# A Tale of Tail Covariances (and Diversified Tails)

## TL;DR

This paper introduces a novel approach to tail diversification in financial time series using tail covariance matrices derived from moments, entropy, and mutual information, with empirical demonstrations on stock data.

## Contribution

It presents a new method linking tail covariance to entropy and mutual information, providing a fresh perspective on tail diversification in finance.

## Key findings

- Tail covariance matrix effectively captures tail diversification.
- Moment contrast functions isolate tail behaviors.
- Empirical results show improved diversification in stock portfolios.

## 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.