The Impact of Options on Investment Portfolios in the Short-Run and the Long-Run, with a Focus on Downside Protection and Call Overwriting

Round 1

Reviewer 1 Report

Normally in scientific articles the first person is not used, even if there is only one author, "we" is usually used.
In the introduction it is not clear which are the research objectives, since these are multiple and are scattered throughout the article.
The literature review is in point 5, it should be after the introduction. It is not clear from the literature review that the results sought have not been previously explained.
The option definitions do not fit in an article since they correspond more to a textbook. As with implied volatility, it is sufficient to quote from a textbook and use the context directly. Similarly with the risk premium, it is a general and commonly used term.
In that sense, some explanations are common strategies, for example the one represented in Figure 4.
In the conclusions, the first paragraph begins with a general property of options. In the second paragraph it is indicated that solutions have been found, but didn't they already exist? what was the problem with them?
In the third paragraph there are some paragraphs with generalities that are difficult to understand: "My objective was to illustrate that options should not be over-laid on existing portfolio in order to engineer certain outcomes such as enhanced income whilst assuming that the risk, risk-premium, and beta of the portfolio are unaffected".

And finally, the article exceeds the usual length for this type of article.

Author Response

I thank the Reviewer 1 for their comments. To an extent I need to balance my responses as Reviewer 1 has asked for changes whereas Reviewer 2 does not want any changes made. To that end, I tackle the points made by Reviewer 1 as follows:

• Normally in scientific articles the first person is not used, even if there is only one author, "we" is usually used.

Ironically, I have just had a paper that I submitted to a financial journal which I wrote in first person plural (we) returned to me requesting for it to be rewritten in first person singular (I). That is why I wrote this one in first person singular. Nevertheless, my preference, especially for mathematical journals is to write in first person plural, and I have rewritten it accordingly.

• In the introduction it is not clear which are the research objectives, since these are multiple and are scattered throughout the article.

I thank the reviewer for raising this. I have rewritten the introduction, and the abstract to make the objectives clearer. I have removed reference to objectives from the body of the article to avoid any ambiguity, only referring again to the objectives in the conclusion. In particular I have separated the article objectives from my motivation/purpose of writing the article. I think that may have been the cause of some of the confusion. I hope this has helped.

• The literature review is in point 5, it should be after the introduction. It is not clear from the literature review that the results sought have not been previously explained.

I had originally broken with convention and placed the literature review further down the article in order to combine it with a comparison of published results with ours. I have now moved the literature review beneath the introduction. I had to split the old literature review section into two, as the comparison part required definitions and concepts that appear later in the article. Therefore the comparison part now appears as a new section after the worked examples. I think this new structure works better so I thank Reviewer 1 for this comment and hope they agree.

• The option definitions do not fit in an article since they correspond more to a textbook. As with implied volatility, it is sufficient to quote from a textbook and use the context directly. Similarly with the risk premium, it is a general and commonly used term.
  In that sense, some explanations are common strategies, for example the one represented in Figure 4.

I respectfully disagree with Reviewer 1 on this point. If this were a financial journal then we might expect readers to know these terms. But this is a mathematical journal with a special edition on finance. I therefore do not believe that the readers will necessarily be familiar with the terms. Since removing these definitions would render the article impenetrable for those readers, and since the definitions only occupy a couple of paragraphs, I prefer to retain them.

I would also prefer to keep the definition of annualised risk-premium. Whilst the term 'risk premium' is known, there is ambiguity even among those versed in finance as to whether the annualisation of a risk-premium (and risk and Sharpe ratio) is arithmetic or geometric. I wish to keep these definitions in order to be clear on how I have annualised.

I'm not sure I follow the Reviewer 1's comment about Figure 4. Personally, I have not seen such a figure elsewhere in the literature. Since it displays such a critical characteristic of the option strategy using the new formulae appearing in this article, I feel strongly it should remain in the article.

• In the conclusions, the first paragraph begins with a general property of options. In the second paragraph it is indicated that solutions have been found, but didn't they already exist? what was the problem with them?
  In the third paragraph there are some paragraphs with generalities that are difficult to understand: "My objective was to illustrate that options should not be over-laid on existing portfolio in order to engineer certain outcomes such as enhanced income whilst assuming that the risk, risk-premium, and beta of the portfolio are unaffected".

Similar to the first bullet point, I have rewritten the conclusion in order to make it clearer (including the paragraph cited by Reviewer 1). Whilst previous literature covers some special cases and some empirical, ex-post, analyses, I do not believe these formulae do appear elsewhere in the literature, nor any similar ex-ante measures, and I have clarified that point. In particular, the importance of the new formulae are that they apply to ANY strategy - not just call-overwriting, put-protection, or collars. Again, I have highlighted that feature.

• And finally, the article exceeds the usual length for this type of article.

The article is long and I thank the reviewers for their time in reading it. I specifically submitted the article to Mathematics because that journal publishes longer articles. I could split the article into 3 parts (single period, long run, and the appendix) and submit separately for publication, however I'm loathed to do that as I would like this to stand as a single body of work. Therefore I defer to the editors on this point.

I conclude by thanking the reviewers and hope that the revised article satisfies the points raised in their reports.

Reviewer 2 Report

I really liked the article "THE IMPACT OF OPTIONS ON THE INVESTMENT PORTFOLIO IN THE SHORT AND LONG TERM, WITH AN EMPHASIS ON PROTECTION FROM NEGATIVE EFFECTS AND CANCELLATION OF REQUIREMENTS". I didn't see any obvious flaws in the article. In the article, the author analyzes the impact of the introduction of options on the investment portfolio. 

In the first part of the article, the author examines options and further determines the profitability of a portfolio that includes options, trying to avoid ambiguity regarding cost and leverage. Then the author provides closed-form expressions for these summary statistics (expected return, risk and beta) for a portfolio containing any option strategy. The author shows by examples that both expected returns and risk are also decreasing, but at different rates, so that these option strategies affect the Sharpe ratio of the portfolio. In other words, the effectiveness of portfolios can be reduced by the introduction of options.

In the second part of this article, the author examines the long-term distribution of the profitability of an investment portfolio, which includes an option strategy that is consistently repeated. Using simulation, the author demonstrates the result for the strategy examples, showing that convergence to the normal distribution occurs quickly, but depends on the execution price.

I liked the article, I recommend the article for publication without changes and additions.

Author Response

I thank Reviewer 2 for their supportive comments.

Reviewer 1 did request some changes but they related to clarity of wording and structure rather than content. I have made some revisions to satisfy Reviewer 1 (rewriting it in first person plural rather than first person singular; more clearly specifying the objectives of the article in the abstract, intro and conclusion; moving the lit review forward). The article is otherwise unchanged. I feel sure the new revised article will still satisfy Reviewer 2.