The European Physical Journal B - Condensed Matter and Complex Systems

, Volume 11, Issue 1, pp 193-197

First online:

Hierarchical structure in financial markets

  • R. N. MantegnaAffiliated withIstituto Nazionale per la Fisica della Materia, Unità di PalermoDipartimento di Energetica ed Applicazioni di Fisica, Università di Palermo Email author 

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I find a hierarchical arrangement of stocks traded in a financial market by investigating the daily time series of the logarithm of stock price. The topological space is a subdominant ultrametric space associated with a graph connecting the stocks of the portfolio analyzed. The graph is obtained starting from the matrix of correlation coefficient computed between all pairs of stocks of the portfolio by considering the synchronous time evolution of the difference of the logarithm of daily stock price. The hierarchical tree of the subdominant ultrametric space associated with the graph provides a meaningful economic taxonomy.

PACS. 02.50.Sk Multivariate analysis 89.90.+n Other areas of general interest to physicists