Abstract
ABSTRACT This article aims to analyze the shares that make up the Brazilian IBRX100 index, verifying which sectors had the greatest influence on the Stock Exchange in 2018, 2019, and 2020. For this purpose, the theory of graph centrality measures was used to discover the most central shares. A balance analysis of the graphs was also performed, since balanced graphs are more stable, generating a more predictable stock portfolio. This study may help investors to compose a safer stock portfolio and identify which stocks are most correlated with each other. The most central shares can aid in perceiving stock market trends.
Highlights
Graphs are used to model problems involving objects and relationships between them
Noting that the adjacency matrix related to the IBrX100 index had negative values concentrated in the stock of the company Suzano (SUZB3), we may suggest to an investor who wants to build up a balanced portfolio with hedge other IBrX100 shares whereas considering the SUZB3 stock as a hedge
The calculation of the eigenvalues of the Laplacian matrix proves that the graph is balanced, due to the analysis of the centrality of the graphs being impaired by a signed graph, especially regarding the eigenvector centrality, SUZB3 stocks were removed
Summary
Graphs are used to model problems involving objects and relationships between them. Graph theory has many applications. Edges can mean the statistical correlation between two nodes and the vertices represent financial assets (Boginsky et al, 2003, 2005 and 2006) Another type of modeling can be the representation of companies as vertices, and the weighted edges representing the shareholding, i.e. the ratio of capital that a company holds in relation to another (Battiston, 2004; D’errico et al, 2009; Abreu et al, 2019). According to Harary et al 2002, analyzing the correlations can assist in predicting the behavior of the shares and facilitate the structuring of an investment portfolio more suited to the investor’s interests These correlations can indicate whether the shares have similar or opposite behaviors by analyzing whether the price variation occurs in the same direction or not These variations can be represented by graphs with weighted edges, with positive or negative weights indicating similarity or dissimilarity. According to Cartwright’s Principle and Harary’s equilibrium theory 1956, unbalanced graphs are more unstable, so that the kind of relationship between the edges may change more frequently, meaning that the behavior of the graph is more unpredictable
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