Z0955523DISS

1

EMPIRICAL INVESTIGATION OF THE
EFFICIENT MARKET HYPOTHESIS:
A CASE OF THE INDIAN AND U.K. STOCK
MARKETS
By
Z0955523
Submitted to Durham University Business School as a part of
the requirement of the MSc. Management (Finance), 2015.
Word Count: 9461

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Personal declaration:
Word count: 9461
I confirm that this piece of work is a result of my own work. Material from the work of
others not involved in the project has been acknowledged and quotations and
paraphrases suitably indicated.
Furthermore, I confirm that I understand the definition of plagiarism that is used by
Durham University, and that all source material has been appropriate cited and
referenced.
I understand that only the content in the main body of the work will be marked, and that
the content in the Appendices will be checked, but will not contribute to the marking of my
assignment.

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Table of Contents
Acknowledgements....................................................................................................................5

Abbreviations.............................................................................................................................6

Executive Summary...................................................................................................................7

Abstract......................................................................................................................................9

Chapter 1 Introduction.............................................................................................................10

1.1 Background of Study .....................................................................................................10

1.2 Objectives and Limitations of Study..............................................................................11

1.3 Structure of Study ..........................................................................................................11

Chapter 2 The Stock Markets ..................................................................................................12

2.1 The Bombay Stock Exchange (BSE).............................................................................12

Table 2.1.1 Key Bombay Stock Exchange Indices..........................................................12

2.2 The National Stock Exchange (NSE) ............................................................................12

Table 2.2.1 NSE Indices. .................................................................................................12

2.3 London Stock Exchange (LSE) .....................................................................................13

Table 2.3.1 LSE Indices...................................................................................................13

Chapter 3 Literature Review....................................................................................................14

3.1 Efficient Market Hypothesis..........................................................................................14

3.1.1 Development of the concept ...................................................................................14

3.1.2 Random Walk Theory.............................................................................................16

3.1.3 Forms of Market Efficiency....................................................................................16

3.2 Efficient Market Hypothesis – The Model ....................................................................17

3.3 Empirical Evidence of Weak –From Market Efficiency. ..............................................19

3.3.1 Evidence from Developed Markets ........................................................................19

3.3.2 Evidence from Emerging Markets..........................................................................20

Chapter 4 Data & Methodology...............................................................................................22

4.1 Summary of Data...........................................................................................................22

Table 4.1.1 Indices examined in this study......................................................................22

4.2 Time-Series plots of Indices Examined.........................................................................24

Figure 4.2.1 Time-Series plots of Indices Examined.......................................................24

4.3 Index High to Low Difference during Individual Sub Periods......................................25

Table 4.3.1: Index High to Low Difference during Individual Sub Periods....................25

4.4 Time series plots of Daily Returns of Indices Examined ..............................................26

Figure 4.4.1 Time series plots of Daily Returns of Indices Examined............................27

4.5 Hypotheses.....................................................................................................................28

4.6 Statistical Tests for testing the Random Walk Hypothesis and Market Efficiency.......28

4.6.1 Serial Correlations ..................................................................................................28

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4.6.2 Unit Root Test.........................................................................................................30

4.6.3 Runs Test. ...............................................................................................................31

4.6.4 Variance Ratio test..................................................................................................32

Chapter 5 Empirical Results and Findings...............................................................................34

5.1 Descriptive Statistics......................................................................................................34

Table 5.1.1 Descriptive Statistics for Daily Returns........................................................34

Table 5.1.2 Descriptive Statistics for Daily Returns........................................................35

Table 5.1.3 Descriptive statistics of Daily Returns per Sub-Period ................................36

5.2 Augmented Dickey-Fuller (ADF) Unit Root test. .........................................................37

Table 5.2.1. Results of the ADF Unit Root test...............................................................37

5.3 Serial Correlations Test..................................................................................................38

Table 5.3.1.Autocorrelations Coefficients and Ljung-Box Q-statistics for Full period. .39

Table 5.3.2. Results of Ljung-Box Q-statistics for all three sub-periods. .......................40

5.4 Runs Test. ......................................................................................................................42

Table 5.4.1. Results of non-parametric Runs Test...............................................................44

5.5 Variance Ratio Test....................................................................................................45

Table 5.5.1 Results of Variance Ratio Test .....................................................................47

Table 5.5.1 (continued)....................................................................................................48

5.6 Summary of Test Results of Random Walk Hypothesis. ..............................................49

Table 5.6.1 Summary of Results of RWH (accept/reject) ...............................................49

Chapter 6 Conclusion...............................................................................................................50

References................................................................................................................................52

Appendices...............................................................................................................................58

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Acknowledgements
I dedicate this paper to my parents who have supported me throughout my academic
career. I would like to thank Dr. Tahani Coolen-Maturi for her supervision and her
inputs throughout this study. I would also like to thank my colleagues who have
helped me understand concepts which were out of my scope of study. I would like to
thank Durham University for giving me an opportunity to write this dissertation.
Finally, I would like to give all the credit of my achievements to late Dr. Graham Dietz
who gave me a sense of belonging towards this great university and motivated me to
achieve excellence.

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Abbreviations
BSE- Bombay Stock Exchange
NSE- National Stock Exchange
LSE- London Stock Exchange
NYSE- New York Stock Exchange
JB- Jarque-Bera Test
ADF- Augmented Dickey-Fuller Unit Root Test
RWH- Random Walk Hypothesis
ACF- Autocorrelation Function
VR- Variance Ratio

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Executive Summary
This study builds on the theoretical and empirical framework of market efficiency
developed by Eugene Fama in 1965. The notion of market efficiency is based on the
“random walk” in stock prices which has always been subject to curiosity and
consequent research. The RWH states that subsequent price movement of a stock
exhibits a random and unpredictable movement from its previous price. This random
movement is caused due to the random flow of information related to the stock. The
weak-form efficiency hypothesis builds on this concept stating that today’s stock
prices will only reflect todays randomly released information. Therefore, past stock
prices cannot in any way be used to derive information, which could help investors
forecast future patterns and “beat” the market.
However, critics of the efficient market hypothesis state there has been evidence in
the past where investors like Warren Buffet, Peter Lynch and George Soros have
earned astronomical returns by outperforming the market. The supporters of the
market efficiency hypothesis state that these investors ‘beat’ the markets out of luck
and not skill. Past research has also provided certain evidence of ambiguity and
mixed results. Therefore, this study adds to the past evidence on weak-form market
efficiency with a primary aim to examine Indian and the United Kingdom equity
markets and draw a comparison on how the two markets behaved in the short and
long run between 2002 and 2014.
This period was also selected to derive the effects of the 2007-08 global recession
caused due to the collapse of the “housing bubble” in the United States. It also
provides evidence on market efficiency in recent times. Secondary aim of this study
is to discover any potential cross-border integration of developing and emerging
markets. The classical methods of testing for weak-form efficiency hypothesis and
RWH have been applied in this study which include four statistical tests, namely the
serial correlations test, the ADF test, the non-parametric runs test and the variance
ratio tests by Lo and MacKinlay (1988). Results of these tests conclude that the
Indian and United Kingdom markets rejected the weak-form efficiency hypothesis as

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well as the RWH in the long run and accepted the hypotheses in the short run
between 2007 and 2010 as well as suggesting possible cross-border integration.

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Abstract
The primary aim of this study is to examine the weak-form market efficiency
hypothesis and RWH on the Indian and U.K. equity markets in the long and short run.
Markets were tested for a period of 13 year i.e. January 2002 to December 2014.
Historical daily closing prices of the Bombay Stock Exchange and the National Stock
Exchange indices i.e. S&P BSE SENSEX, S&P BSE 100, CNX NIFTY and CNX
NIFTY JR were used to study Indian markets. To study the U.K. markets the FTSE
100 and the FTSE 250 indices of the London Stock Exchange were used. Statistical
tests applied include the serial correlations test, the augmented Dicky-Fuller test, the
non-parametric runs test and the stringent variance ratio test. Findings suggest that
none of the three markets were weak-form efficient in the full sample period, however
between 2007 and 2010, all three markets followed the random walk and thus
accepted the null hypothesis of weak-form market efficiency. Evidence of possible
cross-border integration was provided, however, specific statistical tests must be
applied to derive accurate results on that front.

