On the quantum behavior and clustering properties of correlated financial portfolios

Abstract

We investigate 17 digital currencies making an analogy with quantum systems and develop the concept of eigenportfolios. We show that the density of states of the correlation matrix of these assets shows a behavior between that of the Wishart ensemble and one whose elements are Cauchy distributed. A metric for the participation matrix based on superposition of Gaussian functions is proposed and we show that small eigenvalues correspond to localized states. Nonetheless, some level of localization is also present for bigger eigenvalues probably caused by the fat tails of the distribution of returns of these assets. We also show through a clustering study that the digital currencies tend to stagger together. We conclude the paper showing that this correlation structure leads to an Epps effect.