Weak-Form Efficiency in Karachi Stock Exchange; Evidence from Random Walk Hypothesis

A thesis submitted as the partial requirement for the degree of Doctor of Philosophy (Economics)

by Ms. Musarrat Shamshir

M.A.S. (Economics) Applied Economics Research Center, University of Karachi MSc. (Economics) University of Karachi

Department of Economics, Faculty of Social Sciences University of Karachi, Pakistan

February 2015

Declaration

I hereby declare that the thesis, entitled, “Weak-Form Efficiency in Karachi Stock Exchange; Evidence from Random Walk Hypothesis,” contains no such material that has been accepted for the award of any other degree or diploma at any university or equivalent institution and that, to the best of my knowledge and belief, this thesis contains no material previously published or written by another person, except where due reference is made in the text of the thesis.

This thesis includes two original papers published entitled, “Presence of Day-of-the-Week Effect in the Karachi Stock Market” and “Efficiency in stock markets; A review of literature”, in international peer reviewed journals. The subject matter of the thesis is based on weak-form efficiency of Karachi stock market. I am responsible for the idea and development of the thesis under the supervision of Prof. Dr. Khalid Mustafa.

Musarrat Shamshir February 12, 2015.

Department of Economics University of Karachi

February 14, 2015

Approval of PhD Thesis

This is to certify that Ms. Musarrat Shamshir, D/o Shamshir Ahmad (late) has completed her dissertation entitled “Weak-Form Efficiency in Karachi Stock Exchange; Evidence from Random Walk Hypothesis,” as the partial requirement for PhD degree, under my supervision. I allow her to submit her thesis for awarding the PhD degree under the set rules.

Prof. Dr. Khalid Mustafa Chairperson, Department of Economics University of Karachi.

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Dedication

I dedicate this thesis to my beloved parents (late), who believed in the richness of learning and had supported and encouraged me from the beginning of my studies.

This thesis is also dedicated to my dearest uncle; Professor, Dr. Manzoor Ahmad, Ex-Rector, International Islamic University, who gave me the stimulus to start my PhD studies. He has been a great source of inspiration and a stirring mentor to me throughout my life.

Acknowledgements

First and foremost, I am thankful to Almighty Allah for His countless blessings on me and for the strength, peace and hope to accomplish my objective.

I would like to express gratitude to my PhD supervisor Professor Dr. Khalid Mustafa for his expertise, understanding and dedicated guidance throughout the research work.

My sincere thanks also go to Dr. Shafiq ur Rehman, the Ex-Chairperson Department of Economics and Dr. Abuzar Wajdi for their encouragement and to Dr. Wali Ullah of IBA for his guidance and for the selection of econometric tools and procedures.

I would also like to thank Syed Khalid Hussain, Director Business Development, ABL Asset Management Company for his contribution in making the daily data for KMI-30 index from 2009-2011 available to me, which otherwise turned difficult to find.

Special thanks to Mirza Jawwad Baig, Assistant Professor, Institute of Space and Planetary Astrophysics, for his friendly support and scholastic guidance throughout my research work and publications.

I would like to thank my colleagues Khubaib Ahmad, Syed Ghayas Tahir, Aun Ali, Syed Muhammad Raza and Dr. Riaz Somroo for their co-operation.

My deepest gratitude goes to Prof. Dr. Mervyn Hosein, Ex-Principal Hamdard College of Dentistry; Dean Dentistry, Ziauddin University; for his enduring allure as a comforting and caring friend. He gave me strength and patience to continue my work especially when I was facing difficulties to manage the thesis writing with my time-bound job assignments. Without his intellectual and pedagogic stimulus, heartening spur and considerate behaviour it would not have been possible for me to complete my thesis.

I am grateful to my loving husband Adnan Zaheer for all the support and care without which I would not have been able to achieve this phase of my life. He helped me in every respect and stood by me throughout the journey of my career development. I want to thank my very dear brother Khalid Shamsher; my two affectionate elder sisters, Rashida and Khalida; my darling nieces and nephews for their continuous emotional support and love.

Abstract

The study is aimed at an empirical examination of the weak-form efficiency in Pakistani stock market within the framework of random walk hypothesis. The concept of weak-form efficiency of stock market initially was developed by Fama (1970), under the efficient market hypothesis (EMH), along with two other, strong and semi-strong forms. An efficient market is defined as where “stock prices fully reflect all available information. The efficiency of capital market is one powerful reason investors are so willing to invest in that market. Presence of even weakest form of efficiency in the stock market implies presence of random walk. The current study is based upon KSE, owing to its huge turnover as compared to the other stock exchanges in Pakistan. This particular study is based upon examining the four indices in the exchange and 43 companies selected on the basis of trading frequency of at least 95% days. The study adopted a triangular approach in methodology by using direct and indirect methods for exploring random walk. Directly random walk is tested by applying traditional tests; serial correlation, runs, Kolgomorov-Simirnov, autoregression, variance ratio and unit root tests and ARMA models. However, indirectly random walk is investigated by the presence of seasonal anomalies, volatility clustering, thin-trading and through non-linearity of return series. The empirical findings of the study conducted suggest that Karachi stock exchange does not exhibit weak-form efficiency and random walk for the majority of its firms and indices over the study period. The results reveal the presence of serial correlation and autocorrelation in the returns series of all indices and in most of the firms in the stock market. Similarly, stationary returns at level and non-stationary at difference also reveal the absence of random walk. Significant ARMA values also depict absence of random walk. Presence of anomalies and volatility clustering is found in majority of the indices and in firms. However, the study does support random walk in few of the selected firms and KSE-30 index and to some extent indication of random walk is found in KMI-30 index. Correspondingly, the absence of seasonal anomalies in KSE-30 and to some degree in KMI-30 index is credited to the free-floating methodology of shares in these indices. Similarly, the non-stationary return series of KSE-30 as depicted by unit root tests and GARCH models also supports the evidence of random walk in the index. Likewise, for variance ratio test and ARMA model the null hypothesis for random walk cannot be rejected for KSE-30 index. It is concluded therefore, that for KSE-30 index the evidence found in the study supports the weak-form efficiency. Hence, it can be said that KSE does not follow random walk with exception to KSE-30 index. Auxiliary research on KSE-30 index is however suggested by using a diversified approach and by analyzing weekly and monthly data for the corroboration of the results presented in the study.

Urdu Abstract

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Table of Content

Chapter 1 Introduction to the Thesis ...... 1 1.1 Introduction ...... 1 1.2 Objective and Focus ...... 3 1.3 Outline of the Thesis ...... 5 Chapter 2 Economics of Efficient Markets and Random Walk ...... 7 2.1 Concept of Efficient Market Hypothesis ...... 7 2.1.1 Weak-form market efficiency ...... 8

2.1.2 Semi-strong form market efficiency ...... 8

2.1.3 Strong-form market efficiency ...... 9

2.2 Relative Market Efficiency and Absolute Market Efficiency ...... 9 2.3 Concept of Evolving Market Efficiency...... 10 2.4 The Martingale Model ...... 10 2.5 The Random Walk Model ...... 11 2.5.1 Random walk 1 ...... 12

2.5.2 Random walk 2 ...... 13

2.5.3 Random walk 3 ...... 14

2.6 Importance of Efficient Market and RW Hypothesis on Economic Growth ...... 14 2.7 Deviation from EMH and Random Walk...... 14 2.7.1 Under-reaction and over-reaction ...... 15

2.7.2 Thin-trading...... 17

2.7.3 Calendar Anomalies ...... 17

2.7.3.1 Day-of-the-week effect ...... 17

2.7.3.2 Week-of-the-month effect ...... 18

2.7.3.3 Month-of-the year effect ...... 18

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2.7.3.4 Turn-of-the-month effect...... 18

2.7.4 Size Effect ...... 19

Cha pter 3 Ove rvie w a nd Pe rfo rma nce of Karachi Stock Exchange...... 20 3.1 Role and Importance of Stock Markets in Pakistan ...... 20 3.2 Overview of Pakistani Stock Market...... 21 3.3 Karachi Stock Exchange (KSE) ...... 22 3.4 Karachi Stock Market as Emerging Market ...... 22 3.5 Trading Products and Services ...... 22 3.6 Indices in KSE ...... 23 3.6.1 KSE-100 index ...... 23

3.6.2 KSE-all shares index ...... 24

3.6.3 KSE-30 index ...... 24

3.6.4 KMI-30 index ...... 25

3.7 Growth and Performance of KSE ...... 26 3.8 Demutualization Act, 2012...... 30 3.9 Linkages with the International F inancial Markets ...... 30 Chapter 4 Literature Review ...... 38 4.1 Introduction ...... 38 4.2 Empirical Evidence of Developed Financial Markets ...... 40 4.3 Empirical Evidence of Emerging Financial Markets ...... 43 4.3.1 East European Emerging Markets ...... 44

4.3.2 Latin American Emerging Markets ...... 45

4.3.3 African Emerging Markets ...... 46

4.3.4 Middle Eastern Emerging Markets ...... 48

4.3.5 Asian Emerging Markets ...... 50

4.3.5.1 Empirical Evidence of Pakistani Market...... 53

4.4 Conclusion ...... 56 ix

Table of Content

Chapter 5 Methodology for Examining Weak-form Efficiency ...... 59 5.1 Data Specification and Source...... 59 5.2 Stock Returns Vs Stock Prices ...... 59 5.3 Theory of Rational Expectations and Efficient Market Hypothesis...... 61 5.4 The Random Walk Hypothesis...... 62 5.5 Testing Tools ...... 63 5.5.1 Kolgomorov-Simirnov (K-S)Test ...... 64

5.5.2 Runs test...... 65

5.5.3 Autocorrelation test ...... 66

5.5.4 Autoregression, heteroscedasticity and Breusch-Godfrey (B-G) LM tests ...... 68

5.5.5 Unit root test ...... 69

5.5.5.1 Augmented Dickey-Fuller test ...... 69

5.5.5.2 Phillips-Parron test ...... 71

5.5.5.3 Kwiatkowski, Phillips, Schmidt and Shin test...... 71

5.5.6 Variance ratio test ...... 72

5.5.7 ARMA modeling...... 75

Chapter 6 Analysis and Results ...... 77 6.1 Descriptive statistics ...... 77 6.2 Result of Kolmogorov-Smirnov test ...... 78 6.3 Result of Runs Test ...... 79 6.4 Result of Autocorrelation Test ...... 80 6.5 Results of Autoregression Heteroscedasticity, and Breusch-Godfrey LM Tests ...... 81 6.6 Results of Unit Root Tests...... 82 6.6.1 Augmented Dickey-Fuller Test ...... 82

6.6.2 Phillips-Parron Test ...... 82

6.6.3 Kwiatkowski, Phillips, Schmidt and Shin Test...... 83

Table of Content

6.7 Result of Variance Ratio Test...... 83 6.8 Result of ARMA Models...... 84 Chapter 7 Volatility-Clustering and Random Walk...... 126 7.1 Nature of Volatility-Clustering...... 126 7.2 ARCH and GARCH Models ...... 126 7.3 Empirical Results...... 128 7.3.1 ARCH effect ...... 128

7.3.2 GARCH effect ...... 128

Chapter 8 Seasonal Anomalies ...... 138 8.1 Day-of-the-week Effect ...... 138 8.2 Month-of-the-year Effect...... 141 8.3 Turn-of-the-mo nth Effe ct ...... 143 8.4 Results and Analysis...... 144 8.4.1 Day-of-the-week effect ...... 144

8.4.2 Month-of-the-year effect ...... 144

8.4.3 Turn-of-the-month effect...... 145

Cha pter 9 Thin-Trading and Random Walk ...... 174 9.1 Thin-trading in Emergent Markets ...... 174 9.2 Thin-trading and Market Efficiency ...... 175 9.3 Non-linear trends in Returns and Thin-trading ...... 177 9.4 Results and Ana lys is ...... 179 Chapter 10 Conclusion and Recomme ndations ...... 196 10.1 Summary and Conclusion...... 196 10.2 Implication for the Investors ...... 201 10.3 Suggestions and Recommendations ...... 201 10.4 Limitations of the Thesis ...... 202 10.5 Suggestions for Future Research ...... 203 References ...... 210

Table of Content

List of Tables

Table Description Page

3.1 Decade-wise Market Summary of KSE 28

3.2 Annual Performance of Karachi Stock Exchange 32

6.1 Descriptive Statistics of Daily Returns of KSE indices and 86

Selected Firms

6.2a Result of Kolmogrove Smirov Test on Daily Returns with

Normal Distributio n 88

6.2b Result of Kolmogrove Smirov Test on Daily Returns with

Unifor m Distrib utio n 90

6.3 Result of Runs Test on Daily Returns 92

6.4 Result of Autocorrelation Test on Daily Returns 94

6.5 Results of Autoregression Model Heteroscedasticity and B-G

Tests on Daily Returns 110

6.6.1 Result of ADF Test on Daily Returns 114

6.6.2 Results of PP and KPSS Tests on Daily Returns 116

6.7 Result of Variance Ratio Test on Daily Closing Prices 118

6.8 ARMS Results on Daily Returns 122

7.1 ARCH Analysis on Daily Returns 130

7.2 GARCH Analysis on Daily Returns 136

8.1 Descriptive Statistics of Weekly Returns 147

8.2 OLS Results for day-or-the-week Analysis 150

8.3 Descriptive Statistics of Monthly Returns 156 xii

Table of Content

8.4 Descriptive Statistics of Monthly Returns 160

8.5 Descriptive Statistics of TOM and ROM Period Returns 166

8.6 OLS Results for Turn-of-the-month Analysis 170

9.1 Result of Linear Model for Adjusted Returns 181

9.2 Result of Non-linear Model for Non-adjusted Returns 186

9.3 Result of Non-linear Model for Adjusted Returns 191

10.1 Summary of the Results for Random Walk 204

10.2 Summary of the Results of Unit Root Test for

Random Walk 206

10.3 Significant Days/Months/TOM periods on KSE Returns 207

10.4 Number of Significant Days/Months/TOM Periods on

KSE Returns 209

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List of Figures

Description Page

Figure 3.1 KSE-100 Index from 2001-2014 34

Figure 3.2 KSE-All Share Index from 2001-2014 34

Figure 3.3 KSE-30 Index from 2001-2014 35

Figure 3.4 KMI-30 Index from 2001-2014 35

Figure 3.5 Market Capitalization of KSE from 2001-2014 36

Figure 3.6 Number of New Listed firms in KSE from 2001-2014 36

Figure 3.7 Total Share Volume on KSE from 2001-2014 37

Figure 3.8 Average Daily Share on KSE from 2001-2014 37

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List of Abbreviations

List of Abbreviations ABL Allied Bank Limited ABOT Abbot Laboratories AICL Adamjee Insurance AKBL Askari Bank Ltd APL Attock Petrol Ltd ATRL Attock Refinery Ltd BAFL Bank Al-Falah BAHL Bank AL-Habib BIPL Bank Islami Pakistan Ltd BOP Bank of Punjab DAWH Dawood Hercules DCL Dewan Cement Ltd DGCK D.G.K.Cement EFUG EFU General ENGRO Engro Corporation EPCL Engro Polymer Corporation Ltd FABL Faysal Bank Ltd FCCL Fauji Cement Company Ltd FFBL Fauji Fertilizer Bin Qasim Ltd FFC Fauji Fertilizer Company HBL Habib Bank Ltd HMB Habib Metropolitan Bank HUBC Hub Power Company ICI ICI Pakistan JSBL JS Bank Ltd KAPCO Kot Addu Power Company KASSB KASB Bank Ltd KEL K-Electric LUCK Lucky Cement MEBL Meezan Bank Ltd MLCF Maple Leaf Cement NBP National Bank of Pakistan NML Nishat Mills Ltd NRL National Refinery Ltd OGDC Oil and Gas Development Corporation POL Pak Oilfie lds PSO Pakistan State Oil xv

List of Abbreviations

PTCL Pakistan Telecommunication Ltd SCBPL Standard Chartered Bank Ltd SECP Securities and Exchange Commission of Pakistan SHEL Shell Pakistan SNGC Sui Northern Gas Company SSGC Sui Southern Gas Company UBL United Bank Limited

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Chapter 1

Introduction to the Thesis

1.1 Introduction

The efficient market hypothesis (EMH) has been a major topic of interest for the researchers in the field of economics and finance after the pioneering work by Fama (1965-1970) in the field. Efficiency in the financial market is generally referred to as informational efficiency. He defined an efficient market as the one where, “all available information is reflected in share prices” (Fama, 1970, p.383). In other words, informationally efficient prices in the market constitute an efficient market where random walk is assumed to follow. Fama (1970) has further explained three forms of efficiency, strong-form, semi-strong form and weak- form. Presence of efficiency even in its weakest form implies presence of random walk (RW) implies that stock market follows the RW. Statistically the random-walk theory says that the succeeding price changes are based upon random variables which are independent, and identically distributed (IID).

It can be said that if the stock markets are WF efficient, future prices cannot be anticipated from the past prices and abnormal profits cannot be made in the market. That is, the fair- game prevails in the market and everyone has an equal chance of gaining profit. The theory of efficient stock markets states that there exist always equilibrium in the stock markets and an investor cannot thrash the market. Share price index of any economy responds directly to every economic, political event and helps setting sets behaviors of the economy and an efficient market may attract portfolio investment from various domestic and overseas sources which eventually improve the economic conditions of the economy. Therefore, the efficiency of capital market is one of the powerful tools for attracting investors by providing the sense of protection to them.

Chapter 1

The performance of stock market and especially the efficient stock market has positive implications on the economy. In this respect various studies have been done to inspect the connection between stock market behaviour and economic growth and there are evidences that stock markets are positively related to economic development. It is a well known fact that capital needed for economic growth is generated from the debt and equity markets therefore stock markets can be described as leading indicator of growth variable. Moreover, stock markets may be looked as key determinant of the growth of the financial system of a nation (Kenny and Moss, 1998). It can mobilize savings, creates liquidity of funds and can attract foreign inflow of capital and contribute largely to economic growth (Singh, 1997). Existence of such a stock market which can facilitate the investor for meeting liquidity and risk minimization needs to mobilize savings may be a factor towards economic prosperity. Better portfolio option may increase the savings rate (Levine and Zervos, 1998). At micro level stock markets also provide a platform for companies to grow and fulfill their capital needs at lower cost. Moreover, with the growth of stock markets there is less reliance on debt market, which can reduce the chances of adverse selection and moral hazards in debt markets. Stock markets therefore are able to favour economic growth by mobilizing savings amongst individuals and providing better opportunities for firm financing. Osinubi (2002) reaffirms that investment in securities is a better medium of transforming savings into funds for economic growth and development.

There has been a vast amount of literature developed over the last two decades to check the existence of stock market efficiency especially the random walk on developed and developing countries having emergent markets. Highly contradictory results have been found in case of developed and developing markets. Lo (2008) stated that even after thousands of published articles spreading over many decades, there is still no consensus about the efficiency of stock markets among researchers. It is this inconsistency in results that has provided the motivation to conduct a comprehensive study on Pakistani stock market, by adopting a triangulation approach. Pakistani stock market is comparatively smaller in size, but considerably more dynamic than the other markets of this size (Iqbal, 2012). It consists of three stock markets; Karachi stock exchange (KSE), Lahore stock exchange (LSE) and Islamabad stock exchange (ISE). Karachi stock exchange was formed in

Chapter 1

1947, the other two exchanges, LSE and ISE, were established in 1974 and 1997, respectively. Iqbal (2012) stated that KSE exhibit 85% of the total turnover, while LSE and ISE constitute 14 % and 1% of the total turnover, respectively. In 2013, KSE had 567 listed companies with the market capitalization (cap.) of Rs. 5,154.7 billion. While in LSE there were 441 companies with market cap. of Rs. 4,852.7 billion and in ISE 250 companies were listed with market cap. of Rs. 4,017.2 billion. The daily turnover of shares at KSE in 2013 was 221 million shares, while that of 91 million and 0.12 million respectively, for LSE and ISE.

The current study is based upon KSE, owing to its huge turnover as compared to the other two stock exchanges in Pakistan. During last five years 22 new companies have been listed in KSE with an increase in the total turnout of shares from 429 to 565 billion. The main source of motivation behind doing this investigation is that studies conducted so far have tested KSE-100 index mostly and extremely little work has been done on the other three equally significant indices of the market namely; KSE-30, KSE-all shares, and KMI-30. Furthermore, data employed is at most till 2008 and a study after that is needed to see the evolving trends in efficiency over time. Moreover, Pakistan is facing significant financial and macroeconomic upheavals since 2008, on account of domestic and international factors. Such as, post-impact of world financial crises on remittances, continuous oil price rise, energy crises leading to increase in cost of doing business, fairly high rate of inflation and deteriorating law and order situation and above all threats of terrorism especially in the business city of Karachi. On the other hand for first time in the history of politics in the last 30 years a political government completed its tenure and for the last six years nation is observing democracy with all its flavours. It is imperative therefore, to conduct an up-to-date study which can embark upon the whole stock exchange for examining the efficiency level.

1.2 Objective and Focus

The study is aimed at investigating the efficiency in the KSE within the framework of random walk hypothesis (RWH). The main focus of the thesis is on the weak-form (WF) version of efficiency, which affirms that current stock prices reflect all accessible information embedded in the past period prices of the market. More specifically, market

Chapter 1

efficiency will be investigated and deduced from the underlying stock and index returns behavior, where a WF efficient stock market is one in which the return changes are random and unanticipated.

The evidence of serial dependence in stock returns and possible autocorrelation would imply investor mis-reaction (under-over- reaction) to the influx of new information. This could have serious implications on market efficiency and the presence of such serial dependence of returns encourage return predictability in market in the form of mean reversion or mean aversion trends in the market. Similarly, the deviation of EMH is evident in the markets where seasonal or calendar events have the tendency to reflect profit opportunities in the markets.

Presence of seasonal or calendar anomalies in the market by predicting returns through certain market movements on given days would mean absence of RW in the market. Among such anomalies day-of-the-week (DOW), month-of-the-year (MOY) and turn-of-the-month (TOM) is tested in the thesis. Volatility clustering is a phenomenon where price changes may appear to be unpredictable, but the squared returns may be predictable in the way that large variations are followed by large variations and small variations are followed by small variations in any direction, thus forms volatility clustering with varied level of persistence. This predictability of returns would imply serious implication on market efficiency and random walk.

Volatility clustering is also included in the inference deduction scheme of RW and stock market efficiency. Another violation of EMH can also result in the form of non-linear trends in returns that may exhibit return series similar to random walk, but with the likelihood of predictability. The thesis also investigates the non-linear model for predictability of returns. Finally adjusted returns1 for thin trading are tested for linear and non-linear modeling.

1 Miller et al., (1994) approach for adjusted returns for thin trading methodology is adopted.

Chapter 1

The objective of this study is to cover all four indices of KSE and selected individual firms2 for the examination of WF efficiency within the framework of RWH by adopting a triangular approach of testing weak-form efficiency directly by using contemporary and new tools at the same time deduct the inferences about efficiency through the presence of calendar anomalies, volatility, thin trading and non-linearity in the market. It can be concluded from the empirical evidence found in the study that prices do not move independently and randomly and the KSE under the study period does not follow random walk with noticeable exceptions in KSE-30 index.

1.3 Outline of the Thesis.

The thesis is based on the following outline.

Chapter 2 provides the theoretical framework of EMH and random walk and its role in the growth and development of a country. The chapter also explains the deviation from the efficiency in the form of over-under reaction and calendar anomalies from efficiency, especially calendar anomalies.

Chapter 3 provides the overview of stock market of Pakistan with the special context of Karachi stock market. It also explains the history, growth and performance of the KSE.

Chapter 4 provides the empirical evidence of the past studies conducted on the topic in developed and in emerging markets of Europe, Africa, Middle Eastern and Asian markets, with the special consideration of Pakistani stock market.

Chapter 5 provides the methodological framework of the study and the tools employed for test weak-form efficiency of KSE. Specification of data employed for the study is also discussed in the chapter.

Chapter 6 provides the results and findings of all the tests employed for testing WF efficiency and RW on KSE.

2 Selection is based on frequency of trading in the firms. 43 such firms are selected from the total of 577 companies, on which trading occurs 95%of the total trading days. The notion behind is to maintain consistency in trading days between indices and firms to limit the impact of non trading days.

Chapter 1

Chapter 7 provides the investigation and results of volatility clustering in KSE.

Chapter 8 provides the investigation and results of the calendar anomalies of DOW, MOY and TOM effects on KSE.

Chapter 9 provides the linear and non-linear modeling on adjusted and non-adjusted returns for thin trading on KSE.

Chapter 10 provides the summary and conclusion of the research thesis, policy implications and suggestions for the investors and researchers and finally limitations of the study and recommendations will be discussed.

Chapter 2

Economics of Efficient Markets and Random Walk

This chapter discusses the theoretical aspect of efficiency and random walk and its forms. The deviations from efficiency with its possible reasons are also argued in the later part of this chapter.

2.1 Concept of Efficient Market Hypothesis

The concept of efficiency mostly refers to informational efficiency3. The core factor behind the price-change is the arrival of new information.4 In context with the financial market it refers to the incorporation of available information in setting up of current security prices. Efficiency requires the equilibrium in the market and an equal chance of prices to be higher or lower than the true value of the security at any point in time, all it requires these deviations from the true value to be random and the errors to be unbiased. Alternatively, an instantaneous adjustment of market is synonym to efficiency in the market that comes with a new set of information.

According to the Efficient Market Hypothesis (EMH), by Fama (1965a; 1965b) in his article5, an efficient market is one where returns cannot be exploited by trading in a specific pattern. The EMH is associated with the concept of RW, which in finance literature describes random changes in the prices of stocks such that the current prices cannot be predicted from the previous prices.

The importance of market efficiency cannot be understated. It has enormous implications beyond the statistical independence and random behaviour of the index. The most critical implication of the deviation from EMH can be addressed in the form of lack of trust and

3 Other forms of efficiency are: i. Allocative efficiency; It is related to the optimal allocation of resources and optimal distribution of production. ii. Operational efficiency; It is the related to the cost effectiveness of productive activity and input output ratio.

4 All available public and private information, including insider information

5 “Random Walks in stock market prices.”

Chapter 2

confidence on the market and asset prices. The efficiency of the market is considered as a powerful tool to attract the investors to invest in a particular market. The investor feels safe if the invested funds are protected in a fairly-priced market where the average expected returns on investment are equivalent to the price they pay. The average expected return from a stock is a related to present value of its expected future cash flows which includes volatility, liquidity, and risk of insolvency.

Fama (1970) categorized efficient market hypothesis in three forms: the weak, semi-strong, and strong forms.

2.1.1 Weak-form market efficiency The weak-form of the EMH claims that the current price fully integrates the information embedded in the historical prices only. Therefore, past prices are ineffective and do not play any role to predict future prices. Technical analysis6 techniques are ineffective to produce excess returns in the long run, therefore, technical analysts7 (chartists) oppose weak-form efficiency strongly as in their view any movement in past prices can trace the future trends of prices. Share prices exhibit no serial correlation, implies absence of any such pattern that can predict future asset prices. Weak-form believes to follow the RW in stock prices

2.1.2 Semi-strong form market efficiency The semi-strong form claims that all the publicly accessible information about a firm8 in addition to past prices information is reflected in its stock prices. It implies that all publicly available new information is incorporated instantaneously in an unbiased fashion, such that no excess returns can be earned by investors. Moreover, public information may be relatively costly and difficult to access. It may require more than conventional modes of acquiring information like, professional publications and databases, research journals, annual reports etc. However, it is assumed that whatever information publicly accessed is reflected in the

6 Technical analysis is a methodology for forecasting the direction of prices of securities through the analyzing the trends in the past market data.

7 A technical analyst or a chartist is a securities researcher who analyzes and forecast investments returns and future prices based on past market prices and technical indicators.

8 Firms’ information includes annual published report, income statements, profit announcement, dividend schemes, mergers announcement, expectations regarding macroeconomic indicators (interest rates, inflation rates) etc.

Chapter 2

current prices. It implies that technical analysis techniques will not be able to generate abnormal returns and investors cannot break the market by adopting chartist approach.

2.1.3 Strong-form market efficiency Strong-form efficiency claims that all available information whether public or private is fully absorbed and reflected in the current prices. It means that all relevant information published and non-published which can only be obtained by corporate insiders.9 This is a strong version of efficiency that even insiders’ information is futile in predicting prices, because it is already absorbed in the current prices.

In other words, under strong form firms’ management (insider) even after knowing the inside information is unable to earn excess returns in the market. The justification for this is rooted in the ability of the market to quickly incorporate all public even insider information in such an unbiased manner that all information is fully mirrored in actual stock prices. However, empirical research for strong form has revealed infavourable evidence.

2.2 Relative Market Efficiency and Absolute Market Efficiency

Various studies have been conducted that highlighted the factors that could be responsible for lower or higher levels of efficiency across markets. However, very little work is found on measurement of various efficiency levels across the markets (Lim, 2008a). Campbell et al. (1997) Lo & MacKinlay (1999) and Lo (2008) highlighted the fact that true efficiency does not occur in the real world and that in case of perfect efficiency investor will have no opportunity to earn above normal returns and market eventually may collapse. It is the inefficiencies that create higher than normal returns for compensating the transaction and information obtaining costs. The concept of relative market efficiency is the efficiency of one market in terms of the other market. One of the factors behind different levels of efficiencies in different markets could lie in speed with which available information incorporates into price system. Morck et al. (2000) Llorente et al. (2002) Hou & Moskowtiz (2005)

9 Corporate insiders are individuals who may be employed in the firm (as executives, directors, or sometimes rank-and-file employees) or who has the privilege to access to the firm’s internal affairs (as large shareholders, consultants, accountants, lawyers, etc.)

Chapter 2

contributed for the empirical application on capturing the speed with which stock price incorporates information.

2.3 Concept of Evolving Market Efficiency

Stock market efficiency evolves over time with the development of microstructures of the stock market. Emerson et al. (1997) highlighted the fact by employing the Kalman filter technique to track market efficiency over time on Bulgarian shares. Time-varying autocorrelation coefficients were used in their study to gauge the varying degree of return forecasting over time. If the autocorrelation coefficient gradually become insignificant and converges to zero it implies the market efficiency over time. Several studies have been conducted using the same framework (see for example, Zalewska-Mitura & Hall, 2000; Rockinger & Urga, 2000, 2001; Scotman & Zalewska, 2006).

2.4 The Martingale Model

Martingale model is considered to be the earliest most model of financial stock prices which amoriginates from the history of fair-game with equal chances. A fair-game is one for which the cumulative winnings or wealth next period is equal to the wealth in the current period. . Alternatively, in a fair-game the expected incremental winnings at any stage are zero given the entire history of game or prices. That is, the price has an equal chance to rise and to fall.

(2.1)

= 0 (2.2)

From the forecasting point of view, the martingale process implies the optimum forecast of price at time t+1 price is simply current price at today’s time ‘t’. Another attribute of martingale model is that non-overlapping price variations are uncorrelated. It implies that linear forecasting is ineffective to predict future price changes based on past prices alone.

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Martingale hypothesis was initially considered as the essential condition of efficiency, such that the information set of past asset prices are fully and instantly reflected in present prices of asset. Hence, profits cannot be gained on the information contained in the past price.

However, the traditional martingale has failed to incorporate the trade-off between risk and expected returns. The martingale model later was developed into a more dynamic and statistically powerful model, the random walk model, which is considered to be the most integral part of today’s financial economics.

2.5 The Random Walk Model

The theory of random walk (RW) is also consistent with efficient market hypothesis. In an efficient market, changes in prices are assumed to be random and unpredictable, because new information is assumed to be unpredictable. Therefore stock prices are said to follow a RW. Statistically speaking, in case of RW succeeding price variations are independent, identically distributed (IID) random variables which imply that price change has no meaningful trend to be remembered in future for setting of future prices (Fama, 1965).

The concept of random walk in stock market was first introduced by French economist Jules Augustin Frédéric Regnault (1863) and later was conceded by a French mathematician Louis Bachelier (1900)10. He emphasized that subsequent price changes between any two intervals are independent with mean as zero and variance that increases as the time period between the two intervals increases. The concept was further got strengthen by empirical work of Cowles (1933). The random nature of changes in the prices does not support the investor to gain above normal profits after beating the market. Samuelson (1965) supported the notion and presented proofs by developing practical linear-programming models considering storable commodities that were harvested and subject to decay.

More efficiency means more random and unpredictable price changes and vice versa. But RW is not the only one factor responsible for a sound investment environment. In the modern financial economics with the revolution and development of the financial markets more

10 PhD thesis titled “The Theory of Speculation”.

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complex financial instruments necessitates the choice between risk and expected returns. Expectation about the future rise in prices in particular market attracts the investor and an incentive to hold assets with the associated risk. Therefore, the random walk model is a powerful tool once the asset returns are properly adjusted for risk.

Random walk model is stochastic non stationary AR (1) process. There are primarily two categories of random walk models first, random walk without a drift ( and random walk with a drift .

A time series ( is a random walk with no drift implies ( is expressed as,

(2.3)

In case of random walk price at time is equal to price at time , plus a random shock , a white noise error term such that .

Campbell et al., (1997)11 defined three successive sub-hypotheses of the random walk hypothesis.

2.5.1 Random walk 1 (RW1) According to that the strict version of random walk is RW1 or identical, independent distribution (IID) increments, which implies that increments are uncorrelated and any non- linear function of these increments is also uncorrelated.

The time series increment of the stock prices can be explained by the following equation:

= + (2.4)

Such that IID, with zero mean and constant variance (0, )

Returns or increments can be defined as

11 Campbell, Lo and MacKinlay (1997) defined independent, identically distributed (iid) increments in their famous book, “The Econometrics of Financial Markets”, published by Princeton University Press.

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= = (2.5)

Conditional mean and variance at time t, conditional on an initial value of at time = 0, with the assumption of normal distribution, is given by

= + (2.6)

Var (2.7)

RW is non-stationary with conditional mean and variance linear in time, t.

In order to avoid problems due to limited liability of stock market investment and make corrections for normality lognormal model is used12.

(2.8)

2.5.2 Random walk 2 (RW2) Campbell et al., (1997) identified that because of the broad structural changes in the economy and in financial markets over long periods make the assumption would not hold increment identically distributed over long periods of time. They concluded that the assumption of identically distributed increments is implausible in long run financial time series. Therefore, the assumption of ‘identically distributed increments’ is relaxed in RW2 and unconditional heteroscedasticity or time-varying volatility is allowed in the increments, .

RW2 is weaker than RW1, but it holds the assumption of independency that is

Cov for all (2.9)

And non-linear function

12 Bachelier (1900) and Einstein (1905) used lognormal models for increments. Later it was institutionalized in the asset pricing literature

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Cov = 0, for some (2.10)

2.5.3. Random walk 3 (RW3) The weakest version of random walk, by Campbell et al.,(1997) where the assumption of independency is relaxed. The increments are not uncorrelated. RW3 and assumes the error term in the model to be dependent and uncorrelated, along with heteroscedasticity.

Cov 0, for some (2.11)

2.6 Importance of Efficient Market and RW Hypothesis on the Economic Growth.

The performance of stock market and especially the efficient stock market has positive implications on the economy for two reasons, one is that the share price index of any economy responds directly to every economic, political event and helps setting set behaviors of the economy and second is that an efficient market may attract portfolio investment from various domestic and overseas sources which eventually improve the economic conditions of the economy.

Stock markets can influence economic growth positively through mobilizing savings amongst individuals and providing opportunities to firms for financing. Even an informationally inefficient market can result in profitable investment opportunities based upon technical trading strategies. Enisan and Olufisayo (2009) indicated a positive relation between stock market development and economic growth for Egypt and South Africa. In addition they indorsed a long run economic growth consistent with stock market development.

2.7 Deviation from EMH and Random Walk

Intense competition arises among investors to gain profit with the new information. The ability to gain above the normal returns depends upon the competitive edge of the investor by the way of technical analysis. The tendency of identifying over and under-valued stocks at any point in time helps in evaluating the future price based upon the prices today. However, at equilibrium only small number of investors will be able to receive abnormal profits, due to

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detection of mis-priced stocks. But for the large number of investor technical analysis would not likely to compensate the transaction cost involved in technical analysis.

In recent years, a body of strong empirical evidence against random walk hypothesis presented a sharp challenge to the traditional view and made EMH a controversial issue with an unvoiced support to technical analysis model. Osborne (1962) Granger (1963) Jensen (1978) Black (1986) Poshakwale (1996) Campbell et al. (1997) Lo & MacKinlay (1988) Poterba & Summers (1988) Malkiel (2005) Gupta (2006) Agwuegbo et al. (2010) presented empirical evidence on the basis of some psychological and behavioral aspects and concluded that stock market returns to some extent are predictable. Under these circumstances stock market does not perform efficiently and certain pervasive inconsistencies or anomalies can be observed in the market.

2.7.1 Under-reaction and over-reaction EMH assumes a quick reaction of investors to new information. But evidence revealed certain psychological trends and biases causing under or over-reaction and hence positive or negative serial correlation13 in returns occurs.

A positive serial correlation due to under-reaction equally referred as short-term momentum leads to mean aversion14. It indicate that greater than average returns are likely to be followed by greater than average returns (i.e., a tendency for continuation) and vice versa. On the other hand negative serial correlation due to over-reaction leads to mean reversion15. It indicate that higher than average returns are followed, by lower than average returns (i.e., a tendency toward reversal) and vice versa. While in case of RWH zero correlation would be expected.

Hong & Stein (1999) noticed that, if information disperses gradually among the investors, prices under-react in the short run. Under-reaction implies momentum prevails and

13 The current return series of a security and the return series of the same security over a previous period are serially correlated. 14 Mean aversion means that returns measured over longer periods have higher standard deviation than in an independent series. Moreover, observations tend away from the average 15 Mean reversion means that return series measured over longer periods have lower standard deviation than in an independent series. Moreover, observations tend towards the average.

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momentum traders earn profit by trend-chasing and returns are positively autocorrelated in short term16. Barberis et al., (1998) concluded that the ‘conservatism bias’ do not let investors to update their credentials in the face of new information. Therefore, share prices under-react to new information and stock returns are positively autocorrelated in short term17.

Conversely, most people tend to overreact to unexpected and stirring news events and such behaviour effects stock market prices in the form of over-reaction which describes negative return autocorrelation (De Bondt & Thaler, 1985; 1987). It implies the strategy of buying past losers and selling past winners (Lehmann, 1990). It was found in their study that stocks having high long-term previous returns tend to have lower returns in future and vice versa (long-term reversals).

Daniel et al. (1998) also identidied over- and under-reaction to the arrival of information in the form of existence of significant serial correlation in stock returns. But they refuted the presence of positive return autocorrelations due to under-reaction. They argued that it is the investors’ overconfidence in extracting information signal which leads to over-reaction of prices and results in positive serial correlation in the short term. De Long et al. (1990a; 1990b) also assumed positive return correlation as a result of over-reaction to new information.

It is imperative to estimate how quickly the new information is incorporated in the prices. Brisley & Theobald (1996) and Theobald & Yallup (1998; 2004) developed speed of adjustment estimators. If the value of that coefficient of estimator is equal to unity then the stock prices fully adjust to new information. If on the other hand it is less than unity, it indicates that information is slowly absorbed in the prices. However, value of estimator greater than unity implies over-reaction to news.

Smart investors in the market can earn abnormal returns by taking advantage of under- reaction and over-reaction without bearing extra risk.

16 Short term refers to returns over periods of one year or less. 17 Short term refers to returns over periods of one year or less.

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2.7.2 Thin-trading Thin-trading can be defined as a phenomenon of infrequent trading in a stock market. It arises whenever an asset is not traded at the end of the period over which its return is measured. It suggests higher risk and returns opportunity and reflects lack of information and transparency in the market.

Infrequent trading may cause biased results when determining efficiency. Thin-trading can provoke autocorrelation in the time series of returns which would otherwise reveal serial independence (Siriopoulos, 2001).

2.7.3 Calendar anomalies The evidence of such anomalies in the stock market explains the violation of and divergence from the efficient market hypothesis, at least in weak-form market efficiency, because asset prices are no more random, but become predictable with any seasonal and calendar variation. This induces investors to build up trading strategies to make abnormal profits in the markets (Yalcin & Yucel, 2006). For example, investors may be willing to buy stocks on one specific day and sell on another based upon certain trends in the market on these specific days in order to take benefit from these effects. These differences in returns may be far above normal or below normal; can affect investors in deciding their investment strategy, portfolio selection and portfolio management (Anwar & Mulyadi, 2012). A normal investor usually does not feel safe or encouraged to invest in the market in the presence of such phenomena. They are called seasonal or calendar anomalies, and traditional asset pricing model is unable to fully explain this phenomenon. Therefore, uncovering these volatility patterns in returns might benefit risk management and portfolio optimization of valued investors in the market (Engle, 1993). Among such patterns most recurrent and pervasive are the following.

2.7.3.1 Day-of-the-week effect It is evident from the empirical studies that returns on any specific day of the week are higher or lower than other days. Cross (1973) tested S&P 500 index and noted higher mean return on Friday and lower on Monday. Similarly French (1980) observed lower returns on

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Mondays than any other day of the week. Other studies reported negative mean returns on Monday were conducted by Gibbons & Hess (1981) Lakonishok & Levi (1982) Keim & Stambaugh (1984) Rogalski (1984) Smirlock & Starks (1986) Harris (1986) Lakonishok & Smidt (1988) Flannery & Protopapadakis (1988) Aggarwal & Tandom (1994) Kohers & Kohers (1995) and Kiymaz & Berument (2003).

2.7.3.2 Week-of-the-month effect (Lakonishok & Smidt, 1988) confirmed the turn of the week, turn of the month and turn of the year phenomena in Dow Jones Industrial Average index. Ariel (1990) pointed out that on the trading day prior to holiday mean returns are comparatively higher than the remaining days of the year. Similarly, Kholi & Kohers (1992) identified week of the month phenomenon such that the returns during the first week of a month tend to be significantly positive while during the other weeks of a month are not different from zero.

2.7.3.3 Month-of-the-year effect It says returns in any one month of are higher than in other month during a year. (Rozeff & Kinney, 1976) found seasonal pattern in an equal weighted index of New York Stock Exchange and found average monthly return on January are considerably higher (over one- third returns occurred in January alone) than during other months (January effect).

2.7.3.4 Turn-of-the-month effect According to Lakonishok & Smidt (1988), turn-of-the-month (TOM) period is the duration between last trading day of the preceding month and first three trading days of the new month. While the stock returns of the remaining period is called the rest-of-the- month (ROM).The turn-of-the-month effect describes higher stock returns in the TOM period as compared to rest-of-the-month (ROM). Cadsby & Ratner (1992) found turn-of-the-month effect evident in European, Canadian, US and emerging markets. Hensel & Ziemba (1996) found TOM effects for S&P 500, in a study carried out for daily returns between 1928-1993. These effects have been tested internationally and diversified results can be found in various markets depending upon various institutional differences between developed and energent markets. Wage distribution period may be another determining factor of revising portfolio

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decsions. Investors with monthly wage distribution are expected to re-dress their portfolios at the time of receiving wages. In Pakistan, wage distribution period is beween the last and first week of the previous and susequent month. It is imparative therefore to determine the TOM effects for Pakistani markets as investor is more likely to make investment decsions between TOM period.

2.7.4 Size effect Another most enduring anomaly is the ‘size effect’, implies excess returns for small- capitalization companies. This phenomenon was first discovered by Rozeff & Kinney (1976); Roll (1983). It states that small firms have the tendency to earn higher than expected returns than large firms (Banz, 1981). Keim (1983) found excess returns temporarily concentrated in small firms.

Other well-known anomalies include the value line enigma (Copeland & Mayers, 1982), the relation between price-earnings ratios and expected returns (Basu, 1977).

Most of these anomalies can be exploited up to a certain degree by simple trading strategies, and earn profits over risks (Lehmann, 1990). But factors like risk and transaction cost most of the time do not allow to earn abnormal profits over risks. Moreover, it is also possible that some of the anomalies may arise for a certain period of time and then vanish with the change in dynamics of the markets; some are just a matter of coincidence without considerable substantiality. For example, January effect is largely due to the difference of bid and ask price. Price on last trading day of December can be assumed as bid price and price on first trading day of January could be perceived as ask price.

Whether or not one can accrue abnormal profits due to these anomalies is something, which cannot be answered on the basis of academic literature produced so far.

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Chapter 3 Overview and Performance of Karachi Stock Exchange

This particular chapter is focused on the importance, history, performance, and operations of the stock markets with a special reflection on Karachi stock market.

The objective is to provide the insight about the working and development of Karachi stock market over the study period.

3.1 Role and Importance of Stock Markets in Pakistan

The role of financial markets especially stock market has a key strategic position in the process of economic stability and development. The objective of the stock markets in Pakistan is to enable the Pakistani industry and commerce to attain long term growth and at the same time to provide investor with the viable solution to portfolio management. Stock markets or equity markets are the markets where the shares of publicly held companies are traded either through exchanges or over-the-counter (OTC) markets. The importance of stock markets in any emerging country like Pakistan cannot be denied. Stock markets are considered to be the main source of channelizing capital funds from domestic resources to the investment corporation. This implies that stock markets play a vital and strategic role in the development of a country. Stock markets are leading indicator of economic activity and have positive influence on aggregate demand through investment activities (Husain & Mahmood, 2001). Nishat & Saghir (1991) observed a unidirectional relationship from stock market to consumption and investment in Pakistani stock market.

The role of stock markets in the development of Pakistan is getting crucial day by day for two main reasons; 1. The availability of funds for public enterprises is getting difficult in budgetary allocations due to expanding debt servicing expenditures with greater amount of external debt with the passage of time. 2. Privatization is inevitable for public enterprises running inefficiently and incurring continuous losses. In this environment not only the

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efficient allocation of funds to meet the future requirements of capital funding to corporations is important, but it is also imperative to have investors’ confidence on stock markets. It implies that development and strengthening of such domestic capital markets which can meet the financial requirements necessary for economic and structural changes towards development is the need of the day. The developed capital market will be able to; a) mobilize the funds to bridge the gap between domestic saving and investment; b) efficiently allocate the capital resources to the most productive investment projects; c) increase the confidence of domestic and foreign investor; d) may provide a base for vertical increase in tax revenues. Therefore, inefficiency in the stock market is regarded as a serious constraint to gain investors’ confidence to carry out optimum portfolio and risk management.

3.2 Overview of Pakistani Stock Market

Pakistani stock market is considered an emergent stock exchange market in the developing Asian countries on account of its shallowness, and infrequent trading, lack of information; which is evident from its low turnover despite of having large market share and fairly high volatility. Moreover, the influence of insiders and market makers cannot be ruled out in such markets. Khwaja & Mian (2005) found evidence of insider’s influence in Pakistani stock market. However, with the introduction of corporatization and demutualization act 2012, transparency in trade and discouragement of insider influence may be ensured. Various other measures have been taken up by the stock market to tackle the problem of volatility, maintain transparency and bridging up the information gap by introducing Karachi automated transaction system (KATS), which has the capacity to cater excessive number of transactions per day. Similarly, Central Depository System (CDS) can handle more than one million shares per day and National Clearing System (NCS) has the capability to clear and settle the transactions of all three stock markets very swiftly. Moreover, annual reports of the firms are generated very regularly to keep the investor informed about the financial position and prospects of the company. Annual and quarterly reports of the markets are also made public as part of the awareness program of the stock markets financial stability and risk measurement approach.

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3.3 Karachi Stock Exchange (KSE)

Karachi stock exchange is the oldest and most dynamic stock exchange of Pakistan. It offers diversified quality products and services and is becoming a leading hub of capital formation market domestically and at the same time gaining recognition and linkages internationally. Highly innovative and vibrant companies from every sector of the economy are listed with the exchange. Since the inception the exchange is known for its innovative characteristic and with the passage of time it has become a key factor in the growth of capital market in the economy by making exponential growth in the performance and by developing state of the art technical infrastructure for its domestic and international members.

3.4 Karachi Stock Market as Emerging Market

Karachi stock market is considered as an emerging market. These markets are termed as shallow markets because of their volatility, low liquidity and the low turn-over of shares despite of having large market capitalization. For example, market capitalization of KSE in 2012 is Rs.3518 billions, and the total share volume is Rs.38 billion, i.e., less than 2%. Market capitalization as a percentage of GDP is 19.4 in 2012, while the total value of stocks traded was 5.3% of GDP as compared to a developed market of USA, where the market capitalization %age of GDP is 114% in 2012, while total value of shares traded is 131.6% of GDP.

3.5 Trading Products and Services

KSE is providing access to a variety of products to its members in brokerage houses domestically and internationally through the state of the art technical connectivity. i. Equity contracts (Ready Markets): It is none other than conventional share market, often termed as regular market, where buyers and sellers interact and make trade of shares. The settlement of such trade is based on T+2 counter system, that is settlement occurs 2 days after the trading.

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ii. Deliverable futures contracts: These are the forward trading contracts of a stated instrument with physical delivery of that particular instrument. Settlement of such contracts occurs 30 days after the purchase of contract. iii. Cash Settlement Futures Contracts: This contract is a standard contract of trading of a certain instrument at a certain date in future at a specified price. The settlement is made in cash only at 30, 60, or 90 days after the purchase of contract. iv. Stock index futures: These are traded in terms of number of contracts. Each contract is traded on a fixed value of the index. The settlement time is 90 days after the purchase of contract. v. Debt contracts: The debt contracts are settled in debt market of the exchange where the debt instruments like TFCs, Bonds, T-Bills, Commercial Papers, Participation Term Certificate, Corporate and Federal Bonds are traded. A debt market provides an environment where debt instruments can be traded between the buyers and sellers. The debt market is referred as a bond market if the trading of municipal, corporate and federal bond issues or national savings bond is taking place. It is known to be as credit market if the traded instrument is a mortgage. The market is also termed as fixed income market if the debt instruments like, fixed income securities are traded. The market becomes TFC market if the trading of TFCs occurs in the market. vi. OTC markets: Traditionally, in the Over-The-Counter (OTC) Market, trading occurs through a network of brokers, who keeps inventories of securities to assist the buy and sell orders of investors. OTC market is not a listed market on exchange but their trading activities are being constantly monitored by the exchange.

3.6 Indices in KSE

Following four indices are operational in KSE.

3.6.1 KSE-100 index KSE -100 index was launched on November 1, 1991, with initial base value of 1,000 points. The basic objective of launching of KSE-100 was to provide a responsible benchmark index by which investors can compare the performance of stock prices over a period of time. Thus

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KSE-100 index is an indicator that was designed to track the performance of Pakistan’s equity and share market. The KSE-100 index is considered as a benchmark for performance and growth of the stock market at the same time acts as a major leading indicator of Pakistan’s economic activity such as the gross national product, consumer price index, etc.

The KSE-100 index comprises of 100 companies with almost 90 percent of the total market capitalization on the basis of following selection criteria. i. Sector rule: Largest market capitalization in any of 32 sectors excluding bond/mutual fund sector. ii. Firm rule: The remaining index comprises of largest market capitalization companies in descending order. In other words a company to be listed must follow either rule 1 or 2 or both.

