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A decision-theoretic foundation for reward-to-risk performance measures

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  • Schuhmacher, Frank
  • Eling, Martin
Abstract
In this paper we prove that partial-moments-based performance measures (e.g., Omega, Kappa, upside-potential ratio, Sortino–Satchell ratio, Farinelli–Tibiletti ratio), value-at-risk-based performance measures (e.g., VaR ratio, CVaR ratio, Rachev ratio, generalized Rachev ratio), and other admissible performance measures are a strictly increasing function in the Sharpe ratio. The theoretical basis of this result is the location and scale property and two other plausible and mild conditions. Our result provides a decision-theoretic foundation for all these frequently used performance measures. Moreover, it might explain the empirical finding that all these measures typically lead to very similar rankings.

Suggested Citation

  • Schuhmacher, Frank & Eling, Martin, 2012. "A decision-theoretic foundation for reward-to-risk performance measures," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 2077-2082.
    • Handle: RePEc:eee:jbfina:v:36:y:2012:i:7:p:2077-2082
    DOI: 10.1016/j.jbankfin.2012.03.013
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    More about this item

    Keywords

    Asset management; Performance measurement; Sharpe ratio; Location and scale condition; Risk and reward measurement;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors
    • G29 - Financial Economics - - Financial Institutions and Services - - - Other

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