Black–Litterman Portfolio Optimization with Dynamic CAPM via ABC-MCMC

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Clarity between the researc problems and methdolocy adopted is lacking may be improved .

The testing is done in US market but it can be benfited if done in BRICS country as the market is shifting towards the BRICS rather focus on US .Cross market testing can be done.

Explaination could be more how bayesian model improved over traditioonal model.

Research focus on Bayersain and non parametric anothre robust checl can be done sensitivity or simulation as appropriate fit by author .

 

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The paper proposes a methodology for portfolio optimization by integrating the Black-Litterman model with expected returns generated through simulations under a dynamic Capital Asset Pricing Model (CAPM) with conditional betas, estimated via Approximate Bayesian Computation Markov Chain Monte Carlo (ABC-MCMC). The novelty of the paper is its contribution to the development of financial theory and the applicability of the proposed advanced portfolio optimization techniques in highly liquid and globally integrated markets such as the United States. 

In general, the paper is well-written with clearly presented originality, detailed methodology, and discussed findings. The topic fits well with the scope of the special issue, with a particular contribution to advances in financial markets. Here are minor comments that authors may consider to further improve the paper from a discipline-specific to a more interdisciplinary perspective.

1. The Abstract is a stand-alone section of the paper. Define all acronyms.
2. In the Introduction, add specific objectives. This part serves as the outline of the Results.
3. Define the assets in Tables 1 and 2, otherwise, change them to simpler codes/numbers, or justify why abbreviations were used.
4. Improve the quality of all figures and make sure that all fonts are readable without zooming in.
5. Explain first the curves in Figure 2 before doing the interpretation, analysis, and implications.
6. In the Discussion, highlight the novelty of the findings/proposed model relative to existing studies.
7. Provide a broader implication/application of the study beyond the case of the US stock market. For instance, the applicability of the proposed model in the case of markets in European and/or developing countries.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The paper makes an important and original contribution by integrating ABC-MCMC estimation into the Black–Litterman portfolio framework, demonstrating both methodological innovation and empirical relevance. The manuscript is well-structured and offers valuable insights, particularly in showing how dynamic CAPM with conditional betas can improve portfolio performance during crisis periods. The work is suitable for publication, but several minor revisions are necessary to improve clarity, consistency, and contextualization before final acceptance.

 

Minor Revisions Requested: The authors should first ensure that all notation is consistently introduced and aligned between text and equations, particularly in Section 2.3 where symbols such as z_t, \beta_{low}, \beta_{med}, and \beta_{high} require clearer definitions. A short discussion of the model’s limitations, especially regarding computational intensity and the scalability of the method to larger asset universes, would strengthen the practical impact. The discussion section would also benefit from a more explicit comparison with other Bayesian approaches to portfolio optimization, such as those using stochastic volatility priors or particle filtering, to better situate the contribution in the literature. In terms of presentation, figures should be accompanied by more detailed captions so that they are interpretable on their own, and Table 2 would gain from additional commentary explaining the economic rationale behind the concentrated allocations observed in May 2020. Finally, a light proofreading is advised to correct minor grammatical issues and to shorten long sentences in the Introduction.

 

Conclusion: In summary, this is a rigorous and timely contribution to the field of portfolio optimization. With the suggested minor revisions, the manuscript will be clearer and better contextualized, and I recommend its acceptance pending these adjustments.

Comments on the Quality of English Language

Th English is Good.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf