Management of market risk: case study of modelling volatility in Vietnam stock market

This thesis employ the GARCH type models, both symmetric and asymmetric including ARCH 1, GARCH 1,1, GARCH-M 1,1, EGARCH 1,1 and TGARCH 1,1 to examine the sufficient models for capturing

  

MASTER OF BUSINESS ADMINISTRATION

MANAGEMENT OF MARKET RISK:

CASE STUDY OF MODELLING VOLATILITY

IN VIETNAM STOCK MARKET

  

BY

LAM VAN BAO DAN

  

MASTER OF BUSINESS ADMINISTRATION

MANAGEMENT OF MARKET RISK:

CASE STUDY OF MODELLING VOLATILITY

IN VIETNAM STOCK MARKET

A thesis submitted in partial fulfillment of the requirements for

the degree of Master of Business Administration

Abstract

The thesis concerns with market risk management It has implications for businesses and investors, especially those hold investment in stocks In particular, the thesis investigates the technique to model stock volatility in Vietnam stock market

The rapid growth of Vietnam stock market recently has received a great attraction of local and global investors However, like other emerging stock markets, this growth has accompanied with high risk Over the past thirty years, a huge number of articles have discussed the volatility of stock returns in developed and emerging capital markets Unfortunately, even though Vietnam stock market has started trading from

2000, there has been relatively little work done on modelling and forecasting the return volatility in Vietnam stock market

This thesis employ the GARCH type models, both symmetric and asymmetric including ARCH (1), GARCH (1,1), GARCH-M (1,1), EGARCH (1,1) and TGARCH (1,1) to examine the sufficient models for capturing the characteristics of the return volatility in Vietnam stock market The data set of VN-Index over nine year period from March, 2002 to December, 2011 which divided into four periods including before crisis, crisis, recovering and whole period The findings suggest the sufficiency of ARCH (1), GARCH (1,1) and GARCH-M (1,1) models in capturing properties of conditional variance in Vietnam stock market The results also provide the indicator of the risk-reward relationship and show the weak evidence of asymmetry in the return series in Vietnam stock market

Table of Contents Page

I INTRODUCTION 8

1.1 Background of the Thesis 8

1.2 Research Questions and Objectives 11

1.2.1 Research Questions 11

1.2.2 Research Objectives and Implications 11

1.3 Vietnam Stock Market Overview 11

1.3.1 Introduction 11

1.3.2 VN-Index 16

1.4 Outline of the Thesis 20

II LITERATURE REVIEW 21

2.1 Volatility Definition 21

2.2 The Characteristics of Volatility in Financial Market 22

2.3 Literature Review 23

III DATA AND METHODOLOGY 35

3.1 Data 35

3.2 Descriptive Statistics 37

3.2.1 Histogram and Statistics Definition 37

3.2.2 Descriptive Statistics of Return Series for the Period before Crisis 39

3.2.3 Descriptive Statistics of Return Series for Crisis Period 40

3.2.4 Descriptive Statistics of Return Series for Recovering Period 41

3.2.5 Descriptive Statistics of Return Series for the Whole Period 42

3.2.6 Conclusions 43

3.3 Methodology 44

3.3.2 Testing for ARCH Effects 45

IV EMPIRICAL RESULTS 53

4.1 Testing for ARCH Effect 53

4.2 Empirical Results of Different Periods 54

4.2.1 Empirical Results of the Period before Crisis 54

4.2.2 Empirical Results of the Crisis Period 57

4.2.3 Empirical Results of the Recovering Period 58

4.2.4 Empirical Results of the Whole Period of Vietnam Stock Market 59

V SUMMARY AND IMPLICATIONS 62

5.1 Summary and Implications 62

5.2 Limitations and Recommendations for Further Research 63

VI APPENDIX 65

6.1 Appendix-1: Testing for ARCH Effect 65

6.1.1 Before Crisis Period (From March, 2002 to December, 2007) 65

6.1.2 Crisis Period (From January, 2008 to December, 2009) 66

6.1.3 Recovering Period (From January, 2010 to December, 2011) 67

6.1.4 Whole Period (From March, 2002 to December, 2011) 68

6.2 Appendix-2: GARCH Models Analysis 69

6.2.1 Before Crisis Period (From March, 2002 to December, 2007) 69

6.2.2 Crisis Period (From January, 2008 to December, 2009) 74

6.2.3 Recovering Period (From January, 2010 to December, 2011) 79

6.2.4 Whole Period (From March, 2002 to December, 2011) 84

REFERENCES 89

List of Tables

List of Figures

Figure 8 Histogram of daily return series of VN-Index

I would also like to thank all my friends in the program for supporting and encouraging

me to finish this thesis

Finally, special thanks also go to my wife and my family for their love and staying beside me during my study

I INTRODUCTION

Investing in emerging stock markets can make a large return but also creates a big loss for businesses because of high volatility (high risk) Therefore, finding a technique to model volatility is important for businesses and investors investing in stock market This thesis will investigate the volatility models which best fits the Vietnam stock market conditions Modelling volatility will help businesses and investors understand and better manage risks involved in their investment

Volatility is more and more important in financial market There are a huge number of researches and discussions for volatility in the past thirty years and especially in the recent years This is because volatility is a special indicator in financial market It is a key factor in many securities pricing formula as well as the value-at-risk models

Even though volatility is unobservable, it plays an important role in making investment decision On the other hand, it is also the interest of the policy makers in financial markets The policy makers are interested in the impact of volatility on the stability of the financial market and hence on the economy

Because of the above implications, volatility is the focus of several studies for estimation and forecast The volatility index (VIX) and Nasdaq Volatility Index (VXN) that defined as a weighted of prices for a range of options on the S&P 500 index and the Nasdaq 100 index have started trading from 2006 It is calculated in real time by Chicago Board Option Exchange (CBOE) These are two of the world’s most popular index of investors concerning to future stock market volatility The goal is to estimate the implied volatility of the stock market over the next 30 days It is proven that the low volatility index, the high trader confidence