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Chapter 1 Introduction
1.1 Background of Study
Financial markets are an integral part of a country’s economy. According to Blake
(2004) they benefit international trade, create liquidity, and accumulate investor
wealth consequently helping economic agents in accurately forecasting
developments in the financial industry. However, these benefits depend upon the
state of the market i.e. emerging and developed markets. According to Worthington
and Higgs (2004) the common notion relating to emerging and developing markets is
that the former are less efficient than the latter. This is possibly due to various factors
like thin trading, lack of technological developments, higher transactional costs and
slow reactions to new information. Analysts and economists often claim that stock
prices and returns exhibit a behaviour called a “random walk”. According to Fama
(1995) this implies that stock price movements exhibit independent and identical
movement and that no information from past stock prices can be used to forecast
future movements or patterns. The theoretical concept weak-form efficiency is based
on this “randomness”. At no given point of time can any investor or group of investors
expect to earn abnormal returns via forecasting or selective trading. Fama (1995)
also states that the RWH is an independence test. Hypothesis of this states that
salient features of stock prices are “a white noise process, a stable autoregressive
pattern, a unit root process, or a low correlation dimension”. Recent studies have
applied the variance ratio test to check for dependence in stock prices and returns as
financial time series exhibit time-varying volatility.
Extensive empirical research based on the validity of the weak-from market efficiency
hypothesis has been done in the past based on emerging and developed stock
markets and have produced mixed and inconclusive results. Past studies prove that
majority of developed markets are consistent with the weak-form efficiency
hypothesis1
. Evidence from emerging markets are mixed with equal evidence of
acceptance and rejection2
of weak-form market efficiency hypothesis.
1
Explained in Section 3.3.1
2
Explained in Section 3.3.2

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1.2 Objectives and Limitations of Study
Motivated by the practical and theoretical significance of the RWH, especially with
reference to emerging and developed markets, this study aims to test the Indian and
U.K. equity markets for weak-form market efficiency and compare their behaviour.
Consideration must also be given to past evidence relating the thin trading in
emerging markets leading to biased results. Daily data has been used in this study
which might exhibit similar bias. Therefore as suggested by Lo and MacKinley (1988)
this study uses a longer test period to amplify the random walk test. The key
objective of this study is to only test for weak-form efficiency hypothesis based on
analysis of financial time-series data. Thus it excludes technical trading rules and
adjustments for transaction costs. It only provides a concise discussion of the
findings limited only to specific indices.
1.3 Structure of Study
The study is divided as follows: Chapter 2 discusses the Indian and U.K. stock
exchanges, Chapter 3 states the development of the market efficiency concept, the
existing theoretical literature, the random walk theory and forms of market efficiency,
and evidence of weak-form efficiency from emerging and developed markets.
Chapter 4 consists of the data and methodology and the hypotheses of this study.
Chapter 5 presents the empirical results. Chapter 6 summarizes the results and
draws the conclusion to this study. It also gives the scope for future research.

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Chapter 2 The Stock Markets
2.1 The Bombay Stock Exchange (BSE)
Founded in 1875, The BSE (Mumbai) trades securities including equity, debt
instruments, derivatives & mutual funds. Equities are traded on the basis of the
indices included in the BSE. According to Poshakwale (1996), the BSE is known for
its price stability as between 1987-94, its annual price fluctuation was at 25.71% only
after the LSE (22%) and the NYSE (23.9%). BSE is divided into 16 indices of which
the SENSEX, BSE 100, BSE 200 and BSE 500 are most significant. These consist of
well diverse, most liquid and stable stocks listed on the BSE from key industries.
Table 2.1.1 Key Bombay Stock Exchange Indices.
Source: BSE India (http://www.bseindia.com/)
2.2 The National Stock Exchange (NSE)
Founded in 1992, The NSE is located in Mumbai and spreads its activities over 364
cities. According to the NSE Fact book (2014), it is a combination of modern
technology and regulated efficiency resulting in screen based transparent and open
trading, demutualization of exchange governance and acts as market for equity, debt
and derivative instruments. NSE is divided into 11 broad indices of which the NIFTY,
NIFTY JUNIOR, CNX 100, CNX 200 and CNX 500 are the most significant.
Table 2.2.1 NSE Indices.
Source: NSE India (http://www.nseindia.com/index_nse.htm)
Index Composition Methodology
Market Cap. (% of BSE total Market
capitalisation)
SENSEX 30 Float Adjusted market capitalization weighted 50
BSE 100 100 Float Adjusted market capitalization weighted 75
Index Composition Methodology
Market Cap. (% of NSE total
Market capitalisation)
NIFTY 50 Float Adjusted market capitalization weighted 66
NIFTY JUNIOR 50 Float Adjusted market capitalization weighted 12
CNX 100 100 Float Adjusted market capitalization weighted 79

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Of the 5 indices, the NIFTY and the NIFTY JUNIOR are most significant, with the
latter being an extension to the former. The NIFTY constitutes of 50 most liquid and
stable stock listed in the NSE from 23 key sectors, while the NIFTY JUNIOR consists
of the next most liquid stocks listed in the NSE.
2.3 London Stock Exchange (LSE)
The LSE founded in 1802 consists of five key indices, namely the FTSE 100, FTSE
250, FTSE SmallCap, FTSE All-Share (500) and the FTSE Fledgling. Of these the
FTSE 100 and the FTSE 250 are largest and most trusted indices constituting stocks
of 100 and 250 most liquid companies respectively. According to the FTSE Factsheet
(2014), the market capitalization for the FTSE 100 and FTSE 250 is
£1,790,781million and £353,805million respectively. According to the LSE Factsheet
(2014), the LSE is well connected to emerging markets with 158 Emerging Trade
Funds (ETF). A total of 152 companies from emerging markets are listed on the LSE
of which 29 are Indian, 41 are Chinese and 23 from Bangladesh.
Table 2.3.1 LSE Indices
Source : FTSE U.K. (www.ftse.com)
Index Composition Methodology Market Capitalisation
FTSE 100 100 Float Adjusted market capitalization weighted £1,709
m
FTSE 250 250 Float Adjusted market capitalization weighted £353,805m
FTSE 350 350 Float Adjusted market capitalization weighted £1,940
m
FTSE All Share 500 Float Adjusted market capitalization weighted £2,350

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Chapter 3 Literature Review
This section looks at the past “economic” literature regarding the efficient market
hypothesis. Section 3.1.1 introduces market efficiency followed by the Random Walk
theory in Section 3.1.2. Section 3.1.3 discusses forms of market efficiency followed
by the Efficient Market Hypothesis model in Section 3.2. Lastly, Section 3.3 provides
the past empirical evidence of weak-form efficiency relating to developed and
emerging markets.
3.1 Efficient Market Hypothesis
3.1.1 Development of the concept
A market is considered to be efficient when the financial assets or stocks integrate all
available and relevant information, which prevents investors from earning abnormal
returns. The notion of efficient market roots down to the 16th
century when Italian
mathematician Giloramo Cardano indirectly likened the stock market and market
efficiency to gambling in his book “Liber de Ludo Aleae” (The Book of Games of
Chance). According to a French stockbroker Jules Renault (1863), “the longer an
investor hold a security, the higher the possibility of him winning or losing on its price
variations”. According to Gibson (1889), “when securities became publically available
in an open market, the value which they acquire may be regarded as the judgment of
the best intelligence concerning them”. However, this was ignored only until modern
laureates like Eugene Fama (1965) and Paul Samuelson (1965) conceived the term
“efficient markets” in their papers “Random walks in stock prices” and “ Proof that
properly anticipated prices fluctuate randomly” respectively. Samuelson (1965) stated
that an informationally efficient market is one wherein the prices of assets and
securities are arbitrary and they integrate all “information and expectations of market
participants”. To quote Samuelson (1965), “in competitive markets there is a buyer
for every seller. If one could be sure that a price would rise, it would have already
risen”. He added that such opinions play a vital role in inferring that there must be
randomness in the pattern in the changes in competitive prices, known as the
random walk. However, Samuelson (1965) failed to clarify the idea of an efficiently
functioning market due to ambiguous evidence. According to Fama (1965), “in an
efficient market, on the average, competition will cause the full effects of new

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information on intrinsic values to be reflected ‘instantaneously’ in actual prices”.
Enhancing Samuelson (1965) findings, Fama (1970) defined efficient markets as – “A
market in which prices always ‘fully reflect’ available information”. Fama (1970)
introduced the use of computers for empirical studies and practically applied the
efficient market hypothesis by constructing models from the data and information
available to general investors. Fama’s (1970) produced substantial empirical and
methodological concepts in the form of event studies, econometric tests of single and
multi-factor linear asset-pricing models as well as a collection of anomalies and
patterns in stock, bond, and commodity and currency markets. According to Findlay
and Williams (2000), Fama (1970) recognized that efficient markets occur due to
three conditions. Firstly, transaction costs do not appear. Further, Fama (1970)
adopted the fact that “relevant information” is available to all investors cost-free.
Finally, he stated “on the implications of current information for the current price and
distributions of future prices of each security, the current price of security should “fully
reflect” all available information. However, it is should not be taken for granted that if
any of the above conditions fail, then the markets will be inefficient. If adequate
number of investors possess available information, then markets will still be efficient.
Fama (1970) and Ball (1994) state that disruption of any of the three conditions
would lead to an ineffective reflection of prices to information.
Alexakis (1992) states that the market efficiency hypothesis indicates informational
efficiency. He adds, “Information efficiency is the kind of efficiency when price, under
certain assumptions, reflect fully and very quickly, theoretically instantaneously, every
piece of information concerning the traded securities”. If time is t and all relevant
information is It, then at t stock prices must reflect all relevant information available at
t i.e. It. This is therefore complies with all the Efficient Market Hypothesis conditions.
Current prices at time t should not integrate any past information as stock prices at
time t-t1 would have already reflected all information (It-It1) released in the past at t-t1.
Cootner (1964) stated that since new information is released in a random manner,
prices changes due to this information should also behave in a random manner. This
proposition makes forecasting of prices and gaining abnormal profits from these
forecasts almost impossible.

