Volatility in stock return series of vietnam stock market

It suggests that many previous studies may haveoverestimated the degree of volatility persistence existing in financial time series.The small value of coefficients of the dummies represe

NGUYỄN THỊ KIM NGÂN

VOLATILITY IN STOCK RETURN SERIES

OF VIETNAM STOCK MARKET

MASTER THESIS

-o0o -NGUYỄN THỊ KIM NGÂN

VOLATILITY IN STOCK RETURN SERIES

OF VIETNAM STOCK MARKET

MAJOR: BANKING AND FINANCE MAJOR CODE: 60.31.12

MASTER THESIS INSTRUCTOR: Dr VÕ XUÂN VINH

Ho Chi Minh City – 2011

Vinh, for his valuable time and enthusiasm His whole-hearted guidance,encouragement and strong support during the time from the initial to the final phaseare the large motivation for me to complete my thesis.

I also would like to thank all of my lecturers at Faculty of Banking and Finance,University of Economics Hochiminh City for their English program, knowledge andteaching during my master course at school

In addition, my thanks also go to my beloved family for creating good andconvenient conditions for me throughout all my studies at University as well ashelping me overcome all the obstacles to finish this thesis

Lastly, I offer my regards and blessings to all of those who supported me in anyrespects during the completion of the study

structural breaks in return variance of VNIndex in the Vietnam stock market byusing the iterated cumulative sums of squares (ICSS) algorithm The relationshipbetween Vietnam stock market’s volatility shifts and impacts of global crisis is alsodetected Using a long-span data, the results show that daily stock returns can becharacterized by GARCH and GARCH in mean (GARCH-M) models whilethreshold GARCH (T-GARCH) is not suitable About structural breaks, whenapplying ICSS to the standardized residuals filtered from GARCH (1, 1) model, thenumber of sudden jumps significantly decreases in comparison with the raw returnseries Events corresponding to those breaks and altering the volatility pattern ofstock return are found to be country-specific Not any shifts are found during globalcrisis period In addition, because the research is not able to point out exactly whatevents caused sudden changes, the analysis on relationship between theseinformation and shifts is just in relative meaning Further evidence also reveals thatwhen sudden shifts are taken into account in the GARCH models, reduction in thevolatility persistence is found It suggests that many previous studies may haveoverestimated the degree of volatility persistence existing in financial time series.The small value of coefficients of the dummies representing breakpoints inmodified GARCH model implies that the conditional variance of stock return ismuch affected by past trend of observed shocks and variance.

Our results have important implications regarding advising investors on decisionsconcerning pricing equity, portfolio investment and management, hedging andforecasting Moreover, it is also helpful for policy-makers in making andpromulgating the financial policies

TABLE OF CONTENTS iii

LIST OF FIGURES v

LIST OF TABLES vi

ABBREVIATIONS vii

1: INTRODUCTION 1

2: LITERATURE REVIEW 5

2.1 Common characteristics of return series in the stock market 5

2.2 Volatility models suitable to the stock return characteristics 6

2.3 Identification of breakpoints in volatilities and influence of the regime changes 7

2.4 Events related to regime changes 9

2.5 Sudden changes in economic recession? 10

2.6 Overstatement of ICSS algorithm in raw returns series 10

3: HYPOTHESES 12

4: RESEARCH METHODS 13

4.1 Stationarity 13

4.2 Testing for stationarity 14

4.2.1 Autocorrelation diagram 14

4.2.2 Unit root test 15

4.3 GARCH model 16

4.3.1 ARMA 16

4.3.1.1 Moving average processes - MA(q) 17

4.3.1.2 Autoregressive processes - AR(p) 17

4.3.1.3 ARMA processes 18

4.3.1.4 Information criteria for ARMA model selection 19

4.3.2 ARCH & GARCH Model 20

4.3.2.1 ARCH Model 20

4.3.2.2 GARCH Model 21

5: DATA AND EMPIRICAL RESULTS 27

5.1 Data 27

5.2 Empirical results 29

5.2.1 Suitable models for stock return series of Vietnam 29

5.2.1.1 Choosing suitable ARMA model 29

5.2.1.2 Test for ARCH effect 30

5.2.1.3 GARCH models 31

5.2.2 Identification of break points and detection of related events 33

5.2.2.1 Breakpoints in raw returns 33

5.2.2.2 Breakpoints in filtered returns 38

5.2.2.3 Analysis of each volatility period 44

5.2.2.4 General comments on events and volatility corresponding to sudden changes detected by ICSS algorithm 57

5.2.3 Combined model after including dummies 57

6: CONCLUSION 60

Implications of the research 60

Limitations of the study 61

REFERENCE 62

APPENDIX 66

Table A1 Descriptive statistics of Vietnam stock market’s daily stock return 66

Table A2 Correlogram and Q-statistic of VNIndex daily rate of return 67

Table A3 Unit Root Test on VNIndex’s daily return 68

Table A4 Summary for estimation results of all ARMA models 69

Table A5 Statistically significant ARMA models with C constants 70

Table A6 Statistically significant ARMA models without C constants 72

Table A7 Estimation results of GARCH models 74

Table A8 Estimation results of GARCH-M models 77

Table A9 Estimation result of TGARCH model 79

Table A10 Estimation result of GARCH model modified with sudden changes 80

Table A11 ICSS code on WINRAT 81

Figure 5.2 Structural breakpoints in volatility in raw returns 38 Figure 5.3 Structural breakpoints in volatility in filtered returns 39

Table 5.1 Descriptive statistics of Vietnam stock market’s daily return series 27

