Relationship between trading volume and stock return in Viet Nam

MINISTRY OF EDUCATION AND TRAINING
UNIVERSITY OF ECONOMICS HO CHI MINH CITY
---------------------------------------------

ĐỖ NGỌC HOÀNG YẾN

RELATIONSHIP BETWEEN TRADING
VOLUME AND STOCK RETURN IN
VIETNAM’S STOCK MARKET
Major : FINANCE – BANKING
Code : 60.31.12
MASTER THESIS

Instructor: Dr HỒ VIẾT TIẾN

HO CHI MINH CITY, SEPTEMBER 2011


ABSTRACT

This thesis investigated the relationship between return and trading volume in the
Vietnam’s stock market in the context of Granger causality test and GARCH model
test. The sample, including two market indices and thirty seven largest market
capitalization listed companies during the period since they firstly traded through July
2011, was used. The dynamic relation as marked by lead –lag relationship from return
to volume was confirmed at both market level and firm level. I also found the
evidences supported the interaction between two exchanges in Vietnam. When testing
the mixture distribution hypothesis, the results indicated that volume was not a good
proxy for information arrival in the stock market due to the persistence of volatility
remained in most of the cases. This finding was similar to other emerging markets
which less agreed with the mixture distribution hypothesis.

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CONTENTS

Abstract ...................................................................................................... i
Contents ................................................................................................... ii
List of Tables ........................................................................................... iv
Chapter 1: Introduction
1.1 Introduction .......................................................................................... 1
1.2 Research background ............................................................................ 1
1.3 Problem statement ................................................................................ 3
1.4 Research objectives and questions ....................................................... 4
1.5 Research methodology and scope ......................................................... 5
1.6 Thesis structure ..................................................................................... 5
Chapter 2: Literature Review
2.1 Theoretical background ........................................................................ 7
2.2 Empirical studies
2.2.1 Studies on volume- price change relation ........................................... 9
2.2.2 Studies on volume- volatility relation.............................................. 11
Chapter 3: Research Methodology
3.1 Hypotheses ......................................................................................... 15
3.2 Data Description ................................................................................. 15
3.2 Econometric Methodology
3.2.1 Stationary and Unit Root test .......................................................... 16
3.2.2 Cointegration ................................................................................. 17
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3.2.3 Granger Causality tests ................................................................... 19
3.2.4 ARCH models ................................................................................. 21
3.2.5 GARCH models ............................................................................. 23
3.2.6 Threshold GARCH models ............................................................. 23
Chapter 4. Empirical results
4.1 Market level analysis
4.1.1 Descriptive statistic for markets ...................................................... 25
4.1.2 Unit root test and Granger causality test .......................................... 26
4.1.3 GARCH(1,1) test and TGARCH (1,1) test ...................................... 27
4.2 Firm level analysis
4.2.1 Descriptive statistic .......................................................................... 29
4.2 .2Granger causality test ...................................................................... 30
4.2.3 Restricted and unrestricted GARCH(1,1), TGARCH (1,1) test ........ 33
Chapter 5. Conclusion and Implication
5.1 Main findings ..................................................................................... 35
5.2 Implications ........................................................................................ 35
References .............................................................................................. 37
Appendix 1 .............................................................................................. 41

iii


LIST OF TABLE

Table 4. 1 Descriptive statistics of two market indices. ............................. 25
Table 4. 2 Stationary test for market indices ............................................. 26
Table 4. 3 Cointegration test (Unit root test for residuals) ......................... 26
Table 4. 4 Granger causality test at market level ....................................... 27
Table 4. 5 ARCH effect test for indices .................................................... 28
Table 4. 6 GARCH (1,1) model and TGARCH (1,1) model for indices .... 29

Table 4.7 Granger causality test at firm level ........................................... 31
Table 4.8 ARCH effect test for firms ....................................................... 33

Table A1 Descriptive statistics of firms .................................................... 41
Table A2 Unit root test for return and volume of firms ............................ 43
Table A3 Cointegration test at firm level ................................................. 44
Table A4 GARCH (1,1) model with and without volume for firms .......... 45
Table A5 TGARCH(1,1) model with and without volume for firms ........ 47
Table A6 List of 37 sample firms with their symbol ............................... 48

