Portfolio Allocation as an Inverse Problem

Posted: 19 Dec 2008 Last revised: 12 Oct 2009

See all articles by Guillaume Simon

Guillaume Simon

Capital Fund Management

Anna Simoni

University of Toulouse 1 - Toulouse School of Economics (TSE)

Date Written: October 5, 2009

Abstract

Proceeding to portfolio allocation in the framework of Markowitz, a numerical inconsistency may occur when the sample covariance matrix of assets returns has to be inverted. This is mainly caused by the magnitude of its lowest eigenvalues. In this paper, we tackle the Markowitz problem as an inverse problem and give a spectral justification for the causes of instability of the inverse when computing the sample covariance matrix for portfolio allocation. We particularly detail the regularizing effect of two techniques commonly accepted in practice: Black-Litterman and shrinkage. Our aim is to make a spectral analysis of these techniques and to analyze whether they can be related to regularization schemes or interpreted within a Bayesian setting.

Keywords: Portfolio Allocation, Black-Litterman, Shrinkage, Inverse Problems, Regularization

JEL Classification: G00, G11

Suggested Citation

Simon, Guillaume and Simoni, Anna, Portfolio Allocation as an Inverse Problem (October 5, 2009). Available at SSRN: https://ssrn.com/abstract=1317479

Guillaume Simon (Contact Author)

Capital Fund Management ( email )

23 rue de l'Université
Paris, 75007
France

Anna Simoni

University of Toulouse 1 - Toulouse School of Economics (TSE) ( email )

Place Anatole-France
Toulouse Cedex, F-31042
France

HOME PAGE: http://simoni.anna.googlepages.com/

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