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14-03-2020 | Focus

Improving portfolios global performance using a cleaned and robust covariance matrix estimate

Authors: Emmanuelle Jay, Thibault Soler, Eugénie Terreaux, Jean-Philippe Ovarlez, Frédéric Pascal, Philippe De Peretti, Christophe Chorro

Published in: Soft Computing | Issue 12/2020

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Abstract

This paper presents how the use of a cleaned and robust covariance matrix estimate can improve significantly the overall performance of maximum variety and minimum variance portfolios. We assume that the asset returns are modelled through a multi-factor model where the error term is a multivariate and correlated elliptical symmetric noise extending the classical Gaussian assumptions. The factors are supposed to be unobservable and we focus on a recent method of model order selection, based on the random matrix theory to identify the most informative subspace and then to obtain a cleaned (or de-noised) covariance matrix estimate to be used in the maximum variety and minimum variance portfolio allocation processes. We apply our methodology on real market data and show the improvements it brings if compared with other techniques especially for non-homogeneous asset returns.

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Available only for authorised users

A spiked structure denotes a covariance model where some eigenvalues are located out of the “bulk”, like outliers.

A Toeplitz matrix is a diagonal-constant matrix.

Data are available upon request.

The number of group is \(p=6\) and the quantiles used are \(q_\theta \) and \(q_{1-\theta }\) with \(\theta \in [1\%, 2.5\%, 5\%, 10\%, 15\%, 25\%, 50\%]\).

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Title: Improving portfolios global performance using a cleaned and robust covariance matrix estimate
Authors: Emmanuelle Jay
Thibault Soler
Eugénie Terreaux
Jean-Philippe Ovarlez
Frédéric Pascal
Philippe De Peretti
Christophe Chorro
Publication date: 14-03-2020
Publisher: Springer Berlin Heidelberg
Published in: Soft Computing / Issue 12/2020
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-020-04840-9

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