Head of Investment Solutions, Deutsche Asset Management, Mainzer Landstr. 178-190, 603227 Frankfurt, Germany Tel: +49 69717063461; Fax: +49 15112100340; e-mail: bernd.scherer@db.com

Revised 7 November 2003.

Abstract

A wide variety of risk–return ratios are routinely reported in sales pitches as well as academic publications. Little attempt has been made, however, to look at the small sample distributions of these estimators in order to derive confidence bands. The reason for this has been the extreme difficulty of working out the required statistics for most risk–return ratios. Rather than following classical statistics, this paper relies on a general and robust method which not only provides confidence intervals for arbitrary risk–return ratios, sample sizes and distribution, but is also fairly easy to implement.