Hierarchical Structure in Financial Markets

I find a topological arrangement of stocks traded in a financial market which has associated a meaningful economic taxonomy. The topological space is 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 information useful to investigate the number and nature of the common economic factors affecting the time evolution of logarithm of price of well defined groups of stocks. Financial markets are well defined complex systems. They are studied by economists, mathematicians and, recently, also by physicists. The paradigm of mathematical finance is that the time series of stock returns are unpredictable [1]. Within this paradigm, time evolution of stock returns are well described by random processes. A key point is if the random processes of stock returns time series of different stocks are uncorrelated or, conversely, if common economic factors are present in financial markets and are driving several stocks at the same time. Common economic factors were originally introduced by Ross in