High-dimensional covariance matrix estimators on simulated portfolios with complex structures

TL;DR

This paper introduces advanced high-dimensional covariance matrix estimators tailored for complex portfolio structures, demonstrating improved financial metrics and risk management strategies through simulations and empirical data analysis.

Contribution

It presents novel two-step covariance estimators combining random matrix theory and hierarchical methods for high-dimensional portfolio allocation.

Findings

Hierarchical nested covariance models reveal complex system interactions.

Two-step estimators outperform traditional methods in financial metrics.

Empirical data reproduces stylized facts of complex covariance structures.

Abstract

We study the allocation of synthetic portfolios under hierarchical nested, one-factor, and diagonal structures of the population covariance matrix in a high-dimensional scenario. The noise reduction approaches for the sample realizations are based on random matrices, free probability, deterministic equivalents, and their combination with a data science hierarchical method known as two-step covariance estimators. The financial performance metrics from the simulations are compared with empirical data from companies comprising the S&P 500 index using a moving window and walk-forward analysis. The portfolio allocation strategies analyzed include the minimum variance portfolio (both with and without short-selling constraints) and the hierarchical risk parity approach. Our proposed hierarchical nested covariance model shows signatures of complex system interactions. The empirical financial data reproduces stylized portfolio facts observed in the complex and one-factor covariance models. The two-step estimators proposed here improve several financial metrics under the analyzed investment strategies. The results pave the way for new risk management and diversification approaches when the number of assets is of the same order as the number of transaction days in the investment portfolio.