CONDITIONAL VOLATILITY AND ASSET PRICING (An Empirical...
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CONDITIONAL VOLATILITY AND ASSET
PRICING
(An Empirical Evidence from Emerging Economies)
Researcher: Supervisor:
Kashif Hamid Dr.Arshad Hasan
REG NO. 10-FMS/PHDFIN/F09
Department of Business Administration
Faculty of Management Sciences
INTERNATIONAL ISLAMIC UNIVERSITY,
ISLAMABAD, PAKISTAN
2017
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CONDITIONAL VOLATILITY AND ASSET PRICING
Empirical Evidence from Emerging Economies)
Researcher: Supervisor:
Kashif Hamid Dr. Arshad Hasan
REG NO. 10-FMS/PHDFIN/F09
Faculty of Management Sciences
INTERNATIONAL ISLAMIC UNIVERSITY ISLAMABAD
PAKISTAN
iii
CONDITIONAL VOLATILITY AND ASSET PRICING
(An Empirical Evidence from Emerging Economies)
Kashif Hamid
REG. NO. 10-FMS/PHDFIN/F09
Submitted in partial fulfillment of the requirements for the
PhD degree with the specialization in Finance
at the Faculty of Management Sciences,
International Islamic University,
Islamabad
``
Dr. Arshad Hasan August, 2017
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ABSTRACT
This study investigates the relative performance of linear versus nonlinear methods to
predict volatility and return in equity markets. The study is performed on the
EAGLEs and NEST markets, including China, India, Indonesia Pakistan,
Bangladesh and Malaysia by using daily data of equity markets from the period
January 4, 2000 to December 30, 2010. Nonlinear and asymmetric ARCH ef f ects
have been test by Lagrange Multiplier test. A range of models from random walk
model to multifaceted ARCH class models are used to predict volatility. The results
reveal that MA (1) model ranks first with use of RMSE criterion in linear models. With
regards to nonlinear models for predicating stock return volatility, the ARCH,
GARCH-in-Mean (1, 1) model and EGARCH (1, 1) model perform well. GARCH-
in- Mean model outperforms on the basis of AIC, SIC and Log Likelihood
method. It is concluded that GARCH specification is best in performance to
capture the volatility. GARCH in mean model is extended with the macroeconomic
variables in the variance equation for SS, BSE, JCI, KSE, KLSE and DSE. The
macroeconomic variables include CPI, Term Structure of interest rate, industrial
production and oil prices. Data for Macroeconomic variable is on monthly basis for the
period Jan 2000 to Dec 2010. For SS, BSE, JCI, DSE, KLSE and KSE markets the
conditional mean is significant and models the persistency in long run scenario and
suggests for an integrated process. The model indicates that oil price have positive
impact on volatility for SS. For BSE change in industrial production index and interest
rate change have negative coefficients which indicate that industrial growth and increase
in interest rate change has negative relationship with the volatility for this economy. For
JCI the model indicates that change in growth in industrial production has positive
impact on volatility. For KSE, ARCH and GARCH terms are not significant but growth
rate in real sector and oil price has significant impact on volatility. However DSE has no
significant results. For KSE the model indicates that inflation has positive impact on
volatility but change in oil price has negative effect on volatility. Bullish market effect
is quite significant in explaining the volatility capturing ability for all the equity
markets. The TGARCH(1,1) model is estimated for SS, BSE, JCI, DSE KLSE and
KSE returns series and results indicate that asymmetric effect exists for all the
equity markets which indicates the presence of leverage effect. Study concludes that
TGARCH (1,1) model is a potential envoy of the asymmetric conditional volatility
procedure for the daily frequency of the data regarding to equity markets of SS, BSE,
JCI, DSE, KLSE, and KLSE. Further GARCH-in-mean model is extended with value
at risk that indicates the variables for variance equation are statistically significant and
the VaR have significant impact on all equity markets in explaining the conditional
volatility. In Last GARCH-in-Mean Model is extended with the semi-variance and
results indicate that the downside risk causes rise in the volatility. It has ability to
capture the asymmetric behavior of equity returns and reports the fat tails of the returns.
It is concluded that volatility plays a significant role in asset price determination.
Keywords: Conditional volatility, linear, nonlinear, Asymmetric effect,
Macroeconomic Variables, Bullish, Value at Risk, Semi-Variance.
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FORWARDING SHEET
The thesis entitled CONDITIONAL VOLATILITY AND ASSET PRICING (An
Empirical Evidence from Emerging Economies) submitted by KASHIF HAMID in
partial fulfillment of PhD degree in Finance has been completed under my guidance and
supervision. I am satisfied with the quality of student’s research work and allow him to
submit this thesis of further process of as per IIU rules & regulations.
Date: Signature:
Name:
vi
(Acceptance by the Viva Voce Committee)
Title of Thesis: CONDITIONAL VOLATILITY AND ASSET PRICING (An Empirical
Evidence from Emerging Economies)
Name of Student KASHIF HAMID
Registration No REG NO. 10-FMS/PHDFIN/F09
Accepted by the Faculty of Management Science, Department of Business
Administration, INTERNATIONAL ISLAMIC UNIVERSITY, ISLAMABAD in partial
fulfillment of the requirements for the PhD Degree in Finance
Viva Voce Committee
Dean
Chairman/Director/Head
External Examiner
Supervisor
Member
(Day, Month, Year)
vii
viii
COPYRIGHT PAGE
The copy rights of the thesis entitled “Conditional Volatility and Asset Pricing (An
Empirical Evidence from Emerging Economies)” are reserved with the author KASHIF
HAMID©.
ix
STATEMENT OF UNDERSTANDING
DECLARATION
I hereby declare that the research work is my own work and no part of this thesis is
copied out from any source. It is further declared that this research is entirely my
personal effort made under the sincere guidance of my supervisor Dr. Arshad Hasan. No
segment of this work presented in this research thesis has been submitted in support of
any other degree /qualification of this or any other university or institute of learning.
KASHIF HAMID
REG NO. 10-FMS/PHDFIN/F09
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ACKNOWLEDGEMENT
By the core of heart, thanks to almighty ALLAH, the most gracious and caring to all of us because HE
has provided us good health, creative thoughts, loving parents, brilliant teachers, good friends and
nerves to complete the Research work. The most special praises and honors are for the GREAT HOLY
PROPHET MUHAMMAD (Peace by upon him) who enlightened the spirit of mankind with the
strengths and essence of Islam and guided to attain the purposeful knowledge where ever from the
world. It is a matter of enormous respect and pleasure for me to articulate profound spirit of affection
and sincerest feeling of appreciation to my respected and honorable supervisor Dr. Arshad Hassan, for
his kind supervision, true guidance, keen interest, valuable suggestions and sympathetic attitude
throughout my research work. I tender my sincere thanks to honorable Dr Syed Zulfiqar Ali Shah , Dr
Zaheer for their highness, kind of support and motivation throughout the PhD. I tender my sincere
thanks to Dr Iqrar Khan Vice Chancellor, Prof. Dr. Ejaz Bhatti, Dr. Anwar-ul-Haq Gondal, and
Bahadur Ali Kang University of Agriculture, Faisalabad for their inspiring guidance and unstained
help during my study period. I pay my gratitude to my Great Mother (Safia Bibi), Great Father (Haji
Abdul Hamid Boparai), who always desired to see me glittering high on the skies of success. Without
their day and night prayers, sacrifices, encouragement, moral and financial support, the present project
would have been merry dream. My gratitude will remain incomplete if I don’t mentioned my sweet
Brothers Ch. Atif Hamid Boparai, Ch. Asif Hamid Boparai , Dr Saleem Yousaf and Waseem Yousaf,
AMIN and Dr Naeem, Wife (Dr. Kishwar Naheed, Assistant Professor Forensic Medicine (PMC) ,
My sweet Daughter Aleeza Faryal Boparai and Son Hashir Kashif Boparai, Friends (Usman
Khurram, Shahid Imdad, Dr.Inam-ul-Haq, Ahmad Fraz,, Jahanzeb Hundal, Muhammad Jawad
Aulakh, Faisal Mushtaq Sahi, Tahir Suleman, Waseem Ghaffar) whose prayers always with me and
great contribution during whole my studies. Words are deficient to communicate my self-effacing
obligation to my great parents for support and prayers for my successful completion of education.
KASHIF HAMID
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TABLE OF CONTENTS
Ch.
No.
TITLE Page
No.
ABSTRACT…………………………………………………………. iv
COPYRIGHT PAGE………………………………………………... vi
STATEMENT OF UNDERSTANDING……………………………. ix
ACKNOWLEDGEMENT…………………………………………… x
TABLE OF CONTNETS……………………………………………. xi
LIST OF FIGURES………………………………………………….. xix
LIST OF TABLES…………………………………………………... xiv
LIST OF APPENDIX………………………………………………... xiv
LIST OFABBREVIATIONS………………………….……………. xx
1 INTRODUCTION…………………………………………………… 1
1.1 Brief Statement of Study……………………………………. 2
1.2 Problem Statement ……………………...………………….. 11
1.3 Theoretical Framework …………………..…………..…….. 11
1.3.1 Efficient Market Theory……………………… 11
1.3.2 Volatility Theories…………………………….. 12
1.3.2.1 Leptokurtosis…………………………….. 12
1.3.2.2 Volatility Clustering or Volatility Pooling 12
1.3.2.3 Leverage Effects………………………… 12
1.3.3 Asset Pricing Theories…………………….. 13
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1.4 Significance of the Study……………………………………. 14
1.5 Contribution of the Study …………………………………... 16
1.6 Objectives of the Research ………………………………….. 18
2 LITERATURE REVIEW……………………………………………. 19
2.1 HYPOTHESES OF THE STUDY ……………….…..……... 37
3 DATA AND METHODLOGY……………………………………… 38
3.1 Emerging and Growth-Leading Economies….……………… 39
3.2 NEST ……………………………………………………….. 39
3.3 Stock Market Return 39
3.4 Methodology………………………………………………… 40
3.4.1 Sign and size test………………………………….. 40
3.4.2 The Mean Equation………………………………….. 41
3.4.3 Linear Models ……………………………………. 42
3.4.3.1 Random Walk Model 42
3.4.3.2 Autoregressive Model – (AR) 42
3.4.3.3 Moving Average Model – (MA) 43
3.4.3.4 Exponential Smoothing Model (ESM) 43
3.5 Non-Linear Models ………………………………… 43
3.5.1 The ARCH Model …………………………………. 43
3.5.2 The GARCH Model ……………………………….. 44
3.5.3 Asymmetric GARCH Models 45
3.5.4 Threshold GARCH……………………………….... .. 45
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3.5.5 The EGARCH Model ……………………………….. 46
3.5.6 GJR-GARCH Model ……………………………... 47
3.5.7 Volatility Switching Model………………………….. 47
3.5.8 Quadratic ARCH (QARCH) ………………………... 48
3.6 Econometric Models ……………………………….. 48
3.6.1 Volatility and Return ……………………………. 48
3.6.1.1 Model 1: Return, Volatility and
Macroeconomic Model …………………………
48
3.6.1.2 Model 2(a): Return, Volatility and Market
Conditions Asymmetries ………………………..
50
3.6.1.3 Model 2(b): Return, Volatility and Market
Asymmetric Conditions, Good News and Bad News
Effect….
51
3.6.1.4 Model 3: Return, Volatility and Value at Risk ….. 51
3.6.1.5 Model 4: Return, Volatility and Semi-variance ……. 52
4 RESULTS AND DISCUSSION……………………………………. 54
4.1 Econometric Models For China …………………… 76
4.2 Econometric Models For India…………………….. 83
4.3 Econometric Models For Indonesia………………. 91
4.4 Econometric Models For Bangladesh ……………… 98
4.5 Econometric Models For Malaysia 105
4.6 Econometric Models For Pakistan 112
4.7 Summary of the Results 120
5 CONCLUSION……………….…………………………. 135
5.1 Implications of the study…………………………… 146
REFERENCES ……………………………......................... 148
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APPENDICES…………………………………………... 159
LIST OF TABLES
Table-
No.
TITLE Page
No.
1 Descriptive Statistics for Daily Market Returns ………………….... 55
2 Positive and Negative Returns Summary ………………………….. 57
3 Sign- and Size Bias Tests ……………………………………..……. 59
4 Lagrange-Multiplier Test of ARCH Effects for GARCH model........ 60
5 Lagrange-Multiplier Test of ARCH Effects FOR GJR-GARCH....... 61
6 Lagrange -Multiplier Test of ARCH Effects FOR EGARCH …… 61
7 Lagrange-Multiplier Test of ARCH Effects FOR VS-GARCH …… 62
8 Lagrange-Multiplier Test of ARCH Effects FOR Q-GARCH …….. 63
9 Estimates of GARCH (1, 1) Model………………………………..... 64
10 Estimates of EGARCH (1, 1) Model ………………………………. 65
11 Estimates of GJR-GARCH (1, 1) Model……………………………. 66
12 Estimates of VS-GARCH (1, 1) Model ……………………………. 67
13 Estimates of QARCH (1, 1) Model ………………………………… 68
14 Forecasting Performance of Linear and Nonlinear Models of the
Volatility of Stock Returns ………………………………………..... 72
15 Correlation Matrix for Stock Returns …………………………..... 73
16 Conditional Volatility Correlation Matrix ………………………….. 74
17(a) Estimates of GARCH in Mean (1, 1) Model 1: Return, Volatility and
Macroeconomic Model for SS: Impact of Macroeconomic Variables
on Return………………………………………. 76
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17(b) Estimates of GARCH in Mean (1, 1) Model 1: Return, Volatility and
Macroeconomic Model for SS: Impact of Macroeconomic Variables
on Volatility……………………. 77
18(a) Estimates of GARCH in Mean (1, 1) Model 2(a): Return, Volatility
and Market Conditions Asymmetries for SS : Impact of Market
Conditions Asymmetries on Return……………… 78
18(b) Estimates of GARCH in Mean (1, 1) Model 2(a): Return, Volatility
and Market Conditions Asymmetries for SS: Impact of Market
Conditions Asymmetries on Return……………………… 79
19 Estimates of TGARCH Model 2(b): Return, Volatility and Market
Asymmetric Conditions, Good News and Bad News Effect………… 80
20 Estimates of GARCH (1, 1) Model 3: Return, Volatility and
Value at Risk for SS ………………………………………………...
81
21 Estimates of GARCH (1, 1) Model 4: Return, Volatility and Semi
variance for SS………………………………………………… 82
22(a) Estimates of GARCH in Mean (1, 1) Model 1: Return, Volatility and
Macroeconomic Model for BSE: Impact of Macroeconomic Variables
on Return……………………………………….
83
22(b) Estimates of GARCH in Mean (1, 1) Model 1: Return, Volatility and
Macroeconomic Model for BSE: Impact of Macroeconomic Variables
on Volatility……………………. 84
23(a) Estimates of GARCH in Mean (1, 1) Model 2(a): Return, Volatility
and Market Conditions Asymmetries for BSE : Impact of Market
Conditions Asymmetries on Return……………… 85
23(b) Estimates of GARCH in Mean (1, 1) Model 2(a): Return, Volatility
and Market Conditions Asymmetries for BSE: Impact of Market
Conditions Asymmetries on Return……………………… 86
24 Estimates of TGARCH Model 2(b): Return, Volatility and Market
Asymmetric Conditions, Good News and Bad News Effect…………
87
25 Estimates of GARCH (1, 1) Model 3: Return, Volatility and
Value at Risk for BSE ……………………………………………….
89
26 Estimates of GARCH (1, 1) Model 4: Return, Volatility and Semi -
Variance for BSE………………………………………………… 90
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27(a) Estimates of GARCH in Mean (1, 1) Model 1: Return, Volatility and
Macroeconomic Model for JCI: Impact of Macroeconomic Variables
on Return………………………………………. 91
27(b) Estimates of GARCH in Mean (1, 1) Model 1: Return, Volatility and
Macroeconomic Model for JCI: Impact of Macroeconomic Variables
on Volatility……………………. 92
28(a) Estimates of GARCH in Mean (1, 1) Model 2(a): Return, Volatility
and Market Conditions Asymmetries for JCI : Impact of Market
Conditions Asymmetries on Return……………… 93
28(b) Estimates of GARCH in Mean (1, 1) Model 2(a): Return, Volatility
and Market Conditions Asymmetries for JCI: Impact of Market
Conditions Asymmetries on Return……………………… 94
29 Estimates of TGARCH Model 2(b): Return, Volatility and Market
Asymmetric Conditions, Good News and Bad News Effect………… 95
30 Estimates of GARCH (1, 1) Model 3: Return, Volatility and
Value at Risk for JCI ………………………………………………. 96
31 Estimates of GARCH (1, 1) Model 4: Return, Volatility and Semi -
Variance for JCI……………………………………………… 97
32(a) Estimates of GARCH in Mean (1, 1) Model 1: Return, Volatility and
Macroeconomic Model for DSE: Impact of Macroeconomic Variables
on Return………………………………………. 98
32(b) Estimates of GARCH in Mean (1, 1) Model 1: Return, Volatility and
Macroeconomic Model for DSE: Impact of Macroeconomic Variables
on Volatility……………………. 99
33(a) Estimates of GARCH in Mean (1, 1) Model 2(a): Return, Volatility
and Market Conditions Asymmetries for DSE : Impact of Market
Conditions Asymmetries on Return……………… 100
33(b) Estimates of GARCH in Mean (1, 1) Model 2(a): Return, Volatility
and Market Conditions Asymmetries for DSE: Impact of Market
Conditions Asymmetries on Return……………………… 101
34 Estimates of TGARCH Model 2(b): Return, Volatility and Market
Asymmetric Conditions, Good News and Bad News Effect………… 102
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35 Estimates of GARCH (1, 1) Model 3: Return, Volatility and
Value at Risk for DSE ………………………………………………. 103
36 Estimates of GARCH (1, 1) Model 4: Return, Volatility and Semi -
Variance for DSE………………………………………………… 104
37(a) Estimates of GARCH in Mean (1, 1) Model 1: Return, Volatility and
Macroeconomic Model for KLSE: Impact of Macroeconomic
Variables on Return………………………………………. 105
37(b) Estimates of GARCH in Mean (1, 1) Model 1: Return, Volatility and
Macroeconomic Model for KLSE: Impact of Macroeconomic
Variables on Volatility……………………. 106
38(a) Estimates of GARCH in Mean (1, 1) Model 2(a): Return, Volatility
and Market Conditions Asymmetries for KLSE: Impact of Market
Conditions Asymmetries on Return……………… 107
38(b) Estimates of GARCH in Mean (1, 1) Model 2(a): Return, Volatility
and Market Conditions Asymmetries for KLSE: Impact of Market
Conditions Asymmetries on Return……………………… 108
39 Estimates of TGARCH Model 2(b): Return, Volatility and Market
Asymmetric Conditions, Good News and Bad News Effect………… 109
40 Estimates of GARCH (1, 1) Model 3: Return, Volatility and
Value at Risk for KLSE …………………………………………. 110
41 Estimates of GARCH (1, 1) Model 4: Return, Volatility and Semi -
Variance for KLSE………………………………………………… 111
42(a) Estimates of GARCH in Mean (1, 1) Model 1: Return, Volatility and
Macroeconomic Model for SE: Impact of Macroeconomic Variables
on Return………………………………………. 112
42(b) Estimates of GARCH in Mean (1, 1) Model 1: Return, Volatility and
Macroeconomic Model for KSE: Impact of Macroeconomic Variables
on Volatility……………………. 113
43(a) Estimates of GARCH in Mean (1, 1) Model 2(a): Return, Volatility
and Market Conditions Asymmetries for KSE : Impact of Market
Conditions Asymmetries on Return……………… 114
43(b) Estimates of GARCH in Mean (1, 1) Model 2(a): Return, Volatility
and Market Conditions Asymmetries for KSE: Impact of Market 115
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Conditions Asymmetries on Return………………………
44 Estimates of TGARCH Model 2(b): Return, Volatility and Market
Asymmetric Conditions, Good News and Bad News Effect………… 116
45 Estimates of GARCH (1, 1) Model 3: Return, Volatility and
Value at Risk for KSE ………………………………………………. 117
46 Estimates of GARCH (1, 1) Model 4: Return, Volatility and Semi -
Variance for KSE………………………………………………… 118
47 Diagnostic Test 119
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LIST OF FIGURES
FIG.
No.
TITLE Page
No.
1 Daily Mean Returns of China, India, Indonesia, Bangladesh,
Malaysia and Pakistan from January 2000 to December 2010
56
2 Stock Returns of Equity Market 58
3 Conditional Standard Deviation of BSE 70
4 Conditional Variance of BSE 70
5 Conditional Standard deviation of DSE 70
6 Conditional Variance of DSE 70
7 Conditional Standard Deviation of JCI 70
8 Conditional Variance of JCI 70
9 Conditional Standard deviation of KSE 71
10 Conditional Variance of KSE 71
11 Conditional Standard Deviation of KLSE 71
12 Conditional Variance of KLSE 71
13 Conditional Standard deviation of SS 71
14 Conditional Variance of SS 71
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LIST OF ABBREVIATIONS
ABBREVIATIONS COMPLETE WORD
AGARCH Asymmetric Generalized Autoregressive Conditional
Heteroskedasticity
AIC Akaike Information Criterion
AMEX American Stock Exchange
ANST-GARCH Asymmetric Nonlinear Smooth Transition- Generalized Auto
Regressive Conditional Heteroskedasticity
AP-ARCH Asymmetric Power Auto Regressive Conditional
Heteroskedasticity
AR Auto Regressive
ARCH Auto Regressive Conditional Heteroskedasticity
ARMA Auto Regressive Moving Average
BBVA Banco Bilbao Vizcaya Argentaria
BIC Bayesian Information Criterion
BSE Bombay Stock Exchange
CAPM Capital Asset Pricing Model
CGARCH Component Generalized Autoregressive Conditional
Heteroskedasticity
CPI Customer Price Index
DSE Dhaka Stock Exchange
EAGLEs Emerging and Growth Leading Economies
EGARCH Exponential Generalized Auto Regressive Conditional
Heteroskedasticity
EMH Efficient Market Hypothesis
ESTAR Exponential Smoothing Transition Auto Regressive
ESM Exponential Smoothing Model
EWMA Exponentially Weighted Moving Average
FIGARCH Fractionally Integrated Generalized Autoregressive Conditional
Heteroskedasticity
GARCH Generalized Auto Regressive Conditional Heteroskedasticity
GARCH-M Generalized Autoregressive Conditional Heteroskedasticity In
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Mean Model
GDP Gross Domestic Product
GED Generalized Error Distribution
GJR-GARCH Glosten-Jagannathan-Runkle Generalized Autoregressive
Conditional Heteroskedasticity
G7 Great Seven
HML High Minus Low
IID Independent Identical Distribution
JCI Jakarta Stock Exchange
KLSE Kualalumpur Stock Exchange
KSE Karachi Stock Exchange
LM Langrage –Multiplier
LSTAR Long Horizon Smooth Transition Auto Regressive
MA Moving Average
NASDAQ National Association Of Securities Dealers Automated
Quotations
NEST Next to Eagles
NGARCH Nonlinear Asymmetric Generalized Autoregressive Conditional
Heteroskedasticity
NYSE New York Stock Exchange
QGARCH Quadratic Generalized Auto Regressive Conditional
Heteroskedasticity
RWM Random Walk Hypothesis
SIC Schwarz Information Criterion
SMB Small Minus Big
SS Shanghai Stock Exchange
S&P Standard And Poor
TGARCH Threshold Generalized Auto Regressive Conditional
Heteroskedasticity
VS-GARCH Volatility Switching Generalized Auto Regressive Conditional
Heteroskedasticity
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CHAPTER 1
INTRODUCTION
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1. INTRODUCTION:
1.1 Brief Statement of Study
Predicting future returns and volatility remained a central focus for research
advancement in the area of asset pricing. Either it is possible to forecast tomorrow’s
prices with some certainty or not, and profits may be attained successfully or not.
Current information could be used to predict future prices, and with this information,
investment decisions and trading of assets cab be performed sensibly and rationally. It
is not as simple as it is deemed. Due to key and significant role of financial markets in
justifying the economic positions of countries, number of different studies has been
launched to investigate various phenomena’s in this spectrum. Stock returns and its
volatility analysis remain, one of the key facets of the equity markets that have got long
attention in the financial literature. The term volatility means that the stretching of all
expected outcomes regarding to an unsure variable. Volatility also means
unpredictability or fluctuations in expected outcomes in general and considered as
synonym of risk as measured by standard deviation or variance. However from financial
markets perspective it is a rate at which the price of a security rises or falls for given set
of returns. In financial economics the emerging markets means those markets where
economic progress is following the advanced countries. As economic growth is measured
through GDP and is reflected by liquidity in the local debt market, mechanism of equity
markets, exchange markets and having regulatory bodies. In such markets investors seek
out for high returns but such markets have greater level of risk due to domestic
infrastructure problems, political instability, and high volatility in the financial markets.
In sum we can say emerging markets are those markets which have some characteristics
of a developed markets, however it does not fulfill the complete standards of a developed
market. In finance the term asset pricing is described in a manner that how financial
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assets are priced. It means that how much amount one person is ready to pay for an asset
when he buys it. Such price is the representative of the amount which is assigned by the
market in a fair or unfair manner. Financial assets include equity, debt, hybrids and
derivative instruments. Asset pricing movements are managed and controlled through the
law of demand and supply, however prices rises or falls as the value of money behaves.
However if price of a financial asset changes rapidly in a short span of time it leads
towards high volatility otherwise if the price of a security fluctuates in a slow manner, it
is known as low volatility. Non-Linearity is the relationship that cannot be expressed in a
linear combination through its input variables. In non-linearity the association among the
variables is not static but dynamic. When we examine the cause and effect relationship
then Nonlinearity is a common issue. Such occurrence needs complex modeling for
nonlinear events against suggested hypothesis. Nonlinearity leads towards random
behavior generally.
In equity markets rise and fall in the stock prices is a natural and normal phenomenon.
The ups and downs of stock prices are continuous process of day to day market
operation. The movement of stock prices indicates that some forces are behind such
dynamics. The demand and supply function is the basic element in the change of share
prices from one level to another level. Higher the existence of volatility is an indicator
that the stock market is also highly liquid. Asset pricing determination depends upon
the volatility of each security. Particularly a sharp rise in volatility of the stock market
carries a higher change in stock price. Investor’s sentiments perceive that a sharp rise
in stock market volatility leads to an amplifying aspect in the associated risk of equity
investment and as a result investors can move their finances towards a lesser amount of
risky assets. This element demonstrates substantial impact on business investment and
ultimately leads towards economic growth and equilibrium through various directions.
4
In stock market theory the rapid and uncertain changing dynamics in the prices of stock
is a mark of efficient market hypothesis which is not a sign of destructive phenomenon.
However high price fluctuation may create destructive effects due to excessive level of
volatility and may affect the efficiency of the market. These elements may end with
financial market crashes or crises. Crashes or crisis are an integral part of developed and
emerging markets. Pakistan, India China is not beyond these phenomena and many
times this particular scene has been performed in the history. Similarly financial crises
in developed market like United States financial crisis spread speedily as a mark of bad
news and it was observed that the Indian equity markets have been dropped around
about 60 percent and approximate $1.3 trillion in market capitalization have been wiped
out since January 2008. As a result a huge amount of foreign portfolio investors wiped out
during September 2008 to December 2008 and ultimately national investors were
psychologically affected (Kumar, 2009).
The association between stock return and its volatility has marvelous history created by
financial researchers. Conditional volatility and contemporaneous returns have negative
association empirically. In the financial literature it is narrated that due to ups and
downs in changing of conditional volatility, the negative or positive returns are
generally seem associated and this phenomenon is known as asymmetric volatility.
During stock market crashes the existence of asymmetric volatility can be mostly seen
when a large decrease in the prices of the stock is related to an increase in the volatility
of the market (Wu, 2001). Leverage effect is also one of the most important theories
that deem the affiliation between stock price and volatility (Black, 1976; Christie,
1982). A negative return up raises the financial leverage that makes the stock more
risky and cause to an increase in volatility due to leverage effect.
