### Discussion Paper

## Abstract

This study examines the difference in the intraday return-volume relationships of spot and index futures. Quantile regression analyses show that the widening effect of the stock trading volume on the distribution of spot returns disappears within a short period of time, whereas that of the futures trading volume remains over the long term. The short-term effect of the stock volume and the long-term effect of the futures volume are both consistent for contemporaneous trading volumes. Furthermore, the futures volume has a significantly positive effect on the option-implied volatility, whereas the stock volume is only associated with the implied volatility of at-the-money options, which can be traded quickly. In contrast, the implied volatility of out-of-the-money options, which are highly speculative, is strongly related to the futures volume. The findings suggest that the stock volume is mainly induced by hedging demand or disagreements of opinion, whereas the futures volume contains information about price movements.

## Comments and Questions

This paper focuses on the return-volume relationship, using quantile regression. The quantile regression is a useful method which considers tail properties, however, not be generally utilized in the field of finance. Consequently, this paper contains interesting and distinct results that can be extended after in this field.

see attached file

Response to the Referee Report 1

Paper: Differences in the intraday return-volume relationship of spots and futures : A quantile regression approach

Authors: Jaeram Lee, Geul Lee, Doojin Ryu

Thank you very much for giving us the chance of revision and potentially publishing our work to this journal, ...[more]

... the Economics. We answer for the comments of the referee and reflect the comments in the revised paper. We believe that this paper has a potential and clearly contributes to the existing literature. After both referees’ review are completed, we will heavily revise this paper for the publication and improve the quality of this paper. Our answers for the first referee report are as follows.

Comment 1. Summary of the paper

In this paper, the authors study the intraday relationship between asset returns and trading volumes in the market index KOSPI 200 spot and index futures markets, which is highly liquid and with active investor participation. Previous literature have endorsed the relationship between trading volumes and volatility, rather than the level of returns. They employ the quantile regression method (QRM), which is an extended version of OLS to address the relationship between trading volumes and the distribution of returns. QRM is used with a variable with heterogeneous distributions. The dataset, which goes from the 3rd of January 2005 until 30th of June 2014, consists of five-minutes observations of the KOSPI 200 index, trading volumes of KOSPI200 futures, and the implied volatilities constructed from the KOSPI 200 options prices. They run a set of quantile regressions, which are composed by four main variables: (i) the dependent variable, r, is the percentage return of the KOSPI 200 spot index over each five-minute period; (ii) as independent variable, the natural logarithms of the KOSPI 200 spot trading volumes indicated by lsv; (iii) as independent variable, the natural logarithms of the KOSPI 200 futures trading volumes indicated by lfv; (iv) div which measures the first difference of the implied volatility of KOSPI 200 index options. The main results show that the distribution of returns widens following active trading in the spot market. Moreover, the findings indicate a positive relationship between the return volatility and futures transactions. They find that the duration of the return-volume relationship differs for spot and futures trading. Indeed, the positive effect of the spot volume on the return volatility may disappear within five minutes since the relationship between return and volumes in the spot market can be attributable to disagreement rather than market information. On the contrary, the positive relationship between futures trading volumes and the magnitude of stock index movements persist over time.

Author’s response: We appreciate you suggesting the clear and detailed summary. Based on this summary and other comments, we reconstructed the introduction and the conclusion to more clearly show the results of this study.