Table 5.2 Unit Root Test on VNIndex’s daily return 28

Table 5.3 Empirical results of different ARMA models 30

Table 5.4 ARCH effect at 7 th lag 31

Table 5.5 Empirical results of different GARCH-family models 32

Table 5.6 Breakpoints detected by ICSS algorithm in the raw returns 33

Table 5.7 Breakpoints detected by ICSS algorithm in the filtered returns 40

GARCH Generalized Autoregressive Conditional Heteroscedasticity

HOSTC Ho Chi Minh City Securities Trading Center

ICSS algorithm Iterated Cumulative Sums of Squares algorithm

1: INTRODUCTION

Volatility is a fundamental concept in the discipline of finance It can be describedbroadly as anything that is changeable or variable It is associated withunpredictability, uncertainty or risk Volatility is unobservable in financial marketand it is measured by standard deviation or variance of return which can be directlyconsidered as a measure of risk of assets Considerable volatilities have been found

in the past few years in mature and emerging financial markets worldwide As aproxy of risk, modelling and forecasting stock market volatility has become thesubject of vast empirical and theoretical investigations over the past decades byacademics and practitioners Substantial changes in the volatility of financial marketreturns are capable of having significant effects on risk averse investors.Furthermore, such changes can also impact on consumption patterns, corporatecapital investment decisions, leverage decisions and other business cycle Volatilityforecasts of stock price are crucial inputs for pricing derivatives as well as tradingand hedging strategies Therefore, it is important to understand the behavior ofreturn volatility

In addition to return volatility, some relevant problems attracting much interest ofresearchers have been whether or not major events may lead to sudden changes inreturn volatility and how unanticipated shocks will affect volatility over time.Concerning these factors, persistence term should be considered Persistence invariance of a random variable refers to the property of momentum in conditionalvariance or past volatility can explain current volatility in some certain levels Thelarger the persistence is, the higher the past volatility can be explained for thecurrent volatility The persistence in volatility is a key ingredient for accuratelypredicting how events will affect volatility in stock returns and partially determinesstock prices Poterba and Summers (1986) showed that the extent to which stock-return volatility affects stock prices (through a time-varying risk premium) dependscritically on the permanence of shocks to variance Hence, the degree to which

conditional variance is persistent or permanent in daily stock-return data is animportant economic issue.

ARCH models proposed by Engle and Bollerslev (1982) and generalized byBollerslev (1986) and Taylor (1986) have been proved to be sufficient in capturingproperties of time-varying stock return volatility as well as volatility persistence.Literature has found many evidences in supporting the capability of GARCHmodels in volatility estimation (Akgiray (1989) and Pagan, Adrian R et al (1989))rather than other non-GARCH models Since the introduction of simple GARCHmodels, a huge number of extensions and alternative specifications such as GARCH

in mean (GARCH-M), Threshold GARCH (Glosten, Jagannathan et al (1993)), hasbeen proposed in attempt to better capture the characteristics of return series.Meanwhile, a procedure based on an iterated cumulative sums of squares (ICSS) byInclan and Tiao (1994) is commonly used to detect number of significant/ suddenchanges in variance of time series, as well as to estimate the time points andmagnitude of each detected sudden change in the variance

While studies on stock markets in mature and emerging markets are widelyavailable, so far not many researches have focused on Vietnam Although being set

up much later than many countries in the world, since the establishment of the firstsecurities trading center of Vietnam Stock Market in Ho Chi Minh City (HOSTC)

on 28 July 2000, Vietnam stock market has been growing rapidly with improvedtransaction volume and market capitalization At the opening trading session, onlytwo stocks with a total market capitalization of VND986 billion (about 0.28% ofGDP of Vietnam) were traded at the market Vietnam stock market was thencharacterized by the illiquidity of stocks, incomplete legal framework andinsufficient corporate governance system However, over time, along with thedevelopment and world integration of Vietnam’s economy, it has gradually become

a critical channel in terms of mobilizing and distributing capital for short and

long-end of 2010), along with equitization itinerary, the number of listed companies hasincreased to 280 firms with a total market capitalization of VND591 trillion Themarket capitalization represents about 30% of the country’s GDP in 2010(equivalent to VND1,980,000 billion by the General Statistic Office), much higherthan the amount in 2000 Total stock value bought by foreign investors reached overVND15 trillion The stocks in HOSTC can be represented by VNIndex which is amarket-value-weighted index of all commons stocks on the HOSTC The high andrapid growth of Vietnam stock market is, of course, very appealing to domestic andforeign investors.

The main objective of this study is to investigate and to model the characteristics ofstock return volatility in Vietnam stock market The Generalized AutoregressiveConditional Heteroscedasticity (GARCH(p, q)) model is used to capture the nature

of volatility; GJG model (or TGARCH) and GARCH-in-mean (GARCH-M) are forexamining leverage effects and risk – return premium respectively Meanwhile, aprocedure based on iterated cumulative sums of squares (ICSS) is used to detectnumber of (significant) sudden changes in variance in time series, to estimate thetime points and magnitude of each detected sudden changes in the variance Majorevents surrounding the time points of increased volatility are also analyzed At thesame time, the linkage between volatility shifts in Vietnam stock market withimpacts from global crisis in US in 2008 is also mentioned These detectedvolatility regimes are then included in the standard GARCH model to calculate the

"true" estimate of volatility persistence

To solve the problem mentioned above, four research questions needed to beanswered are:

Question 1: What are characteristics of return volatility in Vietnam’s stock market?

Are they similar to the results gained from previous researches?

Question 2: Which volatility models are suitable to the stock return characteristics

found out?

Question 3: How many break points/ regime shifts are founded by using ICSS

algorithm? Are there any sudden changes found in global economic crisis period? And what are notable events corresponding to those regime shifts?

Question 4: How do these regime shifts in stock return variance affect volatilities in

models? And what is the change of persistence in variance after breakpoints are modified in models?

