Risk-Adjusted Performance Attribution and Portfolio Optimizations Under Tracking-Error Constraints

This paper examines whether the risk-adjusted performance attribution process is consistent with portfolio optimization under tracking-error constraints. Since Mina (2003), Bertrand (2005) and Menchero and Hu (2006), risk attribution has been widely used in the performance attribution process.This article analyzes and discusses the information ratio decomposition proposed by Menchero (2007) in the light of the analysis of risk-adjusted performance attribution developed in Bertrand (2005). It is also shown that only optimization under the tracking-error constraint alone is consistent with the risk-adjusted performance attribution process. Indeed, as soon as additional constraints (e.g. on total risk) are introduced, the component information ratios of the decisions are no longer uniform nor equal to the information ratio of the whole portfolio. This means that no equilibrium between expected return and relative risk has been reached