stock market final
TRANSCRIPT
Table of Contents1.INTRODUCTION....................................................................................2
1.1 Structure of the Report.......................................................................41.2 Limitation of study............................................................................5
2.BACKGROUND......................................................................................62.1 Pakistan..............................................................................................6
2.1.1 Introduction.................................................................................62.1.2 The Structure of the Economy....................................................62.1.3 Overview of the Economy........................................................11
2.2 Financial Market..............................................................................132.2.1 Introduction...............................................................................13
2.3 Karachi Stock Exchange..................................................................162.3.1 Introduction...............................................................................162.3.2 Background...............................................................................172.3.3 KSE Index.................................................................................182.3.4 Performance..............................................................................192.3.5 Investment climate....................................................................202.3.6 Karachi Stock Exchange Trading System................................22
3.LITERATURE REVIEW.......................................................................253.1 Efficient Market Hypothesis............................................................25
3.1.1Weak Form Efficiency...............................................................273.1.3 Strong Form Efficiency............................................................28
3.2 Random Walk..................................................................................293.2.1 Chartist Theories.......................................................................293.2.2Fundamental Analysis Theories................................................30
3.3 Empirical Evidence..........................................................................323.3.1 Developing Market...................................................................323.3.2 Developed Market....................................................................39
3.6 Market Anomalies...........................................................................433.7 Emerging Markets.......................................................................48
4.RESEARCH OBJECTIVES...................................................................524.1 Introduction......................................................................................524.2 Research Objective..........................................................................524.3 Problem Statement...........................................................................524.4 Hypothesis.......................................................................................52
4.4.1Central Hypothesis.....................................................................534.4.2Sub-Hypothesis..........................................................................53
5.Applied Data...........................................................................................545.1 Introduction......................................................................................545.2 Data Required..................................................................................545.3 Data Source......................................................................................54
5.4 Transforming Data Structures into Information..............................555.4.1 Log Data...................................................................................555.4.2 Log Returns..............................................................................555.4.3 Reason for Using Log Data......................................................56
6.METHODOLOGY.................................................................................576.1 Introduction......................................................................................57
6.1.1 Distribution of Returns.............................................................576.1.2 Autocorrelation Function (ACF)..............................................596.1.3 Ljung-Box Test.........................................................................616.1.4 Runs Test..................................................................................616.1.5 Unit Root Test...........................................................................636.1.6 Reason for Choosing Above Mentioned Method.....................65
7.EMPIRICAL RESULT...........................................................................667.1 Descriptive Statistics.......................................................................66
7.1.1 Monthly Returns.......................................................................667.1.2 Weekly Returns........................................................................69
7.2 Autocorrelation................................................................................717.2.1 Monthly Index..........................................................................717.2.2 Weekly Index............................................................................73Graph 4: Weekly Index Correlogram................................................73
7.3 Run Test...........................................................................................747.3.1 Monthly Returns.......................................................................747.3.2 Weekly Returns........................................................................76
7.4 Augmented Dickey Fuller Test (ADF)............................................777.4.1 Monthly Returns.......................................................................777.4.2 Weekly Returns........................................................................79
8.CONCLUSION AND RECOMMENDATION.....................................828.1 Conclusion.......................................................................................828.2 Recommendation.............................................................................83
BIBLIOGRAPHY......................................................................................84APPENDIX: A...........................................................................................89APPENDIX: B...........................................................................................91APPENDIX: C...........................................................................................95APPENDIX: D...........................................................................................99APPENDIX: E.........................................................................................115APPENDIX: F.........................................................................................117
1
CHAPTER 1
1.INTRODUCTION The concept of Efficient Market Hypothesis has been widely debated in all
academic circles ever since it was introduced by Fama (1970). The Eugene
Fama’s (1970) article “Efficient Capital Market” provided the basis for the
Efficient Market Hypothesis.
Efficient market hypothesis states that any given time, security prices fully
reflect all the available information. This means neither historical analysis
nor fundamental analysis can help in predicting future stock prices. In
other words what this theory means that it is impossible to outperform the
market by just choosing the best stock, if an investor wants higher returns
all he needs to do is to take more risk. Stock market efficiency is an
important concept, in terms of an understanding the working of the capital
markets. Fama in (1970 and 1991) provided the formal definition of
“Market efficiency”. It was Fama who gave three classification of market
efficiency, which are as follow
I. Weak Form Efficiency
II. Semi- Strong From Efficiency
III. Strong From Efficiency
According to Efficient market hypothesis a market is said to be weak form
efficient if current prices fully reflect all information contained in
historical prices, and hence no investor can earn abnormal returns based
on past history. We can call a market efficient in semi strong form if stock
prices immediately reflect any new publicly available information. A
market is said to efficient in strong form if stock prices reflect all available
information i.e. private and public.
2
Under efficient market hypothesis we believe that security markets are
highly efficient in reflecting any information that would arise, this
information spreads very rapidly and is soon incorporated into the security
prices without any delays. It is because of this reason neither technical nor
fundamental analysis’ would be able to help investor to earn above
average returns.
When we are talking about efficient market hypothesis it is important that
we talk about “random walk” a concept that is associated with efficient
market theory. Basically the term random walk is used in finance to define
a price series that exhibit; a price change that is different from the
previous one. If we look at the logic of the random walk it states that if the
flow of information is random and unchecked then such information
should be immediately incorporated in the price of the stock. This means
if there is any price change that will occur tomorrow, it will only reflect
tomorrow news and will be independent of prices changes that are going
to take place today. As a result of this the prices of the stock will truly
reflect all known information and any investor who does not have any
knowledge about such information will benefit in the same way, as an
expert will if it invests in diversified portfolio. This means that the margin
of the return on such investment will be the same for both of them.
In this study I will be focusing on our central hypothesis that KSE-100
index follows a Random walk and is weak from efficient. I have chosen
Karachi Stock Exchange, KSE-100 index because ample amount of work
has been down on weak and semi- strong form of market efficiency of
developed markets but a lot needs to be done on emerging markets of
Asian countries. Existing empirical research on market efficiency has been
largely limited to developed markets among the studies are Li and Xu
(2002), Millon and Moschos (2000), Abrosimova, Dissanaike and
3
Linowski (2005), Groenewold and Kang (1993), Al-Loughani and
Chappell (1997), Stengos and Panas (1992) Kendall, (1943, 1953), Fama,
1965. Evidence against Random walk hypothesis can be seen from the
work of Fama and French (1988) and Lo and Mackinlay (1988). Evidence
of studies on developing markets can be obtain from Poshakwale (1996),
Alam, Hasan and Kadapakkam (1999), Abraham, Seyyed and Alsakran
(2002), Narayan and Smyth (2004), Onour (2004), Moustafa (2004)
KSE 100 index has been performing well in recent years and was the
second best stock market in Asia for two consecutive years in terms of
performance. This study is conducted to show the evidence of weak form
of market efficiency for KSE-100 index by using Distribution of Returns,
Auto correlation and Ljung Box Q statistics, Run test, and Augmented
Dickey Fuller (ADF).
I hope this study will help all the rational investors in Pakistan financial
market because market efficiency has an influence on the investment
strategy of an investor.
1.1 Structure of the ReportThis report is organized into following chapters.
Chapter 2 gives the background information relating to Pakistan, its
economy, Karachi Stock Exchange and different tools used in Karachi
Stock Exchange and detail information regarding financial markets.
Chapter 3 is the most important chapter. Here I reviewed past literature
relating to efficient market hypothesis, random walk, emerging market and
market anomalies.
Chapter 4 states the research objective, problem statement and hypothesis
for the study.
4
Chapter 5 describes how data for the study will be obtained; it’s
transformation into meaningful information and which econometrics
software will be used.
Chapter 6 explains different methodology that will be used to test our
central hypothesis that KSE-100 index follows random walk and there
exist a weak –form of market efficiency and reason for choosing these
methodology.
The different methods that will be used are listed below
1. Distribution of returns
2. Autocorrelation and Ljung-Box Q statistics
3. Run test
4. Augmented Dickey Fuller (ADF) Test
Chapter 7 deals with the analysis of empirical result of the study.
Chapter 8 explains the main finding for the study and gives some
recommendation for future study.
1.2 Limitation of studyFollowing are some limitation of the study.
1. Historic data for KSE-100 index was not freely available. I was
only able to gather limited data from yahoo finance for period
ranging from July 1997 on wards. Karachi Stock Exchange and
few stockbrokers in Pakistan were contacted but none of them was
able to provide data before July 1997.
2. Limited knowledge and guidance on how to use econometrics
software did affect this study. As result of which I was not able to
perform Variance Ratio test. This is a strong model, which would
help us to further validate our finding regarding the weak for
efficiency of Karachi Stock Exchange.
5
CHAPTER 2
2.BACKGROUND
2.1 Pakistan
2.1.1 IntroductionThe Islamic republic of Pakistan came into being on 14th August 1947 as
result of division in Indo-Pak subcontinent. It shares its boundaries with
China, Afghanistan, India and Iran.
Pakistan has an area of 796,095 Sq.km with a population of 132.35
million according to a census conducted in 1998. It has four provinces:
North West Frontier Province, Sindh, Punjab and Balochistan .The
national language of Pakistan is Urdu, apart from this national language
there are four other languages which are spoken in four provinces and
they are Punjabi, Sindhi, Phusto and balochi. Punjabi is spoken in
Punjab; Sindhi is spoken in Sindh, Phusto in North West Frontier
Province and Balochi in Balochistan.
Pakistan is enriched with natural resources. “The main natural resources
are natural gas, coal, salt and iron. The country has an expanding
industry. Cotton, Textiles, sugar, cement, and chemicals play an
important role in its economy. It is fed by vast hydroelectric power”
[http://www.pakistan.gov.pk/AboutPakistan.jsp ]
2.1.2 The Structure of the EconomyProbably the most striking feature that is manifested in a view of
Pakistan in 2008 compared to 1947 is that Pakistan today is less than
half of what it was in 1947. In 1949-50, fifty-five percent of Pakistan’s
population lived in the then East Pakistan, making it the majority
province in terms of population. Despite this majority, economically the
6
eastern wing was discriminated against and exploited. A section of the
ruling elite of the western wing of Pakistan became the oppressor and
exploiter of the east Pakistani people, leading to their eventual secession
after a long and painful war of liberation ending in 1971.
The contribution made by East Pakistan to Pakistan’s economy and
society was huge, though never fully recognised or appreciated by West
Pakistanis, hence the fist and perhaps most striking feature of Pakistan, a
fact which many born after 1971 no longer consider, is that Pakistan
today is half of what it was in 1947. Nevertheless, no matter how
significant this loss, post-1971 Pakistan seems to have moved on from
the first twenty-five of its 57-years. In fact, the first 57 years of
Pakistan’s history are conspicuously broken into two eras, Pakistan’s
history are conspicuously broken into two eras, which stand for the
formation of two separate countries.
In 1947, Pakistan had very right to be called an” agriculture” country.
Most observers not fully cognisant with structural changes that have
taken place in recent years, make the serious mistake of still calling
Pakistan an agriculture country even after nearly six decades, when there
is little reason to do so. At the time of independence, the major share of
West Pakistan’s1 Gross Domestic Product was from agriculture, which
contributed around 53 percent, compared to the 7.8 percent from
manufacturing and 11.9 percent from retail trade. More than 65 percent
of Pakistan’s labour force worked in agricultural, and almost all of
Pakistan’s exports consisted of primary products, essentially agricultural
commodities like jute and tea that, not surprisingly, originated from East
Pakistan.
1 Data is take from economic survey of Pakistan
7
Since that time a lot had changed in terms of economic structure of
Pakistan, now agriculture contributes only a 23.6 per cent towards
GDP2, while manufacturing is up to 18.4 percent. The services sector
had replaced agriculture as the dominant sector in the economy,
contributing more than half of total GDP. The population employed in
agriculture has also fallen, although at around 48 per cent of the total
labour force, agriculture is still the biggest sector in terms of the
employed labour force.
More importantly, the nature of exports from Pakistan has also changed
dramatically. From 99.3 percent of total exports in 1947, primary
commodities now constitute around 11 per cent only. However, one
must emphasise the fact that although 77 percent of per cent of
Pakistan’s exports are now manufactured goods, with textiles, garments
and yarn making up most of the exports, these figures are less
impressive when we realise that much of these exports still depend
critically on raw cotton.
Despite this dependence, one cannot strictly call Pakistan a ‘one crop’ I-
e cotton country since the value added share of wheat is almost identical
to that of cotton that is about 30 percent, followed by rice that is 17
percent, sugarcane (16%) and other minor crops which contribute about
17 percent. In addition, with the increase in wheat production over
recent years, Pakistan has also become self-sufficient in wheat and the
issue of food security has, for some years to come, been addressed.
These economic changes in structure are also manifested in where
people live. In 1951 when the first census in independent Pakistan was
help, only 17 percent of West Pakistan population lived in areas
2 S. Akbar Zaidi, issues in Pakistan’s Economy (revised and up-dated second edition) Oxford University Press.
8
designated as urban; today estimates suggest that for more than 40
percent live in cities and towns. This shift has major repercussions,
which affected that economy, society and the current political process.
In fact in the context of Pakistan, perhaps the most important political
factor over the last few decades has been the process and extent of
urbanisation and the emergence, and perhaps consolidation, of a middle
class.
With more than 40 percent of the country’s population living in cities
and towns, the economic profile, in terms of consumption and
production patterns, has also changed quite drastically, and again, the
cliché, that ‘Pakistan is mainly an agricultural economy’, is no longer
true. Urbanisation’s impact on social and economic development is also
very significant, and the extent and process of urbanisation was
considered to be an indicator of progress and modernisation. Although
many latter-day modernisers and develop mentalists may no longer hold
that that assumption is true, one cannot overlook the significant
structural change that has been brought about by the process of
urbanisation in fifty years. While only 6 million inhabitants out of
population of 33.8 million in 1947 were residing in towns and cities,
now more than ten times that number does so. This figure is bound to be
larger since there is now consensus amongst social scientist that a huge
proportion of Pakistan is part of the urban economy and urban culture.
Just as the cliché, that ‘Pakistan is an agricultural country’, is repeated
ad nauseum by analysts of the country’s economy, another myth that
prevails and is related to this is that ‘Pakistan is feudal country’. No
matter how one looks at the facts and observes that manner in which
society has evolved, there is no justification for believing, let alone
repeating, what is perhaps Pakistan’s most popular myth. There is no
9
evidence to support this assertion. The green revolution of the sixties,
with its extraordinary impact on the rural areas, agriculture the economy,
and on the social relation of production, put an end once and for all the
myth that Pakistan is a feudal country.
Feudalism is no longer an economically viable and feasible project at the
farm/landlord level, and many a ‘feudal lord’ has had to become a
capitalist farmer or has then turned to other sources of income. While
feudalism in Pakistan died a very long time ago, modern day Pakistan
has seen the demise of agriculturists as a powerful economic, social and
political force. The old social structures associated with feudal have also
been replaced with a market dominated form of existence particularly
free and mobile labour- some thing which also explains the rise in
poverty in rural areas. The huge change in economic, social and hence
political power, from the agriculturist, so called feudal lobby towards an
urban and rural middle class, is also one of the key indicators
highlighting extraordinary structural change in Pakistan in nearly six
decades.
While a growing number of people in Pakistan are increasingly
accepting the view that the power of the ‘feudals’ has considerably
declined on account of demographic and economic structural change and
has been replaced by a mix and variety of middle class elements, it
seems strange that the perceptions that ‘Pakistan is feudal’ still prevails
outside Pakistan, particularly in India. Perhaps the lack of any
democratic culture in Pakistan and the fact that the position of women is
particularly discriminatory and shameful, gives rise to this impression.
Also, while feudalism as a mode of production has dissipated, this does
not mean that oppression and exploitation at the local/micro level has
vanished.
10
What is being emphasised here is that while there are pockets of feudal
tendencies still prevalent in Pakistan, feudalism as dominating and
organising from of social and economic structure is no longer present.
2.1.3 Overview of the EconomyIn a world, which is increasingly globalised and competitive, economic
growth and social development depends on how countries relate in the
rest of the world and on the economic policies that they follow. Apart
from the more standard requirements of adequate capital and skilled
Labour, other factors that have gained importance in explaining
economic development and growth, increasingly include non-economic
criteria, such as the quality of governance in countries, how their
institutions function, and openness and transparency in society, often
reflected through the depth of democracy in that country, with often
dramatically changing regional and global political circumstances, not
least in the countries that constitute and are near South Asia, economics
prospects are increasingly associated with issues of war, peace and
global coalitions and alliances. As a consequence, economic
development has increasingly become a matter of political economy.
Compared to other countries in South Asia, perhaps Pakistan has
experienced a far greater degree of political drama in the last decade.
With governments since 1985 changing every few months, with no
democratically elected government being allowed to complete its tenure
since elections resumed in 1985, the economic consequences have been
quite noticeable, leaving an imprint on social development and society at
11
large. In short period since 1998, however, even Pakistan’s unsettled
path has received some serious jolts.
The reason for giving this background was to enable reader to
understand what has been going in Pakistan and what factors affect the
economy of Pakistan. According to Economic Survey of Pakistan,
Pakistan economy saw a solid economic growth in 2005-06 despite the
oil crisis that the devastating earth quake in Pakistan. Pakistan economy
has been growing at an average rate of 7 per annum, which makes it one
of the fastest growing economies after china and India. As result of
continues economic growth Pakistan was able to achieve a GDP of 6.6
percent in 2005-06. The service sector and industry are the key drivers.
According to economic survey of Pakistan during the fiscal year 2005-
06 the most important economic achievements are as follow
(i) Pakistan has steady pace of economic expansion in the current
dynamic environment which saw a strong performance in service
sector but with a draw back of weaker than expected performance in
large scale manufacturing sector.
(ii) Recent years of strong economic growth has placed Pakistan as
one of the emerging economies of the world.
(iii) There is a growth of 4.7% in real per capita and a growth of
14.2% in per capita income.
(iv) There is boom in over all investment in Pakistan, which is about
20 % of GDP and the major contributor to this growth is investment in
private sector due to positive development in the economy.
(v) The ongoing growth of the economy is supported by the increase
consumer spending.
[http://www.finance.gov.pk/survey/sur_chap_05-06/overview.pdf]
12
2.2 Financial Market
2.2.1 Introduction The basic purpose of the this study is to examine one of Pakistan’s
financial market, which in this case is Karachi Stock Exchange and
check if it is weak form efficient or not, according to the guide lines set
by efficient market hypothesis. A financial market is a place where
different type of financial instrument are traded and based on their
nature the market is further classified into two categories. They are as
follows.
