Parameter Uncertainty in Portfolio Selection: Shrinking the Inverse Covariance Matrix
35 Pages Posted: 16 Feb 2009 Last revised: 10 Sep 2012
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: Suggested Citation
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