Price discovery and information transmission across stock index futures: Evidence from VN 30 Index Futures on Vietnam’s stock market

This article aims to provide empirical evidences to show if futures trading plays the very important role of price discovery and information transmission for spot[r]

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Price discovery and information transmission across stock index futures: Evidence from VN 30 Index Futures on Vietnam’s stock market

Nguyễn Thị Nhunga1, Trần Thị Vân Anha, Nguyễn Tố Ngaa, Vương Thùy Linha

a Faculty of Finance and Banking – University of Economics and Business (UEB) – Vietnam National University (VNU) Abstract: The introduction of the first tradable stock index futures of VN 30 is a very good

signal showing that Vietnam is starting to have a high-level financial market, which brings many expectations about sustainable and safe development of stock market However, risk conerns of this type of derivative products have been raising with many claims since then This article aims to provide empirical evidences to show if futures trading plays the very important role of price discovery and information transmission for spot market Using daily data collected about VN30 Index Futures, VN30 Index, VN-Index from August 10, 2017 to February 28, 2019 that is divided into sub-periods (Increase/Decrease/Recovery), the research verifies VN30 Index Futures’ role of price discovery and information transmission by applying Vector Error Correction Model (VECM) Empirical findings show that there is a stable equilibrium relationship between the two series groups (including VN30 Index Futures, VN30 Index and VN30 Index Futures and VN-Index) during sub-periods or spot and futures markets are integrated and synchronized In particular, VN30 Index Futures’ price discovery and information transmission is clearly seen when the market falls or doesn’t change a lot Keywords: VN30 Index Futures, Price discovery, Information transmission, Spot Futures

Interlinkages, Vector Error Correction Model (VECM), Vietnam’s Derivative Market, Emerging Market

1 Introduction

In August 2017, Vietnam’s derivatives market officially operated with the first tradable index futures of VN 30 This event marked Vietnam as the 42nd country in the World and the 5th country in ASEAN (after Singapore, Malaysia, Indonesia and Thailand) having this high-level financial market VN 30 Index Futures is expected to limit risks and diversify investment products, increase the liquidity and scale of the stock market as well as help the stock market to grow stably and safe, thereby increase its attractiveness to the investors

After more than a year of introduction in Vietnam’s stock market, VN 30 Index Futures has experienced impressive achievements There has been a continuous upward trend in both trading volume and trading value According to the data reported by Ho Chi Minh Stock Exchange (HOSE) and Hanoi Stock Exchange (HNX), in 2018, this first product of derivative witnessed 19,697,764 negotiated contracts The average trading volume reached 78,791 contracts/session, nearly times higher than in 2017 The total value of transactions reached nearly 1.86 million billion VND in 2018, of which, July recorded an impressive number of 257,870 billion VND, 5.94 times higher than January (43,376 billion VND) Besides, the

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number of trading account experienced a great increase of 3.4 times higher than the end of 2017

However, many investors still doubt the role of VN 30 Index Futures, which is believed containing many speculative factors Vietnam’s derivative market is dominated by individual investors (up to 99%) (Nguyễn, 2019), which is shown by the huge number of transactions but most of them are short terms and immediately closed in the same trading session The volume of transactions used for hedging is only around 3-4 billion USD, which accounts for only approximately 2% of the spot market portfolio Moreover, when VN30 Index Futures experienced the boom in trading volume, the spot market witnessed a sharp decline since the peak of 1,200 points of VN-Index in 2018 This market shock raised an argument about consequences of index futures for price volatility on stock market Many people have described Index Futures as “weapons of mass destruction” when referring previous crisis like tulip crisis in Holland or financial crisis of 2007-2008, etc In particular, these concerns are raising day by day when Vietnam intends to continue implementing futures contracts on government bonds in the coming time – according to the roadmap for derivative market development until 2020

The above practice provides an interesting experimental setting to examine if futures trading resulted in discovering price and transferring information to the spot market or not In line with this objective, the research has assessment about the role of VN30 Index Futures after 1.5 years implemented in Vietnam’s stock market, through three distinct phases, including: increase, decrease and recovery To our best knowledge, this is the first paper using daily data to investigate price discovery and information transmission by applying Vector Error Correction Model (VECM), between the VN30 Index Futures and VN-Index as well as VN30 Index In particular, different methods are used and compared to each other to exactly estimate VN30 Index Futures’ roles The findings of the paper will contribute to the literature review on derivatives generally and index futures particularly in emerging countries like Vietnam as well as in different phases of market development (namely increase, decrease and recovery periods) Moreover, the contributions of the study are framed in providing empirical evidences showing if stock index futures play an important role for promoting stable development of spot market These important insights will be germane to propose more appropriate solutions for complete futures market development in Vietnam in the coming time

After Introduction, the second part will review literaturely about index futures and their role for stock market Methodology and data used will be presented in the 3rd part following with the results explanation in the 4th part and a discussion in 5th part The last part will provide some conclusions

2 Literature Review

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The futures contracts are designed with the original purpose to meet the hedging needs (Gong et al, 2016) Individuals or organizations participate in a futures contract to prevent risks and protect themselves against adverse fluctuations that may change the value of their assets or debts, ensure the stability of futures cash flows In addition to this initial purpose, futures contracts also become an appropriate tool for speculating purposes and arbitraging transactions as risk loving investors often prefer the futures market to the spot market (Lean et

al, 2015) With low transaction prices and high leverage (Antoniou et al, 2005; Chen and

Gau, 2010), investment in futures market is less expensive than trading goods or assets on the underlying spot market Therefore, the potential profitability of transactions in the futures market also promises much higher than participating in the spot market and thus attracting many investors In addition, the futures market provides an additional channel of capital mobilization for businesses and governments, facilitating the deployment of new financial products as well as increasing the shock resistance of the financial system (Chui, 2010) In the futures market's activities, the price discovery and information transmission mechanisms are especially important functions

The emergence of the stock index futures market has led many debates about the relationship between the spot and futures market (Aloui et al, 2017; Bohl et al, 2015) as well as whether its appearance affects the stability of the financial market (Kutan et al, 2018; Jian

et al, 2018) Aloui et al (2017) note that the relationship between the spot-futures markets is

different due to the difference in the levels of economic development, i.e the intensity of information transmission between stock indexes and the stock index futures in developed markets may be higher than in emerging markets or due to the level of market openness and trading volumes on futures markets among countries

According to Bohl et al (2015), previous researches on the impact of the introduction of futures market on the underlying spot market led to two conflict results Bohl et al (2015) indicated that the introduction of the futures market in developed financial markets reduces the volatility of the underlying market because market participants are mostly institutional investors, who are well-informed and knowledgeable enough to make appropriate decisions to invest However, in emerging markets such as China, the introduction of futures increases the volatility of the underlying market because there are many individual investors, who have less knowledge and tend to invest in herds The comments on the behavior of private and institutional investors made by Bohl et al (2015) are similar to the ones by Barber and Odean (2008), Kaniel et al (2008)

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contract price is not necessarily the spot price in the future, but it also reflects the price that a market participant can expect for a transaction to perform later instead of accepting uncertain spot prices in the future The futures market price discovery function cannot directly make futures spot price forecasts; however, it provides valuable lead information about futures spot prices (Kang et al, 2013)

