Parameter Uncertainty in Portfolio Selection: Shrinking the Inverse Covariance Matrix

35 Pages Posted: 16 Feb 2009 Last revised: 10 Sep 2012

See all articles by Apostolos Kourtis

Apostolos Kourtis

University of East Anglia (UEA) - Norwich Business School

George Dotsis

National and Kapodistrian University of Athens - Faculty of Economics; Essex Finance Centre, Essex Business School, University of Essex

Raphael N. Markellos

University of East Anglia (UEA) - Norwich Business School

Date Written: April 1, 2011

Abstract

The estimation of the inverse covariance matrix plays a crucial role in optimal portfolio choice. We propose a new estimation framework that focuses on enhancing portfolio performance. The framework applies the statistical methodology of shrinkage directly to the inverse covariance matrix using two non-parametric methods. The first minimises the out-of-sample portfolio variance while the second aims to increase out-of-sample risk-adjusted returns. We apply the resulting estimators to compute the minimum variance portfolio weights and obtain a set of new portfolio strategies. These strategies have an intuitive form which allows us to extend our framework to account for short-sale constraints, high transaction costs and singular covariance matrices. A comparative empirical analysis against several strategies from the literature shows that the new strategies generally offer higher risk-adjusted returns and lower levels of risk.

Keywords: Portfolio Choice, Inverse Covariance Matrix, Parameter Uncertainty, Shrinkage

JEL Classification: C13, C51, C61, G11

Suggested Citation

Kourtis, Apostolos and Dotsis, George and Markellos, Raphael N., Parameter Uncertainty in Portfolio Selection: Shrinking the Inverse Covariance Matrix (April 1, 2011). Journal of Banking and Finance, Vol. 36, No. 9, pp. 2522-2531, 2012. Available at SSRN: https://ssrn.com/abstract=1343502 or http://dx.doi.org/10.2139/ssrn.1343502

Apostolos Kourtis

University of East Anglia (UEA) - Norwich Business School ( email )

Norwich
NR4 7TJ
United Kingdom

George Dotsis

National and Kapodistrian University of Athens - Faculty of Economics ( email )

Greece

HOME PAGE: http://sites.google.com/site/gdotsis/

Essex Finance Centre, Essex Business School, University of Essex ( email )

Wivenhoe Park
Colchester, CO4 3SQ
United Kingdom

Raphael N. Markellos (Contact Author)

University of East Anglia (UEA) - Norwich Business School ( email )

Norwich
NR4 7TJ
United Kingdom

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