A robustness comparison of two market network models

Two market network models are investigated. One of them is based on the classical Pearson correlation as the measure of association between stocks returns, whereas the second one is based on the sign similarity measure of association between stocks returns. We study the uncertainty of identification procedures for the following market network characteristics: distribution of weights of edges, vertex degree distribution in the market graph (MG), cliques and independent sets in the MG and the vertex degree distribution of the maximum spanning tree. We define the true network characteristics, the losses from the error of its identification by observations and the uncertainty of identification procedures as the expected value of losses. We use an elliptically contoured distribution as a model of the multivariate stocks returns distribution. It is shown that identification of statistical procedures based on the sign similarity are statistically robust in contrast to the procedures based on the classical Pearson correlation.