The empirical results of price discovery effect i.e the lead-lag relationship between spot and futures markets are mixed and diverse Booth et al (1999) have argued that futures markets play an important price discovery role for spot markets because of low transaction costs, the ready availability of short positions, low margins, and rapid execution (Booth et al, 1999) Other researchers such as Hong et al (2017), Gong et al (2016), Antoniou et al (2005), Antoniou et al (1995), Nieto et al (1998), Tse (1995) also found that the futures market is a leader in price discovery In contrast Yang et al (2012), Judge and Reancharoen (2014) and Chen and Gau (2009) indicated the leading role of stock markets Many studies such as Jian et

al (2018), Kutan et al (2018), Charteris & Musazdiruma (2017), Kang et al (2013) argued that

there is bi-directional causal relationship between futures and spot markets

Regarding to relationship between the spot-futures market, the mechanism of information transmission is a matter of interest to many researchers According to Liu and An (2011) informationally linked markets refers to markets in which traded assets are fundamentally related to each other However, they also argued that although in those markets are interrelated, but they still have different information transmission mechanism due to different transaction costs, regulations, liquidities and other institutional factors.According to Ross's study (1989), the futures trading can increase information flow leading more volatility in spot market (Ross, 1989) This conclusion was also consistent with the results of the researches conducted by Aloui et al (2017), who investigated the dynamic link between stock indices and the stock index futures in 11 countries In most cases, transactions in the futures market are often more active than the underlying market so that information from this market is often more reliable than information on the spot market In addition, due to its lower trading cost the futures market attracts many investors so that new information being first created in the futures market before transferred to the spot market (Cox, 1976; Charteris and Masadziruma, 2017) Therefore, Cox (1976) concluded that futures transactions would speed up the transmission of information to spot markets This statement was also shared by other researchers such as Antoniou and Holmes (1995), Harris (1989), Chang et al (1999)

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Table 1: Impact of stock index futures’ introduction

Impact Research Methodology

Pr ice Disc ov er y P osit ive

Hong et al (2017) Error Correction Model (ECM) Gong et al (2016) Thermal optimal path method Antoniou et al (2005),

Antoniou & Homes (1995)

GARCH model

Nieto et al (1998) Johansen cointegration methodology

Tse (1995) Error correction model

Vector autoregressive method

Ne

ga

ti

ve

Yang et al (2012) GARCH model

Judge and Reancharoen (2014) Error correction model (ECM) Chen & Gau (2009) Microstructure Model Hasbrouck

(1995)

Ne

utra

l

Jian et al (2018) Multivariate CoVaR model Kutan et al (2018) Positive feedback model

GjR-Garch Model

Charteris & Musazdiruma (2017) GARCH model, EGARCH model

Kang et al (2013) Bivariate GARCH model

Liu & An (2011) MGARCH model

In for m at ion t ran smissi on P osit ive

Aloui et al (2017) Wavelet Methodology

Antoniou et al (2005) Antoniou & Holmes (1995)

GARCH model

Cheng et al (1999) Single factor returns generating model

Cox (1976) Efficient market model

Ne

ga

ti

ve Bohl et al (2015),

Bologna & Cavallo (2002)

GARCH, GJR-GARCH EGARCH models

Ne

utra

l

Kutan et al (2018) Positive feedback model GjR-GARCH Model Charteris & Musazdiruma (2017)

Spyrous (2005)

Baldauf & Santoni (1991)

GARCH model

Liu & An (2011) MGARCH model

Source: Authors

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Vietnam is a typical case showing the impact of futures market introduction on the spot underlying market The majority of market participants in Vietnam are small investors so that low transaction prices and high leverage make investment in futures market cheaper than investing in spot market, which have become an important reason for attracting investors Although the futures market in Vietnam has been in operation for only 1.5 years, it has clearly demonstrated the positive role of the price discovery function as well as supporting destabilization hypothesis This is also the general conclusion of many studies on the impact of futures market implementation in emerging countries Going back to the reality in Vietnam, while the futures market is continuously developing, there is a decline in the underlying market This has led to many concerns about the role of the futures market as a risk management tool for the stability of Vietnam's stock market Therefore, the goal of our research is to evaluate this issue comprehensively

3 Methodology

3.1 Research Design

In fact, VN30 Index is a market-capitalization weighted index which measures the performance of 30 large cap and high liquidity stocks from VN-All share It is expected to reflect truly the market movement Because of its effective performance benchmark, the research believes that it is necessary to refer VN-Index when evaluating the role of VN30 Index Futures That’s why, in line with objective of testing if futures trading resulted in destabilizing the spot market or not, the study investigates the relationship between VN30 Index Futures and VN30 Index as well as VN30 Index Futures and VN-Index

Besides, the spot-futures relationship separately focusses on price discovery and information transmission as indicated in Figure Based on above-mentioned literature review, the research chooses Vector Error Correction Model (VECM) to investigate price discovery and information transmission of VN30 Index Futures on Vietnam’s spot stock market In fact, Vector Error Correction Model allows estimating the short-run and long-run relationships between VN30 Index Futures and VN30 Index as well as VN30 Index Futures and VN-Index Vector Error Correction Model (VECM) is tested on EViews

3.2 Data description

Price Discovery and Information Transmission

(Vector Error Correction Model – VECM)

VN30 Index Futures

VN-Index

VN30 Index

Source: Authors

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In Vietnam, four VN30 Index Futures contracts with different expired dates are traded simultaneously at any given point The four-expired dates are correspondent to the third Thursday of the current month, the next month, and the subsequent two quarter-ending months Investors are required to pay an initial margin of 10% of the purchase price for securities For instance, an investor wants to purchase a contract VN30F1706 which is priced at 70.000.000 VND, he/she can enter into that position by depositing an initial margin requirement of 7.000.000 VND In terms of orders, there are limit order, market order, ATO and ATC In particular, Vietnam determines the price fluctuation range of 7%

The study uses daily close prices of VN30 Index Futures, VN30 Index and VN-Index The sample period spans August 10, 2017 to February 28, 2019 with 388 trading days The data is obtained from official sites of Ho Chi Minh Stock Exchange (HOSE) and Hanoi Stock Exchange (HNX) Figure shows the daily movements of VN30 Index Futures, VN30 Index and VN-Index over the sample period It is clearly seen that there are three distinct phases in the price patterns over period from August 10, 2017 to February 28, 2019 On April 10, 2018, VN-Index, VN30 Index and VN30 Index Futures reach a peak of 1,198.12, 1,168.06 and 1,185.18 accordingly, gaining about 60% of its value in comparison with the moment of launching VN30 Index Futures The next period from April 10 to July 11, 2018 is marked by a reduction of 25% in the stock market This is followed by an accumulation phase for recovery

Given this trend, the study will investigate price discovery and information transmission between the VN30 Index Futures and VN-Index as well as VN30 Index by dividing the sample period into three sub-periods, including: Period A: 10/08/2017 to 10/04/2018; Period B: 11/04/2018 to 11/07/2018 and Period C: 12/07/2018 to 28/02/2019 Table reports summary statistics for the stocgbk index and futures daily return series for each six months in the sample period (Panel A) and corresponding statistics for each of the three sub-periods in the sample period (Panel B) It is obviously seen that returns for VN30 Index Futures is closer to VN30 Index than VN-Index for all periods In particular, it is interesting to observe that the

