Market graph is built on the basis of some similarity measure for financial asset returns. The paper considers two similarity measures: classic Pearson correlation and sign correlation. We study the associated market graphs and compare the conditional risk of the market graph construction for these two measures of similarity. Our main finding is that the conditional risk for the sign correlation is much better than for the Pearson correlation for larger values of threshold for several probabilistic models. In addition, we show that for some model the conditional risk for sign correlation dominates over the conditional risk for Pearson correlation for all values of threshold. These properties make sign correlation a more appropriate measure for the maximum clique analysis.
The problem of comparison of several branches efficiency is formulated as a multiple decision problem. The main difficulty to handle this problem lies in the compatibility condition. Solution of this difficulty, based on a method of combination of testing compatible generating hypotheses is given. The additivity condition of the loss function is investigated. This condition is used to construct the optimal multiple decision statistical procedures for comparison of network branches efficiency. Some examples are given.