On the foundation of performance measures under asymmetric returns

Christian Pedersen and Stephen Satchell

Quantitative Finance, 2002, vol. 2, issue 3, 217-223

Abstract: We examine two performance measures advocated for asymmetric return distributions: the Sortino ratio—originally introduced by Sortino and Price (Sortino F and Price L 1994 J. Investing 59-65)—and a measure based on power utility introduced in Leland (Leland H 1999 Financial Analysts J. 27-36). In particular, we investigate the role of the maximum principle in this context, and assess the conditions under which the measures satisfy it. Our results add further motivation for the use of a modified Sortino ratio, by placing it on a sound theoretical foundation. In this light, we discuss its relative merits compared with alternative approaches.

Date: 2002
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DOI: 10.1088/1469-7688/2/3/304

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