600.00 800.00 1,000.00 1,200.00

8/10/2017 11/10/2017 2/10/2018 5/10/2018 8/10/2018 11/10/2018 2/10/2019

VN30 Index Future VN30 Index VN-Index

Source: HOSE and HNX

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index futures have the highest maximum returns for every six months as well as every sub-period

Table 2: Statistics of VN-Index, VN30 Index and VN30 Index Futures Return Series

Period Max (%) Average (%) Min (%) Standard Deviation (%) VN30 Index Futures VN30 Index VN-Index VN30 Index Futures VN30 Index VN-Index VN30 Index Futures VN30 Index VN-Index VN30 Index Futures VN30 Index VN-Index

Panel A: Every six months

10/08/2017-10/02/2018 3.93 2.78 2.86 0.25 0.23 0.21 -4.83 -5.08 -5.10 1.32 1.04 1.07

11/02/2018-11/08/2018 4.23 3.81 3.77 -0.05 -0.03 -0.02 -4.67 -4.45 -4.34 1.80 1.65 1.55

12/08/2018-28/02/2019 3.60 3.15 2.93 -0.03 -0.03 0.00 -4.98 -4.79 -4.84 1.11 1.06 1.01

Panel B: Sub-periods

10/08/2017

-10/04/2018 3.93 3.81 3.77 0.28 0.28 0.27 -4.83 -5.08 -5.10 1.31 1.07 1.10 11/04/2018-

11/07/2018 4.23 3.67 3.45 -0.47 -0.43 -0.45 -4.67 -4.45 -4.34 2.16 1.97 1.81 12/07/2018

-28/02/2019 3.60 3.15 2.93 0.03 0.02 0.05 -4.98 -4.79 -4.84 1.11 1.05 0.99

Source: Authors

3.3 Methods of Data Analysis

Firstly, the study tests each series for stationarity of VN30 Index Futures and VN30

Index as well as VN-Index by applying the unit root test to the residuals from this regression, called Augmented Dickey-Fuller Test

Call:



There are also three basic regression models as follows:

 No constant, no trend:

 Constant, no trend:  Constant and trend: There are two hypotheses:



is considered as coefficient in results extracted from EViews Software In other words, if t-Statistic is bigger than on Kendall’s tau table, the hypothesis is rejected and otherwise

In addition, the research tries to find out the regression between and as well as

and which is presented in following equations:

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The higher and is, the better the intercept and slope coefficients are In other words, this regression shows a significant relationship between the two variables

Secondly, the study also determines Optimal Lag by using the Akaike Selection

Criterion (AIC) In detail, the lag length is selected when this criterion has the smallest value, because it can make sure the stability of the model

Thirdly, the research tries to find out if the two series (VN30 Index Futures and VN30

Index as well as VN30 Index Futures and VN-Index) are co-integrated in each sub-period sample by using Johansen Co-integration Test with criteria, including maximal eigen value test and trace test There are two hypotheses:

 : No co-integrating equation between VN30 Index Futures and VN30 Index or between VN30 Index Futures and VN-Index

 : Co-integrating equation between VN30 Index Futures and VN30 Index or between VN30 Index Futures and VN-Index

The research will reject hypothesis if the value of the Trace and Max statistics is more than 5% critical value otherwise

Fourthly, based on the econometrics of co-integrated vector autogestions that Engle and

Granger (1987) referred, the research investigates price discovery through Vector Error Correction Model (VECM) In other words, the study tries to show how VN30 Index and VN-Index change while VN30 VN-Index Futures is volatile

We have to investigate two price vectors, including:

 [ ]

There is an estimated VECM as below:

∑ ∑ [1]

Cointegrating equation (long-run model):

[2]

While:

 Y is P1 or P2  X is P0



The first above model incorporates both the short-run and long-run dynamics while the second equation only refers long-run dynamics P1 and P0 as well as P2 and P0 has a long-run relationship only when the coefficient of the co-integrating equation is between -1 and at a statistical significance The coefficient of ETC measures the speed at which the dependent variable returns to equilibrium after a change in independent variable (P0) Moreover, the

research still determines if there is a shot-run a relationship between P1 and P0 as well as P2

and P0 by using Wald Test and Breusch-Godfrey Serial Correction LM Test Finally, the

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4 Empirical Results

Appendices 1, and show the results of Augmented Dickey-Fuller Test With 388

observations, VN30 Index Futures, VN30 Index and VN-Index have p-value and t-Statistic as bellow:

 VN30 Index Futures: p-value = 0.9515 > , t-Statistic = -0.919502, t-Statistic = -3.982074 <0 at 1% and | | | | | | | |

 VN30 Index: p-value = 0.9772 > , tStatistic = 0.615743, tStatistic = -3.981949 <0 at 1% and | | | | | | | |

 VN-Index: p-value = 0.9682 > , t-Statistic = -0.746066, t-Statistic = -3.981949 <0 at 1% and | | | | | | | |

It is clearly seen that VN30 Index Futures, VN30 Index and VN-Index experience constant and trend stationarity with negative t-Statistic at about the 1% level

Besides, by using regression analysis, the research has functions referring the relationship between VN30 Index Futures and VN30 Index as well as VN30 Index Futures and VN-Index as bellow:

It is clearly seen that of 0,9873 and of 0,953 [shown in Appendices & 5] indicate a significant relationship between the two variables In other words, VN30 Index Futures and VN30 Index as well as VN30 Index Futures and VN-Index seem to be so closely aligned

According to Appendix 6, is the best optimal lag for the first sub-period while the second and third sub-periods receive the optimal lag of

In terms of co-integration, Trace and Max-Eigenvalue test indicate co-integrating equations at the 0.05 level between VN30 Index Futures and VN30 Index, VN30 Index Futures and VN-Index [Table and Table 4] In the long-run, VN30 Index Futures experiences a positive impact on VN30 Index and VN-Index The null hypothesis of no co-integration is rejected against the alternative of a co-integrating relationship in the model In the other words, this means that these indices exhibit a long-run relationship, satisfying requirements of Vector Error Correction Model (VECM)

Table 3: Trace and Max-Eigenvalue test for VN30 Index Futures and VN30 Index Unrestricted Cointegration Rank Test (Trace)

Hypothesized Trace 0.05

No of CE(s) Eigenvalue Statistic Critical Value Prob.**

None * 0.047222 19.17645 15.49471 0.0133

At most 0.001434 0.552558 3.841466 0.4573

Unrestricted Cointegration Rank Test (Maximum Eigenvalue)

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None * 0.047222 18.62389 14.26460 0.0096

At most 0.001434 0.552558 3.841466 0.4573

1 Cointegrating Equation(s): Log likelihood -2776.142

Normalized cointegrating coefficients (standard error in parentheses)

VN30_INDEX VN30_INDEX_FUTURES

1.000000 -0.943999

(0.02650) Adjustment coefficients (standard error in parentheses)

D(VN30_INDEX) 0.024923

(0.05039)

D(VN30_INDEX_FUTURES) 0.141552

(0.05623)