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CHAPTER 1: INTRODUCTION
1.1 INTRODUCTION
This chapter explains why the link of volume, return and volatility is worth
investigating in the case of the Vietnamese stock market. In particular, this chapter
divides into six sections. The first section summarizes the structure of the chapter.
The second one provides evidences that tell us why the return – volume relationship
becomes a concern for market participants and policy makers. From this
background information, the third section raises the problem necessary to make
clear for the case of Vietnam. The fourth section covers the research objectives and
research questions. The fifth section describes the methodology and scope. The last
one ends with description about the structure of the thesis.
1.2 RESEARCH BACKGROUND
The relationship between return, volatility, and volume has met the interest of many
researchers over the past years. The motivation comes from the attempt to measure
and model the volatility of financial assets return. Volume is evidenced to be an
important part of pricing financial assets under influence of information arrival. Due
to new information arrival, investors may adjust their expectations and this is the

main source for price and return movements. However, the stock return may remain
unchanged if some investors recognize the information as good news whereas
others find it to be bad news. Clearly, it is necessary to examine the dynamics of
stock return, volatility and trading volume so that it would improve the understanding
of the microstructure of the stock market and then help the participants and policy
makers in their own strategies.
Most previous researches followed two leading theories (hypotheses), the mixture of
distribution hypothesis (MDH) and the sequential information arrival hypothesis
(SAI), to examine the information arrival process in financial markets. In general,
both MDH and SAI hypotheses support a contemporaneous and positive relationship
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between volume and absolute return and assume a symmetric effect for price
changes. As pointed out in MDH, volume of trade can be a proxy of new arrivals
[Clark (1973), Epps and Epps (1976)]. Clark (1973) implies that the value of price
change and trading volume are distributed independently from each other. Also, the
number of information arrivals per time period varies. Lamoureux and Lastrapes
(1990) shows that a serially correlated mixing variable measuring the rate at which
information arrives to the market helps explain the generalized autoregressive
conditional heteroskedasticity (GARCH) effect in the return. According to them,
volume that is considered as an explanatory in the conditional variance equation
eliminates the GARCH effects. Sharma et al. (1996) extend Lamoureux and
Lastrapes (1990) work by bringing out two main forms: (1) the ability of daily trading
volume data to fully capture the information flow on the market return would partly
rest on the degree of market efficiency, and (2) both firm – specific factors and
market – wide factors (which affect volume) can generate volatility. This makes
volume a good or poor proxy for news arrival that contributes to conditional
heteroskedasticity. However, Najand and Yung (1991) and Bessembider and Seguin
(1992, 1993) present evidence against MDH. In addition, Bessembider and Seguin

(1992, 1993) suggest that the volatility –volume relation in the financial markets
depends on the type of trade.
On the other hand, the sequential arrival of information hypothesis (SAI) suggests
gradual popularization of information. According to Grammatikos and Saunders
(1986, p.326), the implication of SAI is that the information is sequentially observed
by each trader in the market. Under SAI framework, McMillan and Speight (2002)
argue that past absolute return provides information on current volume, and past
volume contains information on current absolute return. In other words, this dynamic
relationship is helpful and important to forecast return and volatility by using trading
volume information.

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1.3 THE PROBLEM STATEMENT
The stock market in Vietnam, which is supervised and managed by the State
Securities Commission, has developed rapidly since established in July 2000. With
289 firms listed on Hochiminh Stock Exchange and 384 firms listed on Hanoi Stock
Exchange up to May 2011, the market is considered as a channel for companies to
raise medium and long capital. Regarding capitalization value, it is recorded to
grow considerably from VND270 billions in 2000 (approximate 0.28% GDP) to
VND740,433 billion in 2010, approximate 45.2 percent of Vietnam GDP. The
number of securities trading accounts has reached at 1,103,184 at April 30th 2011,
increasing 25.4 percent compared to one year before. On average, total trading
volume of two exchange is 81,312,559 shares and fund certificates and
VND2,534.93 billions trading value per day is recorded in 2010.
During ten years, Vietnam‟s stock market has shown the ups and downs of a
developing market. In the first five years, the market did not attract the public
attention and made very little distribution to the economy due to the lack of
merchandise and unattractive small listed companies. Since 2006, it has attracted

