On the foundation of performance measures under asymmetric returns
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.
Volume (Year): 2 (2002)
Issue (Month): 3 ()
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