1. Capital Market
2. Money Market
1. Capital Market
The basic role of the capital market is allocation of ownership of
economy’s capital stock. Capital Market is a market where long-term
securities are traded. If government, company and public sector want
to raise long-term finances they move to this market, because it acts as
a platform, which unites lenders and borrowers. Such capital markets
are overlooked by financial regulator such as Financial Services
Authority in United Kingdom and Security and Exchange Commission
in USA and Pakistan, Capital markets are further divided into three
sub markets, which are as follows:
a. Stock Market
b. Bond Market
c. Financial derivatives
13
a. Stock Market
Stock Market is a place where common and preferred shares are
traded. Common shares represent direct ownership in an enterprise
where as preferred shares is a form of loan which can later be
converted into direct ownership (I-e common shares).
The main function of stock exchange is to raise capital for investment
purposes and if there was no capital market then we would be needing
some other platform to raise money for example banks. The capital in
stock market is raised through primary and secondary markets, which
are defined below.
Primary market
As it is clear from the name it is a market place where the securities
are sold when they are first issued and sold to investors. This is market
place where government, companies and public sector can raise long-
term finances by issuing stock or bonds for the first time. Whenever a
company or government has to sell securities in primary market for the
purpose of raising long-term fund they need a syndicate of securities
dealers. These syndicate of security dealer act as underwriters.
Whenever a new stock is issued on such security market it is called
initial public offering.
Secondary Market
Secondary market is a place where already issued securities are traded
among individual investors. In order for market efficiency it is
important that secondary market be highly liquid and transparent.
Because it is a market where securities are sold and transferred from
one investor to another it is very important that investor should have
the confidence the market in which they are trading is transparent.
14
Apart from this, one important issue that should be noted is that it is
not only the raising of the capital, but it is raising of capital in way that
maximizes the benefits to society as a whole.
b. Bond Market
Bond Market is a market where financial instrument with stated
maturity and coupon rates are traded. This maturity can be stated of
fixed. By stated maturity we mean a time period for which coupon
rates are payable. Some good examples of such instruments are
“Bahamas Government, Registered Stock, corporate bonds,
government bonds and mortgaged-backed securities”.
[http://www.colinafinancial.com ]. In Pakistan a good example of such
instrument are government bonds and saving certificates.
c. Financial Derivatives
Financial Derivatives is the most complex of all the markets segments.
This is because this is market where trading in done on underlying
claims. In order to operate in this market you need to employee
professional experts who can advice you how to trade in derivatives.
2. Money Market
Money market is a financial market for raising short-term funds. This
is market is in total contrast with capital market, because capital
markets exist for raising long term finances where as in money market
only short term finances can be raised. Money market is a market
place for bank where they and lend and borrow from each other. The
financial instruments that are used in this market are short-term
15
financial instrument such as Certificate of deposit, Repurchase
agreement etc.
In this paper our interest is only in capital markets and to be more
specific the capital markets of Pakistan that is Karachi Stock
Exchange. This paper will examine if Karachi Stock Exchange is weak
form efficient.
After explaining in detail what is market and what are different types
of markets our next task is to explain what we mean by market
efficiency or what is efficient market.
2.3 Karachi Stock Exchange
2.3.1 IntroductionSecurities markets of Pakistan have registered a period of un-
paralleled growth during the past few years and have been acclaimed
as the fastest growth markets in the world. “As a result of reforms and
liberalization process, our capital market has not only been making
great strides but also adapting itself to new procedures, practices and
patterns.”
[h ttp://www.bluechipmag.com/pi/0705/index.php ]
In the prevailing environment in the country, investment through stock
market has assumed greater importance. The Karachi Stock Exchange
is the biggest and most adaptable Exchange of the country.
With the fast and vast changes in the regulatory framework and
procedures governing the capital market coupled with rising volatility,
it is felt that the investors, who are the real backbone of this market,
need to be fully aware and educated, not only for their own benefit, but
also for improvement of quality investment and for creating a lucrative
investment atmosphere. Investors’ education and training are therefore
16
the most important and effective factors, which demand greater
attention and response from all the major players in the field.
The basic purpose of investors’ education is to create awareness of its
importance in the minds of capable public who will make well-
considered investment decisions based on authentic information rather
than hearsay.
The Karachi Stock Exchange (KSE) and the Securities & Exchange
Commission of Pakistan (SECP) both have been endeavouring to
restore confidence of investors in the stock market by ensuring
adequate transparency and disclosure requirements. In addition, efforts
are also being made to educate investors on investment risks and
rewards, importance and significance of financial planning and, above
all, rights and obligations of investors and means available to them.
2.3.2 BackgroundKarachi Stock Exchange is the largest stock exchange of all the three
stock exchanges in Pakistan. On 18th September 1947 Karachi Stock
Exchange (KSE) was established. On 10th March 1949 it was
converted to Company Limited by Guarantee. KSE stated its business
with only 90 members in the beginning; of these 90 members only half
were actively participating as brokers. Only five companies were listed
with a paid up capital of Rs. 37 million. With the passage of time KSE
progressed and emerging market and is a key institution of the capital
market of Pakistan
17
Table 1: Decade wise Progress
DECADEWISE PROGRESS
YEARNO. OF LISTED
COMPANIES
LISTED
CAPITAL
(Rs. in million)
MARKET
CAPITALISATION
(Rs. In million)
1950 15 117.3 -
1960 81 1,007.7 1,871.4
1970 291 3,864.6 5,658.1
1980 314 7,630.2 9,767.3
1990 487 28,056.0 61,750.0
2000 762 236,458.5 382,730.4
Source: http://www.kse.net.pk
2.3.3 KSE IndexInitially KSE started with 50 indexes. With the passage of time as
market grew there was need to expand the index base, so on
November 1 1991 the KSE-100 was introduced. “The KSE-100 is a
capital weighted index and consists of 100 companies representing
about 86 percent of market capitalization of the Exchange”.
[http://www.kse.com.pk/kse4/phps/aboutkse.php]
18
2.3.4 PerformanceKSE has been performing well in recent years and is growing at a
rapid rate. In 2002 Karachi Stock Exchange received the price of the
best-performing stock market. “KSE has been well into the 3rd year of
being one of the Best Performing Markets of the world as declared by
the international magazine “Business Week”. Similarly the US
newspaper, USA Today, termed Karachi Stock Exchange as one of the
best performing bourses in the world.”
[http://www.kse.com.pk/kse4/phps/aboutkse.php]
During the fiscal year 2005-06 Karachi stock exchange performance
was outstanding as result of which many new records were created
during fiscal year 2005-06. In the history of the capital markets of
Pakistan it was the first time when KSE-100 index crossed the barrier
of 12000 marks. This showed a growth of 64.7 percent over the fiscal
year 2004-05. Similarly there was growth in market capitalization by
70 percent over June 2005 from $33.7 billion to $57billion. The main
reason for such strong performance is that the economic polices
adopted by the government and privatization process that is attracting
foreign investors. As result of successful economic polices KSE was
able to attain a market capitalization equivalent to 46 percent of
estimated GDP of fiscal year 2006.
The first four-month of 2006 was a period of great success for the
KSE; this was the period when every thing was moving towards the
right path. The current growth in KSE can also be attributed to the
reforms carried out by the security and exchange commission of
Pakistan (SECP) for the development of capital markets and corporate
sector. “The reforms introduced over recent years in the fields of risk
management, governance and transparency have contributed
19
significantly towards the growth and development of capital market
and building investor confidence.”
[http://www.finance.gov.pk/survey/sur_chap_05-06/overview.pdf]
2.3.5 Investment climatea. Equity Market
Equity markets is Pakistan were not performing very well before 1991
the reason behind this was that secondary markets were not open to
foreign investor on equal basis with local investor. They were not
allowed the same privileges as local investors as result of it foreign
investment was negligible. But in 1991 government took a bold
decision to open secondary markets to foreign investor with equal
opportunities as local investors. it should be noted rapid increase in
business and finance activities in secondary market are due to
privatisation which opened doors for private sectors which were
previously opened for public sector only.
As result of this liberalization policy there was a rapid growth in
economy; industrial sanctions were removed apart from those sectors,
which have strategic importance. This all saw a great boom in
secondary market of Pakistan.
b. Regulator
Equity markets is Pakistan were not performing very well before 1991
the reason behind this was that secondary markets were not open to
foreign investor on equal basis with local investor. They were not
allowed the same privileges as local investors as result of it foreign
investment was negligible. But in 1991 government took a bold
decision to open secondary markets to foreign investor with equal
opportunities as local investors. It should be noted rapid increase in
20
business and finance activities in secondary market are due to
privatisation, which opened doors for private sectors, which were
previously opened for public sector only.
As result of this liberalization policy there was a rapid growth in
economy; industrial sanctions were removed apart from those sectors,
which have strategic importance. This all saw a great boom in
secondary market of Pakistan.
c. Legal Framework
According to the information obtained from Karachi Stock Exchange
Web site security following ordinance and act regulates markets and
corporate sector of Pakistan:
1. The Companies Ordinance 1984
2. The Securities and Exchange Ordinance 1969
3. The Securities and Exchange Commission Act 1999
[www.kse.com.pk]
d. Investor Specific
Following are the privileges and incentives allowed to foreign
investors
1. First and far most incentive for foreign investor is that they are
given all the privileges that local investor has.
2. Any investment made by foreign investor in capital markets can be
freely transferred along with dividend
3. There is no limitation on the extent of foreign ownership in the
company apart from the life insurance companies.
4. Foreign investors do not require any withholding period to operate
is capital market.
21
d. Limitation
Foreign investor requires permission from central bank of Pakistan for
the transfer of 5% or more shares of any bank or financial institution.
Some general incentives given to all companies listed on Karachi
Stock Exchange are as follow
1. Companies listed at KSE will be allowed discount in corporate
tax till year 2007
2. If mutual fund and modaraba companies distribute 90% of
there income they are exempt from income tax.
3. Companies are not required to pay any turn over tax with
respect to transaction with securities listed on stock exchange
e. Issue Capital
1. If a company has to issue capital it has to issue capital according to
guide lines issued by “Company Ordinance 1984, Companies
(Issue of Capital) Rules, 1996 and Listing Regulations,
Regulations Governing Over the Counter (OTC) Market”
[www.kse.com.pk ]
2.3.6 Karachi Stock Exchange Trading SystemIn order to ensure that participants and investor can trade with fair ease
in Karachi stock exchange a computerized system has been developed
named Karachi Automated Trading System (KATS).This system
ensures that trading at Karachi stock Exchange is fair, transparent,
efficient and cost effective.
Various features attached to this trading system are explained as
follow.
22
a. T+3 Settlement System
As it is clear from the name T+3 settlements all the purchase and sale
of securities is netted and balance is settled on third day from the day
of trade.
Following are some benefits of this system.
1. T+3 Settlement system reduces the market risk by reducing the
time period between the settlements of trade.
2. Settlement risk is also reduce by this system, by providing a
shorted settlement cycle.
b. Provisionally Listed Counter
The companies whose share are not listed on the stock exchange but
make a minimum public offer of specified amount that is 150 million
Rupees use this counter. Company can trade on this counter from the
date of publication. Once the company completes the process of
allotment of shares to subscribers it is automatically moved to the T+3
counter. Once the company moves to T+3 all trading at provisional
counter ceases and if there is any outstanding transaction it is moved to
T+3 counter from the date on listing on this counter.
c. Spot/T+1 Transaction
Spot Transaction is one in which trade is settled immediately within 24
hours. It such type of transaction ownership is transferred immediately
upon payment.
d. Future Contracts
As it is clear from the term future contracts it involves sale and
purchase of securities at some future date. A very important point in it
is sale and purchase is done on price fixed today. Every six month
there is board that determines the name and number of companies that
will deal on this future counter. And this all is done under the guidance
23
of security and exchange commission of Pakistan. The information
about those who will deal on this counter is made public to market
participants in advance.
e. Odd Lot Market
The odd lot market has been created to provide an automated platform
through KATS enabling the investors to trade securities in lots, which
are less than the normal trading units (lots) of the securities approved
for Ready Market. The minimum volume of a buy/sell order may be
one share.
f. OTC Market
OTC stands for over the counter market. This market is in the process
of formation. This market will help in raising finances in a cost-
effective way for enterprisers.
24
CHAPTER 3
3.LITERATURE REVIEW
3.1 Efficient Market HypothesisThe issue of efficient market hypothesis has been widely debated. A lot of
research has been done on this very important topic. Efficient market
hypothesis states that any given time, security prices fully reflect all the
available information. In other words what this theory states, that it is
impossible to outperform the market by just choosing the best stock, if an
investor wants higher returns all he needs to do to take more risk.
Most of the investors buy and sell securities I-e stock under the impression
that stock they are buying are worth more than what they are actually
paying for and when they are selling the stock they assume the securities
they are selling are worth less than selling price. But as we have explained
earlier if we want to earn above average return we will have to take more
chance I-e risk because we simply can not out perform the market with
information that is already known to the market, if the market is efficient
then current prices fully reflect all information then it would not be
possible to make above average return simply by trading. “It further
suggests that the future flow of news (which will determine future stock
prices) is random and unknowable in the present. The EMH is the central
part of efficient market theory
(EMT).”[http://www.answers.com/topic/efficient-market-hypothesis ]
Under efficient market hypothesis we believe that security market are
highly efficient in reflecting any information that would arise, this
25
information spreads very rapidly and is soon incorporated into the security
prices without any delays. It is because of this reason neither technical nor
fundamental analysis’ would be able to help investor to earn above
average returns.
Eugene Fama is the one who bought the answer to the question of does the
security price really reflect all the available information. Fama (1970)
stated, “Prices in an efficient market always fully reflect all available
information”. He also stated that there are some conditions that a capital
market should meet in order to fulfil the phenomena of market efficiency.
The conditions are as follow:
No transaction cost
All information is readily available to all the investors or market
participants free of charge
There is no disagreement on the implication of current information
for the current price and distribution of future prices of each
security.
Current prices of securities should fully reflect all the available
information.
Source: Fama (1970) “Efficient Capital Markets: A review of Theory and
Empirical Work” Journal of Finance, XXV, No.2. pp387
In 1970, Fama produced a classification of market efficiency, which
helped us too usefully scale against which markets can be judged. Fama
gave the following three classification of market efficiency.
Weak Form Efficiency
Semi-strong Form Efficiency
Strong Form Efficiency
26
3.1.1Weak Form EfficiencyMarket is set to exhibit weak form of efficiency when prices discount all
past information. I-e the technical analysis of past data and market
information should not yield abnormal returns on a consistent basis.
Abnormal returns are one, which will beat a ‘buy and hold’ strategy on
a risk-adjusted basis.
Weak form of efficiency can be tested by applying statistical
investigation on time series data I-e prices. If the weak-form of efficient
market holds then the current prices of shares can be quoted as the best
unbiased estimates of the value of the security. If these prices are to be
affected by any thing, then it could only be the introduction of
previously unknown news.” News is generally assumed to occur
randomly, so share price changes must also therefore be random”.
[http://www.absoluteastronomy.com/ref/efficient_market_hypothesis]
3.1.2 Semi-Strong Form Efficiency
Market will show Semi-strong from of efficiency if prices discount all
publicly available information. I-e it implies that excess profits cannot
be made by trading on announcement. But the publicly available
information must be historical.
In order to test the semi-strong-form of efficiency, we would have to
adjust the previously unknown news, that adjustment should be of
reasonable size and the previously unknown news should be
instantaneous.” To test for this, consistent upward or downward
adjustments after the initial change must be looked for, If there are any
such adjustments it would suggest that investors had interpreted the
information in a biased fashion and hence in an inefficient way”
[http://www.absoluteastronomy.com/ref/efficient_market_hypothesis]
27
3.1.3 Strong Form EfficiencyA market is said to exhibit Strong form of Efficiency if prices discount
all privately held information I-e it implies that excess profit cannot be
made from insider information.
To test for strong form efficiency, we basically examine weather an
investor or group of investors have earned excess returns based on inside
information. As we normally don’t have enough data on investor to
perform such test, the group that is normally tested in such studies is
managers of mutual funds.
The theory of efficient market hypothesis came under great criticism
from technical analysis. The reason they gave for such a heavy criticism
is that mostly investor base there expectation on past information, when
we talk about past information we usually mean past prices, earning or
such other indicators. In nut shell their view was since stock prices are
mostly determined my investor expectation, do it only makes sense to
believe that past prices do influence future prices.
The efficient market hypothesis can be tested by different methods, such
as
Auto correlation test
Serial correlation test
Run test
Distribution of return test
Unit Root
Event study etc
As far as my study is concerned regarding the existence of weak form of
efficient market hypothesis I will be applying following test to KSE
indices
1. Distribution of return test
28
2. Auto correlation test and Ljung Box Statistic
3. Run test
4. Unit Root Test
3.2 Random WalkWhenever there is any discussion on the efficient market hypothesis, the
term Random Walk does come in. This is because those who believe in
efficient-markets concept also tend to support the idea of Random walk.
Concept of random walk states that the flow information is random and
the security prices adjusted to any new information that is released. Hence
if the security prices efficiently adjust to new information then no body
can predict about the future security prices. Basically Random Walk
means that the returns of any securities are independent of the past history.
Before we carry on with our discussion on random walk in connection to
efficient market hypothesis, it would be helpful if we discuss two
approaches that are commonly advocated by the professional.
“Chartist” or “technical” theories
Fundamental or intrinsic value analysis theories
3.2.1 Chartist TheoriesChartist theories states that history repeat itself when we are talking
about securities. According to them past patterns of price behaviour in
individual securities will repeat itself in the future. So it is important that
we familiarize our self with past patterns of price behaviour in order to
predict the likely recurrence in the future.
In nutshell chartist theories “assume that the sequence of price changes
prior to any given day is important in predicting the price change for
that day”. [Eugene F.Fama (1965) “Random Walks in Stock Market
Prices” Financial Analysts Journal, Pp 55
29
3.2.2Fundamental Analysis TheoriesChartist theories were not very welcomed by the professional in the
market as result of which Fundamental analysis theories came into
being. According to them the intrinsic value of any security depends on
the earning potential of the security. The term intrinsic value means an
equilibrium value. The earning potential of securities are depended on
the following factors
Quality of management
Outlook of the economy
If a fundamental analysis does a careful study of above mention factors
he would be able to see if the actual price of the security is above or
below its intrinsic value.