Source: Results calculated from EViews Software

Table 4: Trace and Max-Eigenvalue test for VN30 Index Futures and VN-Index Unrestricted Cointegration Rank Test (Trace)

Hypothesized Trace 0.05

None 0.028351 11.94458 15.49471 0.1596

At most 0.002262 0.871805 3.841466 0.3505

Unrestricted Cointegration Rank Test (Maximum Eigenvalue)

Hypothesized Max-Eigen 0.05

None 0.028351 11.07277 14.26460 0.1506

At most 0.002262 0.871805 3.841466 0.3505

1 Cointegrating Equation(s): Log likelihood -2805.025

Normalized cointegrating coefficients (standard error in parentheses)

VN_INDEX VN30_INDEX_FUTURES

1.000000 -0.929120

(0.05973) Adjustment coefficients (standard error in parentheses)

D(VN_INDEX) 0.020273

(0.02902)

D(VN30_INDEX_FUTURES) 0.074826

(0.03261)

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VN30 Index Futures and VN30 Index, VN30 Index Futures and VN-Index contains coefficients (from to 6) Table summarizes equations about estimated VECM and co-integrating (long-run model)

Table 5: Estimated VECM and cointegrating equation (long-run model)

Estimated VECM with P1/P2 as target variable Cointegrating equation (long-run model) VN30 Index and VN30 Index Futures

First sub-period (10/08/2017 -10/04/2018) – 24.94102 Estimated equation:

D(P1) = C(1)*( P1(-1) - 0.958223297798*P0(-1) - 24.9410238488 ) + C(2)*D(P1(-1)) + C(3)*D(P0(-1)) + C(4)

Second sub-period (11/04/2018- 11/07/2018) – 215.8693 Estimated equation:

D(P1) = C(1)*( P1(-1) - 0.775645053007*P0(-1) - 215.869328825 ) + C(2)*D(P1(-1)) + C(3)*D(P1(-2)) + C(4)*D(P0(-1)) + C(5)*D(P0(-2)) + C(6)

Third sub-period (12/07/2018 -28/02/2019) – 0.170651 Estimated equation:

VN-Index and VN30 Index Futures

First sub-period (10/08/2017 -10/04/2018) – 0.072784 Estimated equation:

D(P2) = C(1)*( P2(-1) - 0.997169843843*P0(-1) - 0.0727835852093 ) + C(2)*D(P2(-1)) + C(3)*D(P0(-1)) + C(4)

Second sub-period (11/04/2018- 11/07/2018) – 184.6331 Estimated equation:

Third sub-period (12/07/2018 -28/02/2019) – 207.5733 Estimated equation:

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period (or the second sub-period) experiences the highest coefficient of the co-integrating equation for both pairs (VN30 Index Futures and VN30 Index, VN30 Index Futures and VN-Index) while the lowest level happens in the increased period This means that the long-run relationship between VN30 Index Futures and VN30 Index as well as VN30 Index Futures and VN-Index become stricter when the spot market goes down In comparison with the co-efficiency between VN30 Index Futures and VN-Index, the coefficient of the co-integrating equation between VN30 Index Futures and VN30 Index is always higher while a drop or recovery of stock market but lower when there is an upward trend in market In other words, VN30 Index Futures and VN30 Index become witnesses of much stronger co-integration when the market falls In contrast, the co-integration between VN30 Index Futures and VN-Index is higher than between VN30 VN-Index Futures and VN 30 VN-Index in case of development of market In the other words, concerning the speed at which the dependent variable (VN30 Index or VN-Index) returns to equilibrium after a change in independent variable (VN30 Index Futures), VN30 Index and VN-Index experience the highest level in the second sub-period, when the market is downwards and the lowest rate while there is an upward trend in spot market After a change in VN30 Index Futures, VN-Index returns to equilibrium more quickly than VN30 Index only when the market develops

In brief, there is a long-run relationship between VN30 Index Futures and VN30 Index as well as VN30 Index Futures and VN-Index It is recognized more clearly when the market grows down or doesn’t change a lot The co-integration between VN30 Index Futures and VN-Index is only deeper than between VN30 Index Futures and VN30 Index when the market increases

Moreover, based on p-value [shown in appendices from to 12], it is clearly seen that there is a short-run relationship between VN30 Index Futures and VN30 Index as well as VN30 Index Futures and VN-Index Similar to the long-run relationship, the short-run one experiences the differences between VN30 Index and VN-Index in each sub-period The scenario is the same for the short-run relationship in comparison with the long-run one And

Source: Authors

Figure 3: The coefficient of ETC ( )

-0.040088 -0.416242

-0.243575

-0.073972 -0.338162

-0.097897

-0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05

First sub-period (10/08/2017 -10/04/2018) Second sub-period (11/04/2018- 11/07/2018) Third sub-period (12/07/2018 -28/02/2019)

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Stability Diagnostics indicates that blue trendline are between red boundary The VECM is said to be dramatically stable at about the 5% level

5 Discussion and policy implications

Vector Error Correction Model shows a stable equilibrium relationship between VN30 Index Futures and VN30 Index, VN30 Index Futures and VN-Index This empirical evidence supports theories about the role of derivative instruments generally and index futures particularly In fact, traders prefer investing in diversified portfolio corresponding to index because stock index futures are financial instruments thanks to their lower costs of trading and greater leverage potential futures markets This research results are totally consistent with findings shown by Tse (1995), Nieto et al (1998), Antoniou and Homes (1995), Antoniou et

al (2005), Gong et al (2016) and Hong et al (2017)

In addition, VN30 Index Futures’ importance for VN30 Index is clearer than for VN-Index In a negative or neutral trend of movement, VN30 Index returns to equilibrium rapidly after a change in VN30 Index Futures It seems to be evident because VN30 Index is underlying asset of VN30 Index Futures Naturally, VN30 Index Futures has a closer relation with VN30 Index than with VN-Index However, when the market goes up, VN-Index returns to equilibrium more rapidly than VN30 Index but at the lowest speed The long-run relationship between VN30 Index Futures and VN-Index indicates VN30 Index’s capacity as an effective performance benchmark and a measure of market efficiency in Vietnam stock market

The VN30 Index Futures’ role of price discovery and information transmission witnesses the best level when the market downturns or doesn’t change a lot (or stay unchangeable) and vice versa This reflects investors' psychology in Vietnam stock market In fact, the impact of psychological factors on the market has been very complicated The Vietnamese financial market always contents many high unstable factors, causing market panic as well as making many difficulties for implementing macroeconomic policies Vietnam stock market is considered as a market of individual investors who follows the psychology of the crowd Most of domestic individual don’t deeply receive and understand market information or consult news published by domestic and foreign experts They are less sensitive to market information Therefore, they participate to the market with high risks and short-term vision In addition, the current information is considered incomplete Many rumors affect investors' psychology, causing confusion and Crowd psychology as observed in the previous period

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behavioral finance theory and feedback trading model showed that many Vietnamese investors' psychology may be affected and lead to acts of selling securities, both in the underlying market and in the derivative market The role of VN30 Index’s price discovery and information transmission is expressed the best during the period of market decline