“This study investigates the intraday relationship between returns and trading volumes of stocks and index futures. We perform quantile regressions of spot returns on the stock and futures trading volumes to identify the effect of trading volumes on the return distribution. Our empirical results suggest that both stock and futures volumes extend the distribution of spot returns but that these effects persist for different durations. The effect of stock trading volumes on returns disappears within five minutes, whereas futures trading volumes have a significant influence even after fifteen minutes. When we consider contemporaneous trading volumes, the distribution of returns temporarily widens due to a large contemporaneous stock volume but returns to its original level in fifteen minutes, whereas the effect of a large futures trading volume remains over time. The finding of a short-term effect of the stock trading volume but a long-term effect of the futures trading volume is consistently supported by the results for the option-implied volatility. Only the futures trading volume is significantly and positively related to the implied volatility in the options market. However, an increase in the stock trading volume precedes an increase in the implied volatility of ATM options, which can be traded quickly and is an effective hedging tool. In contrast, the futures trading volume is closely associated with the implied volatility of OTM options, which offer high leverage and are, therefore, favorable for informed trading. Our findings suggest that the return-volume relationship differs significantly for the stock and futures trading volumes. Specifically, the return-volume relationship for stock trading is mainly attributable to disagreements, whereas futures contracts may be a tool for informed trading.”

Comment 2. Is the contribution of the paper potentially significant?

Other empirical papers study the contemporaneous return-volume relationship, the return variance – volume relationship and the dynamic aspects of the return-volume relationship. The contributions of this paper consist in: - Intraday analysis of the relationship between asset returns and trading volumes;

- Focus on Korean financial market;

- Compare the differences in the relationship return-volume between two markets: KOSPI 200 spot and index futures market;

- Use of quantile regression method (QRM) to examine the relationship between trading volumes and the distribution (e.g. the quantiles) of returns.

The research question was already explored in previous literature, therefore the novelty of the paper consists in the dataset and the comparison between two markets. Indeed, it helps to understand the Korean financial markets and it explains the differences between spot and futures markets. The results are in line with previous studies of return-volume relationship.

Author’s response: According to this comment, we have emphasized distinctions of this study from the previous studies in the introduction as follows.

“Extensive theoretical and empirical analyses are collectively conducted across many studies, but each of them have some individual limitations. First, although many studies examine Granger non-causality in the conditional mean and/or variance, this property need not hold for other aspects of the model, including the probability distribution. For instance, Diks and Panchenko (2005) point out that Hiemstra and Jones’ (1994) test may not accurately test Granger non-causality. Therefore, it is necessary to directly examine the relationship between trading volume and the distribution of returns. Second, when derivatives markets exist, they should be considered as alternative means for trading the underlying assets. Specifically, given that market friction related to shorting assets may cause a negative price-volume relationship, the opportunities provided by derivatives markets to take short positions can affect the price-volume relationship. As mentioned by Kocagil and Shachmurove (1998), if the price-volume relationship in the spot market is affected by market frictions regarding short sales, then derivatives markets, in which taking short positions is less costly (Ryu, 2013; Sim, Ryu, & Yang, 2016), must be taken into account to more clearly and thoroughly analyze the effect of short sale restrictions on the price-volume relationship. In addition, the ratio of informed investors in the derivatives market to those in the stock market may be different, suggesting that trading volumes in two markets would also be differently associate with the distribution of returns. Finally, although the relationship between the realized return variance and the trading activity is examined in many related studies (Foucault, Sraer, & Thesmar, 2011; Valenzuela, Zer, Fryzlewicz, & Rheinländer, 2015), the relationship between the option-implied variance, or volatility, and the volume has drawn less attention. Given that the option-implied volatility is an ex-ante expectation of future price fluctuations and is reported to provide information for return forecasting (Giot 2005; Jiang & Tian, 2005; Han, Guo, Ryu, & Webb, 2012; Song, Ryu, & Webb, 2016, 2018), if the trading volume affects the distribution of returns, it should consistently and significantly affect the option-implied volatility as well. Further, since investors in the option market can choose one among the various options with different strike prices suitable for their intentions, volatilities implied in different moneyness categories also reflect different intentions. It means that examining the relationships between trading volume and various implied volatilities can offer a key to understanding the impact of trading volume on the distribution of returns.”

Comment 3. Is the analysis correct?

