Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Journal of Risk and Financial Management - Review

Risk premium and fear of investors in crisis periods: An empirical approach based on Fama - French and Carhart factor models - Manuscript ID: jrfm-2917829.

COMMENTS FOR THE AUTHOR:
Reviewer:

This study analyzes (in a time-series framework) the interactions among five endogenous variables: MKT-RF (the market risk premium), SMB (Small minus Big firms' returns), HML (High minus Low Book-to Market firms' returns), WML (Winners minus Losers, the Momentum factor), and the changes in daily VIX ("investor fear"). The sample is divided into 5 subsamples according to two major financial crises: the Dot-COM and the Sub-Prime (pre-Dot-COM, during Dot-COM, pre-Sub-Prime, during Sub-Prime, and post-Sub-Prime). After comprehensive descriptive statistics of the variables, there are ADF (Augmented Dickey-Fuller) tests for the variables' stationarity. These tests confirm that the five variables are stationary. The analysis continues with Ganger-Causality tests, Vector-Auto-Regression (VAR), and finally an Impulse-Response analysis.

This research relies heavily on Durand, Lim, and Zumwalt (2011), but adds the dimension of crises as subsamples. Adding the dimension of crises changes the findings. The findings emphasize the development and evolution of the variables before, during, and after the crises. In this study, VIX does not affect the risk premium significantly, while in Durand et al. (2011) it does. The authors also find a general negative change in VIX throughout the subsamples.

Remarks: The authors claim in the abstract that the VIX ("fear") is systematically higher on Mondays, except for the period of the Sub-Prime crisis. However, according to Table 7, the VIX is not significantly higher during the Dot-COM crisis as well. Overall, I find the study well-developed and well-written. Besides this small remark, I recommend publishing.

References

 

Durand, R. B., Lim, D., & Zumwalt, J. K. (2011). Fear and the Fama‐French factors. Financial Management, 40(2), 409-426.

 

Author Response

Dear Reviewer,

We would like to thank you for your constructive comments and recommendations. All the suggestions were taken into account when preparing the new version of the manuscript; relevant modifications are now incorporated into the text. This has, in our opinion, improved the quality of the manuscript.

Below we provide a response-rebuttal to each of the issues raised, indicating how each of the recommendations was addressed and indicate the appropriate changes in the text of the revised paper.

Thank you for your consideration of our manuscript.

On behalf of the authors.

…………………………………………………………………………………..

 

The authors claim in the abstract that the VIX ("fear") is systematically higher on Mondays, except for the period of the Sub-Prime crisis. However, according to Table 7, the VIX is not significantly higher during the Dot-COM crisis as well. Overall, I find the study well-developed and well-written. Besides this small remark, I recommend publishing.

RESPONSE: Thank you for your comment. This is a typographical error which has been corrected in the text as follows: “investor fear is systematically higher on average on Mondays than on other days, except during the Sub-Prime crisis and the Dot-COM crisis as well”.

 

Reviewer 2 Report

Comments and Suggestions for Authors

Comments for author File: Comments.pdf

Author Response

Dear reviewer,

 

We would like to thank you for your constructive comments and recommendations. All these suggestions were taken into account when preparing the new version of the manuscript; relevant modifications are now incorporated into the text. This has, in our opinion, improved the quality of the manuscript.

 

Below we provide a response-rebuttal to each of the issues raised, indicating how each of the recommendations was addressed and indicate the appropriate changes in the text of the revised paper.

Thank you for your consideration of our manuscript.

On behalf of the authors.

 

 

…………………………………………………………………….

 

 

Major Comments:

• I am wondering why the authors chose the examination period to start on April 1991 (does it though?) and end on December First, it seems a bit arbitrary. There are available data for VIX since January 1990, while the examination period could be easily extended to include the COVID-19 recession. Second, it is confusing. Does the examination period begin on April 1991 (mentioned in the discussion) or April 1994 (Table 1)? Please extend the examination period or clarify how the start and end dates were chosen.

         RESPONSE: Thank you for your comment. Data was collected since April 1991, as indicated in the text and elsewhere in the text and in other places such as Table 3. The reference to April 1994 in Table 1 is a typographical error which has been corrected.