6 Conclusion

The introduction of VN30 Index Futures in 2018 August in Vietnam marked the appearance of derivative market in Vietnam It is a very good sign of a growing maturity in the national financial market VN30 Index Futures is expected to play a stabilizing role in the stock market Evidently, the debate about the spot-futures relationships has been raising since this derivative product was introduced on Vietnam’s stock market

The study provides the first empirical evidences about a stable equilibrium relationship between the two series groups (including VN30 Index Futures, VN30 Index and VN30 Index Futures and VN-Index) during period from 10 August 2017 to 28 February 2019 By using Vector Error Correction Model (VECM), the research demonstrates higher coefficient of the cointegrating equation and higher coefficient of ETC ( ) when spot-market grows down or doesn’t change a lot The ability of VN30 Index Futures’ price discovery role is reduced while there is an upward trend in spot market Moreover, the relationship between VN30 Index Futures and VN30 Index is stricter than that of VN30 Index Futures and VN-Index while the market is reduced or recovered and vice versa Therefore, it is clearly seen that the research contributes to enrich the existing empirical evidence on price discovery and information transmission between stock indices and stock index Futures in emerging countries like Vietnam The study results are very significant in the context where many claims and concerns about risks brought by this type of derivative products have been raising since it first trading Investors as well as policy makers can refer these proofs to believe in VN30 Index Futures in particular and derivatives in general, and then continue to develop different other derivative products on Vietnam’s stock market in the coming time

However, it is obviously seen that the research is executed in a short period from VN30 Index Futures’ first trading to February 29, 2019 and only focus on the role of price discovery and information transmission while this product still plays other important roles like hedging or risk management or reducing the costs of trading Therefore, the research results cannot fully reflect the total nature of VN30 Index Futures on Vietnam’s stock market There is a need for further follow-up studies with deep analysis, highly specific recommendations and longer (richer) sample of data about all roles of VN30 Index Futures as well as financial behaviors of investors who are trading in Vietnam Stock Market

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Appendix 1: Unit root analysis of VN30 Index Futures series

Null Hypothesis: VN30_INDEX_FUTURES has a unit root Exogenous: Constant, Linear Trend

Lag Length: (Automatic - based on SIC, maxlag=16)

t-Statistic Prob.*

Augmented Dickey-Fuller test statistic -0.919502 0.9515

Test critical values: 1% level -3.982074

5% level -3.421539

10% level -3.133553

*MacKinnon (1996) one-sided p-values Augmented Dickey-Fuller Test Equation

Dependent Variable: D(VN30_INDEX_FUTURES) Method: Least Squares

Sample (adjusted): 388

Included observations: 385 after adjustments

Variable Coefficient Std Error t-Statistic Prob

VN30_INDEX_FUTURES(-1) -0.005988 0.006512 -0.919502 0.3584

D(VN30_INDEX_FUTURES(-1)) -0.046926 0.050512 -0.928989 0.3535

D(VN30_INDEX_FUTURES(-2)) 0.199173 0.050292 3.960307 0.0001

C 6.720445 6.335016 1.060841 0.2894

@TREND("1") -0.007424 0.006336 -1.171693 0.2421

R-squared 0.049032 Mean dependent var -0.446299

Adjusted R-squared 0.039022 S.D dependent var 14.01369

S.E of regression 13.73755 Akaike info criterion 8.091046

Sum squared resid 71713.75 Schwarz criterion 8.142386

Log likelihood -1552.526 Hannan-Quinn criter 8.111408

F-statistic 4.898185 Durbin-Watson stat 1.991679

Prob(F-statistic) 0.000733

Appendix 2: Unit root analysis of VN30 Index series

Null Hypothesis: VN30_INDEX has a unit root Exogenous: Constant, Linear Trend

t-Statistic Prob.*

5% level -3.421478

10% level -3.133517

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VN30_INDEX(-1) -0.003869 0.006284 -0.615743 0.5384

C 5.082810 6.144677 0.827189 0.4086

@TREND("1") -0.009601 0.005702 -1.683735 0.0930

Appendix 3: Unit root analysis of VN-Index series

Null Hypothesis: VN_INDEX has a unit root Exogenous: Constant, Linear Trend

t-Statistic Prob.*

5% level -3.421478

10% level -3.133517

*MacKinnon (1996) one-sided p-values Augmented Dickey-Fuller Test Equation Dependent Variable: D(VN_INDEX) Method: Least Squares

VN_INDEX(-1) -0.004732 0.006342 -0.746066 0.4561

C 5.615799 6.423686 0.874233 0.3825

@TREND("1") -0.008077 0.005725 -1.410805 0.1591

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Appendix 4: Regression between VN30 Index Futures and VN-Index

Source: Authors Source: Authors

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Appendix 6: Optimal lag selection VN30 Index Futures and VN 30 Index in the 1st sub-period

VAR Lag Order Selection Criteria Endogenous variables: P1 P0 Exogenous variables: C Date: 04/02/19 Time: 16:06 Sample: 8/10/2017 4/10/2018 Included observations: 159

Lag LogL LR FPE AIC SC HQ

0 -1648.138 NA 3543764 20.75645 20.79506 20.77213

1 -1155.356 966.9682 7574.246* 14.60825* 14.72406* 14.65528*

2 -1152.328 5.865323 7667.681 14.62048 14.81350 14.69886

3 -1151.253 2.055366 7955.623 14.65727 14.92749 14.76701

4 -1150.064 2.244510 8242.951 14.69263 15.04005 14.83371

5 -1148.309 3.266610 8480.774 14.72087 15.14550 14.89331

6 -1147.864 0.817319 8871.173 14.76558 15.26742 14.96937

7 -1143.125 8.583031 8792.604 14.75629 15.33533 14.99144

8 -1135.339 13.90747* 8387.989 14.70867 15.36491 14.97516

* indicates lag order selected by the criterion

LR: sequential modified LR test statistic (each test at 5% level) FPE: Final prediction error

AIC: Akaike information criterion SC: Schwarz information criterion HQ: Hannan-Quinn information criterion

VN30 Index Futures and VN-Index in the 1st sub-period

0 -1696.279 NA 6493097 21.36200 21.40061 21.37768

1 -1176.031 1020.864 9823.909* 14.86832* 14.98413* 14.91535*

2 -1172.692 6.468674 9906.209 14.87663 15.06964 14.95501

3 -1171.963 1.394408 10323.00 14.91777 15.18799 15.02750

4 -1168.670 6.212569 10416.60 14.92667 15.27409 15.06775

5 -1166.092 4.798874 10606.75 14.94456 15.36919 15.11699

6 -1165.063 1.890249 11013.78 14.98192 15.48376 15.18571

7 -1156.590 15.34788 10415.27 14.92566 15.50470 15.16080

8 -1150.502 10.87339* 10150.57 14.89940 15.55564 15.16589

VN30 Index Futures and VN 30 Index in the 2nd sub-period

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0 -534.2827 NA 368339.4 18.49251 18.56356 18.52018