Its reality volatility and stock price association is much studied in stabled and
5
developed equity markets, but still little concentration has been given in the direction
of wide-ranging study in the field of the volatility modeling in the emerging markets of
ASIA. There is huge difference of various features in between emerging markets and
developed stock markets and this phenomenon is well known by the financial
researchers. Bekaert and Wu (2000) indicated that there are four distinctive
uniqueness of emerging equity market returns, firstly there are higher average
returns sample secondly there exist low degree of relationship with the returns of
developed equity market. Thirdly returns are more predictable and lastly keep high
level of volatility. Such differentiation can have momentous implications for
investment and policy decision makers. Therefore to focus on the empirical evidences
of developed markets findings can mislead policy makers while in decision.
Franses and Van Dijk (2000) stated that future returns are possible to predict for making
the investment decision but it is complex. Malkiel and Fama (1970) argued that
Efficient Market Hypothesis (EMH) is a major pillar in determining the financial time
series data modeling. Study defined that efficient markets are those markets where
prices always reflect all available information. This element directly implies that it is
impossible to outperform the market by means of available information. While
investigating the stock returns, the first concern is expected return or the mean return
and the second element is the risk consideration with respect to certain level of return.
Majorly the investment decisions take into consideration risk scenario but it is
important that the investors should be rewarded for grasping non-diversifiable risk
through higher expected returns on their investment portfolios. Generally risk is
referred as volatility or the variance. Black and Scholes (1973) had taken into
consideration the variance in determining options pricing and developed the model to
estimate the assets prices. Modern portfolio theory assumes that investors are rational
6
and they prefer large returns over small returns and in the same way low risk preferred
over high risk. The interest of the investor lies in the first and second moment along
with the given level of expected return and risk. The complexity of risk is more
complex than the return. Markowitz (1952) narrated that the assets to construct optimal
portfolios, in line with the theory, the forecasts of the expected returns and co-variances
are required for this purpose. The risk that lies in returns is measured through the
corresponding variance, and hence investors should hold an efficient portfolio by means
of mean-variance with the maximum possible return along with given level of variance.
Mandelbrot (1963) documented and realized some predictability in the variance, this
element caused to introduce a family of models that takes into consideration these
predictable behaviors. Such efforts made possible to develop; the Autoregressive
Conditional Heteroscedasticity (ARCH) model as Engle (1982) explained and
Bollerslev (1986) introduced the GARCH model. Family consisting of these models
turned out to be successful. Here one element to be discussed that the volatility does not
behave constantly and in a stable way but huge variations are normally observed that
make complexity while in predictions. In various studies volatility is forecasted and the
performance of the models is analyzed in linear and nonlinear context thereafter the
development of a new model in capturing and forecasting the volatility. Gokcan (2000)
used ARCH and GARCH family models for modeling the volatility it is seen that where
the financial time series are skewed, the linear models are failed to explain the past
volatility and predicting the future volatility. The study used linear vs Non-linear
GARCH versions by taking monthly stock returns of seven emerging economies for the
period Feb 1988 to Dec 1996. It is concluded that even returns show skewed distribution,
GARCH (1,1) model performs better than the EGARCH model.
7
Karmakar (2005) performed evaluation of volatility forecasting techniques from simple to
complex GARCH family models in Indian equity market and concluded that there are
only two competing models i.e random walk model and GARCH(1,1). Further he
identified that existing literature conclude conflicting evidences regarding to forecasting
ability and quality of stock market volatility. In a further study Mutunga, Islam and
Orawo (2015) used the method of estimating functions in predicting and modeling the
volatility of financial returns. Higher order moments are incorporated in the estimation
approach for modeling. First order GJR-GARCH and EGARCH models are used to
predict the volatility for NIKKEI-225 and S&P-500 markets and the mean absolute error,
loss functions, and mean square error is applied to check the predictive ability of the
asymmetric GARCH models. Franses and Van Dijk (2000) concluded that sometimes
volatility is more moderate while other periods may hold high volatility. This particular
element became a reason to develop such models which attributes to trends and patterns
in the time series. Shocks often disturb the trends and these effects might follow the
data for a while; the shocks might even persist for years. The autocorrelation among the
errors terms may cause problems and might lead to invalid projections therefore it
violates the criteria for linear regression models. The size of the shock or even the sign
of a shock influence the volatility level. Generally, negative returns raise the volatility
higher than the positive returns of the similar size. Asymmetric effects are however not
only important in the variance hence the returns can also behave in an asymmetric way.
It is the advantages of nonlinear models that asymmetries are taken into account by
these models which can be seen in the data series. Generally asymmetry means that
huge negative returns look more frequently in comparison to positive returns of the
same size. This phenomenon is commonly indicating the reality that negative returns
8
are related with greater size of risk but it is also observed that positive returns of the
same size are not following this pattern.
This stud also introduces the role of volatility against macroeconomic variables in asset
pricing modeling as well. Pierdzioch, Döpke and Hartmann (2008) explored the linkage
between stock market volatility and macroeconomic factors but in a limited way but not
focused on relation of interrelated volatilities and their predicting power of returns. Study
concluded that stock market volatility likely to increase in the phase of downturns in
business cycle (Schwert, 1989; Hamilton and Lin, 1996; Errunza and Hogan, 1998). Javid
and Ahmad (2009) used macroeconomic factors with stock market return in a conditional
multifactor capital asset pricing model with GARCH-in-Mean model indicate that
conditional model represents very minor advancement in the description of risk and return
relationship regarding to the equity market of Pakistan for this sample period. It is
observed that some stocks are providing a good level of compensation to the investors for
risk. However results indicate that the variance risk is not contributing for risk premium
Here the model is extended in a way that permits variation in economic risk factors
prevailing according to the business conditions of Pakistan and conditioning information
is taken as lagged macroeconomic variables. Moreover the outcomes reveal that the proof
exists in the favor of conditional multifactor capital asset pricing model. The
macroeconomic factors that are experienced to execute comparatively fit in describing
variations in the returns of the assets which consist of inflation risk, consumption growth,
call money rate, term structure of interest rate. However, it is considerable that the market
return, oil price and foreign exchange risk explains significant component of the
variability of stock returns in the time series, and have confined pressure on the asset
pricing and hence concluded that macroeconomic variations can explain expected returns
variation and this variability may contains few business cycle correlations. It is very
9
interesting for investors that such kind of results put the questions that whether
macroeconomic forces capture business cycle fluctuations and how these forces help to
predict stock market volatility or not. The ultimate answer to such dilemma may assist to
redesign and reframe the models of assets pricing as a better and exact solutions to the
practical issues of optimal portfolio selection process, also provide assistance to watch
and administer financial risks in an efficient way. Such kind of results provide more
purposeful and useful answer about systematic financial sector risk to financial analysts,
macroeconomists, central bankers, and big market players to get a wider range of
consideration of latent macroeconomic determinants. Let see a supposition that an
investor wishes to predict volatility of the stock market which is based on macroeconomic
factors. In reality, only a small amount of studies are accessible that report in the support
of the suggestions for using the macroeconomic data for empirical research in finance as
(Christoffersen, Ghysels and Swanson, 2002; Guo, 2003; Clark and Kozicki, 2005) used.
On the other hand, the financial analysts of macroeconomic data has applied for research
on macroeconomic and business-cycle fluctuations as counted by (Croushore, 2001;
Orphanides and Van-Norden, 2002; Orphanides and Williams, 2002; Croushore and
Stark, 2003; Gerberding, Seitz and Worms, 2005) in their relevant studies. This study is
going to take initiative that particular macroeconomic variables are to be identified that
can influence the volatility of the stock returns and this element contributes to the existing
financial literature. There is no proper empirical evidence available yet in the existing
literature that may assist an individual investor, institutional investors, banker and
regulators to answer this question in a justified manner. The determinants of stock market
volatility are commonly expressed as the orders inflow, growth rate of industrial
production and output gap measure. A small number of previous studies have focused, on
the industrial production growth rate as a macroeconomic variable for business cycle
10
fluctuations measurements (Schwert, 1989; Campbell, Lettau, Malkiel, and Xu, 2001).
Hence it is required that, the volatilities produced by various factors can be incorporated
in asset pricing model to forecast the returns of the assets or portfolios and this
phenomenon provides a genuine and logical contribution in the modeling and
predictability of the risk and the return in a nonlinear way.
The reason of doing so is that the study also takes into account the reality that information
set of an investor changes over time. In previous literature, it is generally practiced that to
utilize information set that may comprised of sample data that either macroeconomic
variables assist to predict volatility of stock market or not (Schwert, 1989; Pesaran and
Timmermann, 1995; 2000) found that the value of volatility projections are based on data
of macroeconomic variables that is roughly analogous to the value of volatility
projections based on other parameters or not. Predicting stock market volatility by means
of such parameters does not systematically reduce investors’ average utility. Moreover,
an investor who uses macroeconomic data for volatility forecasting realizes profits in the
market analogous to those investors who would have reaped out returns based on
volatility forecasts from any other parameters. The expected results, explain that an
investor who desires to situate an investment strategy in practice may in general make use
of the results reported in the present research on the macroeconomic determinants of
stock market volatility that is modeled by using historical data of macroeconomic
variables. Therefore this study is expected to introduce new scope of stock volatility in the
emerging markets scenario over which no previous research has determined the predictive
ability of the GARCH family of models in these equity markets.
Summary
At a glance this study introduces the mechanism of conditional volatility and how this
volatility can be modeled to produce the ultimate outcomes for the best interest of the
11
investors and portfolio diversification across the emerging economies. Emerging
economies are those economies where economic progress is following the advanced
countries. In such markets investors seek out for high returns but such markets have
greater level of risk due to domestic infrastructure problems, political instability, and high
volatility in the financial markets. It is visualized that such emerging economies have
high level of volatility and volatility behave in an asymmetric manner. To capture and
model such asymmetric volatility in emerging economies, it is a dire need of present era
to have a comprehensive study for ascertaining the asset pricing. Asset pricing is a quite
difficult and complex phenomenon where returns are behaving in a nonlinear fashion.
1.2 Problem Statement
The behavior of returns and volatility in emerging markets is always a matter of interest and
Pakistan is no exception. Non-linearities and asymmetric pattern in the returns and
volatility in emerging markets are unique attributes of these markets. Emerging markets
have higher volatility and produce higher returns and macroeconomic variables play a
dynamic role in such economies for the movement of returns and volatility. Asset pricing
in the presence of such behavior is still an unaddressed issue.
Therefore this study is an effort to probe into the matter for the induction of conditional
volatility and non-linearities perspective in an asset pricing model.
1.3 Theoretical Framework.
1.3.1 Efficient Market Theory
Fama (1970) introduced efficient market hypothesis as a fair game model. The movement
of prices cannot be predictable because the behavior of prices is random on each day and
prices absorb all available information. Further this study elaborates that the expected
returns are consistent with its risk based upon its historical price trend. Further study
introduced EMH for empirical testing into three broad categories based upon the given
12
information set i.e., i. Weak form of Efficient Market Hypothesis, ii. Semi Strong Form of
Efficient Market Hypothesis iii. Strong Form of Efficient Market Hypothesis.
According to the Random Walk Model the subsequent price changes are identically
distributed and independent for random parameters and hence conclude that future prices
cannot be projected by using historical information and trends. This theory assist to have
an understanding of volatility of asset returns follows random walk or not in an auto
regressive process and either prediction of volatility is possible or not.
1.3.2 Volatility Theories:
Brooks (2008) explained that linear structural and time series models are incapable to
elucidate various important features which are common to much financial data. It can be
explained through these three parameters.
1.3.2.1 Leptokurtosis
Leptokurtosis term means the tendency for returns having distributions that
display fat tails and also surplus peakedness at the mean.
1.3.2.2 Volatility clustering or volatility pooling
This term means that the trend of volatility in the financial markets is shown in
bunches. Mandelbrot (1963) the large returns (of either negative or positive sign)
are expected to pursue large returns and small returns (of either negative or
positive sign) are expected to follow small returns.
1.3.2.3 Leverage effects
Leverage effect show the tendency for volatility to increase more subsequently in
a large price and falls followed by a price climb of the same magnitude.
In short Brooks (2008) found that a very few number of non-linear models are useful for
modeling the financial data. The most famous non-linear financial models are ARCH or
GARCH models used for modeling and forecasting volatility, hence switching models,
13
which permit the behavior of a financial time series to back up various processes at
different points in time. It is the question element that how it may be determined either a
non-linear model may potentially be appropriate for the data set or not? In response to
this query the answer should arrive at least in part from financial theory “a non-linear
model should be applied where financial theory proposes that the relationship between
variables should be such which requires a non-linear model”. Any how the linear versus
non-linear preference may be ended partly on statistical basis and decision should base on
the answer that whether a linear specification is enough to explain all of the most
important features of the data set at hand. Here the most important is that which tools are
available to identify non-linear behavior in financial time series. There are number of
tests for non-linear patterns in time series that are available to the researcher. While
studying asymmetric patterns in mean and variance support is required to a distribution
that can handle these irregularities and to determine asymmetric models for mean and
variance. These theories motivates for this study on the grounds that such element have
not yet been explored with extended parameters in the markets to be studied.
1.3.3 Asset Pricing Theories
Capital asset pricing model (CAPM), originally introduced by (Sharpe, 1964; Lintner,
1965) based upon the mechanics of mean, variance optimization in (Markowitz, 1952)
has launched a simple and compelling theory of asset pricing for more than 20 years. The
theory predicts that the expected return on an individual asset above the risk-free rate is
proportional to the non-diversifiable risk, which can be measured through the covariance
of the asset return along with a portfolio composed of all the available assets in the equity
market. Chen, Roll and Ross (1986) introduced macroeconomic based risk factor model.
Fama and French (1993) introduced SMB and HML in extension to CAPM in a particular
microeconomic based risk factor model. Carhart (1997) extended the Fama French three
14
factor model by including a fourth common risk factor of momentum factor and estimated
it by taking the average return to a set of stocks with the best performance over the prior
year minus the average return to stock with the worst returns. Volatility theories and asset
pricing theories can be extended in a new modeling approach of conditional volatility and
asset pricing.
1.4 Significance of the Study
(Kulp-Tag, 2008; Mutunga, et al., 2015; Mubarik and Javid, 2016) investigated the risk
and return behavior in emerging economies and explored more flexible models that can
provide better risk estimates than the past recent studies. It is important to study
asymmetric or nonlinear patterns in the variance which is closely related to the stability of
emerging markets. Further unstable markets should be investigated, where shocks are
likely to have a more outstanding effect that leads towards greater influence of the shock.
It is important to introduce not only to information variables or impulses, but also to
introduce flexible asymmetric models for mean and variance for the purpose of estimating
the volatility of the returns correctly whereas (Kulp-Tag, 2007; Rashid and Ahmad, 2008;
Tripathy and Garg, 2013) not focused the broader prospective. The present models for
predicting risk provide assistance to some extent, but the complexity in financial time
series data makes it thorny.
Firstly the study also focus on appraise linear and nonlinear models for the variance in
the perspective of forecasting performance. The interest in finding a volatility model
that can describe the data series most correctly the ability to make the best possible
projections of future risk. Secondly this study also support the introduction of
nonlinearities models and explanation of asymmetries for the purpose of identify and
development of better models. One of the most significant elements of this study is to
examine the asymmetric mean-reverting behavior of both mean and variance on the
15
emerging markets in order to investigate asymmetric patterns not only in the variance,
but also in the mean. It also compare mean reversion pattern of negative returns and
positive returns. Where negative returns also tend to result in higher volatility, meaning
negative returns are producing higher risk than positive returns of the same magnitude
as (Nam, Pyun and Avard, 2001; Nam, Pyun and Arize, 2002) desires to explore
asymmetric patterns in the mean and the variance in modeling of financial time series
data. Moreover to probe into the matter of asymmetric market conditions i.e. Bearish
and Bullish. Thirdly the risk-return-information relationship is probed in a new
dynamics which is not expressed by the (Grootveld and Hallerbach, 1999; Yu, 2006;
McMillan and Speight, 2007; Thupayagale, 2010). The concept of asymmetry is needed
to be investigated both in the conditional mean and variance. Lastly the impact of
macroeconomic forces on stock return volatility is needed to study the basis of best
linear or non-linear volatility forecasting model as recommended by (Attari and Safdar,
2013; Omorokunwa and Ikponmwosa, 2014) did not taken into consideration. This study
is significant because it introduces new models of asset pricing based upon volatility by
considering the conditional volatility and non-linear behavior of variations. This study
is quite significant for Investors, Financial analysts, regulators, brokers, financial
institutions, organization management in different domains. It is worth mentioning that
while employing and understanding the stock market volatility in asset pricing that how
much it is beneficial for venturing into a particular stock or portfolio or any policy
decision for better results.
1.5 Contribution of the Study:
Studies on emerging markets have huge thrust regarding to such issues which address
towards the interaction of risk and return forces. This study contributes in the field of
finance in the following manner.
16
It provides an insight about the conditional volatility and nonlinearities in short
run horizon stock returns as well as the in the long run. (Cheong, Nor and Isa,
2007; Ibrahim, 2010; Engle, Ghysels and Sohn, 2013; Ibrahim, 2010).
In almost previous work the predictability have mostly dealt with the behavior of
stock returns in a linear model and the literature lacks issues in asset pricing
regarding to capture the non-linear behavior of stock returns and volatilities
(Rashid and Ahmad, 2008).
This study provides insight about the behavior of risk and return in emerging
markets which is prime area of interest for investors. (Goudarzi and
Ramanarayan, 2011; Tripathy and Garg, 2013).
Study provides the comparison of Linear and Nonlinear Volatility Models for
equity market returns and proposes an appropriate model for volatility in
emerging equity markets. (Kim, Mollick and Nam, 2008; Kulp-Tag, 2008;
Gyesen, Huang and Kruger, 2013; Mutunga, et al., 2015; Mubarik and Javid,
2016).
This study provides insight about the behavior of volatility in stable and unstable
market so that decision makers can take appropriate measures for mitigating
risk. (Koutmos, 1997; Gokcan, 2000; Salman, 2002; Kumar, 2006; Alagidede, 2011;
Tripathy and Garg, 2013; Raza, Arshad, Ali and Munawar, 2015).
This study provides evidence about impact of information asymmetries and
market conditions asymmetries on returns and volatility. (Verhoeven and
McAleer, 2004; Cheong, Nor and Isa, 2007; Liau and Yang, 2008; Zhang and Li,
2008; Ibrahim, 2010).
17
This study proposes a nonlinear volatility based asset pricing model that may help
in optimal decision making in areas of capital investment, financing, merger and
acquisition and equity valuation (Asteriou and Price, 2001).
18
1.6 Objectives of the Research
The objectives of this study are as follows.
1. To compare Linear and Nonlinear Volatility Models for equity market
returns.
2. To study the behavior of volatility in stable and unstable market.
3. To study the Long-run and Short-run behavior of volatility in emerging
equity markets.
4. To explore the impact of information asymmetries on returns and
volatility.
5. To examine the impact of Macroeconomic variables on Stock return
volatility.
6. To develop a volatility based asset pricing model for emerging markets.
19
CHAPTER 2
LITERATURE REVIEW
20
2. LITERATURE REVIEW
The literature review segment presents individual summary, a little description about
relevant methodology, the contribution and brief discussion about the past results
regarding to the relevant studies being held in past or in present. Therefore the present
study may be designed to meet the objectives and present era challenges.
In the first segment review study initiates from existence of nonlinearities in returns
time series. In second segment various studies about volatility, factors for forecasting of
volatilities and related efficiency in performance. The review literature is initiated with
the evidence that different extensions of the traditional ARCH model as (Engle, 1982)
capture the asymmetric behavior in the variance and proposes that the conditional
variance is asymmetric. Moreover, if returns act asymmetrically, it could be possible to
take into consideration contrarian-type strategies in the situation where “loser-stocks”
outperform “winner-stocks”, However studies reveals that stock returns generally revert
more rapidly after negative returns rather than after the positive returns as concluded by
(Sentana and Wadhwani, 1992). The elements and parameter measuring the reverting
behavior and pattern is negative and significant. (Nam, 2003; Nam, Pyun and Arize
2002, 2001) used an Asymmetric Nonlinear Smooth Transition GARCH (ANST-
GARCH) to measure the mean-reversion patterns and possible consideration of
asymmetries in both mean and variance. The asymmetry in the variance refers to the
leverage effect, and the asymmetric aspect in the mean is generally known as the
reverting property of return dynamics. The findings from the research argued that
negative returns usually reverted faster than positive returns.
Koutmos (1997) examined that the emerging Asian equity markets of Philippines, Korea,
Malaysia, Taiwan Singapore, and Thailand act likewise to the developed equity markets
21
regarding to their stochastic property phenomena, volatility clustering and leverage effect.
These outcomes are astonishingly confirmatory.
Nam, Pyun and Avard (2001) investigated the mean reverting behavior and pattern of
monthly stock returns regarding to the indices of AMEX, NYSE, and NASDAQ, by
applying ANST-GARCH models. Study analyses the time varying volatility in return
series and supports to overreaction hypothesis of the study. This particular model shows
the asymmetric patterns of mean reversion as well as risk decimation. The time period is
taken from 1926:01 to l997:12, and results indicated that not only the negative returns
reverts to the positive returns but also faster than positive returns reverse to the negative
returns. However negative returns are actually causing to reduce risk premiums from the
higher predictable volatility. The results support the hypothesis regarding to the market
overreaction. The results indicate that asymmetry is due to the mispricing behavior on the
part of investors who are overreacting to the certain market Good or Bad news. The
results confirms about the arguments for the contrarian strategy of portfolio.
Kulp-Tag (2007) examined the asymmetric behavior regarding to the conditional mean
and variance. Particularly this study modeled short-horizon mean reversion pattern in
mean with an asymmetric nonlinear autoregressive model, along with this phenomenon
the variance is modeled with an (E-GARCH) in the Mean model. In a study of Nordic
stock markets the results indicates that negative returns revert more rapidly to the positive
returns when positive returns generally keep on longer. It further concluded that
asymmetry in both mean and variance can be visualized in all these equity markets and
hence are reasonably alike. Increase in volatility following positive returns after negative
returns is an indication of overreactions in the equity market. So the study revealed that
negative returns cause to increase in variance and positive returns leads towards fall in
variance.
22
Zhang and Li (2008) examined asymmetric aspects in the Stock Market of China. They
anticipated that the stock returns in this equity market show asymmetric dynamics with
negative returns frequently foremost to overreactions. Supplementary it is concluded that
there exist leverage effect in the behavior of volatility and it is true for six ASEAN stock
markets of Philippines, Singapore, Indonesia, Malaysia, Thailand, and Vietnam.
Liau and Yang (2008) evaluated seven equity markets of Asian regarding to the mean and
volatility asymmetric patterns by using daily observation for the January 3, 1994 to
March 31, 2005 and give evidence for asymmetry in mean reversion behavior in these
equity markets. This study is a little attempt to complements the relevant studies by
seeming at the asymmetric mean-reverting behavior by using data following the Asian
crisis.
Ibrahim (2010) examine six ASEAN emerging markets return patterns (Philippines,
Singapore, Indonesia, Malaysia, Thailand, and Vietnam) by applying E-GARCH in mean
model, and famous as AR-EGARCH (1, 1) Model. This study used data from the period
August 2000 to May 2010 and report that these equity markets generally have fast mean
reversion velocity but relatively different dynamics of return patterns. It reveals that there
exist no evidence regarding to the serial correlation in the markets of Thailand and
Singapore. Therefore only the technical trading strategies are relevant for the markets of
Vietnam and Indonesia. By this behavior it may be hypothesized that the emerging
markets follow asymmetric patterns not only in the variance but also in mean.
To meet another challenge for the evaluation of linear versus nonlinear models in terms
of variance forecasting performance. The interest in finding a volatility model that may
elaborate the data series most appropriately lies in the ability to make best possible
forecasting of future risk. The ARCH model of (Engle, 1982) and the GARCH model of
23
(Bollerslev, 1986) have got lots of support, and are used in the development of these
models for the conditional variance.
Engle and Ng (1993) used sign and size bias tests to identify nonlinear or asymmetric
patterns. In different studies the variance is modeled with the linear GARCH as
(Bollerslev, 1986) modeled the variance, and the nonlinear models Quadratic GARCH
(QGARCH) is applied by (Sentana, 1995) the EGARCH by (Nelson, 1991) the GJR-
GARCH by (Glosten, et al., 1993) the TGARCH by (Zakoian, 1994) and Volatility
Switching GARCH (VS-GARCH) is used by (Fornarià and Mele, 1997). Engle (1982)
investigated linear and nonlinear ARCH effects to evaluate the models. Moreover the
Lagrange Multiplier (LM) test and a modified LM test are used by (Lundbergh and
Teräsvirta, 1999) to evaluate the performance. The results indicate that even though the
tests carried out to provide suggestions that whether asymmetric, nonlinear models
should be applied or not and it cannot closely be decided that which nonlinear model
should be used.
Taylor (2004) concluded that the benefit of such models is that they permit the
characteristics in the variance model to take into consideration the sign and size effects
of historical returns or shocks.
Kulp-Tag (2008) examined how volatility in financial markets is modeled in different
ways. Study investigated empirically that how good these models are for volatility,
including both linear and nonlinear, in absorbing third and fourth moments. Study
investigated the Nordic stock markets, including, Sweden, Finland, Denmark and
Norway regarding to the diverse linear and nonlinear models. Nordic markets results
reveal that a linear model have the ability to be used for modeling the financial series,
However many times nonlinear models perform to some extent better in some
situations and cases. Study concluded that the Nordic markets show asymmetric
24
patterns merely to a certain extent. Generally negative shocks have a major effect on
these equity markets; however these effects are not so strong in terms of absorbing
third and fourth moment. Therefore non-linear models outperform linear ones. These
studies justify that it may also be hypothesized that Non linear models perform better
than linear models in term of volatility forecasting for the markets which is studied in
this research. Further justifications also exist in upcoming literature as well.
The concept of asymmetry is considered in two dimensions: First, asymmetry is
associated to the relationship between the conditional variance and the lagged squared
error term and hence (G)ARCH type modeling and extensions are there. Secondly,
asymmetry is considered in the distribution that is applied in the modeling of the
variance and this is accomplished by introducing asymmetric distributions. Bollerslevs
traditional GARCH model is used as starting point or benchmark to estimate the
variance. Two asymmetric extensions are applied first one is the (Nelson, 1991)
EGARCH and secondly Asymmetric Power ARCH (AP-ARCH) by (Ding, Engle and
Granger, 1993). There are three distributions are combined with these models: the
Normal (Gaussian) distribution, the GED (asymmetric), the Student’s t-distribution
(symmetric).
Kim, Mollick and Nam (2008) employed annual returns producing from overlapping
monthly price indices for the Great Seven equity markets. They used LSTAR, ESTAR
models and identified asymmetry and common nonlinearities in the long run horizon of
stock returns. They concluded that asymmetric nonlinear dynamics creates attraction to a
considerable segment of the expected variations in the long-horizon stock returns.
Moreover it is clear that nonlinear models outperform linear models in sample and as well
as in the out of sample forecasting exercises mostly. It is important to analyze linear and
nonlinear model comparison and performance. This study proposes strong permanence of
25
return vibrancy with nonlinear impulse responses. The results of the study provide
purposeful information for the investors in global stock markets regarding to the design
and investment strategies and justify for inferring the hypothesis that volatility influences
return in a non-linear fashion. To meet the next objective the past studies justify that the
risk-return-information relation have investigated in different domains. Both the
contemporaneous and the dynamic relationship are the matter of interest. The concept
of asymmetry is introduced both in the conditional mean as well as in the variance.
Kumar (2006) analyzed the comparative performance of various econometric forecasting
volatility models in connection with stock and Forex markets of India. He ranked
EWMA on the basis of out of sample predications as superior to the other methods
and concluded that EWMA escort to improve in the volatility forecasting of equity
markets and the GARCH (5,1) is leading method in the Forex market.
Banerjee and Sarkar (2006) studied and examine the existence of long memory in the
Indian equity market returns. Study concluded that even though each day stock returns
are not mostly correlated but still there exist good support of long memory existence
evidence in the conditional variance. Further they found that FIGARCH is superior to all
other GARCH family models in the performance and best-fit volatility model is declared.
Moreover the study concludes that in SENSEX returns the presence of leverage effect is
insignificant therefore symmetric volatility models outperforms as they are expected.
