Cross validation based transfer learning for cross-sectional non-linear shrinkage: A data-driven approach in portfolio optimization

Torsten Mörstedt, Bernhard Lutz and Dirk Neumann

European Journal of Operational Research, 2024, vol. 318, issue 2, 670-685

Abstract: Enhanced covariance estimation approaches, such as (non-)linear shrinkage, are well established in the literature. Non-linear shrinkage estimators generally minimize a certain loss function regarding statistical assumptions about the future covariance matrix. At the same time, the problem of covariance estimation is traditionally considered from a rather restrictive view since the only available data to determine the estimation parameters is given by the return history of the actual portfolio constituents. In this study, we propose a novel and purely data-driven perspective on covariance estimation. We present a non-linear shrinkage estimator that determines the estimation parameters using cross validation to be historically optimal on a disjoint dataset of assets according to the given objective, such as minimum variance or maximum risk-adjusted return. We then transfer the historically optimal estimation parameters learned on the disjoint dataset to the actual covariance estimation problem. Thereby, the sample eigenvalues are corrected in a purely data-driven way, agnostic to theoretically derived parameters. Another benefit of focusing on disjoint data is that we address the problem of limited data availability in high-dimensional estimation problems when the number of assets exceeds the history length. Our empirical evaluation, based on a total of six stock market indices and various problem dimensions, shows that our approach outperforms existing cross-sectional estimators in minimizing variance and maximizing risk-adjusted return. While our study is limited to the cross-section, the method of parameter selection using cross validation and transfer learning can also be combined with other estimators, such as time-series methods.

Keywords: Finance; Covariance estimation; Non-linear shrinkage; Data-driven approach; Portfolio optimization (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:318:y:2024:i:2:p:670-685

DOI: 10.1016/j.ejor.2024.05.006

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