Karachi stock exchange is considering adopting free float methodology for KSE-100 index. In this regard a proposal was presented in August 2012, to see the benefits for members, investors, fund managers and the other implications of the migration towards free floating methodology.

3.6.2 KSE-all shares index In order to capture the impact of all of the firms on the performance of stock exchange and to provide the basis of further expansion of the index, another index was introduced in 1995 and became functional on September 18, 1995; KSE-all index is also based on capitalization criterion.

3.6.3 KSE-30 index KSE-30 index was launched and became operational from September 2006. The basic objective of this index was to provide a benchmark index and to act as the true indicator of the performance of equity and share market.

Unlike KSE-100 index, this index is based on free-float market capitalization methodology, at which other major indices of the world, like S&P, MSCI, STOXX and SENSEX are based.

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According to this methodology market capitalization of only those shares are taken into account which are readily available for the purpose of trading in the market and thus excludes the shares held by controlling directors / sponsors / promoters, government and other locked-in shares not available for trading in the normal course.

Thus the KSE-30 index thus calculated reflects the free-float market value of 30 companies included in the index with respect to the base period. KSE-30 index is expected to be more flexible and efficient index as it improves market and sector coverage of the index by improving the free float capacity of stocks. Unlike, KSE-100 index where a company with large capitalization and even with low free floating shares can be included. This may encourage undue influences of manipulators and large shareholders and investors to move index and attain abnormal profits. And this may prevent the stock exchange to act efficient and a true indicator of the performance of capital market.

KSE-30 index is considered to be a better indicator and an improved benchmark of the stock market performance than the KSE-100 index for the following reasons. i. Free-floating index gives weight to the constituent companies as per their actual liquidity present in the market and is not overly influenced by tightly held large-cap companies with actual low free-float of stocks. ii. A Free-float index can be used by the exchange for efficient regulatory purposes since it can be closely monitored for effective risk management and return. iii. Free-float index can be efficient and confidence oriented owing to its capability of excluding the impact of inactive and locked-in shares in the market. iv. Index movement will tend to be unbiased and thus market manipulation incidences can be minimized. However, speculators may use free-float number for framing trading strategies, accordingly.

3.6.4 KMI-30 index Karachi Meezan Index-30 (KMI-30) was introduced in September 2008, exactly two years after the launch of KSE-30 index. It is constituted with thirty companies that have screened

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for Shariat compliance. The index was created as a joint effort by KSE and Al-Meezan Investment Bank. KMI-30 index is also based upon free-float market capitalization methodology, and at any point in time it reflects the market value of free-float shares of selected Shariah-compliant companies with the base period of June 30, 2008. KMI -30 is reconstituted bi-annually. It exhibits all the advantages of free-float methodology as in case of KSE-30 index.

3.7 Growth and Performance of KSE

The stock exchange in the region existed before Pakistan came into being and established in 1934. However, after independence Karachi city was regarded as the main city for financial and business activities, due to influx of migrants including business men from the subcontinent. This has led to the need for a stock exchange in the city. Therefore, Karachi stock exchange was established in September, 1947 shortly after the independence, and took the status of a company in March 1949. The first index introduced in Karachi stock market was KSE-50. When established the KSE index had 5 companies 90 members with a paid up capital of 37 million. Later in 1950 the number of companies reached to 15, with the listed capital of Rs. 117 million.

KSE rapidly grew after that and only in 10 years time the number of listed companies reached to 81, more than 5 times than were in 1950, with the market capitalization of almost Rs.1.9 billion in 1960. After a remarkable growth, during another decade there were 291 companies on its account with about Rs. 5.66 billion market capital in 1970, it had risen to 9.8 billion in 1980. During 1990’s KSE grew at a much greater pace and there were 487 companies with market capital of 61.8 billion on its account in 1990.

With 500 listed companies and market capitalization of almost Rs. 62 billion in 1990, it was the time when the need of a much better representative index was required, therefore, in November 1991, KSE-100 index with a base value of 1000 points was launched, and till date is regarded as the most accepted measure of exchange. The stock market witnessed boom during 1990’s owing to the large number of development including; first the financial

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liberalization resulting in the rise and inflow of foreign portfolio investment, second the process of privatization thus introduction of new portfolios in the market.

Karachi Automated Trading System (KATS) which is computerized trading system was introduced in 2002 with a capacity of 1.0 million trades per day and the ability to provide connectivity to an unlimited number of users.

With further growth in market activity the total number of companies reached to its highest ever level of 762 with the market capitalization of 382.7 billion in 2000. In 1995 All Share Index was introduced in order to recognize KSE-100 index. From 1991 till 2006 there was a period of steady growth and incredible performance in KSE. In 2002, Pakistan stock market was declared as the “best performing market” in the world, and as on May 30, 2008, 654 companies were listed with a market capitalization of Rs. 3,746.203 billion, while in 2003 and 2006 it was ranked at third in the world with 652 listed companies and paid up capital of Rs 517,904.11 million. In 2005, trading on the internet was also started which helped in smooth functioning of the stock exchange. During 2006-2007, market performed fairly well owing to improvement in basic macroeconomic indicators of the economy especially GDP growth and exchange rate stability.

At the same time certain steps were also taken by the then government towards the capital market reforms under the “Capital Development Programme”, especially exemptions of various taxes including corporatization and demutualization taxes, taxes on electronic transfer of security transactions and extending exemptions of capital gain tax, As a result of which mergers and acquisitions occurred at a massive scale, linkages with the international exchange markets developed and market capitalization increased to 32% from 6.3%, during 2006-2007. KSE achieved the award of the “Top 25 companies” for the year 2006. In September 2006, KSE-30 index was launched which is based on free floating system.

However, 2007 appeared as a challenging year for the economy as a whole and for the financial market specifically. Inflating oil price internationally and tightening of monetary policy domestically coupled with deteriorating law and order situations slashed down the

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domestic and foreign investment opportunities and resultant liquidity. Investor preferred money markets over capital markets. As a result of which, KSE faced a serious decline of 11% in its KSE-100 index, 16% in KSE-30 and 10% in KSE-All Shares index despite of a substantial growth by banking sector, energy and communication sectors.

The above situation prevailed during the initial period of 2008, led to significant decline in trading volume which resulted in the imposition of price floor in August 2008, for more than three and a half months. By December index had fallen up to 62 percent and practically activity became zero. However, in the second half a sharp decline in oil prices and a massive influx of remittances provided relief to the balance of payment crises. Key macroeconomic indicators began to get better and finally SBP allowed the discount rate to decrease by 100 bps; that is, from 15% to 14%. Investors’ confidence increased and KSE index increased to 49% by the end of the fiscal year. And after the removal of price-floor, trading resumed on December 15, 2008.

Table 3.1 Decade-wise Market Summary of KSE Year No. of listed Listed Capital Market Capitalization companies Rs.(million) Rs. (million) 1950 15 117 - 1960 81 1007 1871 1970 291 3864 5658 1980 314 7630 9767 1990 487 28056 61750 2000 702 236458 382730 Source: Annual Reports Karachi Stock Exchange

From 2009 onwards market started the recovery period after taking various steps for catering the problem of trading volume in the form of instigating awareness campaigns for the investors and announcing incentives for new companies to get listed in the exchange. Furthermore, planning for launching of additional derivatives and re-launching of OTC markets as a dedicated Venture Enterprise Exchange (VEX) started. To gain investors’

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confidence, transparency was guaranteed by taking risk management measures including introduction of concentration margins and extending the pre-settlement delivery in ready and future contract markets. This resulted in boosting of index by 28.5% from 9722 to 12496 points by the end of June 30, 2011. This made KSE the 5th best performing equity market amongst 12 emerging Asian countries and in November 2012 it achieved the highest recorded 16,218 points, and considered to be the best in the emerging markets of Asia with 644 listed companies and with market capitalization of almost Rs. 2705 billion. The average daily volume of shares traded rose to 131 million in 2012, versus 95 million in the year 2011. Demutualization act was passed during the period which has the capacity to contribute positively to share holder value by ensuring enhanced transparency and providing a disincentive for market maneuvering practices.

During the FY 2013, measures were taken to broaden the debt market by trading government securities in the exchange to attract the wide range of investor. In that context Karachi stock exchange’s ‘Bond Automated Trading (BAT) System was introduced. In June 2013 KSE-100 index achieved the highest ever level of 23,097 with more than double market capital of Rs. 5155 billion as compared to 2009 and ranked amongst the top 10 markets in world in 2013. Stellar growth is observed during the first quarter of the FY 2014, with 36% increase in market capitalization. As per the ratings of Bloomberg Pakistani stock market stood amongst the top-10 performing markets third year in arrow. The key factor behind is the remarkable increase in foreign private investment (FPI) influx from US$ 569 million in FY 2013 to US$ 676 million in FY 2014. As on December 2014, there were 577 companies with the total market capitalization of PKRs 7,023billions. This listing of companies in the stock exchange is done on the basis of rules laid out by Securities Exchange Commissions of Pakistan (SECP) and Karachi Stock Exchange (Guarantee) Limited. The companies listed are categorized in one of the 36 sectors. Out of these, listing in 32 sectors is based on market capitalization rule and rest of the 4 sectors is allocated for bonds, mutual funds and other future contracts.

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3.8 Demutualization Act, 2012

A landmark achievement in Pakistani stock market is the approval of demutualization policy as per Corporatization, Demutualization & Integration) Act, 2012. This Act is part of the SECP’s reforms to bring about structural and regulatory changes through legal reforms in the non bank financial market and the capital market. Demutualization is a well established market form in developed and emerging markets, and acquiring this would mean Pakistan’s capital market at par with the markets of USA, UK, Germany, Australia, Turkey, Hong Kong, Malaysia, Singapore and India. The said Act is expected to expand the market by attracting new domestic and foreign investors and increasing the liquidity of the market. Demutualization is defined as the ‘process of transformation of an organization from its mutual ownership structure to a share ownership structure. The Act requires the stock exchanges to be demutualized within 119 days of its announcement in line with of the execution of various targets with pre-defined timelines. The objective was to convert the present non-profit mutually owned stock markets into for-profit investor-owned organizations and to increase the flexibility and liquidity required to compete in the global competitive environment. In the mutualized market structure the members have the ownership as well as trading rights which can create conflict of interest as member largely control the dealings in the stock markets which can no longer be transparent if members are traders themselves. By creating monopoly they are in a position to manipulate the market affairs and can gain abnormal profits.

3.9 Linkages with the International Financial Markets

A major breakthrough occurred when KSE index was included in DOW Jones indexes and in the Euro Asian Stock Exchange Regional index coupled with the inclusion of 30 Pakistani stocks in Dow Jones SAFE 100 index, which resulted in huge influx of capital.

KSE recomposed its sectors on the methodology of DOW Jones, into; industry, super sectors, sectors and sub sectors and became International Classification Benchmarking (ICB) compliant since 2009-2010 to facilitate international comparisons for foreign investors. This

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has led to integration with NASDAQ, NYSE, London Stock Exchange, Swiss Exchange, IMF, World Economic Forum, The Wall Street Journal, Financial Times, CNBC, and DOW Jones Newswire.

In a nut shell it can be said that the financial reforms in the form of privatization and trade openness in 1990s resulted in the expansion of stock markets not only in the size of capital, but improvements in the performance also. The set up of computerized trading, systematic reduction in the settlement period, introduction of free floating indices and recent demutualization policy are some of the major reforms by stock market of Pakistan, which has enabled the markets to outperform during 2002-2003, 2010-2011, 2012-2013 and 2013-2014.

However, apart from these reforms and structural changes in the market, Karachi stock market is facing challenges since 2008, on account of international and national features and events including, prevailing uncertainty due to international financial crises, incessantly increasing oil prices, increase in exchange rates and subsequent tight monetary policy domestically. As a result of which investors’ confidence shattered, liquidity lessened thereby left serious ramifications on stock market growth.

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Table 3.2 Annual Performance of Karachi Stock Exchange Year 2001 2002 2003 2004 2005 2006 2007 CAPITAL Listed Company 747 711 701 661 662 658 658 Listed Cap (Rs. bn) 233.68 291.24 313.27 405.65 460.50 495.97 631.13 Market Cap (Rs. bn) 296.14 595.21 951.45 1723.45 2361.32 2801.18 4019.42 Market Cap % of GDP N/A 10.00 16.00 25.00 32.00 36.00 46.00 New Listed Comp 3 4 6 17 16 14 16 Listing Cap of new 2.88 6.32 4.56 66.84 28.08 25.21 56.02 comp.(Rs. bn) DEBT INSTRUMENTS New Debt instr. Listed 5 16 6 5 6 6 3 Listed Cap.of new debt 5.66 8.66 2.75 4.78 8.13 6.90 6.00 instrument (Rs. bn) VOLUME Total Share volume 23069.71 41627.00 76380.00 85813.21 69979.16 79454.53 54042.36 (Rs.mn) Av. Daily vol (Rs. mn) 96.91 167.10 308.81 343.70 368.31 348.53 262.48 KSE-100 INDEX Mean 1346.3865 1902.36 3483.911 5274.794 7873.131 10631 12730.57 High 1550.42 2701.42 4601.02 6218.40 10303.13 12273.77 13772.46 Low 1075.16 1322.67 2356.48 4473.03 765.74 6970.59 9504.00 Year end 1273.07 2701.42 4471.60 6218.40 8225.66 9989.41 13772.46 St.dev 96.45184 239.9538 677.736 293.0991 849.55 666.4437 1180.817 CV 1.5475676 11.802908 6.3034189 18.29019 9.5544474 15.692554 9.7114666 KSE-All SHARE INDEX Mean 858.0545 1173.478 2180.243 3415.23 5141.469 7132.141 8855.613 High 971.74 1671.09 2947.11 4104.86 6683.14 4589.51 9758.81 Low 706.69 846.69 1475.20 2837.68 4105.07 8184.60 6399.29 Year end 82.42 1671.09 2833.10 4104.86 5444.32 6708.30 9758.81 St.dev 53.25777 141.5829 449.4545 224.4296 569.8205 427.483 1004.875 CV 0.6461753 0.0847249 0.1586441 0.0546741 0.1046633 0.0637245 0.1029711 KSE-30 INDEX Mean - - - - - 14000.2 High ------17002.75 Low ------12248.97 Year end ------16993.51 St.dev 632.0983 CV 26.884284 KMI-30 INDEX Mean ------High ------Low ------Year end ------St.dev CV

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Table 3.2 (Cont’d) Annual Performance of Karachi Stock Exchange Year 2008 2009 2010 2011 2012 2013 2014 CAPITAL Listed Company 652 651 652 639 590 569 557 Listed Cap (Rs. bn) 706.42 781.79 909.89 943.73 1069.38 1116.01 1160.34 Market Cap (Rs. bn) 3777.70 2120.65 2732.37 3288.66 3518.14 5154.74 7022.69 Market Cap % of GDP 34.00 16.00 18.00 18.00 17.00 23.00 21.00 New Listed Comp 7 8 8 1 4 4 5 Listing Cap of new 14.27 10.71 40.65 4.35 11.86 7.40 19.23 comp.(Rs. bn) DEBT INSTRUMENTS New Debt instrument 7 1 5 2 5 9 5 Listed Listed Cap.of new debt 23.50 4.26 8.650.18 5.00 11.50 12.26 8.78 instrument (Rs. bn) VOLUME Total Share vol. (Rs.mn) 63316.12 28332.78 42959.12 28018.00 38011.00 54319.00 56581.00 Av. Daily vol. (Rs. mn) 238.15 115.64 172.52 112.00 153.00 221.00 229.00 KSE-100 INDEX Mean 12062.93 7600.839 10131.34 11888.15 14240.69 20899.09 29721.19 High 11162.17 12221.43 10677.47 12681.94 14617.97 22757.72 29652.53 Low 15676.84 4815.34 7270.72 9516.42 10842.26 14142.92 29789.85 Year end 12289.03 7162.18 9721.90 12496.03 13801.41 21005.69 21363.16 St.dev 2448.703 1341.792 524.7158 424.1576 1472.554 2587.668 - CV 5.266043 5.7702761 18.721507 29.879641 9.0737212 7.5415558 - KSE-All SHARE INDEX Mean 8672.33 5447.825 7111.673 8257.718 9982.155 14903.6 22018.83 High 11148.68 8791.08 7522.88 8794.69 10251.17 16020.93 21973.16 Low 8038.39 3647.10 5194.43 6652.45 7549.52 9935.78 22064.49 Year end 8834.24 5121.73 6809.60 8663.10 9708.31 14987.53 15150.36 St.dev 1677.586 887.6057 363.7314 289.9332 1069.937 1987.326 - CV 0.1898959 0.1733019 0.0534145 0.0334676 0.1102084 0.1325986 - KSE-30 INDEX Mean 17353.49 5762.458 10218.78 11744.37 11281.54 14151.86 20493.3 High 18996.33 14230.42 10876.61 12476.12 12762.79 17787.71 20415.95 Low 12750.28 4428.10 7711.91 9372.08 10060.64 12246.91 20570.64 Year end 14326.27 7571.08 9556.58 11586.49 11922.13 16207.96 19290.83 St.dev 913.3169 679.5183 166.0939 397.3198 663.1155 473.8845 - CV 15.685979 11.141834 57.537212 29.161622 17.978964 34.202343 - KMI-30 INDEX Mean - 10982.24 15559.34 20590.79 24885.48 36110.97 47875.93 High - 11421.39 16079.33 21344.19 25221.31 38747.31 47686.55 Low - 6322.23 10871.59 14421.31 19436.79 24303.16 48065.30 Year end - 10647.69 14573.54 20936.20 23776.48 36713.89 36759.88 St.dev 2275.668 1188.966 840.8277 2761.72 4255.398 - CV 4.6789294 12.257323 24.899513 8.6093014 8.6276043 -

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Figure 3.1 KSE-100 Index from 2001-2014

Figure 3.2 KSE-All Share Index from 2001-2014

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Figure 3.3 KSE-30 Index from 2001-2014

Figure 3.4 KMI-30 Index from 2001-2014

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Figure 3.5 Market Capitalization of KSE from 2001-2014

Figure 3.6 Number of New Listed Companies in KSE from 2001-2014

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Figure 3.7 Total Share Volume on KSE from 2001-2014

Figure 3.8 Average Daily Share on KSE from 2001-2014

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Literature Review 4.1 Introduction

The concept of market efficiency by in large is connected to the informational efficiency in the markets. In context with the financial market it refers to the incorporation of available information in setting up of current security prices. Consequently, the market is efficient implies that prices adjust quickly in an unbiased manner after arrival of new and relevant information.

The concept of random walk in stock market was first introduced by French economist Jules Augustin Frédéric Regnault (1863) and later was conceded by Louis Bachelier, a French mathematician (1900). The concept further got strengthened by empirical research of Cowles (1933). The random nature of changes in the prices does not allow the investor to always beat the market to gain above normal profits. (Kendal, 1953; Cootner, 1962; Samuelson, 1965) supported the random walk behavior of stock prices. A decade after Samuelson’s (1965) and Fama’s (1965a; 1965b; 1970) landmark papers, many other researchers like LeRoy (1973) Rubinstein (1976) and Lucas (1978) extended the basic framework to cater the risk-averse investors. Thus a ‘neoclassical’ version of the EMH was developed where price changes are random and unpredictable and all investors have ‘rational expectations’ and prices do fully reflect all available information.

However, efficient market hypothesis became a controversial issue on the basis of empirical evidence against efficiency and seasonal anomalies in the stock market. Supporters of this school of thought Summers (1986) Fama & French (1988) Lo & MacKinlay (1988) Poterba & Summers (1988) contradicted random walk characteristic on the basis of certain psychological and behavioral elements and presented evidence against the hypothesis and concluded that stock market returns to a considerable extent are predictable. Since then it has become a debatable issue (Osborne, 1962; Granger, 1963; Jensen, 1978; Black, 1986;

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Poshakwale, 1996; Campbell et al., 1997; Malkiel, 2005; Gupta, 2006; Agwuegbo et al., 2010) and major interest of research. De Bondt & Thaler (1985; 1987) Barberis et al. (1998) Lehmann (1990) Hong and Stein (1999) revealed an anomaly of random walk in the presence of under and over-reaction of price changes and autocorrelation in the stock markets. Calendar anomaly is another consistent deviation from random walk hypothesis observed in the stock markets. Among them day-of-the-week (DOW) effect (Cross, 1973; French, 1980) week-of-the-month effect (Ariel, 1987; Lakonishok and Smidt, 1988) month-of-the-year effect (Rozeff & Kinney, 1976) and turn-of-the-month (TOM) effect (Cadsby & Ratner, 1992) are highly pervasive ones. In a nutshell, even after thousands of articles published on the topic there is no single consensus developed among the researchers and the economists about efficiency of financial markets (Lo, 2008). However, empirical evidence in favour or against EMH can be considered a major contribution towards the strategic trading adeptness of a portfolio manager and of a proficient investor.

Ko & Lee (1991) argued that "if the random walk hypothesis holds, the weak-form of the efficient market hypothesis must hold, but not vice versa.” Hence evidence supporting the RW is the evidence of market efficiency in weak-form. However, defiance of the RW model need not be the evidence of market inefficiency in the weak-form.

According to Kendal (1953) stock prices following a random walk implies that the price changes are independent of one another as well as the gains and the losses. The efficient market increases the investors’ confidence over the market. Stock price reflects best estimate for risk and returns under efficient market by incorporating all available information (Gupta & Basu, 2007).

Lagoard & Lucey (2008) explained the importance of efficient markets for the positive relationship between stock market development and economic development. On the other hand an inefficient market can result in profitable investment opportunities based upon technical trading strategies.

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Enormous studies have been conducted since the seminal work of Fama (1965a) to investigate the degree of efficiency in developed and in emergent markets of the world using various techniques. The investigation of EMH has been continuously receiving an overwhelming response owing to two basic facts; i) informational efficiency plays a significant role in portfolio decision making of investor and the findings have serious implications on investor and on portfolio manager; ii) Contradictory and inconsistent results, even after the extensive published work in this field calls for diversified approaches with innovative methodologies.

4.2 Empirical Evidence of Developed Financial Markets

Earlier studies mostly probed into the behaviour of developed financial markets, mostly of European and US financial markets. Traditionally markets of developed economies are more efficient as compared to emergent markets (Gupta, 2006).

Kendall (1953) investigated British industrial and US commodity share price indices. The study supported random walk on zero correlation rationale. Similar rationale was provided by Working (1934) with small sample. Cootner (1962) picked 45 stocks from New York stock exchange and found similar results at low levels of correlation. Lo & MacKinlay (1988) conducted a vital study on US security prices for the period 1962-1985, by first introducing variance ratio test. The study rejected random walk based on positive serial correlation of weekly and monthly returns. Fama & French (1988) conducted a study on New York Stock Exchange (NYSE) stocks for the 1926-85 period and found large negative autocorrelations for longer periods. Poterba & Summers (1986;1988) applied variance ratio test on Standard and Poor’s composite stock index for the period 1928-1984, for US stocks market as whole for the period 1871-1986, and for sixteen other countries for 1957-1985. They rejected the random walk and found the evidence of positive serial correlation over short periods and negative autocorrlation for longer periods. Contradictory to this Lee (1992) found existence of random walk for the stock markets of US and 10 other industrialized nations namely United Kingdom, France, West Germany, Australia, Belgium, Netherlands, Switzerland, Italy, Japan and Canada, for 1967–1988. Similarly, Choudhry (1994) examined stock

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indices of United States, United Kingdom, Canada, France, Japan, Italy and Germany for the period 1953–1989, by applying unit root test and Johansen method of cointegration using monthly return series and also found unit root and presence of random walk in all stocks.

Poon (1996) tested UK stock markets for random walk, serial correlation, and persistence of volatility and found presence of random walk and found no evidence of mean reversion. Al- Loughani & Chappel (1997) found heteroscedasticity in FTSE 30 index of London Stock Exchange for the period 1983-1989, by employing Lagrange Multiplier (LM) serial correlation test, unit root test and generalized autoregressive conditional heteroscedasticity- in-mean (GARCHM) model.

Chan et al. (1997) conducted a study on 18 international stock markets (Australia, Belgium, Canada, Denmark, Finland, France, Germany, India, Italy, Japan, Netherlands, Norway, Pakistan, Spain, Sweden, Switzerland, the United Kingdom, and the United States ) with 16 amongst them belong to developed world and the rest two; Pakistan and India among the emergent markets for the period 1962-1992. The study was aimed at testing weak-form efficiency. The result from unit root testing revealed the weak-form efficiency in developed markets. However, cointegration test revealed significant cointegration in the return series. Groenewold (1997) vetted the markets of Australia (Statex Actuaries’ Index) and New Zealand (NZSE-40 Index) for the period 1975-1992. The study tested weak-form and semi- strong form efficiency in those markets and used stationarity and autocorrelation tests and found the results to be consistent with weak-form efficiency. However, the granger causality rejected the semi-strong form and at the same time revealed cointegration between the two stock markets.

Lee et al. (2000) tested French futures and options markets using unit root and variance ratio tests. The study found presence of random walk in the markets.

Worthington & Higgs (2004) examined sixteen European equity markets for random walk including, Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and the United Kingdom and

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four emerging markets of Czech Republic, Hungary, Poland and Russia. Augmented Dickey-Fuller (ADF), Phillips-Perron (PP) and multiple variance ratio (MVR) tests were applied. It was found that only Hungary amongst the emergent markets and Germany, Ireland, Portugal, Sweden and the United Kingdom amongst the developed markets follow random walk criterion.

Gan et al. (2005) looked into the stock markets of New Zealand, Australia, US and Japan for the period 1990-2003, and reaffirmed the findings of Groenewold (1997) except for the granger causality between New Zealand and Australian stock markets. The study used conventional methods (ADF and PP unit root test) for finding efficiency levels.

Nakamura & Small (2007) used “small-shuffle surrogate” method to investigate random walk on Standard & Poor's 500 in US market and Nikkei225 in Japanese market, exchange rate and commodity markets and found existence of RW in markets whose first differences are independently distributed random variables.

Torun & Kurt (2008) conducted a study on European Monetary Union Countries taking panel data of stock price index, consumer price index and purchasing power of euro for the period 2000-2007 to investigate weak-form and semi-strong efficiency. The study used panel unit root test, panel cointegration and causality test and found result consistent with weak-form efficiency.

Borges (2010) investigated the stock markets indices of France, Germany, UK, Greece, Portugal and Spain, from January 1993 to December 2007 for the presence of random walk by taking monthly and daily stock returns. He used both parametric and non parametric tests including serial correlation test, runs test, multiple variance ratio test proposed by Lo & MacKinlay (1988), and ADF test. Evidence of random walk was found in all six countries for monthly returns.

However, for the daily returns hypothesis of random walk was rejected for Greece and Portugal.

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Shaker (2013) tested the weak-form efficiency of Finnish and Swedish stock markets by using ADF, variance ratio test proposed by Lo & MacKinlay (1988). This partuclar study rejected the hypothesis of random walk in these markets.

The above empirical literature revealed the evidence weak-form efficiency and random walk in most of the developed financial markets.

4.3 Empirical Evidence of Emerging Financial Markets

An emerging economy is a transitional phase between a developed and developing economy. Compared to developed markets, emerging markets are relatively isolated from capital markets of other countries and have relatively low correlation with developed markets. But during last two decades huge amount of capital inflow from developed economies as a result of globalization and liberalization of financial markets have attracted the researchers to investigate the implications of these changing trends on market efficiency of emerging markets. Therefore particular attention is being paid by researchers to find trends in emerging markets. However, contribution of equity markets in the process of development in developing countries is less and the resultant is weak markets with restrictions and controls (Gupta, 2006).

In emerging stock markets, stock price manipulation by intermediaries (brokers) is a common issue. Greater returns by inside traders (brokers) than outside traders in emerging markets accounts for weak market reforms and limited capital increase (Khwaja & Mian, 2005). China’s worst stock market crime came out as a result of collusion of brokers in the market (Zhou & Mei, 2003). In 2005, the Securities and Exchange Board of India barred 11 brokers for engaging in price manipulation. An intermediary (broker) can manipulate outcomes in equilibrium without losing credibility in the market (Khwaja & Mian, 2005; Siddiqi, 2007). Therefore, efficiency levels in emerging economies are sensitive to the manipulation capacities in the markets (Magnusson & Wydick, 2002).

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4.3.1 East European emerging markets Areal & Armada (2002) studied Portuguese stock market to check for weak-form efficiency. Parametric and non-parametric test were used and found mixed evidence mostly sensitive to methodology used. The study did not reject weak-form efficiency.

Siourounis (2002) investigated Athens stock exchange (ASE) for weak-form efficiency and heteroscedasticity from 1988-1998. The study employed GARCH model and concluded that current volatility is positively related to past realizations. It was also concluded that negative shocks have an asymmetric impact on returns. Chow test, Granger causality test and Newbold test were used for non linearity. Augmented Dickey-Fuller (ADF) and Phillips- Perron (PP) tests with first difference log values of return series were employed to check unit root in the daily return series. The two tests failed to reject random walk at 5% significance level. However, for first difference there is no evidence of unit root. Later another study examined Athens stock market (Samitas, 2004) by using Johansson’s Maximum likelihood procedure and unit root test which showed consistency with the former study. While a recent study by Dicle & Levendis (2011) revealed appearance of inefficiency with DOW effects after performing runs test and Granger causality test on Athens stock market.

Smith & Ryoo (2003) analysed five European emerging markets namely Greece, Hungary, Poland, Portugal and Turkey, by employing multiple variance ratio test. The hypothesis of random walk was rejected in all markets except for Istanbul stock exchange due to higher turnover than other markets.

Guidi et al. (2011) investigated Central and Eastern Europe (CEE) equity markets for the period 1999-2009. Study used autocorrelation analysis, runs test, and variance ratio test for test the hypothesis of random walk. It was concluded that most of the CEE markets do not follow random walk and abnormal profits can be accrued by a well informed investor.

Another study on Istanbul stock exchange (ISE) National 100 index was conducted by Kapusuzoglu (2013) for the period 1996-2012 found contradictory evidence as compared to the findings of Smith & Ryoo (2003). The study aimed at detecting the presence of random

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walk in the returns by using unit root test on daily stock returns and rejected the hypothesis of random walk.

A very recent study by Dragota & Tilica (2014) examined Post Communist East-European Countries. The study aimed at tracing any improvement in efficiency based on the past record and used 20 countries namely Bosnia-Herzegovina, Bulgaria, Croatia, Czech Republic, Estonia, Georgia, Hungary, Kazakhstan, Latvia, Lithuania, Former Yugoslav Republic of Macedonia, Moldova, Montenegro, Poland, Romania, Russia, Serbia, Slovakia, Slovenia, and Ukraine for the period 2008-2010, a period of financial crises. Unit root tests, runs test, filter rules test and variance ration tests were used. In some of the markets the hypothesis of EMH was not rejected.

However, the results were not consistent in all markets. Moreover, the heterogeneity of results was revealed suggesting variable portfolio management techniques for different levels of market efficiency.

Mixed results were observed in case of Eastern European financial markets with traces of weak-form efficiency in stock exchanges of Athens and Turkey.

4.3.2 Latin American emerging markets Urrutia (1995) scrutanized Latin Amirican emerging markets namely Argentina, Brazile, chile and Mexico stocmarkets for random walk hypothesis for the period 1975-1991. By applying variance ratio test it was found that serial correlation is present in all markets. However, runs test indicated weak-form efficiency in studied Latin American markets.

However, when parametric test along with non-parametric test were applied by Worthington & Higgs (2003) to investigate weak-form market efficiency in Argentina, Brazil, Chile, Colombia, Mexico, Peru and Venezuela; it rejected the random walk hypothesis. In another study Maxico and Brazile stocks markets were re-examined for random walk by Grieb & Reyes (1999) by employing variance ratio tests on individual firms and on indices. The result revealed greater tendency of Brazile stock index for random walk than for Mexican stock

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markets. Literature reveals that Brazilian stock markets has shown random walk behaviour and favourable tendencies towards efficiency.

4.3.3 African emerging markets Smith et al. (2002) conducted a study on five medium-sized African stock markets namely, Egypt, Kenya, Morocco, Nigeria and Zimbabwe and two small and comparatively newer markets of Botswana and Mauritius for testing the hypothesis of random walk. The stock market of South Africa was also put under question of random walk. The study used multiple variance ratio tests of Chow & Denning (1993). The hypothesis of random walk was rejected in all seven markets, except for South African market which was found to follow random walk.

Another study in the same era by Magnusson & Wydick (2002) found presence of weak-form efficiency on monthly returns of six out of eight African markets namely Botswana, Cote d’Ivoire, Kenya, Mauritius, South Africa, Ghana, Nigeria and Zimbabwe. The results were then compared with US stock market, Latin American and Asian emerging markets and it was concluded that efficiency levels are sensitive to the efficiency hurdles in developed and emerging economies and market manipulation capacities.

Appiah-Kusia & Menyah (2003) tested weak-form efficiency of 11 African stock markets comprising of Nigeria, Egypt, Kenya, Zimbabwe, Mauritius, Morocco, Botswana, Ghana, Ivory Coast, Swaziland and South Africa. Conditional volatility (heteroscedasticity) was captured by using exponential GARCH-M model. The result showed evidence of weak-form efficiency in Egypt, Kenya, and Zimbabwe. The result also revealed traces of efficiency in Mauritius and Moroccan stock exchanges. Rejection of weak-form efficiency in Botswana stock market was also found very recently when parametric and non parametric (autocorrelation test, Kolmogorov-Smirnov Test, Runs Test, ADF and Phillips-Parron (PP) unit root test ) were applied (Chiwira & Muyambiri, 2012).

Jefferis & Smith (2005) studied changing patterns of market efficiency of African stock markets of South Africa, Egypt, Morocco, Nigeria, Zimbabwe, Mauritius and Kenya over

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time. The study period started in early 1990’s and ended in June 2001. GARCH approach with time-varying parameters and test of evolving efficiency (TEE) were used to detect efficiency over the period of time. The study found Johannesburg stock market (JSE) weak- form efficient throughout the study period, while Egypt, Morocco and Nigeria became efficient at the end of the period. However, contradictory results were revealed with respect to Appiah-Kusia & Menyah (2003) in case of Kenya and Zimbabwe stock markets which showed no tendency towards weak-form efficiency over time. Mauritius stock market exhibited slow tendency to eliminate inefficiency, which is consistent with Appiah-Kusia & Menyah (2003).

Gupta & Basu (2007) investigated market efficiency on emerging African stock markets of Egypt, Kenya, Zimbabwe, Morocco, Mauritius, Tunisia, Ghana, Namibia, Botswana and the West African regional stock exchanges. Non parametric tests (Kolmogorov-Simirnov correlation test and runs tests) were applied. Random walk was rejected except for Namibia, Kenya and Zimbabwe. The results are consistent with Appiah-Kusia & Menyah (2003) in case of Kenya and Zimbabwe.

Mlambo & Biekpe (2007) examined ten African stock markets including, Botswana, Egypt, Ghana, Johannesburg, Kenya, Mauritius, Morocco, Namibia, Tunisia and Zimbabwe and West African Regional Stock Exchange (Bourse Regionale des Valeurs Mobilieres (BRVM). In order to cater thin- trading in almost all the markets returns were calculated on trade-to- trade basis. In Namibia random walk hypothesis was not rejected due to its correlation with Johannesburg stock exchange. Similarly Kenya and Zimbabwe were not rejected as weak- form efficient. On the other hand, Mauritius, Egypt, Botswana and BRVM deviated from random walk hypothesis. The study suggested the need for non linear serial correlation testing in these markets for testing efficiency level, since markets with weak microstructures where return generating process is expected to be non-linear. Therefore, a test on linear correlation could lead to wrong inferences.

Lagoarde-Segot & Lucey (2008) studied Middle-Eastern North African (MENA) stock markets (Turkey, Israel, Jordan, Tunisia, Egypt, Lebanon and Morocco) for the period 1998-

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2004, by employing individual and multiple variance ratio tests, unit root test and ordered logit model to test the efficiency level in these markets. Results revealed distinctive efficiency levels explained by differences in size of stock markets and corporate governance. Prior to this study Al-Khazali et al. (2007) already confirmed random walk hypothesis on MENA stock markets by applying non- parametric variance ratio test.

Another study by Emenike (2010) revealed rejection of random walk in Nigerian Stock Exchange (NSE) across three time periods selected from 1985-2007, by using runs test, Kolmogorov-Smirnov, and Q-Q normal chart. The study also revealed the improvements in NSE trading system over time, have positive impact on efficiency.

Comparatively recent study conducted by Ntim et al. (2011) sheds light on 24 African markets across continent along with eight African national stock price indices. The purpose of the study was to demonstrate the comparison between continent-wide stock prices with the national based African indices. The study used variance ratio test and concluded that continent-wide stock markets have better weak-form informational efficiency as compared to their national counterparts. The study suggests improvements in efficiency of national price indices by integrating their operations continent-wide.

The empirical studies on emerging African markets demonstrated conflicting results for efficiency. Small sized markets with low integration showed evidence against weak-form efficiency and random walk. Studies noticed presence of random walk and weak-form efficiency in markets where improvements in trading systems, liberalization, market integration and better governance is experienced with the passage of time.

4.3.4 Middle Eastern emerging markets Abraham et al. (2002) tested weak-form efficiency in three major Gulf stock markets, of Kuwait, Saudi Arabia, and Bahrain by employing variance ratio test and the runs test for the period 1992 to 1998. The study aimed at identifying the systametic bais in finding efficiency in the market when it is thinly-traded and taking corrective measures to cater that problem. The Beveridge & Nelson (1981) methodology was used to separate the effects of infrequent

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trading thus allowed to draw un-biased inferences. After separating the effects of thin- trading, for three markets random walk hypothesis was not rejected.

Omran & Farrar (2006) tested the random walk hypothesis and calendar anomalies in the emerging stock markets of the Middle Eastern countries. The markets rejected the random walk for all five markets and instead supported the presence of the calendar anomalies. However, the evidence for the Israel Tel100 stock market showed traces of random walk. (Marashdeh & Shrestha, 2008) vetted Emirates securities markets namely Abu Dhabi Securities Exchange (ADX) and Dubai Financial Market (DFM) for the period 2003-2008 by applying unit root and PP tests. Both of the markets were found to follow random walk and weak-form efficient.

Oskooe (2011) selected Iran stock market for testing weak-form efficiency in the market for the period 1999-2009. He employed unit root test for the purpose and concluded that market does not follow random walk and is not weak-form efficient.

Asiri (2008) conducted a study on 40 listed companies in different sectors of Bahrain Stock Exchange (BSE) to test the weak-form efficiency for the period 1990-2000. The techniques used were Dickey-Fuller tests and autoregressive integrated moving average (ARIMA). Both tests supported random walk in each individual sector.

Asiri & Alzeera (2013) tested hypothesis of weak-form efficiency in Saudi Arabia’s stock market; Tadawul. For the purpose the author selected daily returns of sectoral indices as well as all-share index belongs to Tadawul for the period 2006-2012. Parametric and non- parametric tests including Dickey-Fuller, Pearson correlation test, Durbin-Watson test and Wald-Wolfowitzruns test were applied. The result confirmed the presence of weak-form market efficiency for all-share price index and for 11 individual sectors.

The above review shows that Iranian, Gulf and Saudi Arabia markets on the whole are found weak-form efficient after using parametric and non-parametric tests on daily, weekly and monthly returns.

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4.3.5 Asian emerging markets A great deal of research can be found in Asian emerging markets over last two decades especially after liberalization of financial markets in 1990’s, which increased the integration of world markets and huge amount of capital transfer from developed world in emerging markets.

Poshakwale (1996) tested the weak-form efficiency of indian stock market by taking Bombay Stock Exchange (BSE) into consideration. The study followed the path of concluding market inefficiency with the presence of day-of-the-week effect and serial correlation in the return series. The study found absence of random walk in BSE. Gupta & Basu (2007) investigated market efficiency in two major stock markets of India; Mumbai Stock Exchange (BSE) and National Stock Exchange (NSE) of India for the period 1991-2006. The results are consistent with the results of BSE in Poshakwale (1996) with evidence of serial correlation and rejection of random walk hypothesis.

Abeysekera (2001) investigated informational market efficiency in an other South Asian market of Sri Lanka by testing Columbu Stock Exchange for the period 1991-1996. Correlation coefficient test and runs test were applied on daily, weekly and monthly returns of Sensitive Share Index (SSI), which revealed serial correlation in returns and rejected null hypothesis of weak-form efficiency.

Quite a number of studies have been conducted for testing random walk in Bangladesh stock markets and both similar and contradictory results have been found. Most of the work is based on Dhaka Stock Exchange (DSE). Alam et al. (1999) examined DSE from 1986-1995 and concluded that DSE follows random walk. Mobarak & Keasey (2000) examined market efficiency on all listed Dhaka Stock Exchange (DSE) securities. The study applied autocorrelation test, runs test and autoregression test on daily stock prices from 1988-1997. The result revealed presence of autocorrelation which rejects the weak-form efficiency in DSE. On the other hand Islam & Khaled (2005) applied heteroscedasticity-robust Box-Pierce test which reversed the result presented in the previous studies. This particular study showed evidence of weak-form efficiency when monthly data was used. Alam et al. (1999) also

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concluded similar phenomina about Bangaldesh stock market. However, rejection of random walk and efficiency was found by Mobarek et al. (2008) when auto-regressive model (ARIMA) along with runs tests and Kolmogrov-Smirnov normality test were applied. Similar results were captured when Wald test of Dockery & Kavussanos (1996) was applied (Khandoker et al. 2011; Nguyen & Ali, 2011). Wald test was re-employed by Nguyen et al. (2012) on Taiwan stock market to check random walk. The result also showed rejection of random walk in Taiwan stock market.

Mixed results were found in case of five Asian stock markets of Bangladesh, Hong Kong, Malaysia, Sri Lanka and Taiwan by applying variance ratio test developed by Lo & MacKinlay(1988) for period 1986-1995 (Alam et al., 1999). Except Sri Lanka random walk was followed in all markets. Similarly Cooray & Wickramasighe (2007) examined four emerging markets of South Asia including Pakistan, India, Sri Lanka and Bangladesh and found traces of weak-form efficiency except for Bangladesh. Contradictory results were observed about emerging Asian market of Korea, Malaysia, Hong Kong, Singapore and Thailand (Huang, 1995) where rejection of random walk hypothesis on the basis of variance ratio test of Lo & MacKinlay (1988) was found. However, runs test suggested weak-form efficiency in most of the emerging markets (Karemera et al.,1999).

Kim & Shamsuddin (2008) used weekly and monthly data for testing market efficiency by applying non-parametric tests on Asian markets of Hong Kong, Japanese, Korean and Taiwan, Indonesia, Malaysia, Philippines, Thailand and Singapore. They showed how multiple variance ratio test based on wild bootstrap is better to apply over conventional Chow-Denning variance test when the sample size is not very big. The markets of Hong Kong, Japanese, Korean and Taiwan found weak-form efficient by using that technique. The markets of Indonesia, Malaysia and Philippines had shown no traces of efficiency even after liberalization of these markets in eighties. On the other hand Singaporean and Thai markets became efficient after Asian financial crises of nineties revealing the non-sensitiveness of financial crises on efficiency. The result of Hong Kong and Singapore market efficiency are consistent with the previous study of Lima & Tabak (2004). Nikita & Soekarno (2012) also

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revealed weak-form inefficiency and autocorraltion in Indonesian stock market during 2008- 2011.

Another study conducted by Munir et al. (2012) to investigate efficiency of Asean (Association of Southeast Asian Nations) security markets by selecting five Asean stock markets of Indonesia, Malaysia, Phillipines, Singapore and Thailand. The data used for the study ranges from 1990-2009. Two regime threshold auto regressive (TAR) approach was used to cater the possible non-linearity in stock retuns. Diversified results were again found. Malaysia and Thailand stock returns followed random walk, while Indonesia, Phillipines and Singapore revealed non-linear stationary process inconsistent with efficient market hypothesis.

Chinese stock market was tested for random walk by Charles & Darne (2009). Multiple variance ratio tests, Wang-Kim subsampling model, Kim’s wild bootstrap test and multiple Chow-Denning test were employed on two types of return series; first one ‘A’ shares, and the other one ‘B’ shares. ‘A’ shares are only traded in local currency, for domestic investors only. While’B’ shares are traded in foreign currencies and are for domestic and international investors both. It was concluded that shares of ‘B’class having international integration followed did not random walk in their returns, while class ‘A’ is more efficient. The results are also consistent with the previous study of Lima & Tabak (2004)

Phan & Zhou (2014) tested emerging stock market of Vietnam for the period 2000-2013. Using autocorrelation test, variance ratio test, and runs tests Vietnamese stock market was not found efficient in the initial periods of the study but shown gradual improvement in the operations of the market by evidence supporting random walk hypothesis in only VN-index (one of the indices of Vietnamese stock market) during the last years of study period. Phan & Zhou (2014) hold strong influence of investor in the market responsible for the rejection of random walk in the Vietnamese stock market.

Choudhuri & Wu (2003) scrutinized ten emerging stock markets by identifying structural breaks from the time of liberalization of stock markets, and concluded that the extent and

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period of liberalization of stock markets is sensitive to efficiency levels and ignoring structural breaks that arise due to the liberalization can lead to misguided inferences about efficiency. The study selected Argentina, Brazil, Chile, Colombia, Greece, India, Jordan, Korea, Malaysia, Mexico, Nigeria, Pakistan, Philippines, Taiwan, Thailand, Venezuela, and Zimbabwe for the period 1985-1997. By applying Zivot–Andrews sequential test for a random walk to take into account the effects of structural changes in stock prices. The study rejected the random walk hypothesis. They further concluded these structural changes can be explained by other major economic events in the underlying economies.

Uppal, (1993) determined the relationship between Pakistani equity market and international equity markets of Japan, Korea, USA, UK, Australia, and India using GARCH (1,1) technique. However, the weak-form efficiency results seemed to be consistent with only Japan and Korea.

4.3.5.1 Empirical evidence of Pakistani market Pakistani stock market has emerged as one of the outperforming markets of South East Asia in the last two decades. After the financial reforms of 1990s the market gained significant amount of capital inflow from developed markets. Several studies have been conducted on efficiency of Karachi Stock Exchange (KSE), which is regarded as the most dynamic and leading stock market of country.

Uppal (1993) determined the relationship between Pakistani equity market and international equity markets of Japan, Korea, USA, UK, Australia, and India using GARCH (1,1) technique. However, the weak-form efficiency results seemed to be consistent with Japan and Korea.

Khilji (1994) examined the non-linearity of stock returns in Pakistani stock markets and found strong non-linear dependency of stock returns. In his previous study Khilji (1993) examined monthly returns of overall index and share price indices of ten specific industrial groups of Pakistani stock market and found the stock market returns series to be leptokurtic and positively skewed. Linear dependency was found using error-correcting, first-order

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autoregressive model and the Kalman Filter technique. The returns were found constant and equal to long-term expected monthly returns.

Ahmed and Rosser (1995) found speculative bubbles in the Pakistani equity market, by employing Vector Autoregressive (VAR) technique, Hamilton regime-switching model and the Wald test. The authors further pointed out that the Pakistani economy may be subjected to instability and oscillation due to the erratic and complex dynamics of its stock market.

Husain (1997) investigated the random walk in the Pakistani equity markets from 1989-1993, and rejected the hypothesis of random walk in those markets.

Khowaja and Mian (2005) found compelling evidence of price manipulation schemes by inside traders (brokers) in KSE. It was found that brokers annually earn 50%-90% higher returns than those earned by outside investors.

Hameed and Ashraf, 2006 tested for weak-form efficiency taking stock returns from 1998- 2006. Weak-form efficiency was rejected in the market. GARCH model revealed volatility clustering in returns. However volatility was found declining with the imposition of circuit breakers18 in the market and switching on to T+3 from T+5 settlement period.

Cooray & Wickramasighe (2007) examined Pakistani stock market along with three other South Asian markets and witnessed weak-form efficiency in pakistani stock market.

Similarly in another study Mustafa and Nishat (2007) investigated KSE for daily, weekly and monthly stock returns for the period 1991-2003 and found the stock market to be efficient after making adjustments for thin trading.

18 In order to control massive stock price fluctuations, stock exchanges use trading curb or circuit breaker. It is a point at which a stock market is stopped for trading or trading is limit to a certain percentage range of a reference price, for a period of time.

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Mamoon (2008) tested the short to medium term trends and volatility in KSE and found that in 1990’s the stock market had become volatile both on short-term (daily) and medium term (monthly) basis and further found out that there is no systematic relation of stock price volatility with real or nominal macroeconomic volatility. However, no relationship between volatile stock prices and volatile trade volume was found.

Haque, Liu and Nisa (2011) tested KSE for the period 2000-2010 and rejected weak-form efficiency using ADF, PP, autocorrelation and runs test. Similar results were found by Mishra (2011) Mehmood et al. (2012) Haroon (2012) Omer et al. ( 2013).

Aslam et al. (2012) found weak cointegration of developed market with KSE and proposed that investor of developed economies may find better opportunities and can diversify their investment by investing in a market which is not cointegrated with developed markets. Linkages of Karachi Stock Exchange with Dhaka stock exchange were found (Mehar et al., 2011).

Major preceding studies have rejected both random walk and weak-form efficiency hypothesis in Pakistani stock market except for Cooray & Wickramasighe (2007) ; Mustafa & Nishat (2007). Serial correlation and volatility clustering was found in most of the studies by using cointegration test, variance ratio test, runs tests and GARCH (1,1). Volatility is highly persistent in KSE-100 index and least persistent in KSE-30 index; two most traded indices of Pakistani stock market (Shamshir & Mustafa, 2014).

Pakistani stock market is thinly traded therefore, firm level studies are suggested. Moreover, empirical evidence revealed that these studies are based on KSE-100 index of Karachi Stock Exchange; leaving a major gap behind by ignoring other indices in the exchange19. Testing

19 The other three indices operational at Karachi Stock Exchange are; KSE-all share index; KSE-30 index and KMI-30 index.

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on the data of other indices is also suggested which is likely to present more consistent results about Pakistani stock market.

4.4 Conclusion

Informational efficiency and random walk in stock markets has always been a controversial issue, but at the same time supreme focus of interest amongst researchers and investors in the share market since the seminal work of Fama (1965a). This study aimed at revisiting and divulging the existing empirical evidence regarding the informational efficiency and random walk in stock markets of developed and emergent markets. The critical analysis of statistical tools used is out of the purview of this study. Earlier studies were based on the examination of the phenomenon in developed markets. However, examination of efficiency on emergent markets received particular attention of the researcher after the huge inflow of capital in these markets as a result of financial liberalization. Empirical evidence in favour or against EMH can be considered a major contribution towards the strategic trading adeptness of a portfolio manager and of a proficient investor. Mixed results for efficiency and random walk revealed from the review of large amount of literature in case of developed and emerging markets. Existence of random walk was found in US financial markets (Lee, 1992; Choudhry, 1994), while French (1980); Poterba & Summers (1986;1988) rejected random walk for US markets. On the other hand Nakamura and Small (2007) found random walk when “small- shuffle surrogate” method was applied on US stock market data. Similarly, for UK financial markets random walk was not rejected (Lee, 1992; Poon, 1996; Chan et al., 1997; Worthington & Higgs, 2004; Borges, 2010). While Al-Loughani & Chappell (1997) found no evidence of random walk for UK stock exchange.

