The Annals of Applied Statistics

Robust dependence modeling for high-dimensional covariance matrices with financial applications

Zhe Zhu and Roy E. Welsch

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A very important problem in finance is the construction of portfolios of assets that balance risk and reward in an optimal way. A critical issue in portfolio development is how to address data outliers that reflect very unusual, generally non-recurring, market conditions. Should we allow these to have a significant impact on our estimation and portfolio construction process or should they be considered separately as evidence of a regime shift and/or be used to adjust baseline results? In financial asset allocation, a fundamental step is often a mean-variance optimization problem that makes use of the location vector and dispersion matrix of the financial assets. In this paper, we introduce a new high- dimensional covariance estimator that is much less sensitive to outliers compared to its classical counterparts. We then apply this estimator to the active asset allocation application, and show that our proposed new estimator delivers better results compared to many existing asset allocation methods. An important bonus is that on our examples, the method has a smaller proportion of stock weights greater than 10% and, in many cases, a higher alpha. Covariance estimation is more challenging than mean estimation and only locally and not globally optimal solutions are available. Our proposed new robust covariance estimator uses a regular vine dependence structure and only pairwise robust partial correlation estimators. The resulting robust covariance estimator delivers high performance for identifying outliers for large high dimensional datasets, has a high breakdown point, and is positive definite. When the full vine structure is not available, we propose using a minimal spanning tree algorithm to replace missing vine structure.

Article information

Ann. Appl. Stat., Volume 12, Number 2 (2018), 1228-1249.

Received: March 2014
Revised: July 2017
First available in Project Euclid: 28 July 2018

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Zentralblatt MATH identifier

Active asset allocation portfolio selection robust estimation high-dimensional dependence modeling covariance/correlation estimation regular vine


Zhu, Zhe; Welsch, Roy E. Robust dependence modeling for high-dimensional covariance matrices with financial applications. Ann. Appl. Stat. 12 (2018), no. 2, 1228--1249. doi:10.1214/17-AOAS1087.

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