Round 1

Reviewer 1 Report

The paper analyzes interbank systemic risk via community detection and characterizes sub-communities. I think that the topic is interesting, and the bipartite approach, although not a novelty, is an important tool to address such systems. However, there is a point that I think might imply a significant bias in the analysis, for this reason, I suggest a major revision of the analysis.

The resulting projected network (the correlation is indeed a type of projection) is a full network. Modularity has known to suffer from a resolution limit when the number of links increases, and the resolution parameter just moves the resolution limit to another scale, but it does not solve it. Although on weighted networks the resolution limit is less preponderant, in ref[1] was shown that also weighted projected networks suffer from the same bias.  I suggest the author at least check the robustness of their result by retaining only the subset of links with statistically significant correlations as suggested in ref[1], such an approach is much robust with respect to the resolution limit. If qualitatively the results hold, I think might a clear indication that the resolution limit does not play a role in their cluster selection.

[¹]https://journals.aps.org/pre/abstract/10.1103/PhysRevE.96.022321

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper investigates systemic risk referring to the United States financial crisis of 2008 and focusing on the community structure analysis of a bank-asset bipartite network.

Whereas in fact systemic risk has been (especially after the 2008 crisis) the object of several studies involving complex network theory, the novelty of the present investigation is not clear enough. The authors write at line 86-88 “As far as we know, there is no study that use of bank portfolio to establish the correlation network and discuss the systemic risk, which reflects an important innovation of this paper.” This is, to say the least, a surprising statement. Even a simple search on internet suffices to show that this lack of knowledge can quickly (and has to) be amended.The authors should look around and become aware of the fact that, contrary to what they claim, much has been done in this context, and a great deal of papers have been published which keep into account overlapping portfolios. Then, in the paper under review it would be necessary to make some comparison with the literature and better highlight what the new contribution (if sufficiently significant) of the paper is.

New findings should be clearly stated, in case after splitting issues and findings into subsections. And in several points a clearer explanation should be provided. To give just a couple of examples:

- in the lines 145-150 the description of the elements e_{ij} and a_{ij} deserves a clearer description.

- the meaning of the statement “… systemic risk will appear obvious volatility” appearing in the abstract, in the introduction and in the conclusion is not clear.

- in which sense does Figure 5 display “that the number of nodes with high importance in the network is often very small, and the distribution of node importance between different communities is obviously different.”? An explanation of the scatter diagrams is in order.

It has also to be noticed that throughout the paper one continuously finds language, grammar and style inaccuracies. The paper needs the correction of several grammar errorsand possibly extensive rephrasing.

A few further observations follow:

A question: On page 9 the new PageRank values of certain nodes in the sub-network is recalculated. The authors write “The new PR values ranking of these nodes in the sub-network are compared with their PR values ranking in the original network. All the comparing results are shown in Figure 6. It can be seen that for a group of nodes in the same community, their new PR values’ rank in the sub-network is highly consistent with the rank of the PR values of this group of nodes in the original network. Therefore, it can be preliminary asserted that the order trend of the two groups of PR values has a high similarity.” Can the authors explain why they emphasize this fact?

Incidentally, the distance d_{ij} in equation (2) was presented in a paper by Mantegna of 1999, which the authors certainly know (being it quoted in the bibliography). The reference should then be given when introducing d_{ij}.

Some figures would need to be adjusted. The left panel in Fig. 2 should be increased, because right now it is not readable. Similarly, in the Fig. 3 and 4 the colors cannot be distinguished, nor can one read labels.

Sometimes the initial letter of the name of quoted authors is not in capital letters as it should (see for example: diamond, chinazzi, quianting, …).

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

A REVIEW OF

"Community Structure and Systemic Risk of Bank Correlation

Networks —Based on the U. S. Financial Crisis in 2008"

1. REVIEW SUMMARY

The study examines the relationship of the community structure of the U.S. commercial bank correlation network and the systemic risk of geographically-based community sub-networks. The authors contribute methodologically interesting aspects to the determination of systemic risk in financial networks of commercial banks: first, the application of bi-partite bank-asset type network to the determination of bank correlations; second, a geographically-based breakdown of the network of commercial banks. The paper is promising. However, in the present form, there are several severe flaws in the study. Therefore, in this reviewer's opinion, the authors should undertake significant revisions before the paper can be reconsidered for acceptance to Algorithms.

2. STUDY SUMMARY

2.1 Goal

The presumed goal of the study is "to find a method to simplify the financial network model which can divide the network into many sub-networks with different structures, and study the differences of risks between different sub-networks” (lines 94 – 97).

2.2. Research questions

The authors do not appear to propose formal hypothetical and testable claims. However, their main finding can be stated a priori as a deductive hypothesis based on literature: "the systemic risk of relatively small-scale community will appear obvious volatility and is quite likely to be extremely high, while the systemic risk of larger-scale community is relatively stable" (lines 126 – 128).

The ambiguity regarding explicit research questions is a flaw in the paper.

2.3. Theory and methods

In step one of their methodology, the authors use a bank-asset bilateral network to set a bank correlation network. In step two, the authors derive a complete correlation-based bank network. In step three, the authors implement a Louvain algorithm to detect network communities. In step four, the authors apply a Page rank to an algorithm to determine the importance of network nodes. In step five, which is not discussed in the paper, the authors presumably apply systemic risk measurement at the community and sub-community level to conclude the relationship of systemic risk and the community structure.

