Cross-Hedging Portfolios in Emerging Stock Markets: Evidence for the LATIBEX Index

Round 1

Reviewer 1 Report

This paper provides an interesting analysis of possibilities for hedging spot positions on the FTSE LATIBEX Index employing futures on four stock market indices: Euro Stoxx 50, S&P500, Bovespa, and IPC. Generally, the article is well written and its subject is suitable for publication in Mathematics. However, I have the following comments:

• The formula for log returns (p. 5) should be changed – the symbol S_t is used for prices and for returns at the same time.
• In the line 235 one can read “It is also noticed a rise in correlations in the Global 235 Financial Crisis (2008-2009)”. In my opinion, Figure 1 suggests that it was the decrease (at least at the beginning of this period).
• There is no explanation in the text, why Figures 1, 2, 3 show the results only for 2 applied models (without CCC and DVEC).
• Authors should comment why the correlation coefficients between MVHRs for CCC and other models are so small in case of Eurostoxx50 IF (Table 3a).
• Equation (5): Should it be ‘t’ or ‘i’ under ‘min’?
• Why the values of volatility in Table 4.b are expressed in percentages, while in Table 4a they are written as numbers?
• In the lines 363-366 one can read that “the hedge provided by least-squares estimates of the unconditional second order moments achieve a significant reduction of return variance relative to the (…) naïve hedge for the four futures contracts”. Is it really true for Eurostoxx50?
• Please check what numbers are bolded in Table 4.b.
• Line 380: Why the CCC model is excluded from the conclusion that the models achieve similar volatility reductions for EURO STOXX 50, S&P500 and IPC?
• The paragraph in the lines 384-390 is misleading. One can understand that the Authors want to write when the specific model is the best. In fact they want to write which models are the best for specific contracts. E.g. they write that the largest variance reduction was achieved by BEKK model in application to S&P500 (meanwhile better results are for BEKK model in case of other contracts). This paragraph should be rewritten to put different emphasis, according to the Authors, intentions.
• The paragraph in the lines 391-395 is unclear. It looks like something is missing here.
• The value gamma=4 taken in eq. (6) should be justified.
• There is no information in the note for Table 5 which values are bolded.
• The Authors should unified the use of capital letters in the names of the future contracts (e.g. EURO STOXX 50 or Euro Stoxx 50 or Eurostoxx50).
• The Authors should discuss the literature where cross-hedging portfolios are considered.
• The references in the References Section are out of date. Please add recent related work/studies from high impact factor journals, published after 2015.

Author Response

Comments and Suggestions for Authors

 

This paper provides an interesting analysis of possibilities for hedging spot positions on the FTSE LATIBEX Index employing futures on four stock market indices: Euro Stoxx 50, S&P500, Bovespa, and IPC. Generally, the article is well written and its subject is suitable for publication in Mathematics. However, I have the following comments:

 

• The formula for log returns (p. 5) should be changed – the symbol S_t is used for prices and for returns at the same time.

 

It is right. We have corrected it based on the Reviewer's recommendation. In the line 207 of the new version the notation for returns is .

 

 

• In the line 235 one can read “It is also noticed a rise in correlations in the Global 235 Financial Crisis (2008-2009)”. In my opinion, Figure 1 suggests that it was the decrease (at least at the beginning of this period).  

 

The Reviewer is right and we have changed the sentence (found in the new version in the last paragraph of page 7) for:

 

It is also noticed a decrease in correlations in the beginning of Global Financial Crisis (2008-2009), and then an increase at the end of this period.

 

 

• There is no explanation in the text, why Figures 1, 2, 3 show the results only for 2 applied models (without CCC and DVEC).

 

In initial versions of the manuscript we showed graphs for all the models and are found in the Appendix of this document. However, for sake of space, we considered only the two most relevant models. We have included the following sentence at the beginning of page 6 in the new version:

 

For sake of space, we present the two models that exhibit important differences between them, that is, the asymmetric DCC- and BEKK-GARCH(1,1). The graphs for the asymmetric CCC- and DVEC-GARCH(1,1) models are available upon request.

 

 

• Authors should comment why the correlation coefficients between MVHRs for CCC and other models are so small in case of Eurostoxx50 IF (Table 3a).

