Paper: arXiv 2302.13646

Authors: Jan Rosenzweig

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.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a rigorous theoretical framework linking differential entropy, mutual information, and higher-order moments (mixed moment tensors) to model tail dependencies and tail covariances. It grounds these mathematical concepts with empirical applications demonstrating both in-sample and out-of-sample tail diversification on a broad stock universe. While mathematically dense, the methodology offers an innovative perspective on portfolio tail-risk management.

Research Flowchart

  flowchart TD
    A[Goal: Achieve Tail Diversification via Statistical Independence] --> B[Data: Equity Return Time Series]
    B --> C[Method: Apply Moment Contrast Functions]
    C --> D[Compute Mixed Moment Tensor Slices]
    D --> E[Isolate Tail Covariance Matrix]
    E --> F[Outcome: Optimal In- and Out-of-Sample Portfolio Diversification]