Chapter III. The Relationships between Futures Returns, Futures Volume, and Spot
3. Data and Preliminary Analysis
4.3 VAR Results
arbitrage-based transaction and I exclude it from the sample. The regression results are shown in Appendix A, Tables A3 and A4.
After purging the effect of arbitrage, the new regression results show no conclusive change. The patterns reported in Tables A3 and A4 are quite similar to those in Tables 3.4 and 3.5, which confirm the robustness of my conclusions.
4.3 VAR Results
In the final analysis, I augment the VAR model presented by equations (2) to (4).
I put the net open buy of the various trader classes into the model:
All the notations have the same definitions as previously stated.
The spot returns have a high degree of contemporaneous correlation with the futures returns. The correlation coefficient reaches 0.838. Hence, two additional VAR models are constructed to check robustness. One is to exclude the futures returns, and the other is to exclude the spot returns from the model. I only point out the important
3 3 3
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differences, and do not report the detailed results of the two VAR models.7
The results of the augmented VAR parameter estimation are shown in Table 3.6.
The estimation of equation (7) shows that both the lag-one to lag-three TX returns (coefficients 0.3685, 0.1054, and 0.039, respectively) and the lag-two net open buy of foreign institutional traders (coefficient 0.0081) have significantly positive correlation with the TAIEX returns. The coefficients of lag net open buys of futures dealers, domestic institutional traders, and individual trader are either insignificant or negative.
These again confirm that, while futures returns and the net open buy of foreign institutional traders carry information about spot returns, the other three trader classes do not.
[Insert Table 3.6]
The estimation of equation (8) shows the lag-two coefficient (0.0421) of the spot returns appears to be significantly positively correlated with the TX returns. This implies the spot returns also informationally lead the futures returns. As a result, both the TX and the spot returns have predictive power for each other, and take on an asymmetrical feedback relationship. The effect the futures returns have in leading the spot returns is stronger than the inverse leading relationship. In addition, the lag-two net open buy of foreign institutional traders appears to be significantly positively correlated with the futures returns (coefficient 0.0147). The coefficient of lag-two net open buy of futures dealers is also positive and marginal significant (coefficient 0.0059), but its magnitude is canceled out by the negative coefficients. That is, the foreign institutional traders are still the only class whose trades have information content relating to the futures returns.
The estimation result of equation (9) shows that the spot returns (the futures
7 The tables are provided in Appendix A, Tables A5 and A6.
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returns) positively (negatively) lead the net open buy of the foreign institutional traders. The coefficients are all statistically significant at the 1% level. When the spot returns or the futures returns are excluded from the model, only the coefficient of lag-one TX returns on foreign institutional traders’ net open buy is significant negative. When the futures returns are excluded from the model, only the coefficient of the lag-three spot returns is significantly positive. Neither of the other two lag coefficients is significant. The results are consistent with Table 3.4 and Panel A of Table 3.5.
The estimation result of equation (10) shows that the lag-one to lag-three spot returns are negatively correlated with the net open buy of the futures dealers (coefficients -0.2664, -0.1508, and -0.1768, respectively). The lag-one and lag-two coefficients of the futures returns, on the other hand, are significantly positively correlated with the net open buy of the futures dealers (coefficients 0.6825 and 0.106, respectively). When the spot returns are excluded from the model, the coefficient of the lag-one futures returns is significantly positive but the coefficient of lag-three futures returns is significantly negative. Because the positive coefficient is larger than the negative, the conclusion is unchanged. Similarly, when the futures returns are excluded from the model, the coefficient of the lag-one spot returns is positive (0.3574) and reaches the 1% significance level. The coefficient of the lag-three spot returns is negative and is also significant at the 1% level (coefficients 0.1591).
Because the positive coefficient is greater than the negative, the futures dealers’ net open buy informationally lags behind both the spot and futures returns.