The remainder of this thesis is organized as separate sections instead of chapters as

in the conventional way of Vietnam The first reason is that each issue is not largeenough to set up a distinct chapter The second one is the structure of this study isfollowed the method guideline of Brooks (2008) Thus, the research will be asfollows: Section 2 gives a brief literature review; Section 3 formulates hypotheses;Section 4 focuses on the econometric methodology of selected models that haddescribed in literature review and applied in reality by other countries The data andempirical results are then reported in Section 5 Summary and concluding remarksare presented in the last Section

2: LITERATURE REVIEW

2.1 Common characteristics of return series in the stock market

Many studies have documented evidence showing that financial time series have anumber of important common features to financial data such as volatility clustering,leptokurtosis and asymmetry Volatility clustering indicates volatility tendencies infinancial markets occur in bunches That means large stock price changes areexpected to follow large price changes, and small price changes are followed byperiods of small price changes Leptokurtosis means that the distribution of stockreturns is not normal but exhibits fat-tails In other words, leptokurtosis signifieshigh probability for extreme values than the normal law predict in a series.Asymmetry, also known as leverage effect, means that a fall in return is followed by

an increase in volatility greater than the volatility induced by an increase in return.Fama (1965) investigated the behavior of daily stock-market prices in a wide range(from end of 1957 to September 26, 1962) for each of thirty stocks of the Down-Jones Industrial Average The author found that there was some evidence ofbunching in large value of return series and return changes were leptokurtosis infrequency distribution Also on the US stock market but from January 1, 1970through December 22, 1987, Baillie and DeGennaro (1990) studied the dynamics ofdaily expected stock returns and volatility and pointed out high persistence anddeviation from normal distribution with leptokurtosis and negative skewness in thedata Poon and Taylor (1992) in attempt to identify the relationship between stockreturns and volatility on the UK’s Financial Times All Share Index within 1965 –

1989 indicated clustering and high persistence in conditional volatility in thismarket These common characteristics of stock returns series continued to bediscovered in many following researches And recently, Emenike (2010) has foundout the similar features as in previous researches like volatility clustering,leptokurtosis and leverage effects when the author examined the volatility of stockmarket returns in Nigeria Stock Exchange (NSE) from January 1985 to December2008

2.2 Volatility models suitable to the stock return characteristics

To capture the volatility characteristics in financial time-series, several models ofconditional volatility have been proposed A popular class of model was firstintroduced by Engle (1982) Engle (1982) proposed to model time-varyingconditional variance with Auto-Regressive Conditional Heteroskedasticity (ARCH)processes using squared lagged values of disturbances This was later generalized

by Bollerslev (1986) to GARCH (generalized ARCH) model by including the lags

of conditional variance itself The GARCH model given by Bollerslev (1986) hasbeen extensively used to study high-frequency financial time series data However,both the ARCH and GARCH models capture volatility clustering and leptokurtosis,but as their distribution are symmetric, they fail to model the leverage effect Tofulfill this requirement, many nonlinear extensions of GARCH have been proposed.Some of the models include exponential GARCH (EGARCH) originally proposed

by Nelson (1991), GJR-GARCH model (or also known as Threshold GARCH(TGARCH)) introduced by Glosten, Jagannathan et al (1993) and Zakoian (1994).Moreover, ARCH-M specification was also suggested by Engle, Lilien et al (1987)

to capture relationship between risk and return Many researchers applied the abovemodels

Hamilton, Susmel et al (1994) studied US stock returns and reported that ARCHeffects were presented when the stock return series were observed at a highfrequency (daily or weekly returns) Bekaert and Harvey (1997) examinedthoroughly the behaviour of the volatility of stock indexes’ returns in 20 emergingcapital markets (Argentina, Chile, Colombia, Philippines, Portugal, Taiwan, …) forthe period January 1976 to December 1992 With GARCH (1, 1) and asymmetricGARCH models, they found the volatility difficult to model in this context sinceeach country exhibited a specific behaviour F.Lee, Chen et al (2001) used GARCHand EGARCH models for daily returns of Shanghai and Shenzhen index series over

showed high persistence and predictability of volatility In addition, no relationshipbetween expected returns and expected risks was also reported as a result ofdetecting GARCH-M model Also, Alberga, Shalit et al (2008) characterizedvolatility by analyzing Tel Aviv Stock Exchange (TASE) indices using variousGARCH models like EGARCH, GJR and APARCH Their results showed that theasymmetric GARCH model with fat-tailed densities improved overall estimation formeasuring conditional variance Similarly, by utilizing GARCH-type models,Floros (2008) modeled volatility and explained financial market risk on daily datafrom Egypt (CMA General index) and Israel (TASE-100 index) markets duringperiod from 1997 to 2007 The paper used various time series methods, includingthe simple GARCH model, as well as EGARCH, TGARCH, and so on Theconclusion was that the above models could characterize daily returns and that thefluctuation of risk and return were not necessarily on the same trend.

2.3 Identification of breakpoints in volatilities and influence of the regime changes

Relevant to stock market volatility, there are many works aimed at identifying thepoints of change in a sequence of independent random variables Many authors havefound that when the regime changes were taken into account, the above-mentionedhighly persistent ARCH/GARCH effects were reduced Lamoureux and Latrapes(1990) were among the first to study the consequences of jumps in theunconditional variance when the time series is conditionally heteroscedastic Theyanalyzed 30 exchange-traded stocks from January 1, 1963 to November 13, 1979via GARCH (1, 1) to examine the persistence of variance in daily stock return.Their studies pointed out that the standard GARCH model’s parameters when noregime shifts in variance were augmented were overstated and not reliable For lack

of a methodology such as ICSS algorithm, time point detection in sudden variancechange was conducted by dividing the study periods into equally spaced, non-overlapping intervals, within which the variance might be different A relativelyrecent approach to test volatility shifts was Inclan and Tiao (1994)’s iterative

