Ranking Metrics: Extending Acceptability and Performance Indexes
Abstract
This paper develops an axiomatic framework for ranking metrics, a general class of functionals for evaluating and ordering financial or insurance positions. Unlike traditional risk-adjusted performance measures-such as the Sharpe ratio, RAROC, or Omega-that express reward per unit of risk, ranking metrics assign each position a performance level rather than a normalized return. Relying on monotonicity and a new property called cash-quasiconcavity, we derive representation results linking ranking metrics to families of acceptance sets and risk measures, extending the theory of acceptability indices. Classical ratios arise as special cases, while new examples-based on expected-loss, Lambda-quantile, and bibliometric indices-illustrate the framework's flexibility. Empirical applications to portfolio ranking and climate-risk insurance demonstrate its practical relevance.
Keywords
Cite
@article{arxiv.2604.16438,
title = {Ranking Metrics: Extending Acceptability and Performance Indexes},
author = {Asmerilda Hitaj and Elisa Mastrogiacomo and Ilaria Peri and Marcelo Righi},
journal= {arXiv preprint arXiv:2604.16438},
year = {2026}
}