Rates of return of investments whose timings are specified by a probability distribution

Abstract

In this paper we describe an approach for calculating the rates of return of investments whose timing is uncertain. In the framework of the approach, we calculate the expected value of the rate of return. We extend the deterministic Endpoints and Modified Dietz rate of return models by viewing the investments transaction timings as random variables. Our main working assumption is that the transaction timings are uniformly distributed in a certain time interval. We study a series of new rate of return models that have a wide range of practical applications. Our results generalize some well-known rate of return formulas, including the renowned Modified Dietz formula. The models introduced in this paper provide one-period rates of return compliant with the Global Investment Performance Standards (GIPS) requirements. They can be used for GIPS-compliant calculations.