more foreign and domestic investors with lively trading activities in two listed
exchanges. It showed an excellent performance in 2006 when the market
capitalization increased fifteen times, the Vnindex of Hochiminh Stock Exchange
(HOSE) grew 144% and the Hnindex of Hanoi Stock Exchange (HNX) grew
152.6% only in one year. After reaching the highest peak of 1170.67 points in
March 2007, Vnindex went down rapidly under effects of the global recession. The
index fell as low as 239.69 points in February 2009. Since then, the index rose
nearly 2.6 times to 530 points at the beginning of 2010. As being affected by the
changes of the world finance and the difficulties inside the economy, the stock
market of Vietnam continues to perform quietly during the 2010 and the first half of
2011.

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For a young stock market, Vietnam‟s market clearly contains weaknesses. Firstly,
this is an immature market with a weak legal environment and lack of capital. The
Government strictly controls the rules and actively intervenes in stock trading.
Accordingly, investors tend to speculate, and thus cause high market volatility.
Secondly, the lack of transparency is widely known as a biggest problem facing the
traders. Reporting requirements are not well-defined and public information
disclosure is not clear and unreliable. From that reasons, it is harder for investors to
build up a good portfolio in an inefficient market which contains lots of confusing
information.
It is the fact that while most of previous studies focused on developed markets, little
empirical evidences for emerging markets have been found, especially in Vietnam.
This analysis allows us to answer the important question of whether the linkage of
volume, return and volatility in the case of Vietnam market at both market level and
firm level exists.
1.4 RESEARCH OBJECTIVES AND QUESTIONS

To solve the research problem, this study has following objectives:
 To explore the causal relationship of stock return and trading volume
 To find out the trading volume effect on the return volatility
The research problem defined above leads to the following research questions:
 Is there any long run relationship between the trading volume and stock
return in Vietnam?
 Does the causal relationship between stock return and trading volume
exist in Vietnam‟s stock market? If yes then, what is direction and extent
of relationship between these variables?

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 Does ARCH effect exist in stock return of two indices? If yes then, is this
ARCH effect weaker when trading volume is added as an explanatory
variable in GARCH equation?
 Does ARCH effect exist in individual stock return? If yes then, does this
effect reduce when trading volume is included as an explanatory variable
in GARCH equation?
1.5 RESEARCH METHODOLOGY AND SCOPE
The Granger causality and ARCH/GARCH effect tests are employed to test the
proposed hypotheses. Theoretically, these tests are only appropriate when the
variables analyzed, including stock price, the index and trading volume, are
stationary and co-integrated. Therefore, it becomes necessary to conduct various
prior tests of integration and cointegration. In so doing, this thesis will apply the
unit root test (specifically the augmented Dickey-Fuller tests). Following previous
studies, this thesis will employ the Akaike Information Criterion (AIC) and
Schwarz Information Criterion (SIC) to determine the optimal lag lengths.
Data used in Granger causality and GARCH models are collected from two official
sources, namely, Hochiminh Stock Exchange and Hanoi Stock Exchange during the

May 2006 to July 2011 period. I also use the stock price of 37 large size (sorted in
market capitalization) companies as my sample. Similar to most previous studies,
this thesis will use the daily data to meet the required observations in GARCH
models. More details in handling variables will be discussed in chapter three.
1.6 THESIS STRUCTURE
In terms of structure, the thesis has five chapters. After defining the research problem,
questions for the study in chapter one, chapter two reviews previous researches
related to relationship between volume and price change. Chapter three discusses in
detail about the methodology including the data collection and analysis methods, and

5


hypothesis testing to support the model. Data analysis and findings are presented in
chapter four. This chapter presents descriptive results of return –volume and
volatility – volume relation in the aspect of market index and firms. Chapter five ends
with conclusion and implications.