Highly contradictory results have been found in case of emerging markets depending on the size of market, influence of insider trader, market integration, liberalization, trading volume, trading process, and infrequent trading. Various factors are identified for stock market inefficiency in various studies in emerging markets. Weak institutions (Johnson & Mitton, 2003; Fisman, 2001; Bertrand et al., 2002), weak property rights protection, and political shocks (Morck et al., 2000) broker and insider influences (Khwaja & Mian, 2005; Siddiqi,

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2007; Phan & Zhou , 2014) size of stock market (Lagoarde-Segot & Lucey, 2008), volume of turn over (Smith & Ryoo, 2003), market manipulation capacity (Magnusson & Wydick , 2002). The markets of Nigeria, Namibia, Kenya & Zimbabwe and MENA stock markets amongst the African markets revealed traces of efficiency with the passage of time due to improvements in the trading processes, integration with much developed markets, size of the markets, and corporate governance (Lagoarde-Segot & Lucey, 2008; Emenike, 2010; Ntim et al., 2011). But opposite results have been found in case of China’s class ‘B’ and ‘A’ shares. Return series of class ‘B’ shares having international linkages and international investors were found inefficient, while of class ‘A’ shares were found efficient despite of having only domestic investor and trade only in local currency (Charles & Darne, 2009). Similarly, Kim & Shamsuddin (2008) investigated the effects of liberalization and Asian financial crises on the efficiency of Asian emerging markets and found quite stounding results. Their study revealed that markets of Indonesia, Malaysia and Philippines remained inefficient even after liberalization of these markets in eighties. On the other hand Singaporean and Thai markets became efficient after Asian financial crises of nineties.

Laurence (1986), identified that index level returns may result in misleading findings about efficiency due to the thinly traded emerging markets. Abraham et al. (2002) found three Gulf stock markets of Kuwait, Saudi Arabia, and Bahrain weak-form efficient when adjusted for thin trading. Similarly, Mustafa & Nishat (2007) found efficiency in Karachi stock market when adjusted for thin trading.

Choudhuri & Wu (2003) recommended ‘structural breaks’ in returns series with the occurrence of economic and political event(s) that may have the tendency to change the behaviour of stock markets. In that case ignoring the structural break(s) may result in misguided inferences about efficiency.

Various studies have employed various techniques for investigating serial correlation and market eficiency levels in emerging markets. Lots of studies used cointegration test, Lo & MacKinlay (1988) variance ratio test, multiple variance ratio tests of Chow & Denning (1993), runs test for testing serial correlation. ADF unit root test and (PP) test for finding out

Chapter 4

weak-form efficiency and GARCH (1,1) for determining time varying variance. Levels of efficiency and existence or non-existence of random walk is highly sensitive to the methodology used (Areal & Armada, 2002). For example, Istanbul stock exchange was found weak-form efficient by applying varainace ratio test while found inefficient when unit root test was applied (Kapusuzoglu, 2013). Similarly, in another study rejection of random walk hypothesis was concluded for African emerging markets by employing variance ratio test (Smith et al., 2002), while presence of weak-form efficiency was noticed in the same era in African markets after using partial auto-correlation function and Box-Pierce Q-statistics (Magnusson & Wydick, 2002). Rejection of random walk in major Asian emerging stock markets was observed when variance ratio test of Lo & Mackinlay (1988) was used (Huang, 1995) and runs test suggested weak-form efficiency in most of the emerging markets (Karemera et al., 1999). Conversaly, some Latin American emerging markets when tested with variance ratio test, serial correlation was found, while the same countries were found weak-form effcieient for the same period when runs test was applied (Urrutia, 1995). Kim & Shamsuddin (2008) preferred multiple variance ratio test based on wild bootstrap over conventional Chow-Denning variance test, when the sample size is not very big. Mobarak & Keasey (2000) found Dhaka stock exchange inefficient by applying autocorrelation test, runs test and autoregression test, while Islam & Khaled (2005) applied heteroscedasticity-robust Box-Pierce test which reversed the results. Serial correlation and volatility clustering was found in most of the studies on Pakistani stock market by using cointegration test, variance ratio test, runs tests and GARCH (1,1) model. In a comparative study between different indices of Karachi stock market. Shamshir & Mustafa (2014) by using GARCH (1,1) model found least persistent shocks in KSE-30 index and highest persistent volatility in KSE-100 index. However, further studies using weekly and monthly stock returns of share markets are suggested.

Chapter 5

Methodology for Examining Weak-form Efficiency

This chapter includes the basic direct methodology adopted in the study of investigating the weak-form efficiency in the KSE market.

5.1 Data Specification and Source

The study is investigating weak-form efficiency by applying direct methods and indirectly by examining volatility and seasonal anomalies on KSE for the period from January 01, 2009 to August 31, 2014. The study is using the daily closing prices of the four indices operating in the KSE market; KSE-100, KSE-30, KSE all-shares and KMI-30 indices. In addition to that 43 individual companies are selected for the investigation of the same out of total companies listed in the market whose trading days are at least 1350 during the study period (2009-2014). Trading is done on 5 days a week, excluding Saturday and Sundays. The total number of trading days (excluding weekends and holidays) during the study period is 1404. Majority of the data set was obtained from the websites of the KSE and Standard Capital Securities (Pvt) Ltd; a brokerage firm. However, in case of KMI-30 index the closing price data from the whole study period is not available; therefore by using private links in KSE, the data is obtained.

5.2 Stock Returns Vs Stock Prices

To proceed with the investigation of random walk we first calculate the return series of all the indices in the stock exchange. To focus on returns rather than on prices is due to two reasons. First, since the financial markets are considered to be close to perfect competition therefore the size of investment does not influence prices. Secondly, the returns are more attractive from the perspective of investor and at the same time more appropriate to fulfill the approach statistical analysis than prices.

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The simple net returns Ret, on asset between time period -1 and can be written as

Where, is the price of an asset at time . Whereas, gross return can be defined as

Similarly gross returns over a time period k from any previous period t-k can be expressed as

(5.2)

The simple gross return on the asset taking logarithm and defining multi-period return as the sum of continuously single-period returns we have equation 5.4, 5.5 and 5.6, respectively.

Where,

Therefore,

(5.5)

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And,

(5.6)

5.3 Theory of Rational Expectations and Efficient Market Hypothesis

By considering the asset price based on some set values conditional of available information at time t,

= (5.7)

Similarly for one period ahead it can be expressed as

= (5.8)

According to efficient market hypothesis the changes in prices from time t to t+1, cannot be forecasted given the information in , and according to the theory of rational expectations theory, following equation would hold.

(5.9)

Therefore, it implies that

= 0 (5.10)

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5.4 The Random Walk Hypothesis

The financial time series if identically and independently distributed it follows random walk and the stock prices are said to be purely non-predictable and investors are not able to earn above normal returns consistently.

) (5.11)

The same insight as in equation 5.4, implies for

) (5.12)

Where, is the drift, and is independently and identically distributed (IID) with mean 0 and variance and .

In RW1 the series is independent, implies that increments are uncorrelated and any non linear function of the increment is also independent.

Cov and Cov for all k 0

This is the case of RW where conditional mean and variance are both linear in time.

(5.13)

Var (5.14)

In RW2 model independence holds but the series may not be identically distributed. It implies the presence unconditional heteroscedasticity in . This particular phenomenon of time related volatility is highly common feature found in the financial time series.

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The weakest form of random walk is RW3 where increments are uncorrelated, but not independent, that is, the squared increments are correlated.

Cov for some k 0

5.5 Testing Tools

The study applied both parametric and non-parametric tests to check random walk and hence the weak-form efficiency of (Fama, 1970) for the stock market.

Among the non-parametric test Kolgomorov-Simirnov (K-S) and runs test are applied. Among the parametric tests, serial correlation tests, ADF, autoregression model, and ARMA model are used. Variance ratio test of Lo and MacKinlay (1988) is also applied to test the hypothesis.

The main hypotheses of testing random walk and efficiency consist of following null and alternative hypotheses.

Ho: Indices in Karachi Stock Exchange follow random walk, i.e., indices in Karachi Stock Exchange are weak-form efficient.

H1: Indices in Karachi Stock Exchange do not follow random walk, i.e., indices in Karachi Stock Exchange are not weak-form efficient.

Ho: Stock returns of firms in Karachi Stock Exchange follow random walk, i.e., stock returns in Karachi Stock Exchange are weak-form efficient.

H1: Stock returns of firms in Karachi Stock Exchange do not follow random walk, i.e., stock returns in Karachi Stock Exchange are not weak-form efficient.

Chapter 5

5.5.1 Kolgomorov-Simirnov (K-S) test It is a non-parametric test and is named after two Russian mathematicians; Anderi Nikolaevich and Nokolai Vasil’ evich Simirnov, developed the test. Here one sample test is being used to examine the sample cumulative probability distribution. The test can be customized to serve as a goodness of fit for normality. In this case the sample series is compared with standard normal distribution. The return series of KSE indices will be tested for parameters of uniform and normal distribution.

The empirical distribution function for n number of Xi,

(5.15)

Where, is an indicator factor and is equal to 1 if and equal to zero if

The Kolmogrov-Smirnov (K-S) statistics for a given continuous cumulative distribution function F(x) is given by

(5.16)

Hypothesis of Kolmogrov-Smirnov test:

The returns series follow normal distribution. The returns series do not follow normal distribution.

The returns series follow uniform distribution. The returns series do not follow uniform distribution.

The hypothesis regarding the distributional form is rejected if the test statistics D is > than the critical value obtained from the table. Alternatively, for higher sample size the hypothesis

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cannot be accepted if probability of K-S statistics is significant at 1% and 5% level of significance.

5.5.2 Runs test The runs test or Walt-Wolfowitz test is another non-parametric test used to find out serial independence was developed by Abraham Walt and Jacob Wolfowitz. It is based on the intuition that the residuals of the series show a certain pattern of negative and positive values then the series do not follow random walk and serial correlation exists in the series. The runs are the sequence of these changes in the series having the same sign and the ‘length of the run’ is number of elements in it. Too many runs in a series reflect the frequent sign change in the series indicating negative correlation and too few runs indicate positive correlation. The runs test only looks at the number of positive or negative changes and ignores the amount of change from mean. The null hypothesis in runs test is that each element in the sequence is a random variable and is drawn independently from the same series.

The returns series follow random walk. The returns series do not follow random walk.

Where, is the actual number of runs, and is the expected number of runs (mean).

Mean (5.18)

Variance (5.19)

Where, N = total number of observations = = number of positive elements (residuals)

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= number of negative elements (residuals)

The series will follow normal distribution and the null hypothesis of randomness cannot be rejected then following condition is expected:

Prob [ ] = 0.95

For larger samples the hypothesis is rejected if at 5% significance level, runs test statistics (Z) with an absolute value is greater than 1.96 and concludes randomness.

5.5.3 Autocorrelation test In order to test serial correlation between the current and lagged value stock prices spectral analysis tests and autocorrelation test are found in earlier studies for example, in Morgenstern (1963) and Fama (1965) as the tools used for testing serial correlation. These statistical procedures are testing RW3 model of Campbell et al. (1997) which is the least restrictive version of the RWH and only requires un-correlatedness of price. Given a stationary time series of stock returns the kth order autocovariance and autocorrelation coefficients, and respectively, expressed as

(5.20)

= (5.23)

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in case of randomness of return series.

Where,

is the serial correlation coefficient of stock returns of lag k; denotes returns at time t; denotes returns over time period t-k; and k denotes number of lags. The objective is to determine the presence of serial correlation in the series. is a unit free measure and lies between 1 and +1. Positive and negative values of indicate positive and negative correlation. Positive serial correlation is mean-aversion and reflects slow adjustment to new information due to under-reaction. On the other hand negative serial correlation reflects mean-reversion. Zero correlation means randomness of return series. In case of large samples joint hypothesis of all lag values of autocorrelation coefficient is tested by using Ljung-Box (LB) (Q) statistics, a chi-square distribution with degrees of freedom equal to number of autocorrelation (k) is given by,

LB (Q) = (5.24)

Empirical evidence suggested using autocorrelation coefficient in conjunction with Ljung- Box statistics to examine serial correlation is most appropriate tool for large sample size (e.g., Laurence, 1986; Poshakwale, 1996; Mobarek et al., 2008; Patel et al., 2012).

The returns series possesses zero autocorrelation at the first k autocorrelations (

The returns series does not possess zero autocorrelation at the first k autocorrelations (

Chapter 5

For the return series to be stationary with zero autocorrelation the null hypothesis cannot be rejected if all of the autocorrelation coefficients are zero. However, the null hypothesis can be rejected if some are non-zero. Conventionally, the probability value of less than 0.05 (at 5% level of significance) that the estimated coefficient of correlation is zero, indicates that the time series exhibits significant autocorrelations.

5.5.4 Autoregression, Heteroscedasticity and Breusch-Godfrey (B-G) LM tests. Ignoring serial in correlation in a regression means OLS coefficients may be unbiased and consistent, but inefficient and variances of coefficients may be biased; forecast is invalid in this case. The Breusch–Godfrey serial correlation LM test is used for examining autocorrelation in the errors in an autoregressive model. Breusch-Godfrey LM test can be used for AR (1) or AR (p) terms. If the usual statistic is calculated for this model, then the following asymptotic approximation can be used for the distribution of the test statistic;

Consider an AR(1) model

(5.25)

If is first order serially correlated then,

(5.26)

Such that,

Null hypothesis = 0 0

Chapter 5

5.5.5 Unit root test. Unit root testing is regarded as a vital tool for determining the presence of random walk in a series. A series is said to have unit root if it is non-stationary. Stationarity is considered to be an essential, but not sufficient condition for presence of the random walk in a series. Presence of unit root implies the presence of predictability in the price or return series, which is not consistent with random walk model as it requires unpredictability in successive prices or in returns. Therefore, unit root testing in the stock price series is not the sufficient for testing RWH.

(5.27) (5.28)

(5.29)

For the series to be stationary , and

Three different tests are being used here namely: the Augmented Dickey-Fuller (ADF) test, the Phillips Perron (PP) test and the Kwiatowski, Phillips, Schmidt and Shin (SPSS) test.

5.5.5.1 Augmented Dickey-Fuller test. The ADF test is the extended form of Dickey-Fuller (DF) test for determining the unit root in a time series. The difference lies in the consideration of AR(1) process in case of DF while AR(p) process in case of ADF case. The ADF is considered to be more valid where time series is based on daily data as it also involves the lagged difference terms of the dependent variable.

Chapter 5

Following equation with drift and trend will be investigated and compared with the critical values of MacKinnon (1994) in order to determine the significance of the t-statistics associated with

+ + (5.30)

Where, is the first difference of the log of the closing price index of ith index /firm and selected firm.

is the constant of drift parameter.

is the coefficient of trend.

is the coefficient of AR(1) term

are the coefficient of lagged terms and q, is the number of lagged terms, and

is white noise

The null hypothesis for non- stationary series is as follows.

, series has unit root

, no unit root

Failing to reject null hypothesis implies that time series possesses the properties of random walk.

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5.5.5.2 Phillips-Parron test Phillips and Parron (1988) introduced this particular test for the analysis of unit root in a time series. The test is non-parametric in nature and accounts for antocorrelation without adding lagged differences in the regression. The regression equation for the test is given by:

= (5.31)

The in this case may be heteroscedastic. The PP test corrects for any serial correlation and heteroscedasticity present in . Two statistics are to be analyzed in this case

(5.32)

(5.33)

The terms and are estimates of variance parameters. The null hypothesis that the series contains unit root; , series has unit root , series has not unit root

5.5.5.3 Kwiatkowski, Phillips, Schmidt and Shin test

Unlike the PP test it is a parametric test and has a null hypothesis assuming stationarity of a time series around mean or a linear trend. The alternative hypothesis assumes the presence of unit root. The KPSS model assumes the combination of deterministic trend , a random walk and an error term .

(5.34)

Chapter 5

(5.35)

, time series of stock prices from till time , is the deterministic trend, is the random walk process and is the error term of equation 1. is the error term of equation 2, such that

In case of of random walk process , the series is assumed to be stationary. In case , the null hypothesis means that series is stationary around . If on the other hand , then the null hypothesis reflects the stationarity around linear trend. If variance, the series is non-stationary around trend and random walk. , series is stationary and has no unit root.

, series is non-stationary and has unit root

The test statistics is defined by one sided Lagrange Multiplier given as:

Where, = , for , is the partial sums of errors. , denote estimated errors from regression of on constant and time, denotes the estimate of variance.

5.5.6 Variance ratio test Variance ratio (VR) test introduced by Lo and MacKinlay (1988), emerged as one of the primary tools for testing the serial correlation. According to which the ratio of variance of the two-period return to twice the variance of one-period returns . That is if the time series is stationary then the variance ratio VR(2) will be written as:

Chapter 5

(5.39)

Where is the first-order autocorrelation or returns }.

In case of stationary time series of returns the variance ratio is one plus the first-order autocorrelation coefficient, which will turn zero in case of RW1, therefore, 1. If returns are positively correlated in first-order the variance of the addition of two one- period returns will be greater than the sum of one period return’s variance. Hence, autocorrelation is 1, and variances grow faster than linearly.

If returns are negatively correlated in first order the variance of addition of two one-period returns will be lesser than the sum of one period return’s variance. Hence, autocorrelation is 1, and variances grow slower than linearly. In case of higher-order auto correlation it can be generalized for q-period variance ratio

Where,

(5.41)

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And is the kth order autocorrelation coefficient of { .

For and for all , the null hypothesis of no serial correlation cannot be rejected.

1 implies variances grow faster than linearly (positively correlated). Significantly higher than 1 values of implies mean averting series and explosive at higher q levels. implies variances grow slower than linearly(negatively correlated). Significantly lower than 1 values of implies mean reverting series.

The test employed two specifications of the variances: homoscedasticity and heteroscedasticity proposed by Liu and He (1991).

(5.42)

Where, is homoscedastic test statistics and

And is heteroscedastic test statistics is given by:

Where,

And (5.44)

Chapter 5

If the maximum absolute value of Z (q) or is greater than the critical value at a predetermined significance level then the RWH is rejected.

5.5.7 ARMA modeling The ARMA (Box -Jenkins) model is used for examining the random walk in the time series univariate return series. An ARMA model is based on two basic notions; Autoregression (AR); and moving average. The model is known as ARMA (p,q) model where p is the order of the autoregressive part and q is the order of the moving average part. The model assumes that each value in the time series is a linear function of its past values, past errors (AR), and current and past values of other time series (MA). In contrast, ARIMA model involves another third process of integration in conjunction with ARMA in case the series is non- stationary. However this study uses ARMA model on account of the stationarity condition of most of the return series during the study. AR(p) model: (5.45)

Where, are coefficients, is constant and

MA(q) model: (5.46)

Where, are coefficients, is constant and

The ARMA model is the combination of equation (5.45) and equation (5.46)

That is,

Chapter 5

(5.47)

The significant coefficient of autoregression (AR) or moving average (MA) different from zero suggests the violation of independence of return series and rejects the null hypothesis of random walk model and weak-form efficiency in the markets.

Chapter 6

Chapter 6 Analysis and Results

This particular chapter provides the results and findings of testing tools applied in chapter 5, for examining random walk in the KSE indices and selected firms.

6.1 Descriptive Statistics

Table 6.1 exhibits the summary of descriptive statistics of the returns of KSE-100, KSE-30, KSE-all shares and KMI-30 index and 43 selected firms from Jan, 2009-Aug 2014. The mean returns of all four indices and 32 out of 43 firms are positive reveal capital gains in the market over the period. The standard deviation of KSE-30 index is highest (0.4569) reflects the volatility and huge deviation from mean returns in KSE-30 index. For KSE-100 and KAPCO the values of standard deviation are very small, showing less dispersion in the maximum and minimum values of stock prices reflects less volatility in the stock returns of these firms.

According to Gaussian distribution the series is symmetrical about mean when the coefficient of correlation is zero. Positive and negative values of skewness reveal the concentration of values on right and left tails, respectively. The values of skewness greater than zero value in return series of all indices and firms shows asymmetry except for DGKC, LUCK< and POL where the coefficient of skewness is close to zero with values as (0.003, 0.078, 0.088, respectively. KSE-100 and KSE-all shares index and 22 out of 43 firms with negative skewness indicates greater probability of large decreases in returns than rises and remaining 20 firms and KSE-30 and KMI-30 index with positive values of skewness reveals increases in returns. One of the factors of negative skewness in return series is the variation in their earnings announcement dates. The firms with greater dispersion of earnings announcement dates have more negative skewness (Albuquerque, 2010). Another reason of negative skewness is the distribution of good or bad news from companies. Companies usually release good news rather than bad news Damodaran (1985). AICL, DAWH, and NML have very

Chapter 6

high values of negative skewness showing lack of transparency in disseminating fair information to the investor. However, Harvey and Siddique (2000) found that negative skewness collects higher returns. Value of coefficient of kurtosis equal to 3, indicates the normality of series, while greater or lower value indicates the series to be leptokurtic and platykurtic, respectively. Table 7.1 reveals that the return series of all indices and firms to be leptokurtic showing greater volatility in future returns. Very high coefficient of kurtosis in case of DAWH (646.5), NML (620.4) and PTCL (647.1) exhibits slim and long tailed return series reflects the higher probability than usual for extreme price movements to occur in these stocks. Measures of skewness and kurtosis are used to determine the predictability of future returns using past returns. And in financial markets of today profitable trading strategies are based upon the prediction of direction of results (Hong and Chung, 2003). However, these measures may show inconsistent values and cannot be relied upon always (Kim and White, 2003)

Jerqua Bera (JB) test is another good indicator of normal distribution. Higher than zero value of JB test reflects deviations from normal behaviour of return series during the study period in all four indices and selected firms of Karachi stock exchange.

The coefficient of variation is used to compare the volatility of the series. The coefficient is highest in case of HMB (355.6) and lowest in case of KSE-100 index indicates that the KSE- 100 index is least volatile index.

6.2 Results of Kolmogorov-Smirnov Test

Table 6.2a and 6.2b, explain the result of K-S Goodness of fit test to examine the cumulative distribution function of the return series of the indices and selected firms of KSE for normal and uniform distribution parameters, respectively. The probabilities of K-S Z statistics for both normal and uniform distribution are zero (0.000), indicating that at 1% level of significance the hypothesis can be rejected, concluding that all indices of KSE and selected firms under study time period do not follow uniform and normal distribution. Higher values of K-S Z test reflect greater deviations from normal distribution in KSE-30, KMI-30 indices.

Chapter 6

Similarly, higher values of K-S Z test in case of KSE-30, AICL, DAWH and NML indicates greater deviation from uniform distribution. The similar results can be found in many world markets Poshakwale (1996) for India; Gupta & Basu (2007) for African countries; Mobarek, Mollah & Bhuyan (2008) for Bangladesh; Emenike (2010) for Nigeria; Mustafa and Nishat (2007) for Pakistan.

6.3 Result of Runs Test

Results of runs test reveal (Table 6.3) that in KSE-100, KSE-30, KSE all-share and in KMI- 30 indices at 5% level of significance the value of Z-statistics (-2.857,-6.082,-2.911,-2.326, respectively) with an absolute value greater than 1.96, leads to rejection of null hypothesis. It implies absence of random walk in all four indices. Moreover, the observed number of runs is fewer than the expected runs which indicate the presence of negative autocorrelation (Guidi, Gupta & Maheshwari, 2011). Negative autocorrelation indicating the over-reaction in the indices (De Bondt & Thaler 1985, 1987) vis-a-vis in the Karachi stock market and establishes the absence of randomness with mean aversion characteristic. This shows the affinity of over-reaction to unanticipated and shocking news in all four indices. It can be concluded from the results of runs test that prices do not move independently and randomly at the Karachi stock market under the study period indicating exchange and companies does not follow random walk. It is inferred that some investors can make excess profits in the said market by taking advantage of over-reaction to stirring and unanticipated information. Similar results are found in case of Pakistan (Ahmad & Rosser, 1995; Abraham, Seyyed, & Alsakran, 2002; Abeysekera, 2001; Mustafa, 2007; Mishra, 2011; Haque, Liu and Nisa, 2011).

However, in case of 28 firms (ABOT, AKBL, APL, BAFL, BAHL, DCL, EFUG, EPCL, FFCL, FFC, FABL, HBL, HMB, HUBC, ICI, KAPCO, LUCK, MEBL, NBL, NML, OGDC, POL, PSO, PTCL, SHEL, NGC, SSGC, UBL) out of 43 firms the value of Z-statistics is less than 1.96 and p-values greater than 0.1, call for an acceptance of null hypothesis and independent movement of prices in these firms.

Chapter 6

6.4 Results of Autocorrelation Test

The autocorrelation coefficient measures the relationship of the variable at time t with its value in the previous time interval. The autocorrelation coefficients have been computed for the return series in all four indices of Karachi stock Exchange and found significant autocorrelation at various lags for the whole sample period.

Table 6.4 presents the result of the ACF and LB statistics for the daily returns on the KSE- 100, KSE all-share, KSE-30 and KMI-30 indices and selected firms of Karachi stock exchange. To test for the serial correlation in these markets under study period autocorrelation test up to 36 lags were performed for daily stock returns.

Positive autocorrelation indicates over-reaction in the market while negative autocorrelation suggest mean reversion. In both cases it provides strong evidence against market efficiency.

Table 6.4 findings show highest correlation coefficient in first lag in all four indices and firms except for AICL, APL, BAFL, BAHL, BIPL, DAWH, DCL, PCL, FEBL, FFCL, HBL, HMB, JSBL, KASBB, KAPCO, SSGC, and UBL. In other series higher autocorrelation is found at higher lags. However, zero correlation coefficient at various lags in few firms and in KSE-30 and KMI-30 indices indicating randomness at this lag. In KSE-30 zero correlation coefficient is found from lag 3 to 7, 17 to 20, and 25 to 34 indicating no autocorrelation in these lags. It can be concluded that return series is random and future returns cannot be predicted in these lags.

Similarly, KMI-30 shows absence of autocorrelation at lags 14, 15, 17, 20 and 30. DCL, FABL and NML show zero autocorrelation at lag 17, HUBC and ICI at lag10, FEBL at lag 24, HMB at lag 29, PSO at 7, PTCL at lag 32 and SSGC at 20th lag. Both negative and positive correlation can be found in all four indices and selected firms. The results can be compared to the evidences collected for the emergent and developed markets. Claessens, Susmita, and Jack(1995) found the first-order autocorrelation greater than 0.2 in most of the emergent markets including Pakistan, while for developed economies it is generally not

Chapter 6

higher than 0.2. However, the result is consistent in case of KSE-30, KSE-all, KMI-30, and EFUG.

The evidence from Ljung-box statistics also provides the possibility for dependency of future returns to past returns. The rejection of null hypothesis is based on the condition that if p- value is significant at 1% and 5% (p-value < 0.05). Result from table 6.4 shows that null hypothesis cannot be accepted except AICL, HMB, MLCF, NML, and SSGC. Some series show autocorrelation at lower lags and absence at higher lags (APL, BAFL, DAWH, BIPL, FFCL, JSBL, MEBL, OGDC and POL). It can be concluded from the autocorrelation coefficient and Ljung-box statistics that Karachi stock market under the study period shows significant autocorrelation in all four indices and absence of random walk. However, firms indicate a tendency of zero autocorrelation and randomness especially at higher lags. Similarly there is zero correlation evident at various lags of KMI-30 index which is attributed to free-floating nature of shares in these two indices. As evident from the table 6.4 negative autocorrelation in Karachi stock market suggests the over-reaction to unexpected news and information seems to be the strategy to earn above normal returns. The investors adopt mean reversion strategy of buying the stocks which had lower returns in the past in the expectations of higher returns today and selling the stocks having higher returns previously in expectations of lower returns in future.

6.5 Results of Autoregression, Heteroscedasticity and Breusch-Godfrey LM tests

Table 6.5 exhibits the results of autoregression, White noise test for heteroscedasticity and B- G serial correlation test.

The result indicates that most of the return series exhibit autoregression. The value of the coefficient is significantly different from zero at 5% or less level. However, in case of APL, BAHL, BIPL, FCCL, HMB, JSBL, KAPCO, MLCF, MEBL, NML and SSGC the series indicate insignificant values AR(1) coefficients. The test is followed by the White noise test for heteroscedasticity and B-G serial correlation test. The result in Table 6.5, indicate that null hypothesis of no serial correlation implies presence of random walk can be rejected for

Chapter 6

most of the return series during the study period. In case of AICL, APL, BAHL, DAWH, EFUG, ENGRO, FFC, HMB, NBP, NML, SHEL, and SNGC (12 out of 43) the null hypothesis cannot be rejected. However, the two results are consistent in case of return series of AICL, APL and BAHL. The results are consistent with other emergent markets and previous studies of Pakistan (Mobarak et al., 2008; Mustafa and Nishat, 2007).

6.6 Results of Unit Root Tests

6.6.1 Augmented Dickey-Fuller test Table 6.6.1 shows the results of ADF test at level and at first difference conducted on stock prices of all four indices and selected firms to examine stationarity of stock price series. A series is said to have unit root if it is stationary. Rejection of null hypothesis of unit root is a condition conducive for the presence of random walk in a series. The ADF statistics fail to reject the null hypothesis of unit root in Karachi stock market thereby indicating absence of random walk, except for KSE-30, KMI-30, FFC, NBP, OGDC and POL at 0.05 or lower level and MEBL at 0.01 level or lower where the null hypothesis is rejected and tendency of randomness in prices can be concluded. The absence of unit root is observed at first difference. The results are consistent with other emergent markets (Abeysekera, 2001; Worthington and Higgs, 2006; Marashdeh & Shrestha, 2008; Nisar and Hanif, 2012; Youssef and Galloppo, 2013) and Karachi stock market (Mustafa, 2007). As the large majority of stock prices possess t-statistics lower than critical values it can be concluded that the stock prices at Karachi stock market do not possess random walk.

6.6.2 Phillips-Parron test Table 6.6.2 shows the results of PP test at level and at first difference for the determination of presence of unit root on the stock return series. The null hypothesis of unit root of major stock return cannot be rejected exhibiting presence of unit root. The results are consistent with ADF results. If the PP test statistics exceeds the critical values of test it would entail the rejection of null hypothesis of presence of unit root in the series implies the presence of random walk in the market. The stock prices of KSE-30, FFC, HUBC, NBP, OGDC, and POL rejects null hypothesis of presence of unit root in the series at 5% or lower level of

Chapter 6

significance and KMI-30, APL, and MEBL found significant at 1% level showing signs of random walk in these stock returns. However, at difference the returns show nonappearance of unit root.

6.6.3 The Kwiatkowski, Phillips, Schmidt and Shin test The KPSS assumes the null hypothesis of no unit root. Rejection of null hypothesis implies the non-stationary series and presence of random walk. On the other hand if the null hypothesis cannot be rejected, would imply the stationary series and absence of random walk. If LM-statistics exceeds the asymptotic critical value(s) the null hypothesis can be rejected and vice versa. Table 6.6.2 exhibits the results of KPSS test. The null hypothesis cannot be rejected for most of the stock return series except for KMI-30 index, HUBC and MEBL at 1% or higher level of significance and APL for 5% and higher. The result shows consistency with other two test of examining unit root and no unit root exists at difference. The results are consistent with other emergent markets (Lagoarde-Segot & Lucey, 2008 for MENA stock markets; Oskooe (2011) for Iran stock market; the unit root tests support the hypothesis that most of the emergent stock markets do not follow random walk.

6.7 Result of Variance Ratio Test

Variance ratio test statistics is considered to be reliable tool for investigating the RW model under the assumption homoscedasticity and heteroscedasticity both. A random walk series with the assumption of homoscedasticity may possess time varying heteroscedasticity. The unit root tests alone will be unable to provide reliable results for the presence of random walk in the presence dominating short-term fluctuations over the stochastic behaviour of time series. Table 6.7 shows variance ratio test and the values of homoscedastic and heteroscedastic test statistics conducted till 36 lags. The values of Z(q) or significant at 5% or lower will reject the hypothesis under homoscedasticity and heteroscedasticity, respectively. Alternatively, if the maximum absolute value of Z (q) or is greater than the critical value at a predetermined significance level then the RWH is rejected.

Chapter 6

The result show value of variance ratio >1for most of the stock prices except for KSE-all, KSE-30, KMI-30, BIPL, DCL, FCCL, JSBL, KASSB, KAPCO, MLCF, and SCBPL. Among which KSE-30, KAPCO and MLCF are close to zero and null hypothesis of no serial correlation cannot be rejected considering both homoscedasticity and heteroscedasticity modifications. Similarly, for the stock prices of KSE-30, APL, BAHL, EPCL, FFBL, HMB, KAPCO, MLCF, MEBL, NML, and SSGC the null hypothesis cannot be rejected. Variance ratio >1 would mean positive autocorrelation and mean averting behaviour of the investor. Due to slow dispersion of news in the market investor under react in the market and keep short run momentum in the market and may earn above normal profits in the short-run by trend-chasing. Negative autocorrelation among the major stock prices is observed in the market showing mean reversion behaviour prevailing in the market. This is due to shocking and unexpected news events in the market induce the investor to over-react in the market. This will make the investor to adopt the strategy of buying past loser and selling past winners (Lehman, 1990). It is therefore concluded that among the four indices stock prices of KSE- 100 shows negative autocorrelation. KSE-all shares and KMI-30 and KSE-30 are positively autocorrelated. Firm level tendency of random walk reveals the unpredictability of prices in these stocks. It is also concluded that large investors earn profits by over-reaction and small investors by trend-chasing in the market where possible.

6.8 Result of ARMA Models

The study used the dynamic time series model of ARMA to examine whether the stock returns is a linear function of past values of the returns (autoregressive process) and the past values of the disturbance term. The significant coefficients of autoregression (AR) or moving average (MA) in an ARMA model imply the deviation of random walk and deviation from WF efficiency of the return series of KSE selected firms and indices.

Table 6.8 shows the result of ARMA model of ARMA (0,1), ARMA (1,1), ARMA (1,2), and ARMA (2,1) applied on the return series of KSE indices and selected firms. When AR (1) is equal to 1, it implies that variation of return values from one period to another is due to lag values of disturbance terms only. This also implies that return series does not depend on the

Chapter 6

past information of the return series and random walk. It is found that AR (1) for the whole sample is less than 1, which is the violation of random walk. However, except for KSE-30, KMI-30 and EFUG, AR (1) reveals supportive evidence for random walk. Similarly, the return series of KSE-100, KSE-all shares, KMI-30, and majority of the firms are significant for ARMA (0,1). On the other hand for the return series of BAHL, BIPL, HMB, JSBL, KAPCO, MICF, MEBL, NML and SSGC the null hypothesis of random walk cannot be rejected.

In case of ARMA (1,2) the model is not significant for KSE-100, KSE-all shares, ABOT, ABL, ATRL, BAFL, BIPL, DGKC, DCL, POL, and UBL.

The model ARMA (2,1) is best fitted for all except for AICL, AKBL, APL, DAEH, EFUG, ENGRO, FFC, FABL, HUBC, KASSB, NRL, SHEL, SNGC, UBL.

It can be concluded that the majority of the return series of indices and selected firms rejects the null hypothesis of random walk. However, in case of KSE-30 index and for few selected results support the indications of random walk during the study period.

Chapter 6

Table 6.1 Descriptive Statistics of Daily Returns of KSE Indices and Selected Firms

Std. Obs. Mean Deviation Skewness Kurtosis JB CV KSE100 1404 0.00112 0.01106 -0.168 5.762 451.40 9.893 KSEALL 1403 0.00110 0.01720 -0.831 273.089 4328733.00 15.675 KSE30 1404 0.02206 0.45694 21.537 463.239 12545525.00 20.711 KMI30 1402 0.00138 0.04291 0.334 369.719 7894230.00 30.989 ABOT 1379 0.00128 0.02017 -0.069 4.577 143.96 15.754 AICL 1403 -0.00052 0.03629 -14.492 395.757 9120050.00 -70.025 ABL 1396 0.00084 0.02078 -0.870 10.006 3028.69 24.861 AKBL 1403 0.00017 0.02533 -0.699 11.112 3957.55 150.392 APL 1403 0.00100 0.01880 -3.800 56.428 187750.40 18.836 ATRL 1401 0.00093 0.02431 0.139 4.491 129.67 26.146 BAFL 1402 0.00040 0.02344 0.152 6.140 580.89 58.149 BAHL 1402 0.00039 0.02130 -5.497 69.158 283798.70 54.332 BIPL 1403 0.00025 0.03455 0.816 6.613 917.40 137.229 BOP 1403 -0.00030 0.03324 0.393 5.669 451.93 -112.504 DGKC 1403 0.00094 0.02377 0.003 3.406 9.65 25.392 DAWH 1399 -0.00090 0.04347 -20.948 646.538 24242465.00 -48.154 DCL 1403 0.00051 0.05128 1.023 21.003 19176.70 101.316 EFUG 1377 -0.00013 0.02634 -0.856 12.495 5336.26 -196.808 ENGRO 1403 0.00038 0.02482 -1.226 14.579 8181.73 64.683 EPCL 1403 -0.00023 0.02472 0.564 5.042 317.66 -108.863 FCCL 1404 0.00094 0.02809 0.631 7.151 1100.00 29.758 FFBL 1403 0.00081 0.01892 -0.117 7.208 1037.35 23.284 FFC 1118 0.00050 0.02353 -7.181 130.621 964325.50 47.374 FABL 1404 0.00025 0.02755 0.157 5.985 526.81 108.123 HBL 1403 0.00070 0.02064 -1.662 19.490 16528.06 29.544 HMB 1393 0.00006 0.02092 -1.459 15.920 10174.79 355.625 HUBC 1403 -0.00102 0.01613 0.213 7.777 1343.67 -15.862 ICI 1403 -0.00102 0.01613 0.213 3.891 49.78 -15.862

Chapter 6

Table 6.1(Cont’d) Descriptive Statistics of Daily Returns of KSE Indices and Selected Firms

Std. Obs. Mean Deviation Skewness Kurtosis JB CV JSBL 1403 -0.00009 0.03935 1.300 9.888 3165.09 -423.029 KASBB 1386 -0.00178 0.04275 0.353 6.497 734.19 -24.020 KEL 1403 0.00090 0.04079 1.319 17.173 12140.24 45.141 KAPCO 1403 0.00046 0.01438 -0.748 10.370 3303.45 31.307 LUCK 1403 0.00175 0.01997 0.078 3.939 52.90 11.404 MLCF 1403 0.00132 0.03615 0.891 8.477 1937.43 27.469 MEBL 1392 0.00052 0.02230 -0.073 6.106 560.43 43.271 NBL 1404 0.00013 0.02613 -3.355 36.765 69272.16 199.930 NRL 1404 0.00049 0.02004 0.063 4.229 89.23 40.854 NML 1404 0.00034 0.03935 -20.331 620.448 22408155.00 116.659 OGDC 1403 0.00121 0.01599 0.374 5.307 343.60 13.172 POL 1403 0.00125 0.01637 0.088 5.521 372.98 13.108 PSO 1403 0.00071 0.01979 -0.746 11.891 4747.94 27.954 PTCL 1403 0.00029 0.02260 1.411 647.183 24259036.00 79.055 SCBPL 1391 0.00068 0.02752 0.190 5.618 405.24 40.280 SHEL 1400 -0.00016 0.02097 -1.187 16.535 11006.99 -130.331 SNGC 1403 -0.00011 0.02155 -0.490 9.976 2898.47 -187.815 SSGC 1403 0.00059 0.02344 -0.582 11.834 4637.75 39.862 UBL 1403 0.00116 0.02073 -0.172 5.348 328.90 17.797

Chapter 6

Table 6.2a Result of Kolmogrov Smirov Test on Daily Returns with Normal Distribution

Normal Parameters Most Extreme Differences KS-Z Test Asymptotic(2- Std. Mean Absolute Positive Negative tailed) Deviation KSE100 0.00112 0.01106 .069 .069 -.069 2.601 .000 KSEALL 0.00110 0.01720 .167 .163 -.167 6.254 .000 KSE30 0.02206 0.45694 .474 .474 -.441 17.777 .000 KMI30 0.00138 0.04291 .291 .283 -.291 10.906 .000 ABOT 0.00128 0.02017 .071 .071 -.059 2.631 .000 AICL -0.00052 0.03629 .133 .118 -.133 4.980 .000 ABL 0.00084 0.02078 .082 .072 -.082 3.052 .000 AKBL 0.00017 0.02533 .104 .097 -.104 3.909 .000 APL 0.00100 0.01880 .124 .112 -.124 4.638 .000 ATRL 0.00093 0.02431 .077 .077 -.061 2.866 .000 BAFL 0.00040 0.02344 .072 .072 -.072 2.693 .000 BAHL 0.00039 0.02130 .141 .125 -.141 5.298 .000 BIPL 0.00025 0.03455 .110 .110 -.066 4.137 .000 BOP -0.00030 0.03324 .094 .094 -.083 3.508 .000 DGKC 0.00094 0.02377 .060 .060 -.056 2.231 .000 DAWH -0.00090 0.04347 .159 .129 -.159 5.942 .000 DCL 0.00051 0.05128 .117 .117 -.099 4.367 .000 EFUG -0.00013 0.02634 .069 .069 -.060 2.572 .000 ENGRO 0.00038 0.02482 .067 .059 -.067 2.517 .000 EPCL -0.00023 0.02472 .083 .083 -.064 3.092 .000 FCCL 0.00094 0.02809 .088 .088 -.064 3.306 .000 FFBL 0.00081 0.01892 .092 .092 -.088 3.429 .000 FFC 0.00050 0.02353 .162 .135 -.162 5.402 .000 FABL 0.00025 0.02755 .100 .100 -.082 3.754 .000 HBL 0.00070 0.02064 .103 .098 -.103 3.856 .000 HMB 0.00006 0.02092 .079 .073 -.079 2.945 .000 HUBC -0.00102 0.01613 .079 .079 -.070 2.943 .000 ICI -0.00102 0.01613 .079 .079 -.070 2.943 .000 JSBL -0.00009 0.03935 .096 .096 -.063 3.606 .000 KASBB -0.00178 0.04275 .080 .080 -.054 2.991 .000

Chapter 6

Table 6.2a (Cont’d) Result of Kolmogrov Smirov Test on Daily Returns with Normal Distribution

Normal Parameters Most Extreme Differences KS-Z Test Asymptotic(2- Std. Mean Absolute Positive Negative tailed) Deviation KEL 0.00090 0.04079 .117 .117 -.096 4.386 .000 KAPCO 0.00046 0.01438 .103 .098 -.103 3.869 .000 LUCK 0.00175 0.01997 .063 .063 -.057 2.354 .000 MLCF 0.00132 0.03615 .091 .091 -.058 3.412 .000 MEBL 0.00052 0.02230 .070 .069 -.070 2.596 .000 NBP 0.00013 0.02613 .114 .096 -.114 4.260 .000 NRL 0.00049 0.02004 .081 .081 -.068 3.017 .000 NML 0.00034 0.03935 .167 .132 -.167 6.275 .000 OGDC 0.00121 0.01599 .080 .080 -.068 2.987 .000 POL 0.00125 0.01637 .089 .089 -.074 3.319 .000 PSO 0.00071 0.01979 .085 .085 -.080 3.180 .000 PTCL 0.00029 0.02260 .071 .071 -.067 2.675 .000 SCBPL 0.00068 0.02752 .072 .072 -.060 2.669 .000 SHEL -0.00016 0.02097 .107 .107 -.099 4.011 .000 SNGC -0.00011 0.02155 .075 .075 -.056 2.814 .000 SSGC 0.00059 0.02344 .078 .078 -.065 2.937 .000 UBL 0.00116 0.02073 .074 .074 -.066 2.758 .000

Chapter 6

Table 6.2b Result of Kolmogrov Smirov Test on Daily Return with Uniform Distribution

Uniform Parameters Most Extreme Differences KS-Z Asymptotic(2- Test Minimum Maximum Absolute Positive Negative tailed) KSE- -.051349 .053012 .293 .286 -.293 10.980 .000 100 KSE- -.366078 .353884 .457 .443 -.457 17.122 .000 ALL KSE-30 -.340728 9.897477 .959 .959 -.027 35.922 .000 KMI-30 -.937344 .945183 .475 .475 -.471 17.775 .000 ABOT -.124488 .056266 .472 .064 -.472 17.513 .000 AICL -.991321 .097409 .861 .043 -.861 32.234 .000 ABL -.173788 .070099 .542 .092 -.542 20.257 .000 AKBL -.207033 .099603 .511 .127 -.511 19.125 .000 APL -.284447 .048790 .741 .008 -.741 27.759 .000 ATRL -.106454 .140664 .357 .357 -.221 13.356 .000 BAFL -.117068 .132447 .334 .334 -.284 12.505 .000 BAHL -.316571 .048773 .761 .005 -.761 28.477 .000 BIPL -.145508 .186941 .346 .346 -.239 12.950 .000 BOP -.140089 .177455 .333 .333 -.244 12.471 .000 DGKC -.071036 .097261 .289 .289 -.158 10.832 .000 DAWH -1.34109 .086717 .902 .026 -.902 33.734 .000 DCL -.499274 .469232 .409 .353 -.409 15.304 .000 EFUG -.283198 .097441 .605 .127 -.605 22.447 .000 ENGRO -.267204 .048790 .680 .001 -.680 25.487 .000 EPCL -.084367 .109639 .321 .321 -.207 12.033 .000 FCCL -.153107 .165667 .321 .321 -.316 12.040 .000 FFBL -.130986 .085894 .431 .201 -.431 16.130 .000 FFC -.408519 .069045 .761 .042 -.761 25.429 .000 FABL -.164219 .109759 .412 .186 -.412 15.419 .000 HBL -.214886 .048790 .668 .001 -.668 25.033 .000 HMB -.198182 .056226 .608 .032 -.608 22.676 .000 HUBC -.097198 .085243 .342 .299 -.342 12.804 .000 ICI -.097198 .085243 .342 .299 -.342 12.804 .000 JSBL -.141651 .311128 .497 .497 -.146 18.616 .000 KASBB -.228924 .217065 .318 .286 -.318 11.846 .000

Chapter 6

Table 6.2b (Cont’d) Result of Kolmogrov Smirov Test on Daily Returns with Uniform Distribution Uniform Parameters Most Extreme Differences KS-Z Asymptotic(2- Test Minimum Maximum Absolute Positive Negative tailed) KEL -.292478 .352023 .403 .403 -.334 15.079 .000 KAPCO -.103215 .065768 .450 .206 -.450 16.874 .000 LUCK -.071365 .097499 .318 .318 -.196 11.908 .000 MLCF -.141412 .248800 .440 .440 -.187 16.483 .000 MEBL -.121912 .082623 .392 .184 -.392 14.624 .000 NBP -.282919 .048790 .695 .001 -.695 26.032 .000 NRL -.083501 .048790 .368 .084 -.368 13.777 .000 NML -1.20161 .063327 .906 .010 -.906 33.941 .000 OGDC -.051293 .095606 .420 .420 -.145 15.724 .000 POL -.071688 .058147 .344 .205 -.344 12.884 .000 PSO -.178270 .048788 .614 .014 -.614 23.015 .000 PTCL -.143101 .110122 .376 .229 -.376 14.090 .000 SCBPL -.118784 .135341 .311 .311 -.252 11.609 .000 SHEL -.214584 .082625 .562 .113 -.562 21.020 .000 SNGC -.209114 .058292 .610 .025 -.610 22.831 .000 SSGC -.227849 .084083 .571 .088 -.571 21.374 .000 UBL -.129382 .097313 .380 .216 -.380 14.234 .000

Chapter 6

Table 6.3 Result of Runs Test on Daily Returns

Cases < Cases >= Total Number of Asymptotic Test Value Z Test Value Test Value Cases Runs (2-tailed) KSE100 0.00112 703 701 1404 649 -2.883 .004 KSEALL 0.00110 700 703 1403 648 -2.911 .004 KSE30 0.02206 1329 75 1404 120 -6.086 .000 KMI30 0.00138 740 662 1402 656 -2.349 .019 ABOT 0.00128 768 611 1379 700 1.006 .314 AICL -0.00052 744 659 1403 630 -3.749 .000 ABL 0.00084 743 653 1396 650 -2.479 .013 AKBL 0.00017 779 624 1403 668 -1.403 .161 APL 0.00100 761 642 1403 697 -.024 .981 ATRL 0.00093 749 652 1401 640 -3.123 .002 BAFL 0.00040 745 657 1402 680 -1.032 .302 BAHL 0.00039 728 674 1402 710 .484 .629 BIPL 0.00025 798 605 1403 742 2.873 .004 BOP -0.00030 792 611 1403 653 -2.055 .040 DGKC 0.00094 727 676 1403 642 -3.186 .001 DAWH -0.00090 716 683 1399 645 -2.950 .003 DCL 0.00051 806 597 1403 712 1.369 .171 EFUG -0.00013 685 692 1377 693 .190 .850 ENGRO 0.00038 722 681 1403 658 -2.347 .019 EPCL -0.00023 759 644 1403 687 -.580 .562 FFCL 0.00094 793 611 1404 678 -.717 .473 FEBL 0.00081 753 650 1403 650 -2.616 .009 FFC 0.00050 557 561 1118 557 -.179 .858 FABL 0.00025 765 639 1404 672 -1.364 .172 HBL 0.00070 762 641 1403 680 -.930 .352 HMB 0.00006 737 656 1393 715 1.068 .286 HUBC -0.00102 703 700 1403 690 -.668 .504 ICI -0.00102 703 700 1403 690 -.668 .504 JSBL -0.00009 732 671 1403 743 2.238 .025 KASBB -0.00178 686 700 1386 804 5.916 .000

Chapter 6

Table 6.3 (Cont’d) Result of Runs Test on Daily Returns

Cases < Cases >= Total Number of Asymptotic Test Value Z Test Value Test Value Cases Runs (2-tailed) KEL 0.00090 804 599 1403 740 2.864 .004 KAPCO 0.00046 733 670 1403 714 .691 .489 LUCK 0.00175 733 670 1403 666 -1.878 .060 MLCF 0.00132 758 645 1403 696 -.105 .917 MEBL 0.00052 751 641 1392 748 2.987 .003 NBL 0.00013 719 685 1404 692 -.566 .572 NRL 0.00049 752 652 1404 660 -2.117 .034 NML 0.00034 711 693 1404 684 -1.009 .313 OGDC 0.00121 771 632 1403 690 -.303 .762 POL 0.00125 735 668 1403 682 -1.012 .312 PSO 0.00071 738 665 1403 682 -.996 .319 PTCL 0.00029 741 662 1403 694 -.336 .737 SCBPL 0.00068 740 651 1391 772 4.220 .000 SHEL -0.00016 722 678 1400 689 -.605 .545 SNGC -0.00011 730 673 1403 693 -.446 .655 SSGC 0.00059 769 634 1403 718 1.186 .236 UBL 0.00116 731 672 1403 692 -.495 .620