There are a lot of models that can be implied for modelling and forecasting volatility including ARCH/GARCH models and non-GARCH models However, ARCH model

proposed by Engle (1982) and generalized by Bollerslev (1986) are said to be most sufficient for capturing the characteristics of the time varying stock return volatility From the introduction of the GARCH model, a huge number of GARCH extensions or GARCH family such as GARCH in mean (GARCH-M) (Bollerslev, 1986), EGARCH (Nelson, 1991), Threshold GARCH (TGARCH) (Glosten, Jagannathan and Runkle, 1993), Asymmetric GARCH model (AGARCH) (Engle, 1990), etc have been studied and proven to be sufficient for modelling and forecasting stock return volatility However, different papers support different models and show the conflicts in implication The empirical results argue that different models are suitable for different markets and in different time periods

Therefore, we will employ several widely accepted GARCH models including ARCH, GARCH, GARCH-M, TGARCH and EGARCH to investigate the volatility of Vietnam stock market in this thesis From the results of the study, we will suggest the sufficient GARCH models for capturing the properties of return volatility in Vietnam stock market

There have been numerous researches focusing on modelling stock price volatility However, most of them have discussed about the developed capital markets The emerging markets have not received much attention Recently, the emerging markets, especially the fast development countries such as China, Brazil, India, Russia, Mexico and the ASEAN countries has increasingly attracted the investors to diversify their portfolios

Vietnam stock market has just been traded more than ten years It has significantly developed in recent years and has received a great attraction of many investors, both local and foreign They made considerable amount of profits during the boom time of 2006-2007 However, the market went down in 2008 and 2009 due to the effect of world financial crisis that results in a big loss for many businesses and investors

Comparing with the other stock markets in the region, Vietnam stock market is a small and young market It has the typical characteristics of the young emerging financial market such as illiquidity of stock, incomplete legal system, unstable investors and sensitive to financial shocks It is a promising stock market but requires high risk management technique to avoid the unexpected shocks

The data set to be used in this thesis is the daily VN-Index of Ho Chi Minh City stock exchange (HOSE) The sufficient source of data is received from the data base of Vietnam stock market news and information official website (www.vietstock.vn) and Vietcombank Securities Company Ltd (www.vcbs.com.vn) The time period of the data set is from March, 2002 to December, 2011 which is the time of this study The reason for choosing the data set from March, 2002 instead of July, 2000 (starting time

of trading of Ho Chi Minh City Securities Trading Center (HOSTC)) is that there were only three trading days per week before March, 2002

The world financial crisis in 2008 and 2009 has negative impacted on the stock markets around the world and Vietnam is one of the most critical impacted countries The impact of the crisis to Vietnam stock market was clearly reflected on the VN-Index of Ho Chi Minh City Stock Exchange The VN-Index went down unbreakable from 1,002.7 on 15th November, 2007 to the bottom of 235.5 on 24th February, 2009 Even though the VN-Index has recovered from the end of 2009 but it has not reached

to haft of the peak value at 1,170.68 on 12th March, 2007 To provide a more accuracy analysis, the data set will be splitted into four periods including before 2008 (before crisis period), from 2008 to 2009 (crisis period), from 2010 to 2011 (recovering period) and from 2002 to 2011 (whole period of Vietnam stock market) We will examine whether the applied GARCH models are sufficient for Vietnam stock market in different periods

1.2 Research Questions and Objectives

1.2.1 Research Questions

The thesis will study the stock return volatility in Vietnam stock market by employing different ARCH/GARCH models, both symmetric and asymmetric specifications including ARCH, GARCH, GARCH-M, TGARCH and EGARCH Based on the problem statement and background of the study, the key questions of this thesis need to

be answered are as follows:

 What are the best fit models among the employed ARCH/GARCH models for forecasting and estimating the volatility of Vietnam stock market?

 The second question is that what is the predictable risk in Vietnam stock market based on the estimation results?

1.2.2 Research Objectives and Implications

To answer the above questions, the main objectives of the thesis are to describe the market risk in different periods and examine the predictability of the return volatility in Vietnam stock market across the alternative employed GARCH models

The implications of the thesis are to provide the management technique for market risk

in Vietnam stock market for businesses and investors and suggest the best fit models for forecasting and estimating the stock return volatility quantitatively On the other hand, the empirical results contribute to the literature of Vietnam financial market analysis for academy, policy making and investment

1.3.1 Introduction

From the renovation time in the end of 1980s, there were the ideas and discussions for establishment of official securities market in Vietnam to meet the requirement of market economy and to create a new channel of fund raising for development and

investment Therefore, the project of research and establishment of the securities market was then participated by a number of government agencies and institutes, the results of which were later submitted to the Government As the request and authorization of the Government, the State Bank of Vietnam (SBV) together with the Ministry of Finance to carry out their researches of the issues relevant to the operation

of the securities market, propose the suitable model for Vietnam’s securities market, provide part of the future regulatory staff with basic training in securities and securities market, study the actual operations of some securities markets in the region and in the world, etc

On 28th November, 1996, the State Securities Commission of Vietnam (SSC) was established under the Government’s Decree No 75/CP This is the first step and the foundation of Vietnam stock market SSC is the governmental agency with the mission

of organizing and regulating the operations in the field of stock and stock market in Vietnam SSC plays a decisive role in preparing necessary conditions for setup of the stock market Its major task is to organize and regulate the stock and stock market operations, with the focal mission of facilitating the process of fund mobilization for development investment, ensuring the orderly, safe, transparent, equitable and efficient operation of the stock market, and more important, protecting investors’ legitimate rights and interests