Fama (1965) stated “The starting point for any Random walk theorist is
that the major security exchanges are good example of “efficient”
markets”. [Eugene F.Fama (1965) “Random Walks in Stock Market
Prices” Financial Analysts Journal, Pp 56]
An efficient market is one where prices at any time fully reflect all the
available information. Which means in efficient market intense
competition among the investors leads to situation where at any point in
time the actual price of the security will be good estimate of its intrinsic
value. Hence according to Fama (1965) a market “where successive
price changes in individual securities are independent is by definition a
Random walk market”. [Eugene F.Fama (1965) “Random Walks in
Stock Market Prices” Financial Analysts Journal, Pp 56]
It can now be stated that change in stock price cannot be predicted based
on their historic values, we cannot predict the future price if we use the
past history. We cannot say that random walk hypothesis will provide an
30
exact explanation of the behaviour of stock market prices, but practically
we still accept this model though it does not fit the facts exactly.
This concept of market efficiency arose accidentally. It was the work of
Kendall (1953) who gave us the idea of efficiency. He studied the
changes in the weekly prices of the UK market for 29 weeks and
concluded that there was no trend or pattern in them and those
successive changes were independent of each other. Hence he concluded
that they had a random movement and the past data I-e historic data does
not contain any useful information upon which we can predict the future
price. He went on saying that the profit made by the investor by trading
on stock market is only because they take chances I-e risk. So we can
say that it was luck, inside information, speed of reaction to the news
and the scale of operation. Kendall findings upset my financial
economist.
In 1961 Alexander, stated that randomness in prices changes exists
because market is so efficient that they adjust instantly to the new
information. It was he who stated that filter techniques do not succeed in
beating buys and hold strategy, because of the transaction and taxation
cost involved. There was a drawback in his work, which was the filter
techniques he used was not an exactly a random process. But he was the
first to acknowledge that we do not need random walk to ensure
efficiency. The concept was endorsed by Osborne (1959) and Fama
(1973) years later, which later gave the concept of “fair game”.
In 1965 Fama conducted research on Dow 30 Industrial Companies for a
period of five years for serial correlation. He took natural logarithm of
prices for up to sixteen lags and concluded that there was no substantial
evidence of linear dependence. Fama also studied the behaviour of
prices in terms of direction. He stated that the daily price changes were
31
followed by similar changes random sign. Though this was not a proper
explanation of random walk process, was talked as a sign of market
efficiency. According to him these fluctuation were result of reaction to
new information.
3.3 Empirical EvidenceIn this section we will look at some previous studies done on the topic of
efficient market hypothesis. I have divided this section into two group
developed market and developing market.
3.3.1 Developing Market Poshakwale (1996) studied the evidence on weak from efficiency and
day of the week effect in the Indian stock market. In order to conduct the
study Sunil gathered its data from Bombay stock exchange national
index for the period starting from 2nd January 1987 to 31st October. In
order to compare the result of Indian stock market with international
market its index values are converted into US dollar by using daily
exchange rate quotation.
Sunil Poshakwale applied frequency distribution test, Kolmogorov
Smirnov Goodness of Fit Test, runs test and Serial Correlation
Coefficients Test, to test the weak form of Indian Stock market and
week of the day effect. The conclusion that was drawn on the base of
these tests was that Indian Stock market is not efficient in weak form but
there is an evidence of day of the week effect.
Alam, Hasan and Kadapakkam (1999) studied the existence of weak
form of market efficiency in five Asian stock markets; which are Hong
32
Kong, Malaysia, Sirlanka, Bangladesh and Taiwan. The test they used to
check Lo and Mackinlay call this phenomenon Variance-ratio test,
which was developed, in 1988 and 1989. They used this method on
monthly stock index on above mention stock markets.
Monthly stock index data was obtained from different sources. For Hong
Kong, Malaysia and Taiwan stock markets the data was obtained from
Pacific Basin Capital Market Databases (PACAP). For Sri Lanka data
was obtain from Sri Lankan Stock Market but for Bangladesh data was
collected from various issues of Dhaka Stock Exchange Bulletin.
The result indicated that Bangladesh, Hong Kong, Malaysia and Taiwan
do follow random walk hence this means that there is existence of weak
form of market efficiency in those markets. The result also implies that
Sir Lanka stock exchange does not follow a random walk, but there is
not enough evidence to prove that there is no existence of weak form of
market efficiency.
Abraham, Seyyed and Alsakran (2002) tested the random walk
behaviour and weak form efficiency of Gulf stock markets. The gulf
markets that were tested are Kuwait, Saudi Arabia and Bahrain. Of the
above mentioned stock market Saudi Arabia is the biggest stock market,
it has 74 listed companies and has a market capitalization of $43 billion
in 1998. Variance-ratio test and run test were used to check the random
behaviour and weak form of market efficiency of these stock markets.
These two tests were applied on weekly data of these stock markets for
the period of October 1992 to December 1998. data for Kuwait Stock
Exchange was obtained from Kuwait investment agency, Saudi Arabia
Monetary Authority provided data for Saudi stock market and Financial
Analysis Unit of the Bahrain Stock Exchange provided data for Bahrain
stock exchange.
33
A major problem faced by them was of infrequent trading on the
observed index. To counter this problem they used the Beveridge and
Nelson (1981) methodology for estimating the true index.
The result for variance –ratio test showed that all three stock market
rejected the existence of random walk in all three-gulf markets when
performed on observed indices. But when performed on correct indices
we found that we cannot reject the existence of random walk in stock
markets of gulf and they are Bahraini and Saudi markets. But this does
hold good for Kuwait even after using correct indices after adjusting for
infrequent trading. Run test suggest that only Kuwait stock market is
efficient in weak form if this test is applied on observed indices. This
means that other two stock markets are not efficient in weak form. But
when they applied this test to correct indices they found that all the three
stock markets were efficient in weak form.
Narayan and Smyth (2004) studied the market efficiency of South
Korea’s market. In order to check the efficiency of the market they
applied Augmented and Fuller (ADF) Unit Root test, Zivot and Andrews
(1992) one break and Lumsdiane and Papell (1997) two-break unit root
test to support the central hypothesis of existence of random walk in
Korea’s stock market.
The data on which this these test were performed were obtained from
OECD Main Economic Indicators for the period1981-2004. Monthly
indices were obtained from them.
The conclusion drawn by them was that there is an existence of random
walk in stock indices of Korea’s stock market and that this market is
consistent with efficient market hypothesis.
Onour (2004) studied the existence of weak-form Efficiency of Saudi
Stock Exchange Market. In order to check the efficiency of Saudi stock
34
market the author applied Run test and Mean-Square-of-Successive
Difference test also called as von Neumann Ratio test. The main
hypothesis of this study is that the data is random.
These tests were applied on daily price indices of Saudi stock market
from the period of March 1st 2003 to August 30th 2004.
Until 1980’s Saudi stock remained informal, it is only in 1984 that some
structural changes were made and Saudi Arabia Monetary Agency
(SAMA) was introduced. The main task of Saudi Arabia Monetary
Agency is to regulate day-to-day trading in stock market. In the same
year that is 1984 Saudi Share Registration Company (SSRC) was also
established. In 1990 Electronic Securities Information (ESIS) was
developed and is operated by SAMA.
The conclusion that was drawn on the basis of these tests was that Saudi
stock markets are not efficient in weak form. The writer also stated that
the main reason of this inefficiency is that information is not freely
available to market participants and lack of regulatory body. The write
gave following recommendation to enhance the efficiency of the market.
1. Security and Exchange Commission should be established as
regulatory body.
2. Securities Deposit Centre should be solely responsible for
operations and registering the ownership of securities traded on
stock exchange
3. Regulation of brokerage business and imposing penalties on
violations of disclosure and transparency requirements.
Moustafa (2004) tested the weak form of market efficiency of the United
Arab Emirates Stock Market. For the purpose of the study data was
obtained from United Arab Emirates Stock Market for the period of
October 2nd, 2001 to September 1st, 2003. Because of infrequent trading
35
on United Arab Emirates Stock Exchange writer used individual stock
prices rather that stock index returns to test the efficiency. In total there
are 55 actively traded stocks in United Arab Emirates. Out of these 55
stock studies was conducted on these 43 stocks.
As these 43 stock do not follow normal distribution that is why
nonparametric Run test was applied to test the central hypothesis that
United Arab Emirates Stock Market follows a random walk and hence in
efficient in weak form.
The conclusion that was drawn from the result was that out of 43 stocks,
40 stocks follow random walk at 5 percent level of significance. Hence
the result supports the central hypothesis that United Arab Emirates
Market is efficient in weak form. This result was a surprise as UAE
market is newly developed market.
Hasan (2004) studied the Random Walk hypothesis applied to Dhaka
Exchange. For the purpose of this study statistical analysis are applied
on daily closing prices of Dhaka Stock Exchange for a period of January
1st, 1990 to December 7th, 2000. This data was obtained from
DATASTREAM online database. Statistical test that were used to test
the null hypothesis of random walk are Unit Root test and Variance
Ratio test.
On the basis of the tests author concluded that Dhaka Stock Exchange is
does poses a random walk and hence it is efficient in weak form.
Abeysekera (2001) studied the presence of weak form of market
efficiency of Colombo Stock Market for the period of January 1991 to
November 1996. There has been no published study on the efficiency of
Colombo Stock Market for the above mention period. This is the first
study that studies the weak form of efficient market hypothesis for the
securities listed on Colombo Stock Market.
36
Colombo Stock Market emerged in 1985 after restructuring of Colombo
Share Brokers Association that had been in operation for over a century.
Previously Colombo Stock Market operated on “Call-Over system”
which was replaced by “open-out-cry system” for transaction.
For the purpose of this study daily, weekly and monthly returns of stock
indices from January 1991 to November 1996 were used. To test the
existence on weak form of market efficiency Run test and auto
correlation test were performed on the data.
The conclusion that was drawn on the basis of the test was that Colombo
Stock Market is not efficient in weak form of market efficiency. This
result was not a surprise, as it is conventionally believed that emerging
markets are not as information efficient as their developed countries
counterpart. Furthermore it was discovered there is no presence day-of-
the week effect or month-of- the year effect in Colombo Stock Market
for the period of the study.
Omet, Khasawneh and Khasawneh (2002) studied the efficiency of
Jordanian Stock Market and relationship between returns and
conditional volatility. Jordanian Stock market was established in 1978
after recognizing the importance of having a security market. The study
tested the efficiency of Jordanian Stock Market and volatility effects and
provides answer for three core questions.
1. What factors affect the stock returns in the Jordanian Stock
Market?
2. How efficient is Jordanian Stock Market is pricing its securities?
3. What is the relationship between returns and conditional volatility?
For the purpose of the study daily indices of Jordanian stock market for
the period of 1992-2000 were taken. In order to answer the above
question Generalized Autoregressive Conditional Heteroskedasticity
37
(GRACH) model is used. The conclusion that was drawn on the basis of
this test was that Jordanian Stock Market lacks market efficiency. Only
in two indices author were able to find a strong relationship between risk
and return, but rest of them showed high volatility.
Okeahalam and Jefferis (1999) did an event study for three stock
exchanges namely Botswana, Zimbabwe and Johannesburg. The data for
this study was obtained form different sources. The primary source of
data are the stock broker Botswana ltd, data world, Zimbabwe (Pty) and
I-Net RSA (Pty) Ltd. Weekly stock prices along with earning
announcement were obtained from these data bases for a period of one
year, that is from September 1996 to 1997.data belonged to retail and
banking sector.
Event study is conducted to examine if markets are Semi-Strong form
efficient. In this study event study was conducted for Botswana,
Zimbabwe and Johannesburg stock markets. This means these markets
were tested for semi-strong form of market efficiency. In order to
perform the event study Cumulative Abnormal Return (CAR) was used.
The study showed that Botswana, Zimbabwe stock markets are not semi-
strong form efficient because these markets are not efficient enough to
react instantaneously to new earning announcement. But the analysis
also shows that only Johannesburg stock market is semi-strong form
efficient. This means that Johannesburg stock market is efficient enough
to react instantaneously to new earning announcement release.
Magnusson and Wydick (2002) examined how efficient are Africa’s
Emerging Stock Market. For the purpose of the study eight largest
African stock markets were chosen. Author tested these markets for the
existence of weak form of efficient market hypothesis. For the purpose
of the study data was obtained International Finance Corporation (IFC)
38
Emerging Markets Database, which is considered to be the most reliable
database for stock market activity of emerging markets. Monthly data
was obtained from IFC. One important draw back in this study which
was pointed out in this study is that some the African markets are quite
new and the researcher were not able to find a long time series of data.
The writer of the study found that out of eight six African market
followed the weak form of efficient market hypothesis. The research
also showed that the African market don’t pass the same high standard
hurdles for weak form of market efficiency as the developed markets of
USA etc do. The results obtained from this study were compared with
similar test on South–east and Latin America. Conclusion that was
drawn from such comparison was that emerging African stock markets
compare favorable with other emerging stock markets that are
southeast and Latin America stock market.
3.3.2 Developed MarketLi and Xu (2002) studied the efficient market hypothesis on New
Zealand stock exchange. They used four stock exchange indexes of New
Zealand Stock exchange. The indexes they used are NZSE 10, NZSE 30,
NZSE 40 and NZSE SC. They tried to test weak and semi strong form of
market efficiency of these indexes. NZSE 40 is the main market index
and covers top 40 stock listed on New Zealand stock exchange. NZSE
30 represents most liquid securities listed on stock exchange. NZSE 10
represent the top 10 securities listed and NZSE SC comprise of small
companies that cannot be listed in NZSE 40. Data is obtained from stock
exchange data software called Datex.
Random walk, contintegration and granger test were adopted to check
the weak and semi-strong form of market efficiency. These test showed
that small firms are weak form efficient and to some extent semi-strong
39
efficient as well. The result showed that NZSE 10 is not even weak form
efficient but NZSE 30 and 40 are weak form efficient but not semi-
strong form efficient.
Millon and Moschos (2000) studied the validity of the weak form
market efficiency applied to the London stock exchange. They used FT-
30 index for there study. They performed Grach-M model test,
Autocorrelation function and variance ratio test. On the basis of the
result they concluded that there was no prove of existence of random
walk hypothesis but the weak-form market efficiency hypothesis cannot
be rejected.
Abrosimova, Dissanaike and Linowski (2005) tested the weak-form
efficiency of the Russian Stock Market. For the purpose of this study
daily, weekly and monthly index we obtained from Russian Trading
System for a period of September 1995 to 1st May 2001. The initial data
was transformed into natural logarithmic data for the purpose of
analysis. Authors performed Unit Root test, Autocorrelation and
Variance ratio test. All the tests are conducted at 95% of confidence
level.
On the basis of the test it was concluded that only monthly data
supported the null hypothesis of random walk and weekly and daily data
rejected this hypothesis. So it can be said that if we use monthly data
then Russian Stock Exchange is Efficient in weak form. But this
efficiency is not backed if performed on weekly and daily returns.
Furthermore in order to study linear and non linear dependence in daily
and weekly data, ARIMA and GARCH models were built.
Groenewold and Kang (1993) studied the semi-strong efficiency of
Australian share market. The semi-strong efficiency of Australian stock
market has been tested before by Sharpe (1983), Hogan. Sharpe and
40
Volker (1982), Saunders and Tress (1981). Result of these studies
concluded that Australian stock market is not semi-strong form efficient.
Since weak- form of efficiency is necessary condition for the existence
of semi-strong form, because if the market is not weak form efficient
nothing can be done to show that market will be semi-strong efficient
that is why it would be wise to perform some initial test for weak form
efficiency.
For the purpose of weak- form efficiency test, data of four indexes of
prices of share traded on Australian stock exchange was used for the
period of 1980-1988. Autocorrelation test, Likelihood –ratio (Lr) test
and unit root. The conclusion that was drawn on the basis of above
mention test was that Australian Stock Market is efficient in weak form.
The next step in the study was to test Australian Stock Market for Semi-
Strong form. For this purpose the data that was used comprise of four
variables namely; Share Prices, Money Supply, Real Government
Expenditure and the Real Price Level. Note that all these variables were
used in log form. The data was obtained from different sources, which
are; Reserve Bank of Australia, ABS catalogue number 8501.0, 6203.0,
and 6412.0.
An event study was conducted and the conclusion of the study was in
contrast to those studies, which have been conducted earlier. It would be
safe to say; that issue of Semi-strong form of market efficiency for
Australian stock market for period of 1980’s is not a settled issue and
more work needs to be done.
Al-Loughani and Chappell (1997) studied the weak-form efficiency of
London stock exchange for FTSE30. There are a lot of studies that were
conducted on the same topic but they all used the test for serial
41
independence namely Autocorrelation and Run test. This study applies
more sophisticated test.
For the purpose of this study data comprises of daily observation of
FTSE30 for a period of 30th June 1983 to 16th November 1989. The basic
reason for choosing this period was unchanging economic policies.
For the purpose of this study Augmented Dickey-Fuller test (ADF) and
Brock, Dechert and Scheinkman (BDS) test was used to check the said
data for weak –form of market efficiency for FTSE30. On the basis of
the study it was concluded that FTSE30 of London stock exchange is not
efficient in weak form or the weak form of efficient market hypothesis is
not valid for FTSE30.
Groenewold (1997) studied the efficiency of Australia and New
Zealand stock market using daily observation on the Statex Actuaries’
Price index for Australia and NZSE-40 index for the New Zealand. This
paper tests the weak and semi-strong form of market efficiency for
Australia and New Zealand stock market. The data consisted of four
aggregate indexes for Australia and Two for New Zealand for the period
of 1975-1992.
In order to test weak form of efficiency for both stock markets two
methods were adopted and they are testing for stationary of the log
prices process and then test the Autocorrelation of the returns. The
autocorrelation test showed that there is an evidence of predictability of
returns for both stock markets but the stationary test showed that both
the markets are consistent with weak form of efficient market
hypothesis.
In order to check Australian and New Zealand stock market for Semi-
Strong form of market efficiency, two tests were adopted and they are;
Cointegration and Granger Causality test. The indexes for both Australia
42
and New Zealand stock market were found not to be cointegrated and
hence both the markets are semi-strong efficient. More over when daily
data was used there was some evidence of Granger causality in both
direction but when weekly and monthly data was used there was an
evidence of Ganger causality in one direction that is from Australia to
New Zealand.
