Monte Carlo-Based VaR Estimation and Backtesting Under Basel III

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Please see the attached document.

Comments for author File: Comments.pdf

Author Response

Thank you very much for your valuable comments and suggestions. We have carefully addressed each point and revised the manuscript accordingly. Please see the attached response document for detailed replies.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The paper compares two methods for Value-at-Risk modelling of a portfolio. First of all, the paper is very well written and it is clear what the author is doing. The figure choices are also excellent and it portrays the authors findings clearly. I have a few comments to help improve the paper though:

1. p-hacking: The author uses p-values as a selection criteria in the OLS setup. The problem with this approach is that t-tests were not designed to be used as variable selection and leads to bias. Hastie et al. (Elements of statistical learning) and references therein show this extensively. A better approach would be to use variable selection procedures (such as LASSO) or more elaborate sensitivity analyses (such as bootstrap inclusion frequencies) to determine which factors to include in the regression.
2. Normality of errors in OLS: The author doesn't show whether the residuals are normally distributed. The t-tests used in OLS rely on the normality of residuals.
3. Multivariate normal factor returns: This assumption has huge ramifications for the results that the author seems to be unaware of. For instance, the author says that the factor based approach leads to "a more centred distribution", but this may simply be a consequence of assuming a normal distribution, rather than "diversified portfolio behaviour".
4. Relation to risk literature: I am not opposed to the overall message of the paper, namely using factor-based methods, but the author needs to relate it to the overall risk literature. Specifically, how is the approach related to copulas (for example)? Through \Sigma, the author introduces factor cross dependencies, which can be translated into a very specific coupling of risks.
5. Exceedence only backtesting: exceedence count is only 1 way to test VaR. It doesn't inform us about clustering of violations which can indicate market volatility or model misspecification that simple counting of exceedence misses. Please see Christoffersen's work for other ways to test VaR.

Author Response

Thank you very much for your valuable comments and suggestions. We have carefully addressed each point and revised the manuscript accordingly. Please see the attached response document for detailed replies.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

General Overview:

The manuscript titled "Monte Carlo-Based VaR Estimation and Backtesting Under Basel III" addresses a relevant and technically significant problem in financial risk management. It compares two Monte Carlo-based Value-at-Risk (VaR) modeling techniques using real market data: a historical return-based method and a CAPM-style factor-based model. The research has clear regulatory and practical applications under Basel III, especially regarding model backtesting. The methodology is robust, the data is publicly sourced and reproducible, and the overall contribution is timely and appropriate for academic and industry benchmarking. However, there are several structural, clarity, and content issues that warrant a major revision before acceptance.

Comments and Suggestions for Authors:

• [Page 1, Abstract, Lines 6–21]: While informative, the abstract could be made clearer by avoiding jargon like "interpretable exposures" and stating the main conclusion more explicitly. Also, mention the regulatory zone outcomes (red/yellow) briefly to highlight real-world relevance.
• [Page 2, Lines 25–41]: The introduction lacks a direct statement of the hypothesis. The author could consider inserting a line after Line 36, such as: "This study hypothesizes that the factor-based VaR model offers more accurate exception predictions under Basel III than the return-based model."
• [Page 3, Lines 87–121]: The regression diagnostics in Table 1 are sound, but the discussion does not explain why SPY and IWF, despite low p-values, are omitted. The author could clarify the rationale (e.g., high VIF) more directly in the text.
• [Page 4, Lines 165–174]: The limitations are listed but not contextualized. The author could strengthen this section with more precise examples, e.g., "Tail risk underestimation due to the assumption of multivariate normality may result in undercapitalization during crisis periods."
• [Page 6–7, Figures 2 & 3]: The figures illustrate exception points well, but the text fails to interpret why breaches cluster. The author should add a sentence after Line 258, such as: "These clusters coincide with macroeconomic announcements or volatility surges, indicating structural sensitivity."
• [Page 8, Lines 263–293]: The rolling backtesting analysis lacks clear comparative commentary. The author could consider adding a paragraph synthesizing the differences between fixed and rolling estimates across both models.
• [Page 9, Lines 314–326]: The conclusion would benefit from a summary table or bullet points that clearly state each model's pros and cons.
• [References, Pages 10–11]: The author could include recent literature on VaR backtesting failures or alternative distributions (e.g., t-distributions, EVT) to expand context (e.g., McNeil et al., 2015).

Minor Concerns:

• [Page 2, Line 45]: Define financial tickers (e.g., XLK, MTUM) at first mention. These may be unfamiliar to readers from other fields.
• [Page 3, Table 1]: Add a footnote explaining what VIF values imply (e.g., "VIF > 10 indicates severe multicollinearity risk").
• [Page 5, Table 2]: Add confidence intervals for VaR estimates to reflect uncertainty from simulation.
• [Page 6, Figure 1]: Include sample sizes and axis labels with units (e.g., portfolio returns in %).
• [Page 7, Lines 247–259]: Improve visual captioning by explaining the significance of "red zone" classifications in the figure captions.
• [Throughout]: Replace vague terms such as "interesting," "significant," or "better" with specific metrics or numerical comparisons.
• [Page 10, Lines 327–330]: Mention possible model extensions using non-normal copulas or GARCH-based factor volatility to encourage future exploration.