 

We acknowledge the Reviewer for highlighting this possible inconsistency. We have performed the estimation again to find differences, but we did not find variations on our results. In a related study, Chang et al. (2013) found a minimum correlation of 0.59 (between CCC and DCC), though the authors employ exchange rates. On the other hand, Lai (2019) argues “A key topic that has been little explored is whether the comparison results are different when various multivariate GARCH specifications are employed for hedge ratio calculation.” Therefore, this will be an interesting topic for future research. We have added the following paragraph after Table 3a in page 10:

 

Surprisingly, for the case of Eurostoxx50 IF, the linear correlation coefficients between the MVHRs for the asymmetric CCC and other models are so small, contrary to the findings of Chang et al. (2013) for example, though the authors examine exchange rates and employ the original CCC and DCC versions. However, this topic is little explored in the literature as stated by Lai (2019), and thus, more research is needed to find the plausible reasons for this result.

 

 

• Equation (5): Should it be ‘t’ or ‘i’ under ‘min’?

 

The Reviewer is right and we have corrected it in the new version.

 

 

• Why the values of volatility in Table 4.b are expressed in percentages, while in Table 4a they are written as numbers?

 

Since Table 4a shows daily variance we have expressed the figures in numbers (multiplied by 10³). While Table 4b exhibits annualized volatility, therefore we have written these values in percentage format. Anyway, we could change the format of the tables as per any Reviewer suggestion.

 

 

• In the lines 363-366 one can read that “the hedge provided by least-squares estimates of the unconditional second order moments achieve a significant reduction of return variance relative to the (…) naïve hedge for the four futures contracts”. Is it really true for Eurostoxx50?

 

Thanks to the Reviewer for this comment we have changed the sentence (page 12) for:

 

Table 4b presents the same information, but in terms of annual volatility. We can deduce that the naïve hedge of taking the opposite position in the selected futures contract reduces volatility when using futures on the EUROSTOXX 50 and IPC, but not with the S&P500 and BOVESPA. On the other hand, the hedging provided by the least squares estimates of the second-order unconditional moments achieves a significant reduction in the variance of the return relative to the unhedged position for all four futures contracts. While in relation to naive hedge, the reduction in variance is appreciable with all contracts, except for EUROSTOXX 50.

 

 

 

• Please check what numbers are bolded in Table 4.b.

 

We are very grateful with the Reviewer for this comment. We have corrected it in the new version.

 

 

• Line 380: Why the CCC model is excluded from the conclusion that the models achieve similar volatility reductions for EURO STOXX 50, S&P500 and IPC?

 

Thanks to the Reviewer for this comment. We have includee the CCC model in the new version.

 

• The paragraph in the lines 384-390 is misleading. One can understand that the Authors want to write when the specific model is the best. In fact they want to write which models are the best for specific contracts. E.g. they write that the largest variance reduction was achieved by BEKK model in application to S&P500 (meanwhile better results are for BEKK model in case of other contracts). This paragraph should be rewritten to put different emphasis, according to the Authors, intentions.

 

The Reviewer is right and we have rewritten the paragraph (page 13) as follows:

 

Therefore, the best models in terms of largest variance reduction per each index futures contract to hedge the LATIBEX index may be identified. For EUROSTOXX 50 IF, the best models are the Error Correction Model (ECM) and Naive Hedging while for the S&P500 futures, these are the asymmetric BEKK- and DCC-GARCH(1,1) specifications. The asymmetric CCC- and DVEC-GARCH(1,1) models outperform for the BOVESPA futures and the asymmetric BEKK- and CCC-GARCH(1,1) models work well for the IPC futures. Even more importantly, regarding the IF candidates that seem to provide the best hedge for LATIBEX positions are the BOVESPA and EUROSTOXX 50 futures contracts.

 

 

• The paragraph in the lines 391-395 is unclear. It looks like something is missing here.

 

The Reviewer is right and we have changed the sentence in the new version (page 13) for:

 

An interesting result is the reduction of variance found with the EUROSTOXX 50 futures, since the LATIBEX market has its trading platform in Europe as well as the EUROSTOXX 50 futures.

