A Balanced Portfolio Can Have a Higher Geometric Return Than the Risky Asset^†

Round 1

Reviewer 1 Report

The exposition of the paper and the abstract, should pay attention to clarifying 

(1) The research question

(2) Why we care about the research question

(3) What the authors do in this paper

(4) What the authors find in this paper

(5) Why the findings are important

These 5 points must be reflected in the abstract first. Currently, the abstract does not mention that the findings can be of use for pensions or target-date mutual funds.

The methods should be exposed more clearly. Specifically, 

(A) The main concept that the formulas are after seems to be the potential for first-order stochastic dominance. If so, this relevance should be highlighted, if not, then the main takeaway from these formulas should be highlighted, for example, the relevance with the figure (the figure should be numbered, too).

(B) Perhaps Section 2 should be re-organized into two subsections, one with "theoretical underpinnings" behind the concept of balanced portfolios and a subsection with "data and empirical analysis", so that a reader can easily navigate through the paper. Definitely the role of the paper's figure should be central in the exposition.  

The McLean and Pontiff reference is McLean and Pontiff (2016), not McLean and Pontiff (2015). 

Author Response

Reply to referee 1:

We are very grateful for your close reading of our paper and for your helpful comments and suggestions, which have really improved the paper and its exposition. Below we respond to each of your comments. In each case, we cite your comment in italics before stating our responses in regular font.

The exposition of the paper and the abstract, should pay attention to clarifying 

• The research question

The research questions of “A Balanced Portfolio Can Have a Higher Geometric Return than the Risky Asset” is whether a balanced portfolio can have a higher geometric return than a portfolio that just consist of the risky asset. In particular, risky asset may have a larger expected return but may lose a large fraction of its value in a recession so that the answer is not clear a priori. We clarified this in the current text.

 

(2) Why we care about the research question

We clarified this in the current text. These results are of interest for academics and for those who have to choose an asset allocation, such as pension fund managers, designer of target-date funds, and individual investors.

 

(3) What the authors do in this paper

We use a theoretical model and estimation results to answer our research question.

(4) What the authors find in this paper

We find that a balanced portfolio can have a higher geometric return than a portfolio that just invests in a risky asset.

 

(5) Why the findings are important

These results are useful for those who have to choose an asset allocation, such as pension fund managers, designer of target-date funds, and individual investors. We clarified this in the current text.

These 5 points must be reflected in the abstract first. Currently, the abstract does not mention that the findings can be of use for pensions or target-date mutual funds.

Thank you for this comment. We rephrased the abstract.

The methods should be exposed more clearly. Specifically, 

(A) The main concept that the formulas are after seems to be the potential for first-order stochastic dominance. If so, this relevance should be highlighted, if not, then the main takeaway from these formulas should be highlighted, for example, the relevance with the figure (the figure should be numbered, too).

We rephrased this discussion emphasizing that the formula shows that there is no first-order stochastic dominance even when the risk premium is strictly positive.

(B) Perhaps Section 2 should be re-organized into two subsections, one with "theoretical underpinnings" behind the concept of balanced portfolios and a subsection with "data and empirical analysis", so that a reader can easily navigate through the paper. Definitely the role of the paper's figure should be central in the exposition.  

We followed your advice and reorganized section two and split it into a theoretical part and a part about the data and empirical analysis. We also discuss the paper’s figure in more detail.

The McLean and Pontiff reference is McLean and Pontiff (2016), not McLean and Pontiff (2015). 

Thank you; we updated this.

Thank you so much for your comments and suggestions.

Author Response File: Author Response.pdf

Reviewer 2 Report

The topic of the study is relevant, but the manuscript is a work in progress (not complete). The theoretical background, rationale/aim of the studies and limitations should be provided to improve the quality of the manuscript.

The first paragraph in the Introduction is substantially part of the abstract. I suggest the author(s) adjust their abstract to expressly include the aim of the study and the method used.

The U.S and the United States are used interchangeably. I suggest either of them be used throughout the manuscript.

The statement 'the Nikkei 225 Index produced real returns of −21% from 1990 to 2019' also needs a recent citation from 2019.

The Figure and the Table in the manuscript must be named, numbered and source provided. Also, the figure and the table must be mentioned and adequately interpreted in the manuscript. 

Similarly, the findings should be argued and compared with similar studies by other scholars.