SSC decided Bank of Investment and Development of Vietnam (BIDV), one of the biggest state-owned commercial banks in Vietnam as the designated settlement bank of Stock Trading Center BIDV is in charge of making credit and debit balance payments

of all securities transactions Several other domestic banks and securities companies have been authorized to accept custody of securities, with HSBC, Standard Chartered bank and Deutsche bank Ho Chi Minh City branches currently the only banks providing custody services for foreign investors Custody is based on a central

two local banks and three foreign banks and thirteen licensed securities companies Of these, nine have been licensed to conduct a full range of securities services including underwriting, brokerage, custody, research, portfolio management and trading

Four years later, the first official stock exchange market was launched in Ho Chi Minh City so call Ho Chi Minh City Securities Trading Center (HOSTC), opening the first pages of Vietnam stock market Right after launching, HOSTC started trading the first time on 28th July, 2000 with two listed companies those are Refrigeration Electrical Engineering Joint Stock Corporation (REE) and Saigon Cable and Telecommunication Material Joint Stock Company (SAM) with the total capitalization of $16.87 million After five years operation of HOSTC, the second securities trading center (HASTC) started trading in Ha Noi In August, 2007 the securities trading centers were renamed and upgraded to stock exchange as Ho Chi Minh City stock exchange (HOSE) and Ha Noi stock exchange (HNX) After eleven years of development, even critically impacted by the world financial crisis in 2008 and 2009, it has been witnessed the great development of Vietnam stock market, especially the booming time in 2006 and 2007 Vietnam stock market now operates with 774 listed companies in both HOSE and HNX The current market capitalization of approximately $55.68 billion equal to 48%

of the country’s GDP The market capitalization represents about 43% of the country’s GDP in 2007 which almost double the amount in 2006 (22.7%) However, the financial crisis in 2008 has seriously impacted on Vietnam stock market and led to the drop of market capitalization to below 20% of the country’s GDP In 2009, together with the recovery of the world economy, the market capitalization of Vietnam stock market rapidly increased to nearly 38% of the GDP by end of 2009 and reached to 48% of the GDP by end of 2011 It is expected to be around 80% to 110% of the country’s GDP in

2020

The number of securities companies and trading account rapidly increase There were only three securities companies at the end of 2000 but it has rapidly increased to 105

securities companies at the end of 2011 The number of trading accounts are also witnessed the impressing increase from around 3,000 trading accounts at the end of

2000 to more than one million trading accounts at the end of 2011

Figure 1 to 4 show the number of listed companies, market capitalization, number of securities companies and number of trading accounts respectively in Vietnam stock market from July, 2000 to December, 2011

Figure 1: Number of listed companies from 2000 to 2011

Figure 2: Market capitalization from 2000 to 2011

Figure 3: Number of securities companies from 2000 to 2011

Figure 4: Number of trading accounts from 2000 to 2011

At the beginning, an overall foreign ownership limit of 20% for stocks and 40% for bonds were implemented In July, 2003, in an effort to improve liquidity for the stock market, the government raised the foreign ownership limit for stock to 30% and totally

removed foreign ownership limit of a particular issuer’s bonds However, foreign investors on the Stock Trading Center of Vietnam must register through a custodian licensed to hold securities on behalf of the investors Once registered, a securities transaction code is issued to the foreign investor that will permit securities trading The automatic order-matching system is applied for operation on Vietnam stock market The system operated based on the computerized order process following time and price priority The system capacity is 300,000 orders per day There were only two trading sessions per day before June, 2006 It was increased to three trading sessions per day then after

Similar to the other young emerging stock markets, Vietnam stock market is small, high volatility, and herb behavior reaction The authority has set the daily price limit regulation for all stock traded on HOSTC from the beginning stage However, the price limitation is not always fixed It has been adjusted several times to meet the requirements and adapt to the situation changes The price limitations in HOSE over different periods are shown in table 1 below

Table 1: Price limitations in HOSE over different periods

The VN-Index is computed by comparing the current market value with the base value that was started as 100 points on the first trading day of HOSTC on 28th July, 2000 The base value will be adjusted in the following cases: a) new listed; b) stopped trading; c) changing of market capitalization

The Figure 5 describes the performance of VN-Index over the past eleven years In general, the VN-Index series has upward trend from the end of 2000 to the end of 2007 but has downward trend in 2008 and 2009 Even it has recovered from the end of 2009 but it is still highly fluctuated and has never reached the peak value of March, 2007

Figure 5: Performance of VN-Index from 2000 to 2011

Figure 6: Performance of VN-Index in 2007

Figure 7: Performance of VN-Index in 2009

Source: State Securities Commission

It can be said that the Vietnam stock market started slowly The VN-Index moved up

rapidly developed in 2006 and really boomed in the year 2007 The number of new listed companies, amount of market capitalization, VN-Index and trading volumes significant increased this time As a result, the VN-Index hit the recorded high at 1170.67 in March, 2007

The years 2008 and 2009 were the crisis time of Vietnam stock market The world financial crisis has seriously impacted on Vietnam stock market The investors run away and the VN-Index recorded the loss of approximately 80% to the bottom at 235.5

in February, 2009 It was even worse in Ha Noi stock exchange that the HNX Index dropped below the starting point of 100 Fortunately, the recovery of the world economy from end of 2009 has pulled the Vietnam stock market turning back However, the growth of Vietnam stock market has not been steady and accompanied with many unforeseen risks The fluctuation in VN-Index values can be explained as the unstableness of the macroeconomics of Vietnam and the unbalance of supply and demand in the market

Vietnam stock market is a young market with the typical characteristics of emerging market such as high volatility, illiquidity, incomplete legal system, unstable investors and sensitive to financial shocks Compared with the other Asian capital markets, Vietnam stock market can be seen as the smallest and the most illiquid market but it has been considered as rapidly increasing, high potential and fruitful market It has recently received a great attraction of the local and foreign investors However, this rapid growth has been accompanied with high risk Market risk management and volatility forecast are not an easy task for the businesses and investors in the stock market Over the past thirty years, a huge number of articles have discussed about volatility of stock returns of the capital markets around the world Unfortunately, there has been relatively little work done on modelling and forecasting stock return volatility

in Vietnam stock market

1.4 Outline of the Thesis

The thesis includes five sections and is organised as follows:

Section 1 briefly introduces background of the stock volatility and the objectives of the thesis This section also provides an overview of Vietnam stock market including the development of Vietnam stock market and the market index

The second section reviews the previous study in modelling stock return volatility as well as presents the volatility definition and its characteristics

Section 3 describes the data and the descriptive characteristics of the data set This section discusses the research methodology for testing the ARCH effects the data set and introduces the ARCH/GRACH family for modelling the stock return volatility Section 4 illustrates the empirical results and explains the key points of the analysis by GARCH models in modelling volatility of Vietnam stock market

Section 5 summarizes the findings and the implications of the thesis This section also provides the paper’s limitations and recommendations for future research possibilities

II LITERATURE REVIEW

2.1 Volatility Definition

Stock price volatility is the relative rate at which the price of a securities moves up and down The volatility of stock price can be seen by looking at the range between lowest and highest price over time periods The greater the difference is, the more volatile the price The stock price volatility is computed by the conditional variance of standard deviation 2 of daily change in price (Pagan and Schwert, 1990)

Statistically, the volatility is often measured as the conditional variance as the below equation:

 

2 2

1

11

n i i

R n



Where, R is the return and μ is the mean return

The standard deviation  is able to be computed from any distribution The probability can only be statistical meaningful if  comes with a distribution such as normal distribution or t-distribution The volatility is used to measure the risk of financial figures over the time period

The daily return of the stock price at the time t is computed that:

Where, Rt is the daily return of stock price and Pt is the stock price at time t

It can be said that stock price volatility plays an important role in decision on stock price option When the stock price volatility increases, the stock price will move farther away from the strike price

2.2 The Characteristics of Volatility in Financial Market

According to several empirical researches, the financial market volatility has some of following features that make it be a risk measure factor in many value-at risk models even though it is unobservable directly

The first feature is the clustering of volatility or volatility persistence There are the evidences that the changes of the stock price followed by the other changes It means that large changes in the price of stock are often followed by other large changes, and small changes are often followed by small changes (Engle and Patton, 2001) This behavior has been reported by several other studies, such as Fama (1965), Chou (1988), Schwert (1989) and Baillie et al (1996) The implication of such volatility clustering is that volatility shocks today will influence the expectation of volatility many periods in the future This feature can be applied to forecast the future volatility

in the financial market The future volatility can be predicted by the current and past volatility Volatility is said to be persistent if today’s return has a large effect on the forecast variance many periods in the future

The second characteristic is mean reversion of volatility The volatility reversion said that the volatility changes following the past values It means that a high volatility period will lead to the normal volatility period and vice versa, a low volatility period will create the way for rising of volatility In general, a normal level of volatility will

be returned eventually or it is statistically stability A long term forecast will take into account this feature of volatility that the volatility will be come back to normal level from whichever they are This characteristic is also supported by the work of Tsay (2005) in the book of analysis of financial time series

Another feature is the asymmetric effect of positive and negative shocks This feature sometimes described as leverage effect or risk premium effect In the volatility theory, when the price of stock falls, the volatility of stock will increase The negative shocks

positive news will reduce the volatility and then increase the demand of stock As a result, the stock value followed by the increased or decreased volatility can be predicted by the news The evidence is also found by the studies of Nelson (1991), Glosten et al (1993) and Engle and Ng (1993)

According to the result of several researches, the volatility of stock return series is not constant over time It is different with the assumption in the traditional value-at-risk models that the volatility was assumed to be constant over time This feature is important in selection of the sufficient models for modelling stock return volatility Last but not least, it is found in some empirical studies such as King and Wadhwani (1990), Pan et al (1999) and Abidin and Zhang (2011) that the volatility spillover between the international stock markets In addition, the correlation among the volatility of stock return seems to be stronger than the stock return itself This especially found during the time of financial crisis, for example the global financial crash in 1987, financial crisis in Southeast Asia in 1997 and the recent global financial crisis in 2008

Several value-at-risk models listed in the previous studies were proven to be sufficient for modelling the stock price volatility such as Exponentially Weighted Moving Average (EWMA), ARCH/GARCH family, Stochastic Volatility (SV) On the other hand, different models support different markets and in different time period Among these models, ARCH/GARCH type models are the most widely used models for estimating and forecasting stock return volatility in the previous studies for both mature and emerging markets In this thesis, thus we just focus on the ARCH/GARCH type models for estimating and forecasting the volatility of Vietnam stock market The purpose of this part of the thesis is to review various ARCH/GARCH family models that used to apply for forecasting and estimating the volatility of stock market

From the result, we will suggest the sufficient models for modelling the volatility of Vietnam stock market

Fama (1965) found out the effects of volatility clustering, leptokurtosis, and leverage to the characteristics of stock returns Engle (1982) introduced the Autoregressive Conditional Heteroskedasticity (ARCH) to model volatility by relating the conditional variance of the disturbance term to the linear combination of the squared disturbances

in the past

The traditional econometrics time series models in the past generally assumed that the conditional variance is constant over the time or the normal distribution of stock return However, the financial studies recently have confirmed that financial time series vary over time or non-normal distribution (Mandelbrot, 1963; Fama, 1965) The variance of the financial time series is affected by the news and the behavior of the investors, especially in emerging markets ARCH model is the first model to capture the financial time series without the assumption of constant variances In ARCH model, the financial time series shall include the error terms varying over time (or the residuals from the past) and the constant value, therefore allowing for conditional heteroskedaticity in stock return analysis is reasonable

