Mean Reversion Lessens Mean Blur: Evidence from the S&P Composite Index

Round 1

Reviewer 1 Report

There are many recent, more robust tests for mean reversions of stock data (see, for instance, Nguyen et al. 2022, Journal of Risk and Financial Management).  The methods used in your paper are very dated.  It is essential that you include some of the modern tests to check the robustness of your results.  Such tests include multiple unit root, independence and spectral tests. 

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Mean Blur is Countered by Mean Reversion: Evidence from the S&P Composite Index

By  Luigi Buzzacchi and Luca Ghezzi

 

Outline

The paper indicates that, for the S&P Composite Index returns over a long period from 1871 to 2022, even if returns are assumed i.i.d. and normally distributed, we cannot estimate the annual mean return well. It has a 95% confidence interval between 3.87% and 9.56%.  Under mean reversion, however, return are not independent over time and the long-term return variance is less than the short-term variance.  This may suggest that, under mean reversion, the mean blur may not be as serious for long-term average returns.

Comments

The result that, even with a very long data period and making the most generous assumptions, we cannot obtain a precise estimate of mean returns of a market aggregate.  While the approach to show this is very basic, the result is surprising.  I did not expect to see this wide of a rang for mean returns.

This is a bit thin for a full paper, so the authors appear to search for additional results. Here I have some problems.

1.       It is true that under mean reversion the long-run average returns are less variable (this is the basis for the variance ratio test in Poterba and Summers and other papers).  However, this seems to be insufficient support for your claim that there is no mean blur under mean reversion.

2.       Rescaled range analysis is sometimes used to detect mean reversion.  However, in that case we should find that Hhat < 0.5. You find Hhat > 0.6 which provides evidence against mean reversion. Not clear what function the Rescaled range analysis has in your paper.

3.       You use the term “accepted” where it is common practice to state “not rejected”.  This is especially bothersome when you are using a test with low power.

4.       In the conclusion you state “..random walk hypothesis tacitly implies that means are blurred,…” Very unclear what you mean by this.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

It is important to note that, as shown by Lumsdaine/Papell (97), Andrews (92/93), Lee and Stracizich (2003), Enders and Lee (2012), simple unit root tests such as the ADF and PP tests performed in your paper can lead to inaccurate results if there are structural breaks in the data.  Further, based on my experience years ago dealing with the data that you used and similar data sets, structural breaks are not uncommon.  As such, I suggest that you perform the UR tests again allowing for structural breaks in the data and use the break dates identified (if any) by the aforementioned models to re-test your hypothesis.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Paper has improved sufficiently.

Author Response

Thanks for your collaboration!