Distance matrix method for network structure analysis

The distance matrix method goes in line with the network analysis of market structure such as clustering analysis (Focardi and Fabozzi, 2004), geometry of crashes (Araujo and Louca, 2007), degree distribution of nodes (Boss et al., 2004; Liu and He, 2009) etc. These methods allow, among other things, to investigate the time evolution of correlations in time series such as stocks. The analysis of such time series correlations has emerged from investigations of portfolio optimization. The standard approach is based on the cross-correlation matrix analysis and optimizations of share proportions (see e.g. Adams et al., 2003; Cuthberson and Nitzsche, 2001). The basic question regarding what the most desirable proportion are among different shares in the portfolio lead to the introduction of a distance between time series, and in particular, of the ultrametric distance, which has become a classical method of correlation analysis between stocks (Bonanno et al., 2001; Mantegna and Stanley, 2000). The method allows to analyze the structure of the market, and therefore, simplifies the choice of shares. In fact, this question about structure of the stock market should be tackled before portfolio optimization.