Cheong, Nor and Isa (2007) investigated the volatility behavior in asymmetry and long-
memory sense regarding to the daily returns of the Malaysian equity market for a period
of 1991–2005. Clustering volatility, leverage effect and long-memory behavior of the
volatility are captured through asymmetric GARCH models and by including the realized
volatility in GARCH for the final period. Crosswise the periods, the results indicate that
mixture of symmetric and asymmetric GARCH modeling are fitted for volatility
26
capturing. It is concluded that the existence of long-memory volatility permits us to rank
the degree of market inefficiency, which may also allows to the reject the efficient market
hypothesis in Malaysian equity market. In CGARCH and FIGARCH models the
diagnostic tests indicates better specification with no significance of iid except in the
whole period. Lastly, the GARCH models by including the RV indicate better log-
likelihood but due to the penalty of additional parameter it does not evaluate BIC
criterion.
Leeves (2007) investigated the conditional volatility in Indonesian equity market covering
the Asian crises period. Asymmetric volatility models recommend that all parameters
were found time-varying, along with the inclusion of those which capture asymmetric
response. The study used GJR, NGARCH and AGARCH known as asymmetric models
of conditional volatility on daily stock returns of Indonesian equity market for the period
1990-1999. Results shows that estimations for this period are significant for ARCH and
GARCH effects, however no such significant asymmetric effects exist. Further the results
reveal that the Asian crisis proposes significant asymmetric effects from the shock of
conditional volatility, hence negative shocks create higher volatility than positive shocks.
Ederington and Guan (2010) investigated differentiation regarding to the impact of
likewise large positive and negative return shocks in the equity market of US. EGARCH,
GJR models were applied and results revealed that following large positive shocks of the
returns, models predict larger increase and smaller increase in volatility and how a
negative shock of the same scale falls more speedily. On the other hand asymmetric
econometric models forecast a decrease in volatility preceded by near to zero returns and
prior to the stable market both implied and realized volatility have little change from the
observed levels. By these studies it may also hypothesized that there exist asymmetry in
the variance for emerging markets and negative reactions increases volatility more than
27
positive reactions in emerging markets.
Alagidede (2011) studied return predictability in African emerging stock markets. The
study focused on the behavior of mean, variance and mean reversion patterns. It is
therefore concluded that the single time varying returns can be predicted. Moreover, study
found that volatility clustering, leverage effect and leptokurtosis exist in the data. Further
study found that all African markets provide an evidence of long memory and hence it is
vital indicator of less than perfect arbitrage.
Goudarzi and Ramanarayan (2011) studied BSE- 500 index during the global financial
crisis of 2008-09 by using asymmetric ARCH models regarding to the effects of good
and bad news on volatility. EGARCH and TGARCH models were used to identify the
effects of volatility. The returns behavior of BSE-500 was identified the reaction of
good and bad news asymmetrically. Existence of the leverage effect shows that the
bad news has a greater impact on volatility than good news. Particularly this stylized
fact shows that the innovation sign has a significant impact on the return’s volatility
and the influx of negative news in the equity market created increase in volatility more
than good news and hence it is concluded that bad news in the BSE-500 increases
volatility higher than good news. Such behaviors motivates to hypothesized that
information asymmetries may have impact on volatility and returns
Tripathy and Garg (2013) studied stock market volatility prediction of six emerging
economies by using daily data from January 1999 to May 2010. The used ARCH,
GARCH, TGARCH GARCH-M and EGARCH models. However it is concluded
that there prevails positive association between risk and stock return in Brazilian
stock market only. Results reveal that volatility shocks are significantly consistent
in all economies. Moreover asymmetric GARCH models shows sound existence of
asymmetric effects in stock returns in all equity markets. Results indicate the presence of
28
leverage effect in the stock returns series and shows that bad news creates higher impact
on volatility. Further this study reveals that the rise in volatility is excessively with
negative shocks in the return series. From such behaviors in markets it may also
hypothesized for the underlying study the returns of the emerging markets follow
asymmetric pattern in mean in which positive returns are followed by more positive
returns but negative returns revert to positive returns faster that positive reverts to
negative returns.
Gyesen, Huang, Kruger (2013) evaluated the predictive ability of the returns of
Johannesburg Stock Exchange by taking macroeconomic variables through linear and
nonlinear models. They used, ARMA, Markov switching, Dynamic Regression models,
asymmetric models of GARCH and EGARCH to capture the conditional heteroskedasity.
They found that the most significant model is Markov switching model in sample fit and
further EGARCH and Two-state model Dynamic Regression is the most significant for
out of sample fit. They found that the predictive performance of nonlinear models is not
better than linear models due to crises period which indicates the advantage of nonlinear
considerations of conditional volatility lessens for the sample period. Mutunga, Islam and
Orawo (2014) investigated the existence of leverage effects in the daily returns series of
NIKKEI-225 and S&P-500 for the period 2008 to 2011 by EGARCH and GJR-GARCH)
with Maximum Likelihood Estimate and EF approaches. Recently (Raza, Arshad, Ali
and Munawar, 2015) estimated and predicted the volatility of KSE-100 returns through a
number of GARCH family models by taking a period from June, 2002 to May, 2013.
They used ARMA specifications and tried to identify the best fitted GARCH model for
volatility forecast. They applied GARCH, GJR-GARCH, EGARCH and APARCH
models and concluded that GARCH (1,1) is fitted model with student’s t- distribution
and with GED, GARCH(1,1) is best prediction model and same with EGARCH(1,1).
29
Sharma and Vipul (2015) compared the forecasting ability of the recently proposed
GARCH model by using daily returns with standard GARCH model and predicted the
conditional volatility of sixteen equity markets indices for the period of fourteen years.
They found that relative predicting performance of the GARCH and EGARCH models
based on realized volatility is more sensitive to the selection of the loss criterion. EWM
with realized measures generally outperforms the Realized GARCH model in out-of-
sample forecast and results provide robustness. In a recent study (Albuquerque,
Eichenbaum, Luo and Rebelo, 2016) proposed a simple theoretical framework for asset
pricing in which the central role is played by demand shocks. Such shock increases
valuation risk but permit the model to take into consideration the key asset pricing
element such as equity premium, Moreover express weak correlations between the
fundamentals and stock returns. Mubarik and Javid (2016) investigated the volatility
forecasting by using GARCH family models for KSE market from the period July 1998 to
June 2011. They used error statistics of these forecasts to measure the performance of the
model. They identified that only EGARCH model has negative leverage effect from all
asymmetric models and bad news cause to decrease the volatility and good news cause to
increase in the volatility. The asymmetric models perform better in Pakistan than the
symmetric model in out-of sample forecasting context. Huynh (2017) tested the
conditional asset pricing models in the international equity markets and concluded that by
taking new instruments to capture the time variation in risk exposure can significantly
decrease the bias element in unconditional alpha. To explore the explanatory variables
this study has further reviewed the literature to identify the gaps in the previous literature.
Asteriou and Price (2001) studied the impact of politically instability on economic growth
of United Kingdom during the period 1961 to 1997. They used GARCH-M model along
with six variables that quantify political instability and analyzed its impact on growth.
30
The outcomes revealed that negative effects of instability exist on growth and have
positive impact on growth volatility.
Salman (2002) applied GARCH-in-mean model for the risk-return relationship, and
concluded that both risk and return are integrated with information given to the market
participants. This relationship has been investigated with various methods; employing
traditional regression analysis, GARCH applications and co-integration analysis. It is
inferred from such studies that it may also hypothesized there exist a significant positive
relationship between risk and return.
Lee and Rui (2002) investigated the dynamic relationship between trading volume and
stock returns on a daily basis. Mestel, Gurgul & Majdosz (2003) explored the
association among stock returns, volatility of the returns and trade volume. The results
indicate weak support for both the contemporary and the dynamic relationship between
stock returns and trading volume on the Austrian market. However in a similar paper
(Gurgul, Majdosz and Mestel, 2005) provided no evidence regarding to the relationship
of stock returns and trading volume for the Polish market. Glosten et al. (1993) argue
that an interest rate variable in the variance equation reduces the persistence, and
interest rates are of helpful in modeling and predicting volatility. There has not been
any proof of interest rates providing better predictions; adding interest rates into the
mean equation does not give better models, but benefits in the volatility modeling
seems to be present. Glosten et al. (1993) further stated that with the help of nominal
interest rates, it could be possible to forecast periods of relatively large excess returns
and significantly less volatility. This alone supports the use of interest rates as an
information variable for the variance. Batra (2004) examined the volatility pattern in
Indian stock markets regarding to the asymmetric behavior and time varying volatility of
stock returns by using GARCH model. The study analyzed impulsive shifts and the
31
likelihood of chance of these rapid shifts in volatility along with the important political
and economic events even in inside and outside of the country. Moreover the study
evaluated various cycles in the equity market regarding to the variation in duration,
amplitude and volatility in terms of bear and bull stages for the concerned period.
Results show that the stock market liberalization has no any direct inference on the
volatility of stock returns. Further results indicate that there exist no structural changes
around liberalization event and the time period regarding to the volatility breaks in
trading transactions. It is found that the bull phase is longer and the bull amplitude
phase is greater. Moreover in these phases the magnitude of volatility is also higher.
Finally, the results reveal that that volatility has been decreased after the liberalization
stage for bear and bull phases of the equity market cycles. Hence it is concluded that
the equity market cycles influence the volatility in different dynamics regarding to the
bull phase phenomenon.
Leduc and Sill (2007) used an equilibrium model to evaluate the significance of monetary
policy for the time prior to 1984 as a result of decline in United State inflation and output
volatility. Results indicate that monetary policy is playing an important role in decreasing
the inflation volatility, however it played a little role in decreasing real output volatility.
Econometric model indicate that the decrease in real output volatility due to smaller TFP
shocks. Under an optimal monetary policy they further investigated the pattern of output
and inflation volatility and found that real output volatility would have been somewhat
lower, and inflation volatility substantially lower.
Kulp-Tag (2008) investigated the relation between return, volatility with volume and
interest rates as impulse variables. The concept of asymmetry in returns and volatility
in this study contributes to the current literature. The risk-return-information
relationship is investigated on the S&P 500 index for daily data. Hence the results
32
suggest that interest rate is not an important information parameter for modeling the
volatility. Asymmetry in mean is modeled with a piecewise regression to take into
consideration the asymmetric autocorrelation in the mean. Asymmetry in mean appears
to be of some significance in modeling conditional mean and variance.
Engle and Rangel (2008) used macroeconomic factors to found volatility their study
concluded that inflation, GDP growth, and short term interest rate are significant
expounding variables that cause to an increase in the volatility. They concluded that
inflation and growth of output are significant positive determinants of volatility.
Engle, Ghysels and Sohn (2013) studied the relationship between macroeconomic forces
and stock market volatility by applying latest set of component models that differentiate
short-run movements from secular actions. They formulated industrial production growth
and inflation to drive the long- term component of model. Hence, it is concluded that
adding economic factors into volatility models performs well in terms of long run
predictions. Further they found that at every day level, industrial production growth and
inflation take into consideration between ten percent and thirty five percent of one day
forward volatility projection. Consequently, the study inferred that macroeconomic
fundamentals play an important even at short horizons in capturing the volatility. It is
concluded that the macroeconomic forces have the ability to capture the volatility in long
run as well as in short run dynamics. These studies justify for hypothesizing that
macroeconomic variables are significant information parameter for modeling the
volatility.
Sangmi and Hassan (2013) evaluated the macroeconomic variables impact on the stock
price behavior and volatility of the Indian equity market. Their study concluded that
there exist a significant relationship between equity market fluctuations and
macroeconomic variables of inflation, interest rate, exchange rate, gold price, money
33
supply and industrial production. Attari and Safdar (2013) used EGARCH model to
generate volatility from KSE return series and identified GDP, Inflation and interest rate
as the key determinants of volatility in Pakistan.
Omorokunwa and Ikponmwosa (2014) examined the relationship between volatility of the
stock market and macroeconomic variables such as GDP, exchange rate, interest rate and
inflation. Empirical evidence is taken for the period of 1980 to 2011 by applying GARCH
model. GARCH model capture the non-linear effects because volatility influence return in
a non-linear fashion. It is the point that we may too hypothesize that the same behavior of
volatility is reflected by KSE returns. They concluded that price behavior in Nigeria is
volatile and the historical information has impact on stock market volatility in Nigerian
equity market. Hence they concluded that exchange rate and interest rate have effect on
stock price volatility in a weak manner and inflation is the major determinant in Nigerian
stock price volatility. They suggested that inflation element should be taken into
consideration in the proper design of targeted monetary policy by taking into the stock
market perception of policies. In finance arbitrage pricing theory guides the relationship
between macroeconomic variables and stock return.
d’Addona and Giannikos (2014) modeled asset pricing with business cycles in regimes
switching in mean and variance equation. They identified model has predictability power
and reports significant results. Further they realized and identified the modeling of
macroeconomic risk in such kind of models. It is evidence that Macroeconomic
variables are significant information parameter for modeling the volatility and this
hypothesis can be established for asset pricing in the emerging economies.
Herskovic, Kelly, Lustig, and Van-Nieuwerburgh (2016) identified that idiosyncratic
volatility leads a strong factor structure for pricing the common factors in idiosyncratic
34
volatility for shocks. Lowest idiosyncratic volatility beta (Systemic Risk) has greater
earning capacity than the highest idiosyncratic volatility beta. Therefore this particular
element of idiosyncratic volatility assists to express the anomalies of asset pricing
modeling as well. Epstein and Ji (2013) volatility and drift is modeled with a utility
approach in a continuous time frame of reference and extension is made in asset pricing
theory with arbitrage free rule, based upon arguments of hedging approach and sharp
predictions can be attained by assuming preference maximization and equilibrium.
Demir, Fung, and Lu (2016) elaborated the performance of CAPM under a general
equilibrium model, can be enhanced significantly by applying conditional consumption
and market return volatilities as modeling factors. Indian market is tested through
portfolios selected by size and book-to-market equity ratio point of view. Conditional
volatility has very low effect on companies having large capitalization than small-growth
and small-value based firms.
Kim and Kim (2016) modeled asset pricing and found strong evidence of Inter-linkages
among the volatilities of 6 equity markets of United States and rejected the null
hypothesis of constant volatility for the capital asset pricing model in the period of
financial crises. The (Brooks and Persand, 2003; Yu, 2006; McMillan and Speight, 2007)
used VaR techniques in the computation of stock return volatility in the Asian emerging
markets. They identified that VaR is significant parameter for volatility modeling.
However, there seem a lot of gap in existing literature with respect to VaR measurement
in various equity markets. Thupayagale (2010) analyzed the prediction performance by
using GARCH model in context with Value-at-Risk estimation by using stock return data.
The results reveals that models with asymmetric effects and having long memory are
important in considering the provision of improved VaR estimates and can escape from
losses in trade. Moreover the results indicate that it can be used to forecast for out-of-
35
sample. It is an important parameter in the computation of Value-at-Risk for derivation of
exact asset-return volatility estimations. It is inferred from the study that Value at Risk is
significant information parameter for modeling the volatility. It may hypothesize that the
same behavior prevails in the equity market dynamics of KSE. Volatility and asset pricing
remained always a hot cake in financial modeling in various context and testified
volatility in the domain of various risk anomalies and firm factors as (Grootveld and
Hallerbach, 1999) indicated that semi-variance is same like to variance but it considers
only values below the average value. This element refines the problems of asymmetry and
known as downside risk. This element can be used to eliminate the probability of loss for
the portfolio. More over this approach considers the element of lower partial moment that
can be tested for empirical financial time series. It is inferred from the study that
downside risk is significant information parameter for modeling the volatility.
Critically the literature review observed the past and recent studies based upon the
dynamics of conditional volatility studies and their relevance to asset pricing in
emerging and developed economies. It is seen that their exist nonlinearities in returns of
the financial time series and volatility can be predicted and the performance of related
efficiency can be measured. Further it is evident that GARCH family models can
capture the asymmetric behavior in the variance Moreover a stochastic property
phenomenon prevails regarding to the volatility clustering and leverage effect in
emerging markets. Empirical analyses also supports to the overreaction hypothesis of the
study and negative returns are actually causing to reduce risk premiums from the higher
predictable volatility. In short it is seen that asymmetry is due to the mispricing behavior
on the part of investors who are overreacting to the certain market Good or Bad news and
this fact confirms the arguments for the contrarian strategy of portfolio. Numerous
studies argue for asymmetric, nonlinear models and majorly results supports that non-
36
linear models outperform linear ones. It is also inferred from the past studies that there
exist a significant positive relationship between risk and return. Further studies also
support with some evidences that information variables suck like macroeconomic
variable, business cycles, trade volume, market liberalization can be helpful in
modeling and predicating the volatility but there exist a sound gap regarding to the
modeling of conditional volatility with reference to the macroeconomic forces, market
conditions asymmetries, value at risk, and downside risk for asset pricing
determination.
37
HYPOTHESES OF THE STUDY
H1. The emerging stock markets follow asymmetric patterns not only in the variance,
but also in the mean.
H2 There exist asymmetry in the variance for emerging markets and negative
reactions increases volatility more than positive reactions in emerging markets.
H3. The returns of emerging markets follow asymmetric pattern in mean in which
positive returns are followed by more positive returns but negative returns revert
to positive returns faster than positive reverts to the negative returns.
H4: Non linear models perform better than linear models in terms of volatility
forecasting.
H5. Information asymmetries have impact on volatility and returns.
H6: Macroeconomic variables are significant information parameter for modeling the
volatility.
H7: There exist a significant positive relationship between risk and return
H8: Volatility influence return in a non-linear fashion.
38
CHAPTER 3
DATA AND METHODOLOGY
39
3. DATA AND METHODOLOGY
Banco Bilbao Vizcaya Argentaria (BBVA) held research in November 2010 and
identified key emerging markets in the world with a new economic concept. Banco
Bilbao Vizcaya Argentaria classified emerging markets into two sets of developing
economies which are as under.
3.1 Emerging and Growth-Leading Economies (EAGLEs)
EAGLEs are defined as emerging economies where the expected incremental GDP would
be larger than the average of the Great Seven (G7) economies in subsequent 10 years, but
not including the USA. Three Asian markets from this group i.e China, India, and
Indonesia are taken for this study.
3.2 NEST: Next to EAGLEs
NEST are defined as emerging economies where the expected incremental GDP is lower
than the mean value of the Great Six economies (G7 excluding the USA’s) but higher
than the average value of the Italy. Three Asian markets from this group i.e Bangladesh,
Malaysia, and Pakistan are taken for this study.
So this study includes six emerging markets from above these two groups which include
China, India, Indonesia, Bangladesh, Malaysia and Pakistan, The data is comprised of
daily prices for the period Jan 4, 2000 to Dec 30, 2010. Stock indices data is taken from
Yahoo Finance and the relevant websites of the equity markets. Eviews-8 and Ox
Metrix-6 Software has been used to test the data.
3.3 Stock Market Returns
Stock market returns are computed by using the following equation.
𝑆𝑟𝑡 = 𝑙𝑛(
𝑝𝑡𝑝𝑡−1
⁄ ) (1)
Srt = Stock Returns
Pt = Closing Price of Stock indices at time t
40
Pt-1 = Closing Price of Stock Indices at 1 time before.
3.4 METHODOLOGY
To meet the objectives of the study, methodology section covers the core dimensions of
the study area and introduces a new econometric approach to model the volatility for
asset pricing in an emerging market scenario.
The volatility in equity markets has been studied from various domains. Some are
focused on linear relationship and some focus on nonlinear relationship.
Malkiel and Fama (1970), and Fama (1991) developed approach to focus on the
Random Walk Hypothesis. When using linear setups for modeling time series data as
for example stock market indices, it is assumed that the series are normally distributed,
or that the logarithmic series, are normally distributed.
The return rt should behave as a random variable with variance δ2 and mean equal to µ
or; rt ~ N µ, δ2. Prices should follow a random, and tomorrow’s price should be
possible to predict from the price today and the information available today;
3.4.1 Sign and Size Bias Test
To study the behavior of volatility in stable and unstable market sign and size bias test is
used. Sign bias test is used to test the either historical positive and negative shocks have a
diverse impact on volatility. In first instance we get the residuals value from the
symmetric GARCH model and then we go for sign bias test in the given below regression
of the squared residuals.
휀�̂�2 = 𝜆0 + 𝜆1 𝑆𝑔𝑛−
𝑡−1+ 𝜇𝑡 (2)
𝑊ℎ𝑒𝑟𝑒 𝑎𝑠 𝑆𝑔𝑛−𝑡−1
= 1 𝑖𝑓 휀�̂�−1 < 0 𝑎𝑛𝑑 𝑆𝑔𝑛−𝑡−1
= 0 otherwise
Sign bias testing involves t-test for coefficient 𝜆1 : However if positive and negative
shocks have diverse effect on volatility then the coefficient 𝜆1 will be statistically
significant.
41
Whether volatility depends upon sign and size of past shocks a sign and size bias test is
used based upon the following regression.
휀�̂�2 = 𝜆0 + 𝜆1 𝑆𝑔𝑛𝑧−
𝑡−1+ 𝜆2 𝑆𝑔𝑛𝑧−
𝑡−1휀�̂�−1 + 𝜆3𝑆𝑔𝑛𝑧+
𝑡−1휀�̂�−1 + 𝜇𝑡 (3)
𝑆𝑔𝑛𝑧+𝑡−1
= 1 − 𝑆𝑔𝑛𝑧−𝑡−1
Null hypothesis for presence of no sign and size bias corresponds to: Ho: 𝜆1 = 𝜆2 = 𝜆3 =
0 . Lagrange Multiplier (LM) test is used to test this element.
3.4.2 The Mean Equation
When we are going to model a variance equation, specifications for the mean equation are
required to be made. While estimating a mean equation model, residuals are mandatory to
model the variance equation for its repossession.
Therefore in this study returns are narrated by the following econometric process:
𝑟𝑡 = Ψ0 + ∑ Ψ𝑖𝑝𝑖=1 𝑟𝑡−𝑖 + ∑ λ𝑖
𝑞𝑖=1 휀𝑡−𝑖 + 휀𝑡 , (4)
Where as Ψ0 is a constant, Ψ𝑖 and λ𝑖are the parameters, 𝑟𝑡is the return at time t and 휀𝑡is
the white noise at time t. Equation (2) is an ARMA (p,q) model that explains returns as
dependent on the previous values of returns and shocks. To select the order of an ARMA
model for each indices and to determine which values of p and q narrates the financial
time series to its best, various combinations of ARMA (p,q) models in different manner is
being estimated. OLS regression is used to estimate. Then estimated variations of Auto
Regressive Moving Average (ARMA) models are matched to one another by visualizing
values of some selected information based criterion. As the Schwarz information criterion
(SIC) deems to provide steady and consistent results, therefore model selection provides
choice and performance by reducing this information criterion.
42
To meet the first objective the study compares the Linear and Nonlinear Volatility
Models for equity market returns and propose an appropriate model for volatility in
emerging equity markets.
3.4.3 Linear Models
The fundamental methods concerned in the estimation of the different financial models,
parameters for an initial period and the usage of these parameters to prior data, thus
composing out of sample prediction. Following are the linear models that may be applied
to test the performance and forecasting: (1) Random walk model, (2) Autoregressive
Model, (3) Moving Average Model, (4) Exponential Smoothing Model.
3.4.3.1 Random Walk Model
The random walk model explains the mechanism of forecasting of stock return volatility
of today is based upon on the observed volatility of yesterday. Rashid and Ahamd (2008)
applied random walk model to test the volatility. The mechanism of Random walk model
can be explained as follows:
𝜎𝑡(𝑅𝑊) = 𝜎𝑡−1 (5 )
Whereas “σt” elaborates the daily volatility as measured in the equation.
3.4.3.2 Autoregressive Model – (AR)
Poterba and Summers (1986) employed investigated the linear model and specified a
stationary AR(1) process for volatility testing of the S&P 500 Index. The simplest and
extensively applied version of the autoregressive model is the first-order autoregressive,
or AR (1), model. The AR (1) process is represented by using following equation.
(1 − ω1𝜆)𝜎𝑡(𝐴𝑅) = 𝜐 + 휀𝑡 (6)
𝜎𝑡 = ω1 𝜎𝑡−1 (7)
Whereas ω1 is the autoregressive parameter, λ is backward shift operator, where as “υ” is
constant term, and εt is the error term at time t.
43
3.4.3.3 Moving Average Model – (MA)
Moving average prediction model takes into consideration the lagged values of the
forecast error to get better the present forecast. Rashid and Ahmad (2008) used MA
model to forecast the volatility. The fist order moving average, or MA (1), takes into
consideration the most recent forecast error and it can be explained as follows:
𝜎𝜏(𝑀𝐴) = 𝑢 + (1 − 𝜓1 𝜎𝑡−1) + 𝜎𝑡−1(𝑀𝐴) + 𝜉𝑡 (8)
Whereas Ψ1 is the moving average parameter whereas “u” is the constant term, and ξt is
the error term at time t.
3.4.3.4 Exponential Smoothing Model (ESM)
Dimson and Marsh (1990) introduced the model of exponential smoothing for the
prediction of return’s volatility:
𝜎𝑡(𝐸𝑆) = 𝜋𝜎𝑡−1(𝐸𝑆) + (1 − 𝜋)𝜎𝑡−1 (9)
As this model indicates that the forecast of volatility is based upon the assumption that it
is a function of the instant past forecast and hence reflect the immediate historical
observed volatility. Therefore smoothing parameter, π, is constrained to be lounge
between 0 and 1. The optimal value of π should be determined empirically. Further to
meet the objective of long-run and short-run behavior of volatility in emerging equity
markets, the below non-linear and asymmetric models is used. Moreover correlation test
is used among the stock returns and further correlation test is used among the conditional
volatilities of the respective markets to identify the degree of relationship.
3.5 Non-Linear Models:
3.5.1 The ARCH Model
Engle (1982) discuss a model known as Autoregressive Conditional Heteroskedasticity
(ARCH) for modeling the variation in the stock prices. This model captures the tendency
for volatility clustering in the given financial time series. The major reason at the back of
44
ARCH model is to grasp time varying variance, and to provide benefits from immediate
past information. Simple first order auto regression can assist to understand the ARCH
model in a dynamic way.
𝑟𝑡 = 𝛼𝑟𝑡−1 + 휀𝑡 (10)
The conditional variance 𝜎2 value can be specified as a function of the historic residuals
of the conditional mean. In simple words if the historical information absorbed in
variance equation then there is a chance that it may improve the prediction. Engle (1982)
proposes the following model,
𝜎𝑡2 = 𝛼0 + 𝛼1𝑟𝑡−1
2 + 휀𝑡 (11)
Where 휀𝑡 ~ 𝑖𝑖𝑑(0,1), Engle (1982) proposes another possible method to parameterize 𝜎𝑡2
in order to grasp the heteroskedastic behavior as,
𝜎𝑡2 = 𝛼0 + ∑ 𝛼𝑖
𝑞𝑖=1 휀𝑡−1
2 , (12)
where 𝛼0 > 0 and 𝛼0 ≥ 0.
3.5.2 The GARCH Model
Bollerslev (1986) introduce GARCH model. The generalized form of ARCH model is
called GARCH model as expressed by (Engle, 1982). GARCH model presents a superior
fit because it considers in a better way with non-negativity constraints. In an econometric
model it requires some numbers of lags to be included. GARCH model is different from
ARCH model because it allows the conditional variance to be modeled by lagged values
along with the historic shocks. Generally GARCH (p, q) model is expressed as following
equation:
𝜎𝑡2 = 𝜓0 + ∑ 𝜓𝑖
𝑞𝑖=1 휀𝑡−𝑖
2 + ∑ 𝜙𝑗𝑝𝑗=1 𝜎𝑡−𝑗
2 (13)
Whereas (p,q) represent the order of the GARCH term as well as ARCH term
respectively. The specified variance term 𝜎𝑡2 is known as conditional variance at time “t”
and 𝜓0 specifies constant element, whereas 𝜓𝑖and 𝜙𝑗 are the parameters and 𝜺𝒕−𝒊𝟐 is the
45
indicator of preceding squared shocks and 𝜎𝑡−𝑗2 indicates previous variances. Brooks
(2008) point out that in most cases GARCH (1, 1), is enough to grab the volatility
clustering. Moreover it is pointed out that higher order is very exceptional used in the
finance studies. GARCH model successfully grasp diverse number of features of
financial time series like volatility clustering and thick tailed returns. The GARCH model
is said to be stationary when the following condition (𝛼 + 𝛽 < 1) is fulfilled. Even if
(α + β = 1) still the process is to be said stationary because the variance is infinite. The
εt is considered to be normally distributed approximately if it is along with an average
value of zero and the time-varying variance is expressed as (εt ~ N (o,𝜎𝑡2)).