Chapter 6

Table 6.4 Result of Autocorrelation Test on Daily Returns KSE-100 KSE-30 KSE-ALL Coeff Ljung Box Prob Coeff Ljung Box Prob Coeff Ljung Box Prob L1 .105 15.38 .000 .665 621.32 .000 -.286 115.06 .000 L2 .041 17.69 .000 .332 776.82 .000 .021 115.66 .000 L3 .012 17.90 .000 .000 776.82 .000 -.025 116.53 .000 L4 .043 20.53 .000 .000 776.82 .000 .035 118.22 .000 L5 .007 20.60 .001 .000 776.82 .000 .002 118.22 .000 L6 .030 21.83 .001 .000 776.82 .000 .033 119.81 .000 L7 -.021 22.45 .002 .000 776.82 .000 .001 119.81 .000 L8 -.044 25.13 .001 .001 776.83 .000 .011 119.99 .000 L9 -.011 25.30 .003 -.001 776.83 .000 -.060 125.09 .000 L10 .057 29.92 .001 -.002 776.83 .000 .075 132.98 .000 L11 -.014 30.21 .001 -.002 776.83 .000 -.024 133.80 .000 L12 -.009 30.33 .002 .000 776.83 .000 -.020 134.37 .000 L13 -.010 30.48 .004 .000 776.83 .000 -.012 134.59 .000 L14 -.005 30.52 .006 -.001 776.84 .000 .026 135.56 .000 L15 .029 31.70 .007 -.001 776.84 .000 -.014 135.84 .000 L16 .006 31.76 .011 -.001 776.84 .000 .025 136.69 .000 L17 -.051 35.46 .005 .000 776.84 .000 -.014 136.99 .000 L18 .007 35.54 .008 .000 776.84 .000 -.001 136.99 .000 L19 -.008 35.63 .012 .000 776.84 .000 -.010 137.14 .000 L20 -.003 35.64 .017 .000 776.84 .000 .011 137.32 .000 L21 -.009 35.76 .023 .001 776.84 .000 -.020 137.89 .000 L22 -.002 35.77 .032 .001 776.84 .000 .001 137.89 .000 L23 -.062 41.27 .011 .000 776.84 .000 -.018 138.37 .000 L24 -.004 41.30 .015 .001 776.84 .000 .000 138.37 .000 L25 .021 41.93 .018 .000 776.84 .000 .013 138.61 .000 L26 .007 42.00 .025 .000 776.84 .000 .004 138.64 .000 L27 -.025 42.87 .027 .000 776.84 .000 -.041 141.02 .000 L28 .014 43.16 .034 .000 776.84 .000 .017 141.43 .000 L29 .039 45.36 .027 .000 776.84 .000 .013 141.67 .000 L30 .063 51.13 .009 .000 776.84 .000 .031 143.09 .000 L31 -.011 51.30 .012 .000 776.84 .000 -.003 143.10 .000 L32 -.044 54.13 .009 .000 776.84 .000 -.013 143.34 .000 L33 -.063 59.81 .003 .000 776.84 .000 -.017 143.78 .000 L34 .012 60.01 .004 .000 776.84 .000 -.002 143.79 .000 L35 -.002 60.02 .005 .001 776.84 .000 .003 143.80 .000 L36 -.052 63.86 .003 .001 776.84 .000 -.024 144.65 .000

Chapter 6

Table 6.4 (Cont’d) Result of Autocorrelation Test on Daily Returns KMI-30 ABOT AICL Coeff Ljung Box Prob Coeff Ljung Box Prob Coeff Ljung Box Prob L1 -.459 295.50 .000 .138 26.17 .000 .073 7.52 .006 L2 -.001 295.50 .000 .059 31.05 .000 -.005 7.55 .023 L3 .006 295.56 .000 -.027 32.06 .000 .019 8.07 .045 L4 -.001 295.56 .000 -.039 34.20 .000 .018 8.50 .075 L5 -.004 295.58 .000 .001 34.20 .000 -.010 8.64 .124 L6 .005 295.62 .000 -.011 34.36 .000 .010 8.78 .186 L7 -.003 295.63 .000 -.058 39.07 .000 -.008 8.87 .262 L8 -.005 295.67 .000 -.019 39.57 .000 .018 9.33 .315 L9 -.001 295.67 .000 -.051 43.15 .000 .028 10.42 .317 L10 -.002 295.68 .000 .028 44.24 .000 .031 11.79 .299 L11 .002 295.68 .000 .045 47.02 .000 .000 11.79 .379 L12 .006 295.73 .000 .038 49.03 .000 .013 12.04 .443 L13 -.003 295.75 .000 .001 49.03 .000 -.027 13.10 .440 L14 .000 295.75 .000 -.003 49.05 .000 -.027 14.14 .439 L15 .000 295.75 .000 .008 49.13 .000 -.039 16.35 .359 L16 .003 295.76 .000 .030 50.40 .000 -.016 16.73 .403 L17 .000 295.76 .000 -.036 52.21 .000 -.019 17.27 .436 L18 -.008 295.84 .000 .034 53.79 .000 -.038 19.35 .370 L19 .004 295.86 .000 -.008 53.88 .000 -.036 21.20 .326 L20 .000 295.86 .000 .035 55.55 .000 -.029 22.36 .321 L21 -.008 295.96 .000 -.023 56.27 .000 -.019 22.87 .351 L22 .007 296.02 .000 .000 56.27 .000 .010 23.01 .401 L23 -.010 296.16 .000 -.038 58.29 .000 -.064 28.84 .186 L24 .006 296.20 .000 .012 58.48 .000 .000 28.84 .226 L25 .006 296.25 .000 -.010 58.63 .000 .008 28.94 .267 L26 -.008 296.35 .000 .050 62.09 .000 .024 29.74 .279 L27 .014 296.63 .000 .019 62.59 .000 .005 29.78 .324 L28 -.005 296.67 .000 -.051 66.28 .000 -.007 29.85 .370 L29 .007 296.73 .000 -.003 66.29 .000 .009 29.97 .415 L30 .004 296.76 .000 -.031 67.63 .000 .011 30.13 .459 L31 .000 296.76 .000 .005 67.66 .000 .011 30.31 .502 L32 -.002 296.77 .000 -.004 67.68 .000 -.014 30.59 .538 L33 -.016 297.13 .000 -.002 67.69 .000 -.002 30.60 .587 L34 .001 297.13 .000 -.003 67.71 .001 -.016 30.99 .616 L35 .004 297.15 .000 .005 67.75 .001 -.025 31.91 .618 L36 -.005 297.19 .000 -.001 67.75 .001 -.012 32.11 .654

Chapter 6

Table 6.4 (Cont’d) Result of Autocorrelation Test on Daily Returns ABL AKBL APL Coeff Ljung Box Prob Coeff Ljung Box Prob Coeff Ljung Box Prob L1 .153 32.95 .000 .109 16.73 .000 .051 3.62 .057 L2 .071 40.06 .000 .027 17.77 .000 -.030 4.90 .086 L3 .052 43.83 .000 -.026 18.75 .000 -.039 7.08 .069 L4 -.025 44.69 .000 -.048 22.00 .000 -.029 8.26 .083 L5 -.018 45.13 .000 -.060 27.10 .000 .023 9.03 .108 L6 -.036 46.93 .000 -.061 32.33 .000 -.011 9.21 .162 L7 -.026 47.87 .000 -.047 35.45 .000 -.028 10.35 .169 L8 -.007 47.94 .000 -.028 36.58 .000 .008 10.44 .236 L9 -.079 56.72 .000 -.005 36.62 .000 -.011 10.59 .305 L10 -.047 59.83 .000 .043 39.24 .000 -.005 10.63 .387 L11 -.037 61.81 .000 .013 39.49 .000 .021 11.25 .423 L12 -.059 66.76 .000 -.033 40.99 .000 .049 14.65 .261 L13 .013 66.98 .000 -.038 42.98 .000 -.026 15.65 .269 L14 -.053 70.91 .000 .032 44.46 .000 -.035 17.34 .238 L15 -.003 70.93 .000 .051 48.11 .000 .029 18.51 .237 L16 .003 70.94 .000 .027 49.14 .000 .034 20.14 .214 L17 -.035 72.68 .000 .044 51.95 .000 .045 23.02 .149 L18 .014 72.94 .000 -.015 52.29 .000 .059 27.91 .063 L19 -.035 74.64 .000 -.022 52.97 .000 .008 28.00 .084 L20 -.053 78.59 .000 -.048 56.24 .000 -.023 28.76 .093 L21 -.051 82.24 .000 .074 64.04 .000 -.001 28.76 .120 L22 .005 82.27 .000 .075 72.05 .000 -.001 28.76 .152 L23 -.046 85.26 .000 .011 72.22 .000 -.025 29.65 .160 L24 -.004 85.29 .000 .029 73.45 .000 -.016 30.01 .185 L25 .010 85.43 .000 .005 73.48 .000 -.004 30.03 .223 L26 .059 90.45 .000 .035 75.26 .000 .029 31.26 .219 L27 .056 94.94 .000 .007 75.32 .000 .026 32.26 .223 L28 .026 95.94 .000 -.010 75.47 .000 -.022 32.95 .238 L29 .046 98.92 .000 .052 79.35 .000 .039 35.10 .201 L30 .028 100.02 .000 .014 79.65 .000 .019 35.63 .220 L31 .088 111.01 .000 -.020 80.23 .000 .009 35.75 .255 L32 .035 112.72 .000 -.013 80.48 .000 .017 36.17 .280 L33 .059 117.63 .000 -.017 80.89 .000 .010 36.30 .317 L34 .025 118.54 .000 -.017 81.30 .000 -.021 36.93 .335 L35 .011 118.73 .000 -.027 82.38 .000 -.010 37.07 .374 L36 .008 118.81 .000 -.015 82.69 .000 .032 38.56 .355

Chapter 6

Table 6.4 (Cont’d) Result of Autocorrelation Test on Daily Returns ATRL BAFL BAHL Coeff Ljung Box Prob Coeff Ljung Box Prob Coeff Ljung Box Prob L1 .173 42.19 .000 .059 4.85 .028 -.006 0.06 .809 L2 -.016 42.54 .000 .003 4.87 .088 .049 3.46 .177 L3 .006 42.59 .000 .033 6.39 .094 .023 4.20 .240 L4 .037 44.54 .000 -.034 7.97 .093 -.010 4.35 .361 L5 .004 44.57 .000 -.027 9.03 .108 .021 4.97 .419 L6 -.017 44.98 .000 -.076 17.21 .009 -.071 12.07 .060 L7 .003 44.99 .000 -.047 20.32 .005 -.022 12.75 .078 L8 .037 46.97 .000 -.044 23.10 .003 -.026 13.70 .090 L9 .002 46.98 .000 -.031 24.43 .004 -.030 14.97 .092 L10 .024 47.78 .000 .055 28.76 .001 .032 16.41 .089 L11 .045 50.61 .000 -.022 29.43 .002 .055 20.64 .037 L12 .073 58.15 .000 .007 29.49 .003 -.012 20.85 .053 L13 .004 58.17 .000 .031 30.88 .004 -.037 22.81 .044 L14 -.014 58.46 .000 -.007 30.94 .006 -.054 27.01 .019 L15 -.006 58.51 .000 -.004 30.97 .009 -.054 31.11 .008 L16 -.013 58.74 .000 .034 32.58 .008 -.013 31.35 .012 L17 -.043 61.31 .000 -.029 33.79 .009 -.019 31.84 .016 L18 -.026 62.26 .000 -.069 40.56 .002 -.037 33.81 .013 L19 -.020 62.86 .000 -.038 42.59 .001 -.038 35.85 .011 L20 .010 63.01 .000 .008 42.67 .002 .059 40.77 .004 L21 -.027 64.06 .000 .007 42.73 .003 .018 41.22 .005 L22 .006 64.10 .000 .026 43.68 .004 -.018 41.69 .007 L23 -.025 65.00 .000 -.037 45.63 .003 -.058 46.47 .003 L24 .018 65.49 .000 .050 49.14 .002 .005 46.51 .004 L25 .005 65.53 .000 .054 53.34 .001 -.026 47.46 .004 L26 .001 65.53 .000 -.044 56.10 .001 .022 48.15 .005 L27 -.031 66.90 .000 -.020 56.69 .001 .049 51.62 .003 L28 -.057 71.51 .000 -.005 56.72 .001 -.008 51.71 .004 L29 -.013 71.74 .000 .048 60.03 .001 .048 55.01 .002 L30 .029 72.92 .000 .031 61.40 .001 -.017 55.42 .003 L31 .013 73.17 .000 -.001 61.40 .001 .063 61.18 .001 L32 .025 74.07 .000 .024 62.21 .001 -.004 61.21 .001 L33 .025 74.95 .000 .016 62.58 .001 -.066 67.48 .000 L34 -.029 76.13 .000 .022 63.29 .002 .029 68.71 .000 L35 .022 76.81 .000 .028 64.42 .002 -.041 71.14 .000 L36 .035 78.54 .000 -.079 73.36 .000 -.020 71.75 .000

Chapter 6

Table 6.4 (Cont’d) Result of Autocorrelation Test on Daily Returns BIPL BOP DGKC Coeff Ljung Box Prob Coeff Ljung Box Prob Coeff Ljung Box Prob L1 -.033 1.56 .212 .128 23.14 .000 .132 24.55 .000 L2 -.058 6.26 .044 -.040 25.43 .000 .009 24.65 .000 L3 -.045 9.15 .027 -.012 25.61 .000 .007 24.73 .000 L4 -.017 9.57 .048 -.011 25.78 .000 -.005 24.75 .000 L5 .013 9.81 .081 -.088 36.68 .000 -.003 24.77 .000 L6 -.021 10.44 .107 -.052 40.45 .000 .014 25.06 .000 L7 -.012 10.65 .154 -.035 42.22 .000 -.036 26.84 .000 L8 .005 10.69 .220 -.012 42.41 .000 .016 27.19 .001 L9 .013 10.94 .280 .047 45.48 .000 .000 27.19 .001 L10 .052 14.81 .139 .089 56.74 .000 .026 28.12 .002 L11 -.039 16.99 .108 .017 57.16 .000 .027 29.18 .002 L12 -.014 17.29 .139 -.011 57.33 .000 .022 29.85 .003 L13 -.015 17.60 .173 .025 58.22 .000 -.005 29.88 .005 L14 -.006 17.66 .223 .020 58.79 .000 .048 33.14 .003 L15 .039 19.80 .180 -.059 63.76 .000 .006 33.19 .004 L16 -.006 19.85 .227 -.042 66.22 .000 -.018 33.65 .006 L17 -.006 19.91 .279 -.011 66.41 .000 -.004 33.67 .009 L18 .014 20.21 .321 -.008 66.50 .000 .035 35.42 .008 L19 .014 20.47 .367 -.053 70.48 .000 .019 35.94 .011 L20 .005 20.50 .427 .000 70.48 .000 -.022 36.65 .013 L21 .006 20.55 .487 .010 70.62 .000 .011 36.84 .018 L22 -.013 20.80 .533 .062 76.17 .000 .032 38.29 .017 L23 -.024 21.65 .542 .022 76.89 .000 -.050 41.86 .009 L24 -.049 25.08 .401 -.009 77.01 .000 .029 43.06 .010 L25 .017 25.50 .435 -.038 79.10 .000 .001 43.06 .014 L26 .036 27.39 .389 .028 80.22 .000 .015 43.40 .018 L27 .009 27.52 .436 .020 80.78 .000 -.014 43.68 .022 L28 -.039 29.69 .378 .005 80.82 .000 .005 43.72 .030 L29 .015 30.01 .414 -.039 83.01 .000 .007 43.80 .038 L30 .057 34.60 .258 .012 83.22 .000 .066 49.96 .013 L31 -.003 34.61 .300 -.031 84.59 .000 -.018 50.43 .015 L32 .019 35.12 .322 -.016 84.98 .000 -.010 50.57 .020 L33 -.004 35.15 .367 .015 85.30 .000 -.014 50.85 .024 L34 .027 36.23 .365 .061 90.62 .000 -.068 57.60 .007 L35 -.012 36.45 .401 .027 91.63 .000 -.029 58.78 .007 L36 .038 38.54 .355 -.017 92.03 .000 -.037 60.74 .006

Chapter 6

Table 6.4 (Cont’d) Result of Autocorrelation Test on Daily Returns DAWH DCL EFUG Coeff Ljung Box Prob Coeff Ljung Box Prob Coeff Ljung Box Prob L1 .051 3.66 .056 -.077 8.33 .004 .217 65.25 .000 L2 .053 7.66 .022 -.015 8.63 .013 .056 69.58 .000 L3 .001 7.66 .054 .006 8.68 .034 .008 69.67 .000 L4 -.003 7.67 .104 .064 14.50 .006 -.056 74.00 .000 L5 .013 7.91 .161 .010 14.63 .012 -.034 75.62 .000 L6 .023 8.63 .196 -.016 15.01 .020 .035 77.33 .000 L7 -.019 9.13 .244 .023 15.76 .027 .026 78.28 .000 L8 -.023 9.88 .274 .004 15.78 .046 .018 78.74 .000 L9 .011 10.06 .345 .016 16.13 .064 .060 83.80 .000 L10 .023 10.80 .373 -.083 25.86 .004 .050 87.30 .000 L11 .039 12.96 .296 -.002 25.86 .007 .007 87.37 .000 L12 -.018 13.44 .338 -.001 25.87 .011 -.009 87.48 .000 L13 .013 13.68 .397 -.054 30.05 .005 -.015 87.79 .000 L14 -.005 13.71 .472 .002 30.05 .008 -.063 93.32 .000 L15 .009 13.82 .539 .049 33.45 .004 -.080 102.28 .000 L16 -.018 14.29 .577 .028 34.55 .005 -.017 102.69 .000 L17 -.010 14.44 .636 .000 34.55 .007 -.024 103.52 .000 L18 .048 17.68 .477 .007 34.61 .011 -.015 103.85 .000 L19 -.025 18.59 .484 .027 35.66 .012 .019 104.34 .000 L20 -.024 19.44 .494 -.008 35.75 .016 -.003 104.36 .000 L21 -.030 20.75 .474 -.018 36.20 .021 -.009 104.47 .000 L22 -.020 21.30 .502 .043 38.87 .015 .007 104.54 .000 L23 -.028 22.41 .496 .039 41.02 .012 -.026 105.45 .000 L24 -.024 23.20 .508 -.003 41.03 .017 .002 105.46 .000 L25 -.004 23.23 .564 -.052 44.83 .009 .030 106.77 .000 L26 -.012 23.44 .608 .024 45.67 .010 .012 106.97 .000 L27 .008 23.54 .656 -.029 46.89 .010 -.006 107.02 .000 L28 .022 24.24 .669 .003 46.90 .014 .044 109.79 .000 L29 .031 25.57 .648 -.027 47.98 .015 .020 110.33 .000 L30 -.004 25.60 .695 .005 48.01 .020 -.021 110.97 .000 L31 -.014 25.87 .727 -.015 48.34 .024 -.007 111.03 .000 L32 -.032 27.31 .703 -.005 48.38 .032 .023 111.79 .000 L33 -.045 30.24 .605 -.004 48.40 .041 .025 112.70 .000 L34 .012 30.43 .643 -.001 48.40 .052 -.017 113.11 .000 L35 .002 30.44 .688 .029 49.57 .052 -.012 113.31 .000 L36 -.003 30.45 .730 -.012 49.78 .063 -.003 113.32 .000

Chapter 6

Table 6.4 (Cont’d) Result of Autocorrelation Test on Daily Returns ENGRO EPCL FABL Coeff Ljung Box Prob Coeff Ljung Box Prob Coeff Ljung Box Prob L1 .141 27.82 .000 .080 8.97 .003 .175 43.12 .000 L2 .009 27.94 .000 -.021 9.57 .008 .058 47.90 .000 L3 -.019 28.46 .000 -.011 9.75 .021 .028 48.99 .000 L4 .004 28.49 .000 .050 13.32 .010 -.034 50.65 .000 L5 -.036 30.29 .000 .022 13.97 .016 -.097 63.89 .000 L6 -.007 30.36 .000 -.022 14.68 .023 -.050 67.43 .000 L7 .007 30.42 .000 -.038 16.72 .019 -.102 82.21 .000 L8 -.030 31.71 .000 .000 16.72 .033 -.081 91.42 .000 L9 -.001 31.71 .000 .048 20.02 .018 -.063 97.12 .000 L10 .014 32.00 .000 .030 21.29 .019 -.058 101.82 .000 L11 -.029 33.21 .000 -.036 23.18 .017 -.060 107.00 .000 L12 .008 33.30 .001 .015 23.49 .024 .005 107.04 .000 L13 -.018 33.77 .001 .037 25.39 .021 .099 120.90 .000 L14 -.027 34.79 .002 -.049 28.82 .011 .069 127.63 .000 L15 -.019 35.28 .002 -.042 31.39 .008 .053 131.69 .000 L16 .016 35.62 .003 .006 31.44 .012 .035 133.40 .000 L17 .033 37.15 .003 -.044 34.16 .008 .000 133.40 .000 L18 .033 38.69 .003 -.040 36.48 .006 .003 133.41 .000 L19 -.059 43.64 .001 -.036 38.30 .005 -.070 140.30 .000 L20 -.048 46.91 .001 .009 38.41 .008 -.074 148.15 .000 L21 -.027 47.93 .001 .033 39.98 .007 -.004 148.18 .000 L22 -.008 48.02 .001 .010 40.12 .010 -.014 148.46 .000 L23 -.036 49.89 .001 -.078 48.89 .001 -.005 148.50 .000 L24 .002 49.89 .001 -.002 48.90 .002 .055 152.87 .000 L25 .026 50.86 .002 .040 51.18 .002 .033 154.46 .000 L26 -.022 51.56 .002 .012 51.37 .002 .023 155.24 .000 L27 -.028 52.71 .002 -.026 52.35 .002 -.021 155.90 .000 L28 .034 54.33 .002 -.028 53.44 .003 .055 160.31 .000 L29 .014 54.60 .003 -.025 54.32 .003 .016 160.70 .000 L30 .003 54.62 .004 .037 56.29 .003 .001 160.70 .000 L31 -.034 56.29 .004 -.024 57.14 .003 .022 161.40 .000 L32 -.056 60.84 .002 -.023 57.88 .003 -.035 163.13 .000 L33 -.037 62.83 .001 .016 58.27 .004 -.022 163.84 .000 L34 .002 62.83 .002 .052 62.09 .002 .004 163.86 .000 L35 -.022 63.54 .002 .012 62.30 .003 -.031 165.24 .000 L36 .016 63.93 .003 -.035 64.07 .003 -.036 167.11 .000

100

Chapter 6

Table 6.4 (Cont’d) Result of Autocorrelation Test on Daily Returns FFBL FFC FCCL Coeff Ljung Box Prob Coeff Ljung Box Prob Coeff Ljung Box Prob L1 .066 6.05 .014 .113 14.29 .000 -.018 0.48 .489 L2 .033 7.63 .022 -.021 14.77 .001 -.096 13.37 .001 L3 -.049 10.98 .012 -.028 15.65 .001 .033 14.93 .002 L4 -.007 11.05 .026 -.044 17.83 .001 .011 15.10 .005 L5 -.031 12.38 .030 -.083 25.61 .000 -.010 15.23 .009 L6 -.098 25.94 .000 -.002 25.61 .000 .008 15.32 .018 L7 -.011 26.11 .000 -.002 25.62 .001 -.086 25.84 .001 L8 -.047 29.19 .000 -.019 26.02 .001 -.010 25.97 .001 L9 .043 31.81 .000 .025 26.73 .002 .028 27.06 .001 L10 .025 32.71 .000 .011 26.86 .003 .014 27.35 .002 L11 .011 32.87 .001 -.013 27.04 .005 .044 30.07 .002 L12 .040 35.19 .000 .024 27.71 .006 -.020 30.63 .002 L13 -.054 39.26 .000 .030 28.76 .007 -.032 32.11 .002 L14 .022 39.93 .000 .020 29.19 .010 .019 32.63 .003 L15 .024 40.71 .000 .005 29.22 .015 .062 38.08 .001 L16 .021 41.33 .000 -.008 29.30 .022 .011 38.27 .001 L17 -.006 41.38 .001 -.019 29.72 .028 -.031 39.63 .001 L18 .029 42.59 .001 .036 31.19 .027 .017 40.03 .002 L19 .025 43.49 .001 .013 31.38 .037 .003 40.04 .003 L20 .028 44.58 .001 -.049 34.07 .026 .014 40.33 .005 L21 .002 44.58 .002 -.051 37.04 .017 -.006 40.37 .007 L22 .014 44.85 .003 .014 37.27 .022 .018 40.84 .009 L23 -.067 51.34 .001 -.033 38.48 .023 -.025 41.74 .010 L24 .000 51.34 .001 .018 38.87 .028 -.003 41.75 .014 L25 .011 51.52 .001 -.019 39.29 .034 -.002 41.76 .019 L26 -.029 52.74 .001 -.007 39.33 .045 .005 41.80 .026 L27 .002 52.74 .002 -.058 43.18 .025 .035 43.52 .023 L28 -.039 54.98 .002 -.056 46.74 .015 .031 44.86 .023 L29 .067 61.49 .000 -.002 46.75 .020 -.019 45.39 .027 L30 .006 61.55 .001 -.031 47.85 .021 .049 48.79 .017 L31 .012 61.75 .001 .003 47.86 .027 .002 48.80 .022 L32 -.070 68.78 .000 -.038 49.50 .025 .006 48.84 .029 L33 -.015 69.11 .000 -.007 49.56 .032 -.038 50.97 .024 L34 .018 69.58 .000 -.049 52.31 .023 -.048 54.35 .015 L35 -.002 69.59 .000 .014 52.53 .029 .041 56.74 .011 L36 .037 71.61 .000 -.020 53.00 .034 -.066 62.95 .004

101

Chapter 6

Table 6.4 (Cont’d) Result of Autocorrelation Test on Daily Returns HBL HMB HUBC Coeff Ljung Box Prob Coeff Ljung Box Prob Coeff Ljung Box Prob L1 .079 8.82 .003 .040 2.24 .134 .105 15.55 .000 L2 .014 9.11 .011 .021 2.84 .241 .017 15.94 .000 L3 .051 12.78 .005 -.015 3.16 .367 -.075 23.93 .000 L4 .014 13.07 .011 -.032 4.64 .327 -.044 26.70 .000 L5 .067 19.38 .002 -.010 4.76 .445 -.022 27.37 .000 L6 -.036 21.26 .002 -.045 7.61 .268 -.046 30.39 .000 L7 -.040 23.49 .001 -.043 10.20 .178 .014 30.67 .000 L8 .001 23.50 .003 -.025 11.05 .199 -.047 33.85 .000 L9 -.052 27.34 .001 -.022 11.75 .228 -.008 33.94 .000 L10 -.022 28.01 .002 .031 13.11 .217 .000 33.94 .000 L11 .010 28.15 .003 .026 14.10 .228 .042 36.47 .000 L12 .002 28.16 .005 -.013 14.33 .280 -.003 36.49 .000 L13 -.026 29.15 .006 .029 15.50 .277 -.031 37.82 .000 L14 -.004 29.17 .010 .027 16.56 .280 .003 37.84 .001 L15 .005 29.21 .015 .059 21.52 .121 .038 39.92 .000 L16 .007 29.28 .022 .058 26.26 .050 .072 47.36 .000 L17 -.017 29.69 .029 .019 26.77 .062 -.002 47.37 .000 L18 -.012 29.91 .038 .025 27.63 .068 .014 47.64 .000 L19 -.029 31.10 .039 -.009 27.75 .088 -.006 47.70 .000 L20 .031 32.50 .038 .005 27.78 .115 .036 49.51 .000 L21 .024 33.30 .043 .011 27.96 .141 -.007 49.59 .000 L22 -.009 33.43 .056 -.079 36.79 .025 .011 49.75 .001 L23 -.060 38.61 .022 -.013 37.05 .032 -.025 50.67 .001 L24 .000 38.61 .030 -.072 44.48 .007 -.022 51.38 .001 L25 -.021 39.24 .035 .003 44.49 .010 -.009 51.50 .001 L26 .026 40.22 .037 -.018 44.95 .012 .009 51.61 .002 L27 .005 40.25 .049 .025 45.81 .013 .014 51.88 .003 L28 -.036 42.08 .043 .023 46.54 .015 .018 52.36 .003 L29 .059 47.01 .019 .000 46.54 .021 .001 52.36 .005 L30 -.012 47.20 .024 .030 47.83 .021 .015 52.67 .006 L31 .001 47.20 .031 .014 48.12 .026 -.013 52.90 .008 L32 -.011 47.37 .039 .023 48.87 .029 .015 53.25 .011 L33 .033 48.96 .036 .012 49.07 .036 .003 53.26 .014 L34 .077 57.60 .007 -.047 52.22 .024 -.007 53.33 .019 L35 .038 59.73 .006 -.014 52.52 .029 -.025 54.24 .020 L36 .056 64.29 .003 -.025 53.41 .031 -.022 54.91 .023

102

Chapter 6

Table 6.4 (Cont’d) Result of Autocorrelation Test on Daily Returns ICI JSBL KASBB Coeff Ljung Box Prob Coeff Ljung Box Prob Coeff Ljung Box Prob L1 .105 15.55 .000 -.008 0.10 .753 -.099 13.74 .000 L2 .017 15.94 .000 -.060 5.10 .078 -.034 15.37 .000 L3 -.075 23.93 .000 -.028 6.22 .102 .042 17.81 .000 L4 -.044 26.70 .000 -.029 7.40 .116 -.001 17.81 .001 L5 -.022 27.37 .000 .065 13.28 .021 -.038 19.79 .001 L6 -.046 30.39 .000 -.038 15.33 .018 .000 19.79 .003 L7 .014 30.67 .000 -.030 16.59 .020 -.002 19.79 .006 L8 -.047 33.85 .000 -.065 22.54 .004 -.001 19.79 .011 L9 -.008 33.94 .000 .034 24.19 .004 -.005 19.84 .019 L10 .000 33.94 .000 .062 29.64 .001 .046 22.80 .012 L11 .042 36.47 .000 .008 29.73 .002 .034 24.43 .011 L12 -.003 36.49 .000 .054 33.80 .001 -.025 25.31 .013 L13 -.031 37.82 .000 .011 33.96 .001 -.029 26.49 .015 L14 .003 37.84 .001 .002 33.97 .002 -.006 26.54 .022 L15 .038 39.92 .000 .013 34.21 .003 -.062 31.91 .007 L16 .072 47.36 .000 -.001 34.21 .005 -.028 33.00 .007 L17 -.002 47.37 .000 -.026 35.19 .006 .036 34.80 .007 L18 .014 47.64 .000 .004 35.21 .009 .017 35.23 .009 L19 -.006 47.70 .000 .006 35.26 .013 .002 35.23 .013 L20 .036 49.51 .000 -.040 37.57 .010 -.008 35.33 .018 L21 -.007 49.59 .000 .016 37.95 .013 .004 35.35 .026 L22 .011 49.75 .001 .035 39.65 .012 -.011 35.51 .034 L23 -.025 50.67 .001 -.009 39.76 .016 -.009 35.63 .045 L24 -.022 51.38 .001 .022 40.48 .019 .025 36.50 .049 L25 -.009 51.50 .001 -.001 40.48 .026 -.039 38.61 .040 L26 .009 51.61 .002 .029 41.66 .027 .018 39.07 .048 L27 .014 51.88 .003 .010 41.80 .034 .025 39.96 .052 L28 .018 52.36 .003 .017 42.23 .041 -.050 43.55 .031 L29 .001 52.36 .005 -.016 42.62 .049 .024 44.38 .034 L30 .015 52.67 .006 -.053 46.59 .027 .010 44.52 .043 L31 -.013 52.90 .008 -.004 46.61 .036 -.057 49.10 .021 L32 .015 53.25 .011 .018 47.07 .042 .026 50.08 .022 L33 .003 53.26 .014 .014 47.35 .051 -.017 50.48 .026 L34 -.007 53.33 .019 -.041 49.80 .039 -.026 51.41 .028 L35 -.025 54.24 .020 -.040 52.06 .032 -.012 51.61 .035 L36 -.022 54.91 .023 .014 52.34 .038 .045 54.52 .025

103

Chapter 6

Table 6.4 (Cont’d) Result of Autocorrelation Test on Daily Returns KEL KAPCO LUCK Coeff Ljung Box Prob Coeff Ljung Box Prob Coeff Ljung Box Prob L1 -.129 23.24 .000 .040 2.21 .137 .093 12.11 .001 L2 -.061 28.48 .000 -.049 5.54 .063 .015 12.41 .002 L3 .032 29.96 .000 -.009 5.66 .129 -.040 14.71 .002 L4 .014 30.25 .000 -.029 6.85 .144 -.006 14.76 .005 L5 .012 30.46 .000 -.017 7.24 .203 -.049 18.16 .003 L6 -.036 32.34 .000 .012 7.43 .283 .013 18.42 .005 L7 .026 33.32 .000 -.020 7.98 .335 -.013 18.65 .009 L8 .007 33.40 .000 -.022 8.66 .372 -.023 19.41 .013 L9 .023 34.13 .000 -.028 9.73 .373 -.003 19.42 .022 L10 .032 35.56 .000 .026 10.67 .384 .017 19.84 .031 L11 -.032 37.04 .000 -.023 11.39 .411 -.006 19.88 .047 L12 .001 37.04 .000 .047 14.54 .267 .043 22.56 .032 L13 -.067 43.41 .000 -.045 17.43 .180 -.006 22.61 .047 L14 .035 45.16 .000 -.019 17.97 .208 .005 22.64 .066 L15 .029 46.36 .000 .020 18.51 .237 .052 26.47 .033 L16 .017 46.75 .000 .022 19.22 .258 -.010 26.60 .046 L17 -.010 46.88 .000 -.017 19.61 .295 -.018 27.04 .057 L18 -.022 47.57 .000 -.003 19.62 .354 .035 28.77 .051 L19 .050 51.16 .000 -.020 20.20 .383 .033 30.29 .048 L20 -.035 52.86 .000 -.039 22.33 .323 .002 30.29 .065 L21 -.015 53.17 .000 -.021 22.94 .347 -.009 30.40 .084 L22 -.039 55.30 .000 .033 24.54 .319 -.042 32.91 .063 L23 .002 55.31 .000 -.048 27.90 .220 -.074 40.67 .013 L24 .032 56.79 .000 -.036 29.79 .192 -.021 41.31 .015 L25 -.024 57.63 .000 .012 29.99 .225 .035 43.03 .014 L26 -.023 58.41 .000 .001 29.99 .268 .054 47.25 .007 L27 .007 58.47 .000 .004 30.01 .314 -.001 47.25 .009 L28 -.012 58.68 .001 -.034 31.67 .288 .028 48.40 .010 L29 .008 58.77 .001 .037 33.60 .254 .044 51.22 .007 L30 .009 58.88 .001 -.006 33.66 .295 .012 51.43 .009 L31 .059 63.79 .000 -.027 34.72 .295 .001 51.43 .012 L32 -.011 63.96 .001 .006 34.76 .338 .009 51.53 .016 L33 -.070 71.08 .000 -.042 37.28 .279 .002 51.54 .021 L34 -.006 71.13 .000 .008 37.38 .316 -.030 52.81 .021 L35 .038 73.26 .000 -.012 37.58 .352 .020 53.39 .024 L36 -.066 79.61 .000 .005 37.61 .395 -.048 56.74 .015

104

Chapter 6

Table 6.4 (Cont’d) Result of Autocorrelation Test on Daily Returns MLCF MEBL NBP Coeff Ljung Box Prob Coeff Ljung Box Prob Coeff Ljung Box Prob L1 .002 0.00 .948 .041 2.32 .127 .114 18.33 .000 L2 -.049 3.44 .179 .066 8.34 .015 .105 33.84 .000 L3 -.005 3.48 .324 -.015 8.65 .034 .012 34.06 .000 L4 .033 4.99 .289 -.027 9.68 .046 .015 34.36 .000 L5 .045 7.90 .162 -.038 11.72 .039 -.045 37.18 .000 L6 -.035 9.61 .142 -.068 18.18 .006 -.027 38.18 .000 L7 -.066 15.84 .027 -.026 19.11 .008 -.066 44.30 .000 L8 .047 18.92 .015 -.064 24.81 .002 -.049 47.65 .000 L9 .050 22.48 .007 -.006 24.86 .003 -.063 53.21 .000 L10 -.037 24.47 .006 .046 27.78 .002 .017 53.62 .000 L11 .025 25.39 .008 .039 29.95 .002 -.005 53.66 .000 L12 .016 25.75 .012 .019 30.43 .002 -.001 53.67 .000 L13 -.016 26.11 .016 -.077 38.88 .000 -.021 54.29 .000 L14 .004 26.13 .025 -.076 46.97 .000 .005 54.32 .000 L15 .007 26.20 .036 -.055 51.17 .000 .025 55.19 .000 L16 -.036 27.99 .032 -.042 53.60 .000 .001 55.19 .000 L17 -.012 28.19 .043 -.012 53.82 .000 .000 55.19 .000 L18 .017 28.57 .054 .013 54.07 .000 -.044 57.98 .000 L19 .006 28.63 .072 .020 54.63 .000 -.013 58.23 .000 L20 -.002 28.64 .095 .016 55.00 .000 -.022 58.90 .000 L21 .002 28.64 .123 .046 58.06 .000 -.053 62.86 .000 L22 .041 30.99 .096 .015 58.36 .000 -.024 63.66 .000 L23 .015 31.29 .116 -.077 66.82 .000 -.043 66.36 .000 L24 -.029 32.50 .115 -.014 67.10 .000 -.025 67.25 .000 L25 -.053 36.60 .063 -.041 69.45 .000 .010 67.39 .000 L26 .025 37.52 .067 .043 72.02 .000 .015 67.70 .000 L27 .009 37.64 .084 .023 72.80 .000 .004 67.72 .000 L28 .001 37.64 .105 .042 75.27 .000 -.023 68.51 .000 L29 .007 37.71 .129 .048 78.52 .000 .016 68.90 .000 L30 -.003 37.73 .157 .057 83.08 .000 .016 69.26 .000 L31 .025 38.66 .162 .032 84.56 .000 .028 70.39 .000 L32 -.004 38.68 .194 .031 85.91 .000 -.009 70.51 .000 L33 -.028 39.77 .194 .015 86.22 .000 .015 70.83 .000 L34 .010 39.92 .224 -.034 87.90 .000 .004 70.85 .000 L35 .003 39.94 .260 -.072 95.39 .000 .019 71.40 .000 L36 .009 40.06 .295 .016 95.74 .000 -.026 72.37 .000

105

Chapter 6

Table 6.4 (Cont’d) Result of Autocorrelation Test on Daily Returns NRL NML OGDC Coeff Ljung Box Prob Coeff Ljung Box Prob Coeff Ljung Box Prob L1 .145 29.70 .000 .028 1.09 .296 .081 9.30 .002 L2 .010 29.85 .000 .018 1.54 .463 .030 10.56 .005 L3 .051 33.46 .000 .003 1.56 .670 -.005 10.59 .014 L4 -.007 33.53 .000 -.004 1.57 .813 .030 11.88 .018 L5 -.006 33.58 .000 -.001 1.58 .904 .032 13.33 .020 L6 .006 33.63 .000 -.011 1.75 .941 .001 13.33 .038 L7 -.062 39.12 .000 -.012 1.96 .962 -.006 13.39 .063 L8 -.007 39.19 .000 -.012 2.16 .976 -.055 17.63 .024 L9 .022 39.89 .000 -.022 2.83 .971 -.010 17.78 .038 L10 .026 40.88 .000 .011 3.01 .981 .015 18.08 .054 L11 .033 42.42 .000 .004 3.04 .990 .004 18.10 .079 L12 .049 45.79 .000 -.015 3.36 .992 .004 18.13 .112 L13 .044 48.52 .000 -.004 3.38 .996 -.065 24.04 .031 L14 -.037 50.42 .000 .007 3.45 .998 .006 24.09 .045 L15 -.054 54.54 .000 .009 3.56 .999 -.010 24.24 .061 L16 -.017 54.98 .000 -.002 3.56 .999 .004 24.26 .084 L17 -.036 56.82 .000 .000 3.56 1.00 -.013 24.52 .106 L18 .025 57.74 .000 -.008 3.66 1.00 .025 25.38 .115 L19 -.009 57.85 .000 -.014 3.94 1.00 .009 25.49 .145 L20 .006 57.90 .000 -.005 3.97 1.00 -.020 26.04 .165 L21 .080 67.01 .000 .005 4.01 1.00 .022 26.70 .181 L22 .038 69.04 .000 .009 4.12 1.00 -.011 26.87 .216 L23 -.010 69.18 .000 -.012 4.32 1.00 -.077 35.32 .048 L24 .080 78.30 .000 .011 4.51 1.00 .014 35.61 .060 L25 .041 80.67 .000 .000 4.51 1.00 .000 35.61 .078 L26 -.013 80.90 .000 -.020 5.08 1.00 .012 35.84 .095 L27 .001 80.90 .000 .008 5.17 1.00 .030 37.15 .092 L28 -.069 87.67 .000 .002 5.18 1.00 .022 37.84 .102 L29 -.005 87.70 .000 .023 5.97 1.00 .033 39.39 .094 L30 .050 91.31 .000 .013 6.20 1.00 .025 40.25 .100 L31 -.018 91.76 .000 .022 6.92 1.00 .057 44.85 .051 L32 -.021 92.43 .000 -.009 7.04 1.00 -.003 44.86 .065 L33 -.032 93.88 .000 -.023 7.83 1.00 -.009 44.99 .080 L34 -.026 94.83 .000 -.012 8.04 1.00 -.050 48.62 .050 L35 -.018 95.31 .000 .004 8.07 1.00 -.010 48.77 .061 L36 -.037 97.28 .000 .004 8.10 1.00 -.036 50.63 .054

106

Chapter 6

Table 6.4 (Cont’d) Result of Autocorrelation Test on Daily Returns POL PSO PTCL Coeff Ljung Box Prob Coeff Ljung Box Prob Coeff Ljung Box Prob L1 .085 10.08 .002 .106 15.76 .000 .139 26.99 .000 L2 .047 13.18 .001 -.007 15.82 .000 -.012 27.19 .000 L3 -.008 13.27 .004 .014 16.08 .001 -.061 32.37 .000 L4 .007 13.34 .010 .010 16.22 .003 -.023 33.12 .000 L5 -.011 13.51 .019 -.009 16.32 .006 -.023 33.84 .000 L6 -.008 13.61 .034 .017 16.73 .010 -.038 35.83 .000 L7 -.001 13.61 .059 .000 16.73 .019 .007 35.91 .000 L8 .020 14.16 .078 .007 16.80 .032 .042 38.37 .000 L9 -.014 14.44 .108 .027 17.79 .038 -.013 38.60 .000 L10 .003 14.45 .153 .052 21.61 .017 -.005 38.64 .000 L11 .043 17.02 .107 .036 23.45 .015 -.028 39.73 .000 L12 -.004 17.04 .148 -.020 24.00 .020 .032 41.15 .000 L13 -.056 21.54 .063 .014 24.28 .029 -.004 41.17 .000 L14 -.084 31.45 .005 .026 25.24 .032 .009 41.29 .000 L15 -.032 32.87 .005 .015 25.58 .043 .030 42.60 .000 L16 -.033 34.42 .005 .001 25.58 .060 -.020 43.15 .000 L17 -.057 39.11 .002 -.019 26.08 .073 .015 43.46 .000 L18 .041 41.49 .001 .011 26.25 .094 -.018 43.90 .001 L19 -.003 41.50 .002 .064 32.11 .030 -.052 47.78 .000 L20 -.063 47.20 .001 .011 32.28 .040 -.083 57.51 .000 L21 .019 47.73 .001 -.021 32.91 .047 .017 57.93 .000 L22 .003 47.74 .001 .001 32.91 .063 -.004 57.95 .000 L23 -.019 48.25 .002 -.014 33.18 .078 -.040 60.24 .000 L24 -.012 48.44 .002 .011 33.37 .097 .008 60.33 .000 L25 -.009 48.56 .003 -.029 34.60 .096 .006 60.39 .000 L26 -.029 49.77 .003 -.024 35.40 .103 .001 60.39 .000 L27 .041 52.18 .003 -.025 36.26 .110 .007 60.46 .000 L28 .074 60.10 .000 .020 36.86 .122 .061 65.79 .000 L29 .080 69.29 .000 .056 41.37 .064 .017 66.19 .000 L30 .038 71.39 .000 .009 41.49 .079 .027 67.27 .000 L31 -.008 71.48 .000 -.015 41.82 .093 -.017 67.69 .000 L32 -.018 71.93 .000 -.017 42.23 .107 .000 67.69 .000 L33 -.043 74.60 .000 -.053 46.20 .063 .008 67.79 .000 L34 .024 75.44 .000 -.004 46.22 .079 -.035 69.58 .000 L35 -.020 76.01 .000 .012 46.43 .094 -.003 69.59 .000 L36 .048 79.35 .000 .013 46.66 .110 -.015 69.90 .001

107

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Table 6.4 (Cont’d) Result of Autocorrelation Test on Daily Returns SCBPL SHEL SNGC Coeff Ljung Box Prob Coeff Ljung Box Prob Coeff Ljung Box Prob L1 -.084 9.79 .002 .146 29.89 .000 .136 25.93 .000 L2 -.004 9.81 .007 .017 30.29 .000 .027 26.94 .000 L3 -.021 10.44 .015 .042 32.74 .000 -.001 26.94 .000 L4 -.023 11.20 .024 .049 36.14 .000 .013 27.17 .000 L5 .033 12.73 .026 .091 47.84 .000 -.023 27.89 .000 L6 -.071 19.83 .003 .010 47.99 .000 .004 27.91 .000 L7 -.040 22.07 .002 -.019 48.48 .000 -.040 30.23 .000 L8 -.070 29.01 .000 -.036 50.32 .000 -.028 31.32 .000 L9 .003 29.02 .001 .017 50.75 .000 -.008 31.42 .000 L10 -.013 29.25 .001 -.038 52.74 .000 .037 33.31 .000 L11 -.007 29.32 .002 -.030 54.03 .000 .017 33.74 .000 L12 .003 29.33 .004 -.045 56.85 .000 .013 33.97 .001 L13 .002 29.34 .006 -.029 58.02 .000 .016 34.32 .001 L14 .013 29.56 .009 -.023 58.75 .000 .028 35.47 .001 L15 .007 29.62 .013 .019 59.27 .000 -.030 36.72 .001 L16 .034 31.28 .012 -.004 59.29 .000 .033 38.25 .001 L17 -.016 31.65 .017 -.004 59.32 .000 .004 38.26 .002 L18 -.015 31.95 .022 -.024 60.12 .000 .004 38.29 .004 L19 -.005 31.98 .031 -.044 62.91 .000 -.004 38.31 .005 L20 -.026 32.92 .034 .013 63.16 .000 -.010 38.45 .008 L21 .006 32.98 .046 -.017 63.58 .000 -.008 38.54 .011 L22 .032 34.42 .044 -.050 67.15 .000 .020 39.09 .014 L23 .016 34.78 .055 .013 67.38 .000 -.019 39.59 .017 L24 -.017 35.19 .066 -.015 67.68 .000 -.027 40.64 .018 L25 .017 35.58 .078 -.053 71.76 .000 -.005 40.67 .025 L26 -.035 37.36 .069 -.037 73.69 .000 -.063 46.30 .008 L27 .030 38.62 .069 -.003 73.70 .000 -.024 47.14 .010 L28 -.059 43.50 .031 .025 74.62 .000 .022 47.83 .011 L29 .041 45.89 .024 .036 76.52 .000 .013 48.06 .014 L30 -.027 46.92 .025 .042 79.01 .000 -.017 48.49 .018 L31 -.019 47.42 .030 .054 83.24 .000 -.005 48.52 .023 L32 .010 47.55 .038 -.011 83.43 .000 .011 48.70 .030 L33 -.036 49.44 .033 .044 86.17 .000 -.020 49.31 .034 L34 .010 49.58 .041 .038 88.22 .000 -.014 49.57 .041 L35 .015 49.89 .049 -.007 88.28 .000 .042 52.12 .031 L36 .001 49.89 .062 .030 89.55 .000 .019 52.67 .036

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Table 6.4 (Cont’d) Result of Autocorrelation Test on Daily Returns SSGC UBL Coeff Ljung Box Prob Coeff Ljung Box Prob L1 .038 1.98 .160 .088 10.84 .001 L2 .007 2.06 .358 .011 11.01 .004 L3 -.027 3.09 .378 .041 13.39 .004 L4 -.016 3.47 .482 -.015 13.71 .008 L5 .028 4.61 .466 -.051 17.39 .004 L6 .001 4.61 .595 .019 17.91 .006 L7 -.026 5.57 .591 -.049 21.36 .003 L8 .007 5.64 .687 -.077 29.84 .000 L9 .005 5.68 .771 -.056 34.21 .000 L10 -.021 6.32 .787 -.039 36.32 .000 L11 .001 6.33 .851 -.012 36.51 .000 L12 .001 6.33 .899 .015 36.85 .000 L13 -.009 6.43 .929 -.001 36.85 .000 L14 .039 8.60 .856 .014 37.11 .001 L15 .041 10.95 .756 .088 48.21 .000 L16 .009 11.08 .805 -.025 49.09 .000 L17 .037 13.00 .736 .015 49.41 .000 L18 .009 13.11 .785 .005 49.45 .000 L19 .019 13.63 .805 -.026 50.39 .000 L20 .000 13.63 .849 -.022 51.08 .000 L21 .059 18.55 .614 -.010 51.23 .000 L22 -.002 18.55 .673 -.005 51.27 .000 L23 -.032 20.02 .641 -.013 51.51 .001 L24 -.039 22.21 .567 .014 51.77 .001 L25 -.018 22.69 .596 .027 52.81 .001 L26 .022 23.38 .611 .075 60.87 .000 L27 -.005 23.42 .662 -.018 61.36 .000 L28 .029 24.65 .647 -.017 61.78 .000 L29 -.009 24.75 .691 .074 69.60 .000 L30 .004 24.77 .736 .009 69.72 .000 L31 -.004 24.79 .777 -.039 71.85 .000 L32 -.007 24.86 .812 -.009 71.98 .000 L33 -.010 25.01 .840 -.008 72.06 .000 L34 -.011 25.19 .863 .016 72.43 .000 L35 -.011 25.37 .884 -.010 72.59 .000 L36 -.018 25.84 .895 -.027 73.60 .000