The ARCH (q) model introduced by Engle (1982) formulates volatility as follows:

2 0

a forecasting model that forecast the error term at time t based on the information known at the previous time The second remark is that there is no any uncertainty of the error term to be forgotten when knowing the past information

ARCH model become a popular forecasting model because of some following reasons: a) ARCH model is simple and easy to handle; b) ARCH model includes the clustering

of volatility; c) ARCH model includes nonlinearities; and d) ARCH model includes the effect of the changes in the financial market

Even a simple model, there are some problems of ARCH model such as confirmation

of many parameters for estimating the volatility of stock returns, how to determine the value of p in the model, non-negativity required of the coefficients in the conditional variance equation To overcome some of these problems, Bollerslev (1986) generalized ARCH (q) model to GARCH (p,q) model by modelling the conditional variance to depend on its lagged values as well as squared lagged values of disturbance into the equation GARCH (p,q) model provides both autoregressive and moving average components in the heteroskedastic variance It is recommended that GARCH model is more detail than ARCH model GARCH (p,q) is specified as follows:

2 0

Where, all parameters α0, αi and βj are required to be positive

A GARCH (0,q) model is the ARCH (q) model Even though GARCH model has been the most popular volatility model and has overcome some of the issues of ARCH model, there are three main weaknesses of GARCH model First, it is the same problem with ARCH model that is non-negativity constraint Second, GARCH model does not include the leverage effect And third, there is no correlation between the conditional variance and conditional mean (Brook, 2002) The awareness of GARCH model’s weaknesses have been pointed out by various extension models

Since the introduction of ARCH models by Engle (1982) and Bollerslev (1986), there are several extensions of their works have been developed to model volatility of stock returns A survey paper by Bollerslev et al (1992) listed more than 100 papers on this subject Some of the more popular models for changing volatility have been proven to

be various forms of GARCH models In these models, the volatility process is time varying and is estimated to be dependent upon both the past volatility and past innovations These models have been used in many applications of stock return data, interest rate data, foreign exchange data, etc in the financial markets

Concerning the effectiveness of the ARCH family models in capturing volatility of financial time series, Hsieh (1989) found that GARCH (1,1) model work well to capture most of the stochastic dependencies in the times series Based on tests of the standardized squared residuals, he found that the simple GARCH (1,1) model is better describing data than a previous ARCH (12) model also estimated by Hsieh (1988) Similar conclusions were found by Taylor (1994), Brooks et al (2003) On the other hand, Bekaert and Harvey (1997) and Aggarwal et al (1999) in their study of emerging markets volatility confirmed the ability of asymmetric GARCH models in capturing asymmetry in stock return volatility

ARCH/GARCH models suggest that the level of risk in financial markets vary over time The risk-return relationship in financial markets is an interesting implementation

of the investors It is widely accepted that investors require larger expected return for assets with higher level of risk Therefore, the stock return in finance may depend on its volatility To model the relationship between changes in volatility with changes in returns, Bollerslev (1986) proposed the GARCH-M model in a multivariate context and extended by Engle et al (1987) The GARCH-M model, or GARCH in mean model, is a complete nonlinear model of asset returns and not only a specification of the error term The conditional variance is involved in mean equation, then when the increase of risk leads to the increase in mean returns

As discussed above, the GARCH models support the symmetric effect of positive and negative shocks on volatility However, the impact of negative shocks is proven higher than the positive news of the same conditions To stimulate this weakness, the

asymmetric GARCH models are developed by several empirical researches Two known asymmetric GARCH models are TGARCH and EGARCH models

well-The Threshold GARCH (TGARCH) model developed by Glosten, Jagannathan and Runkle (1993) presents a dummy variable which is an indicator for sign of error terms The TGARCH model of Zakoian (1994) predicts positive return shocks and negative return shocks have different impact on stock return volatility In 1993, the concept of news impact curve was introduced by Engle and Ng (1993) The news impact curve attempts to characterize the impact of past residual term on the volatility in difference models and capture the differences between the alternative models The simple TGARCH (1,1) is specified as follows:

0 1 1 1 1 1 1

h     h I

Where, It-1=1 if εt-1< 0 and = 0 otherwise

All parameters α0, α1, β1 and γ must satisfy the non-negativity conditions which are the same in GARCH models The value of γ must be greater than zero reflecting the capability of taking into account the leverage effect of TGARCH models

The other important asymmetric GARCH model is the exponential GARCH (EGARCH) originally proposed by Nelson (1991) EGARCH model is possible to catch the leverage effect and eliminate the non-negativity constraint requirement of GARCH models EGARCH model overcomes two major disadvantages of symmetric GARCH models A simple EGARCH (1,1) is expressed as follows:

is displayed under logarithm of stock price volatility that overcomes the non-negativity requirement of coefficients in GARCH models

Thus, ARCH/GARCH family models are the good tools for forecasting and estimating volatility in stock markets In literature, some studies like Campbell and Hentschel (1992), Braun et al (1995) and LeBaron and Blake (2006) provided evidences that stock returns has time-varying volatility

Over the past thirty years, there are several empirical researches using the GARCH family models to discuss the stock volatility in mature markets Argiray (1989) studied the time series behavior of the stock price from 1963 to 1986 obtained from Centre for Research in Security Prices (CRSP) by GARCH (1,1) model The results confirmed that the GARCH (1,1) model is the best fit to daily return series The study pointed out the evidence of significant levels of dependence of daily return series

One year later, Baillie and DeGennaro (1990) used GARCH in mean (GARCH-M) models to examine the relationship between the mean returns and the conditional volatility The 18 years sample of the daily returns from 1st January, 1970 to 22ndDecember, 1987 obtained from the same source of Centre for Research in Security Prices (CRSP) The conclusion showed the weak evidence of relationship between mean returns and conditional variance The results suggested the investors to consider more risk measure for returns beside the conditional volatility

