Target Matrix Estimators in Risk-Based Portfolios
Round 1
Reviewer 1 Report
1. There are many papers dealing with this issue therefore the novelty of this paper needs to be highlighted.
2. The literature review should be extended.
3. The methodolgy needs more solid background.
4. The results should be discussed and compared with other studies.
5. Conclusions should be improved. Policy implications should be added.
Author Response
Point 1: There are many papers dealing with this issue therefore the novelty of this paper needs to be highlighted.
Response 1: Thank you very much for the remarks. I have tried to address this issue inserting more clues in the introduction (see rows 82-90 of the revised version of the manuscript), stressing the novelty of the paper.
Point 2:The literature review should be extended.
Response 2:The Introduction and Section 3 have been revised to address this accordingly. For example, Table 1 lists all the works featuring a proper description of the target matrix in shrinkage for financial applications.
Point 3:The methodology needs more solid background.
Response 3:An extensive review of all the methodologies implemented was already given in the paper. Section 2 introduces the main aspects of risk-based portfolios while Section 3 lists the core aspects of Target Matrices. In order: their mathematical foundations; their past used in the related literature review; a numerical illustration to explain how misspecification in the target matrix affects risk-based portfolio weights. According to the referee indications, we have revised these two Section, also improving the numerical illustration with more realistic assumptions (e.g. positive correlations among the 3 assets considered).
Point 4:The results should be discussed and compared with other studies.
Response 4:In my opinion the comparison with other studies is potentially off-topic as now the focus is on a comprehensive comparison among target matrix models for shrinkage only. In addition, to the best of my knowledge, as I remark in the paper (rows 82-90 of the revised version of the manuscript) there is only one work that addresses the misspecification issue w.r.t. risk-based portfolios, hence I believe more works are needed to do a proper comparison.
Point 5:Conclusions should be improved. Policy implications should be added.
Response 5:Conclusions have been revised and improved accordingly.
Reviewer 2 Report
Dear Authors,
The text is well written. The introduction is easy to follow.
In line 105, you say that the log-returns are used. However, as log-returns are not additive across assets, my question is whether this matters here and why not simple returns are used.
The meaning of EWMA should be mentioned earlier (like line 211), and not in line 252.
Are the numbers in lines 275 to 277 really realistic? The correlation between S&P 500 total return and US Corporate Index total return has been mainly positve in the last years. The correlation between US Corporate Index total return and US Treasury Index total return has historically been positive. Historically, the yield component has dominated the spread component.
The footnote below line 404 tipo "analisys"
The table on page 16 is far too small. Instead of presenting so many numbers maybe there is a possibility to condense the information?
The usage of small and capital letters is very confusing. Sometimes the names are written with capital letters, sometimes not. Like line 616 vs 627 or line 611 vs 634. This should be used consistently throughout the paper.
The paper is very close to Ardia et al. (2017) given the structure, the methodoly, and the findings. The merit of this paper should be stressed more clearly.
It seems that Ardia et al. (2017) used R to do the computation. However, in the paper MATLAB is used. Why and are there any implications?
Thank you very much.
Author Response
Point 1: The text is well written. The introduction is easy to follow.
Response 1: Thank you very much.
Point 2: In line 105, you say that the log-returns are used. However, as log-returns are not additive across assets, my question is whether this matters here and why not simple returns are used.
Response 2: In this work the addictiveness of returns is not an issue, as for example in Ardia et al. (2017) where they need to use simple returns to add them in order to accommodate different out-of-sample horizons using the same frequency. Mine analysis is limited to monthly data/horizon, hence I feel log-returns are consistent with my framework.
Point 3: The meaning of EWMA should be mentioned earlier (like line 211), and not in line 252.
Response 3:Checked and corrected accordingly, thanks.
Point 4: Are the numbers in lines 275 to 277 really realistic? The correlation between S&P 500 total return and US Corporate Index total return has been mainly positve in the last years. The correlation between US Corporate Index total return and US Treasury Index total return has historically been positive. Historically, the yield component has dominated the spread component.
Response 4: I am glad to receive this comment. I have totally revised the numerical illustration, now it features correlation parameters accordingly revised to your suggestion. A remark on this is given in footnote 5, after line 282.
Point 5: The footnote below line 404 tipo "analisys"
Response 5:Checked and corrected accordingly, thanks.
Point 6: The table on page 16 is far too small. Instead of presenting so many numbers maybe there is a possibility to condense the information?
Response 6: to this extent, I have create an ad hoc figure (Figure 4, line 581) to show more clearly the optimal shrinkage intensity parameters. Hence, the Table 4 is more readable since its size is equal to Table 3.
Point 7: The usage of small and capital letters is very confusing. Sometimes the names are written with capital letters, sometimes not. Like line 616 vs 627 or line 611 vs 634. This should be used consistently throughout the paper.
Response 7: The paper underwent a full revision on this. I have carefully checked and modified this across the body of the paper. Now the only abbreviation used is the “EWMA” one. However, abbreviations regarding risk-based portfolios and target matrices remain in Figures and Tables, along with a specific remarks to guide the reader trought the paper and ease the understanding.
Point 8: The paper is very close to Ardia et al. (2017) given the structure, the methodoly, and the findings. The merit of this paper should be stressed more clearly.
Response 8: You are right. I have tried to put more emphasis to this fact through the paper. For example, I have tried to address this issue inserting more clues in the introduction (see rows 82-90 of the revised version of the manuscript), stressing the novelty of the paper. Moreover, I have also inserted some more comments in Section 3.3, as described earlier.
Point 9: It seems that Ardia et al. (2017) used R to do the computation. However, in the paper MATLAB is used. Why and are there any implications?
Response 9: I am glad to receive this comment. I have developed myself the code in MATLAB since I am planning to relise a similar version of the Ardia et al. (2017) R code in MATLAB. I have checked and there are not discrepancies in the calculations of the risk-based portfolio weights with the two codes. In addition, I made my code accessible on my GitHub page. Link is available in the footnote 7, after line 440.
Point 10: Thank you very much.
Response 10: I thank you for your helpful comments and effort into improving my work.
Reviewer 3 Report
This study claims that applying the variance shrinkage method helps portfolio managers reduce weights misspecification. To support their findings, this paper examines robustness and appropriate evidence. Thus, this paper arouse portfolio managers/risk managers interest in a well organized manner.
<Minor Suggestion>
There are some runs on sentences and grammatical errors (especially, tense). The author needs to have a native speaker proofread this manuscript again.
Author Response
Point 1: <Minor Suggestion>
There are some runs on sentences and grammatical errors (especially, tense). The author needs to have a native speaker proofread this manuscript again.
Response 1: As a general premise, I would thank the referee for having spent time in reading the manuscript and giving precious suggestions. The manuscript was carefully checked by a native English speaking and now it seems sounding well. Tenses have been revised, especially across all the body of the paper. Please check the revised version.
