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.
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Mantegna, R.N. Hierarchical structure in financial markets. Eur. Phys. J. B 11, 193–197 (1999). https://doi.org/10.1007/s100510050929
- PACS. 02.50.Sk Multivariate analysis
- 89.90.+n Other areas of general interest to physicists