Dynamic Shrinkage Estimation of the High-Dimensional Minimum-Variance Portfolio

TL;DR

This paper introduces a novel dynamic shrinkage estimator for the high-dimensional minimum-variance portfolio, leveraging random matrix theory to adaptively shrink weights towards a data-driven target, improving portfolio estimation accuracy.

Contribution

It develops a new theoretical framework for dynamic GMV portfolio estimation using shrinkage towards a data-derived target, applicable under weak assumptions and with both overlapping and non-overlapping samples.

Findings

The new estimator outperforms traditional methods in simulations.

The approach is effective in empirical stock return data.

Theoretical results hold under broad conditions, including unbounded spectra.

Abstract

In this paper, new results in random matrix theory are derived which allow us to construct a shrinkage estimator of the global minimum variance (GMV) portfolio when the shrinkage target is a random object. More specifically, the shrinkage target is determined as the holding portfolio estimated from previous data. The theoretical findings are applied to develop theory for dynamic estimation of the GMV portfolio, where the new estimator of its weights is shrunk to the holding portfolio at each time of reconstruction. Both cases with and without overlapping samples are considered in the paper. The non-overlapping samples corresponds to the case when different data of the asset returns are used to construct the traditional estimator of the GMV portfolio weights and to determine the target portfolio, while the overlapping case allows intersections between the samples. The theoretical results are derived under weak assumptions imposed on the data-generating process. No specific distribution is assumed for the asset returns except from the assumption of finite $4+\varepsilon$, $\varepsilon>0$, moments. Also, the population covariance matrix with unbounded spectrum can be considered. The performance of new trading strategies is investigated via an extensive simulation. Finally, the theoretical findings are implemented in an empirical illustration based on the returns on stocks included in the S\&P 500 index.