist Harry Max Markowitz, as the pioneer in the investment risk analysis. This risk representes the investidor’s possibility of having any losses on the investment made. Initially, the analysis made about the performance evaluation did not use any risk mensures, only comparing themselves to the portfolio´s profitability as a pattern, as the Ibovespa Index. Up to the point of the portfolio selection model, proposed by Markowitz and the Capital Asset Princing Model, the risk appears as a investment performance evaluation’s mensure. This way, some researches have developed mensure’s indexes of great portfolio’s performance, as: Treynor Ratio, Sharpe Ratio and Jensen’s Alfa. Based on the Portfolio Selection Theory, developed by Harry Markowitz (1952), the presente research had as goal select de stock portfolio capable of present the maximum return for a given level of risk taken, or a minimum risk for a given expected return. The carteiras were created from the assets that compose the Ibovespa Index during the period from december 2013 to december 2018, identifying the investment share of each share in the portfolio composition; and, then, evaluating the performance of the portfolios with the market and among themselves. As a tool for the portfolio’s optimization calculus the Solver was used, a Microsoft Excel’s resource. The data collect was made in the data bank called Economatica. First, the average risks and returns of each share were calculated, where it was identified that the action with the highest return is MGLU3 with 5.41%, and the one with the highest risk is USIM5 with 22.43% of standard deviation and 2.85 of beta (β). Followed by that, a Simple Portfolio was created, composed of 59 assets with the same weight. This one yielded a return and a higher risk than that of the market portfolio. After that, the Minimum Variance Portfolio, composed by 14 assets, whose objective was to reduce risk in a way that the return was not lower than that of the market portfolio, resulting in a equal return to that of the market and a lower risk than that of the market portfolio. And the last portfolio, called Maximum Return Portfolio, whose the 4 assets composition had the objective of maximizing the return to a risk less than or equal to that of the IBOV portfolio. The results were a superior return than the Ibovespa Index and a risk equal to that of the market portfolio. Starting with the portfolio performance indicators, Treynor Ratio, Sharpe Ratio and Jensen's Alpha, the portfolio that had the best performance in all three analyzes was the Maximum Return Portfolio. It is concluded that the optimized portfolio prove that the investor does not need to invest in all Ibovespa Index’s assets in order to have a satisfactory return, as well as confirms that the Markowitz Portfolio Selection Model is feasible for the formation of an efficient portfolio and the choice between a minimum risk portfolio and maximum return will depend on the behavioral characteristics of the investor, whether it is risk averse or not.