A Note on Portfolio Performance Attribution: Taking Risk into Account

Abstract

In this article, we show that performance attribution considered alone can be misleading. Indeed, a portfolio manager who knows perfectly the distribution of asset’s returns and who performs a relative portfolio optimization according to that information, may be penalized in some of her choices by the performance attribution process. In order to solve this apparent paradox, we propose to take risk into account. We establish that the appropriate definition of risk in this management context is relative risk as measured by the standard deviation of the tracking error. This measure makes it possible to justify the choices which were previously penalized. Moreover, we prove that the information ratio of each decision (asset allocation and security selection) is the same. This means that some equilibrium between expected (or ex-post mean) return and relative risk has been reached.

Keywords: Performance attribution, risk attribution, tracking error, portfolio optimization, efficient frontier, information ratio.

JEL Classification: G11, G12.