A Tale of Tail Covariances (and Diversified Tails)

Abstract

This paper deals with tail diversification in financial time series through the concept of statistical independence by way of differential entropy and mutual information. By using moments as contrast functions to isolate the tails of the return distributions, we recover the tail covariance matrix, a specific two-dimensional slice of the mixed moment tensor, as a key driver of tail diversification. We further explore the links between the moment contrast approach and the original entropy formulation, and show an example of in- and out-of-sample diversification on a broad stock universe.