They use the quantile regression method (QRM) to examine the relationship between trading volumes and the distribution (e.g. the quantiles) of returns rather than conditional mean of returns. It is an appropriate methodology to study variables with heterogeneous distributions and when the relationship among variables is asymmetric. The empirical analysis is well explained and documented. They separate the analysis in two main blocks: return-volume relationship and impact on implied volatility. The results are in line with previous studies of return-volume relationship and provide meaningful implications.

Author’s response: The methodology we use, the QRM, allows us to examine the effect of independent variables on the distribution rather than the conditional mean of dependent variables. We appreciate this comment that emphasize the importance of our methodology.

Investors may participate in the stock market with a wide variety of intentions. For example, if uncertainty in the stock price increases, and, consequentially, there are more disagreements, it could cause more frequent transactions. On the other hand, the abundant liquidity in the market can be one reason of active trading. Further, when transaction costs are low due to this abundant liquidity, informed traders are more likely to exploit their information advantage. However, regardless of the scenarios, trading volume can be increased by both positive and negative information. Therefore, on average, the influence of trading volume on stock returns may be ambiguous. Instead, it would widen the distribution of stock returns. In this way, previous studies have consistently argued that trading volumes are closely associated with the volatility rather than the level of returns. Therefore, to investigate the effect of trading volumes on returns, we should examine the relationship between trading volumes and the distribution of returns rather than that between trading volumes and the conditional mean of returns. We have reflected this in the main text of Section 3.

“Investors may participate in the stock market with a wide variety of intentions. For example, if uncertainty in the stock price increases, and, consequentially, there are more disagreements, it could cause more frequent transactions. On the other hand, the abundant liquidity in the market can be one reason of active trading. Further, when transaction costs are low due to this abundant liquidity, informed traders are more likely to exploit their information advantage. However, regardless of the scenarios, trading volume can be increased by both positive and negative information. Therefore, on average, the influence of trading volume on stock returns may be ambiguous. Instead, it would widen the distribution of stock returns.”

This paper investigate the important return-volume dynamics based on the quantile regression approach by analyzing the high-frequency dataset. The empirical results are clean and convey notable implications and interpretations.

This paper explores the return volatility approach for KOSPI 200 index futures, spot and options using a quantile regression approach. The paper is motivated by the identification of an asymmetry in the literature as it pertains to the distribution of returns, market frictions and limited analysis of option implied volatility. ...[more]

... The paper reports a number of findings and suggests that difference across the products pertain to differences in constraints (short selling) and informativeness.

I raise a few questions for consideration:

1. Assuming that Table 2 quantile relates to returns, Panel A examines returns in the KOSPI spot and concludes the results are distinct from Panel B which assess futures returns in that volume have a long run impact (significance at 5, 10 and 15) but that in Panel A it is the short run. Results for 5 and 15 are significant, the authors should perhaps seek to explain why volumes in 10min are not significant. Suggest utilising snapshots other than 5mins to test robustness, otherwise, modify conclusions. Also perhaps clarify labelling, lsf in first row??

2. The paper refers to spot, can you please clearly identify if this is an ETF or the individual security total volumes. If it is the volume of individual stocks how do the authors control for differences in intraday patterns between small and large-cap stocks and nonsynchronous trading?

3. It would be interesting to test the return number of transactions relation identified Jones et al (1994) RFS.

4. Discussion of results for OIV, also argue for long-run effects but only 10 and 15min volumes are significant in ATM, 5-min are not. Again, would suggest testing with different time intervals and also the inclusion of the contemporaneous volume.

Author Answers to the Second Referee Report

Paper: Differences in the intraday return-volume relationship of spots and futures: A quantile regression approach

Authors: Jaeram Lee, Geul Lee, Doojin Ryu

Thank you very much for giving us the chance of revision and potentially publishing our work to this journal, ...[more]

... the Economics. We answer for the comments of the referee 2 and will revise our paper if the editor decide the official Revise and Resubmit decision. We believe that this paper has a potential and clearly contributes to the existing literature. After the editor’s decision, we will heavily revise this paper for the publication and improve the quality of this paper. Our answers for the second referee report are as follows.