1 -449.3254 161.1259 22590.99 15.70088 15.91403 15.78390

2 -439.8685 17.28328* 18728.68* 15.51271* 15.86796* 15.65108*

3 -436.1521 6.535777 18941.23 15.52249 16.01983 15.71621

4 -434.5076 2.778608 20599.28 15.60371 16.24316 15.85279

5 -431.1515 5.439151 21151.33 15.62591 16.40746 15.93034

VN30 Index Futures and VN-Index in the 2nd sub-period

0 -526.4523 NA 281178.5 18.22249 18.29354 18.25017

1 -446.0692 152.4507 20191.61 15.58859 15.80174* 15.67162

2 -439.8587 11.35020* 18722.33* 15.51237* 15.86762 15.65074*

3 -437.1816 4.707950 19625.74 15.55799 16.05533 15.75171

4 -436.9028 0.471008 22372.91 15.68631 16.32575 15.93538

5 -435.5694 2.161073 24631.93 15.77826 16.55980 16.08268

VN30 Index Futures and VN 30 Index in the 3rd sub-period

VAR Lag Order Selection Criteria Endogenous variables: P1 P0 Exogenous variables: C Date: 04/02/19 Time: 15:56 Sample: 158

Included observations: 150

0 -1256.585 NA 66528.27 16.78114 16.82128 16.79744

1 -991.0956 520.3596* 2036.248 13.29461 13.41503* 13.34353* -986.6917 8.514159 2025.391* 13.28922* 13.48993 13.37076

3 -982.9698 7.096356 2033.091 13.29293 13.57392 13.40709

4 -980.0965 5.401861 2064.179 13.30795 13.66923 13.45473

5 -977.5749 4.673295 2105.776 13.32767 13.76923 13.50706

6 -976.3807 2.181431 2186.799 13.36508 13.88692 13.57708

7 -975.1330 2.245982 2269.603 13.40177 14.00390 13.64640

8 -973.3793 3.109907 2340.045 13.43172 14.11413 13.70897

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VN30 Index Futures and VN-Index in the 3rd sub-period

VAR Lag Order Selection Criteria Endogenous variables: P1 P0 Exogenous variables: C Date: 04/02/19 Time: 15:48 Sample: 158

0 -1256.585 NA 66528.27 16.78114 16.82128 16.79744

1 -991.0956 520.3596* 2036.248 13.29461 13.41503* 13.34353* -986.6917 8.514159 2025.391* 13.28922* 13.48993 13.37076

3 -982.9698 7.096356 2033.091 13.29293 13.57392 13.40709

4 -980.0965 5.401861 2064.179 13.30795 13.66923 13.45473

5 -977.5749 4.673295 2105.776 13.32767 13.76923 13.50706

6 -976.3807 2.181431 2186.799 13.36508 13.88692 13.57708

7 -975.1330 2.245982 2269.603 13.40177 14.00390 13.64640

8 -973.3793 3.109907 2340.045 13.43172 14.11413 13.70897

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Appendix 7: VN30 Index and VN30 Index Futures in the first sub-period Vector Error Correction Estimates

Date: 04/19/19 Time: 08:44

Sample (adjusted): 8/14/2017 4/10/2018 Included observations: 165 after adjustments Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq: CointEq1

P1(-1) 1.000000

P0(-1) -0.958223

(0.02226) [-43.0480]

C -24.94102

Error Correction: D(P1) D(P0)

CointEq1 -0.040088 0.139366

(0.06836) (0.08267)

[-0.58639] [ 1.68576]

D(P1(-1)) -0.024964 0.051903

(0.13744) (0.16620)

[-0.18164] [ 0.31229]

D(P0(-1)) -0.032062 0.017684

(0.11392) (0.13777)

[-0.28144] [ 0.12836]

C 2.714864 2.444492

(0.87701) (1.06058)

[ 3.09559] [ 2.30487]

R-squared 0.005439 0.021548

Adj R-squared -0.013093 0.003316

Sum sq resids 19285.76 28204.19

S.E equation 10.94474 13.23561

F-statistic 0.293494 1.181901

Log likelihood -626.9219 -658.2805

Akaike AIC 7.647539 8.027642

Schwarz SC 7.722834 8.102938

Mean dependent 2.564061 2.628030

S.D dependent 10.87379 13.25761

Determinant resid covariance (dof adj.) 6683.168

Determinant resid covariance 6363.063

Log likelihood -1190.807

Akaike information criterion 14.55523

Schwarz criterion 14.74347

Error Correction Model

Dependent Variable: D(P1) Method: Least Squares Date: 04/19/19 Time: 09:19

Sample (adjusted): 8/14/2017 4/10/2018 Included observations: 165 after adjustments

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Coefficient Std Error t-Statistic Prob

C(1) -0.040088 0.068363 -0.586389 0.5584

C(2) -0.024964 0.137435 -0.181644 0.8561

C(3) -0.032062 0.113922 -0.281441 0.7787

C(4) 2.714864 0.877010 3.095591 0.0023

R-squared 0.005439 Mean dependent var 2.564061

Adjusted R-squared -0.013093 S.D dependent var 10.87379

Wald Test:

Equation: Untitled

Test Statistic Value df Probability

t-statistic -0.281441 161 0.7787

F-statistic 0.079209 (1, 161) 0.7787

Chi-square 0.079209 0.7784

Null Hypothesis: C(3)=0 Null Hypothesis Summary:

Normalized Restriction (= 0) Value Std Err

C(3) -0.032062 0.113922

Restrictions are linear in coefficients

Breusch-Godfrey Serial Correlation LM Test:

F-statistic 0.730154 Prob F(1,160) 0.3941

Obs*R-squared 0.749550 Prob Chi-Square(1) 0.3866

Test Equation:

Dependent Variable: RESID Method: Least Squares Date: 04/19/19 Time: 15:09 Sample: 8/14/2017 4/10/2018 Included observations: 165

Presample missing value lagged residuals set to zero

C(1) -0.035873 0.080274 -0.446881 0.6556

C(2) -1.064172 1.252961 -0.849326 0.3970

C(3) -0.052487 0.129510 -0.405272 0.6858

C(4) 2.861503 3.461905 0.826569 0.4097

RESID(-1) 1.122133 1.313219 0.854490 0.3941

R-squared 0.004543 Mean dependent var 6.35E-16

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-40 -30 -20 -10 10 20 30 40

M8 M9 M10 M11 M12 M1 M2 M3 M4

2017 2018

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Appendix 8: VN30 Index and VN30 Index Futures in the second sub-period Vector Error Correction Estimates

Date: 04/02/19 Time: 14:20

P1(-1) 1.000000

P0(-1) -0.775645

(0.05631) [-13.7737]

C -215.8693

CointEq1 -0.416242 -0.259996

(0.21501) (0.23200)

[-1.93590] [-1.12067]

D(P1(-1)) -0.197878 -0.084612

(0.41819) (0.45123)

[-0.47318] [-0.18751]

D(P1(-2)) 0.182524 0.333804

(0.37745) (0.40727)

[ 0.48357] [ 0.81961]

D(P0(-1)) 0.178409 -0.075543

(0.38673) (0.41729)

[ 0.46133] [-0.18104]

D(P0(-2)) 0.078644 0.004312

(0.35744) (0.38568)

[ 0.22002] [ 0.01118]

C -3.153310 -3.795859

(2.68605) (2.89829)

[-1.17396] [-1.30969]