In the same time, Pagan and Schwert (1990) compared the GARCH (1,2) and EGARCH (1,2) models for monthly stock return volatility on the US stock market from 1834 to 1925 The findings confirmed the importance of nonlinearities in stock return behavior which is not captured by the above GARCH models The results argued that the GARCH (1,2) model provides the weak explanations of the data and the EGARCH (1,2) is closer to the explanation of the data since the reflections of the asymmetric relation between volatility and past returns

Two years later, Bollerslev et al (1992) performed an overview of ARCH model and its numerous extensions and a survey of several empirical applications using financial data The conclusion confirmed that the ARCH type models are sufficient for the volatility process in many areas of finance

Corhay and Rad (1994) employed the GARCH-M (1,1) and AR-GARCH-M (1,1) to estimate and test the relationship between the expected returns and volatility in European stock markets The data was obtained from the three large and active stock markets in Europe including France, Germany, and the U.K for the period from 1stJanuary, 1973 to 30th September, 1991 The empirical results found that there is no statistically significant coefficient estimates for the volatility in the mean equation and that variance might not be appropriate as a measure of risk However, the specification

of autoregressive conditional heteroskedastic (ARCH) models is generally consistent with the stochastic behavior of European stock Indexes

Franses and van Dijk (1996) forecasted the stock volatility of the European stock markets including Germany, the Netherlands, Spain, Italy and Sweden by using the linear GARCH model and its non-linear extensions QGARCH and GJR-GARCH (TGARCH) The observation data set is weekly stock indexes collected in 9 years from the first week of 1986 to the last week of 1994 excluding the time of stock market crashing in 1987 The forecasting results showed that the QGARCH model is best fitted for estimating the stock volatility of these stock markets but GJR-GARCH model

is not sufficient for forecasting

To estimate time-varying betas for asset return, Asgharian and Hansson (2000) used GARCH (1,1) for modelling the stock return series on the Swedish stock market for the period 1983-1996 The findings proved that the measure of the market betas by GARCH (1,1) model is more accurate than the beta estimated by OLS

In the same year, McMillan et al (2000) employed various forecasting models including historical mean, random walk, EWMA, simple GARCH model and

asymmetric GARCH models (TGARCH, EGARCH and CGARCH) for modelling the volatility of UK FTA All Share and Financial Times - Stock Exchange 100 index (FTSE100) on London stock exchange The obtained data was in daily, weekly and monthly frequencies The paper performed both symmetric and asymmetric loss functions The findings from symmetric loss provided the evidence of superior of random walk model to the monthly return series while random walk, moving average, and recursive smoothing models outperformed the other models for weekly returns series and GARCH, moving average and exponential smoothing models outperformed the daily data The conclusion also suggested the most consistency of moving average and GARCH models for all data frequencies

Recently, Vo and Daly (2007) used EGARCH (1,1) for estimating the time series of market and idiosyncratic volatilities amongst companies in Down Johns EuroStoxx 50 Index for the 1992–2001 period The study also modelled the time series characteristics

of the volatility, specifically the trends and risk-return trade-off The findings were that there were a positive trend in both market and firm level Volatility and a statistical significant market risk-return trade-off

There are a huge number of studies discussed about the stock volatility Most of them focus on the volatility of mature financial markets The emerging markets become more and more important in financial investment The investors are interesting in the emerging markets to vary their portfolios The emerging markets are high potential for return but also contain high risks Unfortunately, very little papers have been performed to estimate and model the stock return volatility in emerging markets

De Santis and Imrohoroglu (1994) employed AR(1)-GARCH(1,1) model in their discussion paper for estimating the stock return volatility of the developing countries including Turkey, India, Korea, Philippines, Taiwan, Argentina, Brazil, Colombia, Mexico and Venezuela The paper provided the strong evidence of highly persistence

confirmed to be fitted with these markets On the other hand, these emerging markets contain high risk that requesting appropriate market risk management from the investors

Song et al (1998) used GARCH models to examine the relationship between stock returns and stock return volatility on the Shanghai and Shenzhen Stock Exchanges in China with the sample data from 21st May, 1992 to 2nd February, 1996 The outcomes suggested that the GARCH-M (1,1) model is the best model for estimating the stock return volatility on both Shanghai and Shenzhen stock markets On the other hand, it is found the evidence of the volatility spill-over effect between the two markets

Three years later, Lee et al (2001) used GARCH (1,1), EGARCH (1,1) and

EGARCH-M (1,1) models to examine the characteristics of stock returns and conditional volatility

as well as the relationship between stock returns and volatility in the above stock exchanges The daily returns from 12th December, 1990 to 31st December, 1997 for the Shanghai A index, from 21st February, 1992 to 31st December, 1997 for Shanghai B index, from 30th September, 1992 to 31st December, 1997 for Shenzhen A index and 6thOctober, 1992 to 31st December, 1997 for Shenzhen B index were obtained for analysis Some empirical conclusions from the results were found to be consistent with the findings documented for developed capital markets There was a strong evidence of time-varying volatility and clustering of volatility in all stock markets The volatility is high persistence and is predictable However, the results from EGARCH-M (1,1) model did not find the relationship between expected returns and expected risk that estimated by pricing models

To examine the validity of GARCH models in modelling and testing the volatility for emerging markets, Siouronis (2002) employed various GARCH type models including GARCH (1,1), LGARCH (1,1) and EGARCH-M (1,1) for estimating the volatility of the daily return series on the Athens Stock Exchange Market The paper provided a strong evidence of the asymmetric impact of negative shocks on the daily stock returns

series On the other hand, to capture the volatility caused by the political instabilities,

an exogenous variables was added to GARCH (1,1) model for the mean and conditional variance The empirical result confirmed that the political instabilities increase the return series volatility over time Another finding from the study is the mean of the series does not change during high volatile periods

