Análise de desempenho de portfólios desenvolvidos com base na Teoria Moderna de Carteiras de Markowitz e o Modelo de Índice Único de Sharpe no mercado acionário brasileiro

Abstract

As they are risk-averse, investors have always sought models that bring the best results, with a maximization of profits and a minimization of risks/losses that may exist. Thus, scholars such as Markowitz and Sharpe developed theories that could somehow help investors in selecting an optimized portfolio, giving rise to the Modern Theory of Portfolios by Markowitz (1952), a pioneer in the creation of portfolios with maximum return and reduced risk, and Sharpe's Single Index Model (1963), which in turn was created due to the complexity involved in formulating an optimized portfolio based on MTP. This work aimed to analyze which of the two models have better performance in the Brazilian stock market, as well as to create stock portfolios based on the Modern Portfolio Theory of Markowitz (1952) and Sharpe's Single Index Model (1963). The data obtained for the construction of the portfolios were collected from the Economática database, with data from January 2010 to December 2019 for the development of the portfolios. Using Microsoft Excel software and the Solver tool, it was possible to create an optimized portfolio for each of the ten years studied, finding the fifteen papers with the highest coefficient of variation in the Markowitz and Sharpe portfolios, based on the C* find the cutoff point, that is, the limit of which portfolios would enter the optimization. When comparing the Modern Portfolio Theory with the IBOVESPA, it was observed that even in years where the optimized portfolio had low values, it was still superior to the market, being something ideal for those who invest. Comparing the MIU with the SELIC, the superiority of the model was noticeable, in years when the optimized portfolio reached a 47.11% return, the SELIC was at 6.75%. The Treynor index, the Sharpe index and the Jensen index were used to analyze the performance of each portfolio year after year, the first years with favorable results for the performance of the Markowitz portfolio and the last for the optimized Sharpe portfolio.