R-squared 0.099901 0.128148

Adj R-squared 0.016559 0.047421

Sum sq resids 20897.92 24330.86

S.E equation 19.67228 21.22667

F-statistic 1.198681 1.587420

Log likelihood -260.7281 -265.2910

Akaike AIC 8.890937 9.043033

Schwarz SC 9.100372 9.252468

Mean dependent -4.217833 -4.460417

S.D dependent 19.83720 21.74860

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D(P1) = C(1)*( P1(-1) - 0.775645053007*P0(-1) - 215.869328825 ) + C(2) *D(P1(-1)) + C(3)*D(P1(-2)) + C(4)*D(P0(-1)) + C(5)*D(P0(-2)) + C(6)

C(1) -0.416242 0.215012 -1.935905 0.0581

C(2) -0.197878 0.418189 -0.473178 0.6380

C(3) 0.182524 0.377450 0.483573 0.6306

C(4) 0.178409 0.386728 0.461329 0.6464

C(5) 0.078644 0.357436 0.220024 0.8267

C(6) -3.153310 2.686053 -1.173957 0.2456

Wald Test:

Equation: Untitled

F-statistic 0.107972 (2, 54) 0.8978

Chi-square 0.215945 0.8977

Null Hypothesis: C(4)=C(5)=0 Null Hypothesis Summary:

C(4) 0.178409 0.386728

C(5) 0.078644 0.357436

Test Equation:

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C(1) 0.190568 0.294584 0.646906 0.5205

C(2) -0.567437 0.637018 -0.890770 0.3772

C(3) 0.732810 0.526148 1.392782 0.1696

C(4) 0.398080 0.440552 0.903594 0.3704

C(5) 0.202459 0.367777 0.550494 0.5843

C(6) 3.586351 3.970707 0.903202 0.3706

RESID(-1) 0.122071 0.558756 0.218470 0.8279

RESID(-2) -1.034782 0.527739 -1.960783 0.0553

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Appendix 9: VN30 Index and VN30 Index Futures in the third sub-period Vector Error Correction Estimates

Date: 04/02/19 Time: 14:33 Sample (adjusted): 158

Included observations: 155 after adjustments Standard errors in ( ) & t-statistics in [ ]

P1(-1) 1.000000

P0(-1) -1.005177

(0.03233) [-31.0902]

C -0.170651

CointEq1 -0.243575 0.045839

(0.13778) (0.14456)

[-1.76781] [ 0.31710]

D(P1(-1)) 0.195839 0.329381

(0.17583) (0.18447)

[ 1.11383] [ 1.78557]

D(P1(-2)) -0.078640 -0.081310

(0.16858) (0.17687)

[-0.46649] [-0.45973]

D(P0(-1)) -0.221257 -0.360162

(0.18088) (0.18977)

[-1.22323] [-1.89789]

D(P0(-2)) 0.282943 0.285022

(0.16830) (0.17657)

[ 1.68120] [ 1.61421]

C -0.303877 -0.311057

(0.73460) (0.77071)

[-0.41366] [-0.40360]

R-squared 0.097540 0.100436

Adj R-squared 0.067256 0.070249

Sum sq resids 12453.18 13707.53

S.E equation 9.142123 9.591500

F-statistic 3.220839 3.327161

Log likelihood -559.8742 -567.3118

Akaike AIC 7.301603 7.397572

Schwarz SC 7.419413 7.515382

Mean dependent -0.294452 -0.308387

S.D dependent 9.465983 9.947256

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Dependent Variable: D(P1) Method: Least Squares Date: 04/02/19 Time: 14:34 Sample (adjusted): 158

C(1) -0.243575 0.137783 -1.767813 0.0791

C(2) 0.195839 0.175825 1.113827 0.2671

C(3) -0.078640 0.168579 -0.466488 0.6415

C(4) -0.221257 0.180878 -1.223235 0.2232

C(5) 0.282943 0.168298 1.681197 0.0948

C(6) -0.303877 0.734597 -0.413665 0.6797

Wald Test:

Equation: Untitled

F-statistic 3.829597 (2, 149) 0.0239

Chi-square 7.659195 0.0217

C(4) -0.221257 0.180878

C(5) 0.282943 0.168298

Test Equation:

Dependent Variable: RESID Method: Least Squares Date: 04/02/19 Time: 14:35 Sample: 158

(33)

C(1) -0.020256 0.201178 -0.100687 0.9199

C(2) 0.053584 0.295343 0.181430 0.8563

C(3) -0.115360 0.246506 -0.467982 0.6405

C(4) -0.030135 0.237957 -0.126640 0.8994

C(5) -0.013722 0.224312 -0.061172 0.9513

C(6) -0.008564 0.746263 -0.011476 0.9909

RESID(-1) -0.029102 0.385913 -0.075410 0.9400

RESID(-2) 0.149298 0.249777 0.597725 0.5509

R-squared 0.002922 Mean dependent var -9.64E-15

(34)

Appendix 10: VN-Index and VN30 Index Futures in the first sub-period Vector Error Correction Estimates

Date: 04/19/19 Time: 09:50

P2(-1) 1.000000

P0(-1) -0.997170

(0.03804) [-26.2131]

C -0.072784

CointEq1 -0.073072 0.035938

(0.04794) (0.05640)

[-1.52428] [ 0.63723]

D(P2(-1)) -0.128959 -0.022076

(0.12383) (0.14568)

[-1.04144] [-0.15154]

D(P0(-1)) 0.022958 0.053496

(0.10817) (0.12725)

[ 0.21225] [ 0.42039]

C 2.857903 2.543690

(0.90782) (1.06800)

[ 3.14810] [ 2.38172]

R-squared 0.026330 0.003385

Adj R-squared 0.008187 -0.015186

Sum sq resids 20756.50 28727.77

S.E equation 11.35440 13.35790

F-statistic 1.451258 0.182256

Log likelihood -632.9851 -659.7980

Akaike AIC 7.721031 8.046036

Schwarz SC 7.796327 8.121332

Mean dependent 2.582061 2.628030

S.D dependent 11.40117 13.25761

Schwarz criterion 14.99619

(35)

C(1) -0.073072 0.047939 -1.524285 0.1294

C(2) -0.128959 0.123829 -1.041436 0.2992

C(3) 0.022958 0.108167 0.212250 0.8322

C(4) 2.857903 0.907819 3.148100 0.0020

R-squared 0.026330 Mean dependent var 2.582061

Wald Test:

Equation: Untitled

t-statistic 0.212250 161 0.8322

F-statistic 0.045050 (1, 161) 0.8322

Chi-square 0.045050 0.8319

Null Hypothesis: C(3)=0 Null Hypothesis Summary:

C(3) 0.022958 0.108167

Test Equation:

C(1) -0.011015 0.069326 -0.158885 0.8740

C(2) -0.142213 0.656670 -0.216568 0.8288

C(3) -0.014962 0.127953 -0.116933 0.9071

C(4) 0.404096 2.046002 0.197505 0.8437

RESID(-1) 0.158840 0.720208 0.220548 0.8257

(36)

-40 -30 -20 -10 10 20 30 40

M8 M9 M10 M11 M12 M1 M2 M3 M4

2017 2018

(37)

Appendix 11: VN-Index and VN30 Index Futures in the second sub-period Vector Error Correction Estimates

