On Geometric and Arithmetic Portfolio Performance Indexes

Abstract

The literature of Index numbers contains much discussion of the relative merits of geometric and arithmetic averages of prices and quantities. The controversy on this subject dates from the middle of the nineteenth century and is fully described by Crowe [2], In recent times both types of averages have been applied to security price relatives to measure the performance of groups of securities over time. The purpose of this paper is to demonstrate the properties of these security indexes and to show the relationships between them and an index based upon a more general type of average called the power mean. The concluding section of this paper contains the proof of an interesting and important limit property which provides the conceptual link between geometric and arithmetic security indexes.