Referee 2’s Summary

This paper explores the return volatility approach for KOSPI 200 index futures, spot and options using a quantile regression approach. The paper is motivated by the identification of an asymmetry in the literature as it pertains to the distribution of returns, market frictions and limited analysis of option implied volatility. The paper reports a number of findings and suggests that difference across the products pertain to differences in constraints (short selling) and informativeness. I raise a few questions for consideration:

Referee 2’s Comment 1

Assuming that Table 2 quantile relates to returns, Panel A examines returns in the KOSPI spot and concludes the results are distinct from Panel B which assess futures returns in that volume have a long run impact (significance at 5, 10 and 15) but that in Panel A it is the short run. Results for 5 and 15 are significant, the authors should perhaps seek to explain why volumes in 10min are not significant. Suggest utilising snapshots other than 5mins to test robustness, otherwise, modify conclusions. Also perhaps clarify labelling, lsf in first row??

Our Answer

In our models, we control the effect of the lagged returns and the lagged squared returns. Also, there is a very strong positive relation between lagged squared returns and the lagged spot trading volume. In addition, there is the strong autocorrelation of the spot trading volume. It may cause the significant estimated coefficient of the spot trading volume in 15 minutes. We will try to check those effects and the results with other time intervals than 5-minutes. The label in the first row is misleading, because the estimated coefficients in Panels B and C are not for the spot trading volume. Also, there is a similar problem in Table 3. We adjust labels and footnote in Tables 2 and 3.

Referee 2’s Comment 2

The paper refers to spot, can you please clearly identify if this is an ETF or the individual security total volumes. If it is the volume of individual stocks how do the authors control for differences in intraday patterns between small and large-cap stocks and nonsynchronous trading?

Our Answer

The spot trading volume in this paper, lsv, is the sum of the number of shares traded for all individual stocks. It is difficult to directly control for trading patterns between small and large-cap stocks and nonsynchronous trading because of limitation of dataset, but we will try to solve those problems. Actually, most of the previous studies which considered the stock market trading volume and market returns such as Campbell, Grossman, and Wang (1993, QJE) use the number of traded shares as the aggregate market trading volume. Also, when we use trading value instead of trading volume to consider the size difference in stocks, we check that the empirical result is almost the same as the result for the trading volume.

Referee 2’s Comment 3

It would be interesting to test the return number of transactions relation identified Jones et al (1994) RFS.

Our Answer

Jones et al. (1994, RFS) separated trading volume into the trade size and the number of transactions. Then, they showed that the number of transactions is important to predict return volatility rather than the trade size. Unfortunately, we do not have the specific number of transactions for the stock market. We try to consider different aspects of the trading volume.

Referee 2’s Comment 4

Discussion of results for OIV, also argue for long-run effects but only 10 and 15min volumes are significant in ATM, 5-min are not. Again, would suggest testing with different time intervals and also the inclusion of the contemporaneous volume.

Our Answer

We would try to check the results with other time intervals than 5-minutes. When we include the contemporaneous trading volume, the regression result is similar to the current result although there is a strong negative relationship between the contemporaneous trading volume and changes in the implied volatility.

For your convenience and reference, we attach our answers for the first referee’s comments.

Response to the Referee Report 1

Paper: Differences in the intraday return-volume relationship of spots and futures : A quantile regression approach

Authors: Jaeram Lee, Geul Lee, Doojin Ryu

Thank you very much for giving us the chance of revision and potentially publishing our work to this journal, the Economics. We answer for the comments of the referee and reflect the comments in the revised paper. We believe that this paper has a potential and clearly contributes to the existing literature. After both referees’ review are completed, we will heavily revise this paper for the publication and improve the quality of this paper. Our answers for the first referee report are as follows.