 

I would extend the period to include the COVID-19 recession in order to improve the quality of the study.

RESPONSE: Thank you for the very interesting suggestion. We included the possibility of verifying such a model in the proposals for future research.

 

 

• The NBER business cycles dates in Table 1 are According to NBER, the Great recession (sub-prime crisis) starts on December 2007, not July 2007. Beyond this inconsistency, does it make sense to use the NBER business cycles to define periods of “fear”?

RESPONSE: Thank you for your comment. The following paragraph has been added in the manuscript “In order not to have elements of opportunism and arbitrary in the methodology, it is important to have a definition from an outside third source to define recessions. This is the main utility of using the NBER. Regarding the choice of July 2007 (Q32007) instead of Dec 2007 (Q42007), this was done to strengthen the sample without harming the data, since the July recession economic indicators (unemployment rate) were essentially the same as those for Dec”

 

It is well known that financial markets are forward looking of the real economy; see, for example, Stock and Watson (2003).

RESPONSE: Thank you for your comment. It is included in the proposals for future research.

 

If I were you, I would use the sup MZ test of Ahmed et al. (2017) on the VIX index to detect the volatility structural breaks associated with the recession periods examined rather than set the “structural breaks” determined by the behavior of the real economy.

RESPONSE:  Thank you for your comment. The following paragraph has been added in the manuscript “Also, in future research a few technical issues could be considered, including the use of the sup MZ test of Ahmed, et al (2017). This test allows algorithmic detection of any changes in volatility, caters to unknown breakpoints, and also compares it to the  sup F. This test is useful in curing a key weakness of most regressions, the assumption that the correlation or regression coefficients remain constant in time, or that the structure of the model remains constant. It is a fact that the sup MZ test is a useful test. However, in the case of our research its usefulness is less than its average usefulness for two reasons: First, because it is appropriate to use break points from BERS, so that we are talking about commonly accepted recession periods; second and more importantly, in this paper we do not assume a uniform structure over the whole period, but we compute the coefficients at each period separately. In this way, our paper already contains the possibility to identify changes in the structure of the interaction between different time periods, which is one of the main research questions of our paper”

 

• I applaud the authors for being skeptical about the assumptions of normality, stationarity, However, I have some concerns. First, it is clear that the data do not follow a Gaussian process. Have you thought of estimating a Student’s t VAR (there is code available in R) instead of a normal VAR? Otherwise, what is the point of including testing results for the assumption of normality? In my humble opinion, employing a Student’s t VAR would improve the quality of your study and make it more original.

RESPONSE:  Thank you for your comment. The following paragraph has been added in the manuscript: “Furthermore, future research could use Student’s t VAR in statistical inference instead of a normal VAR. Certainly the use of student's distribution assumption would offer a different approach, although it would require the laborious migration of all data to R. However, both the normal distribution and student's distribution are central, symmetric distributions with significant differences mainly in their asymptotic behavior in the tails. In fact, the normal distribution is more stringent in its conditions, leading to rather safer inferences when detecting a correlation (higher positive predictive value in detecting correlations).”

 

Second, I understand that all of your variables are log differenced to account for stochastic stationarity. But how about deterministic stationarity? If you include a deterministic trend into your model, would it be statistically significant? Stochastic and deterministic stationarity are two distinct sources of model misspecification; see, for example, Andreou and Spanos (2003).

RESPONSE:  Thank you for your comment. We note the possibility of verifying such a model in the proposals for future research adding the following paragraph in the manuscript: “It is a fact that Andreou and Spanos (2003), like others (Lu, M., & Podivinsky, J. M. (2003)), relied on the data of Nelson, C. R.; Plosser, C. I. (1982), in order to examine the existence of trend stationarity in time series. Obviously, this is a working hypothesis which changes the whole model tested as it introduces an additional term, that of trend.

 

Third, what about heteroscedasticity? If you employ a Student’s t model, you would explicitly account for it, yet the fact that you are using data on the daily frequency is problematic in that respect. Why using daily data instead of monthly? Is there a particular reason? Fourth, the discussion on “normality”, “stationarity”, etc. is unnecessarily long. Perhaps you must shorten it and include some of the discussion/tables into the appendix.