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3.1.2 Random Walk Theory
The random walk theory implies that stock prices do not follow any particular pattern
and move randomly. Statistical evidence by mathematician Luis Bachlier (1900)
suggests, “Stock price changes cannot be forecasted since they are a cumulated
series of probabilistically independent shocks which are identically distributed”. It was
stated that movement in stock prices observed the following random walk model;

Pt = Pt-‐1 or ∆Pt = ut

With E (ut) = 0 Var(ut) = σ2
and Cov( ut , us) = 0 t≠s
Here,
Pt = Price of security.
∆Pt = Change in Price.
Empirical studies of Kendal (1953), Grangar and Morgerstern (1963) and Fama
(1965, 1970) supported this model. According to Alexakis (1992), “The random walk
model seemed to contradict the idea of rational security pricing and seemed to imply
that stock prices are exempt from the laws of supply and demand that determine
other prices”. According to Cowles and Jones (1937), “they compared the frequency
of sequences and reversals in historical stock return, where the former pair’s pf
consecutive returns with the same sign, and the latter are pairs of consecutive
returns with opposite signs” (cited in Alexakis, 1992).
3.1.3 Forms of Market Efficiency
According to Fama (1970), Roberts (1959) was the first to present the three forms of
efficient markets. The first kind is the “Weak-form” efficient markets. This is the form
of efficiency stock prices at a particular time reflect all available past information.
According to this efficiency, in no way can past prices help in forecasting future prices
or patterns which would help investors to gain abnormal profits. This hypothesis
simply suggests that stock prices are publically available, thus no investor can make
excess profits from something that “everybody else” is aware of. Even then, with the
use of technical analysis, financial analysts attempt to predict future patterns and
price with past prices and trading volumes. The second kind is the “Semi-strong form”
efficient markets. Stock prices in a semi-strong from efficient market integrate all

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publically available information. This information includes past prices of stocks and
also all publically available financial statements. Non-financial information is also
forms a part of this form of efficiency. The difference between “weak form” and “semi-
strong form” efficiency is that the former consists past information related to stock
prices, while the latter consists of all publically available including non-financial
information. Finally, a market, wherein future prices cannot be forecasted even with
the availability of all inside information as well as all publically available information,
is said to be “strong form” efficient. According to Clarke (2001), systematic
generation of abnormal profits is not possible even with the inside information is not
known to public. This forms the main difference between “semi-strong form” and
“strong form” efficient markets. According to Campbell (1997) and Fama (1970),
strong form efficiency integrates semi-strong and weak form efficiency. Semi-strong
form efficiency integrates weak form efficiency. Thus, rejection of weak form
efficiency means the rejection of semi-strong and strong form efficiency.
3.2 Efficient Market Hypothesis – The Model
The fundamentals of the efficient market hypothesis are based on the following 3
assumptions (Cuthbertson 1996):
1. Arbitrage: A minor portion of rational investors could use arbitrage to eliminate
any inaccuracies in pricing. This nullifies the effects of an average investor
while allowing the marginal investor to establish prices.
2. Rational Investors: This assumption implies that rational investors rightly
adjust their opinions based on the release of any new information.
3. Rationality trade off: There is a trade-off between the trades made by rational
and some irrational traders. Rational ones, keeping the prices in check, cancel
out errors by irrational trades.
Stocks are valued by the NPV (net present value) of their future cash flows, which
are discounted by a certain factor. According to Chung (2006), “security prices fully
reflect all available information and consequently, that in the prices formation all the
relevant information is valued properly”. The costs of trading and information must be

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equal to zero for the efficient market hypothesis to be applicable. Chung (2006)
further stated that the efficient market hypothesis rests even in the case of irrational
investors, consequently, reflecting fundamental values in the prices. According to
Pesaran (2005), the market is unaffected by large irrational investors as they have
uncorrelated trading tactics. Prices of securities continue to reflect information and
are “valued consistently with the fundamentals”. A joint hypothesis of an equilibrium
model of returns along with rational expectations assumption forms the Efficient
Market hypothesis. According to Chung (2006), Muth’s (1961) “doctrine of rational
expectations” stated that being consistent with the “models used to explain behaviour
of economic agents” was the only way the rationality of expectations could be
fulfilled. According to Cuthbertson (1996), given that information Ωt is available at
time t, conditional density function for random variable Yt is ƒ(Yt+1|Ωt). Therefore, the
conditional expectation corresponding to this density function is defined as:
E(Yt+1|Ωt) = ∫∞
∞
Ytƒ(Yt|Ωt)dYt
Definition of an error of forecast is εt+1 = Yt+1—E (Yt+1|Ωt). This consists to two
properties;
Property 1 - The expectation of forecast error is zero when. This is defined as
E (εt+1 Ωt)=0
Property 2 - Uncorrelated forecast errors with information available to
economic actors. This is defined as E (εt+1Ωt|Ωt) =0.
Actual returns must be compared to a returns model in order to approve or reflect the
Efficient Market Hypothesis. A random and unpredictable behaviour of returns would
mean that the Efficient Market hypothesis is approved. According to the hypothesis,
asset At integrates all risk and information. There should be a corresponding variance
in returns and new available information. The variation in prices and new information
should be random. According to Cuthbertson (1996), the Efficient Market hypothesis
incorporates the orthogonality property, wherein “forecast errors do not depend upon
the information set Ωt at time t”. The rational expectations in Efficient Market
hypothesis is defined as:

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At+1 = Et (At+1) + εt+1
Here, the return on asset (At+1) equals expected returns Et (At+1) + forecast error
(Et (εt+1)).Forecast error for next period i.e. εt+1 is not affected by current forecast
error εt as it is “separate, equally distributed and serially uncorrelated”. As stated by
Cuthbertson (1996), “a random variable defined at discrete times follows a random
walk if its expected value in the next period is the same as its most recent value”.
Random walk of a stochastic variable Z will be defined as:
Zt+1=θ + Zt + εt+1
Where, θ is the drift parameter and εt+1 is the forecast error which is independent and
distributed independently. θ=0 implies an absence of drift in the random walk.
3.3 Empirical Evidence of Weak –From Market Efficiency.
3.3.1 Evidence from Developed Markets
Extensive research has been done in the past on developed markets especially the
NYSE and the LSE and other developed European Markets. After reviewing work of
various authors, can be inferred that the serial correlation tests and runs test are the
two most trusted and applied tests to examine the markets for efficiency and random
walks. Kendall (1964) used the serial correlations and runs test to examine the UK
equity market. His data included one composite UK market and 18 industrial indices
from 1928-38. His results did not reject the RWH. Fama (1965) conducted a thorough
examination of the NYSE using the Dow-Jones Industrial Average Index with daily
data of 30 companies. Results proved that correlation coefficient for the data were
extremely minute, thus not rejecting the RWH. Runs tests verified results of the
correlation test. Brealy (1970) and Dryden (1970) tested the U.K market individually
with different set of data but used common tests in the form of serial correlations and
runs test. Both did not reject the RWH for the U.K markets as abnormal profits could
not be yielded due to weak market movement. Sharma and Kennedy (1977)
compared the Bombay stock index to that of the F.T.A 500 (London Financial Times
Actuaries Stock 500) and the S&P 425 (New York Standard and Poor’s U.S 425
Stock). Both the U.K and the U.S markets were found to be efficient in the weak-

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form. Solnik (1973) compared his results from testing European 8 Markets, using the
serial correlations test, to those of Fama’s (1965). Solnik’s (1973) results rejected the
RWH suggesting that abnormal profits could be made on individual stocks but not on
the market as a whole. Significant proof was provided by Fama (1988) wherein
substantial negative serial correlations were found in the long run in the U.S markets.
Poterba and Summers (1986) found a positive serial correlation in the short run after
examining the U.S and 17 other markets.
Lee (1992) examined the U.S and U.K as well as 10 other nations using variance
ratio test and concluded that the RWH is not rejected for these markets. Chan et al.,
(1997) used the Phillips (1987) & Perron (1988) test and concluded that each of the
eighteen nations examined were efficient in the weak-form. Huang (1995), with
heteroscedastic and homoscedastic error terms, applied the variance ratio test on
Asian markets and conclude that Hong Kong, Malaysia, Korea, Singapore and
Thailand integrated positive series correlations. Taiwan, Japan, Indonesia and
Philippines did not reject the RWH. 16 developed markets and 4 emerging markets
were extensively examined by Worthington and Higgs (2004) for random walks based
on a combination of various tests. They conclude that of emerging markets only
Hungary and of developed markets only the United Kingdom, Germany, Portugal and
Ireland were weak-form efficient. Recent evidence by Borges (2008) on examination
of six European markets from January 1993 to December 2007, indicated that U.K.
markets were consistent with the RWH. Konak and Sekar (2015) examined the FTSE
100 using the ADF and Phillips-Perron unit root tests from 2001 to 2009. Evidence
proved that U.K. markets were weak-form efficient.
3.3.2 Evidence from Emerging Markets.
According to Sharma and Kennedy (1977), “composition of outputs may respond
sluggishly to changes in relative price”. Also, perception and differentiation of
investment prospects is difficult for the capital markets. However, contrasting
evidence has also been provided by various authors. Niarchos (1972) examined a
relatively smaller Greek Stock exchange based applying the serial correlation and
runs test. He concluded that the Greek stock exchange did not reject the RWH.
Errunza and Losq (1985) criticized Niarchos (1972) findings as “the sample of Greek
stock suffered from infrequent trading”. The Johannesburg Stock exchange did not