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Table 6.5 Results of Autoregression model, Heteroscedasticity and B-G tests on Daily Returns

Heteroscedasticity LM ARCH Test Constant AR(1) White noise-stat Prob. Q-statistics Prob. Coeff 0.001 0.104 KSE100 t-statistics 3.477 3.897 62.592 0.000 201.518 0.000 P-value 0.001 0.000 Coeff 0.001 -0.286 KSEALL t-statistics 3.227 -11.175 297.885 0.000 363.235 0.000 P-value 0.001 0.000 Coeff 0.007 0.665 KSE30 t-statistics 0.815 33.274 167.293 0.000 249.792 0.000 P-value 0.415 0.000 Coeff 0.002 -0.459 KMI30 t-statistics 1.957 -19.295 166.703 0.000 166.118 0.000 P-value 0.051 0.000 Coeff 0.001 0.137 ABOT t-statistics 2.041 5.145 75.449 0.000 111.274 0.000 P-value 0.041 0.000 Coeff 0.000 0.073 AICL t-statistics -0.460 2.745 0.273 0.873 0.276 1.000 P-value 0.646 0.006 Coeff 0.001 0.154 ABL t-statistics 1.230 5.811 20.621 0.000 61.144 0.000 P-value 0.219 0.000 Coeff 0.000 0.109 AKBL t-statistics 0.171 4.112 14.068 0.001 23.115 0.010 P-value 0.865 0.000 Coeff 0.001 0.051 APL t-statistics 1.822 1.908 0.255 0.880 0.249 1.000 P-value 0.069 0.057 Coeff 0.001 0.174 ATRL t-statistics 1.266 6.592 57.948 0.000 111.328 0.000 P-value 0.206 0.000 Coeff 0.000 0.059 BAFL t-statistics 0.540 2.209 61.627 0.000 207.937 0.000 P-value 0.589 0.027 Coeff 0.000 -0.006 BAHL t-statistics 0.633 -0.241 3.530 0.171 0.576 1.000 P-value 0.527 0.810

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Table 6.5 (Cont’d) Results of Autoregression model, Heteroscedasticity and B-G tests on Daily Returns

Heteroscedasticity LM ARCH Test Constant AR(1) White noise-stat Prob. Q-statistics Prob. Coeff 0.000 -0.033 BIPL t-statistics 0.218 -1.248 18.662 0.000 98.459 0.000 P-value 0.828 0.212 Coeff 0.000 0.128 BOP t-statistics -0.277 4.839 90.215 0.000 130.027 0.000 P-value 0.782 0.000 Coeff 0.001 0.132 DGKC t-statistics 1.260 4.994 81.038 0.000 223.425 0.000 P-value 0.208 0.000 Coeff -0.001 0.051 DAWH t-statistics -0.706 1.912 0.243 0.886 0.043 1.000 P-value 0.481 0.056 Coeff 0.001 -0.077 DCL t-statistics 0.367 -2.889 9.324 0.009 22.089 0.015 P-value 0.714 0.004 Coeff 0.000 0.218 EFUG t-statistics -0.094 8.268 5.354 0.069 10.714 0.380 P-value 0.925 0.000 Coeff 0.000 0.141 ENGRO t-statistics 0.456 5.327 2.281 0.320 6.518 0.770 P-value 0.649 0.000 Coeff 0.000 0.080 EPCL t-statistics -0.384 3.004 46.182 0.000 100.062 0.000 P-value 0.701 0.003 Coeff 0.001 -0.018 FCCL t-statistics 1.198 -0.691 18.860 0.000 91.731 0.000 P-value 0.231 0.490 Coeff 0.001 0.066 FFBL t-statistics 1.405 2.478 121.692 0.000 155.429 0.000 P-value 0.160 0.013 Coeff 0.000 0.109 FFC t-statistics 0.574 4.120 0.048 0.976 0.234 1.000 P-value 0.566 0.000 Coeff 0.000 0.175 FABL t-statistics 0.208 6.685 58.096 0.000 87.791 0.000 P-value 0.836 0.000

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Table 6.5 (Cont’d) Results of Autoregression model, Heteroscedasticity and B-G tests on Daily Returns

Heteroscedasticity LM ARCH Test Constant AR(1) White noise-stat Prob. Q-statistics Prob. Coeff 0.001 0.079 HBL t-statistics 1.222 2.975 21.550 0.000 20.667 0.024 P-value 0.222 0.003 Coeff 0.000 0.040 HMB t-statistics 0.038 1.498 0.974 0.615 1.808 0.998 P-value 0.970 0.134 Coeff -0.001 0.105 HUBC t-statistics -2.083 3.961 31.672 0.000 70.277 0.000 P-value 0.037 0.000 Coeff 0.001 0.215 ICI t-statistics 2.136 8.184 43.686 0.000 85.128 0.000 P-value 0.033 0.000 Coeff 0.000 -0.008 JSBL t-statistics -0.189 -0.316 163.413 0.000 179.945 0.000 P-value 0.850 0.752 Coeff -0.002 -0.099 KASBB t-statistics -1.690 -3.715 66.016 0.000 86.091 0.000 P-value 0.091 0.000 Coeff 0.001 -0.130 KEL t-statistics 0.901 -4.871 18.530 0.000 18.530 0.000 P-value 0.368 0.000 Coeff 0.000 0.040 KAPCO t-statistics 1.064 1.493 19.892 0.000 25.495 0.004 P-value 0.288 0.136 Coeff 0.002 0.093 LUCK t-statistics 2.930 3.504 123.996 0.000 236.998 0.000 P-value 0.003 0.001 Coeff 0.001 0.002 MLCF t-statistics 1.274 0.068 32.110 0.000 141.834 0.000 P-value 0.203 0.946 Coeff 0.001 0.041 MEBL t-statistics 0.843 1.530 121.962 0.000 211.455 0.000 P-value 0.399 0.126 Coeff 0.000 0.114 NBP t-statistics 0.121 4.307 2.417 0.299 1.090 1.000 P-value 0.904 0.000

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Table 6.5 (Cont’d) Results of Autoregression model, Heteroscedasticity and B-G tests on Daily Returns

Heteroscedasticity LM ARCH Test Constant AR(1) White noise-stat Prob. Q-statistics Prob. Coeff 0.000 0.145 NRL t-statistics 0.731 5.509 98.241 0.000 149.649 0.000 P-value 0.465 0.000 Coeff 0.000 0.028 NML t-statistics 0.280 1.045 0.119 0.942 0.015 1.000 P-value 0.780 0.296 Coeff 0.001 0.082 OGDC t-statistics 2.638 3.057 68.545 0.000 179.096 0.000 P-value 0.008 0.002 Coeff 0.001 0.085 POL t-statistics 2.546 3.194 123.037 0.000 284.709 0.000 P-value 0.011 0.001 Coeff 0.001 0.106 PSO t-statistics 1.281 3.994 5.397 0.067 12.513 0.252 P-value 0.200 0.000 Coeff 0.000 -0.478 PTCL t-statistics 0.166 -20.374 194.583 0.000 194.237 0.000 P-value 0.868 0.000 Coeff 0.001 -0.084 SCBPL t-statistics 0.908 -3.141 122.589 0.000 79.481 0.000 P-value 0.364 0.002 Coeff 0.000 0.146 SHEL t-statistics -0.176 5.529 6.494 0.039 15.983 15.983 P-value 0.860 0.000 Coeff 0.000 0.136 SNGC t-statistics -0.233 5.137 1.154 0.562 10.236 0.420 P-value 0.816 0.000 Coeff 0.001 0.038 SSGC t-statistics 0.813 1.413 6.162 0.046 5.967 0.818 P-value 0.416 0.158 Coeff 0.001 0.088 UBL t-statistics 1.976 3.303 51.905 0.000 114.022 0.000 P-value 0.048 0.001

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Table 6.6.1 Result of ADF Test on Daily Returns

ADF Level ADF Difference Lag Lag t-stat Prob Length DW-stat t-stat Prob Length DW-stat KSE-100 -2.197 0.4906 0 1.7819 -33.6010 0.0000 0 2.0008 KSE-ALL -2.013 0.5932 2 2.0043 -32.0252 0.0000 1 2.0049 KSE-30 -3.583 0.0316 1 1.9987 -44.3571 0.0000 0 2.0004 KMI-30 -3.796 0.0170 5 2.0047 -23.7120 0.0000 4 2.0060 ABOT -1.785 0.7120 1 2.0143 -32.4061 0.0000 0 2.0136 AICL -2.593 0.2836 0 1.8433 -34.7722 0.0000 0 1.8433 ABL -3.088 0.1095 1 2.0212 -31.9293 0.0000 0 2.0195 AKBL -1.976 0.6132 1 2.0061 -33.5589 0.0000 0 2.0054 APL -6.219 0.0000 0 1.8987 -35.6930 0.0000 0 2.0009 ATRL -2.983 0.1373 1 1.9651 -31.4058 0.0000 0 1.9633 BAFL -2.686 0.2426 0 1.8745 -35.3610 0.0000 0 1.9774 BAHL -2.851 0.1794 0 1.9940 -37.6487 0.0000 0 2.0009 BIPL -2.071 0.5610 0 2.0584 -38.7606 0.0000 0 2.0082 BOP -2.307 0.4292 1 1.9824 -32.8628 0.0000 0 1.9818 DGKC -1.736 0.7351 1 1.9824 -32.7268 0.0000 0 1.9976 DAWH -1.536 0.8168 0 1.8937 -35.4974 0.0000 0 2.0059 DCL -2.384 0.3879 1 2.0026 -40.4034 0.0000 0 2.0030 EFUG -1.845 0.6821 1 2.0063 -29.7803 0.0000 0 2.0060 ENGRO -2.397 0.3807 1 1.9982 -32.4650 0.0000 0 1.9975 EPCL -2.036 0.5803 1 2.0000 -34.5864 0.0000 0 1.9997 FCCL -1.193 0.9108 0 2.0274 -29.9535 0.0000 1 1.9895 FFBL -2.592 0.2840 0 1.8610 -35.2927 0.0000 0 2.0141 FFC -3.429 0.0479 1 1.9950 -33.5754 0.0000 0 1.9952 FABL -2.692 0.2399 1 2.0182 -31.4400 0.0000 0 2.0164 HBL -2.577 0.2910 0 1.8305 -34.5622 0.0000 0 1.9305 HMB -1.313 0.8841 0 1.9137 -35.8999 0.0000 0 2.0054 HUBC -3.813 0.0161 1 1.9985 -33.7089 0.0000 0 1.9984 ICI -1.273 0.8938 1 1.9812 -29.9338 0.0000 0 1.9809 1% -3.9647 Critical Values 5% -3.4131 10% -3.1285

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Table 6.6.1 (Cont’d) Result of ADF Test on Daily Returns

ADF Level ADF Difference Lag DW- t-stat Prob Length DW-stat t-stat Prob Lag Length stat JSBL -1.916 0.6456 0 2.0005 -37.8603 0.0000 0 2.0086 KASSB -2.610 0.2758 2 1.9980 -28.9054 0.0000 1 1.9983 KEL -2.175 0.5027 1 2.0052 -42.4447 0.0000 0 2.0065 KAPCO -2.681 0.2446 0 1.9028 -36.0616 0.0000 0 2.0032 LUCK -1.937 0.6344 1 2.0000 -34.0383 0.0000 0 1.9998 MLCF -1.449 0.8462 0 1.9881 -37.5098 0.0000 0 2.0074 MEBL -5.381 0.0000 0 1.9048 -35.7516 0.0000 0 2.0004 NBP -3.462 0.0439 2 1.9996 -22.7343 0.0000 1 1.9989 NRL -2.984 0.1371 1 1.9985 -32.4915 0.0000 0 1.9988 NML -1.817 0.6962 0 1.9369 -36.4463 0.0000 0 2.0010 OGDC -3.470 0.0430 0 1.8364 -34.4829 0.0000 0 1.9893 POL -3.798 0.0169 0 1.8239 -34.5031 0.0000 0 2.0100 PSO -2.773 0.2078 1 1.9996 -33.6758 0.0000 0 1.9985 PTCL -1.920 0.6434 1 1.9908 -32.5348 0.0000 0 1.9903 SCBPL -2.458 0.3495 1 2.0131 -40.7400 0.0000 0 2.0131 SHEL -1.733 0.7361 1 2.0014 -32.3084 0.0000 0 2.0010 SNGC -2.983 0.1374 1 2.0068 -32.6724 0.0000 0 2.0055 SSGC -2.778 0.2058 0 1.9066 -36.1696 0.0000 1 2.0088 UBL -2.195 0.4912 1 1.8126 -34.2263 0.0000 0 1.9874 1% -3.9647 Critical Values 5% -3.4131 10% -3.1285

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Table 6.6.2 Results of PP and KPSS Tests on Daily Returns

KPSS PP Level PP Difference Level KPSS diff. t-stat Prob. t-stat Prob. LM stat LM stat KSE-100 -2.499 0.329 -33.792 0.000 0.569 0.065 KSE-ALL -2.256 0.458 -50.660 0.000 0.707 0.051 KSE-30 -3.678 0.024 -44.394 0.000 0.363 0.085 KMI-30 -9.695 0.000 -100.309 0.000 0.272 0.107 ABOT -1.622 0.784 -32.236 0.000 1.012 0.058 AICL -2.831 0.186 -34.772 0.000 0.226 0.033 ABL -3.019 0.127 -32.014 0.000 0.343 0.056 AKBL -1.748 0.729 -33.366 0.000 0.493 0.075 APL -6.221 0.000 -35.728 0.000 0.136 0.152 ATRL -2.776 0.206 -31.331 0.000 0.308 0.083 BAFL -2.603 0.279 -35.469 0.000 0.854 0.048 BAHL -3.019 0.127 -37.648 0.000 0.546 0.035 BIPL -1.864 0.673 -39.237 0.000 0.586 0.076 BOP -2.065 0.564 -32.588 0.000 0.647 0.062 DGKC -1.603 0.792 -32.717 0.000 0.760 0.101 DAWH -1.697 0.752 -35.552 0.000 0.643 0.067 DCL -2.447 0.355 -40.316 0.000 0.766 0.048 EFUG -1.890 0.659 -29.800 0.000 0.883 0.077 ENGRO -2.369 0.396 -32.340 0.000 0.535 0.108 EPCL -1.949 0.628 -34.565 0.000 0.828 0.059 FCCL -1.052 0.935 -38.486 0.000 1.061 0.080 FFBL -2.578 0.291 -35.312 0.000 0.906 0.059 FFC -3.450 0.045 -33.403 0.000 0.818 0.055 FABL -2.319 0.423 -31.058 0.000 0.471 0.072 HBL -2.885 0.168 -34.562 0.000 0.424 0.064 HMB -1.290 0.890 -35.879 0.000 0.794 0.051 HUBC -3.799 0.017 -33.552 0.000 0.215 0.121 Significance Level PP Test KPSS Test Critical Values 0.010 -3.965 0.216 0.050 -3.413 0.146 0.100 -3.129 0.119

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Table 6.6.2 (Cont’d) Results of PP and KPSS Tests on Daily Returns

KPSS PP Level PP Difference Level KPSS diff. t-stat Prob. t-stat Prob. LM stat LM stat ICI -1.427 0.853 -30.144 0.000 0.482 0.180 JSBL -1.787 0.711 -38.079 0.000 0.662 0.070 KASSB -2.767 0.210 -41.352 0.000 0.893 0.085 KEL -2.186 0.496 -42.664 0.000 0.655 0.045 KAPCO -2.656 0.255 -36.129 0.000 0.634 0.062 LUCK -1.936 0.635 -33.920 0.000 0.836 0.120 MLCF -1.438 0.850 -37.519 0.000 1.003 0.147 MEBL -5.380 0.000 -36.007 0.000 0.282 0.088 NBP -3.490 0.041 -33.294 0.000 0.625 0.063 NRL -3.165 0.092 -32.455 0.000 0.668 0.082 NML -1.817 0.696 -36.450 0.000 0.353 0.097 OGDC -3.524 0.037 -34.583 0.000 0.402 0.102 POL -3.880 0.013 -34.495 0.000 0.619 0.054 PSO -2.578 0.291 -33.671 0.000 0.398 0.124 PTCL -1.755 0.726 -32.244 0.000 0.804 0.075 SCBPL -2.009 0.596 -42.746 0.000 1.031 0.035 SHEL -1.926 0.640 -32.566 0.000 0.515 0.050 SNGC -2.729 0.225 -32.587 0.000 0.581 0.054 SSGC -2.828 0.187 -36.155 0.000 0.387 0.041 UBL -2.434 0.362 -34.136 0.000 0.711 0.046 Significance Level PP Test KPSS Test Critical Values 0.010 -3.965 0.216 0.050 -3.413 0.146 0.100 -3.129 0.119

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Table 6.7 Result of Variance Ratio Test on Daily Closing Prices

L4 L8 L12 L16 L20 L24 L28 L32 L36 VR(q) 1.20 1.32 1.33 1.30 1.29 1.28 1.26 1.27 1.27 KSE Z stat 4.04 4.03 3.29 2.56 2.17 1.89 1.64 1.60 1.51 100 Z* stat 2.84 2.86 2.35 1.83 1.56 1.37 1.19 1.17 1.11 VR(q) 0.58 0.55 0.55 0.53 0.52 0.52 0.51 0.51 0.51 KSE Z stat -8.41 -5.64 -4.48 -4.01 -3.59 -3.31 -3.10 -2.88 -2.71 All Z* stat -0.89 -0.80 -0.77 -0.78 -0.78 -0.78 -0.79 -0.78 -0.77 VR(q) 0.77 0.75 0.71 0.68 0.67 0.66 0.65 0.66 0.65 Z stat -4.67 -3.21 -2.94 -2.69 -2.51 -2.36 -2.21 -2.02 -1.91 KSE 30 Z* stat -0.62 -0.57 -0.63 -0.65 -0.67 -0.68 -0.68 -0.66 -0.66 VR(q) 0.31 0.20 0.16 0.14 0.13 0.12 0.11 0.11 0.11 KMI Z stat -13.73 -10.12 -8.39 -7.30 -6.55 -6.01 -5.57 -5.21 -4.92 30 Z* stat -1.26 -1.26 -1.26 -1.26 -1.26 -1.26 -1.26 -1.26 -1.26 VR(q) 1.24 1.24 1.19 1.20 1.21 1.23 1.24 1.25 1.25 Z stat 4.81 2.96 1.87 1.67 1.59 1.56 1.50 1.43 1.36 ABOT Z* stat 3.57 2.29 1.47 1.34 1.30 1.29 1.25 1.22 1.17 VR(q) 1.11 1.15 1.18 1.17 1.10 1.03 0.98 0.95 0.93 Z stat 2.29 1.96 1.85 1.46 0.73 0.20 -0.15 -0.29 -0.39 AICL Z* stat 2.11 1.99 2.03 1.67 0.85 0.23 -0.17 -0.34 -0.44 VR(q) 1.32 1.36 1.31 1.18 1.10 1.04 1.01 1.02 1.05 Z stat 6.46 4.59 3.11 1.55 0.77 0.29 0.07 0.10 0.26 ABL Z* stat 4.49 3.24 2.21 1.11 0.55 0.21 0.05 0.07 0.19 VR(q) 1.17 1.06 0.97 0.92 0.93 0.96 1.01 1.07 1.10 Z stat 3.48 0.79 -0.27 -0.67 -0.51 -0.30 0.06 0.38 0.55 AKBL Z* stat 2.65 0.62 -0.22 -0.54 -0.41 -0.25 0.05 0.32 0.47 VR(q) 1.01 0.90 0.86 0.86 0.89 0.91 0.92 0.93 0.94 Z stat 0.29 -1.28 -1.41 -1.18 -0.79 -0.59 -0.48 -0.40 -0.35 APL Z* stat 0.25 -1.13 -1.26 -1.05 -0.71 -0.53 -0.43 -0.36 -0.31 VR(q) 1.25 1.33 1.40 1.48 1.52 1.53 1.54 1.54 1.55 Z stat 4.99 4.16 4.02 4.12 3.89 3.59 3.39 3.15 3.02 ATRL Z* stat 3.86 3.28 3.20 3.30 3.14 2.91 2.76 2.57 2.48 VR(q) 1.04 1.03 1.01 0.98 0.91 0.86 0.81 0.80 0.77 Z stat 0.84 0.43 0.06 -0.19 -0.71 -0.98 -1.18 -1.20 -1.28 BAHL Z* stat 0.71 0.40 0.05 -0.17 -0.63 -0.86 -1.03 -1.04 -1.10 VR(q) 1.11 1.05 0.94 0.87 0.83 0.80 0.78 0.78 0.80 Z stat 2.19 0.62 -0.57 -1.14 -1.30 -1.40 -1.38 -1.28 -1.09 BAFL Z* stat 1.48 0.42 -0.38 -0.78 -0.89 -0.97 -0.96 -0.90 -0.77

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Chapter 6

Table 6.7 (Cont’d) Result of Variance Ratio Test on Daily Closing Prices

L4 L8 L12 L16 L20 L24 L28 L32 L36 VR(q) 0.86 0.78 0.76 0.74 0.75 0.75 0.75 0.75 0.77 BIPL Z stat -2.76 -2.84 -2.39 -2.18 -1.91 -1.68 -1.59 -1.46 -1.28 Z* stat -2.19 -2.23 -1.88 -1.71 -1.51 -1.33 -1.26 -1.16 -1.02 VR(q) 1.15 1.05 0.99 1.00 0.97 0.96 0.97 0.97 0.98 BOP Z stat 2.98 0.57 -0.06 -0.03 -0.22 -0.26 -0.21 -0.17 -0.14 Z* stat 2.07 0.42 -0.04 -0.03 -0.17 -0.20 -0.16 -0.14 -0.11 VR(q) 1.15 1.05 0.99 1.00 0.97 0.96 0.97 0.97 0.98 DGKC Z stat 2.98 0.57 -0.06 -0.03 -0.22 -0.26 -0.21 -0.17 -0.14 Z* stat 2.07 0.42 -0.04 -0.03 -0.17 -0.20 -0.16 -0.14 -0.11 VR(q) 1.13 1.18 1.18 1.19 1.20 1.19 1.17 1.16 1.14 DAWH Z stat 2.63 2.25 1.84 1.61 1.47 1.30 1.04 0.96 0.80 Z* stat 3.29 3.16 2.59 2.23 2.03 1.78 1.41 1.29 1.07 VR(q) 0.87 0.93 0.94 0.90 0.91 0.93 0.94 0.94 0.94 DCL Z stat -2.55 -0.93 -0.64 -0.82 -0.67 -0.49 -0.37 -0.34 -0.32 Z* stat -1.67 -0.65 -0.47 -0.62 -0.52 -0.38 -0.29 -0.27 -0.26 VR(q) 1.38 1.40 1.45 1.42 1.34 1.31 1.31 1.34 1.37 EFUG Z stat 7.57 5.03 4.48 3.51 2.54 2.12 1.96 1.95 2.00 Z* stat 6.12 4.07 3.66 2.89 2.11 1.78 1.65 1.66 1.72 VR(q) 1.21 1.18 1.15 1.13 1.12 1.08 1.05 1.03 0.98 ENGRO Z stat 4.11 2.22 1.50 1.12 0.94 0.56 0.30 0.15 -0.09 Z* stat 3.26 1.81 1.25 0.95 0.81 0.49 0.27 0.14 -0.08 VR(q) 1.08 1.13 1.16 1.19 1.15 1.12 1.09 1.06 1.04 EPCL Z stat 1.67 1.63 1.63 1.57 1.16 0.82 0.57 0.37 0.24 Z* stat 1.28 1.29 1.32 1.29 0.96 0.68 0.48 0.31 0.20 VR(q) 0.88 0.85 0.82 0.82 0.84 0.86 0.87 0.90 0.92 FCCL Z stat -2.45 -1.91 -1.81 -1.53 -1.20 -0.97 -0.80 -0.57 -0.42 Z* stat -1.85 -1.49 -1.44 -1.22 -0.96 -0.78 -0.64 -0.46 -0.34 VR(q) 1.08 0.98 0.93 0.92 0.94 0.96 0.96 0.96 0.94 FFBL Z stat 1.54 -0.31 -0.73 -0.67 -0.49 -0.28 -0.23 -0.24 -0.30 Z* stat 0.98 -0.21 -0.51 -0.47 -0.35 -0.20 -0.17 -0.17 -0.22 VR(q) 1.12 0.96 0.91 0.92 0.92 0.89 0.86 0.80 0.75 FFC Z stat 2.39 -0.47 -0.89 -0.67 -0.61 -0.76 -0.86 -1.19 -1.36 Z* stat 1.87 -0.37 -0.71 -0.54 -0.51 -0.63 -0.72 -1.00 -1.14 VR(q) 1.32 1.21 1.00 0.92 0.93 0.88 0.87 0.88 0.87 FABL Z stat 6.33 2.65 0.05 -0.65 -0.53 -0.82 -0.81 -0.70 -0.71 Z* stat 4.32 1.88 0.04 -0.47 -0.40 -0.62 -0.61 -0.53 -0.55

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Table 6.7 (Cont’d) Result of Variance Ratio Test on Daily Closing Prices

L4 L8 L12 L16 L20 L24 L28 L32 L36 VR(q) 0.86 0.78 0.76 0.74 0.75 0.75 0.75 0.75 0.77 Z stat -2.76 -2.84 -2.39 -2.18 -1.91 -1.68 -1.59 -1.46 -1.28 BIPL Z* stat -2.19 -2.23 -1.88 -1.71 -1.51 -1.33 -1.26 -1.16 -1.02 VR(q) 1.15 1.05 0.99 1.00 0.97 0.96 0.97 0.97 0.98 Z stat 2.98 0.57 -0.06 -0.03 -0.22 -0.26 -0.21 -0.17 -0.14 BOP Z* stat 2.07 0.42 -0.04 -0.03 -0.17 -0.20 -0.16 -0.14 -0.11 VR(q) 1.15 1.05 0.99 1.00 0.97 0.96 0.97 0.97 0.98 Z stat 2.98 0.57 -0.06 -0.03 -0.22 -0.26 -0.21 -0.17 -0.14 DGKC Z* stat 2.07 0.42 -0.04 -0.03 -0.17 -0.20 -0.16 -0.14 -0.11 VR(q) 1.13 1.18 1.18 1.19 1.20 1.19 1.17 1.16 1.14 Z stat 2.63 2.25 1.84 1.61 1.47 1.30 1.04 0.96 0.80 DAWH Z* stat 3.29 3.16 2.59 2.23 2.03 1.78 1.41 1.29 1.07 VR(q) 0.87 0.93 0.94 0.90 0.91 0.93 0.94 0.94 0.94 Z stat -2.55 -0.93 -0.64 -0.82 -0.67 -0.49 -0.37 -0.34 -0.32 DCL Z* stat -1.67 -0.65 -0.47 -0.62 -0.52 -0.38 -0.29 -0.27 -0.26 VR(q) 1.38 1.40 1.45 1.42 1.34 1.31 1.31 1.34 1.37 Z stat 7.57 5.03 4.48 3.51 2.54 2.12 1.96 1.95 2.00 EFUG Z* stat 6.12 4.07 3.66 2.89 2.11 1.78 1.65 1.66 1.72 VR(q) 1.21 1.18 1.15 1.13 1.12 1.08 1.05 1.03 0.98 Z stat 4.11 2.22 1.50 1.12 0.94 0.56 0.30 0.15 -0.09 ENGRO Z* stat 3.26 1.81 1.25 0.95 0.81 0.49 0.27 0.14 -0.08 VR(q) 1.08 1.13 1.16 1.19 1.15 1.12 1.09 1.06 1.04 Z stat 1.67 1.63 1.63 1.57 1.16 0.82 0.57 0.37 0.24 EPCL Z* stat 1.28 1.29 1.32 1.29 0.96 0.68 0.48 0.31 0.20 VR(q) 0.88 0.85 0.82 0.82 0.84 0.86 0.87 0.90 0.92 Z stat -2.45 -1.91 -1.81 -1.53 -1.20 -0.97 -0.80 -0.57 -0.42 FCCL Z* stat -1.85 -1.49 -1.44 -1.22 -0.96 -0.78 -0.64 -0.46 -0.34 VR(q) 1.08 0.98 0.93 0.92 0.94 0.96 0.96 0.96 0.94 Z stat 1.54 -0.31 -0.73 -0.67 -0.49 -0.28 -0.23 -0.24 -0.30 FFBL Z* stat 0.98 -0.21 -0.51 -0.47 -0.35 -0.20 -0.17 -0.17 -0.22 VR(q) 1.12 0.96 0.91 0.92 0.92 0.89 0.86 0.80 0.75 Z stat 2.39 -0.47 -0.89 -0.67 -0.61 -0.76 -0.86 -1.19 -1.36 FFC Z* stat 1.87 -0.37 -0.71 -0.54 -0.51 -0.63 -0.72 -1.00 -1.14 VR(q) 1.32 1.21 1.00 0.92 0.93 0.88 0.87 0.88 0.87 Z stat 6.33 2.65 0.05 -0.65 -0.53 -0.82 -0.81 -0.70 -0.71 FABL Z* stat 4.32 1.88 0.04 -0.47 -0.40 -0.62 -0.61 -0.53 -0.55

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Table 6.7 (Cont’d) Result of Variance Ratio Test on Daily Closing Prices

L4 L8 L12 L16 L20 L24 L28 L32 L36 VR(q) 1.06 1.06 1.04 1.04 1.00 0.90 0.83 0.78 0.75 NML Z stat 1.23 0.76 0.44 0.32 0.03 -0.69 -1.08 -1.26 -1.37 Z* stat 2.47 1.32 0.75 0.54 0.04 -1.20 -1.90 -2.25 -2.45 VR(q) 1.15 1.22 1.23 1.21 1.19 1.18 1.17 1.19 1.21 OGDC Z stat 2.92 2.84 2.31 1.76 1.46 1.26 1.09 1.13 1.17 Z* stat 2.15 2.09 1.71 1.32 1.10 0.95 0.83 0.87 0.90 VR(q) 1.17 1.10 1.08 1.06 1.06 1.02 0.99 0.99 0.99 PTCL Z stat 3.40 1.29 0.76 0.49 0.42 0.12 -0.09 -0.06 -0.05 Z* stat 2.61 1.02 0.61 0.40 0.35 0.10 -0.07 -0.05 -0.04 VR(q) 1.16 1.20 1.23 1.19 1.13 1.08 1.03 1.03 1.03 POL Z stat 3.20 2.54 2.28 1.65 1.00 0.52 0.17 0.17 0.16 Z* stat 2.12 1.70 1.53 1.11 0.67 0.35 0.12 0.11 0.11 VR(q) 1.15 1.20 1.23 1.26 1.32 1.39 1.43 1.47 1.49 PSO Z stat 3.09 2.48 2.27 2.24 2.45 2.67 2.70 2.75 2.72 Z* stat 2.44 1.99 1.85 1.84 2.04 2.24 2.27 2.33 2.31 VR(q) 1.25 1.39 1.33 1.19 1.13 1.10 1.05 1.03 1.03 SHEL Z stat 4.93 4.94 3.31 1.62 1.00 0.69 0.32 0.15 0.14 Z* stat 3.60 3.68 2.51 1.24 0.78 0.54 0.25 0.12 0.11 VR(q) 0.83 0.73 0.63 0.59 0.57 0.55 0.55 0.53 0.52 SCBPL Z stat -3.37 -3.38 -3.66 -3.51 -3.23 -3.04 -2.84 -2.73 -2.66 Z* stat -2.36 -2.54 -2.84 -2.77 -2.60 -2.48 -2.34 -2.27 -2.23 VR(q) 1.22 1.24 1.21 1.22 1.23 1.22 1.21 1.18 1.17 SNGC Z stat 4.44 3.03 2.14 1.89 1.72 1.52 1.30 1.07 0.92 Z* stat 3.63 2.57 1.86 1.68 1.55 1.38 1.19 0.99 0.86 VR(q) 1.03 0.99 0.98 0.99 1.03 1.07 1.09 1.11 1.12 SSGC Z stat 0.51 -0.07 -0.18 -0.08 0.23 0.50 0.56 0.63 0.64 Z* stat 0.42 -0.06 -0.15 -0.07 0.20 0.44 0.51 0.57 0.58 VR(q) 1.16 1.16 1.05 0.98 0.97 0.96 0.96 0.98 0.98 UBL Z stat 3.30 2.00 0.48 -0.13 -0.21 -0.31 -0.25 -0.12 -0.09 Z* stat 2.50 1.53 0.37 -0.10 -0.16 -0.24 -0.20 -0.10 -0.07

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Chapter 6

Table 6.8 ARMA Results on Daily Returns

ARMA(0,1) ARMA(1,1) ARMA(1,2) ARMA(2,1) MA(1) AR(1) MA(1) AR(1) MA(1) MA(2) AR(1) AR(2) MA(1) Coeff 0.10 0.23 -0.13 0.01 0.10 0.04 0.65 -0.03 -0.55 KSE- t-stat 3.68 1.03 -0.56 0.03 0.24 0.84 1.95 -0.56 -1.65 100 Prob 0.00 0.30 0.57 0.97 0.81 0.40 0.05 0.58 0.10 Coeff -0.30 -0.06 -0.25 -0.06 -0.12 -0.12 0.07 0.04 -0.38 KSE- t-stat -11.87 -0.70 -2.88 NA NA NA 0.24 0.43 -1.31 ALL Prob 0.00 0.48 0.00 NA NA NA 0.81 0.67 0.19 Coeff 0.52 0.59 0.15 0.03 0.94 0.88 1.31 -0.56 -0.52 KSE- t-stat 20.33 18.12 3.76 0.85 51.69 52.93 4.87 -3.19 -1.79 30 Prob 0.00 0.00 0.00 0.40 0.00 0.00 0.00 0.00 0.07 Coeff -0.66 0.00 -0.66 0.45 -1.10 0.31 -0.01 0.00 -0.65 KMI- t-stat -32.52 0.00 -21.34 1.59 -3.92 1.74 -0.16 -0.09 -13.64 30 Prob 0.00 1.00 0.00 0.11 0.00 0.08 0.88 0.93 0.00 Coeff 0.12 0.38 -0.26 0.35 -0.23 0.01 0.12 0.04 0.00 ABOT t-stat 4.63 2.61 -1.65 1.47 -0.93 0.21 0.32 0.75 0.01 Prob 0.00 0.01 0.10 0.14 0.35 0.84 0.75 0.45 0.99 Coeff 0.07 0.91 -0.90 0.91 -0.85 -0.07 0.98 -0.07 -0.92 AICL t-stat 2.80 19.19 -18.36 20.40 -16.33 -2.64 18.60 -2.59 -20.14 Prob 0.01 0.00 0.00 0.00 0.00 0.01 0.00 0.01 0.00 Coeff 0.14 0.48 -0.33 0.46 -0.32 0.01 0.34 0.02 -0.19 ABL t-stat 5.30 3.84 -2.51 2.35 -1.62 0.15 0.98 0.37 -0.57 Prob 0.00 0.00 0.01 0.02 0.11 0.88 0.33 0.71 0.57 Coeff 0.10 0.29 -0.18 0.52 -0.41 -0.05 0.96 -0.12 -0.85 AKBL t-stat 3.93 1.45 -0.90 1.67 -1.34 -1.30 9.13 -4.58 -8.25 Prob 0.00 0.15 0.37 0.10 0.18 0.19 0.00 0.00 0.00 Coeff 0.05 0.77 -0.79 0.05 -0.02 -0.02 0.76 -0.07 -0.73 APL t-stat 2.04 9.80 -10.28 NA NA NA 8.08 -2.72 -7.99 Prob 0.04 0.00 0.00 NA NA NA 0.00 0.01 0.00 Coeff 0.19 -0.12 0.30 -0.26 0.45 0.05 0.32 -0.07 -0.13 ATRL t-stat 7.12 -0.90 2.41 -0.81 1.38 0.67 1.21 -1.31 -0.50 Prob 0.00 0.37 0.02 0.42 0.17 0.50 0.23 0.19 0.62 Coeff 0.06 -0.58 0.64 -0.60 0.67 0.02 -0.32 0.01 0.40 BAFL t-stat 2.24 -4.28 5.01 -3.82 4.23 0.55 -1.42 0.19 1.73 Prob 0.03 0.00 0.00 0.00 0.00 0.58 0.16 0.85 0.08 Coeff -0.01 0.61 -0.60 0.58 -0.60 0.05 0.44 0.05 -0.45 BAHL t-stat -0.22 3.32 -3.22 3.67 -3.73 1.68 2.05 1.74 -2.12 Prob 0.83 0.00 0.00 0.00 0.00 0.09 0.04 0.08 0.03

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Chapter 6

Table 6.8 (Cont’d) ARMA Results on Daily Returns

ARMA(0,1) ARMA(1,1) ARMA(1,2) ARMA(2,1) MA(1) AR(1) MA(1) AR(1) MA(1) MA(2) AR(1) AR(2) MA(1) Coeff -0.04 0.47 -0.54 0.39 -0.44 -0.05 0.31 -0.06 -0.36 BIPL t-stat -1.43 2.27 -2.70 1.81 -2.02 -1.49 1.28 -1.89 -1.45 Prob 0.15 0.02 0.01 0.07 0.04 0.14 0.20 0.06 0.15 Coeff 0.14 -0.17 0.31 0.84 -0.71 -0.15 0.39 -0.09 -0.26 BOP t-stat 5.36 -0.97 1.81 9.32 -7.65 -5.61 1.19 -1.95 -0.78 Prob 0.00 0.33 0.07 0.00 0.00 0.00 0.23 0.05 0.43 Coeff 0.13 0.15 -0.01 0.41 -0.28 -0.04 0.29 -0.03 -0.16 DGKC t-stat 5.02 0.75 -0.07 0.77 -0.52 -0.58 0.47 -0.33 -0.25 Prob 0.00 0.45 0.95 0.44 0.60 0.56 0.64 0.74 0.80 Coeff 0.05 0.87 -0.85 0.88 -0.84 -0.03 0.90 -0.03 -0.86 DAWH t-stat 1.73 12.33 -11.18 12.28 -10.99 -0.97 10.08 -1.03 -10.06 Prob 0.08 0.00 0.00 0.00 0.00 0.33 0.00 0.30 0.00 Coeff -0.08 0.18 -0.25 0.34 -0.42 0.03 -0.10 -0.02 0.02 DCL t-stat -2.99 0.63 -0.92 0.59 -0.74 0.60 -0.23 -0.52 0.05 Prob 0.00 0.53 0.36 0.55 0.46 0.55 0.82 0.61 0.96 Coeff 0.21 0.30 -0.09 0.88 -0.68 -0.17 1.08 -0.19 -0.87 EFUG t-stat 7.84 2.63 -0.73 14.90 -10.52 -5.91 14.75 -6.38 -12.76 Prob 0.00 0.01 0.46 0.00 0.00 0.00 0.00 0.00 0.00 Coeff 0.14 0.19 -0.05 0.73 -0.60 -0.11 0.82 -0.11 -0.69 ENGRO t-stat 5.30 1.07 -0.26 5.01 -4.06 -3.42 4.68 -3.46 -3.93 Prob 0.00 0.29 0.79 0.00 0.00 0.00 0.00 0.00 0.00 Coeff 0.08 0.51 -0.46 0.52 -0.45 -0.05 0.44 -0.05 -0.37 EPCL t-stat 3.16 2.84 -2.48 2.37 -2.02 -1.63 1.46 -1.44 -1.21 Prob 0.00 0.00 0.01 0.02 0.04 0.10 0.14 0.15 0.23 Coeff -0.02 0.34 -0.39 0.23 -0.25 -0.07 -0.15 -0.10 0.12 FCCL t-stat -0.87 1.66 -1.94 1.16 -1.29 -2.43 -0.87 -3.81 0.70 Prob 0.39 0.10 0.05 0.24 0.20 0.02 0.38 0.00 0.48 Coeff 0.06 0.53 -0.49 0.54 -0.50 -0.03 0.47 -0.03 -0.42 FFBL t-stat 2.34 4.20 -3.79 4.00 -3.61 -1.00 2.36 -0.88 -2.12 Prob 0.02 0.00 0.00 0.00 0.00 0.32 0.02 0.38 0.03 Coeff 0.12 0.03 0.08 0.76 -0.66 -0.12 0.84 -0.13 -0.75 FFC t-stat 4.39 0.14 0.39 8.99 -7.63 -4.65 8.49 -4.83 -7.66 Prob 0.00 0.89 0.70 0.00 0.00 0.00 0.00 0.00 0.00 Coeff 0.16 0.48 -0.33 0.61 -0.46 -0.08 0.73 -0.10 -0.56 FABL t-stat 6.26 4.68 -2.98 4.63 -3.39 -2.18 3.47 -2.26 -2.70 Prob 0.00 0.00 0.00 0.00 0.00 0.03 0.00 0.02 0.01

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Chapter 6

Table 6.8 (Cont’d) ARMA Results on Daily Returns

ARMA(0,1) ARMA(1,1) ARMA(1,2) ARMA(2,1) MA(1) AR(1) MA(1) AR(1) MA(1) MA(2) AR(1) AR(2) MA(1) Coeff 0.08 -0.56 0.63 -0.65 0.73 0.03 0.50 -0.01 -0.42 HBL t-stat 2.96 -3.27 3.92 -2.67 2.98 0.73 1.82 -0.17 -1.54 Prob 0.00 0.00 0.00 0.01 0.00 0.47 0.07 0.87 0.12 Coeff 0.04 0.53 -0.51 0.56 -0.53 -0.02 0.46 -0.01 -0.42 HMB t-stat 1.45 2.65 -2.48 2.56 -2.40 -0.74 1.54 -0.47 -1.43 Prob 0.15 0.01 0.01 0.01 0.02 0.46 0.12 0.64 0.15 Coeff 0.10 0.58 -0.53 0.64 -0.56 -0.08 0.65 -0.09 -0.55 HUBC t-stat 3.80 4.17 -3.66 3.66 -3.18 -2.90 3.90 -3.26 -3.33 Prob 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Coeff 0.22 0.02 0.20 -0.64 0.87 0.15 -0.42 0.11 0.64 ICI t-stat 8.44 0.19 1.74 -2.38 3.21 2.41 -1.49 1.60 2.31 Prob 0.00 0.85 0.08 0.02 0.00 0.02 0.14 0.11 0.02 Coeff -0.01 0.43 -0.48 0.38 -0.40 -0.05 0.23 -0.06 -0.25 JSBL t-stat -0.37 2.45 -2.76 2.23 -2.34 -1.78 1.06 -2.31 -1.16 Prob 0.71 0.01 0.01 0.03 0.02 0.07 0.29 0.02 0.25 Coeff -0.11 0.83 -0.89 0.87 -1.00 0.09 0.76 0.07 -0.89 KASBB t-stat -3.99 20.38 0.00 22.36 -21.40 3.25 15.82 2.72 -22.03 Prob 0.00 25.88 0.00 0.00 0.00 0.00 0.00 0.01 0.00 Coeff -0.15 0.35 -0.49 0.49 -0.65 0.07 0.08 -0.04 -0.23 KEL t-stat -5.63 2.80 -4.20 2.46 -3.26 1.60 0.48 -1.18 -1.33 Prob 0.00 0.01 0.00 0.01 0.00 0.11 0.63 0.24 0.18 Coeff 0.04 0.55 -0.56 0.53 -0.51 -0.07 0.45 -0.07 -0.42 KAPCO t-stat 1.68 3.59 -3.64 3.67 -3.45 -2.48 2.34 -2.48 -2.21 Prob 0.09 0.00 0.00 0.00 0.00 0.01 0.02 0.01 0.03 Coeff 0.09 0.43 -0.36 0.52 -0.44 -0.05 0.49 -0.05 -0.41 LUCK t-stat 3.41 2.36 -1.88 2.07 -1.73 -1.40 1.55 -1.29 -1.27 Prob 0.00 0.02 0.06 0.04 0.08 0.16 0.12 0.20 0.20 Coeff 0.00 0.35 -0.37 0.31 -0.32 -0.03 0.02 -0.05 -0.02 MLCF t-stat 0.08 1.62 -1.71 1.47 -1.50 -1.07 0.07 -1.87 -0.10 Prob 0.94 0.11 0.09 0.14 0.13 0.29 0.95 0.06 0.92 Coeff 0.04 0.42 -0.37 -0.30 0.34 0.08 -0.21 0.07 0.25 MEBL t-stat 1.35 1.11 -0.95 -0.98 1.11 2.78 -0.64 2.64 0.76 Prob 0.18 0.27 0.34 0.33 0.27 0.01 0.52 0.01 0.45 Coeff 0.10 0.60 -0.49 0.47 -0.37 0.04 0.33 0.06 -0.23 NBP t-stat 3.60 5.21 -3.95 2.76 -2.14 1.18 1.43 1.47 -1.00 Prob 0.00 0.00 0.00 0.01 0.03 0.24 0.15 0.14 0.32

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Table 6.8 (Cont’d) ARMA Results on Daily Returns ARMA(0,1) ARMA(1,1) ARMA(1,2) ARMA(2,1) MA(1) AR(1) MA(1) AR(1) MA(1) MA(2) AR(1) AR(2) MA(1)

Coeff 0.15 0.67 -0.59 0.74 -0.60 -0.10 0.81 -0.09 -0.68 NRL t-stat 5.67 7.31 -5.82 6.58 -5.22 -3.08 5.42 -2.71 -4.61 Prob 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 Coeff 0.03 0.66 -0.64 0.67 -0.65 -0.01 0.63 -0.01 -0.60 NML t-stat 1.01 2.79 -2.65 2.62 -2.51 -0.37 1.96 -0.30 -1.88 Prob 0.31 0.01 0.01 0.01 0.01 0.71 0.05 0.77 0.06 Coeff 0.08 0.68 -0.62 -0.55 0.64 0.07 0.56 -0.02 -0.49 OGDC t-stat 2.90 4.34 -3.74 -1.85 2.13 2.22 2.89 -0.54 -2.51 Prob 0.00 0.00 0.00 0.06 0.03 0.03 0.00 0.59 0.01 Coeff 0.08 0.45 -0.37 0.44 -0.37 0.00 0.35 0.01 -0.27 POL t-stat 2.95 2.57 -2.03 2.01 -1.65 0.08 0.87 0.23 -0.68 Prob 0.00 0.01 0.04 0.04 0.10 0.93 0.38 0.82 0.50 Coeff 0.11 0.28 -0.18 0.84 -0.73 -0.08 -0.38 0.03 0.48 PSO t-stat 4.13 1.44 -0.91 8.95 -7.54 -2.80 -1.48 0.87 1.90 Prob 0.00 0.15 0.36 0.00 0.00 0.01 0.14 0.38 0.06 Coeff -0.75 0.01 -0.76 0.55 -1.29 0.40 0.03 0.02 -0.77 PTCL t-stat -42.40 0.41 -32.46 3.16 -7.30 2.93 0.63 0.53 -25.55 Prob 0.00 0.68 0.00 0.00 0.00 0.00 0.53 0.60 0.00 Coeff -0.09 0.48 -0.57 0.51 -0.61 0.03 0.35 0.01 -0.46 SCBPL t-stat -3.29 4.19 -5.31 3.72 -4.45 0.99 2.11 0.39 -2.77 Prob 0.00 0.00 0.00 0.00 0.00 0.32 0.03 0.70 0.01 Coeff 0.15 0.85 -0.81 0.86 -0.74 -0.11 0.97 -0.11 -0.85 SHEL t-stat 5.57 19.83 -16.47 19.26 -14.25 -4.04 16.32 -3.81 -16.03 Prob 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Coeff 0.13 0.44 -0.32 0.86 -0.73 -0.11 1.02 -0.12 -0.89 SNGC t-stat 4.97 3.05 -2.12 11.40 -9.22 -3.91 13.38 -4.36 -12.52 Prob 0.00 0.00 0.03 0.00 0.00 0.00 0.00 0.00 0.00 Coeff 0.04 0.57 -0.56 0.58 -0.55 -0.02 0.45 -0.02 -0.42 SSGC t-stat 1.41 4.00 -3.85 3.98 -3.77 -0.83 1.96 -0.76 -1.85 Prob 0.16 0.00 0.00 0.00 0.00 0.41 0.05 0.45 0.06 Coeff 0.09 -0.25 0.33 -0.37 0.46 0.03 0.64 -0.04 -0.56 UBL t-stat 3.31 -1.08 1.49 -0.96 1.19 0.61 3.20 -1.33 -2.77 Prob 0.00 0.28 0.14 0.34 0.23 0.54 0.00 0.18 0.01

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Chapter 7 Volatility-Clustering and Random Walk

7.1 Nature of Volatility-Clustering

The variance of error terms may not be constant over time (presence of conditional heteroscedasticity). Furthermore, current volatility may be the function of past volatility thus gives rise to volatility-clustering which refers to momentum in conditional variance (high volatility followed high volatility and small followed by small volatility either positive or negative). Explaining this time-varying behaviour of variance is important to elucidate the degree of time correlated dependence of returns especially in case of long-termed options and futures contracts (Poterba & Summers, 1986). Black (1976) found negative correlation between stock returns and volatility that is, volatility increases with bad-news and decreases with good-news. More persistence shocks will likely to have considerable effect on investment in long-lived assets (Poterba & Summers, 1986). It was imperative therefore, to develop models to determine that behaviour. Studies found evidence of long-term memory of autocorrelation on returns and suggested models to deal with that problem include, Bollerslev (1986) Nelson (1991) Bollerslev et al. (1992) Ding et al. (1993) Hamilton & Susmel (1994) Baillie & Bollerslev (1994) Baillie et al. (1996).

7.2 ARCH and GARCH Models

This particular study is using the model introduced by Engle (1982) Bollerslev (1987). They suggested the estimated variances of return to change the squared lagged values of the error terms; Autoregressive Conditional Heteroscedastic (ARCH) model as in equation 8.1.

Where δ > 0 and δ ≥ 0 for i > 0 0 1

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The above (ARCH) equation is also used extensively in the literature by several other researchers including Connolly (1989), Baillie & Bollerslev (1990; 1991), Kiymaz and Berument (2003), and Yalcin & Yucel (2006).

Bollerslev (1986) expanded the ARCH model of Engle (1982) by introducing Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model which allows lagged conditional variance to be included in the function to cater to the serial correlation in volatility due to volatility spillover effects over time and leptokurtic error distribution (Connolly, 1989).