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CHAPTER 2: LITERATURE REVIEW
2.1 THEORETICAL BACKGROUND:
Mixture of distritbution hypothesis
The mixture of distribution hypothesis in finance proposes that the net price change
X(t) over period t is the sum of (t) incremental inter – period steps, giving
X((t)) =

X t,i

(2.1)

Accordingly, the heavy tails fluctuation X(t) can be explained by inserting the
number of economic time (randomized time) or the number of information arrivals
that traders meet during t, typically associated with trading volume V(t). The
resulting convolution X((t)) has a mixed distribution that can capture
leptokurtosis, expound heterogeneity, including conditional heteroscedasticity, and
improve model fitting similar to nonparametric.
The mixture has statistical foundation from Probability theory, which concerned
with analysis of random variables, stochastic processes, and events. If y (t):=  X(t)
has density y (y ;) and economic time (t)≥0 has density  (), then the observed
convolution y ((t)) has a density mixture

y ()(y) =



0 y (y: )  () d 

(2.2)

Clark (1973) provides evidence showed that the standard Central Limit Theorem,
which maintains only when the number of random variables added is unchanged
over time, is violated in the case of speculative markets. He proposes the opposite
theorem in which the limit distribution of price changes is subordinate to the normal
distribution. In an attempt to exploit Bochner‟s and Feller‟s work on subordinated
Gaussian processes, Clark builds a model of asset return as following:

7

Denote by µy,, ²y and Ky respectively the mean, variance, and kurtosis of y , and
yz (t) is the conditional variance give random z . If X(t) ≡ X(t): -∞ < t < ∞
is a stochastic process and (t), :N→|R+ is a “driving process” then the
stochastically indexed X((t)) is subordinated to X(t). If (t) is stationary and
independent with mean

µ >0, and X(t)

(0,

X), then the subordinated

fluctuation X((t)) are stationary and independent, and distributed as following

X ((t ) )
For

µ

(0, µ x

X )

(2.3)

reflects the arrival of new information, only the average amount of new

information affects the scatter of imbedded return
normally distributed X(t)

N(0,

X ) and

X . If price fluctuations are

 < ∞ and (t) are independent

of X(t), then price fluctuations have kurtosis K larger than 3, thus, they are
considered to be heavy – tailed. The tails of price fluctuations grow heavier as the
variance of information flow raises. Further, if iid (t) are lognormal with
parameters  c,v² then
(2.4)
And from function (1) the convolution y(t) ≡ X((t)) is lognormal – normally
distributed:
(2.5)

Economic time (t), in which equity return should be heavier tailed during period of
substantial traders activity, may be positively associated with trading volume V(t).
For the log-price X(t) of cotton future prices, Clark specifies the curvilinear
relationship between price variance and trading volume as following:

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X(t) = V (t) , where ,  > 0

(2.6)

In short, the mixture distribution hypothesis creates the framework, in which the
distribution of price change is subordinate to a normal distribution and the positive
relationship between volume traded (in lognormal distribution) and equity return is
concerned. Since Clark‟s (1973) work, a large amount of studies has attempted to
support it.
2.2 EMPIRICAL STUDIES
2.2.1 Studies on volume – price change relation
The most cited and excellent review of research is Karpoff‟s work (1986,1987).
According to his articles, the main reasons for studying the price changes –volume
relation were (i) insight into structure of financial market, (ii) benefit for event
studies which use the volume and price data to reach inferences, (iii) critical time to
the debate over the empirical distribution of speculative markets, and (iv) important
implications to the studies of futures market. In the discussion of two sets of
hypotheses, the mixture of distribution and the sequential arrival of information
(SAI), Karpoff generaled previous studies into empirical conclusion which
suggested the positive and contemporaneous correlation between volume and price
variability.
Clark (1973), Harris (1983), Tauchen and Pitts (1983) and Andersen (1996) among
others, explained the positive correlation between volume and squared value of
price change with daily data on securities. For instant, Clark (1973) assumed
volume, which distribution was lognormal, could be a proxy for price data that were
generated by a conditional normal stochastic process with a changing variance
parameter. Using the same assumption, Harris (1983), Harris (1986), Harris (1987)
and Tauchen and Pitts (1983) showed that a mixture of bivariate normal
distributions could model the joint distribution of daily price changes and volume.

