A Dynamic Structure for High Dimensional Covariance Matrices and its Application in Portfolio Allocation

TL;DR

This paper introduces a dynamic structure for estimating high-dimensional covariance matrices, improving portfolio allocation performance in financial markets from 1995 to 2014.

Contribution

It proposes a novel dynamic estimation method for high-dimensional covariance matrices with proven asymptotic properties and demonstrated superior performance in portfolio allocation.

Findings

Outperforms traditional sample covariance matrix in portfolio allocation

Significantly outperforms market benchmarks from 1995 to 2014

Demonstrates robustness through simulation studies

Abstract

Estimation of high dimensional covariance matrices is an interesting and important research topic. In this paper, we propose a dynamic structure and develop an estimation procedure for high dimensional covariance matrices. Asymptotic properties are derived to justify the estimation procedure and simulation studies are conducted to demonstrate its performance when the sample size is finite. By exploring a financial application, an empirical study shows that portfolio allocation based on dynamic high dimensional covariance matrices can significantly outperform the market from 1995 to 2014. Our proposed method also outperforms portfolio allocation based on the sample covariance matrix and the portfolio allocation proposed in Fan, Fan and Lv (2008).