2 Vt is the variance of the error term ε at time t . Conditional variance depends not only on the squared error term in the previous time period as in ARCH (1), but also on its conditional variance in the previous time period. GARCH (p,q) model is given by following equation:

Apolinario et al. (2006) Hsieh (1990) Gregoriou et al. (2004) Rodriguez (2012) preferred the model in major studies of the kind. Since their work GARCH has become the most widely used model to estimate volatility clustering, explains positive autocorrelation, also referred to as “GARCH effect”. Wilhelmsson (2006) tested the GARCH forecasting performance by using different error distribution and concluded that the GARCH model in conjunction with student’s t distribution is the best performing model in leptokurtic financial data. Baker et al. (2008) concluded that investigation of conditional volatility is sensitive to the specification of underlying distribution. They further concluded that student’s t distribution is a better way to determine conditional volatility through GARCH approach. Prior to this Bollerslev (1987) and Nelson (1991) pointed out the inability of GARCH model with normal distribution with high kurtosis in financial returns. Similarly, Hamilton and Susmel (1994) preferred GARCH model in conjunction with t distribution in financial data with greater value of kurtosis. Therefore following their work GARCH (1,1) model with student’s t distribution is used here.

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V 2 = δ + δ µ 2 + γ V2 t 0 1 t-1 1 t-1 (8.3) Where,

Rate of decay of autocorrelation is explained by ; less than one value of implies existence of stationary solution. closer to 1, implies slower decay, and =1 corresponds to an integrated process. Estimation of volatility clustering by GARCH(1,1) usually results in very close to 1 values of (Cont, 2007).

7.3 Empirical Results

7.3.1 ARCH effect. Here ARCH Lagrange Multiplier (LM) test is conducted using five lags based on Akaike info criterion of the squared series (table 7.1) with null hypothesis that there is no heteroscedasticity (there are no ARCH disturbances) in the model.

Presence of heteroscedasticity can be seen in most of the firms when tested by ARCH LM test. However, for only few firms (13 out 43 selected) the null hypothesis cannot be rejected at 5% or above (table 7.1). Similarly the test is rejected for all four indices. Hence, the results can be applied on to the whole market and concluded that this test rejects the null hypothesis of no heteroscedasticity for the market as a whole. For this reason it is recommended to examine time related changing variance by investigating GARCH effects.

7.3.2 GARCH effect. Table 7.2, shows GARCH (1,1) results with student’s t distribution. The sum of the coefficients of conditional variance and square of error term 1, with value closer to 1, implies high volatility clustering with slow mean reversion (slow decay). 1, with values considerably less than unity implies fast decay. And 1, implies non-

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stationary returns series. GARCH models of all indices except for KSE-30 are stationary and mean reverting with a comparatively fast decay in KMI-30 index with . In KSE-100, the value of coefficient = 0.09, and = 0.89, show that the index is somewhat jumpy and unstable and volatility effects die down slowly. In KSE-all share and KSE-30 the value of coefficients are greater than 0.1 depicting less spiky peaks in the market and comparatively lower values of shows less persistent shocks. In KMI-30 index the value of coefficients, and reveal that the index is least volatile; shocks are temporary and will die out very quickly.

Most of the selected firms are found non-stationary with the condition fulfilling , except for BAHL, FFBL, NBP, NRL and SHEL, where the series is found to be non- stationary.

The value , showing volatility and jumpiness in the market. In case of HBL, the value however, is equal to 0.029, revealing a stable return series. Similarly, for BIPL, DGKC and POL the values of are 0.061, 0.060 and 0.038, respectively showing comparatively stable returns. The GARCH or persistence parameter usually ranges between 0.85 and 0.98, with lower values linked with more jumpiness of the series. Mostly firms have less persistent shock with fast decay especially, in HMB, KASSB, NML and PTCL, where the GARCH values are less than 0.06. Whereas, highly persistent shocks can be observed in BIPL, DGKC, FCCL, HBL, LUCK, and POL. Highest volatility clustering can be predicted in BIPL, DGKC, and in POL return series.

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Table 7.1 ARCH Analysis on Daily Returns

ARCH Prob. Coeff 0.000 0.114 0.157 0.086 0.043 0.160 KSE- Std. 0.000 0.027 0.027 0.027 0.027 0.027 167.91 0.0000 100 t-stat 6.374 4.280 5.881 3.212 1.609 6.048 Prob. 0.000 0.000 0.000 0.001 0.108 0.000 Coeff 0.071 0.111 0.098 0.418 -0.107 -0.119 Std. 0.070 0.027 0.027 0.027 0.029 8.200 KSE-30 250.63 0.0000 t-stat 1.002 4.135 3.623 15.410 -3.653 -0.014 Prob. 0.316 0.000 0.000 0.000 0.000 0.989 Coeff 0.000 0.586 -0.247 0.094 -0.027 0.006 KSE- Std. 0.000 0.027 0.031 0.032 0.031 0.027 364.74 0.0000 All t-stat 1.824 21.869 -7.939 2.969 -0.874 0.228 Prob. 0.068 0.000 0.000 0.003 0.382 0.820 Coeff 0.001 0.303 0.118 -0.100 0.004 0.016 KMI- Std. 0.001 0.027 0.028 0.028 0.028 0.027 166.61 0.0000 30 t-stat 1.438 11.287 4.201 -3.577 0.138 0.579 Prob. 0.151 0.000 0.000 0.000 0.891 0.563 Coeff 0.000 0.180 0.045 0.063 0.073 0.098 Std. 0.000 0.027 0.027 0.027 0.027 0.027 ABOT 105.75 0.0000 t-stat 8.262 6.676 1.634 2.329 2.693 3.655 Prob. 0.000 0.000 0.103 0.020 0.007 0.000 Coeff 0.001 0.014 -0.001 0.001 -0.002 -0.001 Std. 0.001 0.027 0.027 0.027 0.027 0.027 AICL 0.26 0.9983 t-stat 1.825 0.505 -0.037 0.022 -0.059 -0.054 Prob. 0.068 0.614 0.971 0.982 0.953 0.957 Coeff 0.000 0.070 0.106 0.053 0.039 0.074 Std. 0.000 0.027 0.027 0.027 0.027 0.027 ABL 48.33 0.0000 t-stat 6.825 2.608 3.937 1.952 1.441 2.770 Prob. 0.000 0.009 0.000 0.051 0.150 0.006

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Table 7.1 (Cont’d) ARCH Analysis on Daily Returns

ARCH Prob. Coeff 0.001 0.074 0.042 0.038 0.017 0.031 Std. 0.000 0.027 0.027 0.027 0.027 0.027 AKBL 16.53 0.0055 t-stat 7.803 2.762 1.552 1.428 0.646 1.174 Prob. 0.000 0.006 0.121 0.154 0.518 0.241 Coeff 0.000 0.006 0.005 0.002 0.002 0.001 Std. 0.000 0.027 0.027 0.027 0.027 0.027 APL 0.11 0.9998 t-stat 4.506 0.240 0.171 0.074 0.092 0.047 Prob. 0.000 0.810 0.864 0.941 0.927 0.963 Coeff 0.000 0.124 0.106 0.081 0.048 0.080 Std. 0.000 0.027 0.027 0.027 0.027 0.026 ATRL 91.91 0.0000 t-stat 8.752 4.653 3.932 3.010 1.802 3.035 Prob. 0.000 0.000 0.000 0.003 0.072 0.002 Coeff 0.000 0.009 -0.001 -0.005 -0.001 -0.003 Std. 0.000 0.027 0.027 0.027 0.027 0.027 BAHL 0.16 0.9995 t-stat 4.237 0.329 -0.048 -0.180 -0.032 -0.102 Prob. 0.000 0.742 0.962 0.857 0.975 0.919 Coeff 0.000 0.077 0.165 0.145 0.104 0.078 Std. 0.000 0.027 0.027 0.027 0.027 0.026 BAFL 175.39 0.0000 t-stat 6.090 2.873 6.188 5.441 3.894 2.952 Prob. 0.000 0.004 0.000 0.000 0.000 0.003 Coeff 0.001 0.076 0.046 0.088 0.057 0.162 Std. 0.000 0.026 0.026 0.026 0.026 0.026 BIPL 84.18 0.0000 t-stat 7.146 2.862 1.738 3.359 2.170 6.184 Prob. 0.000 0.004 0.083 0.001 0.030 0.000 Coeff 0.001 0.187 0.086 0.097 0.003 0.090 Std. 0.000 0.027 0.027 0.027 0.027 0.027 BOP 121.79 0.0000 t-stat 7.575 7.012 3.169 3.586 0.127 3.384 Prob. 0.000 0.000 0.002 0.000 0.899 0.001 Coeff 0.000 0.112 0.154 0.052 0.174 0.113 Std. 0.000 0.027 0.026 0.027 0.026 0.027 DGKC 206.99 0.0000 t-stat 7.083 4.189 5.849 1.956 6.597 4.245 Prob. 0.000 0.000 0.000 0.051 0.000 0.000

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Table 7.1 (Cont’d) ARCH Analysis on Daily Returns

ARCH Prob. Coeff 0.002 0.005 -0.001 -0.001 -0.001 -0.001 Std. 0.001 0.027 0.027 0.027 0.027 0.027 DAWH 0.04 1.0000 t-stat 1.448 0.183 -0.021 -0.046 -0.035 -0.047 Prob. 0.148 0.854 0.984 0.963 0.972 0.962 Coeff 0.002 0.078 0.012 0.036 0.012 0.073 Std. 0.000 0.027 0.027 0.027 0.027 0.027 DCL 19.73 0.0014 t-stat 5.988 2.916 0.435 1.349 0.452 2.726 Prob. 0.000 0.004 0.664 0.178 0.652 0.007 Coeff 0.001 0.050 0.026 0.030 0.023 0.027 Std. 0.000 0.027 0.027 0.027 0.027 0.027 EFUG 8.34 0.1386 t-stat 7.747 1.846 0.956 1.106 0.855 0.993 Prob. 0.000 0.065 0.339 0.269 0.393 0.321 Coeff 0.001 0.033 0.037 0.036 0.003 0.023 Std. 0.000 0.027 0.027 0.027 0.027 0.027 ENGRO 6.61 0.2509 t-stat 7.555 1.217 1.373 1.344 0.125 0.870 Prob. 0.000 0.224 0.170 0.179 0.900 0.384 Coeff 0.000 0.132 0.081 0.075 0.100 0.000 Std. 0.000 0.027 0.027 0.027 0.027 0.027 EPCL 77.28 0.0000 t-stat 8.701 4.920 2.994 2.792 3.713 -0.016 Prob. 0.000 0.000 0.003 0.005 0.000 0.987 Coeff 0.001 0.074 0.124 0.032 0.029 0.024 Std. 0.000 0.027 0.027 0.027 0.027 0.026 FCCL 40.65 0.0000 t-stat 8.645 2.764 4.625 1.197 1.098 0.926 Prob. 0.000 0.006 0.000 0.232 0.272 0.354 Coeff 0.000 0.241 0.038 0.059 0.028 0.064 Std. 0.000 0.027 0.027 0.027 0.027 0.026 FFBL 123.25 0.0000 t-stat 7.186 9.048 1.400 2.158 1.039 2.425 Prob. 0.000 0.000 0.162 0.031 0.299 0.015 Coeff 0.000 0.004 0.001 0.003 0.008 0.007 Std. 0.000 0.027 0.027 0.027 0.027 0.027 FFC 0.20 0.9992 t-stat 3.069 0.146 0.045 0.116 0.311 0.244 Prob. 0.002 0.884 0.964 0.908 0.756 0.807

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Table 7.1 (Cont’d) ARCH Analysis on Daily Returns

ARCH Prob Coeff 0.000 0.132 0.082 0.050 0.054 0.078 Std. 0.000 0.027 0.027 0.027 0.027 0.027 FABL 72.16 0.0000 t-stat 8.077 4.924 3.064 1.857 1.997 2.912 Prob. 0.000 0.000 0.002 0.064 0.046 0.004 Coeff 0.000 0.077 0.016 0.031 0.023 0.008 Std. 0.000 0.027 0.027 0.027 0.027 0.027 HBL 12.01 0.0347 t-stat 6.405 2.883 0.612 1.150 0.862 0.309 Prob. 0.000 0.004 0.540 0.251 0.389 0.757 Coeff 0.000 0.022 0.005 0.012 0.013 0.011 Std. 0.000 0.027 0.027 0.027 0.027 0.027 HMB 1.38 0.9267 t-stat 7.783 0.824 0.200 0.443 0.492 0.391 Prob. 0.000 0.410 0.841 0.658 0.623 0.696 Coeff 0.000 0.105 0.088 0.025 0.058 0.087 Std. 0.000 0.027 0.027 0.027 0.027 0.026 HUBC 58.03 0.0000 t-stat 7.618 3.946 3.278 0.913 2.180 3.306 Prob. 0.000 0.000 0.001 0.362 0.029 0.001 Coeff 0.000 0.101 0.107 0.055 0.033 0.118 Std. 0.000 0.027 0.027 0.027 0.027 0.027 ICI 77.79 0.0000 t-stat 8.932 3.775 3.983 2.032 1.249 4.441 Prob. 0.000 0.000 0.000 0.042 0.212 0.000 Coeff 0.001 0.352 -0.076 0.055 -0.031 0.115 Std. 0.000 0.027 0.028 0.028 0.028 0.026 JSBL 178.35 0.0000 t-stat 6.654 13.219 -2.689 1.965 -1.098 4.334 Prob. 0.000 0.000 0.007 0.050 0.272 0.000 Coeff 0.001 0.195 0.046 0.064 0.068 0.025 Std. 0.000 0.027 0.027 0.027 0.027 0.027 KASB 91.46 0.0000 t-stat 7.683 7.243 1.667 2.344 2.482 0.943 Prob. 0.000 0.000 0.096 0.019 0.013 0.346 Coeff 0.001 0.096 -0.007 0.100 0.097 0.062 S.E. 0.000 0.027 0.027 0.027 0.027 0.027 KEL 55.84 0.0000 t-stat 5.470 3.567 -0.261 3.740 3.608 2.334 Prob. 0.000 0.000 0.794 0.000 0.000 0.020

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Table 7.1 (Cont’d) ARCH Analysis on Daily Returns

ARCH Prob Coeff 0.000 0.074 0.033 0.070 0.054 0.053 Std. 0.000 0.027 0.027 0.027 0.027 0.027 KAPCO 31.44 0.0000 t-stat 7.321 2.782 1.230 2.631 2.020 1.984 Prob. 0.000 0.006 0.219 0.009 0.044 0.048 Coeff 0.000 0.150 0.116 0.121 0.105 0.127 Std. 0.000 0.027 0.027 0.027 0.027 0.027 LUCK 222.58 0.0000 t-stat 6.694 5.641 4.361 4.537 3.940 4.785 Prob. 0.000 0.000 0.000 0.000 0.000 0.000 Coeff 0.001 0.079 0.045 0.091 0.113 0.193 Std. 0.000 0.026 0.026 0.026 0.026 0.026 MLCF 137.26 0.0000 t-stat 5.637 3.018 1.737 3.520 4.366 7.474 Prob. 0.000 0.003 0.083 0.000 0.000 0.000 Coeff 0.000 0.193 0.142 0.154 0.043 0.010 Std. 0.000 0.027 0.027 0.027 0.027 0.027 MEBL 194.56 0.0000 t-stat 6.684 7.180 5.202 5.649 1.570 0.362 Prob. 0.000 0.000 0.000 0.000 0.117 0.717 Coeff 0.001 0.020 0.011 0.006 0.005 0.013 Std. 0.000 0.027 0.027 0.027 0.027 0.027 NBP 1.10 0.9544 t-stat 5.491 0.733 0.414 0.228 0.200 0.502 Prob. 0.000 0.464 0.679 0.820 0.842 0.616 Coeff 0.000 0.208 0.034 0.108 0.026 0.115 Std. 0.000 0.027 0.027 0.027 0.027 0.027 NRL 137.62 0.0000 t-stat 8.024 7.820 1.243 4.010 0.952 4.341 Prob. 0.000 0.000 0.214 0.000 0.341 0.000 Coeff 0.002 -0.001 -0.001 -0.001 -0.001 0.000 Std. 0.001 0.027 0.027 0.027 0.027 0.027 NML 0.01 1.0000 t-stat 1.490 -0.020 -0.047 -0.024 -0.046 -0.013 Prob. 0.136 0.984 0.963 0.981 0.963 0.990 Coeff 0.000 0.129 0.034 0.154 0.124 0.115 Std. 0.000 0.027 0.027 0.026 0.027 0.026 OGDC 162.99 0.0000 t-stat 6.598 4.837 1.259 5.843 4.664 4.342 Prob. 0.000 0.000 0.208 0.000 0.000 0.000

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Table 7.1 (Cont’d) ARCH Analysis on Daily Returns

ARCH Prob Coeff 0.006 0.316 0.149 -0.126 0.001 0.026 Std. 0.006 0.027 0.028 0.028 0.028 0.027 PTCL 194.75 0.0000 t-stat 1.063 11.788 5.307 -4.455 0.036 0.978 Prob. 0.288 0.000 0.000 0.000 0.971 0.328 Coeff 0.000 0.179 0.095 0.118 0.126 0.117 Std. 0.000 0.027 0.027 0.027 0.027 0.027 POL 238.63 0.0000 t-stat 5.658 6.735 3.522 4.397 4.696 4.428 Prob. 0.000 0.000 0.000 0.000 0.000 0.000 Coeff 0.000 0.048 0.039 0.035 0.030 0.032 Std. 0.000 0.027 0.027 0.027 0.027 0.027 PSO 11.75 0.0384 t-stat 7.755 1.800 1.470 1.312 1.133 1.199 Prob. 0.000 0.072 0.142 0.190 0.258 0.231 Coeff 0.000 0.041 0.063 0.007 0.015 0.023 Std. 0.000 0.027 0.027 0.027 0.027 0.027 SHEL 9.79 0.0814 t-stat 6.857 1.516 2.340 0.250 0.572 0.858 Prob. 0.000 0.130 0.019 0.803 0.567 0.391 Coeff 0.000 0.234 0.046 -0.009 0.043 0.066 Std. 0.000 0.027 0.028 0.028 0.027 0.026 SCBP 103.29 0.0000 t-stat 8.459 8.694 1.680 -0.330 1.572 2.503 Prob. 0.000 0.000 0.093 0.741 0.116 0.012 Coeff 0.000 0.016 0.081 0.007 0.008 0.014 Std. 0.000 0.027 0.027 0.027 0.027 0.027 SNGC 10.27 0.0681 t-stat 8.894 0.611 3.013 0.249 0.296 0.511 Prob. 0.000 0.542 0.003 0.803 0.767 0.609 Coeff 0.000 0.041 0.027 0.027 0.004 0.043 Std. 0.000 0.027 0.027 0.027 0.027 0.027 SSGC 7.72 0.1722 t-stat 8.081 1.540 0.999 1.019 0.162 1.602 Prob. 0.000 0.124 0.318 0.308 0.871 0.109 Coeff 0.000 0.119 0.059 0.094 0.076 0.120 Std. 0.000 0.027 0.027 0.027 0.027 0.027 UBL 100.76 0.0000 t-stat 7.367 4.472 2.193 3.527 2.852 4.504 Prob. 0.000 0.000 0.029 0.000 0.004 0.000

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Table 7.2 GARCH Analysis on Return Series

ARCH + Constant ARCH GARCH GARCH z-stat z-stat z-stat

KSE100 0.000 2.423 0.093 5.014 0.896 48.240 0.9896 KSEALL 0.000 4.593 0.209 5.903 0.735 23.612 0.9440 KSE30 0.000 3.818 0.250 5.880 0.767 28.033 1.0170 KMI30 0.000 6.767 0.490 4.680 0.329 6.632 0.8187 ABOT 0.000 3.540 0.273 4.876 0.726 19.962 0.9992 AICL 0.000 4.949 0.286 5.440 0.627 13.676 0.9135 ABL 0.000 3.157 0.140 4.753 0.827 25.632 0.9671 AKBL 0.000 3.349 0.282 3.606 0.705 15.082 0.9896 APL 0.000 4.052 0.220 5.194 0.774 26.873 0.9941 ATRL 0.000 3.070 0.172 5.554 0.824 33.725 0.9958 BAFL 0.000 2.567 0.071 4.554 0.911 51.741 0.9823 BAHL 0.000 3.295 0.145 3.678 0.865 43.145 1.0108 BIPL 0.000 6.530 0.061 8.211 0.912 99.645 0.9728 BOP 0.000 3.527 0.227 4.407 0.768 22.565 0.9955 DGKC 0.000 2.164 0.061 4.308 0.926 60.025 0.9865 DAWH 0.000 5.032 0.290 6.060 0.644 16.494 0.9345 DCL 0.000 3.198 0.101 3.813 0.864 31.732 0.9654 EFUG 0.000 4.038 0.279 5.699 0.672 14.486 0.9505 ENGRO 0.000 3.740 0.209 4.812 0.724 15.708 0.9325 EPCL 0.000 2.868 0.145 4.560 0.835 28.551 0.9791 FCCL 0.000 2.737 0.074 3.889 0.902 42.780 0.9758 FFBL 0.000 2.315 0.116 4.724 0.893 52.825 1.0089 FFC 0.000 3.728 0.275 4.537 0.780 30.062 1.0554 FABL 0.000 3.407 0.229 4.024 0.751 18.057 0.9801 HBL 0.000 1.290 0.029 4.521 0.966 159.843 0.9953 HMB 0.000 4.511 0.372 4.558 0.532 8.411 0.9040 HUBC 0.000 3.470 0.145 4.457 0.798 21.174 0.9432 ICI 0.000 2.940 0.151 4.760 0.824 26.916 0.9750

Table 7.2 (Cont’d)

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GARCH Analysis on Return Series

ARCH + Constant ARCH GARCH GARCH z-stat z-stat z-stat

JSBL 0.000 2.929 0.088 3.963 0.886 38.263 0.9743 KASBB 0.000 4.677 0.333 4.808 0.501 6.732 0.8344 KEL 0.000 3.312 0.121 3.523 0.825 24.574 0.9456 KAPCO 0.000 3.329 0.231 3.579 0.763 19.569 0.9941 LUCK 0.000 2.151 0.084 4.597 0.904 0.904 0.9872 MLCF 0.000 3.139 0.131 5.028 0.848 36.239 0.9785 MEBL 0.000 3.981 0.253 5.024 0.673 13.743 0.9262 NBP 0.000 4.424 0.383 5.249 0.627 14.202 1.0102 NRL 0.000 1.839 0.131 4.667 0.883 47.549 1.0138 NML 0.000 5.274 0.273 5.323 0.584 11.466 0.8572 OGDC 0.000 2.788 0.107 4.621 0.872 35.633 0.9790 POL 0.000 1.821 0.039 4.031 0.954 96.391 0.9924 PSO 0.000 3.573 0.230 5.108 0.766 23.492 0.9968 PTCL 0.000 5.821 0.384 5.378 0.533 12.258 0.9178 SCBPL 0.000 3.013 0.140 4.704 0.832 28.771 0.9719 SHEL 0.000 3.766 0.407 4.592 0.678 18.577 1.0855 SNGC 0.000 3.712 0.183 4.513 0.734 15.740 0.9163 SSGC 0.000 3.955 0.283 4.468 0.629 10.549 0.9120 UBL 0.000 2.904 0.133 4.930 0.847 31.197 0.9802

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Chapter 8 Seasonal Anomalies This particular chapter is taking the path to conclude about the efficiency with the investigation of seasonal anomalies of day-of-the-week (DOW), month-of-the-year (MOY) and turn-of-the-month (TOM) effects, in Karachi stock exchange.

8.1 Day-of-the-week effect

Daily activity of shares in a market could be high or low during specific days. Similarly returns may be higher or lower in different days of the week. Sometimes, a specific trend can be followed in the market due to this anomalous behaviour. There is no precise explanation for this strange tendency in the market except for that it accounts for inefficiency in such markets. Investors may be willing to buy stocks on one specific day and sell on another based upon certain trends in the market on these specific days in order to take benefit from these effects.

DOW effects were first documented by Fields (1931) when he discovered that increasing return pattern from Friday to Saturday instead of leading to further increase on Monday suddenly turned into negative returns on Mondays. This pattern was further studied by French (1980) by using Fama (1965) model and Clark (1973) model. He concluded the same unexplained phenomenon of negative Monday returns. Various studies have been conducted to explain this phenomenon, but no single study has been able to explain fully. French (1980) linked the anomaly to closing of markets at weekends. Gibbon & Hess (1981) related this phenomenon to settlement period. Furthermore, researches also revealed higher returns on different days in different markets. Basher & Sadorsky (2006) determined highest return on Friday. French (1980) found positive returns on Wednesday. The phenomenon may be observed in developed as well as less developed stock market with more or less equal affinity.

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Some psychological factors could be working behind that trend. For example, investor may feel less optimistic on the first day of the week and gain confidence as week goes by. At the end of the week hopefulness may allow the investor to buy and look forward to the weekend more optimistically. The firms also try not to reveal bad news on Friday in the anticipation of subsiding effect prevailing during the holidays. Alternatively, during the weekend the flare could turn into flame and could build pessimism on the first day of the week.

Typical Monday high and low Friday can be found in many developed and emergent markets. (Cross, 1973; Gibbons & Hess, 1981; Lakonishok & Levi, 1982; Keim & Stambaugh, 1984; Rogalski, 1984; Smirlock & Starks, 1986; Harris, 1986; Lakonishok & Smidt, 1988; Flannery & Protopapadakis, 1988; Aggarwal & Tandom, 1994; Kohers & Kohers, 1995; Kiymaz & Berument, 2003).

Abnormally high returns were observed in different days in different studies. For example French (1980) Gibbon & Hess (1981) Rogalski (1984) Smirlock & Starks (1986) Lakonishok and Smidt (1988) Flannery and Protopapadakis (1988), and Kohers & Kohers (1995) Basher and Sadorsky (2006) determined highest return on Friday. French (1980) also found positive returns on Wednesday.

Similar results were found in other developed countries capital market. Jaffe & Westerfield (1985) determined Tuesday effect in Japanese and Australian capital markets. Solnik & Bousquet (1990) also demonstrated a strong and persistent negative return on Tuesday in case of Paris Bourse. Barone (1990) identified the largest decline in Italian stock prices mostly on Tuesday. Balaban (1995) indentified negative Tuesday for emerging stock markets of Turkey. Mills and Coutts (1995) and Arsad & Coutts (1997) also found calendar anomalies in London Stock Exchange; Mills et al. (2000) for Athens stock market; Rodriguez (2012) for Argentina, Brazil, Chile, Colombia, Mexico, and Peru stock markets; Enowbi et al. (2010) for Egypt, Nigeria and South African stock markets; Georgantopoulos et al. (2011) for Greece and Turkey stock markets.

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Several studies were performed on emerging markets in Asia. Wong & Ho (1986) conducted a study on the Singapore stock market; Wong et al. (1992) on the stock markets of Malaysia, Hong Kong, Singapore, Thailand and Taiwan; Lauterbach & Ungar (1991) on Israeli Stock Market; Choudhry (2000) on Asian stock markets like India, Indonesia, Malaysia, Philippines, South Korea, Taiwan and Thailand; Poshakewale (1996) on Indian Market; Gao & Kling (2005) on Chinese Stock Market; Anwar & Mulyadi (2012) on Jakarta, Singapore and Kuala Lumpur stock exchanges; Chia et al. (2008) for Hong Kong, Singapore and Taiwan; Almonte (2012) on Philippines stock market. They all demonstrated negative mean returns on Monday and high positive mean returns on Friday.

However, conflicting results are reported in case of emergent markets. Aybar (1992) could not observe any weekday effect in stock markets of Saudi Arabia, Kuwait and Turkey. Similarly, Mbululu & Chipeta (2012) did not find DOW effect in South African stock market. Dubois and Louvet (1996) and Brooks & Persand (2001) identified the Tuesday effect in Pacific Rim countries. Basher & Sadorsky (2006) observed Monday effect in Philippines stock market and Friday effect in Taiwan stock market. Rahman (2009) investigated positive returns on Thursday and negative returns on Sunday and Monday. Liew & Chia (2010) reported positive Monday and negative Friday for Bombay stock market. Patel et al. (2012) found high returns on Monday in Asian markets including Indian, Japanese, Chinese and Hong Kong markets.

Various studies have been conducted on week-day effect in context of Pakistan. Khilji (1994) found monthly returns are time dependent. Hussain (1999) indicated no significant differences in stock returns across days. Ali & Mustafa (2001) determined Monday is the best day in which high returns are obtained, but Friday reflected losses. Their study is based on the arrival of the new public information. The study supports the Monday effect because the time between closing day of the week and opening day of the next week has three days of accumulated information which impacts the trading on Monday. Nishat &Mustafa (2002) investigated the day of the week effect in Pakistani stock market. Their analysis found no pattern in mean return on week days, however, a pattern is found in trading volume. Basher & Sadorsky (2006) established Tuesday effect in Pakistani stock market. Husain et al. (2011) used OLS

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regression and concluded that stock market returns for Tuesday are higher and more volatile than other days of the week. Bashir et al. (2011) refuted efficient market hypothesis in banking sector of Pakistan

For investigation of day-of-the-week effect stock returns first descriptive statistics will be examined to see which day has highest or lowest mean returns and the way standard deviation is related to mean returns. Returns are further regressed on Monday, Tuesday, Wednesday, Thursday, and Friday. The dummy variable approach in regression is being used here where each individual dummy variable accounts for the excess return for the particular day.

+ + (8.1)

Where, to represents dummy variables at time t such that; if t is a Monday, then =1

and =0 for all other days; if t is a Tuesday = 1 and = 0 for all other days, and so forth. The OLS technique is applied however, it has two shortcomings. Firstly, the error terms might be autocorrelated, which may lead to misleading results. Therefore, we also used lagged values of the return as one of the deterministic variables (Autoregressive model) Kiymaz & Berument (2003).

+ + (8.2)

Where Rt−1 is the lag value of the returns and i is the lag order up to n , α i is the coefficient of the estimator. Equation (3) is adjusted to lag 1, based on the minimum Akaike-Information Criterion (AIC).

8.2 Month-of-the-year effect

Month-of-the-year effect means that returns are higher in a certain month of the year. January returns found higher as compared to remaining months in U.S. market. Various other share markets (Rozeff & Kinney, 1976; Keim, 1983; Lakonishok & Smidt, 1984; Jaffe &

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Westerfield, 1985a; 1985b). Whereas Keim (1983) and Aggarwal et al. (1990) found higher January returns in small firms then the large firms thus establishing this phenomenon to small firms.

The justification behind small firm effect could lie in the fact that growth capacity in firms with less capital is far greater than in large capital firms. And the outperformance in such firms is fairly reflected in their stock prices. Higher returns in January may be ascribed to more buying following a sell-off occurred during the month of December to compensate the tax losses. Although January effect is found to be diminishing in recent years, due to well- developed tax protection alternatives becoming available with time.

For investigation of MOY effect of stock returns first descriptive statistics will be examined to see which day has highest or lowest mean returns and the way standard deviation is related to mean returns. Returns are further regressed on all months from January till December. The dummy variable approach in regression is being used here where each individual dummy variable accounts for the excess return for the particular day. + +

(8.3)

(8.4)

Where,

Stock return on an index (firm) for any day Dummy variable corresponding to 12 months : Random disturbance term.

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8.3 Turn-of-the-month effect

Turn-of-the-month effect says that stock prices temporarily increase during the last few days and the first few days on account of receiving cash flows due to releasing of pension funds, interest payments and mainly due to salaries, especially in economies where only salaries are distributed only at the end of the month; usually between the last two of the preceding and first three days of the new month. Cash flows thus received are assumed to be reinvested in the stock market, tend to increase buying and hence prices during that fraction of time. Therefore, the chances of capturing capital gains arise during this period. Ariel (1987) examined Dow Jones and provided the evidence that days around the turn-of-the month exhibit high rates of return. In this particular study TOM period constitute one last trading day of the previous month plus 3 first trading days. The rest-of-the-month (ROM) period is defined as the remaining days. (Lakonishok & Smidt, 1988).Lakonishok and Smidt (1988)

For examining of TOM effect stock returns first descriptive statistics will be examined to observe the TOM and ROM period mean returns and the way standard deviation is related to mean returns. Furthermore, returns are regressed on TOM and ROM period (Lakonishok & Smidt, 1988; Cadsby & Ratner, 1992). The dummy variable approach in regression is being used here where each individual dummy variable accounts for the excess return for the particular period.

(8.5) Where,

Stock return on an index (firm) for any day Dummy variable corresponding to TOM days Dummy variable corresponding to ROM days : Random disturbance term. .

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8.4 Results and Analysis

8.4.1 Day-of-the- week effect Descriptive statistics of returns on all days of the week is presented in table 8.1. Result illustrates the values of mean and standard deviation day wise. It is found that mean returns on Monday are negative throughout except for KSE-30 index, ABOTT, DAWH, FFC, ICI, JSBL.

The result of OLS determining DOW effects (table 8.2) indicates diversified behaviour of individual firms and indices. Different firms and indices indicate different DOW results. Significant Monday negative and Friday positive effect are found in KSE-100. In KSE-all shares Wednesday and Friday returns are significant at 5% and 1%, respectively. However, no DOW effects are found in KSE-30 index. The results are consistent with two other studies (Shamshir & Mustafa, 2014; Hafeez et al., 2014). About half of the firms selected are found to possess DOW effects. Out of which large number of the firms exhibit Monday negative and Friday positive effect at 5% or lower level except for ABOTT, DAWH, FFC, KAPCO and MLCF. In case of BAHL and PTCL positive Monday and negative Friday are significant. In a nut shell, conventional Monday negative and Friday positive, effect is prominent in the market at 5% or lower levels.

The significance of lag of dependent variable implies that current prices can be anticipated on the basis of past prices and more than normal returns can be exploited with the likelihood short run anticipation. Result shows statistically significant coefficient lag variable of dependent variable for almost all firms which indicates existence of short run relationship. Therefore, short run future returns can be predicted in the market for large number of selected firms. However, short run future returns are less likely to be predicted for APL, BAHL, BIPL, DAWH, FCCL, HMB, JSBL, MLCF, MEBL, NML and SSGC.

8.4.2 Month-of-the-year effect Table 8.3, reveals the descriptive statistics of monthly indices and the selected firms. Results indicate both positive and negative mean returns. However, in case of the four indices the

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table depicts positive mean returns in all months with highest during March and July. The value of standard deviation is highest in case of KMI-30 index in the month of February. The result reveals traditional January effect present in all indices with mostly positive returns in January for the firms. Mostly returns are lower and negative during the months of April, May, June, August and October. The table further reveals positive mean returns in the months of July, September, and December with very few exceptions in 04, 04, and 05 firms out of 43 firms, respectively. The tax year in Pakistan starts from July 1st and ends on June 30th. Low and mostly negative returns in June indicate large selling and higher and mostly positive returns in July signify large buying in July. The higher returns in July may be attributed to the same reason as in January effect where higher returns in January may be ascribed to more buying following a sell-off occurred during the month of December to compensate the tax losses. Positive returns in most of the companies may be credited to easy monetary policy generally for the months of Nov-Dec during the study period. The regression result in table 8.4 reveals some indications of the MOY effect in all firms. However, in all four indices January effect is significant, which can be attributed to stable and consistent monetary policy stance in January during the study period, and thus developing investor confidence. In Pakistan monetary policy is being revised after every two months since 2009 onwards. In case of firms July month-anomaly is worth noticing and significant July effect can be found in 11 out of 43 (ABOT, ATRL, ENGRO, EPCL, FFC, HBL, HUBC, ICI, LUCK, MLCF, and NBP) firms, which can be attributed to elevated buying by investor in the month of July after a decrease in price in the preceding months of May and June. July effect can be similar to traditional January effect where due to compensate tax losses investor sell-off in December and buy in January. Similar results can be found in a study conducted by Basher & Sadorsky (2006) on Pakistani stock market including other 20 emergent markets.

8.4.3 Turn-of-the-month effect Table 8.5 exhibits the descriptive statistics of TOM days; one last trading day of the previous month plus 3 first trading days of the next month. On the other hand the ROM days are considered as the rest-of-the-month days. The table 8.5 depicts positive mean returns in TOM period in KSE indices and selected firms except for HUBC and KASBB. It is further evident

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from the results that mean values of return are higher in TOM than the rest of the days. In case of four indices the results show positive mean returns in both TOM and ROM period however, higher returns in TOM period than the rest of the days, which is consistent with the firm level outcomes. These finding are consistent with the results of Lakoniskok & Smidt (1988).

Table 8.6 illustrates the OLS results with TOM and ROM as dummy variables in the model. Results reveal significant TOM effect in the stock market. In KSE-100 and KSE-all share TOM effect are found significant at 5% or lower level, however, in case of KSE-30 and KMI-30 indices no TOM effects are found during the study period. According to the OLS result it can be observed that TOM effect is significant at 5% or lower in most (24 out 43) of the selected firms. Out of which 14 are significant at 1% and remaining 10 TOM effects are found at 5% level. While the rest of the month days are statistically non-different from zero. The TOM effect was not tested on the Karachi stock market considering all indices before. However, Zafar et al. (2012) and Khan et al. (2014) did found any evidences of TOM effects in KSE-100 index, but found evidence other seasonal anomalies in the index, thus concluding deviation from weak-form market efficiency and absence of random walk.

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Table 8.1 Descriptive Statistics of Daily Returns

Mon Tue Wed Thu Fri KSE-100 Mean -0.0009 0.0015 0.0017 0.0009 0.0027 Index SD 0.0122 0.0108 0.0112 0.0101 0.0108 KSE-30 Mean 0.0004 0.0017 0.0014 0.0005 0.0009 Index SD 0.0240 0.0125 0.0130 0.0116 0.0242 All Share Mean -0.0020 0.0013 0.0019 0.0009 0.0038 Index SD 0.0250 0.0102 0.0107 0.0097 0.0235 KMI-30 Mean -0.0060 0.0056 0.0038 0.0009 0.0026 Index SD 0.0669 0.0584 0.0366 0.0102 0.0118 Mean 0.0003 0.0013 0.0034 0.0011 0.0007 ABOTT SD 0.0226 0.0190 0.0203 0.0192 0.0186 Mean -0.0028 0.0008 -0.0027 -0.0006 0.0035 AICL SD 0.0264 0.0236 0.0655 0.0240 0.0246 Mean -0.0008 0.0020 0.0018 0.0007 0.0008 ABL SD 0.0221 0.0205 0.0211 0.0190 0.0204 Mean -0.0026 0.0013 -0.0015 0.0007 0.0029 AKBL SD 0.0273 0.0237 0.0259 0.0229 0.0266 Mean -0.0003 0.0008 0.0014 0.0011 0.0022 APL SD 0.0163 0.0216 0.0238 0.0152 0.0165 Mean -0.0028 0.0028 0.0025 0.0013 0.0012 ATRL SD 0.0272 0.0238 0.0248 0.0229 0.0231 Mean -0.0001 0.0013 0.0015 0.0021 -0.0034 BAHL SD 0.0152 0.0155 0.0158 0.0147 0.0364 Mean -0.0034 0.0019 0.0020 -0.0002 0.0020 BAFL SD 0.0255 0.0223 0.0238 0.0227 0.0228 Mean -0.0033 -0.0007 0.0000 0.0015 0.0036 BIPL SD 0.0376 0.0334 0.0310 0.0349 0.0362 Mean -0.0024 -0.0002 0.0011 -0.0022 0.0023 BOP SD 0.0377 0.0345 0.0344 0.0284 0.0311 Mean -0.0015 0.0007 0.0021 0.0002 0.0037 DGKC SD 0.0255 0.0231 0.0234 0.0240 0.0232 Mean 0.0006 -0.0045 -0.0006 -0.0003 0.0016 DAWH SD 0.0265 0.0850 0.0239 0.0240 0.0247 Mean -0.0039 -0.0010 0.0026 0.0019 0.0036 DCL SD 0.0638 0.0495 0.0448 0.0520 0.0465

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Table 8.1(Cont’d) Descriptive Statistics of Daily Returns Mon Tue Wed Thu Fri Mean -0.0019 -0.0012 0.0023 0.0000 0.0017 EFUG SD 0.0270 0.0271 0.0232 0.0298 0.0241 Mean -0.0029 0.0033 0.0000 -0.0003 0.0019 ENGRO SD 0.0255 0.0227 0.0248 0.0282 0.0222 Mean -0.0061 -0.0002 0.0032 0.0007 0.0015 EPCL SD 0.0253 0.0242 0.0266 0.0237 0.0230 Mean -0.0005 -0.0006 0.0018 0.0016 0.0026 FCCL SD 0.0305 0.0265 0.0298 0.0261 0.0269 Mean -0.0015 0.0016 -0.0001 0.0006 0.0030 FFBL SD 0.0192 0.0189 0.0180 0.0173 0.0205 Mean 0.0005 0.0020 -0.0020 -0.0006 0.0014 FFC SD 0.0154 0.0227 0.0288 0.0192 0.0191 Mean -0.0010 -0.0018 0.0012 -0.0011 0.0038 FABL SD 0.0268 0.0280 0.0302 0.0277 0.0246 Mean -0.0017 0.0010 0.0018 0.0021 0.0002 HBL SD 0.0190 0.0212 0.0174 0.0182 0.0267 Mean -0.0017 0.0002 -0.0012 -0.0001 0.0026 HMB SD 0.0206 0.0219 0.0230 0.0204 0.0182 Mean -0.0010 -0.0018 -0.0011 0.0007 -0.0014 HUBC SD 0.0156 0.0145 0.0173 0.0154 0.0173 Mean 5.0446 5.0499 5.0550 5.0412 5.0824 ICI SD 0.3207 0.3239 0.3262 0.3034 0.3747 Mean 0.0005 -0.0036 0.0019 -0.0029 0.0035 JSBL SD 0.0464 0.0357 0.0351 0.0348 0.0417 Mean -0.0003 -0.0022 -0.0034 0.0004 -0.0015 KASBB SD 0.0428 0.0428 0.0427 0.0421 0.0436 Mean -0.0016 0.0008 0.0009 0.0022 0.0021 KEL SD 0.0495 0.0373 0.0347 0.0394 0.0424 Mean 0.0000 0.0008 0.0012 -0.0008 0.0004 KAPCO SD 0.0143 0.0138 0.0131 0.0144 0.0158 Mean -0.0002 0.0017 0.0027 0.0021 0.0032 LUCK SD 0.0203 0.0197 0.0199 0.0191 0.0198 Mean -0.0001 -0.0013 0.0007 0.0027 0.0045 MLCF SD 0.0380 0.0317 0.0348 0.0374 0.0387

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Table 8.1(Cont’d) Descriptive Statistics of Daily Returns

Mon Tue Wed Thu Fri Mean -0.0001 -0.0013 0.0007 0.0027 0.0045 MEBL SD 0.0380 0.0317 0.0348 0.0374 0.0387 Mean -0.0012 0.0024 0.0002 -0.0016 0.0003 NBP SD 0.0225 0.0282 0.0312 0.0257 0.0232 Mean -0.0012 0.0008 0.0010 0.0004 0.0012 NRL SD 0.0208 0.0186 0.0206 0.0200 0.0202 Mean -0.0019 0.0023 0.0026 -0.0003 0.0036 NML SD 0.0254 0.0221 0.0222 0.0222 0.0241 Mean -0.0010 0.0014 0.0017 0.0003 0.0034 OGDC SD 0.0164 0.0152 0.0157 0.0151 0.0173 Mean -0.0009 0.0018 -0.0004 -0.0022 0.0032 PTCL SD 0.0221 0.0204 0.0229 0.0224 0.0252 Mean -0.0013 0.0020 0.0012 0.0015 0.0026 POL SD 0.0164 0.0162 0.0174 0.0157 0.0160 Mean -0.0003 0.0005 0.0017 -0.0003 0.0027 PSO SD 0.0194 0.0205 0.0192 0.0205 0.0189 Mean -0.0015 -0.0016 0.0011 0.0002 0.0022 SHEL SD 0.0209 0.0216 0.0221 0.0182 0.0202 Mean -0.0033 0.0003 0.0012 -0.0003 0.0048 SCBP SD 0.0293 0.0295 0.0256 0.0252 0.0266 Mean -0.0019 0.0000 0.0021 -0.0011 0.0004 SNDC SD 0.0223 0.0219 0.0215 0.0183 0.0233 Mean -0.0007 0.0012 0.0012 -0.0006 0.0022 SSGC SD 0.0228 0.0223 0.0210 0.0209 0.0281 Mean -0.0014 0.0012 0.0030 0.0018 0.0016 UBL SD 0.0220 0.0228 0.0197 0.0174 0.0206

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Table 8.2 OLS Results for Day-of-the-week Analysis

Mon Tue Wed Thu Fri Coeff -0.0013 0.0016 0.0015 0.0009 0.0025 0.1112 Std. 0.0007 0.0007 0.0007 0.0007 0.0007 0.0267 KSE-100 t-stats -2.0371 2.4015 2.3443 1.3694 3.7692 4.1719 Prob 0.0418 0.0165 0.0192 0.1711 0.0002 0.0000 Coeff 0.0346 0.0134 0.0123 -0.0233 0.0002 0.6652 Std. 0.0203 0.0204 0.0204 0.0203 0.0207 0.0200 KSE-30 t-stats 1.7009 0.6552 0.6023 -1.1493 0.0083 33.2892 Prob 0.0892 0.5125 0.5471 0.2506 0.9934 0.0000 Coeff -0.0011 0.0005 0.0020 0.0015 0.0042 -0.2837 Std. 0.0010 0.0010 0.0010 0.0010 0.0010 0.0257 KSE-ALL t-stats -1.1245 0.5569 2.0575 1.5320 4.2180 -11.0525 Prob 0.2610 0.5777 0.0398 0.1257 0.0000 0.0000 Coeff -0.0046 0.0036 0.0051 0.0028 0.0032 -0.4576 Std. 0.0023 0.0023 0.0023 0.0022 0.0023 0.0238 KMI-30 t-stats -2.0456 1.5710 2.2547 1.2394 1.3984 -19.2594 Prob 0.0410 0.1164 0.0243 0.2154 0.1622 0.0000 Coeff 0.0002 0.0008 0.0028 0.0011 0.0005 0.1384 Std. 0.0012 0.0012 0.0012 0.0012 0.0012 0.0268 ABOT t-stats 0.1504 0.6927 2.3286 0.9226 0.3998 5.1727 Prob 0.8804 0.4886 0.0200 0.3564 0.6894 0.0000 Coeff -0.0034 0.0010 -0.0028 -0.0003 0.0035 0.0761 Std. 0.0021 0.0022 0.0022 0.0022 0.0022 0.0267 ADAMJEE t-stats -1.5589 0.4445 -1.3149 -0.1539 1.5948 2.8500 Prob 0.1193 0.6568 0.1888 0.8777 0.1110 0.0044 Coeff -0.0010 0.0020 0.0010 0.0007 0.0006 0.1549 Std. 0.0012 0.0012 0.0012 0.0012 0.0012 5.8507 ABL t-stats -0.8091 1.6462 0.8191 0.5993 0.4978 0.0265 Prob 0.4186 0.1000 0.4129 0.5491 0.6187 0.0000 Coeff -0.0028 0.0013 -0.0014 0.0010 0.0025 0.1126 Std. 0.0015 0.0015 0.0015 0.0015 0.0015 0.0266 AKBL t-stats -1.8748 0.8556 -0.9339 0.7002 1.6688 4.2321 Prob 0.0610 0.3923 0.3505 0.4839 0.0954 0.0000

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Table 8.2 (Cont’d) OLS Results for Day-of-the-week Analysis

Mon Tue Wed Thu Fri

Coeff -0.0006 0.0008 0.0013 0.0012 0.0020 0.0518 Std. 0.0011 0.0011 0.0011 0.0011 0.0011 0.0267 APL t-stats -0.5716 0.7292 1.1645 1.0392 1.7331 1.9397 Prob 0.5677 0.4660 0.2444 0.2989 0.0833 0.0526 Coeff -0.0010 -0.0014 0.0030 -0.0001 0.0033 0.1433 Std. 0.0014 0.0015 0.0015 0.0014 0.0015 0.0265 ATRL t-stats -0.7070 -0.9947 2.0405 -0.0885 2.2252 5.4064 Prob 0.4797 0.3201 0.0415 0.9295 0.0262 0.0000 Coeff 0.0002 0.0014 0.0014 0.0021 -0.0033 -0.0043 Std. 0.0013 0.0013 0.0013 0.0013 0.0013 0.0267 BAHL t-stats 0.1359 1.0917 1.0781 1.6488 -2.5909 -0.1606 Prob 0.8919 0.2751 0.2812 0.0994 0.0097 0.8724 Coeff -0.0041 0.0023 0.0018 -0.0003 0.0020 0.0645 Std. 0.0014 0.0014 0.0014 0.0014 0.0014 0.0267 BAFL t-stats -2.9907 1.6835 1.3257 -0.1954 1.4175 2.4194 Prob 0.0028 0.0925 0.1851 0.8451 0.1565 0.0157 Coeff -0.0031 -0.0008 -0.0001 0.0015 0.0036 -0.0323 Std. 0.0020 0.0021 0.0021 0.0020 0.0021 0.0267 BIPL t-stats -1.5110 -0.3701 -0.0480 0.7147 1.7368 -1.2084 Prob 0.1310 0.7114 0.9617 0.4749 0.0826 0.2271 Coeff -0.0031 0.0005 0.0011 -0.0020 0.0025 0.1308 Std. 0.0020 0.0020 0.0020 0.0020 0.0020 0.0265 BOP t-stats -1.5854 0.2513 0.5380 -1.0304 1.2448 4.9301 Prob 0.1131 0.8017 0.5907 0.3030 0.2134 0.0000 Coeff -0.0020 0.0007 0.0018 0.0001 0.0036 0.1349 Std. 0.0014 0.0014 0.0014 0.0014 0.0014 0.0265 DGKC t-stats -1.4510 0.4985 1.2500 0.0681 2.4965 5.0873 Prob 0.1470 0.6182 0.2115 0.9457 0.0127 0.0000 Coeff 0.0000 -0.0049 -0.0009 0.0003 0.0014 0.0519 Std. 0.0026 0.0026 0.0026 0.0026 0.0026 0.0268 DAWH t-stats -0.0044 -1.8821 -0.3353 0.1313 0.5241 1.9364 Prob 0.9965 0.0600 0.7375 0.8956 0.6003 0.0530

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Table 8.2 (Cont’d) OLS Results for Day-of-the-week Analysis