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reject the RWH when examined by Affleck-Graves and Money (1975) using 50 share
prices based on the serial correlations test. As mentioned earlier, Sharma and
Kennedy (1977) concluded that the BSE followed a random walk. Gandhi, Saunders
and Woodward (1980) found patterns in share prices movements and concluded that
investors could “beat” the market, thus rejecting the RWH for the Kuwait Stock
Exchange. According to Kean (1983), inefficiency in these less developed or
emerging markets is a result of scope of market, trading volumes transaction
expenses and disintegrated information. Based on serial correlations tests, Barnes
(1986) inferred The Kuala-Lampur Stock Exchange to be weak-form efficient.
Poshakwale (1996) examined the Bombay Stock Exchange national index using daily
data from 1987 to 1994. Based on frequency distribution of prices, serial correlation
and runs test, he concluded that Indian stock market was not weak-from efficient and
rejected the RWH for stock prices. Madhusoodanan (1998) tested the SENSEX and
BSE National Index 100 using the variance test ratio for the period January 1987 to
December 1995 and rejected the RWH. Abraham et al,.(2002) examined the Gulf
stock markets and rejected the RWH for the Kuwait, Bahrain and Saudi Arabian stock
markets. Mobarek and Keasey (2002) concluded that the Dhaka stock exchange did
not integrate the RWH based on autocorrelation and runs test. Hasan et.al (2006)
tested six European Emerging markets using the Ljung-Box Q-statistic test, Variance
Ratio and Runs test. Results indicated that only Greece rejected the RWH. Gupta
and Basu (2007) examined the NSE and BSE applying the ADF test and Phillips-
Perron Test and subsequently rejected the null hypothesis of random walk.

22

Chapter 4 Data & Methodology
This study tests and compares the Indian and the U.K market for weak form
efficiency. To test the Indian market, the data used is daily closing prices of the BSE
and NSE, as these form a total of 99.7% of the total cash segment turnover of the
Indian stock market. To test the U.K markets, data from The LSE are used, being the
most dominant stock market of the U.K. DataStream was used to assemble daily
price indices of 6 indices to be tested and the sample period ranges from January 1,
2002 to December 31, 2014.This period is further divided into three sub-periods.
Empirical analysis of this study is based on daily closing prices of the 6 indices during
individual sub-periods and the whole of the sample period.
4.1 Summary of Data
Table 4.1.1 Indices examined in this study
DataStream is used to obtain daily closing prices of 6 indices on 5 weekdays (Monday-Friday) from January 2002
to December 2014. All indices are denominated to U.S.$ to maintain uniformity.
The four indices from BSE and NSE are used as these are the most dependable and
trusted indices used by domestic and foreign investors. As these indices constitute
stocks from various key industries, results from testing these indices can be assumed
to be a fair indication of the market behaviour. The SENSEX and BSE 100 cover
majority of BSE Indices with an aggregate market capitalisation of 62.5% of that of
BSE. The combination of NIFTY and NIFTY JR. results in a broad coverage of the
NSE indices as these two indices have an aggregated market capitalization of 72.5%
of that of NSE. The FTSE 100 index and the FTSE 250 index are being used to test
the LSE. These two indices, form a broad base for the U.K. market with total market
capitalization of approximately $2 trillion.

23

The period of sample data is selected to test the efficiency of the stock markets while
they integrated the effects of the financial crisis of 2008. The sample period has a
reference to two major financial “bubbles” i.e. The “dotcom” bubble (1995-2002), and
the “housing bubble” (2002-2010). This study gives more emphasis to the “housing
bubble since it affected global stock markets with India and the U.K. being no
exception. According to Holt (2009), the U.S. GDP decreased at annual rates of 5.4%
and 6.4% in the 4th
and 1st
quarter of 2008 and 2009 respectively. This lead to the
Dow Jones Industrial Average index falling from 14,279.96 in October 2007 to
6,440.08 in March 2009. According to Bhatt (2012), Foreign Institutional Investors
withdrew $5.5 billion as a reaction to this crisis, which lead to the SENSEX from
15733 points on July 23 to 15160 points on July 27, 2007. On August 1, 2007,
SENSEX fell by 615 points. In the U.K. the FTSE experienced its steepest fall from
6,456.90 on the opening day to 4,434.17 on December 31. Following the collapse of
the U.S. Investment bank Lehman Brothers, the FTSE fell by 8.85%. It further fell by
21.05% after the £500m bail-out of banks by the government. According to Holt
(2008), the U.K GDP fell by 1.5% in the 4th
quarter of 2008, officially leading the
country into recession.
Since the Indian and U.K stock markets and economies were subject to various
factors affecting the performance through the total sample period, we divide the total
period into the following 3 sub-parts:
1. January 1, 2002 – December 31, 2006: The pre-recession
Period.
2. January 1, 2007 – December 31, 2010: The recession period.
3. January 1, 2011 – December 31, 2014 : The post-recession
Period
This is to provide greater variety of accurate evidence of whether or not the stock
markets were weak-form efficient during these specific periods. This evidence can
then be compared to the evidence of the entire sample period to ascertain
differences. Table 4.2 shows the time-series plot of the various indices that are being

24

examined in this study. Visual examination of these plots gives a general consensus
regarding how these indices have been performed during the sample period.
4.2 Time-Series plots of Indices Examined
Figure 4.2.1 Time-Series plots of Indices Examined
Figure 4.2.1 indicates the time series plots for The BSE, The NSE and The LSE indices for the total
sample period of 13 years i.e. January 1, 2002 to December 31, 2014. All indices are denominated in
$U.S. based on weekly exchange rates from January 1, 2002-December 31, 2014. Data Source:
DataStream, 2015.
The most significant observations made while examining these figures are the price
movements of all indices from 2002 leading to the “bubble” in 2008. Both the Indian
SENSEX BSE 100

0
100
200
300
400
500
600
02 03 04 05 06 07 08 09 10 11 12 13 14
S&P BSE SENSEX PRICE
INDEXVALUE
YEAR

0
40
80
120
160
200
02 03 04 05 06 07 08 09 10 11 12 13 14

NIFTY NIFTY JUNIOR
0
50
100
150
200
250
300
350
02 03 04 05 06 07 08 09 10 11 12 13 14
0
20
40
60
80
100
120
140
160
180
02 03 04 05 06 07 08 09 10 11 12 13 14
FTSE 100 FTSE 250
4,000
6,000
8,000
10,000
12,000
14,000
16,000
02 03 04 05 06 07 08 09 10 11 12 13 14
5,000
10,000
15,000
20,000
25,000
30,000
02 03 04 05 06 07 08 09 10 11 12 13 14

25

stock exchanges experienced almost identical price movement throughout the
sample period. According to the time series plots, price movement of SENSEX, BSE
100, NIFTY and NIFTY JUNIOR followed a similar trend. The period from 2002 to
2008 indicates the growth and eventual formation of the “bubble” caused as a result
of the reaction to the sub-prime lending scenario in the United States. Prices of all 4
indices peaked in 2008 and significantly crashed in 2009.
4.3 Index High to Low Difference during Individual Sub Periods.
Table 4.3.1: Index High to Low Difference during Individual Sub Periods.
The table 4.3.1 shows the highest and the lowest price as well as the percentage of difference of all 6
indices during each individual sub period. Data Source: DataStream, 2015.
Key
Sub Period 1 : 01/01/2002 - 31/12/2006
Sub Period 2 : 01/01/2007 - 31/12/2010
Sub Period 2 : 01/01/2011 - 31/12/2014
Index Period High Low Difference (%)
SENSEX Sub Period 1 313.00 58.53 81.30
Sub Period 2 531.47 157.35 70.39
Sub Period 3 462.40 264.09 42.89
BSE 100 Sub Period 1 92.02 16.93 81.60
Sub Period 2 169.87 46.53 72.61
Sub Period 3 139.61 77.38 44.57
NIFTY Sub Period 1 90.21 19.05 78.88
Sub Period 2 160.10 49.62 69.01
Sub Period 3 138.40 77.56 43.96
NIFTY JUNIOR Sub Period 1 161.23 25.49 84.19
Sub Period 2 332.26 69.32 79.14
Sub Period 3 306.39 149.73 51.13
FTSE 100 Sub Period 1 12231.32 5299.04 56.68
Sub Period 2 13963.04 4873.63 65.10
Sub Period 3 11773.55 7617.89 35.30
FTSE 250 Sub Period 1 21930.71 6129.17 72.05
Sub Period 2 24370.95 7938.07 67.43
Sub Period 3 28030.27 14522.53 48.19

