Robustness of sign correlation in market network analysis
Financial market can be modeled as network represented by a complete weighted graph. Differet characteristics of this graph (minimum spanning tree, market graph ad others) give an impotant information on the network. In the pesent paper it is studied how the choice of measure of similarity between stocks influences the statistical errors in the calculation of network characteristics. It is shown tat sign correlation is a robust measure of similarity in contrast with Person correlation widely used in market network analysis. This gives a possibility to get more precise information on stock market from observations.
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.
A class of distribution free multiple decision statistical procedures is proposed for threshold graph identification in correlation networks. The decision procedures are based on simultaneous application of sign statistics. It is proved that single step, step down Holm and step up Hochberg statistical procedures for threshold graph identification are distribution free in sign similarity network in the class of elliptically contoured distributions. Moreover it is shown that these procedures can be adapted for distribution free threshold graph identification in Pearson correlation network.
Market graph is known to be a useful tool for market network analysis. Cliques and independent sets of the market graph give an information about con- centrated dependent sets of stocks and distributed independent sets of stocks on the market. In the present paper the connections between market graph and classical Markowitz portfolio theory are studied. In particular, efﬁcient frontiers of cliques and independent sets of the market graph are compared with the efﬁcient frontier of the market. The main result is: efﬁcient frontier of the market can be well ap- proximated by the efﬁcient frontier of the maximum independent set of the market graph constructed on the sets of stocks with the highest Sharp ratio. This allows to reduce the number of stocks for portfolio optimization without the loss of quality of obtained portfolios. In addition it is shown that cliques of the market graphs are not suitable for portfolio optimization.
The paper deal with uncertainty in market network analysis. The main problem addressed is to investigate statistical uncertainty of Kruskal algorithm for the minimum spanning tree in market network. Uncertainty of Kruskal algorithm is measured by the probability of q incorrectly included edges. Numerical experiments are conducted with the returns of a set of 100 financial instruments traded in the US stock market over a period of 250 days in 2014. Obtained results help to estimate the reliability of minimum spanning tree in market network analysis.
Random matrix theory (RMT) is applied to investigate the cross-correlation matrix of a financial time series in four different stock markets: Russian, American, German, and Chinese. The deviations of distribution of eigenvalues of market correlation matrix from RMT global regime are investigated. Specific properties of each market are observed and discussed.