11 July 2022, at 11.00 • Marco Biagi Foundation

YORAM KROLL, Hebrew University of Jerusalem and Ono Academic College

CARLO ALBERTO MAGNI, Economics Department Marco Biagi, University of Modena and Reggio Emilia


The present research defines an axiomatic foundation for coherent portfolio performance ratios, based on monotonicity, size monotonicity, portfolio riskless translation invariance (PRTI), and concavity. The research proves that the most used performance ratios are not coherent. In fact, it is well known that the Sharpe ratio does not satisfy the monotonicity axiom; furthermore, this research shows that the Kappa ratio, the Omega ratio, the Reward-to-Var ratio, and the Reward-to-CVar ratio do not satisfy PRTI if their fixed threshold is different from the risk-free rate. The research proves that replacing the fixed threshold with a threshold that equals γ times the portfolio’s risk premium plus (1-γ) times the risk-free rate eliminates the above shortcomings and assures coherence of all the analyzed ratios.

The seminar can be followed in precense or live through Microsoft Teams using the link: Coherent Portfolio

Coherent Portfolio Performance Ratios