Stengos and Panas (1992) in their paper testing the efficiency of the
Athens Stock Exchange studied the weak and semi strong form of
market efficiency of Athens Stock Exchange. The Athens Stock
exchange was first established in 1876. Athens stock exchange is semi-
governmental organization and is overlooked by the ministry of
commerce. For the purpose of this study they choose the banking sector.
They analysed daily closing prices of four biggest banks. The four banks
that were studied are KTIMATIKI, ERGASIAS, EMPORIKI and
ETHNIKI. There were 953 observations, which covered a period of
January 1985 to October 1988.
In the study author used BDS test that is Brock, Dechert and
Scheinkman (1987) to test Athens stock market for weak form of market
efficiency. Cointegration test based on the methodology of Granger and
Engle (1987) was used test Semi-Strong form Athens Stock Exchange.
The conclusion that was drawn from test was that Athens Stock market
is efficient in both weak and semi-strong form.
3.6 Market Anomalies There are certain anomalies that have been detected in almost every
capital market on the world. It is because of these anomalies the Efficient
Market Hypothesis has become controversy. There has been a lot of work
done on seasonal variation in financial market. Tooke was one of the first
43
author who commented on such anomalies, according to Tooke (1824):
"Nothing has struck me as being more strange in all the late discussions
and reasoning’s upon the subject of the high and low prices of the last
thirty years, than the little importance which has been attached to the
effects which a difference in the character of the seasons is calculated to
occasion".
a. Months of the Year
The January time anomaly states that monthly returns in January are
usually better than average, whilst returns in June through August are
worse.
This effect is not depended upon hemi-sphere. This means that Tokyo is
affected in the same way as New York. But there is exception to this rule
and that is of Japan and Italy. This January effect is stronger than others in
some decades.
Bentez and Hansson (2005)3 in their paper “Systematic variations in
January” studied the January effect in New York stock exchange. For the
purpose of the study they used five monthly indices from a period 1966 to
2002. The indices that were used in this study are Composite, Industrial,
Transportation, Utility and Finance. The basic model that they used is as
follow
Rkt = μ + δk + ekt
From the study they concluded that January effect couldn’t be rejected.
Rozeff and Kinney (1976) studied the market anomalies and for the
purpose of the study they selected New York Stock Exchange. The data
consisted of all stocks listed on New York Stock Exchange for a period of
1904 to 1974. They concluded in their paper that average return in January
was higher than rest of the month.
3 http://www.fma.org/Stockholm/Papers/januarfma.pdf
44
Bhardwaj and Brooks (1992) in their paper “The January Anomaly:
Effects of Low Share Price, Transaction Costs, and Bid-Ask Bias” studied
the January effect. For the purpose of the study they chose New York
stock exchange and American Stock and Option Exchange (AMEX). They
grouped stocks in 5x5 matrix of portfolio. The stock covered a period of
1967 to 1986. The twenty-year period had 39,556 stocks of which 69% are
listed on the New York stock Exchange and the remaining 31% and on
AMEX.
On the basis of their study they concluded that the firms whose stocks
have low share price earn abnormal returns in January before transaction
costs.
Eleswarapu and Reinganum (1993) in their paper “The seasonal behaviour
of the liquidity premium in asset pricing” studied the seasonal behaviour
of the liquidity premium in asset pricing. The study covered a period of
1961 to 1990.
From the study they concluded that liquidity premium was high in
January, but no such evidence can be found for the rest of the month.
b. The Weekend Effect (or Monday Effect)
Apart from the January anomaly the returns and index returns are also
affected by the weekend effect of Monday effect. The size of this effect
depends on the break, the longer the break the greater will be the effect.
We can back this with the help of the example like during an Easter break
(which consists of Good Friday and Easter Monday) the returns are higher
one day before the break this is Thursday in this case but are really bad
one day after the Easter break that is Tuesday.
Wang, Li, and Erickson (1997) in their paper “A New Look at the Monday
Effect” examined the Monday effect on the stock returns. The sample
period for this study was from 1962 to 1993, which consisted of various
45
stock indices. In this article they stated that the famous weekend effect is
only visible on fourth and fifth weeks of the month during the period of
the study from 1962 to 1993.
French (1980) in paper “Stock returns and the weekend effect” examined
the effect of weekend on stock returns for a period of 1953 to 1977. For
the purpose of the study they developed two models. One is the calendar
time hypothesis and the other is trading time hypothesis. Under the first
hypothesis the expected returns on Monday is three times higher than
other days of the week. Under the second hypothesis it was found that
returns are negative on Monday and are positive on rest of the days.
According to French (1980) the possible reason for this negative return is
day of the week effect not because of the general close market effect. He
further suggested that as a trading strategy it would be profitable to buy
stocks on Monday and sell them on Friday.
Kamara (1997) in paper “New evidence on the Monday seasonal in stock
returns” examined the Monday effect on S&P 500 and a small-cap index
for a period ranging from 1962 to 1993.
From the study it was concluded that Monday effect in S&P returns was
not that prominent in fact it was reducing significantly for the study period
that is from 1962 to 1993. Further to this it was stated that after April 1982
S&P returns did not showed any sign of Monday seasonal effect. This
decrease in Monday effect is due to positive relationship between
institutional versus individual trading. But on the other hand small-cap
index showed a Monday effect for the period of the study.
Agrawal and Tandon (1994) in their paper “Anomalies or illusions.
Evidence from stock markets in eighteen countries” examined five
seasonal patterns in stock market of eighteen countries. The seasonal
46
pattern they studied is the weekend effect, turn of the month, end of
December, monthly and Friday-the-thirteenth effects.
From the study they concluded that weekend effect existed in only nine
countries but daily seasonal effect was present in almost all country, but
interestingly this disappeared in the 1980’s.
C, Time Of The Day Effect
Time is an important element in determining the returns as well. It was
found that returns on Monday lunchtime are the worst of all, rather than
any other time of the day. But in contrast the best time is the Friday after
noon.
d. The Weather
Weather also affects share prices in positive or negative manner. For
example few argue that shine has a positive effect on the people, because
when it is sunny people feel good and are optimistic in their choices and
decision-making.
In 1993 Saunders in its paper “Stock prices and Wall Street weather”
concluded that New York Stock Exchange index has tendency of being
negative when it is cloudy.
Apart from weather over confidence and other environmental factor also
affect the quality of the returns.
All these phenomena have been referred as anomalies because the
Efficient Market Hypothesis cannot explain them. Because of this it is
suggested it is not only the information that set the price of the share.
The existence of these anomalies have forced researcher to question the
existence of efficient market hypothesis and find alternate ways to
investigate the market behaviour.
47
3.7 Emerging MarketsA lot of research has been done on emerging market over past 20 years.
The term Emerging Market is allied with World Bank. A country is
considered to be emerging if its per capita GDP is below certain criteria
but it is expected that they are going to meet that criteria very soon. Of
course the main idea behind it is that a country can be termed as emerging
market if it is putting efforts to change and improve its economic
conditions and raise its economic standards to meet that of developed
world. When we are talking about emerging markets we are talking about
the markets in which public securities are traded in less developed market.
When we are talking about emerging market we are talking about the
market that operates in countries that have low per capita income. Pakistan
has emerged as an emerging market in Asia because of the economic
reforms that have been carried out in the past. Pakistani capital markets
are performing efficiently and are playing its part in the globalisation of
capital markets. On the basis of the research three features of emerging
market have been indicated and they are as follow.
1. Higher average returns
2. High volatility
3. Low correlation
Higher average returns exists in only those markets, which follow a high
economic growth. Where as high volatility and low correlation exist both
across the emerging markets and with developed markets.
As said earlier that these markets have high returns that is why investors in
developed countries are attracted to invested in these countries. The
international investors perceive such markets very lucrative because they
can achieve high returns in relatively short period of time. The reason why
such markets have high returns in because these markets are in countries,
48
which are moving towards, developed countries and hence a lot of
industrialization and economic growth is taking place that is why the
growth rate is very high.
Bekaert and Harvey (2002) in their paper stated that the returns of
emerging market are not normally distributed they further more stated that
the it is not only post liberalization return but the pre –liberalization
returns are also not normally distributed. They also stated that emerging
market is not as efficient as developed market. There exists information
inefficiency in emerging equity markets. The returns in such markets have
a higher degree of serial correlation then that of developed markets. The
reason behind it is infrequent trading and slow adjustment to current
information. Emerging markets doesn’t incorporate company specific
news as swiftly as developed markets do that is why returns in emerging
markets are not affected by such company specific news because emerging
markets are not information efficient and developed markets are. This
study clearly states that there is an evidence of insider trading in these
markets however this doesn’t mean that these markets are inefficient.
Bekaert and Urias (1999) in their paper “Is there a Free Lunch in
emerging market equities?” stated the benefit that can be gained from
holding stocks in emerging markets when talking in terms of global equity
portfolio. They used mean variance analysis and create expected excess
returns with help of covariance estimates that matches a hypothetical
“efficient portfolio”. On the basis of the analysis they concluded that
expected returns from emerging markets stocks are higher than that of
developed equity markets when compared for optimal portfolios.
Emerging markets returns are more predictable than developed equity
market returns. The reason behind this predictability can be the
informational inefficiencies. Bekaert, Erb, Harvey and Viskanta (1996) in
49
their paper “The Cross-Sectional Determinants of Emerging Equity
Market Returns” stated that as emerging markets become more
incorporated in the world capital markets, the relativity of world
information gains more importance and does have a greater impact on
time varying mean returns. The high return in emerging markets is also
accompanied by high volatility. Hence there is a great deal of risk
involved in investment is such market this is because of the fact that such
markets are going through a transaction period and will be going through
unexpected political and economic turns. Thus the value of stock and
bonds can change drastically in such markets without any notice.
The volatility in the returns of emerging markets has several reasons.
Some of the reasons were explained by Divecha,Drach and Stefek (1992)
in their paper “A Quantitative Perspective”. The reason they gave for such
volatility is as follows
1. Political Instability
2. Unstable currency
3. High transaction cost
4. Liquidity problems
Apart from the factors mentioned above a very important factor that is
responsible of volatility is market concentration. Market concentration is
responsible for volatility in a sense that large stock represents large
proportions of over all market capitalization. Hence in such market there
are few chances of diversification as the returns of large stocks dominate
the overall market return. But developed markets are totally different from
emerging markets because the market is not dominated by one large stock
hence the returns are less volatile as there are more chances of
diversification.
50
As the literature points out that emerging markets are risky individually
but as there is low correlation between them and developed markets it acts
as risk reducer for the investor.
Bekaert and Harvey (2002), Bekaert and Urias (1999), Bekaert, Erb,
Harvey and Viskanta (1996), Divecha,Drach and Stefek (1992) all stated
that in principle emerging markets are much less correlated with each
other as compared to developed market. But there is an exception to this
rule and that is if such markets are in specific region such as South East
Asia
Emerging markets economies are not related to one another because of the
few economic and trade links they have with each other as a result there is
a low correlation in them. Hence a modest investment is such markets will
lead to reduction of portfolio risk of an investor rather than increasing the
portfolio risk of an investor.
CHAPTER 4
51
4.RESEARCH OBJECTIVES
4.1 IntroductionAfter detail analysis of existing literatures on the efficient market
hypothesis and the random walk, this chapter concerns with issue of
defining the main problem and research objective. Hence this chapter
concentrates on the problem definition and construction of hypotheses.
4.2 Research ObjectiveThe main objective of this study is to study the weak form efficiency of
Karachi Stock Exchange. We would be studying the existence of weak
form market efficiency. In order to test the weak form of market efficiency
monthly and weekly Index data of Karachi Stock Exchange would be
required. Weak form of market efficiency would be tested through
different statistical procedures.
4.3 Problem StatementAs discussed earlier a lot of research has been done on market efficiency
of developed markets but a little work is done on the efficiency of
developing markets. The purpose of this study is to test KSE -100 index
for the existence of random walk. If we are able to prove that there exists a
random walk, hence we will prove that KSE is efficient in weak form.
4.4 HypothesisAccording to Ryan, Scapens and Theobold (2002, p.130), "In studying the
relationships between variables, the null hypothesis usually denoted by
(Ho) is usually set up as stating there is no relationship between the
variables.”. Usually alternative hypothesis (H1) will support a prediction.
For this study the null hypothesis are as follow.
52
4.4.1Central Hypothesis That price on Karachi stock market follows random walk and is efficient
in weak form.
4.4.2Sub-HypothesisFor testing normal distribution we test the following Hypothesis
Ho: Stock Returns in KSE-100 index follow a normal distribution
H1: Stock Returns in KSE-100 index do not follow a normal
distribution
For Run Test we test the following Hypothesis
Ho: Stock Returns in KSE-100 index follow a random walk
H1: Stock Returns in KSE-100 index do not follow a random walk
For testing autocorrelation we test the following Hypothesis
Ho: ρx = 0
H1: ρx ≠ 0
In order to apply q statistics we will apply the following hypothesis
Ho: ρx is zero at sum of the lag k
H1: ρx is not zero at sum of the lag k
In order to test for the ADF unit root in KSE 100 index following
hypothesis is formed.
Ho: ρ = 1
H1: ρ ≠ 1
For Durbin Watson ‘d’ statistic
Ho: ρx = 0 i-e no autocorrelation then d=2
H1: ρx ≠ 0 then d ≠ 2
CHAPTER 5
53
5.Applied Data
5.1 IntroductionThis chapter will provide detail about type of data required and the source
of the data. Finally this chapter will explain how the data will be
transformed into meaning full information.
5.2 Data RequiredIn order to test Karachi Stock Exchange for the Existence of weak form
efficiency we would require Price Index data of KSE 100 index. Form this
price index data returns will be calculated. The price index comprise of
monthly index and weekly index which cover a period of nine years that is
starting from July 1997 to November 2006. The daily adjusted closing
prices were taken as source document and from this document monthly
and weekly index was obtained. We chose KSE 100 index because it is the
largest index in Pakistan. Karachi Stock Exchange is the largest and most
liquid stock market of Pakistan. According to KSE website “As on June
30, 2006, 658 companies were listed with the market capitalization of Rs.
2,801.182 billion (US $ 46.69) having listed capital of Rs. 495.968 billion
(US $ 8.27 billion). The KSE 100 Index closed at 9989.41 on June 30,
2006.” [www.kse.com.pk]
5.3 Data Source The data which consisted of adjusted closing prices of KSE-100 index was
obtained from the website www.finance.yahoo.com. From the same web
site I was able to obtain monthly weekly and daily adjusted closing values.
5.4 Transforming Data Structures into Information
Microsoft Excel and SPSS will mainly be used for data analysis purposes.
The presentation of the information will then take the following form:
54
5.4.1 Log DataI will take the logarithms of the original data I-e is the share price
indices, which is calculated as follow.
Pt = ln It
Where It represents the original share indices at time t and ln denotes the
natural logarithm.
5.4.2 Log ReturnsAfter calculating the Log of the data next step would be calculating log
returns. Such log returns are obtained from the series of Pt. There are
two kinds of returns, one is simple return also known as change returns
and the other one is continuously compounded returns also known as log
returns. Here in this paper we employ log returns. Log returns will be
calculated with the help of following formula.
Yt = ln It
It-ו
Where
Yt = return on day‘t’
It = index mean value on day‘t’
It-ו=index mean value on day ‘t-1’
ln= natural log.
5.4.3 Reason for Using Log DataThe data was transformed in into log returns, simple because we want to
have a normal data for our analysis and with the help of log function we
will be having continuous compounded normal returns. This method is
55
adopted in almost all the studies that I have gone through, which are
already being discussed in the part of literature review
CHAPTER 6
56
6.METHODOLOGY
6.1 IntroductionThis chapter will explain different methods that will be used in this study
to test if Karachi Stock Exchange is weak form efficient or not. This
chapter will also give a brief reason for choosing the methods that are
mentioned in this report.
Methods
I will be applying four methods in this paper. I will start from very basic
one and move on to more complex one. Following are the test that will be
performed on Returns from the prices of Karachi Stock Exchange (KSE).
I. Distribution of Returns
II. Auto Correlation Function (ACF) and Ljung Box Q Statistics
III. Runs Test
IV. Unit Root Test
6.1.1 Distribution of ReturnsI will start with distribution of return test. This is the very first test to
check if the distribution is normal or not. Because according to EMH
and Random walk theory if the stock prices are random then its
distribution should be normal. And if it is normal we say that it is weak
form efficient. We will calculate the following statistic under the
distribution of returns.
Mean
Standard Error
Median
Standard Deviation
Sample Variance
57
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
As we can see that this test tells us about the average monthly returns,
standard deviation, range of distribution, value of skewness and kurtosis.
I will construct a histogram of the index, and will fit the curve of normal
distribution to see if the distribution is normal or not. We call a
distribution skewed if the distribution is not symmetric and has more of
the tail to one end of the distribution that other. Kurtosis is used to see
how the observation clusters around a central point.
“Skewness is a measure of the asymmetry of a distribution & Kurtosis
measures peakedness of the distribution”
[http://www.statsoft.com/textbook/stbasic.html 11/4/06].
Measure of Skewness and Kurtosis are defined below:
Skewness = [E (Yt-µ) ³]²
[E (Yt-µ) ²]³
Kurtosis = E (Yt-µ) 4
[E (Yt-µ) ²]²
It should be noted here that we could calculate this with the help of
spreadsheet as well.
I will also calculate “t” statistic for mean Kurtosis and Skewness in
order to check its significance.
Jarque-Bera test is test for normality that can be defined as:
58
JB= n [Skewness² + Kurtosis²]/ 6+24
Where n is number of observation, if JB is greater that the critical value
of 5.99 I-e 95% confidence interval the null hypothesis of normal
distribution is rejected and vice versa.
6.1.2 Autocorrelation Function (ACF)According to Gujarati autocorrelation is defined as “lag correlation of a
given series with itself, lagged by a number of time units.” [Damodar
N.,Gujarati Basic Econometrics, Autocorrelation, 3rd, pp443]
One simple method for checking the randomness of prices changes I-e
testing for stationary and testing weak form efficiency is to plot
autocorrelation at successive lags against the length of the lag. If the
price exhibit random walk the returns of the stock are uncorrelated at
all lags and leads.
For non-stationery series auto correlation typically starts very high and
dies away very slowly, where as for pure random series known as white
noise process (which has no auto correlation and zero mean) starts very
low and die out very fast. Hence for such a series value of auto
correlation at a lag is not significantly different from zero.