The estimation of equation (11) shows that the lag-one coefficient of the spot returns is significantly positive (0.1718). When I exclude the futures returns from the model, the result is unchanged. When I exclude the spot returns from the model, the coefficient of lag-two TX returns becomes significantly positive. This indicates the
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net open buy of domestic institutional traders lags behind both spot and futures returns.
The estimation of equation (12) shows that the lag-one and lag-three spot returns are significantly negatively correlated with the net open buy of individual traders (coefficient -0.3405 and -0.1247). On the other hand, the lag-one to lag-three TX returns are significantly positively correlated with the net open buy of individual traders (coefficient 0.2258, 0.182 and 0.1308, respectively). When the spot returns are excluded from the model, the coefficient of the lag-two futures returns is significantly positive. When the futures returns are excluded from the model, the coefficient of the lag-one spot returns is still significantly negative, and the lag-two coefficient becomes significantly positive. The magnitude of these two coefficients is almost identical. These results show that the net open buy of the individual traders is less informative of futures returns.
In addition to the relationship between the TAIEX index returns, TX returns and the net open buy of the four TX trader classes, further insights are contained in Table 3.6. To begin with, it is useful to observe the interaction between the different classes of traders. Because the net open buy of each trader class is affected by its own past behaviors, the persistence of the behavior exists over time. Besides, each trader class also interacts with the other classes to some degree. However, the direction of these interactions is complex. I only present the results that have relatively clear direction.
First, the lag-one and lag-three net open buy of the individual traders is positively correlated with that of the futures dealers (coefficients 0.0510 and 0.0252).
Symmetrically, the lag-one and lag-three net open buy of the futures dealers is also positively correlated with that of the individual traders (coefficients 0.0340 and 0.0424). This shows that the trading behavior between the two groups appears to be a feedback relation. Second, domestic institutional traders have only minimal
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interaction with the other groups. Especially, their trading activity seems to exert no influence on those of the other groups.
In the unreported results,8 I conducted separate Granger tests for each of the three VAR models (the augmented VAR, the VAR excluding spot returns, and the VAR excluding the futures returns). The results fully confirm the above conclusions.
Thus far, I have explained my empirical results by focusing on the information-based effect. However, other perspectives such as trading strategies may also partly interpret our results. For example, Table 3.6 shows that the lags of TX returns are negatively related to the net open buy of foreign institutional traders and positively related to the net open buys of the other three trader classes. This suggests that foreign institutional traders may adopt contrarian strategies, whereas the other three classes of traders may adopt momentum strategies. These findings are not totally consistent with those of Lin et al. (2008) which found that foreign institutional traders and dealers (both futures and securities dealers) are positive feedback traders and individual traders are contrarians. The possible reasons may have two. First, while we use intraday net open buy as a proxy for trading activity, their proxy is daily net buy volume. Second, our sample period is from April 2004 to July 2008, but theirs is from January 2001 to December 2002.
In summary, the main conclusions of this section are as follows. After classifying the futures traders, the futures returns still strongly lead the spot returns, although this relationship is not unidirectional. The spot returns also lead the futures returns, but with a weak significance. This suggests an asymmetric feedback relationship. The net open buy of foreign institutional traders is the only trade to inform changes in both the futures and spot prices. This information effect is one-way in the futures market, but a
8 The results are provided in Appendix A, Tables A7 to A9.
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two-way feedback relationship in the spot market. The net open buys of the futures dealers, domestic institutional traders, and the individual traders have no directionally predictive power for both futures and spot prices.
5. Conclusions
This study uses a unique dataset to explore the intraday information-based relation between the futures market and the spot market. I examine the lead-lag relationship between the TX returns, TX net open buy, and TAIEX returns in the overall market. Also, I categorize the futures traders into foreign institutional traders, futures dealers, domestic institutional traders, and individual traders. Following this, I conduct a detailed analysis of whether the trades of the four trader classes contain different information for the spot and futures markets.
For the overall market, the results indicate that the futures market leads the spot market. However, this leading relationship of futures market is only reflected in futures returns, and not in the overall futures trading activity. When the different sources of trading are not distinguished, observing the overall TX net open buy has no informationally leading effect for either futures prices or spot prices.