Additionally, Yakob and Delpachitra (2006) used the GARCH-M (1,1) model for testing the relationship between risk and return within the framework of the conditional Capital Asset Pricing Model (CAPM) in ten Asia Pacific countries including Australia, China, Japan, India, Malaysia, Hong Kong, Indonesia, Singapore, South Korea, Taiwan The results failed to provide the evidence supporting the positive linear relationship in the Asia Pacific stock markets However, it provided the significant evidence in describing the risk-return relationship in China and Malaysia stock markets One remark from the conclusion is that the investors in both cases are assumed to bear the high risk

Floros (2008) used several GARCH type models including GARCH (1,1), GARCH-M (1,1), TGACRH (1,1), EGARCH (1,1), CGACRH (1,1), AGARCH (1,1) and PGARCH (1,1) for modelling the volatility in the Egypt and Israel stock markets The daily data of CMA index (Egypt) and TASE-100 index (Israel) are used for modelling The empirical results showed the strong evidence of sufficiency of these GARCH models in capturing the characteristics of the data set The conclusion explained that the increase of risk will not raise the returns It also confirmed the more volatile of CMA index from Egypt than TASE-100 index from Israel due to the uncertainty of the Egyptian economy in the estimating period

Recently, Liu et al (2009) investigated how the characteristics of return distribution impact to the performance in forecasting China stock markets volatility by employing GARCH (1,1) model In addition, the skewed generalized error distribution was taken

composite stock price index on the Shanghai and Shenzhen stock market were the empirical sample for discussing and comparing volatility forecast ability The conclusions from the study were that incorporating SGED returns specification into the GARCH (1,1) model provides more accuracy volatility forecasts for China stock markets The empirical results argued the significance of both skewness and tail-thickness in the conditional distribution of returns, and should be considered in making investment decisions estimation models, especially for emerging financial markets One year later, Emenika (2010) investigated the behavior of stock return volatility of the Nigerian Stock Exchange returns using GARCH (1,1) and GJR-GARCH (1,1) (or TGARCH (1,1)) models in the time period from January, 1999 to December, 2008 The empirical results from this study provided the evidence of volatility persistence, fat tail distribution, and leverage effects for the Nigerian stock returns data Specifically, the results of GARCH (1,1) model showed the evidence of volatility clustering in the Nigerian Stock Exchange return series and the results of the GJR-GARCH (1,1) model confirmed the existence of leverage effects in the series

At the same time, Su (2010) employed GARCH (1,1) and EGARCH (1,1) in his study

to analyze the stock price volatility during the crisis period and before the crisis on Chinese stock market The sample data was the daily Hang Seng index from 31stDecember, 1999 to 8th April, 2010 and splitted into two periods: before the crisis (before 2007) and during the crisis period (from 2007-2010) The empirical results showed the better fit of EGARCH model to the sample data than GARCH model in modelling the volatility of Chinese stock returns The result also confirmed that long term volatility is more volatile during crisis period Bad news creates stronger impact than good news in Chinese stock market during the crisis

Abdalla (2012) employed both symmetric and asymmetric models including GARCH (1,1), GARCH-M (1,1), TGACRH (1,1), EGARCH (1,1) and PGARCH (1,1) for modelling stock return volatility in the Saudi stock market The data set was Tadawul

All Share index which was the daily closing prices on the general market index over the period from 1st January, 2007 to 26th November, 2011 The empirical results provided the strong evidence of sufficiency of these models in capturing the features of daily returns On the other hand, the estimated parameters of GARCH (1,1) model indicate the persistence of conditional volatility Another implication is that the positive relationship between the volatility and returns, suggesting by the positive risk premium parameter of GARCH-M (1,1) model The paper confirmed the evidence of asymmetric and leverage effect on the return volatility based on the estimation results from asymmetric models TGARCH (1,1), EGARCH (1,1) and PGARCH (1,1)

Vietnam stock market is seen as the smallest stock market in the area It is a quick development and fruitful market but also attached with many market risks It is hard to find out any paper discussed for return volatility in Vietnam stock markets Tran (2011) employed GARCH family models such as AR(1)-GARCH(1,0), AR(1)-EGARCH(1,0), AR(1)-GARCH-M(1,0) and AR(1)-TGARCH(1,0), etc to examine the time-series characteristics of stock returns and volatility of Vietnam stock exchange The data set is the VN-Index return series of Ho Chi Minh City stock exchange across the period from 2nd January, 2009 to 16th October, 2009 The empirical results provided the evidence of symmetric effects of shocks on volatility and no relation between expected returns and expected risk The finding suggested that the standard GARCH (1,0) model is the best fit model for return dynamics

The results from literature review confirm that the ARCH/GARCH family models including symmetric models (ARCH, GARCH and GARCH-M) and asymmetric models (EGARCH and TGARCH) are sufficient for estimating and forecasting the volatility of emerging stock market like Vietnam We will further examine whether these models are fitted with the data set of Vietnam stock market

III DATA AND METHODOLOGY

The purpose of the thesis is to forecast the market risk and examine the sufficient models for capturing the characteristics of the return volatility in Vietnam stock market across the most widely used GARCH models including ARCH, GARCH, GARCH-M, TGARCH and EGARCH The sufficient source of data using in this thesis is the daily stock prices of the Ho Chi Minh Stock Exchange (HOSE) market index (VN-Index) which is collected from the data base of Vietnam Stock Market News and Information official website (www.vietstock.vn) and Vietcombank Securities Company Ltd (www.vcbs.com.vn)

The VN-Index of HOSE is chosen as representative for the Vietnam market index to be studied in this thesis instead of HNX index because of three reasons Firstly, HOSE was launched first as the previous name of Ho Chi Minh City Securities Trading Center (HOSTC) and has a history of almost five years longer than that of HNX Secondly, HOSE is the largest in total market capitalization and most liquidity stock exchange market in Vietnam Thirdly, HOSE from the beginning was defined as the stock market for the large listed companies in Vietnam while HNX lists the small and medium size companies According to the regulation of the State Securities Commission, the companies listed on HOSE must have the total registered capital higher than 100 billion VND and the minimum required registered capital for being listed in HNX is 30 billion VND