 

And we have rewritten part of the conclusions (like other parts in the manuscript), and the new text (in blue) is as follows: (page 18)

 

A significant reduction in volatility is also achieved when hedging the LATIBEX in the portfolio with EUROSTOXX 50 futures. This could be especially interesting for European investors, who might prefer hedging strategies using futures contracts denominated in their own currency and trading in a market they know well. Future research can be focused on alternative models for dependence, such as copulae, and alternative financial hedging instruments.

 

 

• The value gamma=4 taken in eq. (6) should be justified.

 

We appreciate the Reviewer's comment. We have found that usually the risk aversion parameter is between 2 and 4, as per in Fabozzi, Kolm, Pachamanova & Focardi (2007), and without loss of generality, we have chosen γ = 4. In addition, we have added (page 13) the following sentence:

 

Table 5 displays the mean daily return and volatility, as well as skewness, excess kurtosis, and the Certainty Equivalent (in annual and daily terms) for each hedged portfolio as well as for the unhedged LATIBEX position with a specific level of risk aversion e.g., γ = 4, since Fabozzi, Kolm, Pachamanova & Focardi (43) state that risk aversion parameter is between 2 and 4.

 

 

• There is no information in the note for Table 5 which values are bolded.

 

We appreciate the Reviewer’s observation and we have added the following sentence in the footnote of Table 5 (page 14-15):

 

Figures in bold indicate the model that provides the highest Certainty Equivalent (CE).

 

 

• The Authors should unified the use of capital letters in the names of the future contracts (e.g. EURO STOXX 50 or Euro Stoxx 50 or Eurostoxx50).

 

The Reviewer is right and we have corrected it based on the Reviewer's recommendation. All index names are capitalized in the new version of the manuscript.

 

 

• The Authors should discuss the literature where cross-hedging portfolios are considered.

 

We have added in page 2 the following sentence:

 

Cross hedging has been studied extensively, Anderson and Danthine [1] were among the first to discuss cross hedging in a theoretical way, later Eaker and Grant [2] delved into the treatment of cross currency hedging, measuring the effectiveness of hedging when there are no futures on a currency, and recently, there have been several applications of cross-hedging of: Commodities such as [3], who evaluate the effectiveness of cross-hedging of commodities between the metal and spot futures markets; Energy such as [4], who analyze the cross-hedging of aviation fuel with commodity futures; Stock Indices such as [5], who examine the effectiveness of cross-hedging between a UK stock index and global stock index futures from developed and emerging markets; Real Estate such as [6], who analyze the effectiveness of cross-hedging real estate securities with ETFs, among other various applications.

 

 

• The references in the References Section are out of date. Please add recent related work/studies from high impact factor journals, published after 2015.

 

We have added the following references according to the suggestion of the Reviewer:

 

• Chen X., Tongurai J., 2021, Cross-commodity hedging for illiquid futures: Evidence from China’a base metal futures market, Global Finance Journal, 49, 100652.
• Kar, S., Khandelwal P., 2020, Cross-hedging aviation fuel price exposures with commodity futures: Evidence from the Indian aviation industry, IIMB Management Review, 32, 389-401.
• Zainudin, A. D., Mohamad, A., 2021, Cross hedging with stock index futures, The Quarterly Review of Economics and Finance, 82, 128-144.
• Addae-Dapaah, K., Abdullah, K., 2020, Cross Hedging Effectiveness of Real Estate Securities Exchange Traded Funds, Journal of Real Estate Portfolio Management, 26, 74-100.
• Xu, Y., Lien, D., 2020, Optimal futures hedging for energy commodities: an application of the gas model, The journal of futures markets, 40, 1090-1108.
• Habiba, U. E., and Zhang, W., 2020, The dynamics of volatility spillovers between oil prices and stock market returns at the sector level and hedging strategies: evidence from Pakistan. Environmental Science and Pollution Research International, 27, 30706–30715.
• Jin, J., Han, L., Wu, L., & Zeng, H. (2020). The hedging effect of green bonds on carbon market risk. International Review of Financial Analysis, 71, 101509.
• Mensi, W., Hammoudeh, S., Rehman, M. U., Al-Maadid, A. A. S., & Hoon Kang, S., 2020, Dynamic risk spillovers and portfolio risk management between precious metals and global foreign exchange markets, North American Journal of Economics and Finance, 51, 101086
• Sun, H., & Yu, B., 2020, Volatility asymmetry in functional threshold garch model, Journal of Time Series Analysis, 41(1), 95–109.

