Exponential Weighting and Random-Matrix-Theory-Based Filtering of Financial Covariance Matrices for Portfolio Optimization

TL;DR

This paper presents a novel covariance matrix estimator for financial data that combines exponential weighting for heteroskedasticity with random matrix theory to reduce noise, improving portfolio optimization performance.

Contribution

It introduces a new estimator that integrates exponential weighting and random matrix theory, with analytical spectrum calculation for large matrices, enhancing financial covariance estimation.

Findings

The estimator outperforms traditional methods in empirical portfolio optimization.

Analytical spectrum calculation for exponentially weighted random matrices is achieved.

Empirical results demonstrate improved portfolio performance using the new estimator.

Abstract

We introduce a covariance matrix estimator that both takes into account the heteroskedasticity of financial returns (by using an exponentially weighted moving average) and reduces the effective dimensionality of the estimation (and hence measurement noise) via techniques borrowed from random matrix theory. We calculate the spectrum of large exponentially weighted random matrices (whose upper band edge needs to be known for the implementation of the estimation) analytically, by a procedure analogous to that used for standard random matrices. Finally, we illustrate, on empirical data, the superiority of the newly introduced estimator in a portfolio optimization context over both the method of exponentially weighted moving averages and the uniformly-weighted random-matrix-theory-based filtering.