cumulative sums of squares (ICSS) algorithm This algorithm allows forsystematically detecting multiple breakpoints in variance of a sequence ofindependent observations in an iterative way On the foundation that most offinancial time series did not follow assumption of constant variance, theyconsidered series that had stationary behavior for some time and then suddenly thevariability of the error term changes; it remained constant again for some time atthis new value until another change occurred Results gained from the ICSSalgorithm for moderate size (i.e., 200 observations and beyond) was comparable tothose obtained by a Bayesian approach or by likelihood ratio tests Furthermore,reducing the heavy computational burden required by these approaches was also amotivation for the design of ICSS algorithm According to them, this algorithmcould also be used for time series models By applying the ICSS algorithm toresiduals of autoregressive processes, obtained results were similar to those gainedfrom ICSS algorithm to sequences of independent observations Following themethod of Inclan and Tiao (1994), Aggarwal, Inclan et al (1999) detected volatilityshifts of stock returns in emerging markets like Japan, Hong Kong, Singapore,Taiwan, Philippines, Thailand, India, Brazil… over 10 years from May 1985 toApril 1995 The same conclusion was reported that volatility persistence wasdeclined if the breakpoints/ regime shifts were supplemented into the GARCH(1,1)model Similarly, clear effects of regime changes gained from ICSS algorithm onvolatility of stock return and reduction in highly persistent volatility of stock returnwere presented in the studies of Malik and Hassan (2004) for five major DownJones stock indexes in financial, industrial, consumer, health and technology sectorsfrom January 1, 1992 to August 6, 2003; Malik, Farooq et al (2005) for theCanadian stock returns; Wang and Moore (2009) for the stock markets of newEuropean Union (EU) members (including the Czech Republic, Hungary, Poland,Slovakia and Slovenia which were experienced during the period of economy

27, 2006; and Long (2008) for VNIndex in the Vietnam stock market from July

2000 to May 2007

2.4 Events related to regime changes

In addition to interest in high volatility feature of stock markets and influence ofregime shifts on volatility persistence, many works concerned about whether global

or local events were more important in making major shifts in variance of stockreturn and whether these events tended to be social, political or economic Inempirical study on what kind of events corresponding to regime shifts, Aggarwal,Inclan et al (1999) found that high volatility periods were associated with importantpolitical, social and economic events in each country rather than global events andthat important political events tended to be corresponding to sudden changes involatility And in their research, the October 1987 crash was the only global event

in the last decade that caused a significant jump in the volatility of several emergingstock markets like Mexico, Singapore, Malaysia, Hong Kong, US and UK.Aggarwal, Inclan et al (1999)’s findings were the same as those discovered byBekaert and Harvey (1997) and Susmel (1997), and Bailey and Chung (1995)respectively Bacmann and Dubois (2002) examined stock market indexes returns ofArgentina, Mexico, Malaysia, Philippines, South Korea, Taiwan and Thailand fromJanuary 1, 1988 until January 5, 2001 and had similar conclusion as Aggarwal,Inclan et al (1999) that the jumps were country specific and could be diversified Inrecent paper surveying Vietnam stock market, Long (2008) proved that detectedregime changes seemed to coincide with the changes in the stock market operatingmechanism, in the financial market opening for foreign investors, or in politicalevents around that time

Contrary to the above findings, after studying five major Down Jones stock indexes

in financial, industrial, consumer, health and technology sectors in the overall USmarket during 1992 – 2003, the conclusion drawn from the research of Malik andHassan (2004) was that most volatility breaks were associated with global eventsrather than sector-specific news Hammoudeh and Li (2006) also presented the

same viewpoint that major global events were the dominant factors for Gulf Arabstock markets.

2.5 Sudden changes in economic recession?

Of all events studied by some authors, impacts of crises on volatility changes ofstock return has still remained a large concern of many investors and researchers.Fernandez (2006) analyzed whether the Asian crisis in Thailand in July 1997 andthe terrorist attacks of September 11 caused permanent volatility shifts in the worldstock markets Both the iterative cumulative sum of squares (ICSS) algorithm andwavelet-based variance analysis were used to detect structural breaks in volatilityduring 1997–2002 on eight Morgan Stanley Capital International (MSCI) stockindices, comprising developed and emerging economies such as the World, Pacific,Far East, G7, Emerging Asia, North America, Europe, and Latin America The finalresults showed that all indices presented breakpoints around the Asian crisis, butonly Europe appears to have been affected around the days following the 9/11attacks Also, with the same method – ICSS algorithm, Wang and Moore (2009)proved that the evolution of emerging stock markets, exchange rate policy changesand financial crises seemed to cause sudden changes in volatility These papersimplied real influence of crises on stock markets despite at different levels

2.6 Overstatement of ICSS algorithm in raw returns series

As being discussed above, ICSS algorithm has been used widely in many authors’works However, recent literature has shown that the ICSS algorithm tends tooverstate the number of actual variance shifts This originated from ICSS algorithmproposed by Inclan and Tiao (1994) aiming to detect structural breaks in theunconditional variance of time-series This algorithm requires the time-series to beindependent while stock returns are known to violate this assumption because theseseries are conditionally heteroscedastic Hence, in Bacmann and Dubois (2002)’spaper, they pointed out one way to circumvent this problem That was by filtering

standardized residuals obtained from the estimation Filtering returns throughGARCH (1, 1) model helped partly remove both serial correlation and ARCHeffects in return series Therefore, by applying this procedure (and an alternativeone they proposed) to stock market indices of ten emerging markets, Bacmann andDubois obtained results that differed considerably from Aggarwal et al (1999) Thatwas “jumps in variance are less frequent than previously believed” The resultsgained from Bacmann and Dubois (2002)’s research was then applied by someother authors like Fernandez (2006) and Long (2008), of which Fernandez (2006)compared results from using ICSS to both raw and filtered returns and alsoconcluded that the number of shifts substantially decreased in case of filtered return.From the above literature review, this work will continue to enrich the existingempirical literature on exploiting characteristics of stock return volatility inVietnam stock market It will also extend the sample data to cover the period whenglobal economic crisis occurred to evaluate the impacts of such important externalevents on changes on volatility patterns of stock returns as well as relationshipbetween global recession and Vietnam stock market.