ACF is a simple test of stationarity. We can define ACF at lag k, as
ρk = Covariance at lag k
Variance
ρk = E [(Yt-µ) (Yt+k -µ)]
√ E [(Yt- µ) ²] E (Yt+k - µ) ²]
ρk = Cov (Yt, Yt+k)
σ²t
59
Where ρk is the autocorrelation coefficient as a function of the lag k. (ρk
is the covariance between Yt and Yt+k, which is normalized by dividing
it by the variance of Y).
As covariance and variance are measured in the same units of
measurement, therefore ρk is unit less, or pure number. It lies between -1
and +1. If we plot this ρk against k, the graph we obtain is called
correlogram. If the price exhibit random walk the returns of the stock
are uncorrelated at all lags and leads.
a. Choice of Lag Length
The basic rule is to compute ACF up to 1/3rd to 1/4th the length of time
series (KSE price index). Then we will calculate autocorrelation
coefficients for the share price index and its returns respectively.
b. Correlogram
After this we will plot a correlogram to see if they depict the coefficients
falling off to numbers insignificantly different from zero and fluctuate
around it, if it is, the series appears to stationary. If it is not the case the
series is non-stationary.
c. Statistical Significance
In order to see if the calculated ρk is significant we will be constructing
confidence interval for the estimated autocorrelation coefficients to
determine whether they are significantly different from zero. We will be
taking 95% confidence interval in my dissertation. If ρk falls within this
limit we will accept the null hypothesis that value of coefficient at lag k
is zero. If it falls outside the limit we will reject the null hypothesis.
Apart from this we will be performing one other test as well which is as
follow.
60
6.1.3 Ljung-Box TestI will be using the above mention test to test the joint hypothesis that all
the autocorrelation coefficient are zero.
Ljung-Box Test is given as
Q= n (n+2)
6.1.4 Runs TestA Run test which is also called as Geary test is a non parametric test
and is used to examine if the returns are random or not.
According to Gujarati and run is defined as “an uninterrupted sequence
of one symbol such as + or -.”[Gujarati, Basic Econometrics,
Autocorrelation, 3rd ed, pp465]
The number of runs is allocated as sequence of price changes of the
same signs such as (++, ----, +++++++++, -----, +++).
Runs test is adopted to investigate serial dependence in price movement
and movement and compare the expected number of runs with the actual
(observed) number of runs.
We can simple defined run as series of identical signs, which are
followed by a different sign or no sign at all. Hence we can say that run
test checks weather that value one observation influences the values
taken by another observation. We can call an observation independent if
it not influenced by past observation. “The total number of runs is a
measure of randomness, since too many or too few runs suggest
dependence between
61
observations”.4[http://www.iif.edu/data/fi/journal/Fi103/FI103Art3.PDF
20/12/06]
Procedure:
From the returns of the Karachi Stock Exchange Index we will find n1,
n2 and n.
Where
n1 = number of +symbols
n2 = number of –symbols
n = n1+n2
After this we will calculate expected and actual runs and standard
deviation with the help of following formula
Expected Runs = 2*n1*n2 + 1
n
Standard Deviation = √ 2*n1*n2*(2*n1*n2-n1-n2)
(n1+n2)²*(n1+n2-1)
a. Actual Runs
Actual runs can be calculated with the help of n1. This would be done
with the help of ABS on spreadsheet.
Once we have calculated expected, actual runs and standard deviation
our next task will be to calculate Z score.
Z score = | actual- expected|
Std. Dev
At 95% confidence level we know that the value of Z is + 1.96 or -1.96.
We will reject the hypothesis of randomness if the value of our
calculated ‘Z’ falls outside these critical values.
4 http://www.iif.edu/data/fi/journal/Fi103/FI103Art3.PDF
62
The test result is actually a 2-tailed with significance if greater than 2.
“If the null hypothesis of randomness is sustainable, following the
properties of the normal distribution, we should expect that
Prob [E(R) – 1.96 σr < R < E(R) +1.96 σr] =.95
That is, the probability is 95% that the preceding interval will include
R.” [Gujarati Basic Econometrics, Autocorrelation, 3rd ed.pp466]
Decision Rule
Accept null hypothesis of random walk is R falls in the preceding
confidence interval and vice versa.
6.1.5 Unit Root TestI will be using unit root test in order to give more validity to the result.
Unit root test is used for finding the evidence of a random walk
This test was introduced by David Dickey and Wayne Fuller (Fuller,
1976; Dickey and Fuller, 1979). Just consider this simple equation
Yt = ρYt-1 +εt(1)
εt is white noise
If we are able to find any evidence of unit root then this means that ρ=1,
then there exists a random walk without drift, which shows an existence
of non stationary stochastic process. In order to check if ρ is statistically
equal to 1, we can write the above equation as
63
ΔYt = δYt-1 + εt (2)
Where δ = (ρ-1) and Δ is first difference operator
In practice we usually test this equation instead of first one, here we test
the null hypothesis that δ=0 and if δ=0 then ρ=1 then we have unit root.
Hence the time series under consideration is non-stationary.
A point that should be noted here is that if δ =0 then equation 2 will
become
ΔYt = εt (3)
Now the equation 3 means that first order difference of a random walk
time series Yt are stationary this is because εt is white noise error term.
If we estimate the equation 2 and if the result shows that Yt=0 then we
conclude that it is non stationary but if it is less then zero that is it is
negative then it means that Yt is stationary.
We will use the Augmented Dickey-Fuller test (ADF) to indicate
whether the variable Y is trend stationary or difference stationary. If the
stock price is trend stationary, the effects of shock would be momentary,
while if it is difference stationary, it would have a permanent effect.
The Augmented Dickey Fuller (ADY) unite root test is given by as:
6.1.6 Reason for Choosing Above Mentioned MethodThe above stated methods are basically applied because an ample
amount of literature is available on these methods and can be easily
64
understood and performed. Secondly all the research articles that I have
gone through have applied these methods. There are some other methods
that could have been used in this study, but the problem is those methods
are very complex and can’t be performed with recourses that I have. A
good example of one such method is Variance Ratio Test, which cannot
be performed using SPSS software, which is available to us. It is a very
strong test but unfortunately I was not able to apply this method in my
work to prove if KSE-100 index is Weak Form Efficient or not.
CHAPTER 7
65
7.EMPIRICAL RESULT
7.1 Descriptive StatisticsThis test is applied to test if the distribution is normal or not, because the
basic assumption underlying the random walk and efficient market
hypothesis is stock prices are random if distribution is normal. Below we
will discuss the result of descriptive statistics applied to Monthly and
Weekly returns.
7.1.1 Monthly Returns
Table 2: Monthly Returns Descriptive Statistics
Mean .01495358
Std. Error of Mean .009571473
Median .02039852
Mode -.406704(a)
Std. Deviation .101294946
Variance .010
Skewness -.694
Std. Error of Skewness .228
Kurtosis 2.356
Std. Error of Kurtosis .453
Range .647818
Minimum -.406704
Maximum .241114
Sum 1.674801
A Multiple modes exist. The smallest value is shown
The above table gives us descriptive statistics for monthly returns from
1997 to 2006. According to the table the average monthly return of
KSE-100 index is .014 with a standard deviation of .101. The range of
the distribution is .647 (.241114-(-.406704)). The value of the Skewness
(S) is -.694, which shows that distribution is negatively skewed. Also the
value of the Kurtosis (K), which is 2.356, indicates that some of the
66
values lie at the edge of the normal distribution cure. According to
Gujarati for a normal distribution it is necessary that value of the
Skewness should be Zero and that of Kurtosis should be equal to 3. As
we can see from the above table the value of Skewness and Kurtosis is
not 0 and 3 hence we can say that it not normal distribution.
I have also applied Jarque-Bera ((JB) test of normality in order to check
if the distribution is normal or not .the value of JB can be calculated
from the following equation.
JB = n [Skewness² + Kurtosis²]/ 6+24
JB =10.92
According to the above equation the value of JB is equal to10.92. This
shows that distribution is not normal; this is because it exceeds its
critical level of 5.99 at 95% level of confidence.
Graph 1: Histogram for Monthly Returns
67
0.2000000.000000-0.200000-0.400000
RETURNS
30
25
20
15
10
5
0
Fre
quency
Mean = 0.01495358Std. Dev. =0.101294946N = 112
Histogram
If we look at histogram it shows us that though most of the observation
centre around the mean, but due to few negative unusual observation the
overall distribution is not normal. If these observations are removed
from the analysis we might get a perfect normal distribution.
Hence it is proved by the result of Skewness, Kurtosis and Jarque Bera
test that monthly return distribution is not normal. On the basis of the
result we reject our null hypothesis that Stock Returns in KSE-100 index
follow a normal distribution and accept our alternative hypothesis.
68
7.1.2 Weekly Returns
Table 3: Weekly Returns Descriptive Statistics
The above table gives us descriptive statistics for weekly returns from
1997 to 2006. According to the table the average monthly return of
KSE-100 index is .003 with a standard deviation of .041. The range of
the distribution is .304 (.127-(-.176)). The value of the Skewness (S) is
-.777, which shows that distribution is negatively skewed. Also the value
of the Kurtosis (K), which is 2.560, indicates that some of the values lie
at the edge of the normal distribution cure. According to Gujarati for a
normal distribution it is necessary that value of the Skewness should be
Zero and that of Kurtosis should be equal to 3. As we can see from the
above table the value of Skewness and Kurtosis is not 0 and 3 hence we
can say that it not normal distribution.
Mean .00385634Std. Error of Mean .001868465Median .00781439Mode -.176180(a)Std. Deviation .041063750Variance .002Skewness -.777Std. Error of Skewness .111Kurtosis 2.560Std. Error of Kurtosis .222Minimum -.176180Maximum .127950Sum 1.862611
69
We have also applied Jarque-Bera ((JB) test of normality in order to
check if the distribution is normal or not .the value of JB can be
calculated from the following equation.
JB = n [Skewness² + Kurtosis²]/ 6+24
JB = 52.44
According to the above equation the value of JB is equal to52.44. This
shows that shows that distribution is not normal; this is because it
exceeds its critical level of 5.99 at 95% level of confidence.
Graph 2: Histogram for Weekly Returns
0.2000000.1000000.000000-0.100000-0.200000
RETURNS
80
60
40
20
0
Fre
quen
cy
Mean = 0.00385634Std. Dev. = 0.04106375N = 483
Histogram
If we look at histogram it shows us that though most of the observations
centre around the mean, but due to few negative unusual observations
the overall distribution is not normal. If these observations are removed
from the analysis we might get a perfect normal distribution.
70
Hence it is proved by the result of Skewness, Kurtosis and Jarque Bera
test that weekly return distribution is not normal. On the basis of the
result we reject our null hypothesis that Stock Returns in KSE-100 index
follow a normal distribution and accept our alternative hypothesis
7.2 AutocorrelationWith the help of SPSS software we were able to calculate the
Autocorrelation coefficient and Ljung-Box Q-statistics for monthly are
weekly indices of KSE-100 index. Below we have explained the result for
the both.
7.2.1 Monthly IndexGraph 3: Monthly Index Correlogram
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
987654321
Lag Number
1.0
0.5
0.0
-0.5
-1.0
AC
F
Lower ConfidenceLimit
Upper Confidence Limit
Coefficient
M.INDEX
The above figure shows the correlogram for monthly index from July
1997 to November 2006 which is constructed from autocorrelation
coefficient for monthly index of KSE 100 index for the said period
71
shown in Appendix A With the help of this correlogram we will be able
to confirm that that is past prices cannot be used to predict future
prices in other words past prices have no influence on future prices up to
36 lags.
We can say an autocorrelation coefficient is normal if it shows white
noise that is .
If we look at the correlogram we can see that Auto correlation
coefficient, wanders between the 95% confidence limits for the most
part i.e. autocorrelation coefficient lies between upper and lower limit. It
is only lag 8, 20 and 35, which makes a small break through. This might
be due to some event that might have occurred during that time.
Hence we can safely say that there is no Autocorrelation between current
month return and past month return even though lag 8, 20 and 35 cross
the confidence interval.
Based on the correlogram we can say that there exist a weak form of
market efficiency in KSE 100 index and that security prices exhibit a
random walk.
Now if we look at the Ljung Box Q-Statistic from the table given in
Appendix A we are able to confirm that there is no autocorrelation in all
36 lags. This is because at all lags the calculated Ljung Box Q-Statistic
does not exceed the critical value of chi-square distribution. Hence we
conclude from Ljung Box Q-Statistic that all autocorrelation coefficients
are not significantly different from zero and thus past prices are having
no relation with the current prices.
On the basis Autocorrelation test and Ljung Box Q-Statistic we are able
to conclude that there is no autocorrelation between current return and
past return and accept our null hypothesis of is equal to zero is
accepted. Further to this we confirm this weekly security prices follow
72
random walk and hence there exist a weak form of efficiency in KSE
100 Index.
7.2.2 Weekly IndexGraph 4: Weekly Index Correlogram
121
118
115
112
109
106
103
100
97
94
91
88
85
82
79
76
73
70
67
64
61
58
55
52
49
46
43
40
37
34
31
28
25
22
19
16
13
10
741
Lag Number
1.0
0.5
0.0
-0.5
-1.0
AC
F
Lower ConfidenceLimit
Upper Confidence Limit
Coefficient
W.INDEX
The above figure shows the correlogram for weekly index from July
1997 to November 2006 which is constructed from autocorrelation
coefficient for monthly index of KSE 100 index for the said period
shown in Appendix B. With the help of this correlogram we will be able
to confirm that that is past prices cannot be used to predict future
prices in other words past prices have no influence on future prices up to
121 lags.
We can say an autocorrelation coefficient is normal if it shows white
noise that is .
If we look at the correlogram we can see that Auto correlation
coefficient, wanders between the 95% confidence limits for the most
part i-e autocorrelation coefficient lies between upper and lower limit. It
is only lag 1,2,39,56,84,88 and121, which makes a small break through.
73
This might be due to some event that might have occurred during that
time.
Hence we can safely say that there is no Autocorrelation between current
week return and past week return even though lag 1,2,39,56,84,88 and
121 8,20 and 35 cross the confidence interval.
Based on the correlogram we can say that their exist a weak form of
market efficiency in KSE 100 index and that security prices exhibit a
random walk.
But if we look at Ljung –Box Q-statistics in the same table in Appendix
B they tell us a different story. According to figures showed in Ljung –
Box Statistic column in the same table autocorrelation is significant at
first 24 lags, but it is not significant for the rest of the lags. We can see
that the individual Q value for the first 24 lags exceeds the critical Q
value form the chi-square distribution but the over all value of Q for 121
lags which is 113.58 does not exceed the critical limit for Q in chi-
square distribution.
7.3 Run TestResult for Run Test on Monthly and Weekly Returns of KSE -100 index
are explained below.
7.3.1 Monthly Returns Table 4 below shows the result of run test applied on monthly returns of
KSE-100 index for a period of July 1997 to November 2006.
Table 4: Run Test for Monthly Returns
Run Test
74
Number of Observation 112
Actual Number of Runs 50
Expected Number of
Runs 45
Standard Deviation 5.02
Z-Test 0.995315
From the above table we can see that for monthly index the number of
actual runs is 50 and the expected number of the runs is 45. The standard
deviation for monthly returns is 5.02 and Z-Test value is .995315.
As Z-test value is less than the critical value of 1.96 we will accept the
hypothesis of randomness. Now we are going to examine if the null
hypothesis of randomness is sustainable. This can be done with the help
of this formula
[E(R) -1.96 σR ≤ R ≥ E(R) +1.96 σR] =. 95
Source: Gujarati Basic Econometrics, Autocorrelation third Edition
pp466
We will accept the hypothesis of randomness with 95% confidence if R
I-e number or runs lies in the preceding confidence interval and reject it
if it does not lie in it.
The interval for monthly returns of KSE-100 Index at 95% confidence
level is
54.84613 35.15387
75
This clearly includes the figure of actual runs that is 50. Hence we
conclude that monthly return of KSE-100 index follow and random walk
and there exist a weak form of efficiency in Karachi Stock exchange.
7.3.2 Weekly ReturnsTable 5 below shows the result of run test applied on weekly returns of
KSE-100 index for a period of July 1997 to November 2006.
Table 5: Weekly Returns for Run Test
Run Test
Number of Observation 483
Actual Number of Runs 187
Expected Number of
Runs 232.4398
Standard Deviation 23.69387
Z-Test -1.91779
From the above table we can see that for monthly index the number of
actual runs is 187 and the expected number of the runs is 232.4389. The
standard deviation for weekly returns is 23.69387 and Z-Test value is -
1.91779.
As Z-test value is less than the critical value of -1.96 we will accept the
hypothesis of randomness. Now we are going to examine if the null
hypothesis of randomness is sustainable. This can be done with the help
of this formula:
[E(R) -1.96 σR ≤ R ≥ E(R) +1.96 σR] =. 95
76
Source: Gujarati Basic Econometrics, Autocorrelation third Edition
pp466
We will accept the hypothesis of randomness with 95% confidence if R
I-e number or runs lies in the preceding confidence interval and reject it
if it does not lie in it.
The interval for weekly returns of KSE-100 Index at 95% confidence
level is
278.8798 185.9998
This clearly includes the figure of actual runs that is 187. Hence we
conclude that weekly return of KSE-100 index follow and random walk
and there exist a weak form of efficiency in Karachi Stock exchange.
Final we conclude that both monthly and weekly return exhibit random
walk and hence we can say that KSE-100 index exhibit weak form of
efficiency.
7.4 Augmented Dickey Fuller Test (ADF)I applied Augmented Dickey Fuller Test in order to give more validity to
our result. On the basis of ADF the monthly and weekly results are discuss
below.
7.4.1 Monthly ReturnsWe used ADF test in order to give more validity to our result, as this
result is much stronger than earlier test that we performed.
The table 6 below shows the result of ADF for monthly returns for a
period of July 1997 to November 2006.
77
Table 6: ADF Test for Monthly Returns
Null Hypothesis: tseries has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic Based on AIC, MAXLAG=10)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -10.626951 0.000000
Test critical values: 1% level -3.490269
5% level -2.887659
10% level -2.580784
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(tseries)
Method: Least Squares
Date: 31/12/2006 Time: 22:21:00
Included observations: 111 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob
tseries(-1) -1.023198 0.096283 -10.626951 0.000000
C 0.016045 0.009797 1.637749 0.104358
R-squared 0.508859 Mean dependent Var -0.000511
Adjusted R-squared 0.263288 S.D. dependent Var 0.144749
S.E. of regression 0.101906 Akaike info criterion -1.711674
Sum squared resid 1.131951 Schwarz criterion -1.662854
Log likelihood 96.997916 F-statistic 112.932084
Durbin-Watson stat 1.969366 Prob(F-statistic) 0.000000
The above ADF model contains 10 lags. The calculated ADF test value
is grater than the critical values. The calculated ADF value shown in
above table is -10.626951, which is even greater than the critical value at
78
one percent, which is -3.490269. On the basis of this result we reject the
null hypothesis that or in other words we are not able to find any
presence of unit root. As we have rejected the null hypothesis therefore
we accept the alternative hypothesis that . As we conclude that
monthly returns are stationary and posses a random walk.
