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

Round 1

Reviewer 1 Report

The author indicates: “It was proved in Cuthbert, (2018), that any transaction vector could be uniquely partitioned into a sequence of pure investments with strictly decreasing internal rates of return, (IRR). In a subsequent paper Cuthbert, (2021), used the partitioning theorem to derive a new sufficient condition for a transaction to have a unique IRR: and also proved some results on 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 about 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.”

The authors have made a clear presentation and have successfully achieved their goal.

Two weaknesses exits: (1) the lit review could have been more extensive and (2) the conclusion could have been longer, offering more reasons why the study’s findings are important.

I think the article should be accepted for publication, after making minor revisions, addressing the above two weaknesses.

Author Response

Have taken on Reviewer 1’s suggestions, with a new Introduction, and an expanded Conclusion section.

Reviewer 2 Report

Dear author(s)

After a careful review of the manuscript I have decided to accept a paper. Because it sufficiently advances knowledge and/or provides fair scientific contribution.

The comments are for the paper idea and all contents as follows :-

1-There is an unclear motivation and contribution of the paper, and that particularly as regards the distribution of IRRs, and new rends analytical consistencies. 

2-The paper needs to more focusing, in relation the distribution of IRR and investors advantages to which it represents a novel contribution to knowledge or addresses a research question that is substantially and compellingly motivated.

3-I think a weakness of the paper is that it does not set out a clear agenda for future the risk management research .

4- The author should present the findings more clearly and sequentially for readers.

Thank you and wish you well with the manuscript.

Author Response

Comments 1 and 2. Have added a new introduction, and have expanded the conclusion section, which substantively cover these points. The new material makes it clearer that this paper is part of the continuing process of improving understanding of the links between the partitioning theorem, and the IRR structure of a transaction: and that this understanding is potentially important not just for the direct application to rational decision making, but also in helping to design transactions which avoid pathological IRRs.

Comment 3. Addressed in additional material in final section.

Comment 4. Addressed by improved signalling of the structure of the paper in Section 1.