Collective behavior of cryptocurrency price changes

Abstract

Digital assets termed cryptocurrencies are correlated. We analyze cross correlations between price changes of different cryptocurrencies using methods of random matrix theory and minimum spanning trees. We find that the cross correlation matrix exhibits non-trivial hierarchical structures and groupings of cryptocurrency pairs, which are not present in the partial cross correlations. In sharp contrast to the predictions for other financial markets, we discover that most of the eigenvalues in the spectrum of the cross correlation matrix do not agree with the universal predictions of random matrix theory, but the few of the largest eigenvalues deviate as expected. The minimum spanning tree of cryptocurrency cross correlations reveals distinct community structures that are surprisingly stable. Collective behaviors that are present in the cryptocurrency market can be useful for the construction of portfolio of cryptocurrencies as well as for future research on the subject.