The table also shows that R² value is .50, which proves that there is no
correlation between residual or error terms. Also the value of F statistic,
which is 112.92, indicates that model is valid. If we look at Durbin-
Watson Statistic we can see that its value is 1.969, which is almost equal
to 2, which means that there is no auto correlation between residuals.
After looking at all the facts we are able to conclude that monthly
returns follow a random walk and hence investor will not be able to
predict future prices based on past information.
7.4.2 Weekly Returns Like monthly returns I applied ADF test for weekly returns as well.
The table 7 below shows the result of ADF for Weekly returns for a
period of July 1997 to November 2006.
Table 7: Weekly Returns for ADF Test
Null Hypothesis: tseries has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic Based on AIC, MAXLAG=10)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -18.104505 0.000000
Test critical values: 1% level -3.443736
5% level -2.867326
79
10% level -2.569897
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(tseries)
Method: Least Squares
Date: 31/12/2006 Time: 22:26:35
Included observations: 482 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob
tseries(-1) -0.812825 0.044896 -18.104505 0.000000
C 0.003212 0.001848 1.737838 0.082881
R-squared 0.405774 Mean dependent Var 0.000167
Adjusted R-squared 0.108661 S.D. dependent Var 0.052361
S.E. of regression 0.040405 Akaike info criterion -3.575570
Sum squared resid 0.783643 Schwarz criterion -3.558234
Log likelihood 863.712360 F-statistic 327.773113
Durbin-Watson stat 2.001454 Prob(F-statistic) 0.000000
The above ADF model contains 10 lags. The calculated ADF test value
is grater than the critical values. The calculated ADF value shown in
above table is -18.104505, which is even greater than the critical value at
one percent, which is -3.490269. On the basis of this result we reject the
null hypothesis that or in other words we are not able to find any
presence of unit root. As we have rejected the null hypothesis therefore
we accept the alternative hypothesis that . As we conclude that
weekly returns are stationary and posses a random walk.
The table also shows that R² value is .40, which proves that there is no
correlation between residual or error terms. Also the value of F statistic,
which is 327.77, indicates that model is valid. If we look at Durbin-
80
Watson Statistic we can see that its value is 2.001, which is equal to 2,
which means that there is no auto correlation between residuals.
After looking at all the facts we are able to conclude that monthly
returns follow a random walk and hence investor will not be able to
predict future prices based on past information.
81
CHAPTER 8
8.CONCLUSION AND RECOMMENDATION
8.1 ConclusionI have used historic prices for a period ranging from July 1997 to
November 2006 to answer the central hypothesis that Karachi Stock
Exchange follows a Random Walk and is therefore weak form efficient.
The historic data was further divide into weekly and monthly returns.
On the basis of the over all analysis we conclude that Karachi Stock
exchange follows a random walk and hence is weak form efficient in both
weekly and monthly returns series.
I started by analysing the weekly and monthly distribution of returns for
normality. From the analysis I found that KSE-100 index monthly and
weekly distribution diverge from normality. The returns could be normal
for both weekly and monthly returns if few unusual observations were
removed.
Autocorrelation and Q Statistic was next test that was performed on
weekly and monthly returns distribution. According to Autocorrelation
test there was no evidence of autocorrelation in both monthly and weekly
returns and hence we can say that that there exist a weak form of market
efficiency in KSE 100 index and that security prices exhibit a random
walk. Q statistic also confirmed the existence of random walk in monthly
82
returns but the result for weekly returns was bit confusing because the
value of Q statistic exceed the critical limit for the first 24 lags according
to chi-square distribution but the rest of them fall with in the critical value.
The over all value of Q for 121 lags does not exceed the critical limit for Q
in chi-square distribution hence we can say that weekly returns also follow
random walk.
Run test, which is third test in our time series analysis, also confirmed that
both monthly and weekly returns follow random walk. Finally Augmented
Dickey Fuller Test (ADF) was performed which is strongest of the entire
test; this test also confirmed that both monthly and weekly distribution of
returns follow a random walk.
Final I concluded that KSE-100 index does support our central hypothesis
and follows a Random walk and is weak form efficient.
8.2 RecommendationIt is recommended that future research should be done using more power
full tool like Variance ration test and the period of the study should also be
increased to minimum 15 years. It would be worth knowing if KSE -100
index is semi-strong form efficient or not. It is proposed that any further
study on KSE-100 index should include the test of semi-strong form.
83
BIBLIOGRAPHY Journal
1. Abraham, A., Seyyed, F.J., and Alsakran, S.A., August 2002,
“Testing the Random Walk Behavior and Efficiency of the Gulf
Stock Markets”, The Financial Review, Vol. 37, Issue 3, pp. 469
2. Abeysekera, S.P., 2001,”Efficient Markets Hypothesis and the
Emerging Capital Market in Sri Lanka: Evidence from the
Colombo Stock Exchange - A Note”, Journal of Business Finance
& Accounting, Volume 28, Issue 1-2, pp 249-261.
3. Abrosimova, N., Dissanaike, G., and Dirk Linowski, D, D., 2005,”
Testing Weak-Form Efficiency of the Russian Stock Market”,
Journal of Social Science Research Network.
4. Al-Loughani,N., and David Chappell,D.,1997, “ On The Validity
of The Weak-Form Efficient Markets Hypothesis Applied To The
London Stock Exchange” ,Applied Financial Economics,7,pp 173-
176.
5. Agrawal, A., and Tandon, K., 1994"Anomalies or illusions?
Evidence from stock markets in eighteen countries”, Journal of
International Money and Finance, 13, pp.83-106.
6. Alexander, S.S.,(1961) “Price Movement is speculative market:
trends or random walks” Industrial Management Review,
2(May),7-26
7. Bhardwaj, R.K., and Brooks, L.D, 1992, “The January Anomaly:
Effects of Low Share Price, Transaction Costs, and Bid-Ask Bias”,
The Journal of Finance, Vol XL, VII.No2
84
8. Bekaert, G., and Urias, MS., (1999) “Is there a Free Lunch in
Emerging Market Equities?” The journal of Portfolio
Management, spring 1999, pp. 83-95.
9. Bekaert, G, Erb, CB, Harvey, CR and Viskanta, TE., (1996) “The
Behaviour of Emerging Market Returns” Working Paper, Duke
University and Stanford University
10. Copenhagen Business School and Lund Universitet, 2005,
Systematic variations in January.
http://www.fma.org/Stockholm/Papers/januarfma.pdf 02/12/06
11. Divecha, AB, Drach, J and Stefek, D., (1992) “A Quantitative
Perspective” The journal of Portfolio Management, Fall 1992,
pp.41-50.
12. French, K.R., 1980 "Stock returns and the weekend effect,"
Journal of Financial Economics 8, pp.55-69
13. Fama, E.F., 1970, “Efficient Capital Markets: A review of Theory
and Empirical Work” Journal of Finance, XXV, No.2. pp383-417
14. Fama,E.F., (1965)” Random Walks in Stock Market Prices”
Financial Analysts Journal, pp.55
15. Fama, E., And MacBech, J.,1973 “Risk, Return and Equilibrium:
Empirical Test” ,Journal of Political Economy, 81, No.3 May/June,
pp. 607-636
16. Groenewold, N, N., and Kang, K.C., 1993, “The Semi-Strong
Efficiency of the Australian Share Market”, The Economic Record,
Vol, 69, No.207.
85
17. Groenewold, N, N., 1997, “Share Market Efficiency: Test Using
Daily Data For Australia and New Zealand”, Applied Financial
Economics, 7, pp. 645-657.
18. Hasan M.S., 2004, “On the Validity of the Random Walk
Hypothesis Applied To the Dhaka Stock Exchange”, International
Journal of Theoretical and Applied Finance, Vol. 7, No.8
19. Imam, A.M., Hasan, T., and Kadapakkam, P., 1999, “An
Application of Variance-Ratio Test to Five Asian Stock Markets”,
Review of Pacific Basin Financial Markets and Policies, Vol.2,
No.3, pp. 301-315.
20. Kendall, Maurice G., 1953, “ The analysis of Economic time
series, part I: prices “Journal of the Royal Statistical Society,
96,pp.11-25
21. Kamara, A., 1997"New evidence on the Monday seasonal in stock
returns," Journal of Business 70, pp.63-84
22. Li, X., and Xu, J., 2002, “A Note On New Zealand Stock Market
Efficiency”, Applied Economics Letters, 9, 879-883.
23. Millon, A.E., and Moschos, D., 2000, “On The Validity of The
Weak-Form Efficient Markets Hypothesis Applied To The London
Stock Exchange: Comment” Applied Economics Letters, 7,419-
421.
24. Magnusson, M.A., and Wydick, B., 2002,” How Efficient Are
Africa’s Emerging Stock Markets”, The Journal of Development
Studies, Vol.38, No.4, pp 141-156.
86
25. Moustafa, M.A., 2004,” Testing the Weak –Form Efficiency of the
United Arab Emirates Stock Market”, International Journal of
Business, 9(3).
26. Naryan, P.K., and Smyth, R., 2004,” Is South Korea’s Stock
Market Efficient”, Applied Economics Letters, Vol.11, pp.707-710
27. Omet,G., Khasawneh,M., and Khasawneh,J., ,2002, “Efficiency
Test And Volatility Effects: Evidence From The Jordanian Stock
Market”, Applied Economics Letter 9,pp 817-821.
28. Okeahalam, C.C., and Jefferies, K.R., 1999,” An Event Study of
The Botswana, Zimbabwe and Johannesburg Stock Exchange”,
S.Afr.J.Bus Manage, 30(4).
29. Onour, I.A., 2004,” Testing Weak- Form Efficiency of Saudi Stock
Exchange Market”, Journal of Social Science Research Network.
30. Poshakwale, S., 1996, “Evidence on Weak Form Efficiency and
Day of the Week Effect in the Indian Stock Exchange”, Financial
India, Vol. X, No.3, pp 605-616.
31. Rozeff, M.S., and Kinney, W.R., 1976, "Capital market
seasonality: The case of stock returns”, Journal of Financial
Economics 3, pp.379-402.
32. Saunders, E.M.J., 1993"Stock prices and Wall Street weather,"
American Economic Review 83, 1337-1345.
87
33. Stengos, T., and Panas, E., 1992, “Testing the Efficiency of Athens
Stock Exchange: Some Result from Banking Sector”, Empirical
Economics, 17, pp.239-252.
34. Venkat R., Reinganum,E.R., December 1993 “The seasonal
behavior of the liquidity premium in asset pricing”, Journal of
Financial Economics, Volume 34, Issue 3, pp. 373-386
35. Wang, K., Li, Y., and Erickson, J., 1997, “A New Look at the
Monday Effect”, The Journal of Finance, Vol. 52, No. 5, pp. 2171-
2186
Web
1. http://www.pakistan.gov.pk/AboutPakistan.jsp
2. http://www.finance.gov.pk/survey/sur_chap_05-06/overview.pdf
3. http://www.colinafinancial.com
4. h ttp://www.bluechipmag.com/pi/0705/index.php
5. www.kse.com.pk
6. http://www.kse.com.pk/kse4/phps/aboutkse.php
7. http://www.finance.gov.pk/survey/sur_chap_05-06/overview.pdf
88
8. http://www.answers.com/topic/efficient-market-hypothesis
9. http://www.absoluteastronomy.com/ref/
efficient_market_hypothesis
10. http://www.statsoft.com/textbook/stbasic.html
Book
1. Enders, W., 1995, Applied Econometric Time Series. United States
of America: John Wiley & Sons,Inc.
2. Field, A., 2000, Discovering Statistics Using SPSS for Windows,
London: Sage Publication Ltd
3. Gujarati D., 1995,Basic Econometrics, 3rd ed. McGraw Hill
4. Ryan, B., Scapens, R.W. and Theobold, M. (2002), Research
Method and Methodology in Finance and Accounting, 2nd ed,
Thomson, UK.
APPENDIX: A
Monthly Index
Autocorrelation &Box Ljung Statistic
Series: M.INDEX
Lag Autocorrelation Std.Error(a)
Box-Ljung Statistic
Value Df Sig.(b)1 -.023 .093 .059 1 .8072 .070 .093 .633 2 .7293 -.068 .092 1.181 3 .7584 -.016 .092 1.211 4 .8765 .068 .092 1.768 5 .8806 .009 .091 1.777 6 .9397 -.028 .091 1.872 7 .9678 .177 .090 5.725 8 .6789 .054 .090 6.081 9 .732
10 .053 .089 6.428 10 .77811 .010 .089 6.441 11 .842
89
12 -.053 .088 6.798 12 .87113 .037 .088 6.973 13 .90414 .002 .088 6.973 14 .93615 -.146 .087 9.771 15 .83416 .023 .087 9.842 16 .87517 .053 .086 10.225 17 .89418 -.051 .086 10.583 18 .91119 .025 .085 10.670 19 .93420 -.211 .085 16.865 20 .66221 -.075 .084 17.646 21 .67122 .054 .084 18.056 22 .70323 -.018 .083 18.101 23 .75224 .075 .083 18.908 24 .75725 .089 .083 20.073 25 .74326 -.015 .082 20.109 26 .78627 .107 .082 21.831 27 .74628 -.131 .081 24.455 28 .65729 .002 .081 24.456 29 .70630 .097 .080 25.911 30 .68031 -.058 .080 26.448 31 .70032 .062 .079 27.059 32 .71533 .044 .079 27.379 33 .74334 .004 .078 27.381 34 .78235 .167 .078 31.981 35 .61536 -.082 .077 33.119 36 .606
a. The underlying process assumed is independence (white noise).b. Based on the asymptotic chi-square approximation.
90
APPENDIX: BWeekly Index
Autocorrelation Box –Ljung Statistic
Series: W.INDEX
Lag Autocorrelation Std.Error(a)
Box-Ljung Statistic
Value Df Sig.(b)1 .187 .045 16.908 1 .0002 .082 .045 20.160 2 .0003 -.002 .045 20.162 3 .0004 -.015 .045 20.266 4 .0005 -.044 .045 21.207 5 .0016 -.057 .045 22.801 6 .0017 .056 .045 24.320 7 .0018 .008 .045 24.351 8 .0029 .048 .045 25.495 9 .002
10 .010 .045 25.542 10 .004
91
11 -.015 .045 25.649 11 .00712 -.054 .045 27.118 12 .00713 .028 .045 27.506 13 .01114 -.012 .045 27.579 14 .01615 -.030 .045 28.016 15 .02116 .029 .045 28.429 16 .02817 .066 .045 30.635 17 .02218 -.070 .045 33.087 18 .01619 -.022 .045 33.342 19 .02220 -.007 .044 33.364 20 .03121 .043 .044 34.316 21 .03422 -.012 .044 34.394 22 .04523 -.003 .044 34.399 23 .06024 .000 .044 34.399 24 .07825 -.051 .044 35.741 25 .07626 .020 .044 35.940 26 .09327 .010 .044 35.993 27 .11528 .013 .044 36.079 28 .14129 .007 .044 36.106 29 .17030 .029 .044 36.534 30 .19131 -.010 .044 36.583 31 .22532 .033 .044 37.137 32 .24433 .050 .044 38.442 33 .23734 .017 .044 38.594 34 .27035 .007 .044 38.621 35 .30936 .028 .044 39.018 36 .33637 .026 .044 39.373 37 .36438 .015 .044 39.496 38 .40339 .083 .044 43.099 39 .30040 .002 .043 43.101 40 .34041 .003 .043 43.106 41 .38142 -.039 .043 43.896 42 .39143 .004 .043 43.904 43 .43344 -.016 .043 44.035 44 .47045 -.055 .043 45.674 45 .44446 .040 .043 46.515 46 .45147 -.011 .043 46.585 47 .49048 .035 .043 47.230 48 .50449 .051 .043 48.648 49 .48750 -.055 .043 50.263 50 .46351 -.071 .043 53.004 51 .39752 -.014 .043 53.106 52 .431
92
53 .031 .043 53.641 53 .45054 .041 .043 54.551 54 .45355 -.008 .043 54.587 55 .49056 .075 .043 57.697 56 .41257 -.007 .043 57.722 57 .44858 -.026 .043 58.098 58 .47259 .014 .043 58.213 59 .50460 .011 .042 58.278 60 .53961 -.036 .042 59.014 61 .54862 -.013 .042 59.108 62 .58163 -.030 .042 59.617 63 .59864 -.073 .042 62.623 64 .52565 -.070 .042 65.373 65 .46466 -.030 .042 65.891 66 .48167 -.011 .042 65.959 67 .51368 -.012 .042 66.041 68 .54569 -.004 .042 66.050 69 .57870 -.008 .042 66.084 70 .61171 -.005 .042 66.101 71 .64272 -.007 .042 66.126 72 .67373 .055 .042 67.884 73 .64774 .027 .042 68.311 74 .66575 .006 .042 68.329 75 .69476 -.022 .042 68.597 76 .71577 .002 .042 68.600 77 .74278 .019 .042 68.804 78 .76279 -.044 .042 69.911 79 .75880 -.054 .041 71.577 80 .73881 -.029 .041 72.068 81 .75182 .005 .041 72.081 82 .77583 .086 .041 76.399 83 .68284 -.015 .041 76.527 84 .70685 -.054 .041 78.228 85 .68586 -.060 .041 80.320 86 .65287 -.094 .041 85.530 87 .52488 -.078 .041 89.150 88 .44689 -.060 .041 91.268 89 .41490 .004 .041 91.279 90 .44391 -.027 .041 91.705 91 .46092 .013 .041 91.799 92 .48693 -.006 .041 91.820 93 .51594 .012 .041 91.912 94 .542
93
95 .042 .041 92.973 95 .54096 -.010 .041 93.039 96 .56797 -.007 .041 93.071 97 .59498 -.006 .041 93.096 98 .62199 -.008 .040 93.140 99 .647
100 .058 .040 95.169 100 .618101 .031 .040 95.768 101 .628102 .048 .040 97.200 102 .616103 .003 .040 97.206 103 .642104 .029 .040 97.714 104 .655105 .023 .040 98.035 105 .672106 -.012 .040 98.126 106 .695107 .001 .040 98.127 107 .718108 .004 .040 98.135 108 .741109 -.008 .040 98.179 109 .762110 .053 .040 99.947 110 .744111 .075 .040 103.451 111 .682112 .036 .040 104.257 112 .686113 -.045 .040 105.550 113 .678114 -.009 .040 105.598 114 .701115 .022 .040 105.906 115 .716116 .028 .040 106.393 116 .727117 -.021 .040 106.675 117 .743118 -.001 .039 106.676 118 .764119 -.006 .039 106.697 119 .783120 -.056 .039 108.706 120 .761121 -.087 .039 113.598 121 .671
a. The underlying process assumed is independence (white noise).b. Based on the asymptotic chi-square approximation.
