Portfolio Optimization Under Tracking Error and Weights Constraints

45 Pages Posted: 22 Feb 2007

See all articles by Isabelle G. Bajeux-Besnainou

Isabelle G. Bajeux-Besnainou

McGill University - Desautels Faculty of Management

Riadh Belhaj

Conservatoire National des Arts et Metiers (CNAM)

Didier Maillard

Conservatoire National des Arts et Métiers (CNAM); Amundi Asset Management

Roland Portait

Conservatoire National des Arts et Métiers (CNAM); ESSEC Business School

Date Written: February 2007

Abstract

Active portfolio manager performances are commonly assessed against a benchmark. In this case, his/her performance is often measured by the Information Ratio, the maximization of which is equivalent to the maximization of an expected return under a tracking error constraint. In addition, asset managers often deal with weights constraints (for instance, no more than 10% in equity). These constraints are regulatory or inherent to the fund's policy.

We consider a fund manager complying simultaneously with a tracking error (computed for instance, vis-a-vis a bond index) and a weights constraints. These two constraints are not necessarily redundant even when the benchmark complies with the weights constraint. We show, theoretically and through numerical examples that the weights and the tracking error constraints can be simultaneously binding, we consider both equality and inequality weights constraints, derive the analytical and geometrical solutions in both cases and provide financial interpretations based on funds separation. We compute the loss in the Information Ratio due to a weights constraint and analyze the implications on asset allocation and performance measures. In particular, due to the weights constraint, the asset manager may operate under a smaller Information Ratio when free to deviate more from the benchmark (higher Tracking Error). This result undermines the coherence of the Information Ratio as a measure of the ability of asset managers.

Keywords: Tracking Error, Weights constraint, Portfolio Optimization, Information Ratio

JEL Classification: G11, D81

Suggested Citation

Bajeux-Besnainou, Isabelle G. and Belhaj, Riadh and Maillard, Didier and Portait, Roland, Portfolio Optimization Under Tracking Error and Weights Constraints (February 2007). Available at SSRN: https://ssrn.com/abstract=963997 or http://dx.doi.org/10.2139/ssrn.963997

Isabelle G. Bajeux-Besnainou (Contact Author)

McGill University - Desautels Faculty of Management ( email )

1001 Sherbrooke St. West
Montreal, Quebec H3A1G5 H3A 2M1
Canada

Riadh Belhaj

Conservatoire National des Arts et Metiers (CNAM) ( email )

2 rue conté
Paris, 75003
France

Didier Maillard

Conservatoire National des Arts et Métiers (CNAM) ( email )

292, rue Saint-Martin
Paris cedex 03, 75141
France

Amundi Asset Management ( email )

90 Boulevard Pasteur
Paris, 75015
France

Roland Portait

Conservatoire National des Arts et Métiers (CNAM) ( email )

292, rue Saint-Martin
Paris cedex 03, 75141
France

ESSEC Business School ( email )

3 Avenue Bernard Hirsch
CS 50105 CERGY
CERGY, CERGY PONTOISE CEDEX 95021
France

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