Medição de diversidade em redes multiplex : uma análise de investimento no mercado de ações de energia elétrica

Abstract

Diversity analysis is a matter that attracts the interest of a wide range of researchers from multiple areas. In general, its meaning is linked to the idea of variety, difference, heterogeneity and related definitions. However, its characterization depends on the context in which it is being investigated. Therefore, there is variation in the way it is interpreted and measured. In this perspective, many studies rely on the Complex Network Theory to understand and characterize the diversity of real systems described by their complexity. Following this approach, the present work aims to investigate the behavior of a diversity measure U presented in Carpi et al. (2019) in a financial context not yet investigated. This measure takes into account definitions proposed by Weitzman (1992) and reviewed by Bossert et al. (2001), which were allied to measures of distances that measure dissimilarities between graphs. Dissimilarities are related to the structural configurations of connectivity of the entities, nodes or layers, of a multiplex network. In order to evaluate the performance of U, the stock market of Brazilian electric energy sector was used. The applied data refer to historical series of daily paper quotations issued by this segment and were acquired through a base available on the official stock exchange website of the country. The analysis was carried out for four-month terms, aiming different listing periods of shares on the stock exchange. Thus, in each four-month term from 1998 to 2017 a multiplex network was set up, whose layers refer to the selected electric energy papers to compose the network of the respective period. With the application of the diversity measure U, it was possible to identify the most dissimilar stocks in each period, which were destined to the formation of portfolios. In addition, we observed, as expected, the low diversity among stocks, justified by the fact that the group of papers studied belonged to the same market segment. In order to evaluate the performance of the portfolios obtained, the methodology of calculation and adjustment of the Electric Energy Index (IEE) was used and the results showed the measure’s ability to select actions to configure more diversified portfolios.