3.5.3 Asymmetric GARCH Models
No doubt GARCH models performance is excellent in explaining the volatility, but the
squared residuals behavior is still problematic and an unaddressed issue. So the models
anticipate that the positive and negative shocks of same magnitude have the same effects
on variance. It is seen that due to squaring the prior values of shocks and by performing
this computation the sign of the shocks got lost. Therefore, Asymmetric non-linear
models are introduced to resolve this problem
3.5.4 Threshold GARCH (TGARCH)
To meet the objective of impact of information asymmetries of returns and volatility
TGARCH model is used. Zakoian (1994) proposes the Threshold GARCH (TGARCH)
model which is same like to the GJR-GARCH model. The only differentiating point that
in the model of TGARCH, that the conditional standard deviation is modeled as a
replacement for the conditional variance. So the TGARCH (1,1) model can be describes
in this manner.
𝜎𝑡 = 𝜙 + 𝛹|휀𝑡−1| + 𝛾휀𝑡−1𝐷𝑡−1 + 𝛽𝜎𝑡−1 (14)
Whereas Dt−1 is equal to one if εt−1 < 0 and zero if εt−1 ≥0
46
3.5.5 The EGARCH Model
Nelson (1991) presented the Exponential GARCH model famously known as EGARCH
model. This model is relatively more purposeful and useful than the GARCH model
because it allows different impact on the volatility regarding to good news and bad news
phenomena. Moreover it also allows having higher impact on volatility regarding to big
news. Specifically EGRACH model works in two steps. In first step it takes into
consideration the mean and in second step it takes into consideration the variance
component. EGARCH (p, q) model can be expressed in the following manner:
𝑙𝑜𝑔(𝜎𝑡2) = 𝜙 + ∑ 𝜙𝑗
𝑝𝑖=1 |
𝜀𝑡−𝑗
𝜎𝑡−𝑗| + ∑ 𝜆𝑖
𝑞𝑖=1 𝑙𝑜𝑔(𝜎𝑡−𝑖
2 ) + ∑ 𝜔𝑘𝑘𝑖=𝑖
𝜀𝑡−𝑘
𝜎𝑡−𝑘 , (15)
Whereas 𝜙, 𝜆, and 𝜔 shows parameters for conditional variance estimation and 𝜆𝑖
indicates the effect of the prior period measures on the conditional variance. Positive
value of 𝜆𝑖 indicates that a positive change in the equity price is associated with more
positive change and vise versa. The Coefficient 𝜙𝑗 measures the impact of last period
information and expresses the preceding standardized residuals impact on existing
volatility. The term 𝜔𝑘 shows asymmetric effect in the variance and the negativity in 𝜔𝑘
indicate that bad news has higher impact on stock return volatility rather than good news.
EGARCH model show logarithmic time varying conditional variance in which concerned
parameters are allowed to be negative. Therefore this element indicates that the EGARCH
model does not need any non-negativity limits in the stated parameters. This feature
makes the model more attractive than general GARCH model. If (λ < 1), then it indicates
the stationary constraint for an EGARCH (1, 1) model. In the state of symmetry, where
the quantity of positive and negative shocks has equal impacting on the variance, then (ω
= 0). On the other way if ω < 0 the power of a negative or positive shock rationales the
variance to increase or decrease, and if ω > 0 positive and negative shocks rationale the
47
variance to increase or decrease respectively. The natural logarithm of conditional
variance is modeled in the EGARCH (1,1), and can be calculated as,
ln(𝜎𝑡2) = 𝑎 + 𝜔
𝜀𝑡−1
𝜎𝑡−1+ λ |
𝜀𝑡−1
𝜎𝑡−1 − √
2
𝜋 | + 𝛽ln (𝜎𝑡−1
2 ) (16)
Whereas the parameters a, ω, λ and β are constant parameters,
3.5.6 GJR-GARCH Model
Glosten, Jagnathan and Robinston (1993) propose the GJR-GARCH, which one is
generally seen as the simplest model for modeling the asymmetries in the conditional
variance. This model has some resemblance with the TGARCH model and contains the
standard GARCH model, However an additional term that can handle and control the
asymmetry in the variance as follows,
𝜎𝑡2 = 𝜙 + 𝛹휀𝑡−1
2 + 𝜔𝐷⁻𝑡−1 휀𝑡−12 + 𝛽𝜎𝑡−1
2 (17)
Where D-t−1 indicates a dummy variable.
D-t−1 is equal to one if εt−1 < 0 and zero if εt−1 ≥0
3.5.7 Volatility Switching Model
Conditions indicate that the parameters included should be non-negative. Moreover, that
the sum of α and β should be less than (α + β < 1). Fornaria and Mele (1997) developed
Volatility Switching (VS) model and it may take benefit of the mean-reversion behavior
in the conditional variance, and can be computed in this manner,
𝜎𝑡2 = 𝜙 + 𝛼𝛹휀𝑡−1
2 + 𝜆𝛾𝐷𝑡−1 𝑣𝑡−1 + 𝛽1𝜎𝑡−12 (18)
Here the Dt−1 parameter has a value of one if εt−1 > 0 and zero if εt−1 = 0, and with a value
of minus one then εt−1 < 0. Determination and asymmetry in the variance is measured
through the parameter εt2/νt−1 = 𝜎𝑡
2 . Poon and Granger (2003) indicated that regime
switching models have fascinated interest recently from the financial markets and reacted
divergently to large and small shocks. The traditional (ARCH) models cannot handle
such facts.
48
3.5.8 Quadratic ARCH (QARCH)
Sentana (1995) discuss Quadratic ARCH (QARCH) model for the volatility. Commonly
the Q-GARCH(1,1) model can be defined as,
𝜎𝑡2 = 𝜙 + 𝜓휀𝑡−1
2 + 𝜆휀𝑡−1 + 𝛽1𝜎𝑡−12 (19)
The quadratic parameter in this model makes it possible to apply second-order Taylor
approximation to analyze the anonymous conditional variance function of the said model.
The parameters ϕ, ψ, λ and β are constants, and to hold the condition of covariance
stationarity to should be there for the model, so ( ψ + β < 1). The individual parameters
ψ and β should be greater or equal to 0, and λ < 4, ϕ ψ is the positivity requirement to
hold the in the variance.
3.6 Econometric Models
3.6.1 Volatility and Return:
To develop a non-linear volatility based asset pricing model, the below econometric
methodology is proposed for modeling the volatility from various perspective as narrated
below in the given methodology to meet the core objective of the study.
This study explores asset pricing on the basis of volatility. The process is explained as
following. GARCH-Mean model permits the conditional mean to depend on its own
conditional variance. If the risk is captured by the volatility or by the conditional
variance then the conditional variance may enter the conditional mean of X t. To
examine the objective of impact of macro-economic variables on stock return volatility.
The following methodology is used.
3.6.1.1 Model 1: Return, Volatility and Macroeconomic Factors
The macroeconomics variable includes CPI, Term Structure of interest rate, industrial
production and oil prices. Data for Macroeconomic variable is on monthly basis for the
period Jan 2000 to Dec 2010 from the Econstats web resources and other available
49
internet resources. The role of macroeconomic variable in determining volatility is
modeled as under.
𝑋𝑡 = 𝑎0 + 𝛽𝑋𝑡−1 + 𝛾𝜎𝑡2 + 𝜋1 (𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛)𝑡 + 𝜋2 (𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒 𝑐ℎ𝑎𝑛𝑔𝑒)𝑡
+ 𝜋3 (𝐺𝑟𝑜𝑤𝑡ℎ 𝑟𝑎𝑡𝑒 𝑖𝑛 𝑟𝑒𝑎𝑙 𝑠𝑒𝑐𝑡𝑜𝑟)𝑡 + 𝜋4 (𝑂𝑖𝑙 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒)𝑡
+ 휀𝑡 (20)
Whereas Xt is return for t periods and α0 is constant and β,γ and π are slopes and
coefficient. Whereas Xt , dependent variable σ2t is variance and 휀𝑡 is error term.
ℎ𝑡 = 𝛾0 + ∑ 𝛿𝑖
𝑝
𝑖=1
ℎ𝑡−𝑖 + ∑ 𝛾𝑗
𝑞
𝑗=1
𝜇𝑡−𝑗2 + ∑ 𝜇𝑘𝑀𝑘
𝑚
𝑘=1
(21)
Whereas ℎ𝑡 is variance and Mk is a set of macroeconomic explanatory variables that
might help to explain the variance.
Inflation Rate
The consumer price index (CPI) is used as a proxy for inflation because CPI is used as a
broad-based parameter for computing the average change in prices of goods and services
throughout a specific period.
𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 𝑅𝑎𝑡𝑒 = 𝐼𝑟𝑡 = 𝑙𝑛(
𝐶𝑃𝐼𝑡𝐶𝑃𝐼𝑡−1
⁄ ) (22)
Irt= Inflation Rate
CPIt = Closing Value of CPI at time t
CPIt-1 = Closing Value CPI at 1 time before
Interest Rate Change
Treasury bill rates are used as a proxy for the interest rate. Change is computed by log
difference to T- bill rates.
𝐿𝑜𝑔 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑜𝑓 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑅𝑎𝑡𝑒 = 𝐼𝑁𝑟𝑡 = 𝑙𝑛(
𝑇𝐵𝑡𝑇𝐵𝑡−1
⁄ ) (23)
INrt= Interest Rate Change
TBt = Closing T-Bill Price at time t
50
TBt-1 = Closing T-Bill Price at 1 time before
Industrial production Index
Industrial production index is used as a proxy to measure the growth rate in the real
sector. Here the Industrial production is an indicator of overall economic activity in the
economy and can affects on stock return volatility through its impact on expected future
cash flows.
𝐿𝑜𝑔 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑛 𝐼𝑛𝑑𝑢𝑠𝑡𝑟𝑖𝑎𝑙 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝐼𝑛𝑑𝑒𝑥 = 𝐺𝑟𝑜𝑤𝑡h rate in real sector
= 𝐺𝑅𝑟𝑡 = 𝑙𝑛(
𝐼𝑃𝐼𝑡𝐼𝑃𝐼𝑡−1
⁄ ) (24)
GRrt= Growth Rate in Real Sector = Change in Industrial production Index
IPIt = Closing IPI value at time t
IPIt-1 = Closing IPI Price at 1 time before
Oil Prices
Brent oil prices are used as proxy for oil prices. Rise in oil prices causes to an increase in
the cost of production and hence reduce the earnings of the corporate sector due to
decrease in profit margins or reduction in demand of product. Therefore oil prices may
effect on stock returns volatility.
𝐿𝑜𝑔 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑛 𝑂𝑖𝑙 𝑃𝑟𝑖𝑐𝑒𝑠
= 𝐿𝑛𝑂𝑃𝑟𝑡 = 𝑙𝑛(
𝑂𝑃𝑡𝑂𝑃𝑡−1
⁄ ) (25)
LnOPr= Log difference in Oil Prices
OPt = Closing Oil Price at time t
OPt-1 = Closing Oil Price at 1 time before
3.6.1.2 Model 2(a) Returns, Volatility and Market Conditions Asymmetries
To model the impact of information asymmetries on returns and volatility, the following
methodologies is used. Further this study explains the dynamics of asset pricing and
51
volatility in the presence of asymmetric market conditions. The econometric model for
said phenomena is provided below.
𝑋𝑡 = 𝑎0 + 𝛽𝑋𝑡−1 + 𝛾𝜎𝑡2 + 𝜃1 (𝐷)𝑡 + 휀𝑡 (26)
Whereas Xt is return for t periods and α0 is constant and β, γ and θ1 are slopes and
coefficient. Whereas Xt , dependent variable σ2t is variance and 휀𝑡 is error term.
ℎ𝑡 = 𝛾0 + ∑ 𝛿𝑖
𝑝
𝑖=1
ℎ𝑡−𝑖 + ∑ 𝛾𝑗
𝑞
𝑗=1
𝜇𝑡−𝑗2 + ∑ 𝜇𝑘𝐷𝑘
𝑚
𝑘=1
(27)
Dummy 1 Bullish
Dummy 0 Other wise
3.6.1.3 Model 2(b) Returns, Volatility and Market Asymmetries Good
News and Bad News Effect
The specification of the conditional variance equation for TARCH is given by
ℎ𝑡 = 𝛾0 + 𝛾𝜇𝑡−12 + 𝜃𝜇𝑡−1
2 𝐷𝑡−1 + 𝛿ℎ𝑡−1 (28)
Where Dt take the value of 1 for 휀𝑡<0 and 0 otherwise. So it is very clear that good news
and bad news have a diverse impact. Good news has an impact γ, while bad news has an
impact of γ+θ, if θ>0 it indicates that there is asymmetry. On the other hand if θ=0 the
news impact is symmetric.
Dummy 1 Good News
Dummy 0 Other Wise
3.6.1.4 Model 3 Returns, Volatility, and Value at Risk
This study explains the dynamics of asset pricing and volatility in the presence of value at
risk. The econometric model for said phenomena is provided below.
𝑋𝑡 = 𝑎0 + 𝛽𝑋𝑡−1 + 𝛾 (𝑉𝑎𝑙𝑢𝑒 𝑎𝑡 𝑟𝑖𝑠𝑘)𝑡 + 𝜇𝑡 (29)
Whereas Xt is return for t periods and α0 is constant and β and γ are slopes and
coefficient. Whereas Xt , dependent variable and µt is error term.
52
ℎ𝑡 = 𝛾0 + ∑ 𝛿𝑖
𝑝
𝑖=1
ℎ𝑡−𝑖 + ∑ 𝛾𝑗
𝑞
𝑗=1
𝜇𝑡−𝑗2 (30)
Value at Risk (VaR) is a widely applied risk measure for the risk of loss against specific
portfolio of financial assets, probability and time horizon. Value at risk (VaR) measures
the worst expected loss under normal market conditions for a specific time interval at a
given confidence level. Value at risk answer to the question that how much can I lose
with x% probability over a pre-set horizon Jorion (1996).
3.6.1.5 Model 4: Returns, Volatility, Semi-variance
Above stated model are related to total risk as a measure of risk. The total risk is captured
by using S.D which demonstrates above means and below mean value. Investor
appreciates above mean market risk but concerned about downside risk deviation. So the
downside risk is captured by using the following relationship.
𝑋𝑡 = 𝑎0 + 𝛽𝑋𝑡−1 + 𝛾 (𝑆𝑒𝑚𝑖 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒)𝑡 + 𝜇𝑡 (31)
Whereas Xt is return for t periods and α0 is constant and β, and γ are slopes and
coefficient. Whereas Xt, dependent variable ht is variance and µt is error term.
ℎ𝑡 = 𝛾0 + ∑ 𝛿𝑖
𝑝
𝑖=1
ℎ𝑡−𝑖 + ∑ 𝛾𝑗
𝑞
𝑗=1
𝜇𝑡−𝑗2 (32)
Semivarance is a measure of the dispersion of all observations that fall below the average
or target value of a particular data set. The method for semi-variance computations is as
follows:
𝑠𝑒𝑚𝑖𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 =1
𝑛∑ (𝐴𝑣𝑒𝑟𝑎𝑔𝑒 − 𝑟𝑡)2
𝑛
𝑟𝑡<𝑎𝑣𝑒𝑟𝑎𝑔𝑒
(33)
Whereas,
n = Total number of observations below the mean, rt is observed value and average is the
mean or target value of the data set. It is a useful tool in portfolio or assets analysis, semi-
53
variance provides a measure for downside risk. Whereas standard deviation and variance
are the measures of volatility but semi-variance only looks at the negative fluctuations of
an asset. For risk averse investors, the optimal portfolio allocations can be achieved by
minimizing the semi-variance that would limit the likelihood of a large loss.
54
CHAPTER 4
RESULTS AND DISCUSSION
55
4. Results and Discussion
Models expressed in Chapter No. 3 are adopted in this empirical study to explain the
dynamics of returns and volatility. Six emerging market including China, India,
Indonesia, Bangladesh, Malaysia and Pakistan are taken for study as classified in
Chapter No 3. The data is comprised of daily prices for the period 4 Jan 2000 to 30 Dec
2010. In first instance the descriptive statistics explains the behavior of the data as
expressed below in Table 1.
Table 1: Descriptive Statistics for Daily Market Returns;
Period Jan 2000 to Dec 2010
SS BSE JCI DSE KLSE KSE
Mean 0.000274 0.000529 0.000694 0.001056 0.000248 0.000876
Median 0.000154 0.001399 0.001283 7.30E-06 0.000439 0.001332
Maximum 0.090343 0.1599 0.120873 0.282336 0.198605 0.110642
Minimum -0.11304 -0.13794 -0.14726 -0.26907 -0.19246 -0.10097
Std. Dev. 0.017875 0.018715 0.016672 0.015049 0.011773 0.016936
Skewness -0.19992 -0.30136 -0.76478 1.80489 -0.64134 -0.0668
Kurtosis 7.259541 9.662934 12.56576 119.6496 73.08964 7.39603
Jarque-Bera 1810.527 4427.309 9282.658 1347260 486096.5 1913.338
Probability 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Results reported in Table 1 indicate the descriptive statistics for daily logarithmic
returns regarding to the SS (China). BSE index (India), JCI index (Indonesia), DSE
index (Bangladesh), KLSE (Malaysia) and KSE index (Pakistan). DSE and KSE are
generating higher average return but BSE and SS remain is more risky. KSE, BSE,
JCI, KLSE, SS are negatively skewed but DSE is positively skewed. Jarque-Bera
normality test also ensures departure from normality for all market returns.
56
Figure 1: Daily Mean Returns of China, India, Indonesia, Bangladesh,
Malaysia and Pakistan from January 2000 to December 2010
The above returns series are evaluated for heteroscedasticity. However Jarque-Bera
test rejects the null hypothesis of normality and indicates that all the equity market
return series show non-normality. This element exhibits that the series have
tendency of volatility clustering.
Table 2 indicates the number of observations regarding to the negative and positive
returns and summary statistics of returns following each other.
-.3
-.2
-.1
.0
.1
.2
.3
250 500 750 1000 1250 1500 1750 2000 2250
SS BSE JCI
DSE KLSE KSE
57
Table 2: Positive and Negative Returns Summary
SS BSE JCI DSE KLSE KSE
Total observations 2376 2376 2376 2376 2376 2376
Negative Observations 1170 1080 1076 1099 1115 1074
Positive observations 1206 1296 1300 1277 1261 1302
Two Negative Observations 123 142 142 116 125 131
Two Positive Observations 161 134 159 120 130 160
Three Negative Observations 69 74 74 69 78 64
Three Positive Observations 73 80 74 64 54 73
Four Negative Observations 82 63 63 75 70 62
Four Positive Observations 77 105 103 110 103 108
The above table indicates that the numbers of positive returns are more than
negative returns for all the equity markets; It concludes that that positive return are
more often backed up by other positive returns, rather than in the case for negative
returns. It can be predicted that positive returns are more persistent and negative
returns tend to be revert towards positive returns faster. It summarizes that returns
are asymmetric, and positive returns are more continual when negative returns
reverts in fast manner. For these markets, the difference between the number of
positive and negative observations is clear. The smallest difference between
positive and negative returns can be seen for the Chinese equity market. It indicates
most significant asymmetries in mean-reversion are to be observed other than the
Chinese equity market where four negative observations are greater than four
positive consecutive returns. It might be inferred that BSE, KSE, JCI are more
effective than KLSE, SS and DSE equity markets because the pattern indicates for
KLSE and DSE that the number of three consecutive negative observations are
more than that of three consecutive positive returns. Overall all equity markets have
58
mean reverting behavior. Figure 2 indicates the stock returns of KLSE, BSE, DSE
KSE, SS and JCI individually.
F igu re 2 : S tock Returns o f Equ i ty Marke t s
59
This study requires getting a first instance regarding to the use of linear versus
nonlinear models and how these perform, firstly sign and size bias test is
conducted.
Table 3 below indicates the results of estimations for sign-bias test, a negative size-
bias test, and a positive size-bias test.
Below results of the sign-bias test for the six markets provides significant results
for NSB and PSB as well. Results indicates that asymmetry exist and can be
observed properly in the return series.
Table 3: Sign and Size Bias Tests
Test/Index SS BSE JCI DSE KLSE KSE
SB 0.00001
-0.00009
-0.0000715 0.00009 -0.00044
-0.00002
p-value 0.89890
0.10650 0.1684 0.45180
<0.0001 0.58000
NSB -0.00910
-0.02237
-0.019481 -0.00203
-0.06625
-0.01971
p-value <0.0001
<0.0001 <0.0001 0.72980
<0.0001 <0.0001
PSB 0.00708
0.00803
0.00487 0.01539
0.001815
0.00864
p-value <0.0001
<0.00030
<0.04190
<0.00380
0.6061
<0.0001
5% is significance level
Table 3 indicates the results of estimations for sign-bias test (SB), negative size-
bias test (NSB) and positive size-bias test (PSB) for SS, BSE, JCI, DSE, KLSE, and
KSE. The results are significant overall for negative sign bias (NSB) and for
positive sign bias (PSB) as well except KLSE. This initial element indicates that
nonlinear models gain some support. Results indicate that asymmetry exist and can
be observed in the returns series. Coefficients and p-values for sign-bias test,
negative size-bias test and positive size bias test for the equity returns are reported
at P<0.05. The estimation of the negative size bias test indicates that negative
asymmetry can be seen in the returns series. The result of the positive size-bias test
on the other hand, generating significant estimates for the KSE, BSE, DSE SS and
60
JCI and indicates towards positive asymmetry regarding to these equity markets.
However, for the KLSE market, the hypothesis of positive asymmetries is rejected.
In the same way the results of the negative size-bias test, generates significant
estimates for the KSE, BSE, KLSE SS and JCI and indicates towards negative
asymmetry regarding to these equity markets.
However, for the DSE, the hypothesis of negative asymmetries is rejected.
According to the sign and size bias test above, non linear patterns are expected and
being observed because the return series indicates asymmetric patterns. Lagrange
Multiple test for ARCH effects are conducted to further investigate this matter.
Table 4: Lagrange-Multiplier Test of ARCH Effects for GARCH model
Index SS BSE JCI DSE KLSE KSE
F-STAT 0.492191 0.90406 0.154165 0.029158 0.144049 0.174527
P-value 0.6877 0.4383 0.927 0.9933 0.9335 0.9137
Observed R2 1.478146 2.713655 0.463187 0.08762 0.432798 0.524352
P-value 0.6873 0.4379 0.9269 0.9933 0.9334 0.9135
ARCH (lags)-P-
value
1 0.4719 0.3591 0.9037 0.8897 0.5242 0.7495
2 0.3732 0.7049 0.5033 0.8536 0.9339 0.6399
3 0.6822 0.183 0.9939 0.8522 0.8867 0.6555
Table 4 reports the p-values estimated with Lagrange Multiplier (LM) test for GARCH
model. For each return series the lag length for this model 1, 2, 3 is used. The Lagrange
multiplier test is used to test the ARCH effects. The test examines whether
heteroscedasticity or homoscedasticity can be observed in returns series. It is inferred
from above results that no non linear and asymmetric ARCH effect can be directly seen
from the estimation of the L-M test for GARCH model.
61
Table 5: Lagrange-Multiplier Test of ARCH Effects FOR GJR-GARCH
Index SS BSE JCI DSE KLSE KSE
F-STAT 0.347386 0.309062 0.259157 0.020492 0.075447 0.183947
P-value 0.7911 0.8189 0.8548 0.996 0.9732 0.9074
Observed Rs 1.04346 0.928391 0.778529 0.061578 0.226703 0.552645
P-value 0.7907 0.8186 0.8546 0.996 0.9732 0.9072
ARCH (lags)-P-value
1 0.6134 0.5767 0.8949 0.9901 0.661 0.9138
2 0.4102 0.6833 0.4402 0.8838 0.957 0.5725
3 0.7393 0.5064 0.6819 0.8415 0.8598 0.6395
Table 5 reports the p-values estimated with Lagrange Multiplier (LM) test for GJR-
GARCH model. For each return series the lag length for this model 1, 2, 3 is used. The
Lagrange multiplier test is used to test the ARCH effects. The test examines whether
heteroscedasticity or homoscedasticity can be observed in returns series. It is inferred
from above results that no non linear and asymmetric ARCH effect can be directly seen
from the estimation of the L-M test for GJR-GARCH model.
Table 6: Lagrange-Multiplier Test of ARCH Effects FOR EGARCH
Index SS BSE JCI DSE KLSE KSE
F-STAT 1.001568 0.350866 0.02673 0.015085 0.044691 0.147896
P-value 0.3911 0.7885 0.9941 0.9975 0.9875 0.9311
Observed Rs 3.005967 1.053908 0.080322 0.04533 0.134291 0.444355
P-value 0.3907 0.7882 0.9941 0.9975 0.9874 0.9309
ARCH (lags)-P-value
1 0.1529 0.8373 0.8025 0.9272 0.7308 0.5323
2 0.3487 0.9939 0.904 0.9295 0.9953 0.8273
3 0.964 0.3149 0.9548 0.8643 0.9004 0.9275
62
Table 6 reports the p-values estimated with Lagrange Multiplier (LM) test for EGARCH
model. For each return series the lag length for this model 1, 2, 3 is used. The Lagrange
multiplier test is used to test the ARCH effects. The test examines whether
heteroscedasticity or homoscedasticity can be observed in returns series. It is inferred
from above results that no non linear and asymmetric ARCH effect can be directly seen
from the estimation of the L-M test for EGARCH model.
Table 7: Lagrange-Multiplier Test of ARCH Effects FOR VS-GARCH
Index SS BSE JCI DSE KLSE KSE
F-STAT 1.129183 0.240991 0.156607 0.025284 1.251892 0.429145
P-value 0.3359 0.8678 0.9255 0.9946 0.2893 0.7321
Observed Rs 3.388425 0.723974 0.470523 0.075976 3.756063 1.288909
P-value 0.3355 0.8676 0.9253 0.9946 0.289 0.7318
ARCH (lags)-P-value
1 0.9306 0.7238 0.9093 0.9462 0.3392 0.5829
2 0.0911 0.6313 0.499 0.8496 0.6958 0.4701
3 0.4665 0.5476 0.9982 0.8504 0.1036 0.5022
Table 7 reports the p-values estimated with Lagrange Multiplier (LM) test for VS-
GARCH model. For each return series the lag length for this model 1, 2, 3 is used. The
Lagrange multiplier test is used to test the ARCH effects. The test examines whether
heteroscedasticity or homoscedasticity can be observed in returns series. It is inferred
from above results that no non linear and asymmetric ARCH effect can be directly seen
from the estimation of the L-M test for VS-GARCH model.
63
Table 8: Lagrange-Multiplier Test of ARCH Effects FOR QARCH
Index SS BSE JCI DSE KLSE KSE
F-STAT 0.378177 0.226075 0.077633 0.046179 0.158372 0.294874
P-value 0.7688 0.8783 0.9721 0.9868 0.9243 0.8291
Observed Rs 1.135905 0.679177 0.23327 0.138763 0.475823 0.885786
P-value 0.7684 0.8781 0.972 0.9868 0.9242 0.8289
ARCH(lags)-P-value
1 0.5774 0.6842 0.9961 0.8225 0.4955 0.7692
2 0.4165 0.6367 0.6554 0.9688 0.9271 0.5206
3 0.6817 0.5939 0.8545 0.7689 0.9878 0.5386
Table 8 reports the p-values estimated with Lagrange Multiplier (LM) test for QARCH
model. For each return series the lag length for this model 1, 2, 3 is used. The Lagrange
multiplier test is used to test the ARCH effects. The test examines whether
heteroscedasticity or homoscedasticity can be observed in returns series. It is inferred
from above results that no non linear and asymmetric ARCH effect can be directly seen
from the estimation of the L-M test for QARCH model.