After dividing the futures traders into four classes, the TX returns still lead the TAIEX returns. The leading relationship is an asymmetric feedback relationship. That is, the TX returns strongly lead the TAIEX returns, and the TAIEX returns weakly lead the TX returns. In addition, the net open buy of foreign institutional traders have directionally predictive power for both the TX returns and the TAIEX returns. The net open buy of the foreign institutional traders has a one-way leading relationship with the TX returns, but a two-way feedback relationship with the TAIEX returns. The net open buy of the futures dealers, domestic institutional traders, and the individual traders all lag behind the futures and spot returns.
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In sum, this paper reveals that informed traders do choose to trade in the futures market. In particular, foreign institutional traders tend to be the informed traders.
However, due to the low market share foreign institutional traders have in the futures market (less than 8%), the leading relation is difficult to be discerned from the overall market trading activity. This implies that analyses based on overall market trading volume may produce inaccurate results.
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Table 3.1: Summary statistics of the TX transactions
This table reports the summary statistics of the TX trading activity. The transactions are divided into open buy, open sell, close buy, and close sell. The traders are categorized as foreign institutional traders, futures dealers, domestic institutional traders, and individual traders. The statistics in Panel A represent the market share in terms of trading volume for each trader class according to the different transaction types. Panel B shows the average 30-minutes volume traded by each trader class according to the different transaction types.
The statistics in Panel C show that, during the sample period, the average trading frequency of each trader class according to the different transaction types within a 30-minute interval.
Open buy Open sell Close buy Close sell Panel A: Market share (%)
All 27.71 25.36 22.28 24.65
Foreign institutional traders 1.92 2.20 1.85 1.51
Futures dealers 4.73 4.40 4.76 4.95
Domestic institutional traders 0.43 0.88 1.13 0.36 Individual traders 20.62 17.89 14.54 17.83 Panel B: Average volume (30 minutes)
All 1,990 1,842 1,575 1,724
Foreign institutional traders 133 154 130 106
Futures dealers 335 311 339 352
Domestic institutional traders 31 63 82 24 Individual traders 1,492 1,314 1,024 1,242 Panel C: Average frequency (30 minutes)
All 1,019 899 788 890
Foreign institutional traders 49 53 50 40
Futures dealers 135 123 143 147
Domestic institutional traders 11 25 36 9
Individual traders 823 699 559 695
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Table 3.2: Autocorrelations of the spot returns and futures returns
This table shows series correlations of the TAIEX and TX returns. Rs,t represents the 30-minute TAIEX returns. Rf,t represents the 30-minute TX returns. AC represents autocorrelation. t-stat. represents the t-statistic. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively.
Lag
Rs,t Rf,t
AC t-stat. AC t-stat.
1 0.041 (4.08)*** 0.069 (7.52)***
2 0.023 (2.21)** 0.019 (2.08)**
3 0.024 (2.31)** 0.007 (0.80)
4 -0.026 (-2.56)** -0.011 (-1.22)
5 0.023 (2.29)** 0.006 (0.61)
6 0.032 (3.13)** 0.007 (0.73)
7 0.023 (2.23)** 0.019 (2.05)**
8 -0.006 (-0.62) 0.023 (2.48)**
9 -0.045 (-4.36)*** 0.008 (0.82) 10 -0.018 (-1.77)* 0.003 (0.31) 11 -0.007 (-0.68) -0.046 (-4.94)***
12 -0.002 (-0.22) -0.025 (-2.66)***
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Table 3.3: Regression results of the spot returns on the futures returns and net open buy
This table presents the estimated parameters of the regression and the t-statistic. The regression model is:
Rs,t represents the 30-minute TAIEX returns. Rf,t represents the 30-minute TAIEX returns.
