Quick Introduction into the General Framework of Portfolio Theory

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

I recommend the manuscript for publication with minor revisions to address the specific comments. The authors' efforts to balance technical depth with accessibility make this a highly informative and practical survey.

The manuscript provides a concise overview of the GFPT, integrating Markowitz portfolio theory, growth optimal portfolio theory, and the theory of risk measures. The authors emphasize the use of convex analysis and duality to reflect the concavity of reward functions and the convexity of risk measures, also extending the theory to address vector risk analysis. The paper aims to make the complex ideas accessible without delving into excessive technical details, directing readers to a comprehensive monograph for deeper exploration.

The paper is clear and concise. The use of illustrative examples and the connection to practical applications, such as bank balance sheet management, enhance the readability and relevance of the paper.

The paper is well-structured, with a logical flow from the historical underpinnings of portfolio theory to detailed discussions on the efficient frontier and efficient portfolios. The inclusion of appendices for additional reviews on semi-continuity and financial markets is beneficial for readers seeking further clarity.

It effectively highlights key proof concepts and directs readers to the detailed book. This approach balances accessibility with rigor, making it suitable for both practitioners and academics.

 

Comments:

The historical section is comprehensive but might benefit from a brief discussion on the evolution of risk measures beyond the 1990s, incorporating recent advancements and their integration into the GFPT.

also for the double quotes, can try `` " instead of ,, ''

Author Response

Comments 1: The historical section is comprehensive but might benefit from a brief discussion on the evolution of risk measures beyond the 1990s, incorporating recent advancements and their integration into the GFPT.

Response 1: We thank you for your careful review of the paper and constructive suggestions. We rewrote the introduction to Section 2.3 emphasizing research on risk measures since the 1990s. The new introduction and the corresponding new references are highlighted in blue.

Comments 2: also for the double quotes, can try “…” instead of ,,…''  

Response 2: Agree. We have now adjusted the quotation marks everywhere in the manuscript.

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript submitted for peer review presents an overview of the General Framework for Portfolio Theory (GFPT), consolidating the Markowitz portfolio theory, the optimal growth portfolio theory, and the theory of risk measures. It is quite an interesting methodological study in which the authors present a framework for using convex and dual analysis, reflecting the concavity of the reward function and the convexity of risk measures due to diversification effects. The authors indicate that the main goal of the presented scientific investigations was to provide readers with a concise introduction to the key concepts and practical applications of GFPT without delving into excessive technical details. This goal was achieved, although it can be pointed out that the prepared literature review is very modest. Instead of preparing a section with a solid discussion of the proposed solutions in comparison with the publications of the last 5 years, the authors refer interested readers to the extensive monograph by Maier-Paape et al. (2023) for detailed evidence and further research. The manuscript also lacks an indication of the research gap and a presentation of their proposed solutions. The authors argue in the conclusions that they have presented a concise introduction to the general framework of portfolio theory that not only consolidates previous efforts in portfolio optimization but also extends its application to include vector risks that are common in many financial scenarios. For example, the article could be enriched by a case study of the issues studied. However, the authors argue that their goal is to provide readers with a quick guide to the most important results of the general framework of portfolio theory and to demonstrate their practical applications. From an editorial perspective, the article has been prepared correctly and raises no serious objections. I propose to consider enriching the literature on the subject with new works from the last five years, and also to present research questions and problems in the introduction, taking into account the research gap and the authors' contribution to filling it.

Author Response

Comments: I propose to consider enriching the literature on the subject with new works from the last five years, and also to present research questions and problems in the introduction, taking into account the research gap and the authors' contribution to filling it.

Response: We thank you for your careful review and we appreciate your suggestions. We added the third paragraph in the introduction, revised the introduction of section 2.3 and added the last paragraph in the conclusion (each marked in blue). In these new paragraphs, we address the research gap (intro) and research questions (conclusion). New references are also added (also marked in blue).

Reviewer 3 Report

Comments and Suggestions for Authors

The paper Quick Introduction to the General Framework of Portfolio Theory provides a short and concise tour of the main aspects of GFPT. It provides an interesting overview of the historical development of PT, followed by the inclusion of different types and quantities of risks (scalar and vector ones) in the development of PT. I find this highly interesting and potentially plausible by the readership of the journal.

However, there is a risk involved in publishing this manuscript in its present form. Not that the paper is not in a camera-ready format, but the paper is not a self-standing. It calls the same reference (Maier-Paape et al., 2023) 65 times throughout the text. 

Since changing this would be impossible, and would utterly change the aim of the paper (which is actually giving a concise introduction to the GFPT explained in the book references so many times),. I advise changing the type of this manuscript to - REVIEW.

Author Response

Comments: I advise changing the type of this manuscript to - REVIEW.

Response: We thank you for your careful review of the paper and we agree with your suggestion. This is a review paper. We feel it serves a useful role in this special issue on portfolio theory.