The LM-test is performed for all six markets, and for different model specifications. It is
inferred from above results that no nonlinear and asymmetric ARCH effects can be
directly seen from the estimation of the L-M Test as reported from Table 4 to Table 8.
This initial inspiration indicates that nonlinear models may not perform better than linear
ones.
From the above statistical results, it is quite difficult to make concluding remarks about
what type of model for the volatility modeling should be used; either linear model provide
close enough predictions, or nonlinear models produce better estimates? To further
analyze the performance of various volatility models, the estimation results of the models
are presented in Table 9 to 13 regarding to the estimates for GARCH, GJR-GARCH,
EGARCH, VS-GARCH and QGARCH.
64
Table 9: Estimates of GARCH (1,1) Model
Statistics Parameters SS BSE JCI DSE KLSE KSE
Mean Equation
α 0.000412 0.001265 0.001277 0.001482 0.000243 0.001337
p-value [0.1466] <0.0001 <0.0001 <0.0001 [0.3234] <0.0001
β 0.032674 0.084549 0.107033 0.101329 0.166872 0.07255
p-value [0.1153] [0.0002] <0.0001 <0.0001 <0.0001 [0.0009]
Variance
Equation
ψ0 0.00001 0.00001 0.00002 0.000000272 0.00004 0.00002
p-value <0.0001 <0.0000 <0.0001 <0.0001 <0.0001 <0.0001
ψ1 0.06041 0.12469 0.13698 0.57618 0.18238 0.16836
p-value <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
φ1 0.92403 0.86410 0.81281 0.68657 0.53976 0.77399
p-value <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
Diagnostic
Test
AIC- statistics -5.39048 -5.42986 -5.55107 -5.82976 -6.28377 -5.39048
SIC- statistics -5.37833 -5.4177 -5.53892 -5.81761 -6.27161 -5.56946
log likelihood 6406.196 6452.953 6596.896 6927.839 7466.972 6633.161
Table 9 reports results for GARCH model that the coefficient of the conditional mean
equation is significant at p<0.0001 with the exception of SS. ARCH term is significant at
95% confidence interval indicating that past price behavior influence current volatility in
all markets. The GARCH term is also significant at 95% confidence interval which
reports the presence of persistence in volatility. Moreover the coefficient for lagged stock
returns show significance at p<0.05, it indicates that the lagged volatility impact on
current volatility significantly. The coefficient of ψ1 and φ1 are statistically significant at
p<0.0001 representing that the hypothesis regarding to the constant variance model is
rejected. The prominent AIC, Schwarz and the Log Likelihood methods is used for
selecting model.
65
Table 10: Estimates of EGARCH (1,1) Model
Statistics Parameters SS BSE JCI DSE KLSE KSE
Mean Equation α 0.000571 0.000691 0.000718 0.000686 0.0000938 0.001163
p-value [0.027] [0.0104] [0.0141] <0.0001 [0.7117] <0.0001
β 0.032194 0.10651 0.123734 0.0265 0.159429 0.073503
p-value [0.0864] <0.0001 <0.0001 [0.1854] <0.0001 [0.0006]
Variance
Equation
φ -0.27835 -0.50987 -0.79985 -1.20756 -1.3693 -0.99154
p-value <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
φ1 0.137566 0.246907 0.215094 0.506732 0.109477 0.285137
p-value <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
ω1 -0.0169 -0.09939 -0.1176 -0.22111 -0.12507 -0.08131
p-value [0.0033] <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
λ1 0.978043 0.961016 0.923807 0.890609 0.857828 0.906776
p-value <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
Diagnostic
Test
AIC- statistics -5.39321 -5.44409 -5.57206 -5.89131 -6.29023 -5.59198
SIC- statistics -5.37863 -5.42951 -5.55747 -5.87673 -6.27564 -5.5774
log likelihood 6410.436 6470.861 6622.815 7001.931 7475.642 6646.477
Table 10 reports the parameter estimates of the EGARCH (1,1). EGARCH model is used
to study the asymmetric behavior of the prices. The results indicate that there exists
persistence of volatility as coefficient λ1 is significant. The significant value of φ1
indicates that asymmetric behavior exists in the markets. The response of volatility is
adjusting for good and bad news. Bad news creates more volatility in compare to good
news. Similarly size effect is visible from significant value of φ1. It means big change in
price creates more volatility in compare to small change in price. The appropriate model
is selected on the basis of diagnostic test i.e. the model with minimum AIC, SIC and Log
Likelihood value.
66
Table 11: Estimates of GJR-GARCH (1,1) Model
Table 11 reports the parameter estimates of the GJR-GARCH (1,1).
GJR-GARCH Model is used to study the asymmetric behavior of the market. Ψ is
significant and positive which indicates that past price behavior influences current price
volatility. The significant value of β indicates that the volatility once created persistence
and contributes in the volatility of next period. The ω is found significant and persistent
which shows that asymmetric behavior exist in market. It means bad news has more
affect than good news. Market response is higher for bad news in compare to good news.
Statistics Parameters SS BSE JCI DSE KLSE KSE
Mean
Equation
α 0.000305 0.000889 0.000865 0.000966 0.0000705 0.001071
p-value [0.294] [0.0016] [0.0037] <0.0001 [0.7717] [0.0003]
β 0.036869 0.096046 0.128802 -0.00476 0.155966 0.091184
p-value [0.078] <0.0001 <0.0001 [0.8346] <0.0001 <0.0001
Variance
Equation
φ 0.0000055 0.000008 0.00002 0.0000104 0.0000265 0.000019
p-value <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
ψ 0.044324 0.064633 0.038942 0.248242 0.010893 0.083506
p-value <0.0001 <0.0001 [0.0015] <0.0001 [0.1645] <0.0001
ω 0.029219 0.122388 0.170652 0.700513 0.234707 0.142353
p-value [0.0002] <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
β 0.923483 0.854324 0.799465 0.691922 0.657546 0.77912
p-value <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
Diagnostic
Test
AIC- statistics -5.3923 -5.44164 -5.5687 -5.86963 -6.30102 -5.5934
SIC- statistics -5.37771 -5.42706 -5.55411 -5.85505 -6.28644 -5.57881
log likelihood 6409.353 6467.951 6618.827 6976.186 7488.465 6648.157
67
Table 12: Estimates of VS-GARCH (1,1) Model
Statistics Parameters SS BSE JCI DSE KLSE KSE
Mean
Equation
α 0.00036 0.000742 0.000185 0.001341 0.000666 0.001273
p-value [0.1552] [0.3914] [0.8861] <0.0001 <0.0001 <0.0001
β 0.02661 0.094407 0.106763 0.103877 0.139257 0.075048
p-value [0.2023] <0.0001 <0.0001 <0.0001 <0.0001 [0.0003]
Variance
Equation
φ 0.000004 0.000013 0.000016 0.0000081 0.0000037 0.000012
p-value <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
α 0.081748 0.135531 0.139562 0.763083 0.161784 0.170738
p-value <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
β 0.908572 0.831729 0.809099 0.652861 0.813071 0.794783
p-value <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
λ 0.000002 0.000019 0.00000019 0.00000007 0.0000021 0.000001
p-value <0.0001 <0.0001 [0.3308] <0.0001 <0.0001 <0.0001
Diagnostic
Test
AIC-statistics -5.41556 -5.44161 -5.55017 -5.84487 -6.58894 -5.61231
SIC- statistics -5.40096 -5.42458 -5.53557 -5.83026 -6.57434 -5.59772
log likelihood 6428.857 6460.749 6588.502 6935.088 7820.477 6665.005
Table 12 reports the parameter estimates of the VS-GARCH (1,1). Variance equation
indicates that α is asymmetric and p-value is indicating that past previous behavior
influence current volatility. β is significant and reports persistence of volatility in the
market. It means volatility created in one period is continued in subsequent periods.
Coefficient of λ indicates asymmetric behavior in the market. Poon and Granger (2003)
indicated that regime switching models have fascinated interest recently from the
financial markets and reacted divergently to large and small shocks. The traditional
(ARCH) models cannot handle such facts.
68
Table 13: Estimates of QARCH (1,1) Model
Statistics Parameters SS BSE JCI DSE KLSE KSE
Mean
Equation
α 0.00047 0.000731 0.001289 0.000117 0.000276 0.001543
p-value [0.1118] [0.013] <0.0001 [0.3022] [0.1746] <0.0001
β 0.023449 0.091634 0.106138 0.145004 0.206231 0.071
p-value [0.275] <0.0001 <0.0001 <0.0001 <0.0001 [0.0007]
Variance
Equation
φ 0.0000059 0.000012 0.000015 0.0000013 0.0000602 0.000015
p-value <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
ψ 0.064579 0.131899 0.136304 0.597915 0.357793 0.156598
p-value <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
β1 0.917371 0.83431 0.813995 0.716089 0.170982 0.793356
p-value <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
λ -0.00012 -0.00198 0.0000002 0.000434 0.000378 -0.00055
p-value <0.0001 <0.0001 [0.3308] <0.0001 <0.0001 <0.0001
Diagnostic
Test
AIC- statistics -5.38764 -5.44724 -5.55017 -6.27862 -6.35666 -5.59183
SIC- statistics -5.37305 -5.43264 -5.53557 -6.26403 -6.34208 -5.57724
log likelihood 6395.746 6466.423 6588.502 7455.584 7551.36 6640.71
Table 13 reports the estimates of QARCH model the significant negative values of the
parameter λ for all markets except JCI. This indicates that nonlinearity exist with
reference to past price behavior. It can be observed that the parameter ψ is larger than
the parameter λ for all series. When this situation holds (ψ>λ), negative reactions
contributes a greater effect on the conditional variance, instead of positive shocks of the
same size. The parameters estimates of the GJR-GARCH reported in Table 10, indicate
that nonlinear model better than the linear ones. The results for the Volatility-Switching
GARCH model shows similar results. The co-efficient parameter ψ is positive for all
return series and is larger than the parameter λ. These findings indicate that small positive
shocks have a larger impact on the conditional volatility than small negative shocks;
however when the reactions are greater in size, then the effect on volatility is in opposite
direction. This element elaborates that large positive shocks contributes to a smaller
69
increase in volatility rather than large shock is negative.
Conditional standard deviation and conditional volatility graphs are shown in Figure 3 to
Figure 14 as depicted below indicates that the variance is not constant element and it is
time varying aspect. Variance can be modeled to predict the stock returns if suitable
parameters are incorporated in variance equation.
70
Conditional Standard Deviation Conditional Variance
Figure 3 : Conditional Standard Deviation of
BSE
Figure 4 : Conditional Variance of BSE
Figure 5: Conditional Standard Deviation of
DSE
Figure 6 : Conditional Variance of DSE
Figure 7 : Conditional Standard Deviation of
JCI
Figure 8 : Conditional Variance of JCI
.00
.01
.02
.03
.04
.05
.06
.07
00 02 04 06 08 10
Conditional standard deviation
.0000
.0005
.0010
.0015
.0020
.0025
.0030
.0035
.0040
00 02 04 06 08 10
Conditional variance
.00
.04
.08
.12
.16
.20
.24
00 02 04 06 08 10
Conditional standard deviation
.00
.01
.02
.03
.04
.05
00 02 04 06 08 10
Conditional variance
.00
.01
.02
.03
.04
.05
.06
.07
00 02 04 06 08 10
Conditional standard deviation
.000
.001
.002
.003
.004
00 02 04 06 08 10
Conditional variance
71
Conditional Standard Deviation Conditional Variance
Figure 9 : Conditional Standard Deviation of
KSE
Figure 10 : Conditional Variance of KSE
Figure 11 : Conditional Standard Deviation of
KLSE
Figure 12 : Conditional Variance of
KLSE
Figure 13 : Conditional Standard Deviation of
SS
Figure 14 : Conditional Variance of SS
.00
.01
.02
.03
.04
.05
00 02 04 06 08 10
Conditional standard deviation
.0000
.0004
.0008
.0012
.0016
.0020
.0024
00 02 04 06 08 10
Conditional variance
.00
.02
.04
.06
.08
.10
.12
00 02 04 06 08 10
Conditional standard deviation
.000
.002
.004
.006
.008
.010
.012
.014
00 02 04 06 08 10
Conditional variance
.005
.010
.015
.020
.025
.030
.035
.040
00 02 04 06 08 10
Conditional standard deviation
.0000
.0002
.0004
.0006
.0008
.0010
.0012
.0014
00 02 04 06 08 10
Conditional variance
72
Figure 3 to Figure 14 indicates the graphical snap of conditional standard deviations and
conditional variance. Here conditional S.D and Conditional variance different behavior
patterns regarding to the volatility shocks over different time periods. To check the
further performance of linear versus nonlinear models in describing stock return
volatility, the study used the out-of-sample forecasts with Random Walk model. The test
is performed on 2376 observation for forecasting comparison. The decision for the
forecast performance of the models is decided on the root mean squared error (RMSE)
approach: The table below describes the actual error computations for linear and
nonlinear models for the described forecasting period. The performance of the
forecasting is judged by using Root Mean Square Error approach.
Table 14: Forecasting Performance of Linear and Nonlinear Models of the
Volatility of Stock Returns
Model Root Mean Error Square
Linear Models SS BSE JCI DSE KLSE KSE
Random Walk 0.017853 0.018710 0.016662 0.015049 0.011763 0.016927
AR(1) 0.017853 0.018710 0.016662 0.015049 0.011763 0.016927
MA(1) 0.017853 0.018708 0.016661 0.015042 0.011763 0.016926
Exponential
Smoothing
0.018153 0.018830 0.016730 0.015111 0.011959 0.016969
Non-Linear Models
ARCH(1,1) 0.017854 0.018715 0.016399 0.015048 .0117740 0.016945
GARCH(1,1) 0.017854 0.018729 0.016678 0.015055 0.011771 0.016936
EGARCH (1,1) 0.017856 0.018711 0.016662 0.015047 0.011771 0.016931
GJR-GARCH(1,1) 0.017853 0.018715 0.016664 0.015043 0.011771 0.016929
VS-GARCH(1,1) 0.017860 0.018722 0.016685 0.015045 0.011781 0.016940
QARCH(1,1) 0.017861 0.018723 0.016670 0.015077 0.011773 0.016951
These models are ranked on the basis of minimum value of RMSE value for first, second
to onward. In linear models the MA (1) model out performs all the others in an out-of-
73
sample forecasting exercise for all stock returns on the basis of RMSE criterion. The AR
(1) and Random Walk Model appear as second best model and the exponential
smoothing model is ranked last.
Within nonlinear models, the GJR-GARCH model is ranked top for KSE, DSE and SS.
No doubt GJR-GARCH model is dominated over EGARCH (1,1) and GARCH Model
for this time period on the basis of RMSE criteria. It is interesting to note that the ARCH
model is ranked top for JCI and KLSE. GJR-GARCH(1,1) model is ranked second for
these markets. For BSE, EGARCH (1,1) model beating all other model in ranking in an
out-of-sample forecasting when the forecasting for whole period. After comparison of
linear and nonlinear models, it is found that that the GARCH, GJR-GARCH are
outperforming among all the models during the whole volatility periods. Even though
non-linear models dominate the linear models because the nonlinear models superiority
is due to the ability to capture nonlinear patterns that can be expected because the return
series shows asymmetric patterns as it is proved in the Table 9 to 13 estimates. It is
concluded that overall GARCH model outperforms among all the other models due to the
best ability to explain the conditional volatility. The below stated table indicates that the
degree of relationship among the volatilities of these equity markets.
Table 15: Correlation Matrix of Stock Returns
SS BSE JCI DSE KLSE KSE
SS 1
BSE 0.15 1
JCI 0.13 0.36* 1
DSE 0.02 0.05 0.02 1
KLSE 0.17 0.24* 0.33* 0.03 1
KSE 0.05 0.10 0.08 0.04 0.06 1 *Significant at 0.05 level
Stock return correlations indicate that how the returns are associated among these equity
markets. SS has highest degree of positive correlation with KLSE, BSE and JCI but not
74
quite significant. BSE has highest degree of correlation with JCI and KLSE, significant
at p<0.05. Whereas JCI has highest correlation with KLSE significant at p<0.05 and KSE
has positive correlation with BSE but not quite significant however it indicates that the
returns are moving these two economies in one direction.
Table 16: Conditional Volatility Correlation Matrix
σ2SS σ2BSE σ2JCI σ2DSE σ2KLSE σ2KSE
σ2SS 1
σ2BSE 0.41* 1
σ2JCI 0.32* 0.62* 1
σ2DSE -0.01 -0.01 -0.003 1
σ2KLSE 0.03 0.03 0.06 0.002 1
σ2KSE 0.08 0.09 0.004 0.09 0.004 1 *Significant at 0.05 level
Conditional volatility based upon GARCH Model, correlations indicate that how the
conditional volatility is associated among the equity markets. The volatility of SS is
positively correlated with the volatility of BSE and JCI at p<0.05 but negatively
correlated with DSE. However there is high degree of positive association among the
volatility of BSE and JCI significant at p<0.05 but negative correlation exist between
BSE and DSE. Even JCI and DSE has also negative correlations but not significant.
Where there is high degree of relationship among the conditional volatilities of equity
markets that indicates that shock behave in same direction in these equity markets except
the behavior of DSE with SS, BSE and JCI. It is therefore concluded that the movement
of volatility in EAGLEs markets have positive degree of relationship that determines that
how the positive and negative news or shocks behave in these markets, however the
volatility movements in NEST markets are minor correlated. It is clear evidence that the
returns association does not mean the volatility associations. However if volatilities are
75
associated it can be inferred that returns are associated. So volatility modeling has its own
unique attribution.
After a thorough analysis it is identified on the grounds that GARCH model can be tested
for risk return relationship along with macroeconomic models to have a superior look.
Investors who are risk averse and therefore they require an additional premium as
compensation in order to hold a risky asset. Such premium is undoubtedly a positive
function of the risk which means that the higher the risk then higher the premium should
be, if the risk is captured by the volatility or by the conditional variance, and then the
conditional variance may the conditional mean function as well. GARCH model is linked
here with the macroeconomic variables to capture the effect of risk not by the variance
series but also using the standard deviation of the series which have for the mean and
variance equations because the GARCH models allows us to add explanatory variables in
the specification of the conditional variance equation that can have ability to explain the
variance though macroeconomic explanatory variables.
76
4.1 Econometric Models for China
Table 17(a): Estimates of GARCH in Mean (1,1) Model 1: Return, Volatility and
Macroeconomic Model for SS, Impact of macroeconomic variables on
Return
Statistics Parameters SS
Mean Equation 𝑎𝑜 -0.18445
p-value <0.00001
β -0.05183
p-value <0.00001
γ 3.377293
p-value <0.00001
π1 0.074832
p-value <0.00001
π2 -0.48612
p-value 0.2586
π3 0.003622
p-value 0.1264
π4 -0.05254
p-value 0.022
Variance Equation 𝛄𝟎 -0.00029
p-value <0.00001
δ 0.162614
p-value <0.00001
γ1 0.640814
p-value <0.00001
Diagnostic
Test
AIC- Statistics 30.31179
SIC- Statistics 30.53237
Log- Likelihood -1960.27
Table 17(a) indicates that GARCH in mean model is extended with the macroeconomic
variables in the equation for SS. The conditional mean is significant at p < 0.10. So far
as macroeconomic variables are concerned, inflation is significantly related to return
indicating the presence of short term liquidity effect. Similarly, Oil prices change has
significant negative effect on return and increase in oil price decreases returns of stocks.
Model is selected on the basis of AIC, SIC, and Log Likelihood values.
77
Table 17(b): Estimates of GARCH in Mean (1,1) Model 1: Return, Volatility and
Macroeconomic Model for SS, Impact of macroeconomic variables on
Volatility
Table 17(b) indicates the impact of macroeconomic variables on volatility of market has
also been exercised. The results indicate that inflation is significant positively related to
volatility. In high periods of inflation, volatility is on high side, change in oil prices has
Statistics Parameters SS
Mean Equation γ0 0.002981
p-value 0.741
δ 0.167467
p-value 0.0643
γ1 -0.102361
p-value 0.9555
Variance Equation 𝑎0 0.045503
p-value 0.1474
β 0.040354
p-value 0.3943
γ 0.844603
p-value <0.00001
π1 0.000439
p-value 0.0035
π2 -0.02885
p-value 0.2038
π3 -0.0096
p-value 0.1469
π4 -0.0007
p-value 0.8221
Diagnostic Test AIC- Statistics -2.13429
SIC- Statistics -1.91371
Log -Likelihood 148.7286
78
also significant impact on volatility. In the period of rising prices volatility is lower it may
be due to anchoring.
Table 18(a): Estimates of GARCH in Mean (1,1) Model 2(a): Return, Volatility and
Market Conditions Asymmetries for SS. Impact of Market conditions
asymmetries on returns.
Statistics Parameters SS
Mean Equation 𝜶𝟎 -0.01031
p-value <.0.00001
β 0.014674
p-value 0.3441
γ 1.83814
p-value 0.4307
θ1 0.020294
p-value <0.00001
Variance Equation γ0 4.68E-06
p-value <0.00001
δ 0.079233
p-value <0.00001
γ1 0.899044
p-value <0.00001
Diagnostic
Test
AIC- statistics -5.97694
SIC- statistics -5.95991
log likelihood 7095.648
Table 18(a) reports the role of bullish and bearish market.
θ1 value is quite significant and positive which shows that returns are higher in bullish
period. Model is used to study the asymmetric behavior of the market.
θ1 is significant and positive which indicates that past price behavior influences current
price volatility. The significant value of δ indicates that the volatility once created
79
persistence and contributes in the volatility of next period. The γ1 found significant and
persistent which shows that asymmetric behavior exist in market.
Table 18 (b): Estimates of GARCH in Mean (1,1) Model 2(a): Return, Volatility and
Market Conditions Asymmetries for SS. Impact of Market conditions
asymmetries on volatility.
Statistics Parameters SS
Mean Equation 𝜶𝟎 0.002669
p-value <0.00001
β 0.03673
p-value .1154
γ -1.6252
p-value 0.3876
Variance Equation γ0 0.000109
p-value <0.00001
δ 0.68259
p-value <0.00001
γ1 0.16316
p-value <0.00001
μ1 -0.00011
p-value <0.00001
Diagnostic
Test
AIC- statistics -5.38123
SIC- statistics -5.36419
log likelihood 6389.134
Results in Table 18(b) indicate that the negativity of μ1 in bullish effect indicates that
volatility in the bullish market is less than the volatility in bearish market. It means that
in bullish market return are high and volatility is low which offer better risk return
relationship.
80
Table 19: Estimates of TGARCH Model 2(b): Return, Volatility and Market
Asymmetric Conditions, Good News and Bad News Effect.
Statistics Parameters SS
Mean Equation α 0.00029
p-value 0.3369
β 0.028497
p-value 0.1795
Variance Equation γ0 0.00000642
p-value <0.0001
γ1 0.048128
p-value <0.0001
δ 0.029422
p-value 0.0003
θ 0.916989
p-value <0.0001
Diagnostic
Test
AIC- Statistics -5.38909
SIC- Statistics -5.37449
Log-Likelihood 6397.458
TGARCH (1,1) model is estimated for SS returns series by using Gaussian standard
normal distribution AIC, SIC and maximum Log Likelihood values, and ARCH- LM test
are performed to select volatility model that can best model the conditional variance of
the SS returns series. The estimation result of TGARCH (1, 1) models are shown in Table
19. The significant θ indicates persistence in volatility for long run and hence stable
indicator of an integrated process. Variance equation indicates that ARCH term has
coefficient 0.048128 significant at p<0.0001 and the GARCH term coefficient is
0.029422 significant at p<0.001.
The asymmetric effect captured by the parameter estimate θ is positive and significant in
81
the TGARCH (1, 1) that indicates the existence of leverage effect. After finding the
presence of leverage effects in the series by using TGARCH (1,1). However results
indicated that TGARCH(1,1) model can be a potential representative of the asymmetric
conditional volatility process for the daily return series of SS.
From the estimated TGARCH model, it is apparent that good news has an impact of
0.04128 magnitudes for SS and bad news has an impact of (0.048128+0.916989 =
0.965117). Because the leverage effect is significant and hence it is concluded that the
bad news increases higher volatility in SS more than good news.
Table 20: Estimates of GARCH (1,1)Model 3: Return and Value at Risk for SS
Statistics Parameters SS
Mean equation α 0.000263
p-value <0.00001
β -3.99e-18
p-value 1
γ -1443.769
p-value 0.2054
Variance equation γ0 1.36e-35
p-value <0.00001
δ 0.6
p-value <0.00001
γ1 0.15
p-value <0.00001
Diagnostic
Test
AIC- statistics -76.0915
SIC- statistics -76.0769
Log-likelihood 90250.56
Table 20 indicates the relationship of return and the value at risk. GARCH Model is
extended with the Value at Risk in mean equation. The results indicate that the γ1 is
insignificantly related to return. It is inferred that VaR is not significantly related to the
82
returns of SS market. ARCH term is significant at 95% confidence interval indicating that
past price behavior influence current volatility in the market. The GARCH term is
significant at 95% confidence interval which reports the presence of persistence in the
volatility. It indicates that the value at risk is positive but not significant and has no effect
on the price behavior.
Table 21: Estimates of GARCH (1,1) Model 4: Return, Volatility and Semi Variance
for SS
Statistics Parameters SS
Mean Equation α -0.00083
p-value 0.072
𝛽 0.069171
p-value 0.1021
γ 2.448605
p-value <0.00001
Variance Equation γ0 4.04E-05
p-value <0.00001
δ 0.63867
p-value <0.00001
γ1 0.159283
p-value <0.00001
Diagnostic
Test
AIC- Statistics -5.78709
SIC- Statistics -5.75894
Log-likelihood 3067.369
Table 21 indicates the relationship of return, and the Semi-variance. GARCH Model is
extended with the Semi-variance. Semi-variance is downside risk and added into
variance equation. Here semi-variance is significant at p<0.0001 and indicates that results
indicate that as down side risk increases, return also increases. The results indicate that
ARCH term and GARCH term are significant at p<0.0001. Here all the variables for
83
variance equation are statistically significant and the value of the semi-variance is
positive which means if the semi-variance increases it causes to an increase in the return.
4.2 Econometric Models for India
Table 22(a): Estimates of GARCH in Mean (1,1) Model 1: Return, Volatility and
Macroeconomic Model for BSE: Impact of macroeconomic variables
on Return
Statistics Parameters BSE
Mean Equation 𝒂𝟎 0.45
p-value 0.8351
β 0.019134
p-value 0.2465
γ -78.4828
p-value 0.3684
π1 -0.01006
p-value 0.0909
π2 -0.01001
p-value 0.9081
π3 0.001354
p-value 0.9917
π4 0.089325
p-value 0.1947
Variance Equation γ 0.000102
p-value 0.481
δ 0.983127
p-value <0.00001
γ1 -0.005582
p-value 0.3991
Diagnostic
Test
AIC- Statistics -2.176575
SIC- Statistics -1.955996
Log Likelihood 151.4774
Table 22(a) indicates that GARCH in mean model is extended with the macroeconomic
variables in the variance equation for BSE. The conditional mean is not significant. So
far as macroeconomic variables are concerned, inflation has significant negative effect on
return and increase in inflation decrease returns of the stocks. Model is selected on the
basis of AIC, SIC, and Log Likelihood values.
84
Table 22(b): Estimates of GARCH in Mean (1,1) Model 1: Return, Volatility and
Macroeconomic Model for BSE: Impact Of Macroeconomic Variables
On Volatility
Table 22(b) indicates the impact of macroeconomic variables on volatility of market has
also been exercised. The results indicate that inflation is significant positively related to
volatility. In high periods of inflation, volatility is on high side, change in interest rate
Statistics Parameters BSE
Mean Equation γ0 0.037981
p-value 0.0008
δ 0.052035
p-value 0.5144
γ1 -6.825557
p-value 0.0034
Variance Equation 𝑎0 -0.02543
p-value 0.0457
β 0.767876
p-value <0.00001
γ 0.000922
p-value 0.4141
π1 0.0000830
p-value 0.0038
π2 -0.02248
p-value <0.00001
π3 -0.01878
p-value 0.0023
π4 0.006992
p-value 0.0005
Diagnostic Test AIC- statistics -2.197952
SIC- statistics -1.977372
Log -Likelihood 152.8669
85
has negative significant impact on volatility. Similarly change in industrial production has
also negative significant impact on volatility. Therefore in the period of rising prices
volatility is lower it may be due to anchoring. However oil price change has positive
significant impact on volatility. Due to high positive change in oil prices volatility is on
high side.