NBf,t represents the 30-minute net open buy of the TX. et is the residuals. Model 1 regresses the TAIEX returns on the TX returns. Model 2 regresses the TAIEX returns on the TX net open buy. Model 3 regresses the TAIEX returns on both the TX returns and the TX net open buy. Estimates for the intercepts are not reported in this table. t-statistics are presented in parentheses. The Adj. R2 in the table represents the adjusted R-square. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively.
Model 1 Model 2 Model 3
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Table 3.4: Regression results of the spot returns on the net open buy of the four trader classes
This table presents the t-statistic of the parameter estimation of the regression and the estimated parameters from regressing the TAIEX returns on the net open buy of the four trader classes. Panel A uses one of the four trader classes to perform the regressions. Panel B uses the net open buy of four trader classes in the same regression to conduct the parameter estimation. Rs,t represents the 30-minute TAIEX returns. NBj,t represents the 30-minute net open buy of the trader class j in the futures market. FI, D, DI, and I represent the foreign institutional traders, the futures dealers, the domestic institutional traders, and the individual traders, respectively. Estimates for the intercepts are not reported in this table. t-statistics are presented in parentheses. The Adj. R2 in the table represents the adjusted R-square. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively.
j=FI j=D j=DI j=I
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Table 3.5: Regression results of the TX returns on the net open buy of the four trader classes
This table presents the t-statistic of the parameter estimation of the regression and the estimated parameters from regressing the TX returns on the net open buy of the four trader classes. Panel A uses one of the four trader classes to perform the regressions. Panel B uses the net open buy of four trader classes in the same regression to conduct the parameter estimation. Rf,t represents the 30-minute TX returns. NBj,t represents the 30-minute net open buy of the trader class j in the futures market. FI, D, DI, and I represent the foreign institutional traders, the futures dealers, the domestic institutional traders, and the individual traders, respectively. Estimates for the intercepts are not reported in this table. t-statistics are presented in parentheses. The Adj. R2 in the table represents the adjusted R-square. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively.
j=FI j=D j=DI j=I
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Table 3.6: Vector autoregression (VAR) results
This table presents the estimated parameters and the t-statistic of vector autoregression (VAR). The model is:3 3 3 3 3 3
Rs,t represents the 30-minute TAIEX returns. Rf,t represents the 30-minute TX returns. NBFI,t, NBD,t, NBDI,t, and NBI,t represent the 30-minute TX net open buy of the foreign institutional traders, the futures dealers, the domestic institutional traders, and the individual traders, respectively. Estimates for the intercepts are not reported in this table. t-statistics are presented in parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively.
Rs,t Rf,t NBFI,t NBD,t NBDI,t NBI,t
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Appendix A
Table A1: Unit root tests
This table presents the results of the augmented Dickey-Fuller unit root tests using the following equation:
3
1 1
t t i i t i t
x x
x
e
is the differencing operator. xt is one of the following variables: the TX returns (Rf,t), TAIEX returns (Rs,t), overall net open buy (NBf,t), net open buy of foreign institutional traders (NBFI,t), net open buy of futures dealers (NBD,t), net open buy of domestic institutional traders (NBDI,t), net open buy of individual traders (NBI,t). Only the coefficient
is reported in this table. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively.Estimated parameter (
) t-statisticsRf,t-1 -0.9150*** (-53.26)
Rs,t-1 -0.9441*** (-48.70)
NBf,t-1 -0.3121*** (-32.10)
NBFI,t-1 -0.4767*** (-39.66)
NBD,t-1 -0.3488*** (-34.05)
NBDI,t-1 -0.4906*** (-38.53)
NBI,t-1 -0.3305*** (-32.58)
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Table A2: VAR results – unclassified data
This table presents the estimated parameters and the t-statistic of vector autoregression (VAR).
The model is:
Rs,t represents the 30-minute TAIEX returns. Rf,t represents the 30-minute TX returns. NBf,t
represent the 30-minute overall TX net open buy. Estimates for the intercepts are not reported in this table. t-statistics are presented in parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively.
