Análise do risco em uma carteira de investimento: uma aplicação a partir da Teoria de Markowitz

Abstract

The present work have for objective the study of the risks in finance market, from the Markowitz Theory (1952). For this, historical data of the stock prices were used belonging to the Bovespa Index (Ibovespa) between the period of 1 October 2012 to 31 October 2014. To present the gains from diversification of portfolios, were built three portfolios, composed of different ways - the first, composed randomly, was built with equal weights for the 41 selected assets. Starting from the portfolio 1 (one) was formed and optimized the portfolios 2 (two) and 3 (three) proposed by Markowitz (1952), through the tool Solver of Software Excel. With the application of the proposed model, was possible indicate what the ideal combination of the stocks to compose the portfolio. The portfolio 2 (two) searched to maximize the return and the portfolio 3 (three) minimize the risk. Observing these two portfolios optimized compared to the first, can be seen that just the random allocation of capital in business of different sectors is not the safest way to protect the risk, it being possible build portfolios that maximize the risk/return using an optimization method. Analyzing the portfolio 2 (two) can be perceived which the objective function was answered, with the increase of return expectation of 374.6%, and risk reduction of 16.9%. The same is true for portfolio 3 (three), whose objective was to minimize the risk, the highest combined assets of the same helped to reduce the risk by 47.2%, but with a more modest expectation of return, growing only 38.3%. Therefore, with diversification of assets in the portfolio, it is possible to measure and minimize the risk of a satisfactory level of return. It is a useful method to be used, allowing investors to achieve a portfolio with a combination of risk/return that meets your desires and expectations, allocating in the best way their capital.