When all risk-adjusted performance measures are the same: in praise of the Sharpe ratio ‒ a comment

Abstract

Chen et al. [Quant. Finance, 2011, 11, 1439–1447] prove that 11 specific reward-to-risk performance measures are all monotonic transformations of the Sharpe ratio, when the underlying random returns of assets to be combined are multivariate elliptically distributed. Schuhmacher and Eling [J. Bank. Financ., 2012, 36, 2077–2082] show that any so-called ‘admissible’ performance measure is a strictly increasing function in the Sharpe ratio, when the underlying distributions of a given set of portfolio alternatives satisfy the location and scale property. We conclude that both these results are linked to each other by the findings of Owen and Rabinovitch [J. Financ., 1983, 38, 745–752]. Therefore, the findings of Chen et al. [Quant. Finance, 2011, 11, 1439–1447] can be extended to the whole class of admissible performance measures.

Keywords:

• Performance evaluation
• Quantitative finance
• Portfolio management
• Portfolio theory

JEL Classification:

• G10
• G11