Análise da rede "minimum spanning tree" de correlação econômica entre as principais ações mundiais no recente período de instabilidade global

Abstract

In this work we will use the Minimum Spanning Tree (MST) using Correlation Distance to study the relationships between the main global stocks in the period from 2018 to 2024. The Correlation Distance matrix is given by d(i,j) = √2(1−r(i, j)), where r(i,j) is the surface coefficient between the vertices xi and x j. The brightness coefficient varies between -1, perfect anti-transparency, and +1, perfect transparency, and r(ij) = 0, meaning uncorrelated, or independent, variables. Correlation of a variable with itself is always equal to +1, r(i, i) = 1. Thus, d(i,j) varies between 0 for r(i,j)= +1, and 2 for r(ij,j) = -1. Using the distance matrix, we calculate the MST, the network that connects all variables, without cycles, with the shortest distance. To do this, we will use the PRIM algorithm, which searches for the closest vertex to any element of the network already found. We can show the MST through graphs, or reorder the expansion matrix in the order of the MST. With this, we visualize the clusters formed by proximity of variables. We use financial market data composed of the main stock indexes of the countries obtained from the ’Yahoo Finance’ database for the period 2018 - 2024, which included the years 2020-2022 with pandemic and lockdown, allowing a comparison with the years 2018-2019 to understand the economic effects of the lockdown. On the other hand, in the period 2022 and 2023, the Ukraine-Russia war took place, with strong impacts on energy and food prices, and, consequently, on the stock values of several companies.