26

The identical movement in all four Indian indices signify relationships between BSE
and NSE as the shock of the sub-prime crisis had an almost identical effect on both
these stock exchanges. The price high to low difference among SENSEX, BSE 100,
and NIFTY in all Sub Periods are relatively similar. The NIFTY JUNIOR has the
highest difference in all three sub periods, indicating greatest volatility. Similarities
continue as all four indices begin to recover with an upward trend till mid-2010. Post
this, index levels decrease at a lower rate and remain close to the mean levels
towards 2013. Examination of trends in the U.K market reveals certain similarities to
India. The FTSE 100 and FTSE 250 index levels follow a similar upward trend but not
identical movement. Both indices had similar movements through sub-period 2,
however the FTSE 250 showed a steeper recovery. This can be observed from table
4.3.1, where the price high to low difference between the two indices is the least in
sub-period 2. However, even though the FTSE 250 had a greater high at $28030.27
in sub-period 3, the FTSE 100 had a smaller high to low difference at 35.30%
compared to FTSE 250’s 48.19%, indicating lower volatility.
4.4 Time series plots of Daily Returns of Indices Examined
Figure 4.4.1 shows the plots of the daily returns of each of the BSE, NSE and the
LSE indices. Index series returns are based on the continuously compounded
formula stated by Brooks (2004):
Rt = ln (Pt/Pt-1)
Where,
i. Pt = closing price of index at time t.
ii. Pt-1 = closing price of index at time t-1.
iii. Ln = natural logarithm.
As observed in the Indian market, all four indices display similar variations in returns.
Return on all indices range between -15% and 20% throughout the sample period
and lowest at two instances- 2004 and 2008. Levels of variations in all indices were
higher in sub-period 2 indicating the effect of the 2008 “bubble”. Returns on all
indices were highest on May 18, 2009. Variations decrease post 2009 with returns
ranging between -5% and 5% with a few instances of returns outside this range.
Return on the FTSE 100 and the FTSE 250 are less volatile compared to the Indian

27

indices. Both indices show a similar trend but different levels of returns. Returns on
FTSE 100 range between -4% to 4% throughout the sample period except for the
period 2008-2010 when variations ranged from -11% to 13%. However, variations
decreased post this period fluctuating close to zero. FTSE 250 had lower returns but
higher volatility with returns ranging between -2.5% to 2.5% until late 2006. This
increased significantly between 2007-2010 –9% and 9% indicating the effect of the
2008 “bubble”. Variations did diminish to previous normal range with few noticeable
instances reaching up to -5%.
Figure 4.4.1 Time series plots of Daily Returns of Indices Examined
The graph shows the plots of continuously compounded return series of The Bombay Stock
Exchange, The National Stock Exchange and The London Stock Exchange for the entire sample
period of 13 years i.e. January 1, 2002 to December 31, 2014.All data has been obtained from
DataStream, 2015.
S&P BSE SENSEX S&P BSE 100
-.15
-.10
-.05
.00
.05
.10
.15
.20
02 03 04 05 06 07 08 09 10 11 12 13 14
-.15
-.10
-.05
.00
.05
.10
.15
.20
02 03 04 05 06 07 08 09 10 11 12 13 14
CNX NIFTY CNX NIFTY JUNIOR
-.15
-.10
-.05
.00
.05
.10
.15
.20
02 03 04 05 06 07 08 09 10 11 12 13 14
-.15
-.10
-.05
.00
.05
.10
.15
.20
02 03 04 05 06 07 08 09 10 11 12 13 14
FTSE 100 FTSE 250
-.12
-.08
-.04
.00
.04
.08
.12
.16
02 03 04 05 06 07 08 09 10 11 12 13 14
-.100
-.075
-.050
-.025
.000
.025
.050
.075
.100
02 03 04 05 06 07 08 09 10 11 12 13 14

28

4.5 Hypotheses
After considering the above arguments the study defines 2 sets of testable
hypothesis.
India
H0: The Indian stock market accepts RWH /
weak-form efficient.
H1: The Indian stock market rejects RWH / is not
U.K.
H2: The U.K. stock market accepts RWH /
H3: The U.K. stock market rejects RWH / is not
The null hypothesis for both sets of hypotheses is tested using the serial correlations,
runs tests, variance ratio and unit root tests. Sub-periods are tested using serial
correlation, variance ratio and runs test while unit root test is used to test the entire
sample period
4.6 Statistical Tests for testing the Random Walk Hypothesis and Market
Efficiency.
4.6.1 Serial Correlations
The serial correlations test is the most commonly used method in past research to
test randomness. Famous studies by Kendall (1964), Fame (1965), Solnik (1973) and
Poshakwale (1996) applied the serial correlations test to examine the U.K., U.S.,
European and Indian stock markets respectively. Under this test, the serial
correlation coefficients between a series of returns and lagged returns in the same
series are measured. Auto correlations test provide proof whether correlation
coefficient are significantly different from zero. The serial correlation coefficient model
is:

29

𝑝 𝑘 =
!"#(!!,!!!!)
!"# !! !"#(!!!!)
=
!"#(!!,!!!!)
!"#(!!)
Where,
i. 𝑝 𝑘 = Autocorrelation coefficient of time series 𝑟!.
ii. 𝑟! = Return on security at time 𝑡.
iii. 𝑘 = Lag of the period.
iv. 𝐶𝑜𝑣(𝑟!, 𝑟!!!) = Covariance between return of an index over time
period (𝑡 − 1, 𝑡).
v. 𝑉𝑎𝑟 𝑟! = Variance on the return of a security over time period
(𝑡 − 1, 𝑡).
Similarly, the Autocorrelations model is:
𝑝 𝑘 =
!
!!!
(!!!!)(!!!!!!)!
!!!!!
!
!
(!!!)!!
!!!
Where,
i. 𝑦 = Sample mean of series 𝑦.
ii. 𝑘 = Time lag.
iii. 𝑝! = 1 (definition).
The Ljung-Box Q-statistics is used in case of large samples and high order serial
correlation. It is based on the following regression:
𝑄 = 𝑛(𝑛 + 2)
!!
!
!!!
!
!!!
Where,
i. 𝑛 = Sample size.
ii. 𝑝! = Sample autocorrelation at lag𝑘.
iii. ℎ = Number of lags tested.

30

4.6.2 Unit Root Test.
While examining financial series, it is essential to determine the stationarity of the
data. According to Campbell et.al (1997), the unit root test was conceived by Dickey-
Fuller (1981) to test whether the data is either difference-stationary (null hypothesis)
or trend stationary (alternative hypothesis). Presence of unit root in a series indicates
that it is non-stationary. According to Brook (2008), use of non-stationary data
possibly leads to spurious regression as the shocks do not fade gradually. The
Augmented Dickey-Fuller (ADF) test, the Phillips-Peron (PP) test and the Kwiatowski-
Phillips-Schmidt and Shin (KPSS) test are the three tests used to test the null
hypothesis of unit root. The ADF is most commonly used in past research.
ADF has three models i.e. the pure random walk model(A), the model with
constant(B) and the model with constant and time trend(C). These are based on the
following regressions:
i. ∆𝑃! = 𝛾𝑃!!! + 𝑝!∆𝑃!!! + 𝜀!
!
!!!
ii. ∆𝑃! = 𝜇 + 𝛾𝑃!!! + 𝑝!∆𝑃!!! + 𝜀!
!
!!!
iii. ∆𝑃! = 𝜇 + 𝛼! 𝑡 + 𝛾𝑃!!! + 𝑝!∆𝑃!!! + 𝜀!
!
!!!
Where,
i. ∆ = First difference.
ii. 𝑃!= Log of price index.
iii. 𝜇 = Constant.
iv. 𝛾 , 𝑝 = Coefficients to be valued.
v. 𝑞 = Number of lagged terms.
vi. 𝑡 = Trend.
vii. 𝛼! = Estimated coefficient for the trend.
viii. 𝜀! = Assumed white noise error terms.
Here, absolute test statistic (𝜏) value must be compared to the absolute critical value
derived from the ADF test tabulation. Null hypothesis is not rejected if 𝜏-value is less
that the critical value. According to Enders (2004, 182) and Eviews guide (2013), the
sample size determines critical value, as an increase in sample size leads to
decrease in 𝜏-statistic at any given level of significance.

31

4.6.3 Runs Test.
Another commonly applied approach to test for randomness of a series is the non-
parametric runs test. It identifies the independence of successive price changes.
According to Higgs (2004), runs test does not require the series to be normally
distributed unlike the serial correlations test. Poshakwale (1996) states that presence
of significant difference between expected and observed runs implies inaccurate
reactions in the markets which enables investors to gain abnormal returns.
The hypothesis for this test is:
H0: Tested series is Random (insignificant difference between expected
and observed runs).
H1: Tested series is not Random (significant difference between
expected and observed runs)
According to Worthington and Higgs (2004), every change in return is interpreted
based on its movement around the mean. Positive movement implies greater return
than mean, negative movement implies lesser return and zero movement implies
returns being equal to mean. For large sample like the one used in this study, the
Runs test based on the following equation with a standard deviation (𝜎) of runs (𝑚):
𝜎!=
!!
!
!!
!
!!(!!!)!
!!! !!! !!
!
!!!!
!!!
!
!!!
!!(!!!)
!
!
Where,
i. 𝑚 = Expected number of runs.
ii. 𝜎!= Standard deviation of runs (𝑚).
iii. 𝑁 = Number of observations.
iv. 𝑖 = Signs of positive (+), negative (-) and no change.
v. 𝑛! = Total number changes per each category of sign.