9


These two variables were assumed to be conditioned by the rate of information

which is uncorrelated and random. They also used maximum likelihood analysis to
estimate the model in the assumption of lognormal distribution for the mixing
variable.
With less agree to earlier studies, Anderson (1996) added a volume component
which was not information sensitive and a conditional Poisson distribution for the
trading process in order to modify the MDH model. He suggested the modified
model significantly outperformed the standard model.
Studying nine international markets (Canada, France, Hongkong, Italy, Japan,
Netherlands,Switzerland, UK and US), Chen, Firth, and Rui (2001) also found the
positive correlation between absolute value of stock price changes and volume.
Besides the MDH models and SAI models, they explained the relation with another
two models, the rational expectation asset pricing (REAP), and the differences of
opinion (DO). Using daily volume and return data from 1973 -2000, they concluded
that EGARGH models could represent for return of stock index data.
Malabika, Srinivasan and Devanadhen (2008) also confirmed the positive and
contemporaneous relationship between absolute price changes and volumes in six
markets (Hongkong, India, Indonesia, Malaysia, Korea, Tokyo and Taiwan). Based
on VAR model and EGARCH (1,1) model, the dataset in the period from 1st
January 2004 to 31st March 2008 showed the feedback system in Indonesia,
Hongkong, Malaysia and Taiwan. The evidence indicated stronger return causing
volume than volume causing return. They also found that return variance and lagged
trading volume has positive association for most of Asia – Pacific stock markeits
with the stable coefficient over the time. This finding is similar to results of Pyun
Lee and Nam (2000) for Korean market, Bohl and Henke (2003) for Polish market,
and Lucey (2005) for the Irish stock market.

10


In recent years, many researches focused more on Granger causality relationship

between volume- return to contribute the literature. During the decade of the 1990s
data, Kamath, et al (2005) examined the return –volume relation in four merging
markets and found the strong positive correlation between magnitudes of return and
volumes. In Malaysia and Indonesia, they found that causality run in both direction.
On the other hand, in Thailand and South Korea, they found that only return cause
the volume.
Another study of Kamath and Yi Wang (2006) showed similar results in six
developing Asian equity markets during the period from January 2003 and October
2005. In Malaysia, Singapore, South Korea, and Taiwan, they provided evidence
indicated that the market increase was accompanied by rising volume and vice versa.
Moreover, they also found that the correlation between positive return and volume
to be positive and correlation between negative return and volume to be negative.
The absolute return – volume relation was found to be statistically significant
positive in most of six markets, except the Indonesian market. The Granger
causality tests were employed to detect the causal direction between return and
volume. While in Taiwanese market, volume was found to Granger cause return, in
the South Korean market, they found return Granger causing volume. Meanwhile,
the absence of causality between two variables was supported by evidence in case
of Hongkong, Indonesia, Malaysia, and Singapore.
2.2.2

Studies on volume- volatility relation

Another distributions examine the effect of trading volume to the market return by
using generalized autoregressive conditional heteroskedasticity (GARCH) model in
hope of broaden the work of Lamoureux and Lastrapes (1990). The trading volume
is included as an explanatory variable in the conditional variance equation in
GARCH model. It is found to positively affect on conditional volatility.