Table 23(a): Estimates of GARCH in Mean (1,1) Model 2(a): Return, Volatility and
Market Conditions Asymmetries for BSE: Impact of Market Conditions
Asymmetries On Return
Statistics Parameters BSE
Mean Equation 𝜶𝟎 -0.009776
p-value <0.00001
β 0.032477
p-value 0.0245
γ -0.154851
p-value 0.939
θ1 0.019659
p-value <0.00001
Variance Equation γ0 0.00000249
p-value <0.00001
δ 0.882865
p-value <0.00001
γ1 0.115029
p-value <0.00001
Diagnostic
Test
AIC- Statistics -6.130639
SIC- Statistics -6.113607
Log -Likelihood 7277.938
Table 23(a) reports the role of bullish and bearish market behavior in BSE.
θ1 value is significant and positive which shows that returns are higher in bullish period.
Model is used to study the asymmetric behavior of the market.
86
θ1 is significant and positive which indicates that past price behavior influences current
price volatility. The significant value of δ indicates that the volatility once created
persistence and contributes in the volatility of next period. The γ1 found significant and
persistent which shows that asymmetric behavior exist in market.
Table 23 (b): Estimates of GARCH in Mean (1,1) Model 2(a): Return, Volatility and
Market Conditions Asymmetries for BSE: Impact of Market Conditions
Asymmetries On Volatility.
Statistics Parameters BSE
Mean Equation 𝜶𝟎 0.078392
p-value <0.00001
β 0.011061
p-value 0.2685
γ -430.1017
p-value <0.00001
Variance Equation γ0 0.000213
p-value <0.00001
δ 0.008118
p-value 0.6617
γ1 -0.000742
p-value 0.1237
μ1 -0.0000608
p-value <0.00001
Diagnostic
Test
AIC- statistics -5.79246
SIC- statistics -5.77543
Log-Likelihood 6876.858
Results in Table 23(b) indicate that the negativity of μ1 in bullish effect indicates that
volatility in the bullish market is less than the volatility in bearish market. It means that
in bullish market return are high and volatility is low which offer better risk return
relationship.
87
Table 24: Estimates of TGARCH Model 2(b): Return, Volatility and Market
Asymmetric Conditions, Good News and Bad News Effect.
Statistics Parameters BSE
Mean equation 𝜶𝟎 0.000882
p-value 0.0017
β 0.097318
p-value <0.0001
Variance equation γ0 0.00000795
p-value <0.0001
γ1 0.064636
p-value <0.0001
δ 0.123009
p-value <0.0001
θ 0.854005
p-value <0.0001
Diagnostic
Test
AIC- statistics -5.44086
SIC- statistics -5.42627
log-likelihood 6458.865
TGARCH (1,1) model is estimated for BSE returns series by using Gaussian
standard normal distribution AIC, SIC and maximum Log Likelihood values, and
ARCH- LM test are performed to select volatility model that can best model the
conditional variance of the BSE returns series. The estimation result of TGARCH (1,1)
models are shown in Table 24. The conditional mean is significant for TGARCH(1,1)
at p<0.10 that indicates persistence in volatility for long run and hence stable indicator
88
of an integrated process. ARCH and GARCH terms are significant at p<0.0001.
The asymmetric effect captured by the parameter estimate θ is positive and significant
in the TGARCH (1, 1) that indicate the existence of leverage effect. After finding the
presence of leverage effects in the series by using TGARCH (1,1). Diagnostic test identifies
the model performance in comparison to other equity markets. However results indicated
that TGARCH(1,1) model can be a potential representative of the asymmetric
conditional volatility process for the daily return series of BSE.
From the estimated TGARCH model, it is apparent that good news has an impact of
0.064636 magnitudes for BSE and bad news has an impact of (0.064636+0.854005 =
0.918641). Because the leverage effect is significant and hence it is concluded that the
bad news increases higher volatility in BSE more than good news.
89
Table 25: Estimates of GARCH (1,1) Model 3: Return, Volatility and Value at Risk
for BSE
Statistics Parameters BSE
Mean equation 𝜶𝟎 0.000862
p-value <0.00001
β -0.000235
p-value 0.0019
γ -1444.603
p-value <0.00001
Variance equation γ0 0.0000000000294
p-value 0.1063
δ 0.677972
p-value <0.00001
γ1 0.309051
p-value <0.00001
Diagnostic
Test
AIC- Statistics -14.57652
SIC- Statistics -14.56192
Log Likelihood 17293.76
Table 25 indicates the relationship of return and the value at risk. GARCH Model is
extended with the Value at Risk in mean equation. The results indicate that the γ is
negatively related to return significantly. It is inferred that VaR is significantly negatively
related to the returns of BSE market. ARCH term is significant at 95% confidence
interval indicating that past price behavior influence current volatility in the market. The
GARCH term is significant at 95% confidence interval which reports the presence of
persistence in the volatility. It indicates that the value at risk is negative and has effect on
the price behavior.
90
Table 26: Estimates of GARCH (1,1) Model 4: Return, Volatility and Semi variance
for BSE
Statistics Parameters BSE
Mean Equation 𝜶𝟎 0.000964
p-value 0.0302
𝛽 0.095278
p-value 0.0035
γ -0.328351
p-value 0.4079
Variance Equation γ0 0.0000107
p-value 0.0002
δ 0.837336
p-value <0.00001
γ1 0.130067
p-value <0.00001
Diagnostic
Test
AIC- Statistics -5.504929
SIC- Statistics -5.477175
Log-Likelihood 2970.404
Table 26 indicates the relationship of return, and the Semi-variance. GARCH Model is
extended with the Semi-variance. Semi-variance is downside risk and added into
variance equation. Here semi-variance is insignificant which indicates no such effect. The
results indicate that ARCH term and GARCH term are significant at p<0.00001. Here all
the variables for variance equation are statistically significant. The value of the semi-
variance is negative but insignificant.
91
4.3 Econometric Models for Indonesia
Table 27(a): Estimates of GARCH in Mean (1,1) Model 1: Return, Volatility and
Macroeconomic Model for JCI: Impact of macroeconomic variables
on Return
Statistics Parameters JCI
Mean Equation 𝑎𝑜 0.053923
p-value 0.2456
β 0.069918
p-value 0.5526
γ -0.591043
p-value 0.3926
π1 0.300407
p-value 0.7789
π2 -0.55417
p-value 0.0009
π3 0.007209
p-value 0.9306
π4 -0.01217
p-value 0.8477
Variance Equation 𝛄𝟎 0.001803
p-value 0.1589
δ 0.313233
p-value 0.2616
γ1 0.334955
p-value 0.0036
Diagnostic
Test
AIC- statistics -2.175127
SIC- statistics -2.175127
Log Likelihood 165.7209
Table 27(a) indicates that GARCH in mean model is extended with the macroeconomic
variables in the variance equation for JCI. The conditional mean is not significant. So far
as macroeconomic variables are concerned, change in interest rate has significant
negative effect on return and increase in interest rate decrease returns of stocks. Model is
selected on the basis of AIC, SIC, and Log Likelihood values.
92
Table 27(b): Estimates of GARCH in Mean (1,1) Model 1: Return, Volatility and
Macroeconomic Model for JCI: Impact of macroeconomic variables
on Volatility
Table 27(b) indicates the impact of macroeconomic variables on volatility of JCI market.
The results indicate that GARCH term is significant but no macroeconomic variable have
significant impact on volatility.
Statistics Parameters JCI
Mean Equation γ0 0.054889
p-value 0.0004
δ 0.122628
p-value 0.2156
γ1 -9.534224
p-value 0.028
Variance Equation 𝑎0 0.000235
p-value 0.4675
β 1.051728
p-value <0.00001
γ -0.123546
p-value 0.0018
π1 -0.000451
p-value 0.9897
π2 -0.000156
p-value 0.9647
π3 0.004257
p-value 0.6281
π4 0.000331
p-value 0.9116
Diagnostic Test AIC- statistics -2.611354
SIC- statistics -2.349221
Log Likelihood 139.262
93
Table 28(a): Estimates of GARCH in Mean (1,1) Model 2(a): Return, Volatility and
Market Conditions Asymmetries for JCI: Impact of market conditions
asymmetries on Return.
Statistics Parameters JCI
Mean Equation 𝜶𝟎 -0.01011
p-value <0.00001
β 0.058389
p-value <0.00001
γ 4.205766
p-value 0.1239
θ1 0.019622
p-value <0.00001
Variance Equation γ0 0.00000779
p-value <0.00001
δ 0.804274
p-value <0.00001
γ1 0.159444
p-value <0.00001
Diagnostic
Test
AIC- Statistics -6.246748
SIC- Statistics -6.229721
Log-Likelihood 7418.766
Table 28(a) reports the role of bullish and bearish market behavior in JCI .
θ1 value is significant and positive which shows that returns are higher in bullish period.
Model is used to study the asymmetric behavior of the market.
θ1 is significant and positive which indicates that past price behavior influences current
price volatility. The significant value of δ indicates that the volatility once created
persistence and contributes in the volatility of next period. The γ1 found significant and
persistent which shows that asymmetric behavior exist in market.
94
Table 28(b): Estimates of GARCH in Mean (1,1) Model 2(a): Return, Volatility and
Market Conditions Asymmetries for JCI: Impact of market conditions
asymmetries on Volatility.
Statistics Parameters JCI
Mean Equation 𝜶𝟎 0.060109
p-value <0.00001
β 0.049836
p-value <0.00001
γ -401.5648
p-value <0.00001
Variance Equation γ0 0.00018
p-value <0.00001
δ 0.001248
p-value 0.901
γ1 0.001248
p-value <0.00001
μ1 -0.0000574
p-value <0.00001
Diagnostic
Test
AIC- statistics -6.017947
SIC- statistics -6.00092
Log likelihood 7147.294
Results in Table 28(b) indicate that the negativity of μ1 in bullish effect indicates that
volatility in the bullish market is less than the volatility in bearish market. It means that
in bullish market return are high and volatility is low which offer better risk return
relationship.
95
Table 29: Estimates of TGARCH Model 2(b): Return, Volatility and Market
Asymmetric Conditions, Good News and Bad News Effect.
Statistics Parameters JCI
Mean Equation 𝜶𝟎 0.000873
p-value 0.0034
β 0.12872
p-value <0.0001
Variance Equation γ0 0.0000197
p-value <0.0001
γ1 0.038811
p-value 0.0014
δ 0.16792
p-value <0.0001
θ 0.8019
p-value <0.0001
Diagnostic
Test
AIC- statistics -5.56881
SIC- statistics -5.55422
Log Likelihood 6613.397
TGARCH (1,1) model is estimated for JCI returns series by using Gaussian standard
normal distribution AIC, SIC and maximum Log Likelihood values, and ARCH- LM
test are performed to select volatility model that can best model the conditional variance
of the BSE returns series. The estimation result of TGARCH (1, 1) models are shown in
Table 29. The conditional mean is significant for TGARCH(1,1) that indicates
persistence in volatility for long run and hence stable indicator of an integrated
process. ARCH and GARCH terms are significant at p<0.01 and p<0.0001
respectively.
The asymmetric effect captured by the parameter estimate θ is positive and significant
96
in the TGARCH (1, 1) that indicate the existence of leverage effect. After finding the
presence of leverage effects in the series by using TGARCH (1,1). Diagnostic test identify
the model performance in comparison to other equity markets. However results indicated
that TGARCH(1,1) model can be a potential representative of the asymmetric
conditional volatility process for the daily return series of JCI.
From the estimated TGARCH model, it is apparent that good news has an impact of
0.038811 magnitudes for JCI and bad news has an impact of (0.038811+0.8019 =
0.840711). Because the leverage effect is significant and hence it is concluded that the
bad news increases higher volatility in JCI more than good news.
Table 30: Estimates of GARCH(1,1)Model 3: Return, Volatility and Value at Risk for
JCI
Statistics Parameters JCI
Mean equation 𝜶𝟎 0.001024
p-value <0.00001
β -0.00023
p-value 0.0029
γ -1445.39
p-value <0.00001
Variance equation γ0 0.000000000247
p-value <0.00001
δ 0.616544
p-value <0.00001
γ1 0.192066
p-value <0.00001
Diagnostic
Test
AIC- statistics -14.57007
SIC- statistics -14.55547
Log likelihood 17293.39
Table 30 indicates the relationship of return and the value at risk. GARCH Model is
extended with the Value at Risk in mean equation. The results indicate that the γ is
97
negatively related to return significantly. It is inferred that VaR is significantly negatively
related to the returns of JCI market. ARCH term is significant at 95% confidence interval
indicating that past price behavior influence current volatility in the market. The ARCH
and GARCH term is significant at 95% confidence interval which reports the presence of
persistence in the volatility. It indicates that the value at risk is negative and has effect on
the price behavior.
Table 31: Estimates of GARCH (1,1) Model 4: Return, Volatility and Semi variance
for JCI
Statistics Parameters JCI
Mean Equation 𝜶𝟎 0.001311
p-value 0.0062
𝛽 0.127384
p-value 0.0002
γ -2.242415
p-value 0.0003
Variance Equation γ0 0.0000334
p-value <0.00001
δ 0.73389
p-value <0.00001
γ1 0.115699
p-value <0.00001
Diagnostic
Test
AIC- statistics -5.623841
SIC- statistics -5.595794
Log-likelihood 2995.071
Table 31 indicates the relationship of return, and the Semi-variance. GARCH Model is
extended with the Semi-variance. Semi-variance is downside risk and added into
variance equation. Here semi-variance is significant at p<0.0001 and indicates that results
indicate that as down side risk increases, return also increases. The results indicate that
98
ARCH term and GARCH term are significant at p<0.0001. Here all the variables for
variance equation are statistically significant and the value of the semi-variance is
positive which means if the semi-variance increases it causes to an increase in the return.
4.4 Econometric Models for Bangladesh
Table 32(a): Estimates of GARCH in Mean (1,1) Model 1: Return, Volatility and
Macroeconomic Model for DSE: Impact of macroeconomic variables
on Return
Statistics Parameters DSE
Mean Equation 𝑎𝑜 0.236073
p-value 0.7643
β 0.225684
p-value 0.0441
γ -51.18882
p-value 0.7833
π1 -0.075689
p-value 0.9227
π2 0.124938
p-value 0.9839
π3 0.030717
p-value 0.8098
π4 -0.022235
p-value 0.6752
Variance Equation 𝛄𝟎 0.003747
p-value 0.0378
δ 0.096005
p-value 0.8043
γ1 0.031218
p-value 0.7807
Diagnostic
Test
AIC- statistics -2.47035
SIC- statistics -2.24977
Log Likelihood 170.5725
Table 32(a) indicates that GARCH in mean model is extended with the macroeconomic
variables in the variance equation for DSE. The conditional mean is not significant. So
far as macroeconomic variables are concerned, No variable has significant effect on
return. Model is selected on the basis of AIC, SIC, and Log Likelihood values.
99
Table 32(b): Estimates of GARCH in Mean (1,1) Model 1: Return, Volatility and
Macroeconomic Model for DSE: Impact of Macroeconomic Variables
On Volatility
Table 32(b) indicates the impact of macroeconomic variables on volatility of market has
also been exercised. The conditional mean is significant at p < 0.10. The results indicate
that change in industrial production is significant positively related to volatility. In high
Statistics Parameters DSE
Mean Equation γ0 0.013387
p-value 0.8344
δ 0.18549
p-value 0.281
γ1 0.630617
p-value 0.0809
Variance Equation 𝑎0 0.003017
p-value 0.0255
β 0.281912
p-value 0.3439
γ 0.050296
p-value 0.5335
π1 -0.007829
p-value 0.8639
π2 0.019059
p-value 0.5356
π3 0.02559
p-value 0.0066
π4 0.001387
p-value 0.6658
Diagnostic Test AIC- statistics -2.47089
SIC- statistics -2.25031
Log Likelihood 170.6076
100
growth period of industrial production, volatility is on high side, Therefore in the period
of high industrial production volatility is higher it may be due to anchoring.
Table 33(a)`: Estimates of GARCH in Mean (1,1) Model 2(a): Return, Volatility and
Market Conditions Asymmetries for DSE: Impact of market conditions
asymmetries on Return.
Statistics Parameters DSE
Mean Equation 𝜶𝟎 -0.002155
p-value <0.00001
β 0.110589
p-value <0.00001
γ 0.072776
p-value 0.0003
θ1 0.00571
p-value <0.00001
Variance Equation γ0 -0.000000397
p-value 0.413
δ 0.679755
p-value <0.00001
γ1 1.100461
p-value <0.00001
Diagnostic
Test
AIC- statistics -6.21952
SIC- statistics -6.19413
log likelihood 4537.917
Table 33(a) reports the role of bullish and bearish market behavior in DSE.
θ1 value is significant and positive which shows that returns are higher in bullish period.
Model is used to study the asymmetric behavior of the market. θ1 is significant and
positive which indicates that past price behavior influences current price volatility. The
significant value of δ indicates that the volatility once created persistence and contributes
101
in the volatility of next period. The γ1 found significant and persistent which shows that
asymmetric behavior exist in market.
Table 33 (b): Estimates of GARCH in Mean (1,1) Model 2(a): Return, Volatility and
Market Conditions Asymmetries for DSE: Impact of market conditions
asymmetries on Volatility.
Statistics Parameters DSE
Mean Equation 𝜶𝟎 0.0000801
p-value 0.6576
β 0.254173
p-value <0.00001
γ -0.28069
p-value 0.6848
Variance Equation γ0 -0.00000114
p-value <0.00001
δ 0.638496
p-value <0.00001
γ1 0.760665
p-value <0.00001
μ1 0.0000242
p-value <0.00001
Diagnostic
Test
AIC- statistics -6.15358
SIC- statistics -6.12819
log likelihood 4489.881
Results in Table 33(b) indicate that the negativity of μ1 in bullish effect indicates that
volatility in the bullish market is less than the volatility in bearish market. It means that
in bullish market return are high and volatility is low which offer better risk return
relationship.
102
Table 34: Estimates of TGARCH Model 4: Return, Volatility and Market
Asymmetric Conditions, Good News and Bad News Effect.
Statistics Parameters DSE
Mean Equation 𝜶𝟎 0.000978
p-value <0.0001
β -0.0044
p-value 0.8468
Variance Equation γ0 0.0000104
p-value <0.0001
γ1 0.248296
p-value <0.0001
δ 0.700479
p-value <0.0001
θ 0.691989
p-value <0.0001
Diagnostic
Test
AIC- statistics -5.8688
SIC- statistics -5.8542
Log Likelihood 6969.329
TGARCH (1,1) model is estimated for DSE returns series by using Gaussian
standard normal distribution AIC, SIC and maximum Log Likelihood values, and
ARCH- LM test are performed to select volatility model that can best model the
conditional variance of the DSE returns series. The estimation result of TGARCH (1, 1)
models is shown in Table 34. The conditional mean is significant for TGARCH(1,1)
that indicates persistence in volatility for long run and hence stable indicator of an
integrated process.
The asymmetric effect captured by the parameter estimate θ is positive and significant
in the TGARCH (1, 1) that indicate the existence of leverage effect. After finding the
presence of leverage effects in the series by using TGARCH (1,1). Diagnostic test identifies
103
the model performance in comparison to other equity markets. However results indicated
that TGARCH(1,1) model can be a potential representative of the asymmetric
conditional volatility process for the daily return series of DSE.
From the estimated TGARCH model, it is apparent that good news has an impact of
0.248296 magnitudes for DSE and bad news has an impact of (0.248296+0.691989 =
0.940285). Because the leverage effect is significant and hence it is concluded that the
bad news increases higher volatility in DSE more than good news.
Table 35: Estimates of GARCH (1,1) Model 3: Return, Volatility and Value at Risk
for DSE
Statistics Parameters DSE
Mean equation 𝜶𝟎 0.001236
p-value <0.00001
𝛽 -0.000319
p-value 0.1624
γ -1444.617
p-value <0.00001
Variance equation γ0 0.0000000012
p-value 0.1435
δ 0.623584
p-value <0.00001
γ1 0.203615
p-value <0.00001
Diagnostic
Test
AIC- statistics -13.0943
SIC- statistics -13.0797
Log likelihood 15542.42
Table 35 indicates the relationship of return and the value at risk. GARCH Model is
extended with the Value at Risk in mean equation. The results indicate that the γ is
negatively related to return significantly. It is inferred that VaR is significantly negatively
104
related to the returns of DSE market. ARCH term is significant at 95% confidence
interval indicating that past price behavior influence current volatility in the market. The
GARCH term is significant at 95% confidence interval which reports the presence of
persistence in the volatility. It indicates that the value at risk is negative and has effect on
the price behavior.
Table 36: Estimates of GARCH (1,1) Model 4: Return, Volatility and Semi -Variance
for DSE
Statistics Parameters DSE
Mean Equation 𝜶𝟎 0.00108
p-value 0.0612
𝛽 0.041587
p-value 0.5749
γ 0.132842
p-value 0.8353
Variance Equation γ0 0.0000115
p-value <0.00001
δ 0.685167
p-value <0.00001
γ1 0.870101
p-value <0.00001
Diagnostic
Test
AIC- Statistics -6.31919
SIC- Statistics -6.28823
Log-Likelihood 2972.859
Table 36 indicates the relationship of return, and the Semi-variance. GARCH Model is
extended with the Semi-variance. Semi-variance is downside risk and added into
variance equation. Here semi-variance is insignificant which indicates no such effect. The
results indicate that ARCH term and GARCH term are significant at p<0.00001. Here all
the variables for variance equation are statistically significant. The value of the semi-
variance is negative but insignificant.
105
4.5 Econometric Models for Malaysia
Table 37(a): Estimates of GARCH in Mean (1,1) Model 1: Return, Volatility and
Macroeconomic Model for KLSE: Impact of macroeconomic variables
on Return
Statistics Parameters KLSE
Mean Equation 𝑎𝑜 -1.077428
p-value 0.0644
β 0.052962
p-value 0.0151
γ 0.086962
p-value 0.3243
π1 -1.40529
p-value 0.3356
π2 -0.064
p-value 0.2548
π3 0.043531
p-value 0.6056
π4 0.067772
p-value <0.00001
Variance Equation 𝛄𝟎 0.0000195
p-value 0.3955
δ 0.870101
p-value <0.00001
γ1 0.685167
p-value <0.00001
Diagnostic
Test
AIC- statistics -6.31919
SIC- statistics -6.28823
Log Likelihood 2972.859
Table 37(a) indicates that GARCH in mean model is extended with the macroeconomic
variables in the variance equation for KLSE. The conditional mean is not significant. So
far as macroeconomic variables are concerned, oil price has significant positive effect on
return and increase in change in oil price increase returns of stocks. Model is selected on
the basis of AIC, SIC, and Log Likelihood values.
106
Table 37(b): Estimates of GARCH in Mean (1,1) Model 1: Return, Volatility and
Macroeconomic Model for KLSE: Impact of Macroeconomic
Variables On Volatility
Table 37(b) indicates the impact of macroeconomic variables on volatility of market has
also been exercised. Change in industrial production has also positive significant impact
on volatility. Therefore in the period of high industrial growth volatility is on high side.
Statistics Parameters KLSE
Mean Equation γ0 -2.653122
p-value <0.00001
δ 0.123042
p-value 0.0018
γ1 0.144553
p-value <0.00001
Variance Equation 𝑎0 -0.000407
p-value <0.00001
β 0.955296
p-value <0.00001
γ 0.147641
p-value <0.00001
π1 0.004064
p-value 0.735
π2 -0.00016
p-value 0.9627
π3 0.013666
p-value <0.00001
π4 0.000542
p-value 0.4442
Diagnostic Test AIC- statistics -0.74306
SIC- statistics -0.52248
Log Likelihood 58.29916
107
Table 38(a): Estimates of GARCH in Mean (1,1) Model 2(a): Return, Volatility and
Market Conditions Asymmetries for KLSE: Impact of market conditions
asymmetries on Return.
Statistics Parameters KLSE
Mean Equation 𝜶𝟎 -0.006751
p-value <0.00001
β 0.09896
p-value <0.00001
γ 3.320108
p-value 0.3083
θ1 0.013051
p-value <0.00001
Variance Equation γ0 0.0000227
p-value <0.00001
δ 0.447227
p-value <0.00001
γ1 0.392705
p-value <0.00001
Diagnostic
Test
AIC- statistics -6.79421
SIC- statistics -6.7772
log likelihood 8075.13
Table 38(a) reports the role of bullish and bearish market behavior in KLSE.
θ1 value is significant and positive which shows that returns are higher in bullish period.
Model is used to study the asymmetric behavior of the market.
θ1 is significant and positive which indicates that past price behavior influences current
price volatility. The significant value of δ indicates that the volatility once created
persistence and contributes in the volatility of next period. The γ1 found significant and
persistent which shows that asymmetric behavior exist in market.
108
Table 38 (b): Estimates of GARCH in Mean (1,1) Model 2(a): Return, Volatility and
Market Conditions Asymmetries for KLSE: Impact of market conditions
asymmetries on Volatility.
Statistics Parameters KLSE
Mean Equation 𝒂𝟎 0.011048
p-value <0.00001
β 0.052288
p-value <0.00001
γ -123.455
p-value <0.00001
Variance Equation γ0 1.36E-04
p-value <0.00001
δ 0.018836
p-value 0.0734
γ1 0.017636
p-value <0.00001
μ1 -0.0000992
p-value <0.00001
Diagnostic
Test
AIC- statistics -6.70759
SIC- statistics -6.69058
log likelihood 7972.266
Results in Table 38(b) indicate that the negativity of μ1 in bullish effect indicates that
volatility in the bullish market is less than the volatility in bearish market. It means that
in bullish market return are high and volatility is low which offer better risk return
relationship.
109
Table 39: Estimates of TGARCH Model 2(b): Return, Volatility and Market
Asymmetric Conditions, Good News and Bad News Effect.
Statistics Parameters KLSE
Mean Equation 𝒂𝟎 7.05E-05
p-value 0.7717
β 0.155966
p-value <0.0001
Variance Equation γ0 2.65E-05
p-value <0.0001
γ1 0.015143
p-value 0.1645
δ 0.234707
p-value <0.0001
θ 0.657546
p-value <0.0001
Diagnostic
Test
AIC- statistics -6.30102
SIC- statistics -6.28644
Log Likelihood 7488.465
TGARCH (1,1) model is estimated for KLSE returns series by using Gaussian
standard normal distribution AIC, SIC and maximum Log Likelihood values, and
ARCH- LM test are performed to select volatility model that can best model the
conditional variance of the KLSE returns series.
The estimation result of TGARCH (1, 1) models is shown in Table 39. The conditional
mean is significant for TGARCH(1,1) that indicates persistence in volatility for long
run and hence stable indicator of an integrated process.
The asymmetric effect captured by the parameter estimate θ is positive and significant
in the TGARCH (1, 1) that indicate the existence of leverage effect. After finding the
presence of leverage effects in the series by using TGARCH (1,1) the SIC were used to
110
select the best model for returns series. The model with lowest value of SIC fits the
data best. The results are presented in table 39. TGARCH (1,1) were the lowest
respectively as compare to the other equity markets and significant, therefore the study
concludes that TGARCH(1,1) model can be a potential representative of the
asymmetric conditional volatility process for the daily return series of KLSE.
From the estimated TGARCH model, it is apparent that good news has an impact of
0.015143 magnitudes for KLSE and bad news has an impact of (0.015143+0.657546 =
0.672689). Because the leverage effect is significant and hence it is concluded that the
bad news increases higher volatility in KLSE more than good news.