94
APPENDIX: CRuns Test for Monthly Returns
RETURNS N1 N2 ACTUAL
-0.064562828 0 1
0.074685009 1 0 1
0.043647936 1 0 0
-0.042233384 0 1 1
0.049626843 1 0 1
0.01907274 1 0 0
-0.146074847 0 1 1
-0.012592558 0 1 0
0.002596111 1 0 1
0.084925587 1 0 0
95
0.096365437 1 0 0
0.057058396 1 0 0
0.090280304 1 0 0
0.002635825 1 0 0
0.053537448 1 0 0
0.082570742 1 0 0
-0.037079793 0 1 1
0.082862406 1 0 1
-0.035381765 0 1 1
-0.089563135 0 1 0
-0.061119217 0 1 0
0.202276088 1 0 1
0.081643125 1 0 0
0.110514432 1 0 0
0.043226794 1 0 0
0.021724304 1 0 0
-0.024329567 0 1 1
0.010573553 1 0 1
0.00203234 1 0 0
-0.040575411 0 1 1
0.012327873 1 0 1
0.06147275 1 0 0
0.053554406 1 0 0
-0.000198312 0 1 1
0.07944319 1 0 1
0.094523523 1 0 0
0.073226304 1 0 0
-0.063109649 0 1 1
-0.1023722 0 1 0
0.125981743 1 0 1
0.144994926 1 0 0
0.093409252 1 0 0
96
0.06555096 1 0 0
0.066487997 1 0 0
0.12394309 1 0 0
-0.059047815 0 1 1
-0.059615704 0 1 0
0.167027163 1 0 1
0.003211809 1 0 0
0.121056379 1 0 0
0.02212279 1 0 0
0.099487374 1 0 0
0.009826652 1 0 0
0.062214062 1 0 0
-0.132473473 0 1 1
0.016373877 1 0 1
0.056238435 1 0 0
0.086151535 1 0 0
0.241113803 1 0 0
-0.064707391 0 1 1
-0.034653512 0 1 0
0.215535921 1 0 1
-0.104616479 0 1 1
0.023753589 1 0 1
-0.106090176 0 1 1
-0.008148614 0 1 0
0.00769498 1 0 1
0.031688056 1 0 0
-0.071926727 0 1 1
-0.026637922 0 1 0
-0.030980623 0 1 0
0.16674298 1 0 1
-0.154550271 0 1 1
-0.049425599 0 1 0
97
0.03017371 1 0 1
-0.023839706 0 1 1
0.022220752 1 0 1
-0.01041424 0 1 1
-0.212812163 0 1 0
-0.050575283 0 1 0
0.035156153 1 0 1
0.085253235 1 0 0
0.229766425 1 0 0
0.121754971 1 0 0
0.04767967 1 0 0
-0.008348 0 1 1
-0.006002179 0 1 0
-0.036842632 0 1 0
0.171346605 1 0 1
-0.147260939 0 1 1
0.09881714 1 0 1
0.04647356 1 0 0
0.131852449 1 0 0
0.028061991 1 0 0
-0.048399863 0 1 1
-0.106029963 0 1 0
0.22204517 1 0 1
-0.278006089 0 1 1
0.135329873 1 0 1
0.053204599 1 0 0
0.045416646 1 0 0
-0.16768004 0 1 1
-0.406704498 0 1 0
0.005880708 1 0 1
-0.079655308 0 1 1
0.044170183 1 0 1
98
-0.086083962 0 1 1
-0.010448017 0 1 0
-0.05636971 0 1 0
0.013590529 1 0 1
0.048409364 1 0 0
-0.121274278 0 1 1
68 44 50
Expected= [(2*n1*n2)/n1+n2] +1
Std.Deviation= sqrt [2xn1xn2x (2xn1xn2-n1-n2)]/ [(n1+n2) ^2x (n1+n2-1)]
Z= [actual-expected]/Std.Deviation
APPENDIX: DRun Test for Weekly Returns
Returns N1 N2Actual Runs
-0.0234 0 1
0.015297 1 0 1
-0.00313 0 1 1
-0.04615 0 1 0
-0.02793 0 1 0
0.05699 1 0 1
-0.00023 0 1 1
0.038674 1 0 1
0.019768 1 0 0
0.031758 1 0 0
0.001941 1 0 0
99
-0.02044 0 1 1
0.05936 1 0 1
-0.09717 0 1 1
0.014925 1 0 1
-0.03458 0 1 1
0.039677 1 0 1
0.009305 1 0 0
0.022731 1 0 0
0.019237 1 0 0
-0.01547 0 1 1
0.018375 1 0 1
0.020647 1 0 0
-0.02495 0 1 1
-0.04917 0 1 0
-0.02991 0 1 0
-0.01867 0 1 0
-0.05814 0 1 0
-0.01508 0 1 0
0.029902 1 0 1
-0.05701 0 1 1
-0.0107 0 1 0
0.016636 1 0 1
0.038488 1 0 0
0.002294 1 0 0
0.045388 1 0 0
0.044523 1 0 0
-0.08604 0 1 1
-0.01145 0 1 0
0.016958 1 0 1
0.02676 1 0 0
0.029976 1 0 0
100
0.026345 1 0 0
0.021252 1 0 0
0.033966 1 0 0
0.033917 1 0 0
0.00684 1 0 0
-0.00246 0 1 1
0.008764 1 0 1
0.022018 1 0 0
0.017716 1 0 0
0.014544 1 0 0
0.015748 1 0 0
0.04148 1 0 0
0.014005 1 0 0
0.003488 1 0 0
-0.06656 0 1 1
0.036609 1 0 1
0.037781 1 0 0
0.005579 1 0 0
0.030455 1 0 0
0.005724 1 0 0
0.012691 1 0 0
0.026545 1 0 0
0.036759 1 0 0
0.022303 1 0 0
-0.03679 0 1 1
0.032841 1 0 1
-0.02407 0 1 1
-0.02444 0 1 0
-0.00703 0 1 0
0.01652 1 0 1
0.015409 1 0 0
-0.00655 0 1 1
101
0.007249 1 0 1
0.018151 1 0 0
0.109173 1 0 0
-0.12115 0 1 1
-0.01512 0 1 0
0.031258 1 0 1
0.011002 1 0 0
0.00046 1 0 0
-0.05633 0 1 1
-0.01064 0 1 0
-0.00047 0 1 0
-0.04731 0 1 0
-0.17618 0 1 0
-0.01092 0 1 0
0.088117 1 0 1
0.059539 1 0 0
0.068865 1 0 0
0.06618 1 0 0
0.038056 1 0 0
0.024764 1 0 0
0.007621 1 0 0
0.028044 1 0 0
0.03742 1 0 0
0.016033 1 0 0
0.028149 1 0 0
0.03419 1 0 0
0.024564 1 0 0
0.022146 1 0 0
0.003429 1 0 0
0.006626 1 0 0
0.006596 1 0 0
0.024287 1 0 0
102
0.003755 1 0 0
-0.02337 0 1 1
0.004561 1 0 1
0.016804 1 0 0
0.018344 1 0 0
0.031988 1 0 0
0.006865 1 0 0
-0.02472 0 1 1
-0.02793 0 1 0
-0.01405 0 1 0
-0.00279 0 1 0
0.013631 1 0 1
-0.00144 0 1 1
0.010081 1 0 1
-0.02233 0 1 1
0.003988 1 0 1
-0.01212 0 1 1
0.018615 1 0 1
0.047296 1 0 0
-0.02762 0 1 1
-0.02555 0 1 0
0.004023 1 0 1
-0.02575 0 1 1
-0.0015 0 1 0
0.01027 1 0 1
-0.01357 0 1 1
0.018023 1 0 1
0.004328 1 0 0
-0.03191 0 1 1
0.038466 1 0 1
0.039885 1 0 0
0.008508 1 0 0
103
0.023272 1 0 0
0.017146 1 0 0
0.002997 1 0 0
0.012332 1 0 0
-0.00586 0 1 1
-0.0013 0 1 0
-0.00272 0 1 0
0.02613 1 0 1
0.016567 1 0 0
0.024634 1 0 0
0.021277 1 0 0
0.018246 1 0 0
0.018859 1 0 0
0.001286 1 0 0
0.024804 1 0 0
0.03185 1 0 0
0.023183 1 0 0
0.031242 1 0 0
0.023544 1 0 0
-0.00474 0 1 1
-0.04254 0 1 0
-0.00609 0 1 0
-0.04287 0 1 0
-0.01177 0 1 0
0.006982 1 0 1
-0.05288 0 1 1
-0.04781 0 1 0
0.031154 1 0 1
0.000352 1 0 0
0.009746 1 0 0
0.064445 1 0 0
-0.04268 0 1 1
104
0.072806 1 0 1
0.054148 1 0 0
0.014806 1 0 0
0.028611 1 0 0
0.047181 1 0 0
0.022618 1 0 0
0.02773 1 0 0
0.012925 1 0 0
0.038341 1 0 0
0.01371 1 0 0
0.006182 1 0 0
0.025182 1 0 0
0.010355 1 0 0
0.016226 1 0 0
0.022567 1 0 0
-0.02626 0 1 1
0.022281 1 0 1
0.032602 1 0 0
0.012476 1 0 0
0.034278 1 0 0
0.042938 1 0 0
0.036726 1 0 0
0.020427 1 0 0
-0.05244 0 1 1
0.018716 1 0 1
-0.02532 0 1 1
-0.02498 0 1 0
-0.12423 0 1 0
0.029326 1 0 1
0.044328 1 0 0
0.030874 1 0 0
0.0526 1 0 0
105
0.029243 1 0 0
0.044666 1 0 0
0.025586 1 0 0
-0.02611 0 1 1
0.032372 1 0 1
0.019676 1 0 0
-0.02976 0 1 1
0.025539 1 0 1
0.057526 1 0 0
0.036034 1 0 0
0.004226 1 0 0
0.004744 1 0 0
0.018861 1 0 0
0.013421 1 0 0
-0.02735 0 1 1
0.017207 1 0 1
0.02504 1 0 0
0.04378 1 0 0
0.015032 1 0 0
0.020228 1 0 0
-0.00205 0 1 1
-0.00866 0 1 0
0.008594 1 0 1
-0.00966 0 1 1
0.017006 1 0 1
-0.00518 0 1 1
0.006371 1 0 1
0.044357 1 0 0
0.016664 1 0 0
7.82E-05 1 0 0
-0.06773 0 1 1
-0.01045 0 1 0
106
-0.05712 0 1 0
0.025569 1 0 1
-0.00421 0 1 1
0.002853 1 0 1
0.004546 1 0 0
-0.00964 0 1 1
-0.01393 0 1 0
0.003845 1 0 1
0.019273 1 0 0
0.042213 1 0 0
0.029086 1 0 0
0.011865 1 0 0
-0.04684 0 1 1
0.066062 1 0 1
0.090202 1 0 0
0.031822 1 0 0
0.07293 1 0 0
0.008913 1 0 0
0.071103 1 0 0
-0.10091 0 1 1
0.016887 1 0 1
0.016279 1 0 0
0.003385 1 0 0
-0.01985 0 1 1
-0.00143 0 1 0
-0.01232 0 1 0
-0.00121 0 1 0
0.100859 1 0 1
0.059676 1 0 0
0.044944 1 0 0
0.006823 1 0 0
-0.00546 0 1 1
107
0 0 0 0
-0.08987 0 1 0
-0.00928 0 1 0
-0.00806 0 1 0
-0.01691 0 1 0
0.050394 1 0 1
-0.02076 0 1 1
0.007814 1 0 1
-0.01418 0 1 1
-0.04006 0 1 0
0.004438 1 0 1
-0.04501 0 1 1
0.009759 1 0 1
-0.0269 0 1 1
0.016509 1 0 1
-0.01057 0 1 1
0.0236 1 0 1
-0.00945 0 1 1
0.011635 1 0 1
-0.01777 0 1 1
0.004643 1 0 1
-0.01692 0 1 1
0.011604 1 0 1
0.0363 1 0 0
-0.00121 0 1 1
-0.01982 0 1 0
-0.03303 0 1 0
-0.01664 0 1 0
-0.01448 0 1 0
-0.04904 0 1 0
0.010559 1 0 1
0.012084 1 0 0
108
0.042416 1 0 0
-0.02423 0 1 1
-0.0126 0 1 0
-0.04985 0 1 0
0.034805 1 0 1
0.080756 1 0 0
0.04258 1 0 0
0.033696 1 0 0
-0.06067 0 1 1
-0.03864 0 1 0
-0.03697 0 1 0
-0.0384 0 1 0
0.022312 1 0 1
-0.01098 0 1 1
-0.02819 0 1 0
-0.02302 0 1 0
0.010578 1 0 1
0.008201 1 0 0
-0.00198 0 1 1
-0.014 0 1 0
0.040518 1 0 1
0.009014 1 0 0
-0.04634 0 1 1
0.001859 1 0 1
0.004215 1 0 0
-0.00443 0 1 1
-0.02972 0 1 0
0.048779 1 0 1
0.016303 1 0 0
-0.00386 0 1 1
-0.00034 0 1 0
0.019174 1 0 1
109
0.06438 1 0 0
-0.05228 0 1 1
-0.02415 0 1 0
-0.10704 0 1 0
0.005141 1 0 1
-0.07754 0 1 1
-0.05058 0 1 0
-0.04655 0 1 0
0.012454 1 0 1
0.012179 1 0 0
-0.02866 0 1 1
-0.0011 0 1 0
-3.5E-05 0 1 0
0.033007 1 0 1
0.015641 1 0 0
-0.03783 0 1 1
0.02157 1 0 1
0.12795 1 0 0
-0.05384 0 1 1
0.028387 1 0 1
-0.02417 0 1 1
0.097243 1 0 1
0.080847 1 0 0
0.062515 1 0 0
0.000682 1 0 0
0.011752 1 0 0
0.026153 1 0 0
0.072412 1 0 0
0.032393 1 0 0
0.013667 1 0 0
0.021897 1 0 0
-0.01306 0 1 1
110
0.003542 1 0 1
0.032568 1 0 0
0.019331 1 0 0
-0.09026 0 1 1
0.031014 1 0 1
0.005239 1 0 0
0.030844 1 0 0
-0.00048 0 1 1
-0.0088 0 1 0
-0.04738 0 1 0
-0.05524 0 1 0
0.08813 1 0 1
-0.02046 0 1 1
-0.0357 0 1 0
0.049756 1 0 1
0.04838 1 0 0
0.044804 1 0 0
-0.01805 0 1 1
0.056585 1 0 1
-0.00777 0 1 1
-0.066 0 1 0
-0.01102 0 1 0
-0.04205 0 1 0
-0.10337 0 1 0
0.07556 1 0 1
0.057442 1 0 0
0.038638 1 0 0
0.0325 1 0 0
0.067802 1 0 0
-0.02024 0 1 1
-0.02912 0 1 0
-0.00448 0 1 0
111
0.00558 1 0 1
-0.00107 0 1 1
0.066426 1 0 1
0.060921 1 0 0
0.013511 1 0 0
0.04348 1 0 0
0.008229 1 0 0
-0.03716 0 1 1
-0.03291 0 1 0
0.00703 1 0 1
0.025979 1 0 0
-0.0485 0 1 1
-0.00749 0 1 0
0.013223 1 0 1
0.000575 1 0 0
-0.04144 0 1 1
-0.05575 0 1 0
0.046011 1 0 1
0.0484 1 0 0
0.093795 1 0 0
0.018691 1 0 0
0.038426 1 0 0
-0.03814 0 1 1
-0.11268 0 1 0
-0.15666 0 1 0
0.015332 1 0 1
0.026207 1 0 0
-0.01278 0 1 1
0.103036 1 0 1
-0.01522 0 1 1
0.025047 1 0 1
-0.0091 0 1 1
112
-0.00839 0 1 0
0.055448 1 0 1
-0.04093 0 1 1
0.08256 1 0 1
0.127494 1 0 0
-0.11022 0 1 1
-0.0104 0 1 0
-0.14728 0 1 0
-0.04474 0 1 0
-0.02323 0 1 0
0.044487 1 0 1
-0.14775 0 1 1
-0.16783 0 1 0
-0.0845 0 1 0
-0.00662 0 1 0
-0.03411 0 1 0
0.008243 1 0 1
0.043857 1 0 0
-0.02208 0 1 1
0.026151 1 0 1
-0.04431 0 1 1
-0.01762 0 1 0
-0.03391 0 1 0
0.00432 1 0 1
-0.02709 0 1 1
0.028043 1 0 1
0.0389 1 0 0
0.007742 1 0 0
0.048182 1 0 0
-0.08703 0 1 1
-0.05068 0 1 0
0.018844 1 0 1
113
-0.00625 0 1 1
-0.02006 0 1 0
-0.01687 0 1 0
0.009608 1 0 1
0.012583 1 0 0
-0.01973 0 1 1
-0.03425 0 1 0
-0.01497 0 1 0
-0.05483 0 1 0
0.00102 1 0 1
0.048853 1 0 0
0.013631 1 0 0
0.01177 1 0 0
-0.00795 0 1 1
-0.01708 0 1 0
0.054926 1 0 1
0.01165 1 0 0
-0.05109 0 1 1
-0.02324 0 1 0
-0.05965 0 1 0
0.012701 1 0 1
0.003878 1 0 0
0.071369 1 0 0
0.055687 1 0 0
0.056877 1 0 0
289 193 187
Expected= [(2*n1*n2)/n1+n2] +1
Std.Deviation= sqrt [2xn1xn2x (2xn1xn2-n1-n2)]/ [(n1+n2) ^2x (n1+n2-1)]
114
Z= [actual-expected]/Std.Deviation
APPENDIX: E
KSE-100 INDEX MONTHLY INDEX
DATE INDEX DATE INDEX DATE INDEX01-Nov-06 10619.47 01-Apr-02 1898.95 01-Sep-97 1849.702-Oct-06 11327.71 01-Mar-02 1868.11 04-Aug-97 1762.2901-Sep-06 10512.52 01-Feb-02 1765.95 02-Jul-97 1989.5101-Aug-06 10063.54 02-Jan-02 1620.18 03-Jul-06 10497.66 03-Dec-01 1273.06
01-Jun-06 9989.41 01-Nov-01 1358.16 02-May-06 9800.69 01-Oct-01 1406.05 03-Apr-06 11342.17 03-Sep-01 1133.43 01-Mar-06 11485.9 01-Aug-01 1258.43 01-Feb-06 11456.12 03-Jul-01 1228.89 02-Jan-06 10523.37 01-Jun-01 1366.43 01-Dec-05 9556.61 02-May-01 1377.61
