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

Taras Bodnar, N. Parolya, Erik Thorsén

Research output: Contribution to journalArticleScientificpeer-review

19 Downloads (Pure)

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+ɛ, ɛ >0, moments. Also, the population covariance matrix with unbounded largest eigenvalue 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.

Original languageEnglish
Pages (from-to)1334-1349
Number of pages16
JournalIEEE Transactions on Signal Processing
Volume71
DOIs
Publication statusPublished - 2023

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Fingerprint

Dive into the research topics of 'Dynamic Shrinkage Estimation of the High-Dimensional Minimum-Variance Portfolio'. Together they form a unique fingerprint.

Cite this