Abstract
This paper proposes a set of desirable axioms to characterize performance measures in the context of portfolio management. A performance measure consistent with the axioms is called “ideal”. We observe that a popular performance measure, Farinelli–Tibiletti (FT) ratio [S. Farinelli & L. Tibiletti (2008) Sharpe thinking in asset ranking with one-sided measures, European Journal of Operational Research 185 (3), 1542–1547], which captures potential-seeking behavior, is not ideal. It violates a very important property of portfolio theory, the diversification. As an alternative, we propose a new ideal performance measure, upside beta ratio (UBR). To examine its performance, we rank mutual funds for UBR and other four performance measures — Sharpe, Sortino, FT and Jensen’s alpha — and then we compare the rankings of UBR with the rankings of other ratios. In addition, the performance of top-ranked funds are compared through back-testing and out-of-sample analysis. Our findings reveal that the UBR performs significantly better than the other ratios in most scenarios. Finally, in order to check robustness of the new measure, a parameter sensitivity analysis is presented.
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