32

According to Ma and Barnes (2001), the standardised Z-statistic applied to interpret
the Runs test is defined as:
𝑍 =
!!!±
!
!
!!
, 𝑍 ~ 𝑁(0,1)
Where,
i. 𝑅 = Actual number of runs.
ii.
!
!
= Correction factor for continuity adjustment.
4.6.4 Variance Ratio test
This study applies the variance ratio test stated by Lo and MacKinlay (1988) to test
the returns series for the RWH under the assumptions of homoscedasticity and
heteroscedasticity. According to Chung (2006), if a particular returns series accepts
null hypothesis of random walk, it would imply that “variance of q period returns
should be q times as large as one-period returns”. This can be defined as:
𝑉𝑅 𝑞 =
!"#[!! ! ]
! × !"#[!!]
= 1 + 2 1 −
!
!
𝜌(𝑘)!!!
!!!
Where,
I. rt(k)= rt + rt-1 +...+ rt-k+1
II. 𝜌(𝑘)= kth
order of autocorrelation coefficient of rt.
According to Campbell et.al. (1997), null hypothesis if variance ratio test can be
tested by using standardized asymptotic standard normal test statistics derived by Lo
and MacKinlay(1988).Test statistic Z(q) under null hypothesis of homoscedasticity is
defined as:
Z (q) =
!" ! !!
!(!)
!
!
~ N (0,1)
Where
Φ 𝑞 =
2(2𝑞 − 1)(𝑞 − 1)
3𝑞(𝑛𝑞)
Here,
I. nq = number of observations

33

II. Φ 𝑞 = asymptotic variance of variance ratio under homoscedasticity.
According to Worthington and Higgs (2004), rejection of null hypothesis under
homoscedasticity could be due top presence of heteroscedasticity or/and auto
correlations. According to Campbell et. All (1997), “As long as returns are
uncorrelated, even in the presence of heteroscedasticity the variance ratio still
approach unity as the number of observations increases without bound, for the
variance of the sum of uncorrelated increments still equal the sum of the variances”.
The test statistic for the heteroscedasticity-consistent method derived by Lo and
MacKinley (1988) is defined as:
Z* (q) =
!" ! !!
!∗ !
!
!
~ N (0,1)
And
𝛿 𝑘 =
𝑛𝑞 𝑝! − 𝑝!!! − 𝜇
!
𝑝!!! − 𝑝!!!!! − 𝜇
!!"
!!!!!
𝑝! − 𝑝!!! − 𝜇
!!"
!!!
!
Where,
I. 𝛿 𝑘 = heteroscedasticity-consistent estimator
II. 𝑝! = price of stock at time t
III. 𝜇 = average return.
IV.
According to Darrat and Zhong (2000), a positive autocorrelation in series can be
inferred if variance ratio is one.

34

Chapter 5 Empirical Results and Findings
5.1 Descriptive Statistics.
Table 5.1.1 indicates the descriptive statistics of daily returns series for all 6 indices
for the full sample. Statistics prove that all indices had positive mean returns with
Indian indices having higher returns and volatility than the U.K. indices. The NIFTY
JR. and the FTSE 250 had the highest and the lowest mean returns of among all
indices.
Table 5.1.1 Descriptive Statistics for Daily Returns.
According to Table 5.1.2 skewness values indicate that the NSE and LSE indices
were negatively skewed, thus increasing probability of diminishing returns. Though
values are not significantly different from zero, they are enough to reject null
hypothesis. Significant Kurtosis values indicate leptokurtic distribution among all
indices implying central distribution. JB statistics are significant at 5% level of
significance same being the case with corresponding p-values. Thus rejecting null
hypothesis of normal distribution.
The table indicates the descriptive statistics of continuously compounded daily returns for all 6 indices for full
sample period i.e. 01/01/2002 – 31/12/2014. N indicates number of observations. Mean, Minimum and Maximum
values are multiplies by 102
.
Time
Series
N
Mean
Maximum
Minimum
Standard
Deviation

BSE

SENSEX
3391
0.00055
0.19052
-‐0.11907
0.01694

BSE
100
3391
0.00058
0.18551
-‐0.11984
0.01702

NSE

NIFTY
3391
0.00053
0.19402
-‐0.13305
0.01711

NIFTY
JR.
3391
0.00071
0.16892
-‐0.13793
0.01853

LSE

FTSE
100
3391
0.00048
0.12219
-‐0.10538
0.01426

FTSE
250
3391
0.00031
0.09435
-‐0.0905
0.01351

35

Table 5.1.2 Descriptive Statistics for Daily Returns.
Table 5.1.3 indicates the standard deviations and Jarque-Bera (J.B.) statistics for
returns series of all indices in individual sub-periods. Most remarkable evidence from
this tabulation is that the BSE and NSE indices were most volatile during sub-period
2 i.e. the period of global recession. Contrastingly, the LSE indices did not show such
levels of volatility through all the periods. Even though the NSE was established to
make Indian markets more efficient, the 2008 recession outmuscled any such
attempts. J.B. statistics for all indices in all period are significant at 5% level same
being the case with corresponding p-values. Thus null hypothesis of normal
distribution was rejected for all indices in all three sub-periods.
This table depicts Jarque-Bera normality tests for daily stock returns series for all 6 indices for full sample period
i.e.01/01/2002-31/12/2014.
Time
Series
N
Skewness
Kurtosis
Jarque-‐Bera
Jarque-‐Bera
p-‐values

BSE

SENSEX
3391
0.0182
11.6552
10581.5200
0.000

BSE
100
3391
0.1426
11.3206
9793.4190
0.000

NSE

NIFTY
3391
-‐0.0974
12.3324
12310.9400
0.000

NIFTY
JR.
3391
-‐0.4988
10.1384
7340.3200
0.000

LSE

FTSE
100
3391
-‐0.1186
12.2493
12095.4600
0.000

FTSE
250
3391
-‐0.3141
8.52311
4369.4320
0.000

36

Table 5.1.3 Descriptive statistics of Daily Returns per Sub-Period
This table depicts Jarque-Bera normality tests for daily stock returns series for all 6 indices for 3 individual
sample periods as mentioned below. Jarque-Bera statistics were examined at 5% level of significance with critical
value at 5.99 from Chi-Squared distribution table.
Sample Period 1 : 01/01/2002-31/12/2006
Time
Series
N
Standard
Deviation
Jarque-‐Bera
Jarque-‐Bera
p-‐values

BSE

SENSEX
3391
0.013725
2963.035
0.0000

BSE
100
3391
0.014058
3199.311
0.0000

NSE

NIFTY
3391
0.014253
4327.454
0.0000

NIFTY
JR.
3391
0.016375
5293.797
0.0000

LSE

FTSE
100
3391
0.011147
549.3598
0.0000

FTSE
250
3391
0.008893
344.9119
0.0000

Sample
Period
2
:
01/01/2007-‐31/12/2010

Time
Series
N
Standard
Deviation
Jarque-‐Bera
Jarque-‐Bera
p-‐values

BSE

SENSEX
3391
0.022568
1915.843
0.0000

BSE
100
3391
0.022496
1789.142
0.0000

NSE

NIFTY
3391
0.022437
2414.121
0.0000

NIFTY
JR.
3391
0.024036
987.1003
0.0000

LSE

FTSE
100
3391
0.010768
549.3598
0.0000

FTSE
250
3391
0.019002
405.3918
0.0000

Sample
Period
1
:
01/01/2011-‐31/12/2014

Time
Series
N
Standard
Deviation
Jarque-‐Bera
Jarque-‐Bera
p-‐values

BSE

SENSEX
3391
0.013676
187.7839
0.0000

BSE
100
3391
0.013712
164.7944
0.0000

NSE

NIFTY
3391
0.013923
207.9089
0.0000

NIFTY
JR.
3391
0.014236
107.337
0.0000

LSE

FTSE
100
3391
0.011384
356.366
0.0000

FTSE
250
3391
0.011518
235.5909
0.0000

37

5.2 Augmented Dickey-Fuller (ADF) Unit Root test.
Since unit root is an essential condition for RWH, we used the most commonly
applied ADF Unit Root test to all 6 indices. The results are presented in Table 5.2.1.
The ADF was applied with intercept, intercept and trend and without intercept and
trend and levels and first difference.
Table 5.2.1. Results of the ADF Unit Root test.
The results from table 5.2.1 indicate that at levels, all 6 indices are not stationary as
all t-statistics are insignificant. This implies that the ADF test accepted null hypothesis
of stationarity at level. However, t-statistics at First difference were for all indices
were significant at 5% significance level, therefore rejecting null hypothesis. These
results give certain evidence of random walk in the all the indices tested. However,
presence of random walk behaviour on price indices does not imply that returns
follow the identical behaviour. According to Chung (2006), if white noise
characteristics exist in returns, there is a probability that equivalent stock prices
Result of the Augmented Dickey-Fuller unit root test on stock prices for all 6 indices for the full period are
presented below. The length of lags was selected automatically with the Schwartz Info Criterion. Test
statistics (t) are presented for only constant, with constant and trend and without constant nor trend. Test-
statistics are tested at 5% significance level. P-values are examined at 5% level.
H0 – Non-stationary / unit root. H1 – Stationary / no unit root. Critical Value of 5% - ±1.96
LEVEL
BSE NONE(t) p-value INTERCEPT(t) p-value
INTERCEPT
& TREND(t) p-value
BSE
Sensex
1.561481 0.9714 -1.732304
0.4148 -1.602946 0.792
BSE 100 1.530649 0.9695 -1.845211 0.3588 -1.650725 0.7726
NSE
Nifty 1.436155 0.9629 -1.695298 0.4336 -1.694275 0.7539
Nifty Jr. 1.665512 0.9772 -1.976725 0.2974 -1.91936 0.6440
LSE
FTSE 100 0.392567 0.7970 -1.692473 0.4351 -1.797199 0.7062
FTSE 250 1.213131 0.9429 -1.215128 0.6702 -1.725212 0.7401
FIRST DIFFERENCE
BSE NONE(t) p-value INTERCEPT(t) p-value
INTERCEPT &
TREND(t) p-value
BSE
Sensex
54.53223** 0.0001** -54.57796** 0.0001** -54.57796** 0.0001**
BSE 100 53.78599** 0.0001** -53.83513** 0.0001** -53.84835** 0.0000**
NSE
Nifty 54.69678** 0.0001** -54.73756** 0.0001** -54.7439** 0.0000**
Nifty Jr. 51.30482** 0.0001** -51.36392** 0.0001** -51.37683** 0.0000**
LSE
FTSE 100 28.81193** 0.0000** -28.8117** 0.0000** -28.80774** 0.0000**
FTSE 250 54.06268** 0.0001** -54.08214** 0.0001** -54.07442** 0.0000**

