How to Select a Portfolio Performance Measure?

This paper reviews the main dimensions underlying the selection of a classical portfolio performance measure, namely the Sharpe Ratio, Jensen's alpha, the Modified Jensen's alpha, the Treynor Ratio, and the Information Ratio. We first examine how they differ from each other according to the risk (input of performance) and measurement (link between input and output) dimensions. Next, we analyze, from the point of view of the investor, which type of risk (total, systematic, and specific) should be used as the input of performance evaluation. We distinguish the normative approach, in which the investor tries to optimize her portfolio choice, with the positive approach, for which the asset allocation is supposed to be given. We also address the issue of the selection of the appropriate measure from the portfolio manager's point of view. We show that it primarily depends on the stability of rankings produced with the selected measure. Numerical illustrations of these selection criteria are provided through a simplified, yet realistic example