Correspondence: Philippe Bertrand, University of Aix-Marseille 2 GREQAM, UMR-CNRS 6579 2, rue de la Charité 13236, Marseille Cede 02, France. E-mail: philippe.bertrand@univmed.fr

¹is a professor of finance at Université Aix-Marseille 2 and Euromed Marseille School of Management. He is also a member of the GREQAM Research Center. He conducts active research in portfolio management, performance evaluation and portfolio insurance. He was formerly the head of Financial Engineering at CCF Capital Management.

Received 16 October 2008; Revised 16 October 2008.

Abstract

This paper examines whether the risk-adjusted performance attribution process is consistent with portfolio optimisation under tracking-error constraints. Since Mina (2003), Bertrand (2005, 2008b) and Menchero and Hu (2006), risk attribution has been widely used in the performance attribution process. This paper analyses and discusses the information ratio decomposition proposed by Menchero (2007) in the light of the analysis of risk-adjusted performance attribution developed by Bertrand (2005). It is also shown that only optimisation under the tracking-error constraint alone is consistent with the risk-adjusted performance attribution process. Indeed, as soon as additional constraints (for example, on total risk) are introduced, the component information ratios of the decisions are no longer the same or equal to the information ratio of the whole portfolio. This means that no equilibrium between expected return and relative risk has been reached.