38

followed a random walk. This would give clear evidence of unpredictability in the
returns. Acceptance of null hypothesis of non-stationarity is consistent with previous
findings in the Indian markets by Khan (2013), Jain & Jain (2013) and Misra & Mishra
(2012). Similarly findings of Worthington and Higgs (2004) and Konak and Sekar
(2015) proved the presence of Unit Root in U.K. indices. However, evidence by
Mishra, Das and Pradhan (2009) proved that Indian markets were inefficient from
January 2007 to July 2009. Evidence from our study is inconsistent with this
particular examination, which could be due to difference in indices and time period
studied.
5.3 Serial Correlations Test
Results of first 15 lags of autocorrelation coefficients and corresponding Ljung-Box
Q-statistics and p-values for 1st
to 12th
order auto correlation of all index returns are
presented in Table 5.3.1. All Auto Correlation Functions (ACF) are examined at 5%
significance level.
At lag 1, the Nifty Jr. and FTSE 100 have the highest and lowest ACF respectively. At
one lag of 6, there is significant negative correlation in all BSE and NSE indices.
Similar evidence is found in the LSE indices at lag 5 and 6. This implies a mean
aversion in returns. Similar evidence exists in the BSE and LSE indices at lag 10-11
and 9-10 respectively. There is considerable evidence of ACF being non-zero at 5%
significance level, however, this is not enough to accept or reject auto correlation.
Ljung-Box Q-statistics give clear evidence that null hypothesis of no-serial
correlations is rejected. All Q-statistics for all indices from 1st
through 12th
order are
significant at 5% level. The p-values below 0.05 also indicated that null hypothesis
was rejected for the sample. Therefore, hypothesis of serial correlation is rejected.

39

Table 5.3.1.Autocorrelations Coefficients and Ljung-Box Q-statistics for Full
period.
P-values examined at 5% significance level. Asterisks ** denote that the absolute value of the Q-statistics
and p-value exceed the respective critical and significance values and thus reject null hypothesis
H0 – No Serial correlations. H0 – Presence of Serial correlations. Q-stat degree of freedom at 5%.
Bombay Stock Exchange
National Stock
Exchange London Stock Exchange
SENSEX BSE 100 NIFTY NIFTY JR. FTSE 100 FTSE 250
Full Sample : 01/2002 -12/2014
Lags.
1 0.064** 0.078** 0.061** 0.124** -0.037** 0.073**
2 -0.017 -0.005 -0.016 0.015 -0.028 -0.012
3 -0.004 0.006 -0.002 0.023 -0.086** -0.043**
4 0.040 0.043** 0.045** 0.030 0.058** 0.018
5 -0.001 0.001 0.002 -0.011 -0.072** -0.034**
6 -0.046** -0.044** 0.047** -0.040** -0.029 -0.037**
7 -0.028 -0.019 -0.024 -0.010 0.041** 0.016
8 0.018 0.022 0.015 0.029 0.044** 0.027
9 0.069** 0.064** 0.061** 0.059** -0.038** -0.016
10 0.052** 0.053** 0.050 0.076** -0.029 -0.027
11 -0.054** -0.051** -0.056** -0.021 -0.010 -0.017
12 -0.021 -0.019 -0.019 -0.017 0.009 0.023
13 0.058** 0.051** 0.057** 0.048** 0.011 0.028
14 0.036** 0.040** 0.038** 0.039** 0.013 0.054**
15 0.009 0.010 0.011 0.014 -0.010 0.005
Q(1) 14.017** 20.599** 12.773** 52.480** 4.6243** 18.242**
(0.000) (0.000) (0.000) (0.000) (0.032) (0.000)
Q(2) 14.968** 20.697** 13.682** 53.217** 7.2790** 18.702**
(0.001) (0.000) (0.001) (0.000) (0.026) (0.000)
Q(3) 15.030** 20.831** 13.702** 55.000** 32.441** 24.949**
(0.002) (0.000) (0.003) (0.000) (0.000) (0.000)
Q(4) 20.502** 26.977** 20.678** 58.057** 43.796** 26.044**
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
Q(6) 27.561** 33.439** 28.126** 64.003** 64.200** 34.511**
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
Q(8) 31.279** 36.343** 30.875** 67.192** 76.382** 37.859**
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
Q(10) 56.972** 59.758** 52.382** 98.662** 84.209** 41.185**
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
Q(12) 68.328** 69.895** 64.232** 101.32** 84.846** 43.948**
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

40

Table 5.3.2. Results of Ljung-Box Q-statistics for all three sub-periods.
Table 5.3.2 provides Ljung-Box Q-statistics for the 3 sub periods. Sub period 1
rejected null hypothesis of no serial correlations for all indices at 5% significance
level except for FTSE 250 at 6th
order. Corresponding p-values supported this claim.
For sub period 2, the SENSEX, the BSE 100 and the NIFTY show clear evidence of
Ljung Box Q-statistics are represented as Q (1) to Q (12) to examine 1st to 12th order autocorrelations for
three individual sub periods. Under the null hypothesis of no autocorrelation, it is distributed as 𝓍2
with
1 and 12 degree of freedom respectively. P-values are present in parentheses. Asterisks ** denote that
the absolute value of the Q-statistics and p-value exceed the respective critical and significant values
and thus reject null hypothesis.
H0 – No Serial correlations. H1 – Presence of Serial correlations. Q-stat degree of freedom at 5%.

Bombay Stock Exchange
National Stock
Exchange
London Stock
Exchange
BSE SENSEX BSE 100 NIFTY
CNX NIFTY
JR. FTSE 100
FTSE
250
Sub Period 1:01/01/200-12/2006
Q(1) 5.359** 9.9517** 12.773** 34.059** 6.126** 7.128**
Q(2) 10.990** 16.738** 13.682** 41.984** 6.352** 7.417**
Q(3) 11.052** 16.998** 13.702** 42.171** 22.133** 8.118**
Q(4) 26.596** 35.928** 20.678** 57.599** 22.142** 9.122**
Q(6) 27.185** 36.683** 28.126** 62.492** 31.243** 11.195
Q(8) 34.191** 44.439** 30.875** 71.218** 36.679** 22.110**
Q(10) 42.949** 51.599** 52.382** 91.395** 46.594** 23.470**
Q(12) 44.964** 53.821** 64.232** 92.666** 49.693** 23.730**
Sub Period 2:01/2007-12/2010
Q(1) 3.899** 5.139** 2.415 10.181** 1.693 6.040**
Q(2) 3.940 5.390 2.423 14.192** 4.045 6.417**
Q(3) 3.952 5.477 2.433 16.219** 12.347** 9.550**
Q(4) 4.348 5.752 3.131 16.262** 25.998** 11.393**
Q(6) 9.004 9.909 8.587 19.559** 35.128** 15.518**
Q(8) 10.914 11.388 10.055 22.369** 41.900** 17.068**
Q(10) 26.479** 25.643** 22.850** 33.872** 46.709** 19.830**
Q(12) 35.729** 34.334** 33.793** 35.702** 48.222** 22.998**
Sub Period 3 :01/2011-12/2014
Q(1) 4.967** 7.046** 5.559** 18.234** 0.092 4.553**
Q(2) 5.160 7.551** 5.677 19.128** 0.469 4.902
Q(3) 5.954 7.787 6.306 19.454** 3.314 8.845**
Q(4) 6.016 7.857 6.469 19.457** 6.109 12.733**
Q(6) 10.759 12.723** 12.196 21.075** 7.707 17.152**
Q(8) 12.113 14.190 13.593 23.727** 8.174 17.359**
Q(10) 12.208 14.305 13.639 24.770** 9.463 17.404
Q(12) 13.437 15.690 15.078 26.505** 9.892 18.506