RESPONSE:  Thank you for your comment. The following paragraph has been added in the manuscript: “In addition, it would be interesting in the future to test whether there are trend terms in the volatility of the model. Andreou and Spanos (2003), like others (Lu and Podivinsky, 2003), relied on the data of Nelson and Plosser (1982), in order to examine the existence of trend stationarity in time series. Obviously, this is a working hypothesis which changes the whole model tested as it introduces an additional term, that of trend”.

 

 

• As mentioned earlier, your study lacks In order to improve its originality, I would advise you to also consider the CMA and RMW factors of Fama and French (2015) and/or the traded liquidity factor of Pastor and Stambaugh (2003); data is available on Kenneth French’s and Robert Stambaugh’s data libraries. The relationship between “fear” and those factors has not been investigated before. In my humble opinion, it will improve the quality of your study.

RESPONSE:  Thank you for your very interesting suggestion. However, it greatly extends the scope of this research and therefore we mention it as a suggestion for future research. Possibly our group will also address this idea in a future paper.

 

 

• The number of observations varies significantly from one subperiod to For example, it is 2,523 for one subperiod but 166 for another. Hence, the statistical significance of your results is expected to vary from one subperiod to another due to the differing statistical power of your hypotheses tests.

RESPONSE:  Thank you for your comment. We have already referred in a previous comment to this feature of the survey, which is necessitated by reality itself and the length of time periods. The following sentence has been added to the manuscript: “The fact that the number of observations varies significantly from one subperiod to another is necessitated by reality itself and the length of time periods.”

 

• I would advise you to use a 5% significance level for the “shorter” subperiods but a 1% significance level for the “longer” subperiods when discussing statistically significant results; see, for example, Kim and Ji (2015) and Michaelides (2021).

RESPONSE:  Thank you for your comment. The following sentence has been added to the manuscript: “It should be noted that, following Kim and Ji (2015) and Michaelides (2021), different levels of statistical significance could be used per period when discussing statistically significant results  (i.e.5% significance level for the “shorter” subperiods but a 1% significance level for the “longer” subperiods). However, this would be quite arbitrary and would have the disadvantage of reduced comparability between the results of the different phases. Furthermore, statistical science itself, through its mathematical embeddedness, has the competency of taking into account the sample size. Future research could address this issue.”

 

Minor Comments:

• Table 1: “Octomber” and “1,66”

REPLY:  Thank you for your comment These typographical errors have been corrected.

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

It's perplexing to me. The authors haven't revised their paper; instead, they've merely appended a paragraph to the conclusion, hinting to readers that my comments and suggestions should be considered in future work.

Overall, I'm baffled by the responses from the authors. None of them seem to make any sense. Their reasoning seems inconsistent. On one hand, they advocate for an external definition of recessions, citing the NBER business cycle dates. Yet, they arbitrarily select July 2007 over December 2007 based on high unemployment rates without providing clear justification. It's as if they made the decision by flipping a coin or consulting some form of mystical divination. I proposed a formal test using the VIX index to identify periods of "fear," but unfortunately, the authors chose to disregard this suggestion entirely, opting instead to present their biased empirical findings. It's frustrating to encounter such disregard for established statistical principles. Despite the clear issues with the distribution, the authors cling to the normal distribution, arguing that it provides safer inferences for correlation detection. This assertion seems to dismiss the substantial body of work in distribution theory by respected scholars. I find it baffling that they would prioritize convenience over statistical rigor, especially when alternative distributions like the Student's t distribution could offer more appropriate modeling in this context.

In my opinion, this manuscript falls short of the standards required for publication. In fact, it seems to have regressed significantly from its previous iteration.

Author Response

We owe many thanks for their constructive comments and recommendations. All these suggestions were taken into account when preparing the new version of the manuscript; relevant modifications are now incorporated into the text. This has, in our opinion, improved the quality of the manuscript.

The most important changes we made are:

• We redesigned the whole data on which the statistical analysis was carried out, extending the whole data period by ten years while we have included the Covid-19 crisis with updated data up to February of 2024.
• We have fixed various typographical or other morphological issues, as well as we performed new formulation of some tables.