The chapters such as Materials and Methods, and Results and Discussion should be presented. 

 

 

 

Author Response

Reply to referee 2:

We are very grateful for your close reading of our paper and for your helpful comments and suggestions, which have really improved the paper and its exposition. Below we respond to each of your comments. In each case, we cite your comment in italics before stating our responses in regular font.

The topic of the study is relevant, but the manuscript is a work in progress (not complete). The theoretical background, rationale/aim of the studies and limitations should be provided to improve the quality of the manuscript.

We now include a section “Theoretical model” and clarify the implications of this model for the return of a balanced portfolio.

The first paragraph in the Introduction is substantially part of the abstract. I suggest the author(s) adjust their abstract to expressly include the aim of the study and the method used.

Thank you. We rephrased the abstract.

The U.S and the United States are used interchangeably. I suggest either of them be used throughout the manuscript.

Thank you. We now use “U.S.” throughout.

The statement 'the Nikkei 225 Index produced real returns of −21% from 1990 to 2019' also needs a recent citation from 2019.

The data is from Bloomberg and we now mention this in a footnote. Thank you.

The Figure and the Table in the manuscript must be named, numbered and source provided. Also, the figure and the table must be mentioned and adequately interpreted in the manuscript. 

We followed your suggestions. Thank you.

Similarly, the findings should be argued and compared with similar studies by other scholars.

We compare our findings to a recent paper about target-date funds.

The chapters such as Materials and Methods, and Results and Discussion should be presented. 

Thank you for your comments. Our materials are the stock market return and 10-year Treasury bond return. Our result is that a balanced portfolio will have a larger geometric return when the risk premium is about the size of the historical risk premium of the world stock returns.

Author Response File: Author Response.pdf

Reviewer 3 Report

This paper compares the geometric returns of a balanced portfolio (mix of stocks and bonds) to an all stocks or all bonds portfolios for US stocks when the risk premium is low. Thus, the empirical relevance of the results is dependent on the value of the risk premium. There is a vast literature on estimating the risk premium some of which is discussed in the paper. Perhaps you could add a paragraph discussing the range of estimates and also add some papers such as Harvey et al (2021) and Shirvani et al (2021).

References

Harvey, D., Leybourne, S., Sollis, R. and Taylor, R. (2021), Real-time detection of regimes of predictability in the US equity premium, Journal of Applied Econometrics 36, 45-70.

Shirvani, A., Stoyanov, S., Fabozzi, F. and Rachev, S. (2021), Equity premium puzzle or faulty economic modelling?. Review of Quantitative Finance and Accounting 56, 1329–1342.

Author Response

Reply to referee 3:

Thank you for your close reading of our paper and for mentioning two additional references. We now refer to these in our paper.

Round 2

Reviewer 2 Report

I can see the authors have improved the quality of their manuscript. Nevertheless, there are a few issues left unaddressed.

I still can not find the aim of the study and the method used in the abstract.

Both in-text citations and the list of references still look somewhat.

"The chapters such as Materials and Methods, and Results and Discussion should be" expressly presented, not as a subchapter.

 

Author Response

Reply to referee 2:

Thank you very much for your close reading of our paper and for your helpful comments and suggestions, which have really improved the paper and its exposition. Below we respond to each of your comments. In each case, we cite your comment in italics before stating our responses in regular font.

I can see the authors have improved the quality of their manuscript.

Thank you very much.

Nevertheless, there are a few issues left unaddressed.

I still can not find the aim of the study and the method used in the abstract.

Thank you for your comment. We now make the following statement in the abstract: “We study whether balanced portfolios have a larger geometric return (and expected log return) than stock portfolios when the risk premium is low. We use a theoretical model and historical data and find that this is the case.”

Both in-text citations and the list of references still look somewhat.

Your comment caused us to review the references and we are satisfied with the relevance of the papers we cite and with the total number of papers that we cite (we have more than half a page of references for a six-page note).

"The chapters such as Materials and Methods, and Results and Discussion should be" expressly presented, not as a subchapter.

Thank you very much for your comment. We were in a bit of a bind here. The editor and another referee made specific suggestions for the section headings. Those suggestions were overlapping and consistent with each other. We think that your suggestions are very good as well but decided to follow their advice and are satisfied with the number of sections and the section titles.

Thank you so much for your comments.