115
02-Nov-05 9026.59 02-Apr-01 1367.05 03-Oct-05 8247.37 01-Mar-01 1324.41 01-Sep-05 8225.66 01-Feb-01 1423.18 01-Aug-05 7796.86 02-Jan-01 1461.6 01-Jul-05 7178.93 04-Dec-00 1507.59
01-Jun-05 7450.12 01-Nov-00 1276.05 02-May-05 6857.67 02-Oct-00 1489.32 01-Apr-05 7104.65 01-Sep-00 1564.78 01-Mar-05 7770.33 01-Aug-00 1518.27 01-Feb-05 8260.06 03-Jul-00 1554.9 03-Jan-05 6747.39 01-Jun-00 1520.73 01-Dec-04 6218.4 01-May-00 1536.65 01-Nov-04 5567.79 03-Apr-00 1901.07 01-Oct-04 5332.24 01-Mar-00 1999.69 01-Sep-04 5217.65 01-Feb-00 1930.61 02-Aug-04 5346.15 03-Jan-00 1772.84 01-Jul-04 5289.92 01-Dec-99 1408.91
01-Jun-04 5279.18 01-Nov-99 1247.4 04-May-04 5497.79 01-Oct-99 1189.32 01-Apr-04 5430.43 01-Sep-99 1199.29 01-Mar-04 5106.66 02-Aug-99 1206.51 06-Feb-04 4840.37 01-Jul-99 1251.79 02-Jan-04 4841.33 01-Jun-99 1054.67 01-Dec-03 4471.6 03-May-99 1222 03-Nov-03 4068.29 01-Apr-99 1107.02 01-Oct-03 3781.03 01-Mar-99 1056.75 01-Sep-03 4027.34 01-Feb-99 926.21 01-Aug-03 4461.47 04-Jan-99 900.58 01-Jul-03 3933.37 01-Dec-98 945.24
02-Jun-03 3402.47 02-Nov-98 1050.97 02-May-03 3099.04 01-Oct-98 841.7 01-Apr-03 2902.41 01-Sep-98 1111.46 03-Mar-03 2715.71 03-Aug-98 970.78 03-Feb-03 2399.14 01-Jul-98 920.48 02-Jan-03 2545.07 01-Jun-98 879.61 02-Dec-02 2701.41 04-May-98 1040.19 01-Nov-02 2285.87 01-Apr-98 1562.22 01-Oct-02 2278.54 02-Mar-98 1553.06 02-Sep-02 2018.75 02-Feb-98 1681.83 01-Aug-02 1974.58 01-Jan-98 1609.16 01-Jul-02 1787.59 01-Dec-97 1753.82
03-Jun-02 1770.11 03-Nov-97 1772.24 02-May-02 1663.34 01-Oct-97 1875.01
116
APPENDIX: FKSE 100 INDEX WEEKLY INDEX
DATE INDEX DATE INDEX DATE INDEX27-Nov-06 10619.47 24-Oct-05 8319.29 04-Oct-04 5342.9420-Nov-06 10870.9 17-Oct-05 8290.32 27-Sep-04 5245.8213-Nov-06 10705.87 10-Oct-05 8860.9 20-Sep-04 5080.6706-Nov-06 10739.45 03-Oct-05 8542.38 13-Sep-04 5045.9130-Oct-06 11246.7 26-Sep-05 8225.66 06-Sep-04 5172.2116-Oct-06 11565.25 19-Sep-05 8179.9 30-Aug-04 5318.7309-Oct-06 10924.58 12-Sep-05 7934.54 23-Aug-04 5393.9902-Oct-06 10927.05 05-Sep-05 7889.25 16-Aug-04 5409.0525-Sep-06 10512.52 29-Aug-05 7789.76 09-Aug-04 5335.8218-Sep-06 10306.75 22-Aug-05 7585.7 02-Aug-04 5343.5211-Sep-06 9984.57 15-Aug-05 7311.92 26-Jul-04 5289.9204-Sep-06 9965.21 08-Aug-05 7150.65 19-Jul-04 5409.3728-Aug-06 10170.97 01-Aug-05 7418.61 12-Jul-04 5387.84
117
21-Aug-06 9584.79 25-Jul-05 7178.93 05-Jul-04 5453.5515-Aug-06 10562.88 18-Jul-05 7353.85 28-Jun-04 5352.9707-Aug-06 10406.4 11-Jul-05 7535.81 21-Jun-04 5105.6931-Jul-06 10772.58 04-Jul-05 7588.94 14-Jun-04 5248.6724-Jul-06 10353.52 27-Jun-05 7464.6 07-Jun-04 5384.4817-Jul-06 10257.63 20-Jun-05 7350.46 31-May-04 5362.8610-Jul-06 10027.09 13-Jun-05 7398.73 24-May-04 5502.7203-Jul-06 9836.04 06-Jun-05 7345.29 17-May-04 5511
26-Jun-06 9989.41 30-May-05 7213.17 10-May-04 5454.6919-Jun-06 9807.53 23-May-05 6467.15 04-May-04 5529.1912-Jun-06 9607.11 16-May-05 7300.09 26-Apr-04 5430.4305-Jun-06 9849.83 09-May-05 7411.33 19-Apr-04 5406.98
29-May-06 10346.23 02-May-05 7183.25 12-Apr-04 5582.2822-May-06 10660.39 25-Apr-05 7104.65 05-Apr-04 5371.6315-May-06 10861.31 18-Apr-05 7101.38 29-Mar-04 5161.608-May-06 11511.54 11-Apr-05 7512.91 22-Mar-04 5117.8702-May-06 11686.44 04-Apr-05 7593.3 15-Mar-04 5000.1424-Apr-06 11342.17 28-Mar-05 7596.87 08-Mar-04 4915.1417-Apr-06 12007.6 21-Mar-05 7964.95 01-Mar-04 4900.4310-Apr-06 12136.83 14-Mar-05 9499.42 23-Feb-04 4840.3703-Apr-06 11936.59 07-Mar-05 9603.73 16-Feb-04 4868.8127-Mar-06 11485.9 28-Feb-05 8793.69 09-Feb-04 4875.1620-Mar-06 11459.58 21-Feb-05 8285.4 26-Jan-04 4888.4513-Mar-06 10951.08 14-Feb-05 7734.03 19-Jan-04 4762.3706-Mar-06 10474.2 07-Feb-05 7238.76 12-Jan-04 4684.1227-Feb-06 11415.29 31-Jan-05 6968.46 05-Jan-04 4570.1420-Feb-06 11546.79 24-Jan-05 6798.01 29-Dec-03 4473.9313-Feb-06 11352.63 17-Jan-05 6746.4 22-Dec-03 4393.0406-Feb-06 11052.86 10-Jan-05 6559.83 15-Dec-03 4310.9730-Jan-06 10726.46 03-Jan-05 6318.9 08-Dec-03 4305.4323-Jan-06 10447.56 27-Dec-04 6218.4 01-Dec-03 4199.9509-Jan-06 10227.87 20-Dec-04 6045.8 24-Nov-03 4068.2902-Jan-06 9886.3 13-Dec-04 5842.59 17-Nov-03 3975.0626-Dec-05 9556.61 06-Dec-04 5700.82 10-Nov-03 3852.7919-Dec-05 9491.47 29-Nov-04 5575.96 03-Nov-03 3763.1412-Dec-05 9514.83 22-Nov-04 5556.87 27-Oct-03 3781.0305-Dec-05 9431.81 18-Nov-04 5520.17 20-Oct-03 3945.3628-Nov-05 9226.41 08-Nov-04 5483.88 13-Oct-03 3969.4521-Nov-05 9064.39 01-Nov-04 5352.3 06-Oct-03 4143.3314-Nov-05 8933.51 25-Oct-04 5332.24 29-Sep-03 4192.3907-Nov-05 8793.93 18-Oct-04 5458.32 22-Sep-03 4163.2231-Oct-05 8436.62 11-Oct-04 5433.48 15-Sep-03 4389.31
DATE INDEX DATE INDEX DATE INDEX08-Sep-03 4604.27 12-Aug-02 1843.26 16-Jul-01 1260.5801-Sep-03 4463.04 05-Aug-02 1815.76 09-Jul-01 1312.1
118
25-Aug-03 4461.47 29-Jul-02 1779.4 03-Jul-01 1306.2918-Aug-03 4418.2 22-Jul-02 1783.05 25-Jun-01 1366.4311-Aug-03 4142.45 15-Jul-02 1798.56 18-Jun-01 1353.1604-Aug-03 4323.08 08-Jul-02 1783.17 11-Jun-01 1390.0628-Jul-03 4019.52 01-Jul-02 1800.47 04-Jun-01 1367.321-Jul-03 3807.66 24-Jun-02 1770.11 28-May-01 1381.8314-Jul-03 3751.7 17-Jun-02 1779.3 21-May-01 1349.607-Jul-03 3645.88 10-Jun-02 1768 14-May-01 1362.41
30-Jun-03 3477.86 03-Jun-02 1691.29 07-May-01 1346.6523-Jun-03 3400.08 27-May-02 1663.34 30-Apr-01 1370.7916-Jun-03 3307.09 20-May-02 1663.21 23-Apr-01 1364.4409-Jun-03 3264.62 13-May-02 1779.76 16-Apr-01 1387.7202-Jun-03 3141.82 06-May-02 1798.45 09-Apr-01 1371.71
26-May-03 3099.04 29-Apr-02 1904.16 02-Apr-01 1322.8119-May-03 3079.94 22-Apr-02 1856.09 26-Mar-01 1324.4112-May-03 3003.35 15-Apr-02 1863.92 19-Mar-01 1350.9205-May-03 2972.41 08-Apr-02 1858.61 12-Mar-01 1396.2928-Apr-03 2924.57 01-Apr-02 1850.18 26-Feb-01 1419.7221-Apr-03 2859.31 26-Mar-02 1868.11 19-Feb-01 1440.4314-Apr-03 2935.38 18-Mar-02 1894.31 12-Feb-01 1512.8307-Apr-03 2870.7 11-Mar-02 1887.04 06-Feb-01 1496.9431-Mar-03 2778.62 04-Mar-02 1851.02 29-Jan-01 1478.9624-Mar-03 2744.17 26-Feb-02 1774.51 22-Jan-01 1417.5417-Mar-03 2651.7 18-Feb-02 1723.64 15-Jan-01 1452.3110-Mar-03 2540.25 11-Feb-02 1703.31 08-Jan-01 1470.7203-Mar-03 2448.65 04-Feb-02 1785 26-Dec-00 1545.924-Feb-03 2399.14 28-Jan-02 1670.89 18-Dec-00 1493.0210-Feb-03 2528.31 21-Jan-02 1526.77 11-Dec-00 1377.1903-Feb-03 2481.43 14-Jan-02 1478.95 04-Dec-00 1319.7827-Jan-03 2545.07 07-Jan-02 1374.93 27-Nov-00 1276.0520-Jan-03 2609.44 31-Dec-01 1362.73 20-Nov-00 1355.8613-Jan-03 2954.62 24-Dec-01 1269.2 13-Nov-00 1409.2706-Jan-03 2869.23 10-Dec-01 1403.96 06-Nov-00 1462.3430-Dec-02 2744.82 03-Dec-01 1380.45 30-Oct-00 1519.5923-Dec-02 2661.37 26-Nov-01 1358.16 23-Oct-00 1486.0616-Dec-02 2525 19-Nov-01 1353.57 16-Oct-00 1502.4709-Dec-02 2452.23 12-Nov-01 1380.7 09-Oct-00 1545.4302-Dec-02 2345.11 05-Nov-01 1382.67 02-Oct-00 1581.4225-Nov-02 2285.87 29-Oct-01 1399.81 25-Sep-00 1564.7818-Nov-02 2346.34 22-Oct-01 1401.51 18-Sep-00 155211-Nov-02 2271.6 15-Oct-01 1267.05 11-Sep-00 1555.0704-Nov-02 2227.34 08-Oct-01 1193.65 04-Sep-00 157728-Oct-02 2294.62 01-Oct-01 1141.19 28-Aug-00 1514.3821-Oct-02 2236.76 24-Sep-01 1133.43 21-Aug-00 1500.7914-Oct-02 2111.72 18-Sep-01 1139.64 15-Aug-00 1571.97
119
07-Oct-02 2036.98 10-Sep-01 1139.64 07-Aug-00 1569.0530-Sep-02 2028.39 03-Sep-01 1246.8 31-Jul-00 1562.4523-Sep-02 2018.79 27-Aug-01 1258.43 24-Jul-00 1569.3916-Sep-02 1981.07 20-Aug-01 1268.61 17-Jul-00 1616.7409-Sep-02 1954.66 13-Aug-01 1290.25 10-Jul-00 1539.7702-Sep-02 2008.85 06-Aug-01 1226.84 03-Jul-00 1514.8726-Aug-02 1974.58 30-Jul-01 1252.58 26-Jun-00 1520.7319-Aug-02 1925.75 23-Jul-01 1242.83 19-Jun-00 1521.24
DATE INDEX DATE INDEX DATE INDEX12-Jun-00 1492.35 24-May-99 1185.23 04-May-98 1551.9105-Jun-00 1399.3 17-May-99 1314.31 27-Apr-98 1562.22
29-May-00 1474.4 10-May-99 1218.66 20-Apr-98 1616.4322-May-00 1510.44 03-May-99 1150.63 06-Apr-98 1603.1615-May-00 1681.08 28-Apr-99 1107.02 30-Mar-98 1534.3708-May-00 1672.46 19-Apr-99 1071.62 24-Mar-98 1568.6201-May-00 1807.31 12-Apr-99 1001.37 16-Mar-98 1528.1324-Apr-00 1901.07 05-Apr-99 1021.84 09-Mar-98 1597.3617-Apr-00 1991.66 30-Mar-99 1052.03 02-Mar-98 1625.7610-Apr-00 1967.01 22-Mar-99 1056.75 23-Feb-98 1681.8303-Apr-00 1943.2 15-Mar-99 1050.87 16-Feb-98 1674.5827-Mar-00 1999.69 08-Mar-99 1052 09-Feb-98 1720.5720-Mar-00 2001.9 01-Mar-99 984.39 02-Feb-98 1672.9913-Mar-00 2001.97 22-Feb-99 926.21 27-Jan-98 1609.1606-Mar-00 1936.97 15-Feb-99 913.78 19-Jan-98 1596.7528-Feb-00 1906.91 08-Feb-99 874.9 12-Jan-98 1521.6421-Feb-00 1980.43 01-Feb-99 867.73 05-Jan-98 1660.0114-Feb-00 1938.17 25-Jan-99 900.58 29-Dec-97 1746.3107-Feb-00 1705.39 18-Jan-99 930.71 23-Dec-97 1713.7131-Jan-00 1799.73 11-Jan-99 924.19 15-Dec-97 1724.4624-Jan-00 1749.36 04-Jan-99 900.49 08-Dec-97 1759.4117-Jan-00 1792.16 28-Dec-98 945.24 01-Dec-97 1789.3512-Jan-00 1626.09 21-Dec-98 952.35 24-Nov-97 1772.2403-Jan-00 1499.8 14-Dec-98 939.84 17-Nov-97 1750.0827-Dec-99 1408.91 07-Dec-98 939.3 10-Nov-97 1784.9520-Dec-99 1407.95 30-Nov-98 979.04 03-Nov-97 1847.1513-Dec-99 1391.5 23-Nov-98 1035.17 27-Oct-97 1875.0106-Dec-99 1355.58 16-Nov-98 988.62 20-Oct-97 1980.6829-Nov-99 1260.89 10-Nov-98 941.91 13-Oct-97 1978.6622-Nov-99 1220.7 02-Nov-98 857.58 06-Oct-97 1884.3215-Nov-99 1204.13 26-Oct-98 841.7 29-Sep-97 1858.8108-Nov-99 1178.05 19-Oct-98 809.97 22-Sep-97 1837.0601-Nov-99 1193.54 12-Oct-98 841.46 15-Sep-97 1851.7225-Oct-99 1189.32 05-Oct-98 941.82 08-Sep-97 1883.6118-Oct-99 1151.21 28-Sep-98 1101.55 01-Sep-97 1782.9411-Oct-99 1129.17 21-Sep-98 1084.79 26-Aug-97 1762.29
120
04-Oct-99 1235.83 14-Sep-98 1056.73 18-Aug-97 1854.6627-Sep-99 1198.09 07-Sep-98 1070.32 11-Aug-97 1898.2720-Sep-99 1191.83 31-Aug-98 965.53 04-Aug-97 2014.9413-Sep-99 1155.63 24-Aug-98 980.34 28-Jul-97 1989.5107-Sep-99 1156.18 17-Aug-98 956.09 21-Jul-97 1981.8130-Aug-99 1166.4 10-Aug-98 964.83 14-Jul-97 1845.323-Aug-99 1223 03-Aug-98 972.96 07-Jul-97 1745.3516-Aug-99 1292.46 27-Jul-98 920.48 02-Jul-97 1648.8509-Aug-99 1183.43 20-Jul-98 958.94 02-Aug-99 1207.89 13-Jul-98 882.95 26-Jul-99 1251.79 06-Jul-98 777.26 19-Jul-99 1191.03 29-Jun-98 867.83 12-Jul-99 1134.78 22-Jun-98 876.9 05-Jul-99 1085.06 15-Jun-98 1016.05
28-Jun-99 1104.82 09-Jun-98 1062.54 21-Jun-99 1044.04 01-Jun-98 1087.51 14-Jun-99 1052.18 25-May-98 1040.19 07-Jun-99 1123.97 18-May-98 1205.81
31-May-99 1136.43 11-May-98 1426.16
121
122