Date: 04/02/19 Time: 14:25

P2(-1) 1.000000

P0(-1) -0.824207

(0.04834) [-17.0508]

C -184.6331

CointEq1 -0.338162 -0.127215

(0.22906) (0.26535)

[-1.47631] [-0.47943]

D(P2(-1)) -0.398425 -0.217485

(0.40386) (0.46785)

[-0.98654] [-0.46487]

D(P2(-2)) 0.019779 0.042390

(0.37158) (0.43045)

[ 0.05323] [ 0.09848]

D(P0(-1)) 0.288373 0.014005

(0.35156) (0.40726)

[ 0.82026] [ 0.03439]

D(P0(-2)) 0.192538 0.238654

(0.33494) (0.38801)

[ 0.57484] [ 0.61507]

C -3.902071 -4.087229

(2.53382) (2.93525)

[-1.53999] [-1.39246]

R-squared 0.094271 0.107296

Adj R-squared 0.010407 0.024638

Sum sq resids 18564.52 24912.78

S.E equation 18.54150 21.47901

F-statistic 1.124093 1.298071

Log likelihood -257.1762 -266.0001

Akaike AIC 8.772540 9.066669

Schwarz SC 8.981974 9.276103

Mean dependent -4.399667 -4.460417

S.D dependent 18.63874 21.74860

(38)

C(1) -0.338162 0.229059 -1.476309 0.1457

C(2) -0.398425 0.403862 -0.986537 0.3283

C(3) 0.019779 0.371584 0.053229 0.9577

C(4) 0.288373 0.351563 0.820260 0.4157

C(5) 0.192538 0.334943 0.574836 0.5678

C(6) -3.902071 2.533822 -1.539994 0.1294

Wald Test:

Equation: Untitled

F-statistic 0.366305 (2, 54) 0.6950

Chi-square 0.732610 0.6933

C(4) 0.288373 0.351563

C(5) 0.192538 0.334943

Test Equation:

(39)

C(1) -0.029958 0.337151 -0.088858 0.9295

C(2) -0.408667 0.601495 -0.679419 0.4999

C(3) 0.199533 0.538339 0.370645 0.7124

C(4) 0.046827 0.410315 0.114124 0.9096

C(5) 0.122715 0.356096 0.344612 0.7318

C(6) -0.157513 4.645476 -0.033907 0.9731

RESID(-1) 0.393960 0.622284 0.633087 0.5295

RESID(-2) -0.401797 0.514682 -0.780670 0.4385

(40)

Appendix 12: VN-Index and VN30 Index Futures in the third sub-period Vector Error Correction Estimates

Included observations: 155 after adjustments Standard errors in ( ) & t-statistics in [ ]

P2(-1) 1.000000

P0(-1) -0.810212

(0.14259) [-5.68209]

C -207.5733

CointEq1 -0.097897 -0.038483

(0.05240) (0.05645)

[-1.86810] [-0.68168]

D(P2(-1)) 0.237658 0.351783

(0.14807) (0.15951)

[ 1.60505] [ 2.20542]

D(P2(-2)) -0.001104 0.054754

(0.15102) (0.16269)

[-0.00731] [ 0.33655]

D(P0(-1)) -0.228819 -0.391557

(0.14321) (0.15427)

[-1.59778] [-2.53805]

D(P0(-2)) 0.213972 0.166633

(0.14473) (0.15591)

[ 1.47840] [ 1.06875]

C -0.493507 -0.172235

(0.72185) (0.77761)

[-0.68367] [-0.22149]

R-squared 0.094318 0.097381

Adj R-squared 0.063926 0.067092

Sum sq resids 11852.02 13754.09

S.E equation 8.918732 9.607774

F-statistic 3.103383 3.215032

Log likelihood -556.0397 -567.5746

Akaike AIC 7.252125 7.400963

Schwarz SC 7.369935 7.518773

Mean dependent -0.571290 -0.308387

S.D dependent 9.218240 9.947256

(41)

Dependent Variable: D(P2) Method: Least Squares Date: 04/02/19 Time: 14:38 Sample (adjusted): 158

C(1) -0.097897 0.052405 -1.868096 0.0637

C(2) 0.237658 0.148069 1.605049 0.1106

C(3) -0.001104 0.151023 -0.007309 0.9942

C(4) -0.228819 0.143211 -1.597776 0.1122

C(5) 0.213972 0.144732 1.478397 0.1414

C(6) -0.493507 0.721845 -0.683674 0.4952

Wald Test:

Equation: Untitled

F-statistic 3.184739 (2, 149) 0.0442

Chi-square 6.369478 0.0414

C(4) -0.228819 0.143211

C(5) 0.213972 0.144732

Test Equation:

Dependent Variable: RESID Method: Least Squares Date: 04/02/19 Time: 14:39 Sample: 158

(42)

C(1) 0.024053 0.065768 0.365725 0.7151

C(2) 0.205016 0.342598 0.598414 0.5505

C(3) -0.052970 0.257617 -0.205615 0.8374

C(4) 0.018227 0.148219 0.122973 0.9023

C(5) 0.066344 0.176607 0.375659 0.7077

C(6) 0.106749 0.749417 0.142443 0.8869

RESID(-1) -0.240105 0.362742 -0.661917 0.5091

RESID(-2) -0.012130 0.233894 -0.051859 0.9587

(43)

Appendix 13: Unit root analysis of return series of VN30 Index Futures, VN30 Index and VN-Index

Null Hypothesis: R_VN30_INDEX_FUTURES_ has a unit root Exogenous: Constant

t-Statistic Prob.*

5% level -2.868829

10% level -2.570719

*MacKinnon (1996) one-sided p-values

Augmented Dickey-Fuller Test Equation

Dependent Variable: D(R_VN30_INDEX_FUTURES_) Method: Least Squares

R_VN30_INDEX_FUTURES_(-1) -0.845966 0.072813 -11.61835 0.0000

D(R_VN30_INDEX_FUTURES_(-1)) -0.203494 0.049863 -4.081036 0.0001

C 0.000556 0.000713 0.780059 0.4358

S.E of regression 0.013964 Akaike info criterion -5.696842

Sum squared resid 0.074492 Schwarz criterion -5.666037

Log likelihood 1099.642 Hannan-Quinn criter -5.684625

Null Hypothesis: R_VN30_INDEX_ has a unit root Exogenous: Constant

t-Statistic Prob.*

5% level -2.868829

10% level -2.570719

Augmented Dickey-Fuller Test Equation Dependent Variable: D(R_VN30_INDEX_) Method: Least Squares

(44)

D(R_VN30_INDEX_(-1)) -0.157522 0.050225 -3.136324 0.0018

C 0.000577 0.000641 0.900012 0.3687

Null Hypothesis: R_VN_INDEX_ has a unit root Exogenous: Constant

t-Statistic Prob.*

5% level -2.868829

10% level -2.570719

Augmented Dickey-Fuller Test Equation Dependent Variable: D(R_VN_INDEX_) Method: Least Squares

R_VN_INDEX_(-1) -0.858895 0.072102 -11.91224 0.0000

D(R_VN_INDEX_(-1)) -0.161695 0.050205 -3.220707 0.0014

C 0.000620 0.000618 1.002645 0.3167