Unveiling the embedded coherence in divergent performance rankings

This paper focuses on analyzing functional relationships among performance measures, centered on the adjusted differential risk premium between the asset and the benchmark and on Sharpe-1994 ratio. First, we develop a risk normalization procedure for variance and Aumann-Serrano riskiness which turns contradictory rankings into coherent ones, and combines the effects of correlation and outliers into the analysis. On this basis, we deduce functional connections among performance measures, arriving at a new indicator which expresses performance as the addition of three effects due to Sharpe ratio, correlation and outliers. We show it is a strictly increasing function of Homm-Pigorsch ratio.