Table 40: Estimates of GARCH (1,1) Model 3: Return, Volatility and Value at Risk
for KLSE
Statistics Parameters KLSE
Mean equation 𝒂𝟎 0.000253
p-value <0.00001
𝛽 0.000000000000000423
p-value <0.00001
γ -1443.769
p-value <0.00001
Variance equation γ0 2.27E-34
p-value 1
δ 0.6
p-value <0.00001
γ1 0.15
p-value <0.00001
Diagnostic
Test
AIC- statistics -74.1106
SIC- statistics -74.096
Log likelihood 88012.31
Table 40 indicates the relationship of return and the value at risk. GARCH Model is
extended with the Value at Risk in mean equation. The results indicate that the γ is
111
negatively related to return significantly. It is inferred that VaR is significantly negatively
related to the returns of KLSE market. ARCH term is significant at 95% confidence
interval indicating that past price behavior influence current volatility in the market. The
GARCH term is significant at 95% confidence interval which reports the presence of
persistence in the volatility. It indicates that the value at risk is negative and has effect on
the price behavior.
Table 41: Estimates of GARCH (1,1) Model 4: Return, Volatility and Semi -Variance
for KLSE
Statistics Parameters KLSE
Mean Equation 𝒂𝟎 0.000112
p-value 0.6745
𝛽 0.167394
p-value <0.00001
γ 4.192136
p-value <0.00001
Variance Equation γ0 0.000000108
p-value 0.0031
δ 0.993485
p-value 0.0085
γ1 0.002947
p-value <0.00001
Diagnostic
Test
AIC- statistics -6.4278
SIC- statistics -6.40069
Log-likelihood 3570.214
Table 41 indicates the relationship of return, and the Semi-variance. GARCH Model is
extended with the Semi-variance. Semi-variance is downside risk and added into
variance equation. Here semi-variance is significant at p<0.0001 and indicates that results
indicate that as down side risk increases, return also increases. The results indicate that
112
ARCH term and GARCH term are significant at p<0.0001. Here all the variables for
variance equation are statistically significant and the value of the semi-variance is
positive which means if the semi-variance increases it causes to an increase in the return.
4.6 Econometric Models for Pakistan
Table 42(a): Estimates of GARCH in Mean (1,1) Model 1: Return, Volatility and
Macroeconomic Model for KSE: Impact of macroeconomic variables on
Return
Statistics Parameters KSE
Mean Equation 𝑎𝑜 -0.02412
p-value 0.5558
β 0.130553
p-value 0.1364
γ 4.710384
p-value 0.3995
π1 -0.26877
p-value 0.7967
π2 -0.20189
p-value 0.0629
π3 0.028855
p-value 0.799
π4 0.051474
p-value 0.5839
Variance Equation 𝛄𝟎 0.004096
p-value 0.5562
δ 0.506381
p-value 0.543
γ1 -0.039771
p-value 0.6934
Diagnostic
Test
AIC- statistics -1.90705
SIC- statistics -1.68647
Log Likelihood 133.9585
Table 42(a) indicates that GARCH in mean model is extended with the macroeconomic
variables in the variance equation for KSE. The conditional mean is not significant. So
far as macroeconomic variables are concerned, change in interest rate has significant
negative effect on return and increase in change in interest rate decreases returns of
stocks. Model is selected on the basis of AIC, SIC, and Log Likelihood values.
113
Table 42(b): Estimates of GARCH in Mean (1,1) Model 1: Return, Volatility and
Macroeconomic Model for KSE: Impact of macroeconomic variables on
Volatility
Table 42(b) indicates the impact of macroeconomic variables on volatility of the market
has also been exercised. The results indicate that inflation is significant positively related
to volatility. In high periods of inflation, volatility is on high side. Therefore in the period
of rising prices volatility is lower it may be due to anchoring. However oil prices change
has negative significant impact on volatility.
Statistics Parameters KSE
Mean Equation γ0 -0.007216
p-value 0.2205
δ 0.158823
p-value 0.6197
γ1 2.671622
p-value 0.0002
Variance Equation 𝑎0 0.0031
p-value 0.0407
β 0.568143
p-value 0.0019
γ -0.051422
p-value 0.1251
π1 0.107572
p-value 0.0413
π2 -0.00577
p-value 0.3292
π3 0.00836
p-value 0.2609
π4 -0.02372
p-value 0.0027
Diagnostic Test AIC- statistics -2.01419
SIC- statistics -1.79361
Log Likelihood 140.922
114
Table 43(a): Estimates of GARCH in Mean (1,1) Model 2(a): Return, Volatility and
Market Conditions Asymmetries for KSE: Impact of market conditions
asymmetries on Return.
Statistics Parameters KSE
Mean Equation 𝜶𝟎 -0.009421
p-value <0.00001
β 0.046784
p-value 0.0032
γ 0.018471
p-value 0.2375
θ1 2.835369
p-value <0.00001
Variance Equation γ0 0.00000773
p-value <0.00001
δ 0.824566
p-value <0.00001
γ1 0.131085
p-value <0.00001
Diagnostic
Test
AIC- Statistics -6.16624
SIC- Statistics -6.14921
Log- Likelihood 7323.241
Table 43(a) reports the role of bullish and bearish market behavior in KSE .
θ1 value is significant and positive which shows that returns are higher in bullish period.
Model is used to study the asymmetric behavior of the market.
θ1 is significant and positive which indicates that past price behavior influences current
price volatility. The significant value of δ indicates that the volatility once created
persistence and contributes in the volatility of next period. The γ1 found significant and
persistent which shows that asymmetric behavior exist in market.
115
Table 43 (b): Estimates of GARCH in Mean (1,1) Model 2(a): Return, Volatility and
Market Conditions Asymmetries for KSE: Impact of market conditions
asymmetries on Volatility.
Statistics Parameters KSE
Mean Equation 𝒂𝟎 0.077709
p-value <0.00001
β 0.036694
p-value 0.0004
γ -513.4456
p-value <0.00001
Variance Equation γ0 0.000174
p-value <0.00001
δ -0.002288
p-value 0.2645
γ1 0.000737
p-value 0.266
μ1 -0.0000445
p-value <0.00001
Diagnostic
Test
AIC- Statistics -5.94868
SIC- Statistics -5.93165
Log- Likelihood 7065.103
Results in Table 43(b) indicate that the negativity of μ1 in bullish effect indicates that
volatility in the bullish market is less than the volatility in bearish market. It means that
in bullish market return are high and volatility is low which offer better risk return
relationship.
116
Table 44: Estimates of TGARCH Model 2(b): Return, Volatility and Market
Asymmetric Conditions, Good News and Bad News Effect.
Statistics Parameters KSE
Mean Equation 𝒂𝟎 0.001061
p-value 0.0003
β 0.091333
p-value <0.0001
Variance Equation γ0 1.84E-05
p-value <0.0001
γ1 0.083396
p-value <0.0001
δ 0.142722
p-value <0.0001
θ 0.778899
p-value <0.0001
Diagnostic
Test
AIC- statistics -5.59246
SIC- statistics -5.57786
Log Likelihood 6641.447
TGARCH (1,1) model is estimated for KSE returns series by using Gaussian
standard normal distribution AIC, SIC and maximum Log Likelihood values, and
ARCH- LM test are performed to select volatility model that can best model the
conditional variance of the KLSE returns series.
The estimation result of TGARCH (1, 1) models is shown in Table 44. The conditional
mean is significant for TGARCH(1,1) that indicates persistence in volatility for long
run and hence stable indicator of an integrated process.
The asymmetric effect captured by the parameter estimate θ is positive and significant
in the TGARCH (1, 1) that indicate the existence of leverage effect. After finding the
presence of leverage effects in the series by using TGARCH (1,1).
Diagnostic test identify the model performance in comparison to other equity markets.
However results indicated that TGARCH(1,1) model can be a potential
representative of the asymmetric conditional volatility process for the daily return
117
series of KSE.
From the estimated TGARCH model, it is apparent that good news has an impact of
0.083396 magnitudes for KSE and bad news has an impact of (0.083396+0.778899 =
0.862295). Because the leverage effect is significant and hence it is concluded that the
bad news increases higher volatility in KSE more than good news.
Table 45: Estimates of GARCH (1,1)Model 3: Return, Volatility and Value at Risk
for KSE
Statistics Parameters KSE
Mean equation 𝒂𝟎 0.00876
p-value <0.00001
𝛽 -2.86E-16
p-value .998
γ -1443.16
p-value <0.00001
Variance equation γ0 6.09E-34
p-value 1
δ 0.6
p-value <0.00001
γ1 0.15
p-value 0.0006
Diagnostic
Test
AIC- statistics -73.069
SIC- statistics -73.0544
Log likelihood 86702.4
Table 45 indicates the relationship of return and the value at risk. GARCH Model is
extended with the Value at Risk in mean equation. The results indicate that the γ is
negatively related to return significantly. It is inferred that VaR is significantly negatively
related to the returns of KSE market. ARCH term is significant at 95% confidence
interval indicating that past price behavior influence current volatility in the market. The
118
GARCH term is significant at 95% confidence interval which reports the presence of
persistence in the volatility. It indicates that the value at risk is negative and has effect on
the price behavior.
Table 46: Estimates of GARCH (1,1) Model 4: Return, Volatility and Semi variance
for KSE
Statistics Parameters KSE
Mean Equation 𝒂𝟎 0.001303
p-value 0.0068
𝛽 0.02814
p-value 0.3677
γ -1.085048
p-value 0.2422
Variance Equation γ0 0.0000105
p-value <0.00001
δ 0.842199
p-value <0.00001
γ1 0.120431
p-value <0.00001
Diagnostic
Test
AIC- statistics -5.58359
SIC- statistics -5.5549
Log-likelihood 2889.926
Table 46 indicates the relationship of return, and the Semi-variance. GARCH Model is
extended with the Semi-variance. Semi-variance is downside risk and added into
variance equation. Here semi-variance is insignificant which indicates no such effect. The
results indicate that ARCH term and GARCH term are significant at p<0.00001. Here all
the variables for variance equation are statistically significant. The value of the semi-
variance is negative but insignificant.
119
Table 47: Diagnostic -Test
Diagnostic –
Test
SS BSE JCI DSE KLSE KSE
Model 1
a. Mean
Equation
AIC- statistics 30.312 -2.1765 -2.1751 -2.47035 -6.3191 -1.9070 SIC- statistics 30.532 -1.9559 -2.1751 -2.24977 -6.2882 -1.6864 Log Likelihood -1960.2 151.47 165.72 170.5725 2972.85 133.958
b.
Variance
Equation
AIC- statistics -2.1342 -2.1979 -2.6113 -2.47089 -0.7430 -2.0141
SIC- statistics -1.9137 -1.9773 -2.3492 -2.25031 -0.5224 -1.7936
Log Likelihood 148.728 152.866 139.26 170.6076 58.2991 140.92
Model
2(a)
a.Mean
Equation
AIC- statistics -5.9769 -6.130 -6.0179 -6.21952 -6.7942 -6.1662 SIC- statistics -5.9599 -6.1136 -6.0009 -6.19413 -6.777 -6.1492 Log Likelihood
7095.64 7277.9 7147.2
4537.917 8075.1 7323.24 b.
Variance
Equation
AIC- statistics -5.3812 -5.7924 -5.5688 -6.15358 -6.7075 -5.9486
SIC- statistics -5.3641 -5.7754 -5.5542 -6.12819 -6.6905 -5.9316
Log Likelihood 6389.13
6876.85 6613.39 4489.881 7972.26 7065.10
Model
2(b)
AIC- statistics -5.3890 -5.4408 -5.5688 -5.8688 -6.3010 -5.5924
SIC- statistics -5.3744 -5.4262 -5.5542 -5.8542 -6.28644 -5.5778
Log Likelihood 6397.45 6458.86 6613.39 6969.329 7488.46 6641.44
Model 3 AIC- statistics -76.091 -14.576 -14.570 -13.0943 -74.110 -73.06 SIC- statistics -76.076 -14.561 -14.555 -13.0797 -74.09 -73.054 Log Likelihood
90250.5 17293.7 17293.3 15542.42 88012.3 86702.
Model 4 AIC- statistics -5.7870 -5.5049 -5.6238 -6.31919 -6.427 -5.5835 SIC- statistics -5.7589 -5.4771 -5.5957 -6.28823 -6.400 -5.554 Log Likelihood
3067.36 2970.40 2995.07 2972.859 3570.21 2889.92
Table 47 indicates the summary of diagnostic test for all equity markets. AIC, SIC and
Log likelihood values are used to select the model that may best model the conditional
mean and conditional variance for these equity markets in a best way. First of all for
model 1(a), KSE, JCI and BSE market has lower values for AIC, SIC, Log Likelihood
and it indicates that the conditional mean can be modeled in these economies for asset
pricing in a best way along with the extension of macroeconomic variables. For Model
1(b) AIC, SIC and Log likelihood values are used to select the model that may best model
the conditional variance for these equity markets in a best way. SS,BSE, KLSE and KSE
market has lower absolute values for AIC, SIC, Log Likelihood and it indicates that the
120
conditional variance can be modeled in these economies for asset pricing in a best way
along with the extension of macroeconomic variables. However the performance of the
model 1(b) cannot be rejected for other economies as well. The diagnostic test for model
2(a) mean equation indicate that the conditional variance can be modeled in a preeminent
way for SS, BSE, KSE and JCI markets respectively along with asymmetric market
conditions. However the performance of this model cannot be rejected for other
economies as well. The conditional variance equation of Model 2(a) variance indicates
that SS, BSE, JCI and KSE have lower absolute values and performing well in capturing
the variance. Moreover Model 2(b) also ensures that the Good News and Bad News effect
can be modeled for SS, BSE, JCI and KSE in an excellent way based upon diagnostic test
value. Further Model 3 ensures that BSE JCI and DSE can be modeled along with VaR to
explain the risk return relationship in these economies. Finally Model 4 is performing the
best for KSE, BSE, JCI and SS to capture the return in these markets along with the semi-
variance. However the performance of the model cannot be rejected for other equity
markets as well.
4.7: Summary of the Results
This segment presents the summarized results of the analysis performed in previous
section of the study. Table 1 indicates that DSE and KSE are generating higher
average return but BSE and SS is more risky. KSE, BSE, JCI, KLSE, SS are
negatively skewed but DSE is positively skewed. Jarque-Bera normality test also
ensures departure from normality for all market returns. The returns series are
evaluated for heteroscedasticity. However Jarque-Bera test rejects the null
hypothesis of normality and indicates that all the equity market return series show
non-normality. Table 2 indicates that the numbers of positive returns are more than
negative returns for all the equity markets. The smallest difference between positive
121
and negative returns can be seen for the Chinese equity market. It indicates most
significant asymmetries in mean-reversion are to be observed other than the
Chinese equity market where four negative observations are greater than four
positive consecutive returns. It might be inferred that BSE, KSE, JCI are more
effective than KLSE, SS and DSE equity markets because the pattern indicates for
KLSE and DSE that the number of three consecutive negative observations are
more than that of three consecutive positive returns. Overall all equity markets have
mean reverting behavior. Table 3 indicates that results are significant overall for
negative sign bias (NSB) and for positive sign bias (PSB) as well except KLSE.
Results indicate that asymmetry exist and can be observed in the returns series.
Coefficients and p-values for sign-bias test, negative size-bias test and positive size
bias test for the equity returns are reported at P<0.05. The estimation of the
negative size bias test indicates that negative asymmetry can be seen in the returns
series. The result of the positive size-bias test on the other hand, generating
significant estimates for the KSE, BSE, DSE SS and JCI and indicates towards
positive asymmetry regarding to these equity markets. However, for the KLSE
market, the hypothesis of positive asymmetries is rejected. In the same way the
results of the negative size-bias test, generates significant estimates for the KSE,
BSE, KLSE SS and JCI and indicates towards negative asymmetry regarding to
these equity markets. However, for the DSE, the hypothesis of negative
asymmetries is rejected. According to the sign and size bias test above, non linear
patterns are expected and being observed because the return series indicates
asymmetric patterns. Lagrange Multiple test for ARCH effects are conducted to
further investigate this matter. Table 4 to 8 reported the p-values estimated with
Lagrange Multiplier (LM) test for GARCH, EGARCH, GJR-GARCH,VS-GARCH
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and QARCH model respectively. The Lagrange multiplier test is used to test the ARCH
effects. It is inferred from above results that no non linear and asymmetric ARCH effect
can be directly seen from the estimation of the L-M test for GARCH,EGARCH, GJR-
GARCH,VS-GARCH and QARCH model respectively. This initial inspiration indicates
that nonlinear models may not perform better than linear ones. Table 9 to 13 regarding to
the estimates for GARCH, GJR-GARCH, EGARCH, VS-GARCH and QGARCH. Table
9 reports results for GARCH model that the coefficient of the conditional mean equation
is significant at p<0.0001 with the exception of SS. ARCH term is significant at 95%
confidence interval indicating that past price behavior influence current volatility in all
markets. The GARCH term is also significant at 95% confidence interval which reports
the presence of persistence in volatility. Moreover the coefficient for lagged stock returns
show significance at p<0.05,. The coefficient of ψ1 and φ1 are statistically significant at
p<0.0001 representing that the hypothesis regarding to the constant variance model is
rejected. Table 10 reports the parameter estimates of the EGARCH (1,1). EGARCH
model is used to study the asymmetric behavior of the prices. The results indicate that
there exists persistence of volatility as coefficient λ1 is significant. The significant value
of φ1 indicates that asymmetric behavior exists in the markets. Similarly size effect is
visible from significant value of φ1. It means big change in price creates more volatility
in compare to small change in price. Table 11 reports the parameter estimates of the GJR-
GARCH (1,1). GJR-GARCH Model is used to study the asymmetric behavior of the
market. Ψ is significant and positive which indicates that past price behavior influences
current price volatility. The significant value of β indicates that the volatility once
created persistence and contributes in the volatility of next period. The ω is found
significant and persistent which shows that asymmetric behavior exist in market. It
means bad news has more affect than good news. Market response is higher for bad news
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in compare to good news. Table 12 reports the parameter estimates of the VS-GARCH
(1,1). Variance equation indicates that α is asymmetric and p-value is indicating that past
previous behavior influence current volatility. β is significant and reports persistence of
volatility in the market. It means volatility created in one period is continued in
subsequent periods. Coefficient of λ indicates asymmetric behavior in the market. The
traditional (ARCH) models cannot handle such facts. Table 13 reports the estimates of
QARCH model the significant negative values of the parameter λ for all markets
except JCI. This indicates that nonlinearity exist with reference to past price
behavior. The performance of the forecasting is judged by using Root Mean Square
Error approach. Table 14 indicates the Forecasting Performance of Linear and Nonlinear
Models of the Volatility of Stock Returns. These models are ranked on the basis of
minimum value of RMSE value for first, second to onward. In linear models the
MA (1) model out performs all the others in an out-of-sample forecasting exercise
for all stock returns on the basis of RMSE criterion. The AR (1) and Random Walk
Model appear as second best model and the exponential smoothing model is ranked
last. Within nonlinear models, the GJR-GARCH model is ranked top for KSE, DSE
and SS. No doubt GJR-GARCH model is dominated over EGARCH (1,1) and
GARCH Model for this time period on the basis of RMSE criteria. It is interesting
to note that the ARCH model is ranked top for JCI and KLSE. GJR-GARCH(1,1)
model is ranked second for these markets. For BSE, EGARCH (1,1) model beating
all other model in ranking in an out-of-sample forecasting when the forecasting for
whole period. Table 15 provides results of Correlation among Stock Returns. Stock
return correlations indicate that how the returns are associated among these equity
markets. SS has highest degree of positive correlation with KLSE, BSE and JCI but not
quite significant. BSE has highest degree of correlation with JCI and KLSE, significant at
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p<0.05. Whereas JCI has highest correlation with KLSE significant at p<0.05 and KSE
has positive correlation with BSE but not quite significant however it indicates that the
returns are moving these two economies in one direction. Table 16 presents Conditional
Volatility Correlations among equity markets. Conditional volatility based upon GARCH
Model, correlations indicate that how the conditional volatility is associated among the
equity markets. The volatility of SS is positively correlated with the volatility of BSE and
JCI at p<0.05 but negatively correlated with DSE. However there is high degree of
positive association among the volatility of BSE and JCI significant at p<0.05 but
negative correlation exist between BSE and DSE. Even JCI and DSE has also negative
correlations but not significant. Where there is high degree of relationship among the
conditional volatilities of equity markets that indicates that shock behave in same
direction in these equity markets except the behavior of DSE with SS, BSE and JCI.
Table 17(a) indicates that GARCH in mean model is extended with the macroeconomic
variables in the equation for SS. The conditional mean is significant at p < 0.10. So far
as macroeconomic variables are concerned, inflation is significantly related to return
indicating the presence of short term liquidity effect. Similarly, Oil prices change has
significant negative effect on return and increase in oil price decreases returns of stocks.
Table 17(b) results indicate that inflation is significant positively related to volatility. In
high periods of inflation, volatility is on high side, change in oil prices has also significant
impact on volatility. Table 18(a) reports the role of bullish and bearish market.
θ1 value is quite significant and positive which shows that returns are higher in bullish
period. Model is used to study the asymmetric behavior of the market.
θ1 is significant and positive which indicates that past price behavior influences current
price volatility. The significant value of δ indicates that the volatility once created
persistence and contributes in the volatility of next period. The γ1 found significant and
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persistent which shows that asymmetric behavior exist in market. Results in Table 18(b)
indicate that the negativity of μ1 in bullish effect indicates that volatility in the bullish
market is less than the volatility in bearish market. Table 19 indicates that the
asymmetric effect is captured by the parameter estimate θ which is positive and
significant in the TGARCH (1, 1) that Indicates the existence of leverage effect and it is
apparent that good news has an impact of 0.04128 magnitudes for SS and bad news has
an impact of (0.048128+0.916989 = 0.965117). Because the leverage effect is
significant and hence it is concluded that the bad news increases higher volatility in SS
more than good news. Table 20 results indicate that the γ is insignificantly related to
return. It is inferred that VaR is not significantly related to the returns of SS market.
ARCH term is significant at 95% confidence interval indicating that past price behavior
influence current volatility in the market. The GARCH term is significant at 95%
confidence interval which reports the presence of persistence in the volatility. It indicates
that the value at risk is positive but not significant and has no effect on the price behavior.
Table 21 indicates that semi-variance is significant at p<0.0001 and indicates that results
indicate that as down side risk increases, return also increases. The results indicate that
ARCH term and GARCH term are significant at p<0.0001. Here all the variables for
variance equation are statistically significant and the value of the semi-variance is
positive which means if the semi-variance increases it causes to an increase in the return.
Table 22(a) indicates that GARCH in mean model is extended with the macroeconomic
variables in the variance equation for BSE. The conditional mean is not significant. So
far as macroeconomic variables are concerned, inflation has significant negative effect on
return and increase in inflation decreases returns of stocks. Table 22(b) indicates the
impact of macroeconomic variables on volatility of market has also been exercised. The
results indicate that inflation is significant positively related to volatility. In high periods
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of inflation, volatility is on high side, change in interest rate has negative significant
impact on volatility. Similarly change in industrial production has also negative
significant impact on volatility. Therefore in the period of rising prices volatility is lower
it may be due to anchoring. However oil price change has positive significant impact on
volatility. Due to high positive change in oil prices volatility is on high side. Table 23(a)
reports the role of bullish and bearish market behavior in BSE .
θ1 value is significant and positive which shows that returns are higher in bullish period.
Model is used to study the asymmetric behavior of the market.
θ1 is significant and positive which indicates that past price behavior influences current
price volatility. The significant value of δ indicates that the volatility once created
persistence and contributes in the volatility of next period. The γ1 found significant and
persistent which shows that asymmetric behavior exist in market. Results in Table 23(b)
indicate that the negativity of μ1 in bullish effect indicates that volatility in the bullish
market is less than the volatility in bearish market. It means that in bullish market return
are high and volatility is low which offer better risk return relationship. The estimation
result of TGARCH (1,1) models are shown in Table 24 for BSE. The conditional
mean is significant for TGARCH(1,1) at p<0.10 that indicates persistence in volatility
for long run and hence stable indicator of an integrated process. ARCH and GARCH
terms are significant at p<0.0001. The asymmetric effect captured by the parameter
estimate θ is positive and significant in the TGARCH (1, 1) that indicate the existence
of leverage effect. After finding the presence of leverage effects in the series by using
TGARCH (1,1). From the estimated TGARCH model, it is apparent that good news has
an impact of 0.064636 magnitudes for BSE and bad news has an impact of
(0.064636+0.854005 = 0.918641). Because the leverage effect is significant and hence
it is concluded that the bad news increases higher volatility in BSE more than good
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news. Table 25 results indicate that the γ is negatively related to return significantly. It is
inferred that VaR is significantly negatively related to the returns of BSE market. ARCH
term is significant at 95% confidence interval indicating that past price behavior influence
current volatility in the market. The GARCH term is significant at 95% confidence
interval which reports the presence of persistence in the volatility. It indicates that the
value at risk is negative and has effect on the price behavior. Table 26 indicates the
relationship of return, and the Semi-variance. GARCH Model is extended with the Semi-
variance. Semi-variance is downside risk and added into variance equation. Here semi-
variance is insignificant which indicates no such effect. The results indicate that ARCH
term and GARCH term are significant at p<0.00001. Here all the variables for variance
equation are statistically significant. The value of the semi-variance is negative but
insignificant. Table 27(a) indicates that GARCH in mean model is extended with the
macroeconomic variables in the variance equation for JCI. The conditional mean is not
significant. So far as macroeconomic variables are concerned, change in interest rate has
significant negative effect on return and increase in interest rate decreases returns of
stocks. Model is selected on the basis of AIC, SIC, and Log Likelihood values. Table
27(b) indicates the impact of macroeconomic variables on volatility of JCI market. The
results indicate that GARCH term is significant but no macroeconomic variable have
significant impact on volatility. Table 28(a) reports the role of bullish and bearish market
behavior in JCI.
θ1value is significant and positive which shows that returns are higher in bullish period.
Model is used to study the asymmetric behavior of the market.
θ1 is significant and positive which indicates that past price behavior influences current
price volatility. The significant value of δ indicates that the volatility once created
persistence and contributes in the volatility of next period. The γ1 found significant and
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persistent which shows that asymmetric behavior exist in market. Results in Table 28(b)
indicate that the negativity of μ1 in bullish effect indicates that volatility in the bullish
market is less than the volatility in bearish market. It means that in bullish market return
are high and volatility is low which offer better risk return relationship. The estimation
result of TGARCH (1, 1) models for JCI are shown in Table 29. The conditional mean
is significant for TGARCH(1,1) that indicates persistence in volatility for long run
and hence stable indicator of an integrated process. ARCH and GARCH terms are
significant at p<0.01 and p<0.0001 respectively. The asymmetric effect captured by
the parameter estimate θ is positive and significant in the TGARCH (1, 1) that indicate
the existence of leverage effect. From the estimated TGARCH model, it is apparent that
good news has an impact of 0.038811 magnitudes for JCI and bad news has an impact
of (0.038811+0.8019 = 0.840711). Because the leverage effect is significant and hence
it is concluded that the bad news increases higher volatility in JCI more than good news.
Table 30 indicates the relationship of return and the value at risk. GARCH Model is
extended with the Value at Risk in mean equation. The results indicate that the γ is
negatively related to return significantly. It is inferred that VaR is significantly negatively
related to the returns of JCI market. ARCH term is significant at 95% confidence interval
indicating that past price behavior influence current volatility in the market. The ARCH
and GARCH term is significant at 95% confidence interval which reports the presence of
persistence in the volatility. It indicates that the value at risk is negative and has effect on
the price behavior. Table 31 indicates semi-variance is significant at p<0.0001 and
indicates that results indicate that as down side risk increases, return also increases. The
results for JCI indicate that ARCH term and GARCH term are significant at p<0.0001.
Here all the variables for variance equation are statistically significant and the value of
the semi-variance is positive which means if the semi-variance increases it causes to an
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increase in the return. Table 32(a) indicates that GARCH in mean model is extended with
the macroeconomic variables in the variance equation for DSE. The conditional mean is
not significant. So far as macroeconomic variables are concerned, No variable has
significant effect on return. Table 32(b) indicates that the conditional mean is significant
at p < 0.10 for DSE. The results indicate that change in industrial production is
significant positively related to volatility. In high growth period of industrial production,
volatility is on high side, Therefore in the period of high industrial production volatility is
higher it may be due to anchoring. Table 33(a) reports the role of bullish and bearish
market behavior in DSE.
θ1 value is significant and positive which shows that returns are higher in bullish period.
Model is used to study the asymmetric behavior of the market.