 

Author Response File: Author Response.pdf

Reviewer 2 Report

The work is an empirical study from financial markets. It applies well-known methods for the well-known financial problem. Literature on hedging with multivariate GARCH models is very broad and authors should add some new citations. The novelty of the paper is low and it is the study of the Latibex index, for which there is no futures contract. The study has a certain practical value.

The work is fairly well written, but I found three mistakes that need to be corrected:

Row 87, The abbreviation DVEC does not mean vector error correction,

Row 197, In the title of Table 1 there is a lack of word “futures”. It should be: and on stock market futures indices,

Row 347, How is hpit calculated (period-t volatility of the hedged portfolio)? We do not know the variance of the hedged portfolio for the specific day.

Author Response

Comments and Suggestions for Authors

 

The work is an empirical study from financial markets. It applies well-known methods for the well-known financial problem.

 

• Literature on hedging with multivariate GARCH models is very broad and authors should add some new citations.

 

We have added the following references according to the suggestion of the Reviewer:

 

• Chen X., Tongurai J., 2021, Cross-commodity hedging for illiquid futures: Evidence from China’a base metal futures market, Global Finance Journal, 49, 100652.
• Kar, S., Khandelwal P., 2020, Cross-hedging aviation fuel price exposures with commodity futures: Evidence from the Indian aviation industry, IIMB Management Review, 32, 389-401.
• Zainudin, A. D., Mohamad, A., 2021, Cross hedging with stock index futures, The Quarterly Review of Economics and Finance, 82, 128-144.
• Addae-Dapaah, K., Abdullah, K., 2020, Cross Hedging Effectiveness of Real Estate Securities Exchange Traded Funds, Journal of Real Estate Portfolio Management, 26, 74-100.
• Xu, Y., Lien, D., 2020, Optimal futures hedging for energy commodities: an application of the gas model, The journal of futures markets, 40, 1090-1108.
• Habiba, U. E., and Zhang, W., 2020, The dynamics of volatility spillovers between oil prices and stock market returns at the sector level and hedging strategies: evidence from Pakistan. Environmental Science and Pollution Research International, 27, 30706–30715.
• Jin, J., Han, L., Wu, L., & Zeng, H. (2020). The hedging effect of green bonds on carbon market risk. International Review of Financial Analysis, 71, 101509.
• Mensi, W., Hammoudeh, S., Rehman, M. U., Al-Maadid, A. A. S., & Hoon Kang, S., 2020, Dynamic risk spillovers and portfolio risk management between precious metals and global foreign exchange markets, North American Journal of Economics and Finance, 51, 101086
• Sun, H., & Yu, B., 2020, Volatility asymmetry in functional threshold garch model, Journal of Time Series Analysis, 41(1), 95–109.

 

 

The work is fairly well written, but I found three mistakes that need to be corrected:

 

• Row 87, The abbreviation DVEC does not mean vector error correction,

 

We appreciate to the Reviewer for this comment and we have changed it for Diagonal VEC (DVEC) in the new version.

 

• Row 197, In the title of Table 1 there es a lack of word "futures". It should be: and on stock market futures indices,

 

We acknowledge the Reviewer’s comment and we have changed the title for:

 

Table 1. Descriptive statistics for returns on LATIBEX and on stock market futures indices

 

• Row 347, How is hpit calculated (period-t volatility of the hedged portfolio)? We do not know the variance of the hedged portfolio the specific day.

 

Thanks to the Reviewer for this comment. The Eq. (5) is wrong. The results show the variance of the daily returns of the Covered Portfolio, considering the total period. We have changed the equation and the sentence in the new version (page 11) of the manuscript for:

 

So, given a class of models indexed by i, i = 1, 2,…,m we should prefer model i such that

 

where  denotes the variance of returns for the hedged portfolio estimated with model i. Table 4a displays the results, as well as for the unhedged position (b_t-1 = 0) and for the naïve hedge (b_t-1 = 1), together with the percent reduction in variance relative to the unhedged position in LATIBEX, .

 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

I have only one note: Please check what numbers are bolded in Table 4.b once again (S&P500).

Author Response

Thanks to the Reviewer for the comment. We have changed the table 4.b in the new revised version as in the attached file.

Author Response File: Author Response.pdf