3. BROAD ISSUES NOTED

3.1. Introduction needs to be re-written. It is grammatically poor, which can be improved with good editing. However, the more serious flaw is the logical and argumentative ambiguity. The authors do not clearly state their goals, claims, and research questions.

3.2. The authors lack the description for the last analytical steps of their methodology. Accordingly, several issues remain unaddressed (see specific comments)

3.3. The authors lack a discussion of the data choices made given their research goals. For example, they focus on commercial banks while seemingly ignoring bank holding companies. It is not clear whether the dataset includes off-balance sheet items. It is unclear why the authors chose not to include the pre-crisis data and particularly data from 2007. Literature shows that in 2008, many banks have already re-balanced their risky portfolios substantially. Thus, it would be more appropriate to consider the bilateral network from 2007 rather than 2008. It is also not clear why a static bilateral network was chosen and not a dynamic one.

3.4. The choice of geographic state-based community is suspect, given that most U.S. larger banks operate across state lines.

3.5 The authors' choice of the initial bank-asset bilateral network is flawed conceptually. First, since bank distress and default are connected with liquidity constraints, bank liabilities must be included as a critical channel for accumulating systemic risk. The authors have only the story of one side of the balance sheet while appearing to ignore both liabilities and off-balance sheet items.

3.6. The authors do not explain why only six types of assets are included. Similarly, they do not examine critically whether this typology is sufficiently granular to investigate the bank heterogeneity.

 

4. ADDITIONAL SPECIFIC COMMENTS

4.1. The authors do not provide a measurable definition of systemic risk.

4.2. Introductory paragraph contains three potential “claims” left unsupported and unaddressed in the paper. Claim 1: “With the increasingly close links among financial institutions, the financial system has gradually formed a complex financial network with financial institutions as nodes.” Claim 2: “The increase of financial network connectivity will help to reduce individual risks through diversification on the one hand; on the other hand, it is also very likely to make the financial system face the threat of systemic risk events.” Claim 3: “With the continuous active opening of the financial market, the relationships among financial institutions becomes more complex, which will also aggravate the systemic risk faced by the financial system.”

4. Claim 3 above implies the network is being opened. This is the wrong choice of words, certainly for the United States. Perhaps, the authors are looking for the idea that markets are becoming interconnected through a continual globalization process. If so, this needs to be clarified and addressed in the study design. The international component is missing from the study, which would make this challenging to sustain other than a speculative point.

4.4 Lines 42 – 43 appear highly speculative and unsupported: “and even leads to a sharp, short, super cyclical retrogression of the economy.”

Author Response

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Author Response File: Author Response.pdf

Reviewer 4 Report

The authors proposed an algorithm based on the division of community structure to study bank systemic risk under a network perspective.

Major comments

1) It is not clear the reason why the authors do not exploit the granulary of bank balance sheet data. They consider only six types of assets, even if in theory they have more detailed information. The authors should discuss if, by exploring the granularity of the data, the results remain the same or if the study depends on the selection of the six variables. The heterogeneity in loans, securities and other assets may be high. For this reason, it would be useful to distinguish between different risk factors (e.g. sectors), in order to try to better catch possible asset commonalities.

2) The analysis performed in this study is not a real interconnectedness study since the data do not allow one to find possible asset commonalities. The inputs of the algorithm are the weigths of the different types of assets in the bank portfolio. These weigths give an idea of the business model of the banks, but in my view are not enough to measure bank interconnectedness. If I am correct, the authors should clarify this aspect.

3) It would be interesting to study more recent data (Q4 2020), to assess if and how the systemic risk changed over time.

Minor comments

1) There are typos in the paper, some related to the citation of the references in the main text of the paper some in the text (e.g. page 3, we analysis of the differences).

2) Equation 4 - "W" should be in capital letter.

3) I suggest to find a shorter title for the work.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

I agree with the authors that the SVN approach cannot be directly applied being the bipartite weighted; however, a correlation metric will have a null expectation and a null hypothesis might be tested. Nevertheless, I agree that being the SVN approach tested on a different setup, its superior stability must be proved, which cannot be addressed in this work. 
I appreciate the stress test they did removing low-weight links, which of course shows a low overlap (accuracy) but has extremely high precision with respect to the initial partition. Having that the filtered partition that is a nested subset of the full information partition, I think is a strong indication that the initial clustering was not due only to a random fluctuation of the sample modularity landscape, which is one of the biggest bias that affects modularity maximization on large link density networks.

For this reason, I think the paper improved considerably and I think can be accepted in the current form. 

Reviewer 2 Report

The authors answered the questions contained in the first report and some improvements have now been introduced in the paper.

 

I would simply suggest a couple of minor changes in the wording of two statements which do not yet sound completely clear.

 

• In the line 285, in “the most important several nodes always tend to be clustered …” I think the word “several” could be suppressed (in any case, this sentence should be a little bit rephrased);
• In the line 289, in “the distribution of node importance between different communities …”, I think that “between” should be better substituted by “in”: the distribution of node importance in different communities …
• In line 300, in “Based on that a node’s importance reflects the important position of the node …”, one could better write: Since the node’s importance reflects the important position … (or: based on the fact that a node’s importance …).

Reviewer 4 Report

Tha authors seem to address the comments I raised in my previous review. I suggest to use the new title as proposed by the authors "Community Structure and Systemic Risk of Bank Correlation Networks".