Comment 1. Summary of the paper

In this paper, the authors study the intraday relationship between asset returns and trading volumes in the market index KOSPI 200 spot and index futures markets, which is highly liquid and with active investor participation. Previous literature have endorsed the relationship between trading volumes and volatility, rather than the level of returns. They employ the quantile regression method (QRM), which is an extended version of OLS to address the relationship between trading volumes and the distribution of returns. QRM is used with a variable with heterogeneous distributions. The dataset, which goes from the 3rd of January 2005 until 30th of June 2014, consists of five-minutes observations of the KOSPI 200 index, trading volumes of KOSPI200 futures, and the implied volatilities constructed from the KOSPI 200 options prices. They run a set of quantile regressions, which are composed by four main variables: (i) the dependent variable, r, is the percentage return of the KOSPI 200 spot index over each five-minute period; (ii) as independent variable, the natural logarithms of the KOSPI 200 spot trading volumes indicated by lsv; (iii) as independent variable, the natural logarithms of the KOSPI 200 futures trading volumes indicated by lfv; (iv) div which measures the first difference of the implied volatility of KOSPI 200 index options. The main results show that the distribution of returns widens following active trading in the spot market. Moreover, the findings indicate a positive relationship between the return volatility and futures transactions. They find that the duration of the return-volume relationship differs for spot and futures trading. Indeed, the positive effect of the spot volume on the return volatility may disappear within five minutes since the relationship between return and volumes in the spot market can be attributable to disagreement rather than market information. On the contrary, the positive relationship between futures trading volumes and the magnitude of stock index movements persist over time.

Author’s response: We appreciate you suggesting the clear and detailed summary. Based on this summary and other comments, we reconstructed the introduction and the conclusion to more clearly show the results of this study.

“This study investigates the intraday relationship between returns and trading volumes of stocks and index futures. We perform quantile regressions of spot returns on the stock and futures trading volumes to identify the effect of trading volumes on the return distribution. Our empirical results suggest that both stock and futures volumes extend the distribution of spot returns but that these effects persist for different durations. The effect of stock trading volumes on returns disappears within five minutes, whereas futures trading volumes have a significant influence even after fifteen minutes. When we consider contemporaneous trading volumes, the distribution of returns temporarily widens due to a large contemporaneous stock volume but returns to its original level in fifteen minutes, whereas the effect of a large futures trading volume remains over time. The finding of a short-term effect of the stock trading volume but a long-term effect of the futures trading volume is consistently supported by the results for the option-implied volatility. Only the futures trading volume is significantly and positively related to the implied volatility in the options market. However, an increase in the stock trading volume precedes an increase in the implied volatility of ATM options, which can be traded quickly and is an effective hedging tool. In contrast, the futures trading volume is closely associated with the implied volatility of OTM options, which offer high leverage and are, therefore, favorable for informed trading. Our findings suggest that the return-volume relationship differs significantly for the stock and futures trading volumes. Specifically, the return-volume relationship for stock trading is mainly attributable to disagreements, whereas futures contracts may be a tool for informed trading.”

Comment 2. Is the contribution of the paper potentially significant?

Other empirical papers study the contemporaneous return-volume relationship, the return variance – volume relationship and the dynamic aspects of the return-volume relationship. The contributions of this paper consist in: - Intraday analysis of the relationship between asset returns and trading volumes;

- Focus on Korean financial market;

- Compare the differences in the relationship return-volume between two markets: KOSPI 200 spot and index futures market;

- Use of quantile regression method (QRM) to examine the relationship between trading volumes and the distribution (e.g. the quantiles) of returns.

The research question was already explored in previous literature, therefore the novelty of the paper consists in the dataset and the comparison between two markets. Indeed, it helps to understand the Korean financial markets and it explains the differences between spot and futures markets. The results are in line with previous studies of return-volume relationship.

Author’s response: According to this comment, we have emphasized distinctions of this study from the previous studies in the introduction as follows.