Below we provide a response-rebuttal to each of the issues, indicating how each of the recommendations was addressed and indicate the appropriate changes in the text of the revised paper.

Thank you for your consideration of our manuscript.

1. I am wondering why the authors chose the examination period to start on April 1991 (does it though?) and end on December 2015. First, it seems a bit arbitrary. There are available data for VIX since January 1990, while the examination period could be easily extended to include the COVID-19 recession. Second, it is confusing. Does the examination period begin on April 1991 (mentioned in the discussion) or April 1994 (Table 1)? 

 Response: Thank you for your comment. Initial Data were collected since April 1991, as indicated in the text such as Table 3. The reference to April 1994 in Table 1 is a typographical error which has been corrected. However, the initial time of the data, expanded by two months, to January 1994. Furthermore, the ending point of the data expanded by 10 years approximately, covering the covid’19 period. The whole period of the data starts from January 1994 and ends on February of 2024.

   

2. Please extend the examination period or clarify how the start and end dates were chosen. I would extend the period to include the COVID-19 recession in order to improve the quality of the study.

 Response: Thank you for your comment. As mentioned above, we have fixed this issue by conducting a major extension of the data period.

 

3. The NBER business cycles dates in Table 1 are inconsistent. According to NBER, the Great recession (sub-prime crisis) starts on December 2007, not July 2007. Beyond this inconsistency, does it make sense to use the NBER business cycles to define periods of “fear”? 

 Response: Thank you for your comment. In order not to have elements of opportunism and arbitrary in the methodology, it is important to have a definition from an outside third source to define recessions. This is the main utility of using the NBER. Regarding the choice of July 2007 (Q32007) instead of Dec 2007 (Q42007), the issue is fixed by reassessing the period in accordance to NBER.

 

4. Itiswell known that financial markets are forward looking of the real economy; see, for example, Stock and Watson (2003). If I were you, I would use the sup MZ test of Ahmed et al. (2017) on the VIX index to detect the volatility structural breaks associated with the recession periods examined rather than set the “structural breaks” determined by the behavior of the real economy.

 Response: Thank you for your comment. The fact is that on many points in this investigation a multitude of alternative controls could be carried out. One of these options would be to apply the sup MZ test of Ahmed, M., Haider, G., Zaman, A. (2017This test allows algorithmic detection of any changes in volatility ,caters to unknown breakpoints, and also compare it to the sup F. This test is useful in curing a key weakness of most regressions, the assumption that the correlation or regression coefficients remain constant in time, or that the structure of the model remains constant. It is a fact that the sup MZ test is a useful test. However, in the case of our research its usefulness is less than its average usefulness for two reasons: First, because it is appropriate to use break points from BERS, so that we are talking about commonly accepted recession periods; second and more importantly, in this paper we do not assume a uniform structure over the whole period, but we compute the coefficients at each period separately. In this way, our paper already contains the possibility to identify changes in the structure of the interaction between different time periods, which is one of the main research questions of our paper.

However, the research question of comparing the NBER structural points, with any other brake structure inducted by statistics, may be a specific autonomous research. In this direction we pose the elements found by our graphical examination of the data (specifically the scatter dot matrix), which offers slight elements of more composite structure than the one hypothesized with NBER.

5. I applaud the authors for being skeptical about the assumptions of normality, stationarity,  However, I have some concerns. First, it is clear that the data do not follow a Gaussian process. Have you thought of estimating a Student’s t VAR (there is code available in R) instead of a normal VAR? Otherwise, what is the point of including testing results for the assumption of normality? In my humble opinion, employing a Student’s t VAR would improve the quality of your study and make it more original. 

 Response: Thank you for your comment. Certainly the use of student's distribution assumption would offer a different approach, although it would require the laborious migration of all data to R. However, this approach is mentioned as a proposal to future works.

 

6. Second,I understandthat all of your variables are log differenced to account for stochastic stationarity. But how about deterministic stationarity? If you include a deterministic trend into your model, would it be statistically significant? Stochastic and deterministic stationarity are two distinct sources of model misspecification; see, for example, Andreou and Spanos (2003). 