3: HYPOTHESES

Basing on the mentioned research questions and the above literature review, thehypotheses are formulated as follows:

Volatility characteristics of return series and corresponding models:

Literature review pointed out that volatility pooling, high persistence and normality distribution are common features to many series of financial asset returns.These phenomena are parameterized by GARCH, GARCH-M and TGARCHmodels Therefore, the hypotheses are proposed as below:

non-Hypothesis 1: Return volatility in Vietnam stock market has similar characteristics

as found in financial theory (Answer in Section 5.1 and 5.2.1.3)

Hypothesis 2: GARCH models are suitable to characterize volatility of Vietnam

stock market’s return series.(Answer in Section 5.2.1.3)

Breakpoint identification and influence of regime shifts on volatility persistence:

To identify sudden jumps in return variance, ICSS algorithm proposed by Inclanand Tiao (1994) is one of methods that has been applied so popularly in recentstudies (Aggarwal, Inclan et al (1999), Malik, Farooq et al (2005), Long (2008),Wang and Moore (2009), etc) Events contributing to sudden changes in volatilitywere found to be local or global, depending on particular situation of each country.Some stock markets were discovered to have breakpoints around the crisis periodswhile others were not An interesting thing is that the variance persistence wasreduced when regime shifts were combined into standard GARCH model Hence,for Vietnam stock market, two following hypotheses are suggested:

Hypothesis 3: Many breakpoints (including in economic crisis period) are found by

ICSS algorithm in research periods All sudden changes are corresponding to remarkable events (Answer in Section 5.2.2.1 and 5.2.2.2)

Hypothesis 4: These regime shifts in stock return variance strongly affect

4: RESEARCH METHODS

To conduct the research, the thesis firstly examine the data for autocorrelation andstationarity of Vietnam stock market’s return series on the basis of the Ljung-Box(LB) and Augmented Dickey-Fuller (ADF) test statistics to check whether the datacan be meaningful in modeling forecast Based on the results gained fromautocorrelation diagram and reference to Akaike information criterion (AIC) andSchwarz’s (1978) Bayesian information criterion (SBIC), we will estimate andchoose a suitable model for mean equation of return in form of autoregressivemoving average (ARMA(p,q)) models

The next step is testing for the presence of ARCH effects and estimating GARCHmodels Appropriate models are then selected also on the basis of AIC and SBIC.After that, following the previous studies of Aggarwal, Inclan et al (1999), Malikand Hassan (2004) and so on, shifts in return volatility are detected with the iteratedcumulative sums of squares (ICSS) algorithm At last, suitable GARCH model isestimated with dummy variables corresponding to the breakpoints to check changes

in parameters of models if any

The following are the methods and models applied in this research Most of themare based on literature of Brooks (2008)

4.1 Stationarity

The first concept is whether a series is stationary or not According to literature ofBrooks (2008), a stationary series can be defined as one with a constant mean,constant variance and constant autocovariances for each given lag An examination

of whether a series can be viewed as stationary or not is essential for the followingreasons:

 The stationarity or otherwise of a series can strongly influence its behaviourand properties To illustrate this feature, the term ‘shock’ is usually used to denote achange or an unexpected change in a variable or perhaps simply the value of theerror term during a particular time period ‘Shocks’ to the system will gradually die

away in a stationary series Particularly, a shock during time t will have a smaller effect in time t +1, a smaller effect still in time t + 2, and so on.

 The use of non-stationary data can lead to spurious regressions If standardregression techniques are applied to non-stationary data, the end result could be aregression that ‘looks’ good under standard measures (significant coefficient

estimates and a high R2), but which is really valueless Such a model would betermed a ‘spurious regression’

Gujarati (2003) claimed that if a series is non-stationary, its behavior is studied only

in the time period covered by the paper Therefore, generalization for other periodscan not be reached For forecasting purpose, non-stationary series will not haverealty value because in forecasting time series, volatility trends of past and currentdata are assumed to be maintained for future phases And therefore, forecast forfuture time can not be implemented if the data itself often changes Hence, the basiccondition for forecast of a time series is its stationarity

4.2 Testing for stationarity

Two popular methods for testing stationarity are autocorrelation diagram and unitroot test

k

r r

r r r r p

1

2

1

) (

) )(

The above equation is called autocorrelation function and denoted as ACF Theautocorrelation test aims to determine whether the serial-correlation coefficients aresignificantly different from zero We have two hypotheses as:

H0: pk=0

H1: pk  0

If a time series is random, autocorrelation coefficients are random variables withnormal distribution and mean 0 and their variances are 1/N Therefore, withstandard error of autocorrelation coefficient of 1 /N , we can create a confidenceinterval for pk If pkis out of that confidence interval, the null hypothesis is rejected

To test the joint hypothesis that all autocorrelations are simultaneously equal tozero, the Ljung–Box portmanteau statistic (Q) is used The last two columns inautocorrelation plot are Ljung–Box Q-statistics and corresponding probabilityrespectively The Ljung–Box Q-statistics are given by:

N

Q

1

2 ) 2 (Where p j is the jth autocorrelation and N is the number of observations Under the

null hypothesis of zero autocorrelation at the first k autocorrelations

(p1  p2  p3   p k  0 ), the Q-statistic is distributed as chi-squared with degrees

of freedom equal to the number of autocorrelations (k)