θ1 is significant and positive which indicates that past price behavior influences current
price volatility. The significant value of δ indicates that the volatility once created
persistence and contributes in the volatility of next period. The γ1 found significant and
persistent which shows that asymmetric behavior exist in market. Results in Table 33(b)
indicate that the negativity of μ1 in bullish effect indicates that volatility in the bullish
market is less than the volatility in bearish market. It means that in bullish market return
are high and volatility is low which offer better risk return relationship. The estimation
result of TGARCH (1, 1) models is shown in Table 34. The conditional mean is
significant for TGARCH(1,1) that indicates persistence in volatility for long run and
hence stable indicator of an integrated process. The asymmetric effect captured by the
parameter estimate θ is positive and significant in the TGARCH (1, 1) that indicate the
existence of leverage effect. After finding the presence of leverage effects in the series by
using TGARCH (1,1). However results indicated that TGARCH(1,1) model can be a
potential representative of the asymmetric conditional volatility process for the daily
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return series of DSE. From the estimated TGARCH model, it is apparent that good news
has an impact of 0.248296 magnitudes for DSE and bad news has an impact of
(0.248296+0.691989 = 0.940285). Because the leverage effect is significant and hence
it is concluded that the bad news increases higher volatility in DSE more than good
news. Table 35 indicates the relationship of return and the value at risk. GARCH Model
is extended with the Value at Risk in mean equation. The results indicate that the γ is
negatively related to return significantly. It is inferred that VaR is significantly negatively
related to the returns of DSE market. ARCH term is significant at 95% confidence
interval indicating that past price behavior influence current volatility in the market. The
GARCH term is significant at 95% confidence interval which reports the presence of
persistence in the volatility. It indicates that the value at risk is negative and has effect on
the price behavior. Table 36 indicates the relationship of return, and the Semi-variance.
GARCH Model is extended with the Semi-variance. Semi-variance is downside risk and
added into variance equation. Here semi-variance is insignificant which indicates no such
effect. The results indicate that ARCH term and GARCH term are significant at
p<0.00001. Here all the variables for variance equation are statistically significant. The
value of the semi-variance is negative but insignificant. Table 37(a) indicates that
GARCH in mean model is extended with the macroeconomic variables in the variance
equation for KLSE. The conditional mean is not significant. So far as macroeconomic
variables are concerned, oil price has significant positive effect on return and increase in
change in oil price increases returns of stocks. Table 38(a) reports the role of bullish and
bearish market behavior in KLSE. θ value is significant and positive which shows that
returns are higher in bullish period. θ is significant and positive which indicates that past
price behavior influences current price volatility. The significant value of δ indicates that
the volatility once created persistence and contributes in the volatility of next period. The
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γ1 found significant and persistent which shows that asymmetric behavior exist in market.
Results in Table 38(b) indicate that the negativity of μ1 in bullish effect indicates that
volatility in the bullish market is less than the volatility in bearish market. The
estimation result of TGARCH (1, 1) models for KLSE is shown in Table 39. The
conditional mean is significant for TGARCH(1,1) that indicates persistence in
volatility for long run and hence stable indicator of an integrated process. The
asymmetric effect captured by the parameter estimate θ is positive and significant in
the TGARCH (1, 1) that indicate the existence of leverage effect. After finding the
presence of leverage effects in the series by using TGARCH (1,1) the SIC were used to
select the best model for returns series. From the estimated TGARCH model, it is
apparent that good news has an impact of 0.015143 magnitudes for KLSE and bad news
has an impact of (0.015143+0.657546 = 0.672689). Because the leverage effect is
significant and hence it is concluded that the bad news increases higher volatility in
KLSE more than good news. Table 40 indicates that the γ is negatively related to return
significantly. It is inferred that VaR is significantly negatively related to the returns of
KLSE market. ARCH term is significant at 95% confidence interval indicating that past
price behavior influence current volatility in the market. The GARCH term is significant
at 95% confidence interval which reports the presence of persistence in the volatility. It
indicates that the value at risk is negative and has effect on the price behavior. Table 41
indicates the relationship of return, and the Semi-variance. GARCH Model is extended
with the Semi-variance. Semi-variance is downside risk and added into variance
equation. Here semi-variance is significant at p<0.0001 and indicates that results indicate
that as down side risk increases, return also increases. The results indicate that ARCH
term and GARCH term are significant at p<0.0001. Here all the variables for variance
equation are statistically significant and the value of the semi-variance is positive which
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means if the semi-variance increases it causes to an increase in the return. Table 42(a)
indicates that GARCH in mean model is extended with the macroeconomic variables in
the variance equation for KSE. The conditional mean is not significant. So far as
macroeconomic variables are concerned, change in interest rate has significant negative
effect on return and increase in change in interest rate decreases returns of stocks. Table
42(b) indicates the impact of macroeconomic variables on volatility of the market has
also been exercised. The results indicate that inflation is significant positively related to
volatility. In high periods of inflation, volatility is on high side. Therefore in the period
of rising prices volatility is lower it may be due to anchoring. However oil prices change
has negative significant impact on volatility. Table 43(a) reports the role of bullish and
bearish market behavior in KSE .
θ1 value is significant and positive which shows that returns are higher in bullish period.
Model is used to study the asymmetric behavior of the market.
θ1 is significant and positive which indicates that past price behavior influences current
price volatility. The significant value of δ indicates that the volatility once created
persistence and contributes in the volatility of next period. The γ1 found significant and
persistent which shows that asymmetric behavior exist in market. Results in Table 43(b)
indicate that the negativity of μ1 in bullish effect indicates that volatility in the bullish
market is less than the volatility in bearish market. It means that in bullish market return
are high and volatility is low which offer better risk return relationship. The estimation
result of TGARCH (1, 1) models is shown in Table 44. The conditional mean is
significant for TGARCH(1,1) that indicates persistence in volatility for long run and
hence stable indicator of an integrated process. The asymmetric effect captured by the
parameter estimate θ is positive and significant in the TGARCH (1, 1) that indicate the
existence of leverage effect and it is apparent that good news has an impact of 0.083396
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magnitudes for KSE and bad news has an impact of (0.083396+0.778899 = 0.862295).
Because the leverage effect is significant and hence it is concluded that the bad news
increases higher volatility in KSE more than good news. Table 45 indicates that the γ is
negatively related to return significantly. It is inferred that VaR is significantly negatively
related to the returns of KSE market. ARCH term is significant at 95% confidence
interval indicating that past price behavior influence current volatility in the market. The
GARCH term is significant at 95% confidence interval which reports the presence of
persistence in the volatility. It indicates that the value at risk is negative and has effect on
the price behavior. Table 46 indicates the relationship of return, and the Semi-variance.
GARCH Model is extended with the Semi-variance. Semi-variance is downside risk and
added into variance equation. Here semi-variance is insignificant which indicates no such
effect. The results indicate that ARCH term and GARCH term are significant at
p<0.00001. Here all the variables for variance equation are statistically significant. The
value of the semi-variance is negative but insignificant. Table 47 indicates the summary
of diagnostic test for all equity markets. AIC, SIC and Log likelihood values are used to
select the model that may best model the conditional mean and conditional variance for
these equity markets in a best way. First of all for model 1(a), KSE, JCI and BSE market
has lower values for AIC, SIC, Log Likelihood and it indicates that the conditional mean
can be modeled in these economies for asset pricing in a best way along with the
extension of macroeconomic variables. For Model 1(b) AIC, SIC and Log likelihood
values are used to select the model that may best model the conditional variance for these
equity markets in a best way. SS,BSE, KLSE and KSE market has lower absolute values
for AIC, SIC, Log Likelihood and it indicates that the conditional variance can be
modeled in these economies for asset pricing in a best way along with the extension of
macroeconomic variables. However the performance of the model 1(b) cannot be
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rejected for other economies as well. The diagnostic test for model 2(a) mean equation
indicate that the conditional variance can be modeled in a preeminent way for SS, BSE,
KSE and JCI markets respectively along with asymmetric market conditions. However
the performance of this model cannot be rejected for other economies as well. The
conditional variance equation of Model 2(a) variance indicates that SS, BSE, JCI and
KSE have lower absolute values and performing well in capturing the variance. Moreover
Model 2(b) also ensures that the Good News and Bad News effect can be modeled for SS,
BSE, JCI and KSE in an excellent way based upon diagnostic test value. Further Model 3
ensures that BSE JCI and DSE can be modeled along with VaR to explain the risk return
relationship in these economies. Finally Model 4 is performing the best for KSE, BSE,
JCI and SS to capture the return in these markets along with the semi-variance.
The summarized results of the study elaborate the empirical evidences regarding to the
models for EAGLEs and NEST markets.
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CHAPTER 5
CONCLUSION
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5. CONCLUSION
This study investigates different linear and nonlinear models for the conditional variance
in first instance. It compares linear and non-linear models and identified the model that
best performs in forecasting the return and volatility dynamics in EAGLEs and NEST
markets. The study also tests the robustness of model for out-of-sample volatility forecast.
The study investigates the comparative capability of various linear and nonlinear models
so that a model can be identified for the asset pricing which can perform better to absorb
the volatility effect. The study covers the period from 4th January 2000 to 30th December
2010. The results of estimations for sign-bias test (SB), negative size-bias test
(NSB) and positive size-bias test (PSB) for SS, BSE, JCI, DSE, KLSE, and KSE
indicates that there exists negative sign bias (NSB) and positive sign bias (PSB) for
all the equity markets except KLSE. This initial element indicates that nonlinear
models have some support. Results indicate that asymmetry exist and can be
observed in the returns series. Coefficients and p-values for sign-bias test, negative
size-bias test and positive size bias test for the equity returns are reported at
P<0.05. The estimation of the negative size bias test indicates that negative
asymmetry can be seen in the returns series. The result of the positive size-bias test
on the other hand, generating significant estimates for the KSE, BSE, DSE SS and
JCI and indicates towards positive asymmetry regarding to these equity markets.
However, for the KLSE market, the hypothesis of positive asymmetries is rejected.
In the same way the results of the negative size-bias test, generates significant
estimates for the KSE, BSE, KLSE SS and JCI and indicates towards negative
asymmetry regarding to these equity markets.
However, for the DSE, the hypothesis of negative asymmetries is rejected. It is
hence concluded that due to sign and size bias test, non linear patterns are expected
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and being observed because the return series indicates asymmetric patterns. Further
Lagrange Multiple test for ARCH effects is conducted to further investigate this
matter. The LM-test is performed for all six markets, and for different model
specifications. It is inferred from above results that no nonlinear and asymmetric
ARCH effects is proved.
The forecasting models includes random walk, autoregressive, moving average,
exponential smoothing and nonlinear ARCH-class models including GARCH,
EGARCH, GJR-GARCH, VS-GARCH and QGARCH models. The estimates of
GARCH model indicates that ARCH term is significant at 95% confidence interval
indicating that past price behavior influence current volatility in all markets. The
GARCH term is also significant at 95% confidence interval which reports the presence of
persistence in volatility. Moreover the coefficient for lagged stock returns show
significance at p<0.05, it indicates that the lagged volatility has impact on current
volatility representing that the hypothesis regarding to the constant variance is rejected.
EGARCH model is used to study the asymmetric behavior of the prices. The results
indicate that there exists persistence of volatility as coefficient λ1 is significant. The
significant value of φ1 indicates that asymmetric behavior exists in the markets. The
response of volatility is adjusting for good and bad news. Bad news creates more
volatility in compare to good news. Similarly size effect is visible from significant value
of φ1. It means big change in price creates more volatility in compare to small change in
price. GJR-GARCH Model is used to study the asymmetric behavior of the market. Ψ is
significant and positive which indicates that past price behavior influences current price
volatility. The significant value of β indicates that the volatility once created persistence
and contributes in the volatility of next period. The ω is found significant and persistent
which shows that asymmetric behavior exist in market. It means bad news has more
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affect than good news. Market response is higher for bad news in compare to good news.
In VS-GARCH (1,1) variance equation indicates that α is asymmetric and p-value is
indicating that past previous behavior influence current volatility. β is significant and
reports persistence of volatility in the market. It means volatility created in one period is
continued in subsequent periods. Coefficient of λ indicates asymmetric behavior in the
market. Poon and Granger (2003) indicated that regime switching models have fascinated
interest recently from the financial markets and reacted divergently to large and small
shocks. The traditional (ARCH) models cannot handle such facts. The estimates of
QARCH model indicates that nonlinearity exist with reference to past price
behavior. It can be observed that the parameter ψ is larger than the parameter λ for
all series. When this situation holds (ψ>λ), negative reactions contributes a greater
effect on the conditional variance, instead of positive shocks of the same size. The
parameters estimates of the GJR-GARCH indicate that nonlinear model better than
the linear ones. The results for the Volatility-Switching GARCH model show
similar results. The co-efficient parameter ψ is positive for all return series and is
larger than the parameter λ. These findings indicate that small positive shocks have
a larger impact on the conditional volatility than small negative shocks; however
when the reactions are greater in size, then the effect on volatility is in opposite
direction. This element elaborates that large positive shocks contributes to a
smaller increase in volatility rather than large shock is negative and confirms H2
The results of Asymmetric GARCH model indicate that there exists leverage
effect in these economies and the impact of news is asymmetric. It shows that
equity market volatility increases with bad news and leads towards lowering the
stock returns. It suggests that negative innovations found in returns lead towards
positive innovations in the volatility level. It is concluded for all the equity
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markets that the conditional volatility increases in a higher proportions immediate
after the negative innovations. All theses above discussed facts confirms the H1,
H2 and H3 for this study. This element is also found in this study that it is
consistent with the volatility feedback proposition as reported by Tripathy and
Garg (2013). It is observed that among linear models of stock return volatility, the
MA(1) i s r an ked first using the RMSE criterion and in nonlinear models, the
ARCH ,GJR-GARCH, GARCH(1, 1) model and EGARCH (1, 1) model perform
well and results are closer to each other. AIC, Schwarz and Log Likelihood
method conclude that GARCH model outperforms all other model. So it is
concluded that GARCH specification is best in performance to capture the
volatility. The study confirms H4 that that non-linear models outperforms than the
linear models in volatility forecasting. Within nonlinear models, the GJR-GARCH
model is ranked top for KSE, DSE and SS. No doubt GJR-GARCH model is
dominated over EGARCH (1,1) and GARCH(1,1) Model for this time period on the
basis of RMSE criteria. It is interesting to note that the ARCH model is ranked top
for JCI and KLSE. GJR-GARCH(1,1) model is ranked second for these markets.
For BSE, EGARCH (1,1) model beating all other model in ranking in an out-of-
sample forecasting when the forecasting for whole period. After comparison of
linear and nonlinear models, it is found that that the GJR-GARCH-model clearly
stands first and outperforms all the models during the whole volatility periods.
Even though non-linear models dominate the linear models because the nonlinear
models superiority is due to the ability to capture nonlinear patterns that can be
expected because the return series shows asymmetric patterns. It is concluded that
overall GARCH model outperforms among all the other models due to the best
ability to explain the conditional volatility where there is high degree of relationship
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among the conditional volatilities of equity markets that indicates that shock behave in
same direction in these equity markets except the behavior of DSE with SS, BSE and JCI.
It is therefore concluded that the movement of volatility in EAGLEs markets have
positive degree of relationship that determines that how the positive and negative news or
shocks behave in these markets, however the volatility movements in NEST markets is
less correlated. It is clear that the returns association does not mean the volatility
associations. However if volatilities are associated it can be inferred that returns are
associated. So volatility modeling has its own unique attribution.
Further GARCH in mean model is extended with i.e. macroeconomic variables
for SS, BSE, JCI, DSE, KLSE and KSE. The macroeconomics variable includes CPI,
Term Structure of interest rate, industrial production and oil prices. Data for
Macroeconomic variable is on monthly basis for the period Jan 2000 to Dec 2010.
Impact of macroeconomic variable on return and volatility is tested in mean and variance
equation simultaneously. Impact of macroeconomic variable on return equation indicates
that for SS market, the conditional mean is significant. So far as macroeconomic variables
are concerned, inflation is significantly related to return indicating the presence of short
term liquidity effect. Similarly, Oil prices change has significant negative effect on return
and increase in oil price decreases returns of stocks. Impact of macroeconomic variable
on volatility equation for SS market indicates that inflation is significant positively related
to volatility. In high periods of inflation, volatility is on high side, change in oil prices has
also significant impact on volatility. In the period of rising prices volatility is lower it may
be due to anchoring. Impact of macroeconomic variable on return equation indicates that
for BSE the conditional mean is not significant. So far as macroeconomic variables are
concerned, inflation has significant negative effect on return and increase in inflation
decreases returns of stocks.
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The impact of macroeconomic variables on volatility of market has also been observed
for BSE. The results indicate that inflation is significantly positively related to volatility.
In high periods of inflation, volatility is on high side, change in interest rate has negative
significant impact on volatility. Similarly change in industrial production has also
negative significant impact on volatility. Therefore in the period of rising prices volatility
is lower it may be due to anchoring. However oil price change has positive significant
impact on volatility. Due to high positive change in oil prices volatility is on high side.
GARCH in mean model is extended with the macroeconomic variables in the variance
equation for JCI. The conditional mean is not significant. So far as macroeconomic
variables are concerned, change in interest rate has significant negative effect on return
and increase in interest rate decreases returns of stocks. The impact of macroeconomic
variables on volatility of JCI market is exercised and the results indicate that GARCH
term is significant but no macroeconomic variable have significant impact on volatility.
GARCH in mean model is extended with the macroeconomic variables in the variance
equation for DSE. The conditional mean is not significant. So far as macroeconomic
variables are concerned, No variable has significant effect on return. The impact of
macroeconomic variables on volatility of market has also been exercised. The conditional
mean is significant at p < 0.10. The results indicate that change in industrial production is
significant positively related to volatility. In high growth period of industrial production,
volatility is on high side, Therefore in the period of high industrial production volatility is
higher it may be due to anchoring. GARCH in mean model is extended with the
macroeconomic variables in the variance equation for KLSE. The conditional mean is
not significant. So far as macroeconomic variables are concerned, oil price has significant
positive effect on return and increase in change in oil price increases returns of stocks.
142
The impact of macroeconomic variables on volatility of KLSE has also been observed.
Change in industrial production has also positive significant impact on volatility.
Therefore in the period of high industrial growth volatility is on high side.
GARCH in mean model is extended with the macroeconomic variables in the variance
equation for KSE. The conditional mean is not significant. So far as macroeconomic
variables are concerned, change in interest rate has significant negative effect on return
and increase in change in interest rate decreases returns of stocks. The impact of
macroeconomic variables on volatility of KSE market has also been exercised. The
results indicate that inflation is significantly positively related to volatility. In high
periods of inflation, volatility is on high side. Therefore in the period of rising prices
volatility is lower it may be due to anchoring. However oil prices change has negative
significant impact on volatility. It is concluded that macroeconomic variables are
significant parameters for explaining the returns of stock as well as volatility in these
markets. Hence it is proved that Macroeconomic variables are significant information
parameter for modeling the volatility in these economies and confirms to H6
Further the role of bullish and bearish market is tested in all the equity market. θ value is
quite significant and positive which shows that returns are higher in bullish period.
Model is used to study the asymmetric behavior of the market. θ is significant and
positive which indicates that past price behavior influences current price volatility. The
significant value of δ indicates that the volatility once created persistence and contributes
in the volatility of next period. The γ1 found significant and persistent which shows that
asymmetric behavior exist in market for EAGLE’S and NEST markets.
Moreover results indicate that the negativity of μ1 in bullish effect indicates that volatility
in the bullish market is less than the volatility in bearish market. It means that in bullish
market return are high and volatility is low which offer better risk return relationship in
143
the equity markets of SS, BSE, JCI, DSE, KLSE and KSE. This study accepts H5 of
study that information asymmetries have impact on return and volatility.
TGARCH (1,1) model is estimated for SS, BSE, JCI, DSE, KLSE and KSE returns
series by using Gaussian standard normal distribution. The significant θ indicates
persistence in volatility for long run and hence stable indicator of an integrated
process for SS, BSE, JCI, DSE, KLSE and JCI market. The asymmetric effect
captured by the parameter estimate θ is positive and significant in the TGARCH (1, 1)
that indicates the existence of leverage effect. The leverage effect is significant and hence
it is concluded that the bad news increases higher volatility in all these markets more
than good news. However results indicated that TGARCH (1,1) model can be a
potential representative of the asymmetric conditional volatility process for the daily
return series of SS, BSE, JCI, DSE, KLSE and JCI and confirms H2 and H3
Further the relationship of return and the value at risk is explored for all the equity
markets. GARCH Model is extended with the Value at Risk in mean equation. It is
concluded that that the γ is insignificantly related to return and it is inferred that VaR is
not significantly related to the returns of SS market. Whereas the results for BSE market
indicate that the γ is negatively related to return significantly and it is inferred that VaR is
significantly negatively related to the returns of BSE market. Moreover the results
indicate that the γ is negatively related to return significantly and hence it is inferred that
VaR is significantly negatively related to the returns of JCI market. Further GARCH
Model is extended with the Value at Risk in mean equation for DSE market. The results
indicate that the γ is negatively related to return significantly. It is inferred that VaR is
significantly negatively related to the returns of DSE market. GARCH Model is extended
with the Value at Risk in mean equation. The results indicate that the γ is negatively
related to return significantly. It is inferred that VaR is significantly negatively related to
144
the returns of KLSE market. GARCH Model is extended with the Value at Risk in mean
equation. The results indicate that the γ is negatively related to return significantly. It is
inferred that VaR is significantly negatively related to the returns of KSE market.
In last the relationship of return, and the Semi-Variance is explored for all the equity
markets. GARCH Model is extended with the Semi-variance. Semi-variance is downside
risk and added into variance equation. Here semi-variance is significant at p<0.0001 and
indicates that as down side risk increases, return also increases. The results indicate that
ARCH term and GARCH term are significant at p<0.0001. Here all the variables for
variance equation are statistically significant and the value of the semi-variance is
positive which means if the semi-variance increases it causes to an increase in the return
for SS, KLSE and confirms for H7. The coefficient value of the semi-variance is
negative but insignificant for BSE, JCI, KSE, DSE and rejects H7
AIC, SIC and Log likelihood values are used to select the model that may best model the
conditional mean and conditional variance for these equity markets in a best way. First of
all for model 1(a), KSE, JCI and BSE market has lower values for AIC, SIC, Log
Likelihood and it indicates that the conditional mean can be modeled in these economies
for asset pricing in a best way along with the extension of macroeconomic variables. For
Model 1(b) AIC, SIC and Log likelihood values are used to select the model that may
best model the conditional variance for these equity markets in a best way. SS,BSE,
KLSE and KSE market has lower absolute values for AIC, SIC, Log Likelihood and it
indicates that the conditional variance can be modeled in these economies for asset
pricing in a best way along with the extension of macroeconomic variables. However the
performance of the model 1(b) cannot be rejected for other economies as well. The
diagnostic test for model 2(a) mean equation indicate that the conditional variance can be
modeled in a preeminent way for SS, BSE, KSE and JCI markets respectively along with
145
asymmetric market conditions. However the performance of this model cannot be rejected
for other economies as well. The conditional variance equation of Model 2(a) variance
indicates that SS, BSE, JCI and KSE have lower absolute values and performing well in
capturing the variance. Moreover Model 2(b) also ensures that the Good News and Bad
News effect can be modeled for SS, BSE, JCI and KSE in an excellent way based upon
diagnostic test value. Further Model 3 ensures that BSE JCI and DSE can be modeled
along with VaR to explain the risk return relationship in these economies. Finally Model
4 is performing the best for KSE, BSE, JCI and SS to capture the return in these markets
along with the semi-variance.
Hence it is concluded that there exist a significant positive relationship between risk
and return in all the equity markets and confirms the H7. The emerging stock markets
follow asymmetric patterns not only in the variance, but also in the mean and prove the
hypothesis of the study. No doubt there exists asymmetry in the variance for emerging
markets and negative reactions increases volatility more than positive reactions in
emerging markets. Study further concludes that small positive shocks have a larger
impact on the conditional volatility than small negative shocks; however when the
reactions are greater in size, then the effect on volatility is in opposite direction.
This element elaborates that large positive shocks contributes to a smaller increase
in volatility rather than large shock is negative. The returns of emerging markets
follow asymmetric pattern in mean in which positive returns are followed by more
positive returns but negative returns revert to positive returns faster than positive
reverts to the negative returns. It provides that volatility influences returns in a non-
linear fashion and confirms to H8. Efficiency of the market is a question mark this
leads towards anomalous behavior in these economies. It is finally concluded that
volatility plays a significant role in pricing of financial assets in emerging economies.
146
Emerging market behavior for conditional volatility is modeled to estimate the riskiness
of financial assets at a certain period of time. The standard finance models can tested in
the perspective of behavioral finance to capture the conditional volatility for asset
pricing as well. Therefore it is advised to the investors that they may use investment
strategies by analyzing recent and historical news, information shocks and can forecast
the future market movements based upon these models and can use this information
for selecting optimal portfolio for efficient risk management to harvest stream of
benefits in these equity markets. It is finally concluded that the conditional
volatility modeling for asset pricing provides excellent solutions.
5.1 Implications of the Study
The equity market of each economy is performing differently regarding to their different goals
objective, risk forbearance, and their common interest in the financial market. Individual or group
of investors must have an understanding of the different cultures and political and legal status
before making international equity market investment to gain a potential level of leveraged
portfolio returns in that financial market. The major Implications of this study are that there
should be an equal level of importance to pay more consideration to the traverse effects of
political and financial policies among these emerging economies in order to support
influx of capital inflows and a safe business environment for all investment portfolios.
This study implicates that the investors in these economies should prefer non-linear
models to forecast returns. Moreover the study implicates that volatility has asymmetric
patterns so the investors must consider the market conditions asymmetries to forecast
returns. Further the study indicates that volatility is higher in unstable market than stable
one so the investors should be vigilant this dynamic. Macroeconomic variables play
significant role in explaining the volatility and return so these parameters should be part
of decision making. One of the most important implication of this study suggest that to
147
have a less impact of shocks on the stock returns and volatility, it is recommended that
there should be competent investors for the real application of financial strategy regarding
to the adjustment of the quantity for their portfolio in reaction to the shocks regarding to
the different factors. Moreover, an investor may lessen their risk while considering
investment strategy by taking those companies which have sound financial performance,
fundamentals and reasonable business models. Therefore investors may employ
investment strategies by interpreting each country economic factors, business
environment, market conditions asymmetries, past and present news and to project the
future equity market movements to harvest crop of benefits in the equity markets.
Other implications suggest that investors should also be advised to be more rational
towards satisfactory financial products and market information as well as best investment
guidance while selecting investment portfolios for the efficient and effective management
of equity market risks. Further this study implies that it is the crucial time that these
emerging economies have to reframe the equity market rules and regulations, Moreover it
is also necessary to reshape the institutional arrangement so that investors may be able to
achieve diversified portfolio returns. In future study the same model may be applied to
other emerging and developed markets so that generalizibility of the model can be
explored. Other macroeconomic variables may also be considered for modeling the asset
pricing mechanism.
148
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Web Resources:
http://en.wikipedia.org/wiki/Emerging_markets
http://www.sharegyan.com/investment-gyan/benefits-of-stock-market-volatility-714/
http://informationarbitrage.com/post/698392191/who-really-benefits-from-volatility
http://en.wikipedia.org/wiki/Volatility_(finance)
http://www.creb.org.pk/CurrrentResearchDetails.aspx?CRID=12
http://www.investopedia.com/terms/s/semivariance.asp#ixzz1ujNGLVvW
https://en.wikipedia.org/wiki/Emerging_and_growth-leading_economies
https://en.wikipedia.org/wiki/Emerging_markets#BBV_Research
APPENDICES:
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Figure 4: Trends of Equity Markets
Figure 2: Trend of KSE BSE and JCI
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Figure 3: Trend of KLSE SS and DSE
161
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Figure 4: Stock Returns of Equity Markets
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164
Figure 5: Conditional Volatility Plots for SS
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Figure 6: Conditional Volatility Plots for BSE
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Figure 7: Conditional Volatility Plots for JCI
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Figure 8: Conditional Volatility Plots for DSE
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Figure 9: Conditional volatility Plots for KLSE
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Figure 10: Conditional Volatility Plots for KSE