 Response: Thank you for your comment. It is a fact that Andreou and Spanos (2003), like others (Lu, M., & Podivinsky, J. M. (2003)), relied on the data of Nelson, C. R.; Plosser, C. I. (1982), in order to examine the existence of trend stationarity in time series. Obviously this is a working hypothesis which changes the whole model tested as it introduces an additional term, that of trend. However, we note the possibility of verifying such a model in the proposals for future research.

 

7.Third, what about heteroscedasticity? If you employ a Student’s t model, you would explicitly account for it, yet the fact that you are using data on the daily frequency is problematic in that respect. Why using daily data instead of monthly? Is there a particular reason? Fourth, the discussion on “normality”, “stationarity”, etc. is unnecessarily long. Perhaps you must shorten it and include some of the discussion/tables into the appendix.

 Response: Thank you for your comment. While this is a very accurate comment, we have to consider that using data on a daily basis, rather than on a monthly average, is almost imperative because of the wide variation in the length of the time periods under consideration, some of which last several years and some of which last a few months. If we apply the approach of taking account monthly average values, then we will face the situation of some period’s time series consisting of some values, like some decades at maximum.

 8. The number of observations varies significantly from one subperiod to another. For example, it is 2,523 for one subperiod but 166 for another. Hence, the statistical significance of your results is expected to vary from one subperiod to another due to the differing statistical power of your hypotheses tests. I would advise you to use a 5% significance level for the “shorter” subperiods but a 1% significance level for the “longer” subperiods when discussing statistically significant results; see, for example, Kim and Ji (2015) and Michaelides (2021).

Response: Thank you for your comment. We provide different statistical levels, in stationarity tests, as well as in correlation coefficients. We have already referred in a previous comment to this feature of the survey, which is necessitated by reality itself and the length of time periods. Indeed we could use different levels of statistical significance per period.

However, we have the disadvantage of reduced comparability between the results of the different phases

Round 3

Reviewer 2 Report

Comments and Suggestions for Authors

I now believe the paper is much improved. However, I still have a few minor comments before publication.

1. After the sentence, "The change in the correlation mechanism within a selected period implies that there are probably structural events that change the behavior of the market at time points other than the selected ones that mainly come from NBER."; you should explicitly mention that you ignored the structural breaks for simplicity.

2. In the long paragraph beginning "Furthermore, future research could use...", I believe you include a lot of uneccessary information, which may give the wrong impression to the reader. I would advise you to keep it simple. You may open your paragraph with a statement, "We acknowledge that our research has certain limitations, which could be addressed in future work." Then you can list the four limitations using clear and compact sentences, without being defensive. Here's a suggestion, but feel free to use it or modify it as you like: "First, given that the Normal distribution assumption is violated, using a more appropriate distribution, such as the Student's t distribution, could offer a different modeling approach and potentially lead to different empirical results. Second, our empirical results might be sensitive to the presence of deterministic trends in the model's volatility, which we assumed were absent in our analysis (see Andreou and Spanos (2003); Lu and Podivinsky (2003) for details). Third, as discussed in Kim and Ji (2015) and Michaelides (2021), the usage of varying levels of statistical significance might have been more appropriate due to the differing sample sizes of our subsamples. Fourth, our model does not include the common CMA and RMW factors from Fama and French (2015) or the traded liquidity factor from Pastor and Stambaugh (2003)."

 

Author Response

Dear Author,

We owe many thanks for your constructive comments and recommendations. All these suggestions were taken into account when preparing the new version of the manuscript; relevant modifications are now incorporated into the text. 

Below we provide a response-rebuttal to each of the issues, indicating how each of the recommendations was addressed and indicate the appropriate changes in the text of the revised paper.

1. .After the sentence «the change in the correlation mechanism….» you should explicitly mention that that you ignored the structural breaks for simplicity.

 Response: Thank you for your comment. We have clearly note the proposed sentence.

   2. In the long paragraph beginning «furthermore, future research ….» I believe you include a lot of unnecessary information. You may open your paragraph with ….

 Response: Thank you for your comment. We have adopted the whole proposed paragraph to our discussion. .