4.2.2 Unit root test

Unit root test is popularly used test to verify whether a time series is stationary ornot The early and pioneering work on testing for a unit root in time series was done

by Dickey and Fuller (Fuller (1976); Dickey and Fuller (1979)) The basic objective

of the test is to examine the null hypothesis that = 1 in

t t

against the one-sided alternative  < 1 Thus the hypotheses of interest are

 H0:  = 1 (series contains a unit root )

 H1:  < 1 (series is stationary)

In practice, the following regression is employed, rather than (4.1), for ease ofcomputation and interpretation

t t

Dickey - Fuller (DF) tests are also known as τ - tests, and can be conducted

allowing for an intercept, or an intercept and deterministic trend, or neither, in thetest regression The null hypothesis of a unit root is rejected in favour of thestationary alternative in each case if the test statistic is more negative than thecritical value

4.3 GARCH model

There are two equations estimated in a basic model, one for the mean which is asimple ARMA model and another for the variance which is identified by aparticular ARCH specification

4.3.1 ARMA

Time series models are an attempt to capture empirically relevant features of theobserved data that may have arisen from a variety of different (but unspecified)structural models AutoRegressive Integrated Moving Average (ARIMA) model is

an important class of time series models, firstly introduced by Box and Jenkins(1976)

4.3.1.1 Moving average processes - MA(q)

The simplest class of time series model that one could entertain is that of the

moving average process Let ut (t = 1, 2, 3, ) be a white noise process with E(ut)

= 0 and var(ut) = 2 Then

q t q t

t t

A moving average model is simply a linear combination of white noise processes,

so that yt depends on the current and previous values of a white noise disturbanceterm In other words, current value of y at time t depends on not only currentinformation but also information in the past However, most recent news has muchvalue than previous ones

To identify qth lag, we can use autocorrelation plot as follows: autocorrelation

function (acf) will has significant non-zero trend and equal zero after qth lag whilepartial autocorrelation function (pacf) has zero trend immediately

(The partial autocorrelation function, or pacf, measures the correlation between anobservation k periods ago and the current observation, after controlling forobservations at intermediate lags (i.e all lags < k) i.e the correlation between yt

and yt−k, after removing the effects of yt−k+1, yt−k+2, , yt−1)

4.3.1.2 Autoregressive processes - AR(p)

An autoregressive model is one where the current value of a variable, y, depends

upon only the values that the variable took in previous periods plus an error term

An autoregressive model of order p, denoted as AR(p), can be expressed as

t p t p t

t

y 1 12 2    

where u t is a white noise disturbance term and  presents average value of theseries.

This expression can be written more compactly using sigma notation as below:





p

i 1 i1

 is the importantcondition to ensure stationarity of the series y t

The same as in MA(q), pth lag can be determined by using autocorrelation plot byfollowing method: autocorrelation function (acf) has zero trend immediately while

partial autocorrelation function (pacf) has significant non-zero trend until pthlag and

equal zero after pthlag

Generally, few time series satisfy conditions of AR(p) or MA(q) models but theyoften combines the two models That means a stationary series may be in form of anARMA(p, q) model

4.3.1.3 ARMA processes

An ARMA(p, q) model is the combination of AR(p) and MA(q) models Similar to

AR(p) and MA(q), ARMA (p, q) is also appropriate for stationary series Such a

model states that the current value of some series y depends linearly on its own

previous values plus a combination of current and previous values of a white noiseerror term The model could be written

 An autoregressive process has:

 a geometrically decaying acf

 a number of non-zero points of pacf = AR order

 A moving average process has:

 a number of non-zero points of acf = MA order

 a geometrically decaying pacf

 A combination autoregressive moving average process has:

 a geometrically decaying acf

 a geometrically decaying pacf

4.3.1.4 Information criteria for ARMA model selection

The identification stage would now typically not be done using graphical plots ofthe acf and pacf The reason is that when real data is relative complex and itunfortunately rarely exhibits the simple patterns in autocorrelation plots Using theacf and pacf becomes very hard to interpret and thus difficult to specify anappropriate model for the data Another technique, which removes some of thesubjectivity involved in interpreting the acf and pacf, is to use what are known asinformation criteria

There are several different criteria; but the two most popular information criteria are

Akaike (1974)’s information criterion (AIC), Schwarz (1978)’s Bayesian information criterion (SBIC) These two criteria are the most popular ones used in

analyzing time series like ARIMA, ARCH, GARCH… These are expressedrespectively as

T

k AIC ln(ˆ 2 ) 2

) (ln ) ˆ

T

k SBIC  where ˆ 2 is the residual variance (also equivalent to the residual sum of squares

divided by the number of observations, T ), k is the total number of parameters estimated and T is the sample size.

It is said that a model that minimizes the value of an information criterion should bechosen In general, such criteria may often lead to contradictory results and differentconclusions are inevitable However, general principal is choosing model thatcontain many criteria having lower values than the others

4.3.2 ARCH & GARCH Model

Although the properties of linear estimators are very well researched and very wellunderstood, it is likely that many relationships in finance are intrinsically non-linear Some important features common to much financial data, includingleptokurtosis, volatility clustering and leverage effects are unable to explain inlinear model Numerous types of non-linear models have been found out, but some

of the most popular non-linear financial models in modelling and forecastingvolatility are the Autoregressive Conditionally Heteroscedastic (ARCH) orGeneralized ARCH (GARCH) models

4.3.2.1 ARCH Model

Engle (1982) proposed to model time-varying conditional variance with ARCHprocesses using lagged disturbances ARCH models have capability in capturingsome important stylised facts of many economic and financial data These include

changes of either sign (volatility clustering or autocorrelation in volatility ) Underthe ARCH model, the ‘autocorrelation in volatility’ is modelled by allowing the

conditional variance of the error term, σ2t, to depend on the immediately previous

value of the squared error:

2 2

2 1 1 0

q j

j  0   0 , 1 , 2 , ,

model where the error variance depends on q lags of squared errors.