MON TUE WED THU FRI

Coeff -0.0037 -0.0017 0.0024 0.0019 0.0037 -0.0770 Std. 0.0030 0.0031 0.0031 0.0030 0.0031 0.0267 DCL t-stats -1.2137 -0.5610 0.8013 0.6191 1.1989 -2.8840 Prob 0.2251 0.5749 0.4231 0.5360 0.2308 0.0040 Coeff -0.0031 -0.0007 0.0022 -0.0005 0.0019 0.2196 Std. 0.0015 0.0015 0.0015 0.0015 0.0016 0.0263 EFUG t-stats -2.0340 -0.4464 1.4501 -0.2945 1.1683 8.3348 Prob 0.0421 0.6554 0.1473 0.7684 0.2429 0.0000 Coeff -0.0030 0.0037 -0.0004 -0.0005 0.0018 0.1464 Std. 0.0015 0.0015 0.0015 0.0015 0.0015 0.0265 ENGRO t-stats -2.0530 2.4979 -0.2762 -0.3288 1.2038 5.5329 Prob 0.0403 0.0126 0.7824 0.7423 0.2289 0.0000 Coeff -0.0063 0.0004 0.0030 0.0003 0.0014 0.0848 Std. 0.0015 0.0015 0.0015 0.0015 0.0015 0.0266 EPCL t-stats -4.3436 0.2839 2.0796 0.2098 0.9481 3.1842 Prob 0.0000 0.7765 0.0377 0.8339 0.3432 0.0015 Coeff -0.0003 0.0013 0.0017 0.0024 -0.0006 -0.0184 Std. 0.0017 0.0017 0.0017 0.0017 0.0017 0.0267 FCCL t-stats -0.1881 0.7536 1.0059 1.4669 -0.3753 -0.6905 Prob 0.8508 0.4512 0.3146 0.1426 0.7075 0.4900 Coeff -0.0016 0.0021 -0.0003 0.0005 0.0029 0.0707 Std. 0.0011 0.0011 0.0011 0.0011 0.0011 0.0266 FFBL t-stats -1.4247 1.8414 -0.2890 0.4874 2.5647 2.6594 Prob 0.1545 0.0658 0.7726 0.6260 0.0104 0.0079 Coeff 0.0004 0.0021 -0.0020 -0.0003 0.0014 0.1104 Std. 0.0013 0.0013 0.0013 0.0013 0.0013 0.0266 FFC t-stats 0.3096 1.6882 -1.5908 -0.2017 1.0966 4.1560 Prob 0.7569 0.0916 0.1119 0.8402 0.2730 0.0000 Coeff -0.0017 -0.0013 0.0011 -0.0011 0.0038 0.1771 Std. 0.0016 0.0016 0.0016 0.0016 0.0016 0.0262 FABL t-stats -1.0322 -0.8058 0.7033 -0.6698 2.3156 6.7514 Prob 0.3022 0.4205 0.4820 0.5031 0.0207 0.0000

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Table 8.2 (Cont’d) OLS Results for Day-of-the-week Analysis

Mon Tue Wed Thu Fri

Coeff -0.0015 0.0013 0.0017 0.0020 0.0000 0.0792 Std. 0.0012 0.0012 0.0012 0.0012 0.0012 0.0267 HBL t-stats -1.2487 1.0421 1.3660 1.5959 -0.0254 2.9684 Prob 0.2120 0.2976 0.1722 0.1107 0.9797 0.0030 Coeff -0.0017 0.0005 -0.0015 0.0003 0.0026 0.0421 Std. 0.0012 0.0012 0.0012 0.0012 0.0013 0.0268 HMB t-stats -1.3747 0.4275 -1.1931 0.2597 2.0185 1.5712 Prob 0.1695 0.6691 0.2330 0.7951 0.0437 0.1164 Coeff -0.0009 -0.0019 -0.0010 0.0006 -0.0013 0.1058 Std. 0.0010 0.0010 0.0010 0.0010 0.0010 0.0266 HUBC t-stats -0.9269 -2.0296 -1.0059 0.6673 -1.3793 3.9795 Prob 0.3541 0.0426 0.3146 0.5047 0.1680 0.0001 Coeff -0.0028 0.0016 0.0034 0.0004 0.0033 0.2201 Std. 0.0012 0.0012 0.0012 0.0012 0.0012 0.0263 ICI t-stats -2.4032 1.3643 2.8323 0.3261 2.7168 8.3770 Prob 0.0164 0.1727 0.0047 0.7444 0.0067 0.0000 Coeff -0.0001 -0.0028 0.0016 -0.0030 0.0035 -0.0061 Std. 0.0023 0.0023 0.0023 0.0023 0.0024 0.0267 JSBL t-stats -0.0622 -1.2147 0.6834 -1.2750 1.4751 -0.2289 Prob 0.9504 0.2247 0.4945 0.2025 0.1404 0.8190 Coeff -0.0019 -0.0022 -0.0035 -0.0002 -0.0018 -0.0993 Std. 0.0025 0.0026 0.0026 0.0025 0.0026 0.0268 KASB t-stats -0.7534 -0.8751 -1.3633 -0.0962 -0.6914 -3.7044 Prob 0.4514 0.3817 0.1730 0.9234 0.4895 0.0002 Coeff -0.0010 0.0010 0.0007 0.0019 0.0024 -0.1296 Std. 0.0024 0.0024 0.0024 0.0024 0.0025 0.0267 KEL t-stats -0.4156 0.4064 0.2851 0.7838 0.9644 -4.8621 Prob 0.6777 0.6845 0.7756 0.4333 0.3350 0.0000 Coeff 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 Std. 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 KAPCO t-stats 0.1361 1.0881 1.6318 -0.8163 0.8164 8.43E+16 Prob 0.8918 0.2767 0.1030 0.4145 0.4144 0.0000

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Table 8.2 (Cont’d) OLS Results for Day-of-the-week Analysis

Mon Tue Wed Thu Fri

Coeff -0.0005 0.0016 0.0021 0.0017 0.0029 0.0944 Std. 0.0012 0.0012 0.0012 0.0012 0.0012 0.0267 LUCK t-stats -0.4316 1.3631 1.7996 1.4183 2.4434 3.5371 Prob 0.6661 0.1731 0.0721 0.1563 0.0147 0.0004 Coeff 0.0001 -0.0016 0.0005 0.0027 0.0045 0.0008 Std. 0.0021 0.0021 0.0022 0.0021 0.0022 0.0267 MLCF t-stats 0.0491 -0.7254 0.2442 1.2539 2.0558 0.0304 Prob 0.9609 0.4683 0.8071 0.2101 0.0400 0.9757 Coeff -0.0021 0.0010 0.0022 0.0011 0.0004 0.0410 Std. 0.0013 0.0013 0.0013 0.0013 0.0014 0.0269 MEBL t-stats -1.5902 0.7259 1.6171 0.8119 0.3307 1.5253 Prob 0.1120 0.4680 0.1061 0.4170 0.7409 0.1274 Coeff -0.0011 0.0025 0.0000 -0.0012 0.0003 0.1147 Std. 0.0015 0.0015 0.0016 0.0015 0.0016 0.0266 NBP t-stats -0.7387 1.6313 -0.0260 -0.7919 0.2070 4.3136 Prob 0.4602 0.1031 0.9793 0.4286 0.8360 0.0000 Coeff -0.0012 0.0009 0.0010 0.0003 0.0010 0.1466 Std. 0.0012 0.0012 0.0012 0.0012 0.0012 0.0264 NRL t-stats -1.0557 0.7882 0.8117 0.2629 0.8409 5.5457 Prob 0.2913 0.4307 0.4171 0.7927 0.4005 0.0000 Coeff -0.0062 0.0026 0.0023 -0.0004 0.0034 0.0325 Std. 0.0023 0.0023 0.0023 0.0023 0.0024 0.0268 NML t-stats -2.6512 1.0891 0.9952 -0.1921 1.4200 1.2151 Prob 0.0081 0.2763 0.3198 0.8477 0.1558 0.2245 Coeff -0.0013 0.0017 0.0016 0.0003 0.0033 0.0876 Std. 0.0009 0.0009 0.0009 0.0009 0.0010 0.0267 OGDC t-stats -1.3661 1.8375 1.6698 0.3446 3.4664 3.2783 Prob 0.1721 0.0663 0.0952 0.7305 0.0005 0.0011 Coeff 0.0072 0.0054 0.0007 0.0004 -0.0119 -0.4781 Std. 0.0058 0.0059 0.0059 0.0058 0.0060 0.0235 PTCL t-stats 1.2355 0.9195 0.1137 0.0620 -2.0017 -20.3335 Prob 0.2168 0.3580 0.9095 0.9505 0.0455 0.0000

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Table 8.2 (Cont’d) OLS Results for Day-of-the-week Analysis

Mon Tue Wed Thu Fri

Coeff -0.0015 0.0023 0.0010 0.0015 0.0024 0.0900 Std. 0.0010 0.0010 0.0010 0.0010 0.0010 0.0266 POL t-stats -1.5831 2.3513 0.9901 1.5755 2.3876 3.3800 Prob 0.1136 0.0188 0.3223 0.1154 0.0171 0.0007 Coeff -0.0009 0.0006 0.0016 -0.0005 0.0027 0.1088 Std. 0.0012 0.0012 0.0012 0.0012 0.0012 0.0266 PSO t-stats -0.7584 0.4905 1.3298 -0.4345 2.2736 4.0930 Prob 0.4484 0.6239 0.1838 0.6640 0.0231 0.0000 Coeff -0.0016 -0.0013 0.0006 0.0000 0.0019 0.1468 Std. 0.0012 0.0012 0.0012 0.0012 0.0013 0.0265 SHEL t-stats -1.3363 -1.0408 0.5019 -0.0080 1.5215 5.5448 Prob 0.1817 0.2981 0.6158 0.9937 0.1284 0.0000 Coeff -0.0029 0.0004 0.0012 -0.0001 0.0049 -0.0802 Std. 0.0016 0.0016 0.0016 0.0016 0.0017 0.0267 SCBP t-stats -1.7908 0.2621 0.7097 -0.0615 2.9707 -3.0105 Prob 0.0735 0.7933 0.4780 0.9509 0.0030 0.0027 Coeff -0.0021 0.0002 0.0021 -0.0014 0.0005 0.1383 Std. 0.0013 0.0013 0.0013 0.0013 0.0013 0.0265 SNGC t-stats -1.6375 0.1422 1.6815 -1.0734 0.3874 5.2246 Prob 0.1018 0.8870 0.0929 0.2833 0.6985 0.0000 Coeff -0.0008 0.0011 0.0010 -0.0008 0.0022 0.0399 Std. 0.0014 0.0014 0.0014 0.0014 0.0014 0.0267 SSGC t-stats -0.6085 0.7698 0.7262 -0.6086 1.5636 1.4963 Prob 0.5430 0.4416 0.4678 0.5429 0.1181 0.1348 Coeff -0.0011 0.0015 0.0025 0.0012 0.0014 0.0886 Std. 0.0012 0.0012 0.0012 0.0012 0.0013 0.0267 UBL t-stats -0.8789 1.2425 2.0024 0.9883 1.0782 3.3220 Prob 0.3796 0.2143 0.0454 0.3232 0.2812 0.0009

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Table 8.3 Descriptive Statistics of Monthly Returns

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec KSE-100 Mean 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Index SD 0.02 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 KSE-30 Mean 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Index SD 0.02 0.01 0.02 0.02 0.05 0.01 0.01 0.01 0.01 0.01 0.01 0.01 Mean 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 KSE-ALL SD 0.01 0.01 0.01 0.01 0.05 0.01 0.01 0.01 0.01 0.01 0.01 0.01 KMI-30 Mean 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Index SD 0.02 0.14 0.01 0.01 0.01 0.01 0.01 0.08 0.01 0.01 0.01 0.01 - Mean 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 ABOTT 0.01 SD 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.03 0.02 0.02 0.01 0.02 - - Mean 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 AICL 0.01 0.01 SD 0.03 0.03 0.03 0.03 0.03 0.03 0.02 0.03 0.02 0.02 0.02 0.10 Mean 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 ABL SD 0.03 0.02 0.03 0.02 0.02 0.02 0.01 0.01 0.02 0.02 0.02 0.02 Mean 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 AKBL SD 0.03 0.03 0.04 0.03 0.02 0.02 0.02 0.03 0.02 0.03 0.02 0.02 Mean 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 APL SD 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.02 0.03 0.03 0.01 0.01 Mean 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 ATRL SD 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.02 0.03 0.03 0.01 0.01 - Mean 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 BAHL 0.01 SD 0.02 0.02 0.05 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.01 0.01 Mean 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 BAFL SD 0.03 0.02 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02

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Table 8.3 (Cont’d) Descriptive Statistics of Monthly Returns

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec - - Mean 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 BIPL 0.01 0.01 SD 0.04 0.04 0.05 0.05 0.04 0.04 0.03 0.03 0.03 0.03 0.02 0.03 - - Mean 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 BOP 0.01 0.01 SD 0.04 0.04 0.04 0.04 0.04 0.04 0.02 0.03 0.03 0.02 0.02 0.03 Mean 0.00 0.00 0.01 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 DGKC SD 0.03 0.03 0.03 0.03 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.02 - - Mean 0.01 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 DAWH 0.01 0.01 SD 0.03 0.03 0.14 0.02 0.02 0.02 0.02 0.03 0.03 0.02 0.02 0.02 - - Mean 0.00 0.00 0.02 0.00 0.00 0.00 0.00 0.00 0.00 0.00 DCL 0.01 0.01 SD 0.05 0.06 0.08 0.06 0.07 0.07 0.04 0.05 0.05 0.04 0.03 0.05 - - Mean 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 EFUG 0.01 0.01 SD 0.03 0.03 0.03 0.03 0.03 0.02 0.02 0.02 0.02 0.03 0.02 0.02 Mean 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 ENGRO SD 0.03 0.03 0.04 0.02 0.02 0.02 0.02 0.03 0.02 0.02 0.02 0.02 Mean 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 EPCL SD 0.03 0.03 0.03 0.03 0.03 0.02 0.02 0.03 0.02 0.02 0.02 0.02 Mean 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 FCCL SD 0.03 0.04 0.04 0.04 0.03 0.02 0.02 0.03 0.03 0.03 0.02 0.02 Mean 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 FFBL SD 0.03 0.02 0.03 0.02 0.02 0.02 0.01 0.02 0.02 0.02 0.02 0.02 - Mean 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 FFC 0.01 SD 0.02 0.06 0.02 0.02 0.01 0.02 0.01 0.01 0.01 0.02 0.01 0.01 - Mean 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 FABL 0.01 SD 0.04 0.03 0.04 0.02 0.02 0.02 0.02 0.02 0.03 0.03 0.03 0.02

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Table 8.3 (Cont’d) Descriptive Statistics of Monthly Returns

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Mean 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 HBL SD 0.02 0.02 0.04 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.01 0.01 - Mean 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 HMB 0.01 SD 0.02 0.02 0.04 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.01 Mean 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 HUBC SD 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.02 0.02 0.01 0.01 Mean 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 ICI SD 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 - - Mean 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 JSBL 0.01 0.01 SD 0.04 0.06 0.05 0.04 0.04 0.04 0.02 0.04 0.04 0.03 0.03 0.03 - - - Mean 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 KASBB 0.02 0.01 0.01 SD 0.06 0.04 0.05 0.04 0.04 0.05 0.04 0.04 0.05 0.03 0.04 0.04 Mean 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 KEL SD 0.06 0.03 0.07 0.05 0.04 0.03 0.03 0.06 0.03 0.03 0.04 0.03 Mean 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 KAPCO SD 0.02 0.01 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.02 0.01 0.01 Mean 0.00 0.00 0.01 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 LUCK SD 0.02 0.02 0.02 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.01 Mean 0.00 0.00 0.01 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.01 0.00 MLCF SD 0.04 0.04 0.06 0.04 0.03 0.03 0.03 0.04 0.03 0.03 0.03 0.03 Mean 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 MEBL SD 0.03 0.03 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 - Mean 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 NBP 0.01 SD 0.03 0.02 0.05 0.03 0.02 0.02 0.02 0.03 0.02 0.02 0.02 0.02

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Table 8.3 (Cont’d) Descriptive Statistics of Monthly Returns

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Mean 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 NRL SD 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 Mean 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 NML SD 0.03 0.02 0.03 0.02 0.02 0.02 0.02 0.03 0.02 0.03 0.02 0.02 Mean 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 OGDC SD 0.02 0.02 0.02 0.02 0.01 0.02 0.01 0.02 0.02 0.02 0.01 0.01 Mean 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 PTCL SD 0.03 0.02 0.02 0.03 0.02 0.03 0.02 0.03 0.03 0.02 0.01 0.01 Mean 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 POL SD 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.02 0.02 0.02 0.01 0.01 Mean 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 PSO SD 0.02 0.02 0.03 0.02 0.02 0.02 0.01 0.02 0.03 0.02 0.02 0.01 - Mean 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 SHEL 0.01 SD 0.02 0.02 0.02 0.03 0.02 0.01 0.01 0.02 0.02 0.02 0.01 0.01 Mean 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 SCBP SD 0.04 0.03 0.04 0.03 0.03 0.03 0.02 0.03 0.03 0.03 0.02 0.02 Mean 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 SNDC SD 0.02 0.02 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.03 0.02 0.02 Mean 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 SSGC SD 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.04 0.02 0.02 Mean 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 UBL SD 0.03 0.02 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02

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Table 8.4 OLS Results for Month-of-the-year Analysis

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec ------0.70 0.13 0.26 0.05 0.19 0.22 Coeff. 0.03 0.11 0.07 0.20 0.02 0.02 KSE- Std. 0.15 0.23 0.17 0.19 0.20 0.22 0.26 0.18 0.20 0.21 0.27 0.31 100 ------4.53 0.67 1.01 0.26 0.88 0.82 t-stat 0.14 0.64 0.35 0.91 0.11 0.05 Prob. 0.00 0.89 0.52 0.73 0.50 0.37 0.32 0.80 0.91 0.38 0.41 0.96 ------0.81 0.03 0.34 0.01 0.09 0.26 Coeff. 0.03 0.04 0.12 0.20 0.04 0.08 KSE- Std. 0.15 0.22 0.17 0.19 0.05 0.21 0.25 0.19 0.21 0.22 0.26 0.30 30 ------5.43 0.56 1.34 0.05 0.40 0.98 t-stat 0.15 0.24 0.63 0.93 0.21 0.27 Prob. 0.00 0.88 0.81 0.53 0.58 0.36 0.18 0.96 0.83 0.69 0.33 0.79 - - - - - 0.68 0.00 0.26 0.04 0.18 0.24 0.04 Coeff. 0.13 0.09 0.01 0.18 0.01 KSE- Std. 0.16 0.23 0.17 0.18 0.04 0.22 0.27 0.18 0.20 0.21 0.27 0.30 All - - - - - 4.29 0.01 0.98 0.20 0.87 0.88 0.14 t-stat 0.75 0.50 0.13 0.85 0.07 Prob. 0.00 0.99 0.46 0.62 0.90 0.40 0.33 0.84 0.95 0.39 0.38 0.89 - - - - 0.72 0.03 0.17 0.59 0.02 0.09 0.21 0.24 Coeff. 0.09 0.13 0.24 0.18 KMI- Std. 0.14 0.02 0.16 0.18 0.22 0.23 0.27 0.03 0.21 0.20 0.25 0.30 30 - - - - 5.00 1.47 0.76 2.18 0.68 0.44 1.08 0.96 t-stat 0.56 0.72 1.06 0.59 Prob. 0.00 0.14 0.58 0.48 0.45 0.29 0.03 0.50 0.66 0.28 0.34 0.56 Coeff. 0.00 0.00 0.00 0.01 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 ABOT - - - 1.21 3.34 0.36 0.91 3.75 1.17 0.93 0.20 1.17 t-stat 2.22 1.91 0.85 Prob. 0.03 0.06 0.23 0.00 0.72 0.36 0.00 0.39 0.24 0.35 0.84 0.24 - - - 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Coeff. 0.01 0.01 0.01 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 AICL - - - - 0.37 0.98 0.24 0.57 1.24 0.25 0.20 1.26 t-stat 1.55 1.42 1.58 2.42 Prob. 0.12 0.71 0.33 0.81 0.57 0.16 0.22 0.11 0.80 0.84 0.21 0.02 Coeff. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 ABL - - - - 1.19 1.86 0.09 0.06 1.20 2.50 0.87 0.03 t-stat 0.12 0.82 1.18 0.36 Prob. 0.90 0.24 0.41 0.06 0.93 0.95 0.23 0.24 0.72 0.01 0.38 0.98 Coeff. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 AKBL - - - - - 0.77 0.74 1.19 0.67 1.19 0.62 0.81 t-stat 1.03 0.29 1.26 0.61 1.31 Prob. 0.44 0.30 0.46 0.77 0.21 0.54 0.23 0.19 0.51 0.23 0.54 0.42

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Table 8.4 (Cont’d) OLS Results for Month-of-the-year Analysis

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Coeff. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 APL - - - 2.65 0.30 1.50 0.61 0.63 1.21 0.01 1.13 0.40 t-stat 0.15 0.73 0.93 Prob. 0.01 0.77 0.13 0.54 0.88 0.53 0.23 0.99 0.46 0.35 0.26 0.69 Coeff. 0.00 0.00 0.01 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.01 0.00 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 ATRL ------3.03 0.88 2.63 0.03 0.76 2.14 t-stat 0.50 0.42 0.37 1.14 2.16 0.62 Prob. 0.62 0.67 0.00 0.38 0.71 0.26 0.01 0.03 0.98 0.45 0.03 0.54 - 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Coeff. 0.01 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 BAHL - - - 1.76 0.58 1.13 0.18 1.36 0.79 0.38 1.00 0.56 t-stat 5.01 0.06 0.04 Prob. 0.08 0.56 0.00 0.26 0.86 0.96 0.17 0.97 0.43 0.71 0.32 0.58 Coeff. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 BAFL - - - - - 0.25 0.74 1.81 0.53 0.90 1.51 0.74 t-stat 1.46 0.41 0.34 0.42 1.41 Prob. 0.80 0.14 0.46 0.68 0.74 0.68 0.07 0.16 0.60 0.37 0.13 0.46 - - 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Coeff. 0.01 0.01 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 BIPL - - - - 0.72 0.02 1.73 0.84 0.23 0.92 0.40 0.44 t-stat 0.12 1.83 1.79 0.57 Prob. 0.47 0.99 0.08 0.90 0.40 0.07 0.82 0.07 0.36 0.57 0.69 0.66 - 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Coeff. 0.01 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 BOP ------0.77 0.76 1.12 1.00 0.96 t-stat 1.24 0.22 0.06 0.41 1.40 1.89 0.25 Prob. 0.22 0.83 0.95 0.68 0.44 0.16 0.45 0.06 0.26 0.80 0.32 0.34 Coeff. 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 DGKC - - - - - 3.51 0.15 0.74 2.22 0.31 0.38 0.98 t-stat 0.35 0.02 0.39 2.13 0.45 Prob. 0.72 0.98 0.00 0.69 0.88 0.46 0.03 0.03 0.65 0.76 0.70 0.33 - 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 Coeff. 0.01 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 DAWH ------2.01 1.36 0.14 0.43 t-stat 0.96 1.45 0.59 0.49 0.99 0.21 1.08 0.53 Prob. 0.34 0.04 0.15 0.55 0.62 0.32 0.83 0.28 0.17 0.60 0.89 0.67

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Table 8.4 (Cont’d) OLS Results for Month-of-the-year Analysis

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec - 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Coeff. 0.01 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.01 0.01 0.01 DCL - - - - - 0.57 2.60 0.07 0.20 0.66 0.27 0.98 t-stat 0.19 0.53 1.08 1.46 0.75 Prob. 0.85 0.57 0.01 0.60 0.95 0.28 0.84 0.15 0.51 0.45 0.79 0.33 Coeff. 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 EFUG - - - - - 2.42 0.81 0.61 0.72 0.88 0.30 0.24 t-stat 1.53 0.12 0.71 2.03 1.89 Prob. 0.13 0.02 0.90 0.48 0.42 0.04 0.54 0.06 0.47 0.38 0.77 0.81 - 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Coeff. 0.01 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 ENGRO - - - - - 2.62 1.28 0.21 0.64 0.90 1.52 1.75 t-stat 0.23 2.44 1.25 1.96 0.96 Prob. 0.01 0.20 0.84 0.82 0.52 0.01 0.37 0.21 0.13 0.05 0.08 0.34 - 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Coeff. 0.01 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 EPCL ------0.75 1.96 0.19 0.79 0.78 0.55 t-stat 0.71 0.99 2.21 0.67 0.03 0.04 Prob. 0.48 0.46 0.05 0.32 0.85 0.03 0.43 0.51 0.44 0.97 0.58 0.97 Coeff. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 FCCL - - - - 1.29 1.93 0.49 0.70 1.56 0.10 0.69 0.20 t-stat 0.07 0.30 1.58 0.87 Prob. 0.20 0.95 0.05 0.63 0.49 0.77 0.12 0.11 0.92 0.38 0.49 0.84 Coeff. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 FFBL - - - - 1.29 1.93 0.49 0.70 1.56 0.10 0.69 0.20 t-stat 0.07 0.30 1.58 0.87 Prob. 0.20 0.95 0.05 0.63 0.49 0.77 0.12 0.11 0.92 0.38 0.49 0.84 - 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Coeff. 0.01 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 FFC ------3.38 1.69 0.82 1.12 1.45 0.27 t-stat 4.23 0.74 0.52 0.26 0.02 0.57 Prob. 0.00 0.00 0.09 0.41 0.46 0.61 0.26 0.80 0.98 0.15 0.57 0.79 Coeff. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 FABL - - - - - 1.60 1.25 0.10 1.22 0.92 1.62 0.53 t-stat 1.53 0.89 1.51 1.35 0.69 Prob. 0.11 0.13 0.21 0.37 0.92 0.13 0.22 0.18 0.36 0.11 0.49 0.60

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Table 8.4 (Cont’d) OLS Results for Month-of-the-year Analysis

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Coeff. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 HBL - - - - - 2.19 0.68 2.51 0.02 0.09 0.81 0.68 t-stat 0.30 1.01 0.37 0.54 0.32 Prob. 0.77 0.03 0.31 0.71 0.59 0.50 0.01 0.98 0.75 0.93 0.42 0.50 - 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Coeff. 0.01 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 HMB - - - - - 0.27 0.88 1.06 1.38 0.72 1.52 0.60 t-stat 0.22 3.96 0.01 0.28 1.16 Prob. 0.79 0.83 0.00 0.38 0.99 0.29 0.78 0.25 0.17 0.47 0.13 0.55 Coeff. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 HUBC ------1.59 1.32 t-stat 1.52 0.58 0.60 2.14 0.80 0.40 2.50 1.70 0.24 0.04 Prob. 0.13 0.56 0.55 0.03 0.43 0.69 0.01 0.09 0.11 0.19 0.81 0.97 Coeff. 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 ICI - - - - 0.98 2.34 1.33 0.60 2.89 1.23 0.71 1.46 t-stat 0.34 0.86 0.74 0.34 Prob. 0.33 0.74 0.02 0.18 0.55 0.39 0.00 0.46 0.22 0.73 0.47 0.14 - 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Coeff. 0.01 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 JSBL - - - - - 0.35 1.36 0.70 0.48 0.61 0.42 0.16 t-stat 0.69 1.16 0.09 1.77 0.57 Prob. 0.73 0.17 0.48 0.49 0.63 0.25 0.93 0.08 0.54 0.57 0.67 0.87 - - 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Coeff. 0.01 0.01 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 KASB ------0.31 0.75 0.71 0.65 t-stat 3.23 0.97 0.45 0.58 1.40 0.12 0.45 0.56 Prob. 0.00 0.76 0.45 0.33 0.66 0.48 0.56 0.16 0.90 0.65 0.57 0.52 Coeff. 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 KEL - - - 0.41 0.05 1.76 0.43 0.40 0.55 0.24 0.59 0.25 t-stat 1.00 0.24 0.69 Prob. 0.68 0.96 0.08 0.67 0.69 0.32 0.58 0.81 0.81 0.49 0.56 0.80 Coeff. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 KAPCO - - 2.17 0.26 0.81 0.71 0.31 0.98 1.06 0.83 0.44 0.32 t-stat 1.46 2.54 Prob. 0.03 0.14 0.80 0.42 0.48 0.75 0.33 0.29 0.41 0.01 0.66 0.75

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Chapter 8

Table 8.4 (Cont’d) OLS Results for Month-of-the-year Analysis

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Coeff. 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 LUCK - - 1.08 1.23 2.94 1.61 0.88 2.48 0.64 0.87 0.44 0.44 t-stat 0.51 0.93 Prob. 0.28 0.22 0.00 0.11 0.61 0.38 0.01 0.35 0.52 0.38 0.66 0.66 - 0.00 0.00 0.01 0.00 0.00 0.00 0.01 0.00 0.00 0.01 0.00 Coeff. 0.01 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 MLCF ------0.55 0.12 2.85 2.77 2.38 t-stat 0.24 0.42 0.60 1.54 0.36 0.65 0.18 Prob. 0.58 0.90 0.00 0.81 0.68 0.55 0.01 0.12 0.72 0.52 0.02 0.85 Coeff. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 MEBL ------0.28 0.00 0.97 1.56 1.49 t-stat 0.13 0.50 0.05 0.16 0.23 0.06 0.15 Prob. 0.90 0.61 0.78 0.96 0.88 1.00 0.33 0.82 0.12 0.95 0.14 0.88 - - 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Coeff. 0.01 0.01 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 NBP ------1.25 1.17 2.06 1.44 0.34 0.65 t-stat 2.29 0.33 0.27 0.44 2.70 0.04 Prob. 0.21 0.24 0.02 0.74 0.79 0.66 0.04 0.01 0.15 0.97 0.73 0.52 Coeff. 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 NRL ------0.75 3.41 0.55 0.75 0.35 1.22 t-stat 0.26 1.25 0.68 1.95 0.06 0.15 Prob. 0.45 0.80 0.00 0.58 0.45 0.73 0.22 0.21 0.50 0.05 0.95 0.88 - 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 Coeff. 0.01 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 NML - - - - - 0.44 1.00 1.06 1.42 0.02 1.07 0.58 t-stat 0.22 0.15 0.11 0.59 3.21 Prob. 0.66 0.83 0.32 0.88 0.91 0.56 0.29 0.00 0.16 0.98 0.29 0.56 Coeff. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 OGDC - - 0.11 1.02 0.95 0.92 0.97 0.57 1.89 1.68 0.96 0.83 t-stat 0.04 0.05 Prob. 0.91 0.31 0.34 0.36 0.33 0.57 0.06 0.97 0.96 0.09 0.34 0.41 Coeff. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Std. 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 PTCL - - - - 0.23 0.08 0.08 0.01 0.15 0.15 0.26 0.16 t-stat 0.36 0.02 0.29 0.14 Prob. 0.82 0.93 0.93 0.99 0.88 0.72 0.88 0.98 0.79 0.77 0.87 0.88

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Chapter 8

Table 8.4 (Cont’d) OLS Results for Month-of-the-year Analysis

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Coeff. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 POL - - 1.43 0.77 2.43 0.24 0.13 1.89 0.73 0.53 1.01 1.03 t-stat 0.32 0.06 Prob. 0.15 0.44 0.02 0.75 0.81 0.89 0.06 0.46 0.95 0.60 0.31 0.30 Coeff 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 PSO - - - - - 0.18 0.95 1.35 1.31 1.60 1.25 0.24 t-stat 0.22 0.33 1.36 0.12 0.29 Prob 0.86 0.34 0.18 0.83 0.19 0.74 0.11 0.17 0.91 0.77 0.21 0.81 Coeff. 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 SHEL ------3.82 0.63 0.56 0.36 1.41 0.67 t-stat 1.36 0.41 2.61 1.19 1.99 0.72 Prob. 0.18 0.68 0.00 0.01 0.53 0.24 0.57 0.05 0.72 0.47 0.16 0.50 Coeff. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 SCBP - - - - 0.02 0.75 1.54 0.20 0.19 0.19 1.01 1.03 t-stat 0.89 0.47 0.18 0.10 Prob. 0.99 0.37 0.45 0.12 0.64 0.84 0.85 0.86 0.85 0.92 0.31 0.31 Coeff. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 SNGC ------1.78 1.50 0.88 0.99 1.52 t-stat 1.76 0.88 0.94 2.26 0.26 0.30 1.09 Prob. 0.08 0.08 0.13 0.38 0.38 0.35 0.32 0.02 0.13 0.80 0.76 0.27 - 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 Coeff. 0.01 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 SSGC ------1.24 0.38 1.23 0.68 0.85 3.03 t-stat 0.45 0.14 0.64 2.21 0.52 0.28 Prob. 0.22 0.70 0.22 0.65 0.49 0.89 0.40 0.52 0.00 0.03 0.61 0.78 Coeff. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Std. 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 UBL - - - - - 1.07 2.15 0.80 0.97 1.90 1.64 0.11 t-stat 1.01 0.03 0.03 0.09 0.23 Prob. 0.28 0.03 0.42 0.33 0.31 0.98 0.06 0.98 0.93 0.81 0.10 0.91

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Table 8.5 Descriptive Statistics of TOM and ROM period Returns Std. Jarque- Obs Mean Dev. Skewness Kurtosis Bera CV TOM 284 0.0032 0.01 0.17 3.78 9 3.670019 KSE-100 ROM 1119 0.0006 0.01 -0.3 6.32 529 18.37542 TOM 273 0.0042 0.02 9.31 127.36 179868 5.605432 KSE-30 ROM 1131 0.0263 0.51 19.31 374.25 6565486 19.31589 TOM 284 0.0026 0.01 0.23 3.76 9 4.075573 KSE-ALL ROM 1119 0.0007 0.02 -0.81 259.15 3062009 25.90884 TOM 271 0.0035 0.01 0.4 3.86 16 3.388102 KMI-30 ROM 1130 0.0009 0.05 0.34 308.63 4394061 54.28719 TOM 282 0.0027 0.02 0.08 3.63 5 7.218705 ABOTT ROM 1097 0.0009 0.02 -0.1 4.79 149 22.27173 TOM 282 0.0028 0.02 0.19 3.42 4 8.779849 AICL ROM 1120 -0.0014 0.04 -14.96 384.43 6831409 -28.6292 TOM 281 0.0039 0.02 -1.4 15.39 1890 5.895105 ABL ROM 1114 0.0001 0.02 -0.71 7.98 1244 274.8435 TOM 282 0.0038 0.02 0.77 4.44 52 6.097789 AKBL ROM 1120 -0.0008 0.03 -0.96 12.08 4024 -33.9749 TOM 282 0.0031 0.02 0.12 4.27 20 5.772948 APL ROM 1120 0.0005 0.02 -4.61 69.42 209845 40.13502 TOM 281 0.0051 0.03 0.41 4.38 30 5.442905 ATRL ROM 1117 -0.0001 0.02 -0.02 3.51 12 -194.742 TOM 283 0.004 0.02 0.7 4.21 40 3.984708 BAHL ROM 1118 -0.0005 0.02 -5.94 72.62 232335 -43.2259 TOM 282 0.0023 0.02 0.59 6.95 199 10.52256 BAFL ROM 1119 -0.0001 0.02 0.03 5.87 384 -331.266 TOM 282 0.0033 0.03 1.05 6.28 178 10.20331 BIPL ROM 1120 -0.0005 0.03 0.76 6.68 743 -66.6123 TOM 281 0.002 0.04 0.34 3.94 16 18.28338 BOP ROM 1121 -0.0009 0.03 0.39 6.3 538 -36.7674 TOM 283 0.0043 0.02 0.24 3.25 3 5.688847 DGKC ROM 1119 0.0001 0.02 -0.07 3.41 9 250.0954

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Table 8.5 (Cont’d) Descriptive Statistics of TOM and ROM Period Returns Std. Jarque- Obs Mean Dev. Skewness Kurtosis Bera CV TOM 283 0.0047 0.03 0.03 2.62 2 5.601307 DAWH ROM 1115 -0.0023 0.05 -21.1 606.3 16991973 -19.9974 TOM 282 0.0009 0.06 -2.38 25.52 6225 64.77586 DCL ROM 1120 0.0004 0.05 2.24 18.91 12747 120.412 TOM 281 0.0007 0.03 0.23 3.17 3 38.76796 EFUG ROM 1095 -0.0003 0.03 -1.11 14.63 6399 -77.8735 TOM 283 0.0046 0.02 0.03 2.77 1 5.122933 ENGRO ROM 1119 -0.0007 0.03 -1.49 16.81 9307 -36.7636 TOM 282 0.0051 0.03 0.53 4.14 28 5.38913 MEPCL ROM 1120 -0.0016 0.02 0.53 5.33 306 -15.3169 TOM 282 0.0064 0.03 1.08 4.71 89 4.487043 FCCL ROM 1121 -0.0004 0.03 0.51 7.81 1128 -64.7576 TOM 283 0.0049 0.02 0.9 5.24 98 3.968072 FFBL ROM 1119 -0.0002 0.02 -0.42 7.59 1013 -86.0922 TOM 282 0.0016 0.03 -9.87 142.07 231840 18.45206 FFC ROM 1119 0.0001 0.02 -4.83 69.97 213464 139.5588 TOM 282 0.0013 0.03 0.14 5.07 51 23.43478 FABL ROM 1121 0 0.03 0.15 6.26 502 -2473.24 TOM 282 0.0031 0.02 0.33 3.53 9 6.128557 HBL ROM 1120 0.0001 0.02 -2 21.69 17043 198.8019 TOM 282 0.0022 0.02 -0.18 3.61 6 9.14396 HMB ROM 1110 -0.0005 0.02 -1.74 18.4 11524 -43.4053 TOM 283 -0.0032 0.02 -0.58 9.56 524 -5.12577 HUBC ROM 1119 -0.0005 0.02 0.45 7.14 837 -35.1674 TOM 278 0.0045 0.02 0.21 3.05 2 4.760475 ICI ROM 1108 0.0007 0.02 0.09 4.12 60 26.83624 TOM 282 0.005 0.04 1.51 9.87 661 7.963553 JSBL ROM 1120 -0.0014 0.04 1.25 9.92 2523 -28.3237

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Table 8.5 (Cont’d) Descriptive Statistics of TOM and ROM Period Returns Std. Jarque- Obs Mean Dev. Skewness Kurtosis Bera CV TOM 282 -0.001 0.05 -0.29 5.53 79 -47.7 KASBB ROM 1103 -0.002 0.04 0.57 6.82 730 -21.0483 TOM 282 0.0021 0.04 0.82 8.89 439 16.86692 KEL ROM 1120 0.0006 0.04 1.4 18.09 10989 70.48571 TOM 283 0.0025 0.01 0.75 6.51 171 5.43225 KAPCO ROM 1119 -0.0001 0.01 -1.06 10.97 3174 -231.693 TOM 283 0.0052 0.02 0.41 3.75 15 4.112956 LUCK ROM 1119 0.0009 0.02 -0.06 3.89 37 22.0553 TOM 282 0.0038 0.04 0.89 5.41 105 9.517331 MLCF ROM 1120 0.0007 0.04 0.89 9.3 2000 52.86804 TOM 282 0.0043 0.02 0.61 4.5 44 5.188873 MEBL ROM 1109 -0.0004 0.02 -0.25 6.42 551 -50.4376 TOM 282 0.0043 0.02 0.08 3.09 0 5.375233 NBP ROM 1121 -0.0009 0.03 -3.89 40.77 69465 -29.2568 TOM 282 0.0026 0.02 -0.1 4.07 14 8.156801 NRL ROM 1121 0 0.02 0.1 4.3 81 -718.225 TOM 282 0.0021 0.08 -14.33 228.63 607808 36.45231 NML ROM 1121 -0.0001 0.02 -0.14 3.88 40 -224.509 TOM 282 0.0036 0.02 0.68 6.14 137 4.769529 OGDC ROM 1120 0.0006 0.02 0.25 4.88 177 25.53595 TOM 282 0.0035 0.02 0.67 4.82 60 6.61087 PTCL ROM 1120 -0.0005 0.02 -0.14 5.66 334 -43.8207 TOM 282 0.0039 0.02 0.58 3.99 27 4.163104 POL ROM 1120 0.0006 0.02 -0.04 5.85 379 28.37739 TOM 282 0.0009 0.02 -2.09 19.88 3552 25.78399 SHEL ROM 1117 -0.0004 0.02 -0.84 14.79 6603 -46.9815

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Table 8.5 (Cont’d) Descriptive Statistics of TOM and ROM Period Returns Std. Jarque- Obs Mean Dev. Skewness Kurtosis Bera CV TOM 284 0.0028 0.03 0.63 4.54 47 10.7073 SCBP ROM 1106 0.0001 0.03 0.02 5.92 392 185.6138 TOM 282 0.004 0.02 0.36 3.05 6 5.203685 SNDC ROM 1120 -0.0012 0.02 -0.68 11.45 3421 -18.7056 TOM 282 0.0038 0.02 0.63 3.89 28 5.7309 SSGC ROM 1120 -0.0002 0.02 -0.81 13.11 4895 -106.614 TOM 282 0.0029 0.02 0 4.39 23 7.848794 UBL ROM 1120 0.0007 0.02 -0.26 5.64 338 27.96797

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Table 8.6 OLS Results for Turn-of-the-month Analysis

TOM ROM TOM ROM Coeff. 0.00308 0.000658 Coeff. 0.003145 -0.00055 KSE- Std. 0.000671 0.00033 Std. 0.001537 0.000753 AKBL 100 t-stats. 4.593416 1.995966 t-stats. 2.046214 -0.72914 Prob. 0 0.0461 Prob. 0.0409 0.466 Coeff. 0.004199 0.026347 Coeff. 0.0032 0.0005 Std. 0.02766 0.01359 Std. 0.0011 0.0006 KSE-30 APL t-stats. 0.151804 1.938768 t-stats. 2.8172 0.841 Prob. 0.8794 0.0527 Prob. 0.0049 0.4005 Coeff. 0.00255 0.000748 Coeff. 0.003106 0.000263 KSE- Std. 0.00104 0.000511 Std. 0.001496 0.000732 ATRL ALL t-stats. 2.450755 1.464132 t-stats. 2.076031 0.359029 Prob. 0.0144 0.1434 Prob. 0.0381 0.7196 Coeff. 0.00351 0.000878 Coeff. 0.003639 -0.00037 Std. 0.002609 0.001278 Std. 0.001289 0.000633 KMI-30 BAHL t-stats. 1.345686 0.687282 t-stats. 2.822932 -0.58801 Prob. 0.1786 0.492 Prob. 0.0048 0.5566 Coeff. 0.002199 0.00109 Coeff. 0.001896 4.69E-05 Std. 0.001228 0.000606 Std. 0.001424 0.000698 ABOT BAFL t-stats. 1.790873 1.798016 t-stats. 1.330981 0.067186 Prob. 0.0735 0.0724 Prob. 0.1834 0.9464 Coeff. 0.001622 -0.00103 Coeff. 0.002643 -4.14E-04 Std. 0.002205 0.00108 Std. 0.002095 0.001024 AICL BIPL t-stats. 0.735489 -0.95115 t-stats. 1.261605 -0.40423 Prob. 0.4622 0.3417 Prob. 0.2073 0.6861 Coeff. 0.003539 0.000205 Coeff. 0.001339 -6.82E-04 Std. 0.001261 0.000619 Std. 0.002024 0.000989 ABL BOP t-stats. 2.807482 0.331368 t-stats. 0.661539 -0.68937 Prob. 0.0051 0.7404 Prob. 0.5084 0.4907

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Table 8.6 (Cont’d) OLS Results for Turn-of-the-month Analysis

TOM ROM TOM ROM Coeff. 0.003853 0.000248 Coeff. 0.004153 2.38E-05 Std. 0.00144 0.000707 Std. 0.001144 0.000561 DGKC FFBL t-stats. 2.676285 0.351379 t-stats. 3.630236 0.04236 Prob. 0.0075 0.7254 Prob. 0.0003 0.9662 Coeff. 0.003319 -0.0019 Coeff. 0.000916 3.16E-04 Std. 0.002634 0.001295 Std. 0.0013 0.000637 DAWH FFC t-stats. 1.259787 -1.46409 t-stats. 0.704781 0.496629 Prob. 0.208 0.1434 Prob. 0.4811 0.6195 Coeff. 0.003319 -0.0019 Coeff. 0.001198 8.52E-05 Std. 0.002634 0.001295 Std. 0.001674 0.00082 DCL FABL t-stats. 1.259787 -1.46409 t-stats. 0.715476 0.103992 Prob. 0.208 0.1434 Prob. 0.4744 0.9172 Coeff. 8.81E-05 -0.00017 Coeff. 0.002865 0.000185 Std. 0.001601 0.000793 Std. 0.001253 0.000614 EFUG HBL t-stats. 0.055021 -0.21869 t-stats. 2.286057 0.302154 Prob. 0.9561 0.8269 Prob. 0.0224 0.7626 Coeff. 0.003653 -0.00036 Coeff. 0.002035 -0.0004 Std. 0.001503 0.000738 Std. 0.00127 0.000625 ENGRO HMB t-stats. 2.43106 -0.48817 t-stats. 1.601942 -0.640954 Prob. 0.0152 0.6255 Prob. 0.1094 0.5217 Coeff. 0.004942 -0.00147 Coeff. -0.00363 -0.00039 Std. 0.001495 0.000732 Std. 0.000976 0.000479 EPCL HUBC t-stats. 3.305956 -2.00628 t-stats. -3.72497 -0.814294 Prob. 0.001 0.045 Prob. 0.0002 0.4156 Coeff. 0.003823 0.000258 Coeff. 0.004981 0.000672 Std. 0.001705 0.000835 Std. 0.001238 0.000605 FCCL ICI t-stats. 2.241795 0.309231 t-stats. 4.02473 1.111304 Prob. 0.0251 0.7572 Prob. 0.0001 0.2666

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Table 8.6 (Cont’d) OLS Results for Turn-of-the-month Analysis

TOM ROM TOM ROM Coeff. 0.0043 -0.0011 Coeff. 0.0036 -0.0007 Std. 0.0024 0.0012 Std. 0.0016 0.0008 JSBL t-stats. 1.7952 -0.9551 t-stats. 2.2419 -0.8684 Prob. 0.0728 0.3397 NBP Prob. 0.0251 0.3853 Coeff. -0.0006 -0.0021 Coeff. 0.002401 5.47E-05 Std. 0.0026 0.0013 Std. 0.001217 0.000596 KASB t-stats. -0.2433 -1.6324 t-stats. 1.97303 0.091913 Prob. 0.8078 0.1028 NRL Prob. 0.0487 0.9268 Coeff. 0.002533 0.000542 Coeff. 0.00021 3.76E-04 S.E. 0.002479 0.001214 Std. 0.002392 0.001171 KEL t-stats. 1.021895 0.44604 t-stats. 0.087593 0.321084 Prob. 0.307 0.6556 NML Prob. 0.9302 0.7482 Coeff. 0.0026 0 Coeff. 0.0039 0.0006 Std. 0.0009 0.0004 Std. 0.001 0.0005 KAPCO t-stats. 2.9615 -0.1044 t-stats. 4.0192 1.2249 Prob. 0.0031 0.9168 OGDC Prob. 0.0001 0.2208 Coeff. 0.0052 0.001 Coeff. 0.0031 -0.0004 Std. 0.0012 0.0006 Std. 0.0068 0.0033 LUCK t-stats. 4.2708 1.6524 t-stats. 0.463 -0.1193 Prob. 0 0.0987 PTCL Prob. 0.6434 0.905 Coeff. 0.0037 0.0008 Coeff. 0.0036 0.0007 Std. 0.0022 0.0011 Std. 0.001 0.0005 MLCF t-stats. 1.7011 0.7162 t-stats. 3.6636 1.393 Prob. 0.0892 0.474 POL Prob. 0.0003 0.1639 Coeff. 0.0038 -0.0003 Coeff. 0.0024 0.0003 Std. 0.0014 0.0007 Std. 0.0012 0.0006 t-stats. 2.8022 -0.4568 t-stats. 2.0215 0.5354 MEBL Prob. 0.0051 0.6479 PSO Prob. 0.0434 0.5925

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Table 8.6 (Cont’d) OLS Results for Turn-of-the-month Analysis

TOM ROM Coeff. 0.0003 -0.0002 Std. 0.0013 0.0006 t-stats. 0.2012 -0.3934 SHEL Prob. 0.8406 0.6941 Coeff. 0.0029 0.0001 Std. 0.0017 0.0008 t-stats. 1.731 0.0834 SCBP Prob. 0.0837 0.9335 Coeff. 0.0035 -0.0009 Std. 0.0013 0.0006 t-stats. 2.6521 -1.482 SNGC Prob. 0.0081 0.1386 -6.72E- Coeff. 0.003512 05 Std. 0.001422 0.000696 t-stats. 2.46982 -0.09652 SSGC Prob. 0.0136 0.9231 Coeff. 0.002328 9.05E-04 Std. 0.001259 0.000617 t-stats. 1.848285 1.467983 UBL Prob. 0.0648 0.1423

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Chapter 9 Thin-Trading and Random walk

9.1 Thin-trading in Emergent Markets

Emergent markets can be characterized as illiquid and less transparent markets due to poor information, insider knowledge and manipulations and thin trading (Gandhi et al., 1980; Barnes, 1986; Berglund et al.,1989; Mohamed & Kumar, 1995; (Antoniou et al., 1997; Abdmoulah, 2010).

Since trading is non-synchronous to new information and it is easier for the large investor and an insider to maneuver the market (Barnes, 1986). Low volume of trading results in higher transaction cost for trading and harder for the investor to react on new information resulting in lower number of transactions (Mohamed & Kumar, 1995). Thinly traded markets exhibit higher price volatility and larger spread in bid and asks resulting in price clustering (Antoniou et al., 1997). Stoll & Whaley (1990) further contributed that volitality at opening is higher than the volitality at closing.

Similarly, Dimson (1979) and Berglund et al. (1989) also found that the beta estimate of thinly traded security has downward biased variance while it is upward biased for a frequently traded security.

Infrequent trading has two categories; first, when the trading is done at every consecutive interval, but not at the closing of each interval. This type is referred as non-synchronous trading Scholes & William (1977) focused this form of thin trading. Second, when trading on stock does not occur in each consecutive interval. This type is referred as non-trading. Dimson (1979), Lo & MacKinlay (1990) and Stoll & Whaley (1990) analyzed non-trading and its implications. As the trading interval reduces, non-synchronous trading becomes non- trading. For example, it is possible that in considering monthly interval trading on a certain

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stock occurs at each interval, but not necessarily at the close of each month. But in a fifteen minutes interval it is possible that a particular stock is not traded at each consecutive interval.

Larger bid-ask spread stimulates negative autocorrelation even price changes are serially independent (Roll, 1984).

According to Miller et al. (1994), “Negative first-order autocorrelation in observed price changes is likely for extremely intervals where the price movement attributable to new information may be small relative to the size of the bid-ask spread”.

Therefore, bid-ask spreads are likely to be reflected in autocorrelation more in case of futures (single security) relative to the overall index.

9.2 Thin-trading and Market Efficiency

Several studies have taken different measures for correction of thin trading. Miller et al. (1994) studied S&P index and found positive first-order correlation and further observed the declining effects of infrequent trading on autocorrelation as the volume of trading increases. Infrequent trading model is corrected by redefining autoregressive model with index basis changes. By subtracting the new model from observed future price changes provides “corrected” series, which is assumed to have reduced autocorrelation effects of thin trading (Miller et al., 1994).

Miller et al., (1994) proposed the following innovated model to correct for the effects of thin trading:

(8.1)

Where,

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= true index level change = observed index level innovation = coefficient of infrequent trading.

As, means continuous trading with zero trading gap, implies fully captures the effects of . In that case, with mean zero and variance .

