The Generalized Treynor Ratio

This paper extends the Treynor performance ratio for a single index to the case of multiple indexes. The new measure, called the Generalized Treynor Ratio, preserves the same key geometric and analytical properties of the original Treynor Ratio. The Generalized Treynor Ratio is defined as the abnormal return of a portfolio per unit of premium-weighted average systematic risk, normalized by the premium-weighted average systematic risk of the benchmark. Numerical simulations reveal that the portfolio rankings produced with this measure are more precise and more stable than the ones provided by Jensen’s alpha and the Information Ratio.I wish to thank Wayne Ferson, Pascal François, Eric Jacquier, Lars Tyge Nielsen, Nicolas Papageorgiou, Peter Schotman, Marco Pagano (the Editor) and three anonymous referees, as well as participants at the 2003 International AFFI Conference (Lyon), the 2003 NFA Conference (Qu’ebec) and seminars at Maastricht University and CORE (Louvain-la-Neuve) for helpful comments. The author acknowledges financial support from Deloitte Luxemburg and a research grant of the Belgian National Funds for Scientific Research (FNRS). Part of this research was completed while I was visiting HEC Montr’ eal. All errors remaining are mine.