The Use of the Partitioning Theorem to Prove Further Results Regarding the Distribution of IRRs: And an Open Question

Abstract

In 2018, Cuthbert proved that any transaction vector can be uniquely partitioned into a sequence of pure investments with strictly decreasing internal rates of return (IRRs). In a subsequent paper, Cuthbert used the partitioning theorem to derive a new sufficient condition for a transaction to have a unique IRR and proved some results regarding how the IRRs of a transaction must be distributed. This paper proves some further results on the distribution of IRRs. It also poses an open question regarding the possible relationship between the number of IRRs of a transaction and the relative sizes of the smallest and largest IRRs of the terms in the unique partition of that transaction.