11

Hiemstra and Jones (1994), Gallant et al. (1993) and Tauchen et al. (1996)
presented a positive correlation between trading volume and volatility by using
VAR, Granger causality test and GARCH models. Testing the data from Australian
Stock market in the period 24 April 1989 to 31 December 1993, Brailsford (1994)
presented a diminution in GARCH effect and in the persistence of variance when
trading volume was used. Similarly, in another study of Brailsford (1996), trading
volume - stock return volatility and trading volume – conditional volatility
relationship was also examined in Australian stock market. He found that the result
from GARCH (1,1) model was insignificant when the volume was taken into
consideration.
Sharma et al. (1996) studied the GARCH effects in the NYSE. The paper showed
how the volume explained the GARCH effects in market return. From that reason,
the authors considered a simple GARCH (1,1) model with and without daily
volume, and assumed the conditional normality and conditional t – distribution. The
data covered the period 1986-1989. The results implied that the introduction of
volume did not eliminate the GARCH effects. However, they found that the
coefficient of volume was positive and statistically significant. For market index
data of nine countries, Arago and Nieto (2005) also found that volume effects did
not cancel out GARCH effects at the country index level.
Ragunathan and Pecker (1997) considered the relationship between volume and
price variability for the Australian futures markets over the return series of the
contracts in the period January 1992 to December 1994. Applying models
developed by Schwert (1990), and Bessembinder and Seguin (1993), they suggested
that unexpected volume affected greater on volatility than expected volume.
Hogan et al. (1997) used daily data from 3 January 1988 to 31 December 1991 of
the S&P 500 cash and CME S&P 500 near zero term futures contracts to examine
the relationship between trading volume and market volatility. The results from

12


bivariate GARCH model showed that there was a significant positive relationship
between two variables.
Jacobs and Onochie (1998) also focused on the relationship between return
variability and trading volume in futures markets. They used bivariate GARCH – M
model to test the data set of daily observations for six futures contracts traded on the
LIFFE. The results also supported the positive relationship between trading volume
and price volatility.
Using GMM and Original least square regression method (OLS), Wang and Yau
(2000) continued paying attention to the interesting relationship in futures markets.
Based on two financial futures contracts (S&P 500 and DM) and two metal futures
contracts (gold and silver), the data set covered the period 2 January 1990 to 29
April 1994. The results provided evidence of positive relationship between trading
volume and price volatility, and negative relationship between price volatility and
lagged trading volume.
Applying the model of Bessembinder and Seguin (1993), Wanatabe (2001) found a
considerably significant and positive relationship between price volatility and
unexpected volume for the Nikkei 225 stock index futures. The sample period was
from 24 August 1990 to 30 December 1997. The results also showed that there was
no relationship between volatility and volume when the regulation increased
gradually.
In the work of Illueca and Lafuente (2003), link between spot volatility and trading
volume was not found in the Spanish stock index futures market. However, Pilar
and Rafael (2002) provided evidence of a decrease in the volatility and increase in
trading volume in the Spanish stock market by using a GIR model with a dummy
variable.
Applying VAR model with five lags in addition to a GARCH model to examine the
lagged volume and volatility effects for the two indexes of China, Lee and Rui

13


(2000) explored interesting results. It was evident to note that trading volume did
not Granger cause the stock market return in Chinese markets. However, when
testing the cross – market effects, they found that the US and Hongkong return help
predict return of Shanghai A and B stocks while US and Honkong volume did not
affect on volume in Chinese markets. They also discovered the feedback
relationship of return within the markets in China. Shenzen B return was Granger
caused by Shanghai A volumes, and Shanghai B stock return could be predicted by
Shenzen B volume.
Investigating the GARCH effect on the China‟s stock markets, Wong et al. (2005)
found that it completely disappeared when trading volume was added and the
persistence of volatility decreased gradually in most cases. They also found that the
number of transaction and the turnover affected positively on the conditional
volatility of the Chinese stock market.
In the paper of Jinliang et al. (2009), they emphasized the interaction of GARCH
and volume effects, and the impact of firm size and trading volume on these effects
for individual stocks of the Australian All Ordinaries Index. They concluded the
volume could be a good proxy of information flows and replace the GARCH effect
in the model. Furthermore, they confirmed that the elimination was higher for the
largest trading volume stocks and largest market capitalization stocks. Their results
also showed a stronger volume – volatility relationship for actively traded stocks.
Meanwhile, the thin trading stocks and small firms were found to lead a high
persistence of volatility of GARCH effect in estimated model.
Yet there has been very little research about this issue in the case of Vietnam so far
in both market level and firm level.