The advantage of ARCH formulation is that the parameters can be estimated fromhistorical data and used to forecast future patterns in volatility

4.3.2.2 GARCH Model

One of the weaknesses of the ARCH model is that it often requires many

parameters and a high order q to capture the volatility process To overcome this

shortcoming, Bollerslev (1986) developed the GARCH model The GARCH model

is based on an infinite ARCH specification, which enables to reduce the number ofestimated parameters by imposing nonlinear restrictions This model allows pastconditional variances to be dependent upon previous own lags The basic estimationmodel also consists of two equations, one for the mean which is a simple

autoregressive model and another for the variance which is identified by a particularARCH specification The GARCH (p, q) can be represented as follows:

2

where p is the order of GARCH

q is the order of ARCH process

error, u t, is assumed to be normally distributed with zero mean andconditional variance, 2

t



t

R is return

The value of  is expected to be small All parameters in variance equation must be

positive to ensure that conditional variance 2

t

 is non-negative The sum of  and

 measures the persistence of volatility for a given shock, and a value of 1 wouldentail an integrated GARCH (IGARCH) process, implying that shocks have apermanent effect on the variance of a series

4.4 TGARCH Model

Enforcing a symmetric response of volatility to positive and negative shocks is one

of the primary restrictions of GARCH models However, a negative shock tofinancial time series has been argued to be likely to cause volatility to rise by morethan a positive shock of the same magnitude Therefore, to consider asymmetricbetween positive and negative shocks, many nonlinear extensions of GARCH havebeen proposed, including the so-called GJR model (which is also known asThreshold GARCH or TGARCH) by Zakoian (1994) and Glosten, Jagannathan et

al (1993) The GJR model is a simple extension of GARCH with an additional term

2 1

2 1

2 1 1

For a leverage effect, we would see  > 0 Notice now that the condition for

non-negativity will be  > 0, 1 > 0, β ≥ 0, and 1 +  ≥ 0 That is, the model is still admissible, even if γ < 0, provided that 1 + γ ≥ 0.

In this model, good news and bad news have differential effects on the conditionalvariance Good news has an impact of 1, while bad news has an impact of  + 1

If  > 0 then the leverage effect exists between bad news and good news, while if

 = 0, news impact is symmetric

4.5 GARCH-M model

In most financial models, investors are supposed to be rewarded for takingadditional risk by obtaining a higher return This concept is operationalised byletting the return of a security be partly determined by its risk Engle, Lilien et al.(1987) suggested an ARCH-M model where the conditional variance of assetreturns is incorporated into the conditional mean equation Since GARCH modelsare now considerably more popular than ARCH, it is more common to estimate aGARCH-M model In this way, GARCH-M model is given by the followingspecification:

2



If δ is positive and statistically significant, then increased risk, given by an increase

in the conditional variance, leads to a rise in the mean return Thus δ can be

interpreted as a risk premium In some empirical applications, the square root form,

ICSS algorithm was introduced by Inclan and Tiao (1994) to detect sudden changes

in variance caused by shocks Let the εt be a series with zero mean, and anunconditional variance σ2

t This time series of interest has a stationary variance over

an initial time period until a sudden break takes place The variance is thenstationary until the next sudden change occurs This process repeats through time,giving a time series of observations with a number of NT breakpoints in theunconditional variance along the sample with T observations Denoted variance foreach interval is  j, j 0 , 1 , 2 ,N Tand 1 12   N T is a set of correspondingbreakpoints:

2 0

2 

 t  1t1

= 2 1

 1t2

…

= 2

T N

C D

upper and lower boundaries for variance changes When the maximum of the

absolute value of Dkis greater than the critical value, there is a change point

Let define k* as the point in time at which the maximum absolute value of Dk isreached Then, if maxk (T 2/ D k (standardized distribution of Dk) at k* falls

outside the pre-determined boundaries, k* is taken as an estimate of the changepoint Inclan and Tiao (1994) computed and pointed out critical values of 1.358being the 95th percentile of the asymptotic distribution of max standardized Dk.

Upper and lower boundaries can be set at +/- 1.358

However, Inclan and Tiao (1994) claimed that using the Dk function to find out themultiple break points simultaneously may be questionable due to the “masking

effect” Therefore, “an iterative scheme based on successive application of Dk topieces of the series, dividing consecutively after a possible change point is found”,

is suggested Firstly, the Dk function is applied to the whole samples to find out thefirst possible break point (k1*) Secondly, each of the two sub-series divided by

k1*continues to be examined by the Dk function This process is continued until the

maximum standardized Dk is no longer larger than the critical value 1.358 After allthe break points are detected, the last procedure is to check the existence andconvergence of possible break points The last procedure is implemented by

applying Dk function for each phase from (ki-1* +1) to ki+1* with k0*=0 and i=1,2,…,NT until the number of change points does not change and the points found innew pass are “close” to those on the previous pass

In addition, according to Inclan and Tiao (1994), this algorithm can be also included

as part of the residual diagnostics for practitioners fitting time series models.Through simulation results, it is showed that when the ICSS algorithm is applied toresiduals of autoregressive processes, similar results to those obtained whenapplying the ICSS algorithm to sequences of independent observation are found

4.7 Combination of GARCH model and sudden changes

Lamoureux and Latrapes (1990) and some other researchers showed that volatilitypersistence was overestimated when standard GARCH models were applied to aseries with underlying sudden changes in variance Regime shifts should be addedinto the standard GARCH model to get reliable parameter estimates in theconditional variance equation Hence, after finishing the detection of the breakpoints that cause sudden changes, the ARCH/GARCH model specified by equations(4.3) to (4.6) is be modified as follows:

1

2 1

2 2

2 1 1

  is the constant term that stands for the average volatility of the firstvolatility regime, ignoring any effect of past residuals on the conditional variance

 The coefficients of D1 , D 2 , , Dn show how the subsequent regimes’volatility is different from the first regime volatility and how the volatility variesbetween different regimes

5: DATA AND EMPIRICAL RESULTS

5.1 Data

The data employed in this study comprise 2,121 observations of daily closing stockprice index, obtained from the website of Hochiminh Stock Exchange (www.hsx.vn).The sample period is from 1 March 2002 to 31 August 2010 which is the mostupdated data to the time of this study Since securities trading transactions havebeen conducted every working day from March 2002 as today instead of tradingonly once every two working-days, 1 March 2002 is chosen for this thesis to createsynchronization in data To represent for Vietnam stock market index in this thesis,the VNIndex of HOSTC is chosen since HOSTC was launched first and has analmost 4 year-longer history than that of HASTC VNIndex is the capitalization-weighted index of all the companies listed on the Vietnam official stock exchange.Table 5.1 shows the descriptive statistics for daily stock market returns with dailyreturns computed as below:

Rt= ln(Pt/ Pt-1)where Ptis the daily price at time t and Pt-1is the daily price at time t-1.

Table 5.1 Descriptive statistics of Vietnam stock market’s daily return series

and asymmetry The positive skewness coefficient of 0.014 indicates that series areskewed towards the right The kurtosis of the Vietnam stock market’s return is 4.14,implying leptokurtic or the series have distribution with fatter tail and more peaked

at the mean than a normal distribution

Similarly, under the null hypothesis that Jarque-Bera statistic is normal distribution

at value of 0, the Jarque-Bera value of 115.73 here confirms non-normaldistribution of Vietnam stock market’s return as well as another indication of theexcess kurtosis as just concluded

The conclusion that daily return series observed in Vietnam stock market have normality distribution is reasonable, as it is common phenomenon in emergingmarkets’ data set

non-In addition, autocorrelation and stationarity of Vietnam stock market’s return arealso checked on the basis of the Ljung-Box (LB) and Augmented Dickey-Fuller(ADF) test statistics The results are reported in Table A2, A3 in the Appendix andTable 5.2 below It can be seen in Table A2 that there is a significantautocorrelation between stock returns

Table 5.2 Unit Root Test on VNIndex’s daily return

Null Hypothesis: R has a unit root

Exogenous: None

Lag Length: 3 (Automatic based on SIC, MAXLAG=25)

t-Statistic Prob.*

Augmented Dickey-Fuller test statistic -18.95251 0.0000

10%

*MacKinnon (1996) one-sided p-values

The Augmented Dickey-Fuller (ADF) test for stock return series shows the result to

With the features such as autocorrelation and stationary evidenced above, it showsclear volatility clustering and it seems that volatility trend of past and current valuescan provide some predictions about future returns Figure 5.1 below provides anoverview of volatility clustering of daily stock return.

Figure 5.1 Daily return series on HOSE

5.2 Empirical results

5.2.1 Suitable models for stock return series of Vietnam.

5.2.1.1 Choosing suitable ARMA model

For a basic GARCH model, two equations, one for the mean and another for thevariance will be estimated From the described characteristics of the data, with thestationarity of time series, ARMA models may be suitable for mean equation of thiskind of data

Many ARMA models with different orders are identified to find out what is themost appropriate one Table A4 in the Appendix reported the estimation results ofall ARMA models The finding points out that only four models have statistically

significant, indicating the dependence of return on its own previous value andcurrent and previous values of error term These models include ARMA(1,0),ARMA(2,0), ARMA(0,1) and ARMA(1,2) The regression results show that thecoefficients in all the equations are statistically significant at the 1 percent level,coefficients of the constant C are exceptions Hence, models without constant Cseem to be more conformable.

Table 5.3 Empirical results of different ARMA models

 1  2 1 2 AIC SBC ARMA(1,0) 0.294856

-0.271013 (0.0000)

-5.495420 -5.487409

By reference to Akaike information criterion (AIC) and Schwarz’s (1978) Bayesianinformation criterion (SBIC), ARMA(1,2) model with smallest value for AIC andSBIC is the most suitable model for stock return series of Vietnam stock market

5.2.1.2 Test for ARCH effect

Before estimating a GARCH-type model, it is important to test for existence ofARCH effect to make sure this kind of models is appropriate for the data The resultgained from Eview estimation also shows significant ARCH effects up to the 7thlag

as in Table 5.4 At a high frequency of stock return series in Vietnam stock market,the result is consistent with the study of Hamilton, Susmel et al (1994)

Table 5.4 ARCH effect at 7 th lag

Heteroskedasticity Test: ARCH

Test Equation:

Dependent Variable: RESID^2

Method: Least Squares

Date: 11/20/10 Time: 16:56

Sample (adjusted): 3/14/2002 8/31/2010

Included observations: 2112 after adjustments

Coefficient Std Error t-Statistic Prob.

Adjusted R-squared 0.180745 S.D dependent var 0.000463

S.E of regression 0.000419 Akaike info criterion -12.71396

Sum squared resid 0.000369 Schwarz criterion -12.69254

Log likelihood 13433.94 Hannan-Quinn criter -12.70612

Prob(F-statistic) 0.000000

5.2.1.3 GARCH models

A GARCH(p,q) model with more parsimonious is more widely used than an ARCHmodel with too many lags in result estimation GARCH model allows an infinitenumber of past squared errors to affect conditional variance In next step, withARMA(1,2) for mean equation, a number of different GARCH-family models areestimated to capture features of stock return series

Table 5.5 reports the parameter estimates of all conditional volatility family) models that were defined in the previous section and have statisticalsignificance in the return series of Vietnam stock market