Portfolio Optimization Under Tracking Error and Weights Constraints

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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.