With respect to forecast series, the choice of data sampling frequency to give the accurate forecast is a focus of various studies Most of the studies concluded that data frequency is chosen in relation with forecast horizon to improve the forecast accuracy Bollerslev et al (1999) argued that the increase in data frequency improve the performance of forecast models The complication in choosing data frequency to forecast is partly due to the mean reversion property of volatility series In addition, the

daily VN-Index is chosen instead of weekly or monthly index to allow more accurate analysis for stock return volatility On the other hand, daily data was widely employed

in several previous studies such as Aggarwal et al (1999), Lee et al (2001), Yakob and Delpachitra (2006), Floros (2008) and Liu et al (2009) in modelling volatility for emerging capital markets

It should be noted that, from the launch of HOSTC in July, 2000 to the end of February, 2002, the trading sessions were held only once every two working days From March, 2002, securities trading transactions have been conducted every working day The daily stock index data which are the closing market index values of HOSE (VN-Index) for the period from March, 2002 through December, 2011 was collected A total of 2,447 daily observations were obtained from the above sources

The world financial crisis in 2008 and 2009 has negative impacted on Vietnam stock market To provide the accurately verification of the sufficient models for modelling the volatility of Vietnam stock market, we split the data set into four periods The first period is from March, 2002 to December, 2007 (before crisis period) The second period is from January, 2008 to December, 2009 (crisis period) The third period is from January, 2010 to December, 2011 (recovering period) And the whole period of Vietnam stock market from March, 2002 to December, 2011 The return series were computed by the difference in logarithm of the continuously daily stock prices and the closing prices of VN-Index in the previous day:

R t = Log(P t ) – Log(P t-1 ) = Log(P t /P t-1 )

Where, Pt denotes the stock price, Rt denotes the continuously compounded daily returns of the stock market on time t The return series Rt should be identically and independently distributed with zero mean and constant variance It is suggested that the future values of the expected mean and variance of the series cannot be predicted by

3.2 Descriptive Statistics

3.2.1 Histogram and Statistics Definition

Histogram displays the frequency distribution of return series The histogram divides the series range (the distance between the maximum and minimum values) into a number of equal length intervals and displays the number of observations that fall into each length A complement of standard descriptive statistics is displayed along with the histogram All of the statistics are computed using the observations which defined as following:

 Mean is the average value of the series, obtained by adding up the series and dividing by the number of observations

 Median is the middle value (or average of the two middle values) of the series when the values are ordered from the smallest to the largest The median is a robust measure of the center of the distribution that is less sensitive to outliers than the mean

 Max and Min are the maximum and minimum values of the series in the current sample

 Standard deviation is a measure of dispersion or spread in the series The standard deviation is given by:

 

2 2

1

11

n i i

R n



Where n is the number of observations, R is the return and μ is the mean return

 Skewness is a measure of asymmetry of the distribution of the series around its mean Skewness is computed as:

3

* 1

1 n

i i

R S

Where *

 is an estimator for the standard deviation that is based on the biased estimator for the variance ( *

(n 1) /n

distribution, such as the normal distribution, is zero Positive skewness means that the distribution has a long right tail and negative skewness implies that the distribution has a long left tail

 Kurtosis measures the peakedness or flatness of the distribution of the series Kurtosis is computed as:

4

* 1

1 n

i i

R K

 is again based on the biased estimator for the variance The kurtosis

of the normal distribution is 3 If the kurtosis exceeds 3, the distribution is peaked (leptokurtic) relative to the normal; if the kurtosis is less than 3, the distribution is flat (platykurtic) relative to the normal

 Jarque-Bera is a test statistic for testing whether the series is normally distributed The test statistic measures the difference of the skewness and kurtosis of the series with those from the normal distribution The statistic is computed as:

2 3

K n

Where S is the skewness, and K is the kurtosis

The reported probability is the probability that a Jarque-Bera statistic exceeds (in absolute value) the observed value under the null hypothesis of a normal distribution A small probability value leads to the rejection of the null hypothesis of a normal distribution

As the suggestions from the literatures for emerging market, the following

volatility: Mean, standard deviation, skewness, and kurtosis Several studies such as Mandelbrot (1963) and Fama (1965) confirmed that the time series of returns are non-normal and tend to have leptokurtic and fat-tailed distribution Some empirical researches for emerging market found that the return series are often skewed toward the left, indicating that there are more negative than positive observations

3.2.2 Descriptive Statistics of Return Series for the Period before Crisis

The figure 8 summarizes the basic statistical characteristics of the return series of Vietnam stock market in the period before crisis The average daily return is negative and very small comparing with the variable standard deviation The median of daily returns is positive Both mean and median are not significant different from zero On the other hand, the maximum and minimum statistics of the return series in this period are significant different It is concluded that the stock prices in this period generally increase slightly over the time but high fluctuated

The return series distribution displays significant evidence of skewness and kurtosis

At normal distribution, the skewness should be zero and kurtosis should be three The negative skewness confirmed that the series are skewed towards the left with the long left tail, indicating that there are more negative than positive outlying returns in Vietnam stock market Additionally, the series is characterized by a distribution with tails that are significantly fatter than a normal distribution The kurtosis statistic of 5.76 indicates the leptokurtic characteristic of daily return distribution The return series distribution has a more acute peak around the mean than does the normal distribution Jarque-Bera normality test statistic, indicating that the return series is not normal distribution and rejects the null hypothesis of normal distribution The skewness, kurtosis and Jarque-Bera statistics are the evidence to conclude that the daily return series is not normally distribution in this period