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CHAPTER 3: RESEARCH METHODOLOGY
3.1 HYPOTHESES:
Based on the above objectives and research questions, my analysis includes two
components:
-

Regarding the relationship between return and volume, the literature review

pointed out that the causality between them should be considered. Therefore, we
have hypotheses as below:
Hypothesis 1: Return does not Granger cause the volume.
Hypothesis 2: Volume does not Granger cause the volume.
-

Regarding the effect of volume on return volatility, many previous

researches proposed an explanatory power of volume in the conditional variance
equation. So, the hypothesis is:
Hypothesis 3: Trading volume does affect the volatility and make the
persistence of variance reduce significantly.
In more detail, the study would use the Granger causality to test the first two
hypotheses . The last one is investigated with GARCH and TGARCH models.
3.2 DATA DESCRIPTION
The data set consists of daily price and trading volume data for HOSE and HNX
indexes as well as 37 largest market capitalization listed companies. The sample
period for the market indices begins from 20th May 2006 and ends at 14th July 2011.
Meanwhile, the firms are tested during the period from their first traded day until
14th July 2011. In fact, these firms hold around 80% of total market capitalization.

Due to market index counting method in Vietnam, these 37 companies trading
activities may affect considerably to the market movement. However, not all of
them have the large trading volume. It may, therefore, be informative to focus on

15


the sorting securities to better understand the link between volume and volatility
and its difference at market level and firm level.
I calculate the continuously compounded stock return and index return as Rt= log
(Pt / Pt-1) where P is the stock price/index at the day t. All the stock price value was
adjusted to reflect right issues and dividends. I also measure the volume parameter
as VOLt = log (Vt / Vt-1) where V denotes the number of shares trading at day t. All
data is available on official website of HOSE and HNX.

3.3 ECONOMETRIC METHODOLOGY
3.2.1 Stationary and Unit Root test
This research design is completely based on the time series data, which is usually
trended. According to Gujarati (2003), if a time series is not stationary, we can
study its behaviors only in one time period under consideration, thus, we cannot
generalize all other periods. In regression analysis, it leads to the invalidity of the
forecasting results that are usually called as spurious regression phenomenon. From
this reason, testing whether a set of time series is stationary appears to be the first
task of any analysis.
In stationary time series, shocks will be temporary and over time, their effects will
be eliminated as the series revert to their long-run means values. On the other hand,
non-stationary time series will necessarily contain permanent components.
Therefore, the mean and/or the variance of a non-stationary time series will depend
on time, which leads to cases where a series (a) has no long-run mean to which the
series return, and (b) the variance will depend on time and will approach infinity as

time goes to infinity.
Most academic studies are applying the widely approved unit-root test methods,
introduced by Dickey-Fuller (1979). In statistic language, if a time series have a unit
root, it is called “non-stationary”. In this thesis, I concentrate on the augmented
Dickey-Fuller (ADF) test. As the error term is unlikely to be white noise, Dickey

16


and Fuller extended their test procedure suggesting an augmented version of the test
which includes extra lagged terms of the dependent variable in order to eliminate
autocorrelation. The lag length on these extra terms is either determined by Akaike
Information Criterion (AIC) or Schwarz Bayesian/Information Criterion (SBC, SIC),
or more usefully by the lag length necessary to whiten the residuals (i.e., after each
case, we check whether the residuals of the ADF regression are autocorrelated or
not through LM tests and not the DW test.
The three possible forms of the ADF test are given by the following equations:
p

Yt  Yt 1   i Yt i  u t

(3.1)

i 1

p

Yt    Yt 1    i Yt i  u t

(3.2)

i 1

p

Yt    T  Yt 1    i Yt i  u t

(3.3)

i 1

where: Yt : relevant time series; ∆: first difference operator; T: linear trend from time
series and ut: error term.
The difference between the three regressions concerns the presence of the
deterministic elements α and T. For choosing the best one among the three
equations, this thesis will first plot the data (of each variable) and observe the graph
because it can, to which extent, indicate the presence or not of deterministic
regressors.