“Extensive theoretical and empirical analyses are collectively conducted across many studies, but each of them have some individual limitations. First, although many studies examine Granger non-causality in the conditional mean and/or variance, this property need not hold for other aspects of the model, including the probability distribution. For instance, Diks and Panchenko (2005) point out that Hiemstra and Jones’ (1994) test may not accurately test Granger non-causality. Therefore, it is necessary to directly examine the relationship between trading volume and the distribution of returns. Second, when derivatives markets exist, they should be considered as alternative means for trading the underlying assets. Specifically, given that market friction related to shorting assets may cause a negative price-volume relationship, the opportunities provided by derivatives markets to take short positions can affect the price-volume relationship. As mentioned by Kocagil and Shachmurove (1998), if the price-volume relationship in the spot market is affected by market frictions regarding short sales, then derivatives markets, in which taking short positions is less costly (Ryu, 2013; Sim, Ryu, & Yang, 2016), must be taken into account to more clearly and thoroughly analyze the effect of short sale restrictions on the price-volume relationship. In addition, the ratio of informed investors in the derivatives market to those in the stock market may be different, suggesting that trading volumes in two markets would also be differently associate with the distribution of returns. Finally, although the relationship between the realized return variance and the trading activity is examined in many related studies (Foucault, Sraer, & Thesmar, 2011; Valenzuela, Zer, Fryzlewicz, & Rheinländer, 2015), the relationship between the option-implied variance, or volatility, and the volume has drawn less attention. Given that the option-implied volatility is an ex-ante expectation of future price fluctuations and is reported to provide information for return forecasting (Giot 2005; Jiang & Tian, 2005; Han, Guo, Ryu, & Webb, 2012; Song, Ryu, & Webb, 2016, 2018), if the trading volume affects the distribution of returns, it should consistently and significantly affect the option-implied volatility as well. Further, since investors in the option market can choose one among the various options with different strike prices suitable for their intentions, volatilities implied in different moneyness categories also reflect different intentions. It means that examining the relationships between trading volume and various implied volatilities can offer a key to understanding the impact of trading volume on the distribution of returns.”

Comment 3. Is the analysis correct?

They use the quantile regression method (QRM) to examine the relationship between trading volumes and the distribution (e.g. the quantiles) of returns rather than conditional mean of returns. It is an appropriate methodology to study variables with heterogeneous distributions and when the relationship among variables is asymmetric. The empirical analysis is well explained and documented. They separate the analysis in two main blocks: return-volume relationship and impact on implied volatility. The results are in line with previous studies of return-volume relationship and provide meaningful implications.

Author’s response: The methodology we use, the QRM, allows us to examine the effect of independent variables on the distribution rather than the conditional mean of dependent variables. We appreciate this comment that emphasize the importance of our methodology.

Investors may participate in the stock market with a wide variety of intentions. For example, if uncertainty in the stock price increases, and, consequentially, there are more disagreements, it could cause more frequent transactions. On the other hand, the abundant liquidity in the market can be one reason of active trading. Further, when transaction costs are low due to this abundant liquidity, informed traders are more likely to exploit their information advantage. However, regardless of the scenarios, trading volume can be increased by both positive and negative information. Therefore, on average, the influence of trading volume on stock returns may be ambiguous. Instead, it would widen the distribution of stock returns. In this way, previous studies have consistently argued that trading volumes are closely associated with the volatility rather than the level of returns. Therefore, to investigate the effect of trading volumes on returns, we should examine the relationship between trading volumes and the distribution of returns rather than that between trading volumes and the conditional mean of returns. We have reflected this in the main text of Section 3.

“Investors may participate in the stock market with a wide variety of intentions. For example, if uncertainty in the stock price increases, and, consequentially, there are more disagreements, it could cause more frequent transactions. On the other hand, the abundant liquidity in the market can be one reason of active trading. Further, when transaction costs are low due to this abundant liquidity, informed traders are more likely to exploit their information advantage. However, regardless of the scenarios, trading volume can be increased by both positive and negative information. Therefore, on average, the influence of trading volume on stock returns may be ambiguous. Instead, it would widen the distribution of stock returns.”