Rs,t Rf,t NBf,t
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Table A3: Robustness check of Table 3.4
This table presents the t-statistic of the parameter estimation of the regression and the estimated parameters from regressing the TAIEX returns on the net open buy of the four trader classes. If a trader trade TF (or TE) and TX at the same day, then the transaction is excluded from the sample. Panel A uses one of the four trader classes to perform the regressions. Panel B uses the net open buy of four trader classes in the same regression to conduct the parameter estimation. Rs,t represents the 30-minute TAIEX returns. NBj,t
represents the 30-minute net open buy of the trader class j in the futures market. FI, D, DI, and I represent the foreign institutional traders, the futures dealers, the domestic institutional traders, and the individual traders, respectively. Estimates for the intercepts are not reported in this table. t-statistics are presented in parentheses. The Adj. R2 in the table represents the adjusted R-square. ***, **, and * indicate significance at the 1%, 5%, and 10% level,
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Table A4: Robustness check of Table 3.5
This table presents the t-statistic of the parameter estimation of the regression and the estimated parameters from regressing the TX returns on the net open buy of the four trader classes. If a trader trade TF (or TE) and TX at the same day, then the transaction is excluded
from the sample. Panel A uses one of the four trader classes to perform the regressions.
Panel B uses the net open buy of four trader classes in the same regression to conduct the parameter estimation. Rf,t represents the 30-minute TX returns. NBj,t represents the 30-minute net open buy of the trader class j in the futures market. FI, D, DI, and I represent the foreign institutional traders, the futures dealers, the domestic institutional traders, and the individual traders, respectively. Estimates for the intercepts are not reported in this table. t-statistics are presented in parentheses. The Adj. R2 in the table represents the adjusted R-square. ***, **, and
* indicate significance at the 1%, 5%, and 10% level, respectively.
j=FI j=D j=DI j=I
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Table A5: VAR results – excluding the futures returns
This table presents the estimated parameters and the t-statistic of vector autoregression (VAR). The model is:3 3 3 3 3
Rs,t represents the 30-minute TAIEX returns. NBFI,t, NBD,t, NBDI,t, and NBI,t represent the 30-minute TX net open buy of the foreign institutional traders, the futures dealers, the domestic institutional traders, and the individual traders, respectively. Estimates for the intercepts are not reported in this table. t-statistics are presented in parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively.
Rs,t NBFI,t NBD,t NBDI,t NBI,t
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Table A6: VAR results – excluding the spot returns
This table presents the estimated parameters and the t-statistic of vector autoregression (VAR). The model is:3 3 3 3 3
Rf,t represents the 30-minute TX returns. NBFI,t, NBD,t, NBDI,t, and NBI,t represent the 30-minute TX net open buy of the foreign institutional traders, the futures dealers, the domestic institutional traders, and the individual traders, respectively. Estimates for the intercepts are not reported in this table. t-statistics are presented in parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10% level, respectively.
Rf,t NBFI,t NBD,t NBDI,t NBI,t
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This table presents the Granger test of VAR model in Table 3.6.Dependent variable Null hypothesis Chi-square Rs,t δ1i =0, for i=1, 2, 3 445.82***
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Table A8: Granger test II
This table presents the Granger test of VAR model in Table A5.Dependent variable Null hypothesis Chi-square Rs,t η1i =0, for i=1, 2, 3 11.47***
μ1i =0, for i=1, 2, 3 1.86 π1i =0, for i=1, 2, 3 0.14 ω1i =0, for i=1, 2, 3 18.66***
η1i =μ1i =π1i =ω1i =0, for i=1, 2, 3 47.65***
NBFI,t γ2i =0, for i=1, 2, 3 8.87**
μ2i =0, for i=1, 2, 3 22.07***
π2i =0, for i=1, 2, 3 4.86 ω2i =0, for i=1, 2, 3 16.32***
γ2i =μ2i =π2i =ω2i =0, for i=1, 2, 3 47.10***
γ2i =μ2i =π2i =ω2i =0, for i=1, 2, 3 47.10***