Chapter 10. On the Foundation of Performance Measures Under Asymmetric Returns
Christian S. Pedersen and Stephen E. Satchell
We examine two performance measures advocated for asymmetric return distributions: the Sortino ratio—originally introduced by Sortino and Price (1994)
—and a measure based on power utility introduced in Leland (1999)
. 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.
JEL Classification: G00, G11, G12