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Ranking Metrics: Extending Acceptability and Performance Indexes

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  • Asmerilda Hitaj
  • Elisa Mastrogiacomo
  • Ilaria Peri
  • Marcelo Righi

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.

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  • Asmerilda Hitaj & Elisa Mastrogiacomo & Ilaria Peri & Marcelo Righi, 2026. "Ranking Metrics: Extending Acceptability and Performance Indexes," Papers 2604.16438, arXiv.org.
    • Handle: RePEc:arx:papers:2604.16438
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    References listed on IDEAS

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