Application of Benford’s Law on Cryptocurrencies
Bin Liu
Round 1
Reviewer 1 Report
This article presents a very interesting topic and discussion.
The application of Benford's law on the crypto-assets domain is compelling and deserves attention.
However, the article should be better structured. The presentation is sometimes confusing. As a result, the reader cannot easily follow the sequence of the presentation or understand the results consistently.
Many typing mistakes can be found, starting from the abstract (i.e. line 11 (T)he applicability or line 11 spo(r)t sufficiently large number).
The difference between digital currencies (i.e. eNaira) and cryptocurrencies is not well identified and the fact that not all digital currencies or cryptos are based on blockchain technology is not specified.
Identification of crypto-assets classification should be also better presented.
METHODOLOGY
I suggest creating more than one paragraph (so far only 4.1. data, made of only four lines)
i.e. methods (4.1), materials (4.2). Data (4.1) [please merge this paragraph with materials if possible].
RESULTS
Equation (1) should be better explained and detailed (line 80).
I suggest preparing a detailed analysis of each crypto should be consistently presented first (bar-charts are presented only for some of the cryptos).
The discussion should then compare the results
(Data availability can be merged in the methodology).
Identification of limitations is missing
Author Response
Dear reviewer!
we divided your observations and answered all of them in the form of a paragraph starting with the word "ANSWER".
This article presents a very interesting topic and discussion.
The application of Benford's law on the crypto-assets domain is compelling and deserves attention. However, the article should be better structured. The presentation is sometimes confusing. As a result, the reader cannot easily follow the sequence of the presentation or understand the results consistently.
ANSWER: The article has been restructured, the second part of the introduction moved to the start of the Methodology, added requested further explanations to the introduction, and added a quick structure of the article at the end of the introduction.
Many typing mistakes can be found, starting from the abstract (i.e. line 11 (T)he applicability or line 11 spo(r)t sufficiently large number).
ANSWER: The paper has been proofread and typos were corrected.
The difference between digital currencies (i.e. eNaira) and cryptocurrencies is not well identified and the fact that not all digital currencies or cryptos are based on blockchain technology is not specified.
ANSWER: We addressed this by adding a paragraph in section 1 discussing the definition of a cryptucurrency, the underlying data structures used to facilitate transactions, and finally the difference between digital currencies and cryptocurrencies.
Identification of crypto-assets classification should be also better presented.
ANSWER: A paragraph was added in section 1 to strengthen the definition of a cryptocurrency as a transparent, permissioned decentralized ledger of transactions.
METHODOLOGY
I suggest creating more than one paragraph (so far only 4.1. data, made of only four lines) i.e. methods (4.1), materials (4.2). Data (4.1) [please merge this paragraph with materials if possible].
ANSWER: Done as requested, new sections 4.1 and 4.1, data availability merged into 4.2 with a footnote.
RESULTS
Equation (1) should be better explained and detailed (line 80).
ANSWER: This text has been added to better explain the distribution: The quantity $P(d)$ is proportional to the space between $d$ and $d + 1$ on a logarithmic scale. Therefore, this is the distribution expected if the logarithms of the numbers (but not the numbers themselves) are uniformly and randomly distributed.
I suggest preparing a detailed analysis of each crypto should be consistently presented first (bar-charts are presented only for some of the cryptos). The discussion should then compare the results
ANSWER: All non-conformant cryptocurrencies were thoroughly observed and a list of publicly announced anomalies and even frauds was compiled for each of these cryptocurrencies. The two best performing and two cryptocurrencies with the biggest market cap were also observed into details. The results are presented in the remainder of the section. All the other cryptocurrencies can be further analyzed using the available accompanying data~\footnote{Zenodo: \url{https://zenodo.org/record/4682976}, DOI: 10.5281/zenodo.4682976} in the raw aggregated data form, a list of Benford law conformity values and charts.
(Data availability can be merged in the methodology).
ANSWER: the data availability has been merged as instructed, a footnote has been added and the title of the section was changed into Materials as suggested before
Identification of limitations is missing
We acknowledge and note the limitations of the techniques in section 6.
Reviewer 2 Report
This study investigates the applicability of Benford's law to detect possible anomalies and frauds in the cryptocurrency market. The topic is interesting, and more importantly, I think the results have strong practical implications to the regulators and investors. I hope the following comments can help the authors to further improve the paper:
Major comments:
- The results show that some cryptocurrencies conform Benford's Law but others don't. The findings are interesting, but the practical implications are not discussed in details in the manuscript. Contribution of this study can be improved if the authors discuss the practical implications of the key findings in details in Section 1 and 5. More specifically, there are discussions around the problems in the cryptocurrency market in the last paragraph of Page 4. Would Benford's Law help the regulator and investors to solve these problems?
- The authors should consider to provide some basic summary statistics results as well as sample period for each of the cryptocurrencies in the final sample.
Minor comments:
1. Proofreading is needed as there are minor typos in the manuscript, e.g. line 11 of Page 1 "he"; line 44 of Page 2 "then" or "than".
Author Response
Dear reviewer!
We addressed each of your observations and resend the changes as answers in paragraphs starting with the word "ANSWER".
This study investigates the applicability of Benford's law to detect possible anomalies and frauds in the cryptocurrency market. The topic is interesting, and more importantly, I think the results have strong practical implications to the regulators and investors. I hope the following comments can help the authors to further improve the paper:
Major comments:
The results show that some cryptocurrencies conform Benford's Law but others don't. The findings are interesting, but the practical implications are not discussed in detail in the manuscript. The contribution of this study can be improved if the authors discuss the practical implications of the key findings in detail in Section 1 and 5. More specifically, there are discussions around the problems in the cryptocurrency market in the last paragraph of Page 4. Would Benford's Law help the regulator and investors to solve these problems?
ANSWER: Section 1 now includes a paragraph discussing the importance of anomaly detection in public ledgers. We highlight the application of the proposed method as a technology-agnostic technique for preliminary screening of any public ledger. In cases where the high discrepancy is detected, more fine-grained approaches can be applied to identify the cause.
The authors should consider providing some basic summary statistics results as well as a sample period for each of the cryptocurrencies in the final sample.
ANSWER: Starting date and end date of the observation period have been added to the main table. The end date is the same for all cryptocurrencies as this was the decided end date for the whole experiment based on the prerequisites set in section
Minor comments:
1. Proofreading is needed as there are minor typos in the manuscript, e.g. line 11 of Page 1 "he"; line 44 of Page 2 "then" or "than".
ANSWER: The paper has been proofread and typos were corrected.
Round 2
Reviewer 1 Report
The authors addressed all my previous concerns.
Congratulations on this new version.
Author Response
Thank you for your comments
