Ranking Metrics: Extending Acceptability and Performance Indexes

2026-04-06

AI Summary

This study addresses the limitations of traditional risk-adjusted performance measures—such as the Sharpe ratio—in effectively ranking financial or insurance positions. The authors develop an axiomatic framework that introduces monotonicity and cash quasi-concavity to define a novel class of ranking measures, which map positions directly to performance levels rather than standardized returns. This approach establishes theoretical connections with acceptance sets and risk measures, encompassing classical ratio-based metrics while extending to new ranking methodologies grounded in expected shortfall, Lambda quantiles, and bibliometric-inspired constructions. Empirical analyses involving portfolio rankings and climate risk insurance demonstrate both the theoretical coherence and practical applicability of the proposed framework.

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.

Problem

• ranking metrics
• acceptability indices
• risk-adjusted performance
• financial positions
• insurance positions

Innovation

• ranking metrics
• cash-quasiconcavity
• acceptability indices
• risk measures
• axiomatic framework