 

Author Response

Thank you for your helpful feedback. We have revised the manuscript accordingly and provided detailed responses in the attached document.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

This work present compares two VaR simulation approaches using publicly available market data: a historical return-based Monte Carlo model and a risk factor-driven model based on CAPM-style regression. This work is not good for this current form, article should be improve and analysis should be add. This is my comment 

a. Kindly add some calculation value in abstract 

b. Introduction is very bad, please give more discussion previous studies about  Monte Carlo-based Value-at-Risk

c. Motivation and research gap of this paper is not clear

d. Kindly add the main contribution and novelty of this work  

e. kindly remove subsection "2.3.3. Conclusion"

f. Kindly define all variable for all equation 

g. i suggest author include economic rationale and potential sector biases when choosing retained factors 

h. i suggest author present how extreme values or anomalies in historical returns were treated.

i. please consider for author to evaluate model sensitivity to different rolling window lengths or portfolio weight changes.

j. Please add flowchart or algorithm in methodology section 

k. Kindly use Kupiec’s POF test or Christoffersen’s test to statistically validate exception rates.

l. Please consider add more quantitative contrast (e.g., average daily VaR, volatility regimes)

m. discussion is low, kindly improve it and discuss with existing literature

n. check typo and grammatical error

Author Response

Thank you for your feedback. We have revised the manuscript accordingly and provided detailed responses in the attached document.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

1. Line 358: 'The first column' should be replaced by 'The last column'.
2. Lines 434-435, 443-444 and 457-459 are repeating content. I suggest you mention the traffic light system once only.

Author Response

Thank you for pointing this out.

1. The phrase on Line 358 has been corrected as suggested.
2. To address the redundancy across Lines 434–435, 443–444, and 457–459, we have removed the repeated descriptions at Lines 443–444 and 457–459, retaining only the first occurrence for clarity.

We appreciate your careful reading and helpful suggestions.

Reviewer 2 Report

Comments and Suggestions for Authors

Thank you for addressing my comments.

Author Response

Thank you very much for your follow-up review and kind support. We sincerely appreciate your time and are glad that our revisions have addressed your comments.

Reviewer 3 Report

Comments and Suggestions for Authors

Dear Author,

Thank you for your thoughtful and thorough revisions to the manuscript “Monte Carlo-Based VaR Estimation and Backtesting Under Basel III.” I appreciate the care taken in responding to the initial review comments. The updated version reflects a clear improvement in clarity, methodological rigor, and relevance to both academic and applied audiences.

Below are my detailed observations on the revised version:

1. Abstract and Introduction

You have successfully revised the abstract by clarifying technical jargon and clearly stating the main findings, including the number of VaR exceptions and the regulatory zones. This enhances the accessibility and relevance of the study for readers unfamiliar with Basel III classifications.

The introduction now includes a clearer articulation of the scope and objectives, which helps orient the reader. While not hypothesis-driven in a strict sense, your revised framing around the Basel III backtesting outcomes appropriately aligns with the paper's empirical focus.

2. Factor Model Specification and Diagnostics

The improvements made to Section 2.3.1 are commendable. Specifically:

• The rationale for excluding SPY and IWF based on high VIF values is now clearly justified.
• The added commentary on XLK's inclusion despite marginal VIF elevation is a nuanced and defensible modeling choice.
• The inclusion of LASSO regression as a robustness check strengthens the factor selection methodology and demonstrates careful model vetting.

The explanation of factor significance, multicollinearity thresholds, and the added footnotes and references greatly enhance transparency.

3. Backtesting Framework and Basel Classification

Your expansion of Section 4—especially the comparison between historical and rolling backtesting—is a major strength of the revision. It provides empirical evidence on how dynamic recalibration improves model performance. The updated discussion highlights:

• The reduction in exceptions using a rolling window approach;
• The regulatory impact of this shift (e.g., factor-based model improving from red to yellow zone);
• The importance of model responsiveness in volatile market regimes.

These insights are highly relevant for both regulators and practitioners.

4. Figures, Captions, and Visual Interpretation

You have effectively improved the visual components of the manuscript:

• Captions now provide complete descriptions, including Basel III traffic light thresholds.
• Clarification of axes and units (e.g., Figure 1) aids interpretation.
• Figures 2–5 now offer stronger analytical value through enhanced labeling and interpretive commentary.

The clustering of exceptions and its link to macroeconomic volatility is a particularly useful interpretive addition.

5. Conclusion and Forward-Looking Considerations

The revised conclusion now includes a clear and well-reasoned comparison of the two VaR models. The discussion around trade-offs—simplicity vs. structural sensitivity—is well-articulated.

Your mention of possible extensions (e.g., GARCH modeling, copula-based methods) opens up valuable future research directions. This positions your work as both methodologically sound and forward-looking.

6. Minor Edits and Terminology

Thank you for addressing the minor comments, including:

• Definitions of tickers at first mention;
• Replacement of vague terms with specific quantitative descriptors;
• Addition of confidence intervals for simulated VaR estimates (Appendix B3);
• Clarification of red/yellow/green zone logic in both text and visuals.

These refinements contribute to a much more polished and professional manuscript.

Final Assessment

Overall, the manuscript is now clear, rigorous, and suitable for publication in Risks. The transparent use of publicly available data, well-executed Monte Carlo simulation, and alignment with Basel III regulatory standards make this study a valuable reference for academics, educators, and practitioners.

Congratulations on an excellent revision.

Author Response

Thank you very much for your thoughtful and encouraging feedback on the revised manuscript. I really appreciate your recognition of the improvements across various sections. 

Your comments on the Factor Model Specification and Diagnostics were especially helpful. This section improved significantly from your insights on variable selection and model transparency. Your suggestions to clarify multicollinearity thresholds, justify factor inclusion, and introduce robustness checks have substantially strengthened the model specification.

Thanks again for your support and for helping strengthen the manuscript.

Reviewer 4 Report

Comments and Suggestions for Authors

this form can be accept

Author Response

Thank you for your confirmation and support. I appreciate your time and positive feedback.