Ranking Metrics: Extending Acceptability and Performance Indexes

TL;DR

This paper introduces an axiomatic framework for ranking metrics that evaluate financial and insurance positions, extending traditional performance measures with new theoretical insights and practical applications.

Contribution

It develops a unified theory linking ranking metrics to acceptance sets and risk measures, including classical and novel examples, with empirical applications.

Findings

Classical ratios are special cases of the framework.

New examples include expected-loss, Lambda-quantile, and bibliometric indices.

Empirical applications demonstrate practical relevance.

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.