3.2.2 Cointegration
In the case of having two non – stationary variables, we can consider an error as a
combination of two cumulated error processes. According to Asteriou and Hall
(2007), these processes are called stochastic trends and their combination is
expected to produce another non – stationary process. Suppose that, if two

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variables, say X and Y, are really related, the two stochastic trends would be very
similar to each other, and then their combination may be eliminate the non –

stationary. In this special case, the variables are cointegrated. Cointegration
becomes an overriding requirement for any economic model using non-stationary
time series data. If the variables do not cointegrate, we usually face the problems of
spurious regression and econometric work becomes almost meaningless. On the
other hand, if the stochastic trends do cancel to each other, then we have
cointegration.
Suppose that, if there really is a genuine long run relationship between Yt and Xt,
although the variables will rise overtime (because they are trended), there will be a
common trend that links them together. For an equilibrium, or long run relationship
to exist, what we require, then, is a linear combination of Yt and Xt that is a
stationary variable (an I(0) variable). A linear combination of Yt and Xt can be
directly taken from estimation the following regression:
Yt = 1 + 2Xt + t

(3.4)

and taking the residuals:
^

^

^

u t  Yt   1   2 X t

(3.5)

If the error term ( u t ) is trending over time, then the variables are not related, that
means they are not cointegrated. In contrary, if u t is constant over time, it is
stationary, then there is a long run linear relationship between the variables

Yt and X t , and thus they are cointegrated. In other words, Yt and X t are I(1)

variables and u t is I(0), which implies that Yt and X t are cointegrated and β 2 is
the cointegrating parameter.
According to Asteriou (2007), Engle and Granger proposed a straightforward
method to testing for cointegration. However, EG approach just examines the long
run relationship of two variables.

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3.2.3 Granger Causality Tests
A simple test developed by Granger (1969) that examines causality between two
variables has been widely applied in economic policy analysis. Following the VAR
model, the Granger causality test concerns about the ability of one variable to
predict the other. If a variable Xt can be predicted with larger precision by using
past values of the Yt variable rather than not using such past values, all other terms
remaining unchanged, it is said to be Granger – caused by variable Yt.
In Granger causality test, they found three cases of relationship between two
variables. Before that, it involves the estimation of VAR model: (3.6)
rt = 0 +

r t-i +

V t = 0 +

y i V t-i +

 j V t-j + t
 j r t-i + t

(3.6)
(3.7)

where t is uncorrelated white- noise error terms. Then we can have different cases:
Case 1 If lagged V terms in equation (3.6) are statistically different from zero as a
group, and the lagged r terms in equation (3.6) are not statistically different
from zero. In this case, we have that Vt causes Rt.
Case 2 The lagged R terms in equation (3.7) are statistically different from zero as
a group, and the lagged V terms in equation (3.7) are not statistically
different from zero. In this case, we have that Rt causes Vt.

Case 3 Both sets of V and R terms are statistically different from zero as a group in
equation (3.6) and equation (3.7), so that we have bi- directional causality.

Case 4 Both sets of V and R terms are not statistically different from zero in
equation (3.6 ) and equation (3.7), so that Vt is independent of Rt.
The Vector Autoregressive (VAR) method used for estimation and model with four
lags is selected based on SchwarzBayesian (SBC) Criteria.

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More analytically, I perform the following steps in process of conducting Granger
test:
Step 1

Regress Yt on lagged Y terms as in the following model:
r

Yt  a1  1Yt 1   yt

(3.8)

i 1

and obtain the RSS of this regression (which is the restricted one) and
label it as RSSR.
Step 2

Regress Yt on lagged Y terms plus lagged X terms as in the following
model:
r

s

i 1

j 1

Yt  a1  iYt 1    j X t  j   yt

(3.9)

and obtain the RSS of this regression (which is the unrestricted one)
and label it as RSSU.
Step 3

Set the null and alternative hypotheses as below:
s

H0 :

  =0 or X
j 1

j

s

H1 :

Step 4


j 1

j

t

does not cause Yt

 0 or X t does cause Yt

Calculate the F statistic for the normal Wald test on coefficient
restrictions given by:

F

(RSS R  RSS U ) / m
RSS u /( N  k )

(3.10)

where N is the included observations and k = m+n+1 is the number
of estimated coefficients in the unrestricted model.
Step 5

If the computed F value exceeds the critical F value, reject the null
hypothesis and conclude that Xt causes Yt. Similarly, we conduct the

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