As, , means severe infrequent trading implies, trading of a particular stock took place in some previous period. Alternatively, trading is not done on a certain stock for many periods. Miller et al. (1994) further considered the futures prices in order to develop the following MA(1) model for individual securities thin trading, such that:

(8.2)

Where,

observed index level change.

Bid-ask spread coefficient, such that the greater the value of the larger the bid-ask spread. However, due to the complexity of identifying the non-trading interval, Miller et al. (1994) fitted AR(1) on the infrequent trading model, such that:

(8.3)

Estimated residuals from the above equation are used to generate estimates of innovated index level adjusted for thin trading.

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is then substituted for the observed index level changes. This adjustment in the

observed level index is expected to reduce the first-order autocorrelation.

+ (8.5)

The above technique of reducing the impact of thin trading on autocorrelation is applied by Antoniou (1997) on Istanbul stock exchange, Siriopoulos (2001) on Greek capital market, Mustafa and Nishat (2007) on Pakistani stock market, and Harrison & Moore (2012) on MENA stock exchanges.

9.3 Non-linear trends in Returns and Thin-trading

EMH entails the assumption of rationality of investor, which includes unbiased forecasting, risk aversion behaviour and quick response to new information. However, violation of any of these assumptions could lead to non-linear process of generating returns and using a linear model for a non-linear relationship results spuriously. Non-linear systems are chaotic ones and generate a series exhibiting similar patterns to random walk, however, but a predictable return series.

Emergent markets are mostly characterized by non-linear trend in returns due to various imperfections in the markets. Non-linear tendencies in returns grow with the market imperfection and biased behaviours of investors. For example, heterogeneous pricing systems in stock, futures and derivative markets may lead to ambiguity in executing arbitrage transactions between the stock, futures and derivatives which could develop non-linear trends in returns. Another very common explanation for non-linearities is price clustering due to thin trading in the stock market. Likewise, higher transaction cost and under-reaction may also lead to non-synchronous trading lags in the market causing non-linear trends. Psychological deviations from rationalism may be one the prime factors of markets

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distortions and non-linear tendencies. Investor could well be risk lovers at times especially when like to gamble to recover past losses. Similarly, they may not always respond instantaneously to new information and only trade when find economically profitable. These Psychological biases lead to under-reaction and over-reaction in the markets.

Non-linearity in return is empirically evident in both developed and emerging markets. Granger & Anderson (1978) and Rao and Gabr (1980), Rao (1981) studied bi-linear models for stock returns. Similarly, Hinch and Patterson (1985) produced substantial evidence for the non-linear trends of return series rather than a linear one. Savit (1988) also advocated for non-linear return generation process where non-stochastic forecasting errors grow exponentially.

Scheinkman & LeBaron (1989) found non-linear tendencies in stock return series. Similarly, Peters (1991) found evidence on non-linearity in stock, bonds and currency markets. Evidence of non-linear casualty between returns and volume can also be found between Dow Jones stock returns and in New York Stock Exchange trading volume (Hiemstra & Jones, 1994). Similarly, Non-linear risk-return relationship implies time-varying risk-return which is attributed to non-linear returns.

In a nut shell stock markets with non-linear return may also exhibit thin trading phenomenon. Therefore it is imperative to take thin trading into account while looking for non-linear behaviour and degree of predictability in the markets.

Efficiency in non-linear models after correcting for thin trading can be tested by using the following model, Antoniou et al. (1997), Harrison & Moore (2012), originally introduced by Miller et al. (1994)

(8.6)

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Where,

is the return at time adjusted for thin-trading.

(8.8)

For the EMH to hold, , is expected.

Equation (8.8) is estimated recursively throughout the time period in order to find corrective returns for measuring non-linear effects on efficiency after adjustment of thin-trading, in the markets by using following equation.

9.4 Results and Analysis

Table 9.1, provides the value of the parameters of linear model adjusted for thin trading. The table can be compared to AR (1) model the compatible unadjusted for thin trading. Null hypothesis is rejected for the return series without adjustment for thin series in case of the majority of the firms selected and all in indices at KSE. However, in case of 12 out of 43 selected firms (APL, BAHL, BIPL, DAWH, FCCL, HMB, JSBL, KAPCO, MLCF, MEBL, NML and SSGC) returns are found uncorrelated with the previous return values and null hypothesis of independent series is rejected. Similarly, the results of heteroscedasticity and Q-statistics the return series of 28 out of 43 firms are found to be serially correlated up to 36 lagged periods. In case of adjusted for thin trading return series cannot be rejected for weak- form efficiency for almost all selected firms, KSE-all share, and FFBL the return series corrected for thin trading is found to be perfectly serially correlated. KSE-30 and KMI-30 adjusted return series can be found predictable upon past returns. Heteroscedasticity and Q- statistics remained insignificant for 15 and 24 firms in KSE-30 and KMI-30, respectively implies uncorrelated return series after correcting for thin trading. Stock market therefore, appears to have tendencies of weak-form efficiency for most of the firms after correcting for

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thin trading. It is concluded that accounting for thin trading allows the market to have removed apparent weak-form informational inefficiency from majority of the selected firms in KSE.

In case if the investors are risk lover that is, they may be less sensitive to losses than gains consequently gives rise to thin-trading in the market. This particular phenomenon leads to leptokurtic and non-linear character of returns. Table 9.2, provides the result of non-linear model without adjustment for thin trading for testing RW. The estimates lagged returns appear to be significant at 5% or lower levels revealing absence of RW. Five out of 43 firms (BAHL, BIPL, HUBC, KAPCO, and NML) however, appear to be weak-form efficient and absence of predictability in these firms. Test of heteroscedasticity found to reflect significant values of 34 out of 43 firms. In KSE-100 and in KSE-30 the heteroscedasticity coefficient found significant at 1% level. Nearly half of the firms returns found correlated.

Table 9.3 shows the result of non-linear model adjusted for thin trading. Insignificant estimates suggest that null hypothesis cannot be rejected and return series of all firms. However, ABOT, ICI and JSBL show non-linear predictability of returns. Heteroscedasticity and correlation estimates remained significant for 20 firms and all four indices. It can be concluded that adjusted returns for thin-trading suggested by Miller et al. (1994) display prominent impact of thin-trading on market efficiency. Returns adjusted for thin-trading in both linear and non-linear models provide supportive evidence of presence of weak-form efficiency in Karachi stock market.

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Table 9.1 Results of Linear Model for Adjusted Returns

Constant AR(1) Heteroscedasticity LM ARCH Test White noise- Prob. Q-statistics Prob. stat Coeff 0.000 -0.002 KSE-100 t-stat -0.019 -0.069 59.047 0.000 228.916 0.000 Prob 0.985 0.945 Coeff 0.000 1.000 KSE-ALL t-stat 0.000 2.53E+17 35.153 0.000 534.180 0.000 Prob 1.000 0.000 Coeff 0.000 0.130 KSE-30 t-stat 0.001 4.906 1350.809 0.000 1343.481 0.000 Prob 1.000 0.000 Coeff 0.000 -0.124 KMI-30 t-stat -0.033 -4.652 99.312 0.000 142.186 0.000 Prob 0.974 0.000 Coeff 0.000 -0.009 ABOT t-stat -0.056 -0.351 68.153 0.000 21.065 0.176 Prob 0.956 0.726 Coeff 0.000 -0.001 AICL t-stat 0.035 -0.021 0.257 0.879 10.160 0.858 Prob 0.972 0.983 Coeff 0.000 -0.011 ABL t-stat -0.053 -0.405 18.319 0.000 25.894 0.056 Prob 0.957 0.686 Coeff 0.000 -0.003 AKBL t-stat -0.030 -0.124 12.96 0.002 27.308 0.038 Prob 0.976 0.901 Coeff 0.000 -0.003 APL t-stat -0.065 -0.102 0.230 0.892 25.060 0.069 Prob 0.948 0.919 Coeff 0.000 0.012 ATRL t-stat -0.098 0.434 42.318 0.000 18.161 0.315 Prob 0.922 0.664

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Table 9.1 (Cont’d) Results of Linear Model for Adjusted Returns

Constant AR(1) Heteroscedasticity LM ARCH Test White noise- Prob. Q-statistics Prob. stat Coeff 0.000 0.007 BAFL t-stat 0.093 0.246 53.222 0.000 34.916 0.004 Prob 0.926 0.806 Coeff 0.000 -0.003 BAHL t-stat -0.061 -0.127 3.363 0.186 37.367 0.002 Prob 0.951 0.899 Coeff 0.000 -0.007 BIPL t-stat -0.075 -0.253 17.739 0.00 16.389 0.426 Prob 0.941 0.800 Coeff 0.000 0.008 BOP t-stat -0.044 0.299 78.941 0.000 36.290 0.000 Prob 0.965 0.765 Coeff 0.000 0.000 DGKC t-stat -0.039 -0.006 75.358 0.000 11.494 0.778 Prob 0.969 0.996 Coeff 0.000 -0.004 DAWH t-stat 0.029 -0.132 0.289 0.865 11.547 0.775 Prob 0.977 0.895 Coeff 0.000 -0.003 DCL t-stat -0.055 -0.122 9.442 0.009 27.508 0.036 Prob 0.956 0.903 Coeff 0.000 -0.004 EFUG t-stat 0.042 -0.159 3.862 0.145 25.362 0.064 Prob 0.967 0.874 Coeff 0.000 -0.001 ENGRO t-stat -0.045 -0.032 1.869 0.393 12.536 0.706 Prob 0.964 0.975 Coeff 0.000 -0.002 EPCL t-stat -0.059 -0.067 39.541 0.000 25.096 0.068 Prob 0.953 0.946

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Table 9.1 (Cont’d) Results of Linear Model for Adjusted Returns

Constant AR(1) Heteroscedasticity LM ARCH Test White noise- Prob. Q-statistics Prob. stat Coeff 0.000 -0.012 FCCL t-stat -0.117 -0.445 12.418 0.002 35.575 0.003 Prob 0.907 0.656 Coeff 0.000 1.000 FFBL t-stat 0.000 1.71E+17 1172.377 0.000 1345.170 0.000 Prob 1.000 0.000 Coeff 0.000 0.001 FFC t-stat -0.054 0.030 0.030 0.985 23.491 0.101 Prob 0.957 0.976 Coeff 0.000 -0.011 FABL t-stat -0.067 -0.412 41.642 0.000 46.819 0.000 Prob 0.947 0.681 Coeff 0.000 0.003 HBL t-stat -0.066 0.097 21.650 0.000 24.739 0.075 Prob 0.947 0.923 Coeff 0.000 -0.005 HMB t-stat -0.060 -0.169 0.791 0.673 23.277 0.107 Prob 0.952 0.866 Coeff 0.000 -0.004 HUBC t-stat 0.099 -0.162 30.427 0.000 35.347 0.004 Prob 0.921 0.871 Coeff 0.000 0.009 ICI t-stat 0.027 0.345 27.973 0.000 16.548 0.415 Prob 0.978 0.730 Coeff 0.000 -0.010 JSBL t-stat -0.096 -0.372 158.638 0.000 35.517 0.003 Prob 0.924 0.710 Coeff 0.000 -0.005 KASBB t-stat 0.039 -0.193 72.214 0.000 21.662 0.154 Prob 0.969 0.847

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Table 9.1 (Cont’d) Results of Linear Model for Adjusted Returns

Constant AR(1) Heteroscedasticity LM ARCH Test White noise- Q- Prob. Prob. stat statistics Coeff 0.000 -0.014 KEL t-stat -0.117 -0.527 18.470 0.000 30.545 0.015 Prob 0.907 0.598 Coeff 0.000 -0.006 KAPCO t-stat -0.087 -0.217 16.156 0.000 30.938 0.014 Prob 0.931 0.829 Coeff 0.000 -0.004 LUCK t-stat -0.058 -0.146 114.797 0.000 18.891 0.274 Prob 0.954 0.884 Coeff 0.000 -0.009 MLCF t-stat -0.102 -0.340 27.352 0.000 24.75531 0.074257 Prob 0.919 0.734 Coeff 0.000 -0.002 MEBL t-stat -0.030 -0.061 114.061 0.000 48.168 0.000 Prob 0.976 0.951 Coeff 0.000 -0.013 NBP t-stat -0.045 -0.483 1.467 0.480 28.283 0.029 Prob 0.964 0.629 Coeff 0.000 -0.002 NRL t-stat -0.055 -0.075 93.808 0.000 30.556 0.015 Prob 0.956 0.941 Coeff 0.000 -0.002 NML t-stat -0.032 -0.057 0.118 0.943 3.463 1.000 Prob 0.975 0.954 Coeff 0.000 0.000 OGDC t-stat -0.081 -0.006 70.036 0.000 21.282 0.168 Prob 0.935 0.995 Coeff 0.000 -0.006 POL t-stat -0.036 -0.234 121.193 0.000 212.319 0.000 Prob 0.971 0.815

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Table 9.1 (Cont’d) Results of Linear Model for Adjusted Returns

Constant AR(1) Heteroscedasticity LM ARCH Test White noise- Prob. Q-statistics Prob. stat Coeff 0.000 -0.003 PSO t-stat 0.063 -0.095 4.429 0.109 11.920 0.749 Prob 0.950 0.924 Coeff 0.000 -0.136 PTCL t-stat 0.001 -5.142 121.193 0.000 212.319 0.000 Prob 0.999 0.000 Coeff 0.000 -0.012 SCBPL t-stat -0.102 -0.435 116.622 0.000 31.545 0.011 Prob 0.918 0.664 Coeff 0.000 -0.003 SHEL t-stat 0.056 -0.115 4.705 0.095 29.442 0.021 Prob 0.955 0.909 Coeff 0.000 -0.004 SNGC t-stat -0.053 -0.164 0.605 0.739 14.945 0.529 Prob 0.958 0.870 Coeff 0.000 -0.008 SSGC t-stat -0.085 -0.313 4.207 0.122 17.095 0.379 Prob 0.932 0.754 Coeff 0.000 0.003 UBL t-stat -0.066 0.105 48.866 0.000 37.820 0.002 Prob 0.948 0.916

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Table 9.2 Result of Non-linear Model for Non-adjusted Returns

Heteroscedasticity LM ARCH Test White noise- Q-

stat Prob. statistics Prob. Coeff 0.001 0.104 1.304 -0.572 KSE- 2.664 2.685 1.173 -0.014 65.644 0.000 19.092 0.264 100 t-stat Prob 0.008 0.007 0.241 0.989 Coeff 0.001 0.058 -1.512 -4.457 KSE- 3.891 1.613 -19.505 -12.658 9.596 0.088 21.938 0.145 ALL t-stat Prob 0.000 0.107 0.000 0.000 Coeff 0.016 -0.860 -22.981 2.340 KSE-30 t-stat 1.969 -1.875 -18.297 18.404 36.728 0.000 281.818 0.000 Prob 0.049 0.061 0.000 0.000 Coeff 0.001 -0.272 0.579 -0.288 KMI-30 t-stat 0.795 -5.612 23.978 -4.463 2.144 0.829 28.656 0.026 Prob 0.427 0.000 0.000 0.000 Coeff 0.001 0.061 0.698 40.775 ABOT t-stat 1.401 1.706 0.872 3.285 87.522 0.000 20.378 0.204 Prob 0.162 0.088 0.384 0.001 Coeff -0.002 0.205 2.119 1.877 AICL t-stat -1.628 5.284 2.075 1.813 0.161 0.999 7.861 0.953 Prob 0.104 0.000 0.038 0.070 Coeff -0.001 0.102 3.258 24.624 ABL t-stat -0.846 3.129 4.217 3.747 54.074 0.000 29.872 0.019 Prob 0.398 0.002 0.000 0.000 Coeff 0.000 0.132 0.363 -2.321 AKBL t-stat -0.197 3.936 0.630 -0.595 21.754 0.001 25.494 0.062 Prob 0.844 0.000 0.529 0.552 Coeff 0.000 0.027 4.401 15.868 APL t-stat -0.442 0.843 5.200 4.769 2.834 0.726 20.418 0.202 Prob 0.658 0.400 0.000 0.000 Coeff 0.000 0.192 2.058 -12.492 ATRL t-stat -0.508 5.793 3.101 -1.392 88.309 0.000 17.870 0.332 Prob 0.612 0.000 0.002 0.164

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Table 9.2 (Cont’d) Result of Non-linear Model for Non-adjusted Returns

Heteroscedasticity LM ARCH Test White noise- Q-

stat Prob statistics Prob Coeff 0.000 -0.035 -0.177 28.037 BAFL t-stat 0.585 -0.959 -0.353 3.735 70.608 0.000 29.479 0.021 Prob 0.559 0.338 0.724 0.000 Coeff 0.000 0.037 0.329 -0.153 BAHL t-stat 0.312 1.037 0.475 -0.061 3.543 0.617 36.260 0.003 Prob 0.755 0.300 0.635 0.952 Coeff 0.000 -0.051 0.582 0.090 BIPL t-stat -0.484 -1.383 1.402 0.024 21.681 0.001 30.491 0.016 Prob 0.629 0.167 0.161 0.981 Coeff -0.002 0.138 1.234 -4.030 BOP t-stat -1.595 3.564 3.215 -0.869 88.537 0.000 44.986 0.000 Prob 0.111 0.000 0.001 0.385 Coeff 0.000 -0.003 0.788 69.163 DGKC t-stat 0.483 -0.057 1.097 3.653 71.340 0.000 14.517 0.560 Prob 0.629 0.955 0.273 0.000 Coeff -0.002 0.208 2.044 1.393 DAWH t-stat -1.492 4.359 1.458 1.327 1.082 0.897 10.519 0.838 Prob 0.136 0.000 0.145 0.185 Coeff 0.001 -0.068 -0.006 -0.156 DCL t-stat 0.382 -2.065 -0.050 -0.466 13.523 0.019 31.425 0.012 Prob 0.703 0.039 0.960 0.641 Coeff -0.002 0.212 2.885 8.177 EFUG t-stat -2.326 7.354 3.926 2.798 19.768 0.001 26.385 0.049 Prob 0.020 0.000 0.000 0.005 Coeff -0.001 0.133 3.121 11.231 ENGRO t-stat -1.842 4.542 4.161 3.403 9.083 0.106 8.144 0.944 Prob 0.066 0.000 0.000 0.001 Coeff -0.001 0.058 1.602 0.035 EPCL t-stat -1.667 1.422 2.602 0.003 62.955 0.000 22.684 0.122 Prob 0.096 0.155 0.009 0.998

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Table 9.2 (Cont’d) Result of Non-linear Model for Non-adjusted Returns

Heteroscedasticity LM ARCH Test White noise- Q-

stat Prob statistics Prob Coeff 0.001 0.041 -0.159 -9.907 FCCL t-stat 1.397 1.165 -0.395 -2.407 23.774 0.000 57.456 0.000 Prob 0.163 0.244 0.693 0.016 Coeff 0.000 0.059 1.933 3.061 FFBL t-stat 0.032 1.688 3.091 0.343 108.825 0.000 35.621 0.003 Prob 0.974 0.092 0.002 0.731 Coeff 0.000 0.150 0.330 0.230 FFC t-stat 0.356 4.204 0.589 0.158 1.210 0.944 18.478 0.297 Prob 0.722 0.000 0.556 0.875 Coeff -0.001 0.072 1.416 21.159 FABL t-stat -1.230 1.934 3.135 3.720 77.267 0.000 41.335 0.000 Prob 0.219 0.053 0.002 0.000 Coeff 0.000 0.110 1.320 1.533 HBL t-stat 0.178 3.389 1.669 0.323 36.276 0.000 21.169 0.172 Prob 0.859 0.001 0.095 0.746 Coeff -0.001 0.034 2.165 10.357 HMB t-stat -1.226 1.062 2.471 1.913 8.129 0.149 19.983 0.221 Prob 0.221 0.289 0.014 0.056 Coeff -0.001 0.071 -0.825 17.681 HUBC t-stat -1.554 1.965 -1.288 1.460 69.769 0.000 34.086 0.005 Prob 0.120 0.050 0.198 0.145 Coeff 0.000 0.143 2.584 35.467 ICI t-stat 0.123 3.448 3.290 1.850 47.783 0.000 13.083 0.667 Prob 0.902 0.001 0.001 0.065 Coeff -0.002 -0.119 0.646 5.084 JSBL t-stat -1.396 -3.767 1.599 2.725 103.257 0.000 38.007 0.002 Prob 0.163 0.000 0.110 0.007 Coeff -0.002 -0.137 0.121 3.048 KASBB t-stat -1.822 -3.817 0.440 1.487 82.814 0.000 27.869 0.033 Prob 0.069 0.000 0.660 0.137

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Table 9.2 (Cont’d) Result of Non-linear Model for Non-adjusted Returns

Heteroscedasticity LM ARCH Test White noise- Q-

stat Prob statistics Prob Coeff 0.001 -0.046 0.430 -3.723 KEL t-stat 0.485 -1.389 2.242 -4.749 11.367 0.045 35.470 0.003 Prob 0.628 0.165 0.025 0.000 Coeff 0.000 0.055 0.009 -7.187 KAPCO t-stat 0.931 1.541 0.011 -0.533 37.355 0.000 28.967 0.024 Prob 0.352 0.124 0.992 0.594 Coeff 0.002 -0.035 -0.294 81.844 LUCK t-stat 2.736 -0.867 -0.369 4.175 111.054 0.000 20.884 0.183 Prob 0.006 0.386 0.712 0.000 Coeff 0.001 0.009 0.301 -1.593 MLCF t-stat 0.844 0.274 0.745 -0.642 39.010 0.000 40.435 0.001 Prob 0.399 0.784 0.456 0.521 Coeff 0.000 -0.066 1.784 35.519 MEBL t-stat -0.487 -1.733 3.098 3.973 146.044 0.000 37.660 0.002 Prob 0.627 0.083 0.002 0.000 Coeff -0.001 0.173 1.297 2.193 NBP t-stat -0.851 5.059 1.496 0.641 9.987 0.076 24.956 0.071 Prob 0.395 0.000 0.135 0.521 Coeff 0.000 0.139 1.876 1.412 NRL t-stat -0.597 3.120 2.439 0.068 101.174 0.000 24.965 0.070 Prob 0.551 0.002 0.015 0.946 Coeff -0.001 0.077 1.767 1.417 NML t-stat -0.568 1.658 1.389 1.336 0.737 0.981 3.037 1.000 Prob 0.570 0.098 0.165 0.182 Coeff 0.001 0.092 -0.172 -6.504 OGDC t-stat 2.447 2.525 -0.189 -0.331 87.979 0.000 23.505 0.101 Prob 0.015 0.012 0.850 0.741 Coeff 0.001 0.010 2.158 44.368 POL t-stat 1.167 0.235 2.805 1.934 149.431 0.000 23.726 0.096 Prob 0.243 0.814 0.005 0.053

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Table 9.2 (Cont’d) Result of Non-linear Model for Non-adjusted Returns

Heteroscedasticity LM ARCH Test White noise- Q-

stat Prob statistics Prob Coeff 0.000 0.097 1.707 6.982 PSO t-stat 0.077 2.990 2.076 1.193 24.991 0.000 13.656 0.624 Prob 0.939 0.003 0.038 0.233 Coeff -0.002 0.017 0.187 -0.065 PTCL t-stat -0.900 0.184 27.417 -5.659 1.890 0.756 6.182 0.986 Prob 0.368 0.854 0.000 0.000 Coeff 0.000 -0.193 1.220 23.659 SCBPL t-stat -0.393 -5.150 2.675 3.754 87.548 0.000 31.135 0.013 Prob 0.694 0.000 0.008 0.000 Coeff 0.000 0.172 -0.125 -3.953 SHEL t-stat -0.131 5.540 -0.163 -0.921 22.104 0.001 33.457 0.006 Prob 0.896 0.000 0.871 0.357 Coeff -0.001 0.115 1.495 8.033 SNGC t-stat -1.175 3.747 1.852 1.675 9.712 0.084 11.607 0.771 Prob 0.240 0.000 0.064 0.094 Coeff -0.001 0.016 2.027 7.283 SSGC t-stat -0.772 0.488 3.033 1.921 10.211 0.069 8.941 0.916 Prob 0.440 0.626 0.003 0.055 Coeff 0.001 0.106 -0.423 -7.931 UBL t-stat 2.004 3.065 -0.600 -0.816 112.392 0.000 47.092 0.000 Prob 0.045 0.002 0.548 0.415

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Table 9.3 Result of Non-linear Model for Adjusted Returns

Heteroscedasticity LM ARCH Test White noise- Prob Q-statistics Prob stat Coeff 0.000 0.000 0.023 -1.957 KSE-100 t-stat -0.028 0.009 0.023 -0.062 62.404 0.000 19.323 0.252 Prob 0.978 0.993 0.982 0.951 Coeff 0.000 -0.003 0.078 -0.244 KSE-ALL t-stat -0.074 -0.096 0.946 -1.069 10.598 0.060 20.276 0.208 Prob 0.941 0.924 0.344 0.285 Coeff -0.004 -0.028 -0.001 0.000 KSE-30 t-stat -0.061 -0.491 -0.258 0.685 15.419 0.009 199.042 0.000 Prob 0.952 0.624 0.797 0.493 Coeff -0.001 0.149 1.346 0.987 KMI-30 t-stat -0.733 2.666 7.148 6.997 0.305 0.998 13.093 0.666 Prob 0.464 0.008 0.000 0.000 Coeff 0.001 -0.005 -1.805 -1.556 ABOT t-stat 1.198 -0.160 -2.632 -0.157 1350.171 0.000 18.574 0.291 Prob 0.231 0.873 0.009 0.876 Coeff 0.000 0.003 0.185 0.147 AICL t-stat -0.095 0.080 0.226 0.222 0.198 0.999 9.080 0.910 Prob 0.925 0.936 0.821 0.824 Coeff 0.000 0.006 -0.924 -6.039 ABL t-stat 0.532 0.202 -1.237 -1.156 38.194 0.000 29.868 0.019 Prob 0.595 0.840 0.216 0.248 Coeff -0.018 0.946 -1.856 0.500 AKBL t-stat -3.294 8.231 -7.905 5.739 1181.550 0.000 23.176 0.109 Prob 0.001 0.000 0.000 0.000 Coeff 0.000 -0.003 -0.585 -2.057 APL t-stat 0.229 -0.089 -0.662 -0.625 2.523 0.773 23.512 0.101 Prob 0.819 0.929 0.508 0.532 Coeff 0.000 0.016 -0.260 -0.697 ATRL t-stat 0.180 0.459 -0.483 -0.113 68.332 0.000 17.061 0.382 Prob 0.857 0.646 0.629 0.910

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Table 9.3 (Cont’d) Result of Non- linear Model for Adjusted Returns Heteroscedasticity LM ARCH Test

White noise- Q- Prob Prob stat statistics Coeff 0.000 0.016 0.073 -1.949 BAFL t-stat 0.031 0.432 0.148 -0.279 55.049 0.000 35.207 0.004 Prob 0.975 0.666 0.882 0.781 Coeff 0.000 -0.007 -0.156 -0.448 BAHL t-stat 0.023 -0.197 -0.230 -0.191 3.644 0.602 36.720 0.002 Prob 0.982 0.844 0.818 0.849 Coeff 0.000 -0.011 -0.021 0.330 BIPL t-stat -0.052 -0.303 -0.054 0.099 20.609 0.001 17.876 0.331 Prob 0.959 0.762 0.957 0.921 Coeff 0.000 -0.002 0.072 2.179 BOP t-stat -0.159 -0.058 0.217 0.629 80.911 0.000 33.661 0.006 Prob 0.874 0.954 0.828 0.529 Coeff 0.000 -0.024 -0.026 9.852 DGKC t-stat -0.018 -0.517 -0.035 0.478 60.776 0.000 12.427 0.714 Prob 0.986 0.605 0.972 0.633 Coeff 0.001 -0.013 -0.051 -0.008 DAWH t-stat 0.128 -0.258 -0.165 -0.158 1.591 0.810 10.658 0.830 Prob 0.898 0.796 0.869 0.875 Coeff 0.000 -0.003 0.010 -0.010 DCL t-stat -0.073 -0.092 0.092 -0.035 13.556 0.019 27.551 0.036 Prob 0.942 0.927 0.927 0.972 Coeff 0.000 -0.005 0.105 0.332 EFUG t-stat -0.053 -0.187 0.165 0.167 12.918 0.024 27.041 0.041 Prob 0.958 0.852 0.869 0.867 Coeff 0.000 0.005 0.005 -0.021 ENGRO t-stat -0.037 0.156 0.007 -0.008 6.420 0.267 9.983 0.868 Prob 0.970 0.876 0.995 0.994 Coeff 0.000 0.009 -0.183 -1.240 EPCL t-stat 0.123 0.218 -0.318 -0.130 54.471 0.000 27.194 0.039 Prob 0.902 0.828 0.751 0.897

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Table 9.3 (Cont’d) Result of Non-linear Model for Adjusted Returns Heteroscedasticity LM ARCH Test

White noise- Q- Prob Prob stat statistics Coeff 0.000 -0.014 -0.055 -0.273 FCCL t-stat -0.051 -0.387 -0.142 -0.072 16.236 0.006 30.446 0.016 Prob 0.960 0.699 0.887 0.942 Coeff 0.000 1.000 0.000 0.000 FFBL t-stat -1.565 1.03E+17 4.685 13.668 1196.753 0.000 1368.385 0.000 Prob 0.118 0.000 0.000 0.000 Coeff 0.000 0.007 -0.007 -0.047 FFC t-stat -0.051 0.181 -0.013 -0.043 0.954 0.966 22.596 0.125 Prob 0.959 0.856 0.989 0.966 Coeff 0.001 0.035 -0.716 -9.233 FABL t-stat 0.657 0.954 -1.575 -1.822 64.019 0.000 38.557 0.001 Prob 0.511 0.340 0.116 0.069 Coeff 0.000 0.006 -0.613 -3.018 HBL t-stat 0.312 0.182 -0.852 -0.845 38.645 0.000 23.285 0.106 Prob 0.755 0.855 0.395 0.399 Coeff 0.000 -0.001 -0.252 -1.258 HMB t-stat 0.100 -0.018 -0.290 -0.244 6.909 0.227 23.573 0.099 Prob 0.920 0.985 0.772 0.807 Coeff 0.000 -0.003 0.080 -0.430 HUBC t-stat 0.046 -0.087 0.128 -0.038 71.000 0.000 35.317 0.004 Prob 0.964 0.930 0.898 0.970 Coeff 0.000 0.015 0.047 -3.186 ICI t-stat -0.009 0.377 0.066 -0.225 35.279 0.000 13.493 0.636 Prob 0.993 0.707 0.948 0.822 Coeff 0.000 -0.063 -0.525 5.233 JSBL t-stat 0.347 -1.872 -1.468 2.795 61.840 0.000 34.693 0.004 Prob 0.728 0.061 0.142 0.005 Coeff 0.000 -0.026 -0.066 1.175 KASBB t-stat 0.112 -0.721 -0.277 0.759 94.346 0.000 25.276 0.065 Prob 0.911 0.471 0.782 0.448

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Table 9.3 (Cont’d) Result of Non-linear Model for Adjusted Returns Heteroscedasticity LM ARCH Test

White Q- Prob Prob noise-stat statistics Coeff 0.000 -0.024 0.012 0.138 KEL t-stat -0.144 -0.725 0.066 0.192 12.767 0.026 29.874 0.019 Prob 0.886 0.469 0.948 0.848 Coeff 0.000 0.002 -0.597 -6.120 KAPCO t-stat 0.194 0.045 -0.715 -0.499 30.900 0.000 30.812 0.014 Prob 0.846 0.964 0.475 0.618 Coeff 0.000 0.020 0.210 -15.364 LUCK t-stat -0.172 0.462 0.269 -0.751 99.949 0.000 18.229 0.311 Prob 0.863 0.644 0.788 0.453 Coeff 0.000 -0.009 -0.105 0.311 MLCF t-stat 0.027 -0.269 -0.267 0.128 34.963 0.000 24.627 0.077 Prob 0.979 0.788 0.789 0.898 Coeff 0.000 0.026 -0.562 -9.512 MEBL t-stat 0.397 0.712 -0.970 -1.273 133.811 0.000 37.458 0.002 Prob 0.691 0.477 0.332 0.203 Coeff 0.000 -0.015 -0.439 -1.222 NBP t-stat 0.276 -0.426 -0.580 -0.493 5.695 0.337 27.281 0.038 Prob 0.782 0.670 0.562 0.622 Coeff 0.000 0.037 -0.444 -14.910 NRL t-stat 0.268 0.866 -0.632 -0.991 95.391 0.000 27.507 0.036 Prob 0.789 0.387 0.528 0.322 Coeff 0.000 -0.006 -0.159 -0.119 NML t-stat 0.051 -0.120 -0.134 -0.130 0.813 0.976 2.985 1.000 Prob 0.959 0.904 0.894 0.897 Coeff 0.000 0.005 0.218 -4.062 OGDC t-stat -0.184 0.133 0.266 -0.240 87.769 0.000 20.786 0.187 Prob 0.854 0.894 0.790 0.811 Coeff 0.000 0.007 -0.289 -8.766 POL t-stat 0.128 0.158 -0.350 -0.374 152.179 0.000 260.706 0.000 Prob 0.898 0.875 0.726 0.708

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Table 9.3 (Cont’d) Result of Non-linear Model for Adjusted Returns Heteroscedasticity LM ARCH Test

White Q- Prob Prob noise-stat statistics Coeff 0.000 -0.003 -0.138 -0.727 PSO t-stat 0.147 -0.108 -0.177 -0.148 22.030 0.001 11.097 0.803 Prob 0.883 0.914 0.860 0.883 Coeff 0.000 0.000 -0.224 -0.077 PTCL t-stat 0.046 -0.003 -0.110 -0.110 2.248 0.690 5.279 0.994 Prob 0.963 0.998 0.912 0.912 Coeff 0.000 -0.014 -0.386 -0.329 SCBPL t-stat 0.371 -0.364 -1.035 -0.079 91.465 0.000 25.346 0.064 Prob 0.711 0.716 0.301 0.937 Coeff 0.000 0.023 0.011 -2.438 SHEL t-stat -0.019 0.725 0.017 -0.788 16.727 0.005 30.348 0.016 Prob 0.985 0.469 0.987 0.431 Coeff 0.000 0.003 -0.233 -1.113 SNGC t-stat 0.125 0.087 -0.315 -0.286 6.480 0.262 16.061 0.449 Prob 0.901 0.930 0.753 0.775 Coeff 0.000 0.009 -0.700 -3.466 SSGC t-stat 0.436 0.300 -1.005 -0.907 7.997 0.156 18.534 0.294 Prob 0.663 0.765 0.315 0.365 Coeff 0.000 0.011 -0.220 -2.606 UBL t-stat 0.101 0.327 -0.344 -0.345 96.410 0.000 35.403 0.004 Prob 0.920 0.744 0.731 0.730

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Chapter 10 Conclusion and Recommendations

This chapter comprises of summary and conclusion of the results presented from chapter 6 to 9, policy implications and suggestions for the investor and researcher and limitations of the study.

10.1 Summary and Conclusion

This particular research is a methodological triangulation20 and aimed at investigating weak- form efficiency within the framework of RWH in Karachi stock market by examining all four indices operational in KSE, in 43 individual firms selected on the basis of non zero trading on at least 95% of the total trading days during the study period taken from January 01, 2009- August 31, 2014. In order to check the RW among the indices and firms both non-parametric (K-S, runs) tests and parametric test (serial correlation, ADF, PP and KPSS, AR models) are employed on return series of indices and selected firms. Variance ratio test of Lo and MacKinlay (1988) is also applied to test the hypothesis.

Presence of market efficiency implies that past price movements cannot predict future prices, thus limiting the chances of abnormal profits in the stock market. This particular behaviour of market discourages market makers and limits the influence of manipulators thereby; promote investors’ confidence which in turn could generate capital and liquidity thereby induces economic growth and development.

Results of descriptive statistics reveal that all of the return series tested have positive and negative mean values and do not follow normal distribution with skewed tails on both sides and leptokurtic (positive excess kurtosis) peaks. Very high values of kurtosis especially in

20 Denzin (1984) identified four types of triangulation approaches: Data source triangulation, when the researcher looks for different data to remain the same in different contexts; Investigator triangulation, when several investigators examine the same phenomenon; Theory triangulation, when investigators with different viewpoints interpret the same results; and Methodological triangulation, when one approach is followed by another, to increase confidence in the interpretation.

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case of DAWH (646.5), NML (620.4) and PTCL (647.1) imply thin tails and acute peaks. Non-parametric K-S further confirms that series do not follow normal distribution. The test also verifies the same for uniform distribution. The results of runs test show the affinity of over-reaction in indices implies spontaneous reaction to unanticipated and shocking news in all four indices concluding the absence of RW in all four indices. However, in case of 28 out of 43 selected firms the null hypothesis cannot be rejected reveals likeliness of RW in stock returns.

Autocorrelation test was applied on the return series which also reaffirms the rejection of random walk for all indices and for majority of the firms. Evidence of over and under- reaction has been found. LB statistics confirms the results of autocorrelation test. In case of seven firms however, the hypothesis cannot be rejected. Overall negative autocorrelation is found in Karachi stock market suggests the over-reaction to unexpected news and information seems to be the strategy to earn above normal returns. The investors may adopt mean reversion strategy of buying the stocks which had lower returns in the past in the expectations of higher returns today and selling the stocks having higher returns previously in expectations of lower returns in future.

Autoregression test complemented by heteroscedasticity and LM test ascertain the absence of random walk and in return series of indices and selected firms by rejecting the null hypothesis of random walk. Similarly, presence of heteroscedasticity implies series do not follow random walk. The RW however, cannot be rejected for AICL, APL and BAHL stock returns.

Stationarity and presence of unit root and in the series implies the absence of RW in the return series. ADF, PP and KPSS test result found the presence of unit root at level, while the series becomes non-stationary at first level for KSE-100, the same applies for most of the firms. On the other hand, KSE-30, KMI-30 found to be following RW and same can be found for APL, FFC, HUBC, MEBL, NBP, OGDC and POL (7 out of 43 firms). A more reliable variance ratio test is used to ascertain the presence or absence of random walk on KSE.

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Both positive and negative autocorrelation is found in the return series of indices and individual stocks. KSE-100 shows negative autocorrelation, while KMI-30 is positively autocorrelated. Majority of the firms have been found to possess negative correlation and profits are earned by mean reversion trend. For KSE-30 and for 10 other firms the null hypothesis of random walk cannot be rejected revealing unpredictability in KSE-30 and among these few firms. Nonetheless, few of the firms found to be positively correlated. Therefore, it can be concluded that large investors earn profits by over-reaction and small investors by trend-chasing in the KSE market. In case of stationary series ARMA models are reliable over simple regression models. Significant values of ARMA (0, 1), ARMA (0,1) and ARMA(1,0) reveal the rejection of random walk in most of the firms.

The table 10.1 and 10.2 provide the presence of RW among the indices and selected firms by employing the above mentioned test. It can be found that KSE-100 and indices reject the random walk hypothesis while KSE-30 and KMI-30 indices found to have no unit root. Similarly zero autocorrelation was found in KSE-30 for various lags. Therefore, tendencies of random walk can be concluded in these two indices. The credit may be attributed to free float methodology of shares in these indices. However, 18 out of 43 firms including ABOT, APL, BAHL, EFUG, FFC, HMB, HUBC, KAPCO, MICF, MEBL, NBP, NML, ODGC, POL, PSO, SHEL SNGC and SSGC found acceptance of RWH in 3 or more tests applied.

Seasonal anomalies entails the predictability of returns through certain market movements on given days would mean absence of RW in the market. The use of the dummy variable approach in regression is used where each individual dummy variable accounts for the excess return for the particular day/month/TOM days, for determining DOW, MOY and TOM effects.

Significant negative positive Monday and Friday effect is established for KSE-100. Wednesday and Friday returns are significant at 5% and 1%, respectively. Monday is significant on KMI-30 index. However, no DOW effects are found in KSE-30 index. Conventional Monday negative and Friday positive, effect is prominent in the market at 5% or lower levels. Very few firms exhibit no DOW effects during the study period. The absence

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of DOW effects in KSE-30 again can be credited to free float of shares in the index. The significant value of lag of dependent variable in all indices and in most of the firms ascertain the short run relationship between the returns with its lag variable implies the exploitation of abnormal returns on the basis of short run anticipation. The short run dependency of return with lag values and presence of DOW effects in most of the firms reveals absence of random walk in the market.

Although different months are significant for different stock firms, but conventional positive January effect can be concluded at index level for KSE-100, , KSE-30 and for KMI-30 indices. Positive January and July effects are prominent for many of the firms. July effect can be credited to the availability of funds at the start of fiscal year in Pakistan. Firms publish annual reports with the new prospects and positive anticipations about future reducing the information gap on one hand and generating confidence on the other, among the investors.

In KSE-100, and KSE-all shares index, TOM effect is found significant at 5% or lower level. No TOM effects are found in case of KSE-30 and KMI-30 indices. Individual selected firms also confirm the significant returns. In 24 out of 43 selected returns are higher and positive in TOM days. It can be concluded that seasonal anomalies are present in the stock market in all indices and in stock firms. Profit exploitation tendencies are available in the market and the likeliness of price prediction cannot be excluded from the market. Nonetheless, KSE-30 is exhibiting exceptional results as compared to the rest of the indices. KSE-30 is comparatively a new index reflecting the true marginalization of shares in the market at a certain point in time.

Table 10.3, provides the result of significant days, months and TOM periods during the study period at Karachi stock market. Table 10.4 reflects the count on which, a particular day, a particular month and a particular TOM period is significant. Hence, related trading strategies in the market on selected periods to attain higher than normal profits.

Existence of significant seasonal anomalies would mean violation of random walk and weak- form efficiency; returns are not independent and can be predicted by specific market trends.

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Hence, in such market adopting trading strategies accordingly would result in fairly high profits to investors.

Presence of volatility clustering would mean that price changes are not independent. Volatility clustering is reflected by the results of ARCH and GARCH analysis. Significant ARCH and GARCH effects are found in Karachi stock market with various levels of persistence. ARCH plus GARCH coefficients are less than one reveals presence of volatility clustering in the market, with exceptions in few firms’ returns. High volatility clustering with slow mean reversion is found prominent in the studied market. It can also be concluded that KSE-100 index return series exhibit slow decay with sharp peaks. On the other hand in case of KSE-30 the index is less spiky peaks with temporary shock that die out quickly are depicted. In the presence of volatility clustering, it is concluded that Karachi stock market returns do not follow random walk and higher than normal returns can be realized by smarter than normal investors.

Investigations on non-linear models for return series reveal significant departures from weak- form efficiency and random walk. Return series found to have possessed autocorrelation in non-linear models. Returns corrected for thin trading both linear and non-linear permits the market to have removed weak-form inefficiency from all four indices and majority of the selected firms. It can be concluded that corrected returns for thin-trading suggested by Miller at el. (1994) depict a major impact of thin-trading on market efficiency. Returns adjusted for thin-trading in both linear and non-linear models provide supportive evidence of presence of weak-form efficiency in Karachi stock market.

In brief, it is inferred by the empirical results to reject the RWH for indices of Karachi stock market and for majority of the firms selected over the study period, with marked exemptions for KSE-30, where the index provides the supportive indication for the existence of WF efficiency as evident from autocorrelation, unit root and variance ratio tests and from the absence of DOW and TOM effects. It is concluded therefore, that for KSE-30 index the evidence found in the study supports the weak-form efficiency. Hence, it can be said that KSE does not follow random walk with exception to KSE-30 index. Supplementary research

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on KSE-30 index is however suggested by using a diversified approach and by analyzing weekly and monthly data for the corroboration of the results presented in the study.

10.2 Implications for the Investors

The conclusion of the study implies that the market has a tendency to outperform if appropriate trading strategies would be adopted by the investor. The investor seeking mis- priced securities have the opportunity to realize gains instead of searching for the optimum risk-return portfolio selection.

10.3 Suggestions and Recommendations

Over the years KSE has developed state of the art technical support system for the investors and brokers domestically and internationally. The launch of VPN has not only spread the activities of KSE, but at the same time enhanced the transparency of process equally for domestic and foreign investor. However, following measurements are suggested for the improvements in the level of information and to enhance the transparency of processes in the market. i. Information lag can be reduced by making public information free of cost. ii. Companies registered in stock exchange should be asked to publish detailed performance reports quarterly for their share holders. iii. Improvement in the regulatory authorities’ supervision and proper check and balances should be ensured. iv. The credibility of the information provided in the performance report should be ensured. v. Transaction cost should be reduced to attract small investor in the market at the same time to improve the liquidity in the share market. vi. The role of brokers and dealers should be made limited to their registered activities only. vii. Implementation of corporatization and demutualization act 2012 in its true sprit to avoid brokerage malpractices and to restrain insiders influence in the market.

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viii. A reduction in the settlement time length may reduce the speculative practices in the market. ix. The development of innovative and diversified range of products in the market will not only increase the options to the investor, at the same time help maintaining optimum risk-profit investment portfolio for the investor. For that matter research and development (R&D) should be promoted and the budget for R&D should be increased. x. Last, but not the least; improvements in macroeconomic indicators, promoting investment-conducive environment, and improvements in the law and order situation are mandatory conditions for the advancement of stock market and for the economic growth, as well.

10.4 Limitations of the Thesis

i. The study has used various models for the detection of WF efficiency. The validity of the results found depends on the extent to which these models estimate the true market. No doubt, the models used here have been empirically tested number of times before; still there is no assurance that they are equally good for making inferences on the type of market discussed here. ii. The result obtained and inferences are drawn on the basis of sample firms, and the results are assumed to generalize the trends of the whole market. Similarly, the sample of firms that are used here are based on the criterion of trading days up to 95% of the total trading days. However, the impact of infrequent trading present during a single day cannot be realized due to non-availability of data that could separate the effect of intraday thin trading. iii. The return series in question do not follow normal and uniform distribution was revealed, but no further test was conducted to investigate the nature of the distribution they follow. iv. The research framework that is used in this study focuses on whether the hypothesis of random walk can be rejected or not; looking at the efficiency in absolute terms. Efficiency is a continuous process rather than a discrete one. Therefore a study

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that has the tendency to instigate an evolving process of efficiency would be more prolific in nature. v. Significant correlation in the return series would demand for minute by minute data to be analyzed to detect mis-reaction to information in the market. On account of the non-availability of such data, daily returns are used.

10.5 Suggestions for Future Research

i. Efficiency determination is not the end point rather it initiates many other questions whose answers must be explored in further research. For example, it is equally imperative to estimate the speed with which new information is incorporated into the price system, to explore the span of over-and under reaction to information. ii. Economic growth is considered to be another important implication of efficient markets. It is expected that efficiency of stock market would have positive ramifications on long term growth. Empirical work of Atje & Jovanovic (1993) Levine & Zervos (1998) and Beck & Levine (2004) have found significant role of stock market liquidity in promoting economic growth. However, according to them existing evidence is not enough to establish a concrete link between stock market liquidity and economic growth. Therefore, further research is needed as without any connection between market efficiency and economic growth the importance of efficiency would be fruitless. iii. Dynamic approach for finding efficiency should be adopted, since efficiency is an evolving process over time and with the changes in the structural changes in the market. For example, intensity of openness of the market, changes in the regulatory framework as with the implementation of demutualization Act 2012, KSE is anticipated to be more transparent and the insiders influence in maneuvering the market is less likely to occur. This would have positive implication on efficiency stance of the stock market.

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Table 10.1 Summary of the Results for Random Walk

Ljung Variance Runs Autocorrelation Box AR(1) Heteroscedasticity LM Ratio Test Test Stat Test Test KSE -

100 KSE-30 RW KSE-

ALL KMI-30 ABOT RW AICL RW RW RW ABL AKBL RW APL RW RW RW RW RW ATRL BAHL RW RW RW RW RW BAFL RW BIPL RW BOP DGKC DAWH RW RW DCL RW EFUG RW RW RW ENGRO RW RW EPCL RW RW FCCL RW RW FFBL FFC RW RW RW RW FABL RW

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Table 10.1 (Cont’d) Summary of the Results for Random Walk Ljung Variance Runs Autocorrelation Box AR(1) Heteroscedasticity LM Ratio Test Test Stat Test Test HBL RW HMB RW RW RW RW RW RW HUBC RW ICI RW JSBL RW KASBB KEL KAPCO RW RW RW LUCK RW MLCF RW RW RW RW MEBL RW RW NBP RW RW RW NRL NML RW RW RW RW RW OGDC RW RW PTCL RW POL RW PSO RW RW RW SHEL RW RW RW SCBP SNGC RW RW RW SSGC RW RW RW RW RW UBL RW

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Table 10.2 Summary of the Results of Unit Root Tests for Random Walk ADF PP KPSS Indices/ ADF PP KPSS Level Level Level Firms Level Level Level KSE- 100 HBL KSE-30 RW RW HMB KSE- All HUBC RW RW RW KMI-30 RW RW RW ICI ABOT JSBL AICL KASBB ABL KEL AKBL KAPCO APL RW RW LUCK ATRL MLCF BAHL MEBL RW RW RW BAFL NBP RW RW BIPL NRL RW BOP NML DGKC OGDC RW RW DAWH PTCL DCL POL RW RW EFUG PSO ENGRO SHEL EPCL SCBP FCCL SNGC FFBL SSGC FFC RW RW UBL FABL

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Table 10.3 Significant Days/Months/TOM periods on KSE Returns

Mo Tu We Th F Ja Fe M A M Ju J Au Se O No De TO n e d u ri n b ar pr ay n ul g p ct v c M KSE- Si Sig 100 g KSE- Si

30 g KSE- Si Sig All g KMI Si

-30 g ABO Si Si

T g g AIC Si

L g Si Sig ABL g AKB Sig L Si Sig APL g ATR Si Si Sig L g g BAH Sig Sig L BAL

F BIPL BOP DGK Si Si Sig C g g DA

WH DCL Sig EFU Si

G g EPC Si Sig L g FCC Sig L FFB Sig L Si Si

FFC g g

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Table 10.3 (Cont’d) Significant Days/Months/TOM periods on KSE Returns

Mo T We Th F Ja Fe M A M Ju J Au Se O No D TO n ue d u ri n b ar pr ay n ul g p ct v ec M FAB

L Si Si Sig HBL g g HMB Sig HUB Si Si Sig C g g Si Sig ICI g JSBL KAS Si

BB g KEL KAP Si Si Sig CO g g LUC Si Sig K g MLC Si Si

F g g MEB Sig L Si Si Sig Sig NBP g g NRL Sig Si

NML g OGD Sig C PTC

L POL Sig Sig PSO Sig SHE Si Sig L g SCBP SNG Si Sig C g Si Si Sig SSGC g g Si

UBL g

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Table 10.4 No. of Significant Days/Months/TOM periods on KSE Returns Day/Month/TOM Significant Monday 7 Tuesday 3 Wednesday 7 Thursday - Friday 15 January 10 February 3 March 7 April 2 May 3 June 3 July 9 August 5 September 1 October 3 November 1 December 1 TOM 24

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