Topology of Correlation-Based Minimal Spanning Trees in Euronext Paris

The study of the static and dynamic evolution of correlations between different stocks, using the analysis of their correlation matrix properties, plays a vital role in portfolio optimization and risk assessment. The purpose of the study is to examine, based on the concept of ultrametricity, the properties of the French stock market (Euronext Paris) topology in a year-long moving window using the minimum spanning tree (MST) for the period 2006–2013. Each node represents a listed company in the SBF120, and their distance is a function of the correlation matrix element. The findings suggest that although there is a remarkable clustering and coherence in Euronext Paris, reflecting valuable economic insights, companies holding the most significant market capitalization are positioned in the surroundings of the central vertex in the MST.