41

no serial correlation and insignificant values. FTSE 100 was insignificant only at the
1st
and 2nd
order while the Nifty Jr. and the FTSE 250 were significant through all
orders. This indicates that Indian markets gave evidence of higher efficiency
compared to the U.K. market during the great recession between 2007 and 2010.
However, evidence from sub period 1 suggests that the inefficiency and predictability
in stock prices behaviour caused the formation of the bubble towards 2007.In Sub
period 3, i.e. post-recession and recovery period, both the Indian and the U.K.
markets provided evidence of greater efficiency and uncorrelated returns. All BSE
and NSE indices except for the Nifty Jr. were insignificant apart from a maximum of
two instances. The FTSE 100 was insignificant throughout this period while the FTSE
250 showed signs of increasing efficiency. This suggests returns on the tested
indices were not serially correlated during the post-recession period. Therefore null
hypothesis was accepted. Our study also proves that markets are efficient in the
short run, however, inefficient in the long run. However, the serial correlations test is
not the most reliable method of examining markets, therefore this study conducts
three other tests for greater accuracy.
When examined in the long-run, our results are consistent with evidence provided by
Mobark & Keasy (2002), Hasan et.al (2006) and Poshakwale (1996) that emerging
markets are significantly serially correlated. Notably, study by Nisar & Hanif (2012)
proved that the SENSEX rejected null hypothesis of Durbin-Watson serial correlation
from 1997-2011. This period is similar to the one used in this study and thus adds to
existing evidence of weak-form inefficiency in Indian Markets. Regarding U.K., our
results are consistent with those of Worthington and Higgs (2004) who rejected the
null hypothesis of serial correlations in daily returns in the U.K. markets from 1987-
2003. Loughani and Chappel (2010) and Solnik (1973) could not provide clear
evidence of rejection of correlations as the coefficients were too small. Contrary to
Borges (2008), autocorrelations in U.K. indices do not diminish with increasing lags.
Coefficients are significantly larger at the initial and late lags. This is the case for all
indices, except FTSE 100 examined in this study. According to Chung (2006), this
provides evidence that future predictability with historical price embedded in longer
periods of lags is equally effective as short period of lags. This further provides
evidence of liner dependence in all 5 indices.

42

5.4 Runs Test.
Table 5.4.1 represents the results of the non-parametric runs test for returns for the
BSE, the NSE and the LSE. The test examined three sample periods i.e. full period
and sub period 1, 2 and 3. All z-statistics were examined at 5% significance level
only. The p-values were examined at 5% level.
For the full period, all indices are significant at 5% level except for the FTSE 100.
Corresponding p-values support this evidence with only FTSE 100 being greater than
5%. The Negative significant z-statistics indicate that the actual number of runs were
fewer than the expected number of runs as under the null hypothesis. The negative
significant values indicate possible auto correlations in returns. This is consistent with
results of serial correlations test, which rejected null hypothesis for this sample
period.
Results for sub period 1 are consistent with the full period sample. Except FTSE 100,
all other indices are negatively significant at 5% significance level with similar results
of corresponding p-values. These results are consistent with serial correlations.
For sub period 2, the period of the market crash, all indices are seemed to be
insignificant at 5% level. The p-values for the indices are well above 5% levels for all
insignificant indices, thus accepting null hypothesis. Evidence from the serial
correlations is consistent only for the SENSEX, the BSE 100 and the Nifty.
For sub period 3, the post crisis/recovery period/ both BSE and NSE indices were
significant. Both LSE indices were observed to be insignificant. However, these
results are inconsistent with the Ljung-Box Q-statistics presented earlier as only the
Nifty Jr. showed evidence of autocorrelation in this sample.
Results from the Runs test indicate that both BSE and NSE indices were significant
at 5% level in all period except from 2007 to 2010, thus rejecting null hypothesis. The
FTSE 100 was observed as the most consistently insignificant index throughout all
sample periods proving that its returns series accepted null hypothesis. The FTSE
250 followed a random walk after 2006 following the FTSE 100 and remained
consistent until 2014. Results from runs test and Ljung-Box Q-statistics for full period
are consistent with each other. However, runs test results from sub period 2 through
3 indicate that all 6 indices were insignificant while only FTSE 100 and FTSE 250
were insignificant from 2011 to 2014. Thus, it can be concluded that all indices in the
full period did not follow a random walk. However, with a combination of runs and

43

serial correlations test, all 6 indices were observed to accept the null hypothesis only
between 2007 and 2014.
These results are consistent with ones of Poshakwale (1996), Joshi (2012) and Nisar
and Hanif (2012) who proved that Indian stock markets were inefficient in the long-
run. However, our results prove that Indian markets were efficient in the short run i.e.
2007 to 2010, which is consistent with Joshi (2012). Our results are also consistent
with Borges (2008) who proved U.K. markets to be efficient in the short run between
2003-2007.

44

Table 5.4.1. Results of non-parametric Runs Test
Results of the non-parametric runs test for all 6 indices for the full period and the sub periods. Total cases
implies number of observations, M implies Mean, Cases<M imply the number of cases below the mean
and Cases≥M denote number of cases equal to or more than mean. Z-statistics are examined at 5%
significance level with critical level ±1.96. P denoted Probability values are examine at 5%. Asterisks **
denote that the absolute value of the z-statistics and p-value exceed the respective critical and significant
values and thus reject null hypothesis.
H0 – Series follows random walk. H1 – Series does not follow random walk.
Time Series Total Cases Cases<M* Cases≥M*
Number of
Runs
Z-
statistic p
Sample : Full Period
BSE

SP BSE SENSEX 3390 1688 1703 1609 -3.005** 0.003**
SE BSE 100 3390 1674 1717 1583 -3.890** 0.000**
NSE

CNX NIFTY 3390 1684 1707 1611 -2.934** 0.003**
CNX NIFTY JR. 3390 1647 1745 1541 -5.314** 0.000**
LSE

FTSE 100 3391 1647 1745 1742 1.595 0.111
FTSE 250 3391 1641 1750 1634 -2.089** 0.037**
Sample : Sub Period 1
BSE

SP BSE SENSEX 1303 625 678 606 -2.522** 0.012**
SE BSE 100 1303 618 685 580 -3.933** 0.000**
NSE

CNX NIFTY 1303 629 674 612 -2.204** 0.027**
CNX NIFTY JR.
1303 623 680 587
-
3.568** 0.000**
LSE

FTSE 100 1303 520 522 524 0.124 0.901
FTSE 250 1303 652 651 609 -2.411** 0.016**
BSE

SP BSE SENSEX 1044 534 510 525 0.141 0.888
SE BSE 100 1044 523 521 527 0.248 0.804
NSE

CNX NIFTY 1044 521 523 523 0.000 1.000
CNX NIFTY JR. 1044 510 534 511 -0.726 0.468
LSE

FTSE 100 1044 644 659 661 0.476 0.634
FTSE 250 1044 497 547 493 -1.788 0.074
BSE

SP BSE SENSEX 1042 488 554 476 -2.733** 0.006**
SE BSE 100 1042 481 561 466 -3.300** 0.001**
NSE

CNX NIFTY 1042 487 555 470 -3.099** 0.002**
CNX NIFTY JR. 1042 528 514 466 -3.466** 0.001**
LSE

FTSE 100 1042 509 533 545 1.444 0.149
FTSE 250 1042 502 540 531 0.602 0.547

45

5.5 Variance Ratio Test
Table 5.5.1 reports the results of the variance ratio test (VR) tests for all 6 indices.
Log price values have been taken for all indices while Z (q) and Z*(q) are standard
expression for statistic of variance ratio under assumption of homoscedasticity and
heteroscedasticity respectively. As observed previously, the z-statistics are
examined at 5% significance level. Lo and MacKinlay (1988) and Ayadi and Pyun
(1994) stated the variance ratio test as more powerful than the ADF unit root test,
which justifies its application in thus study.
In the full period sample, null hypothesis of random walk is rejected under
homoscedasticity for all indices at all lags at 5% level of significance except for
SENSEX at lag 8 and FTSE 250 at lags 12 and 16. However, according to
Worthington and Higgs (2005), the presence of heteroscedasticity and
autocorrelation in a return series could lead to rejection of null hypothesis under
homoscedasticity. Therefore, heteroscedasticity was calculated for entire sample,
which provided similar results. Null hypothesis under heteroscedasticity was not
rejected for SENSEX, Nifty and both LSE indices at intervals 8, 12 and 16 while
FTSE 100 and BSE 100 accepted it at intervals 12, 16 and 8 respectively. There
was notable efficiency in the FTSE 250 at intervals 8 through 16 where both
homoscedasticity and heteroscedasticity statistics were accepted. SENSEX provided
similar evidence but only at lag 8. Variance ratio of FTSE 250 is more than 1 but not
significant and not increasing progressively, thus accepting null hypothesis. These
results indicate that only FTSE 250 provided sufficient evidence of efficiency in the
later periods accompanied by absence of auto correlation.
For sub period 1, null hypothesis under homoscedasticity and heteroscedasticity was
accepted only for both BSE indices and Nifty at all intervals except 2. Null hypothesis
was rejected under homoscedasticity for all indices except both the BSE indices and
the Nifty at interval 2. Under heteroscedasticity, null hypothesis was rejected for Nifty
Jr. at interval 2, FTSE 100 at 8 and FTSE 250 at 8, 12 and 16. Variance ratios for
both BSE indices & Nifty are not significantly greater than one however increase
progressively, providing rough evidence of auto correlation.
In sub period 2, there is greater evidence of random walk in price movement. Null
hypothesis under homoscedasticity is rejected at interval 2 for both BSE indices, BSE
100 and FTSE 250 at 5% significance level. Homoscedastic statistics reject FTSE

46

100 at intervals 4 and 8 only, accepting at all other intervals. Null hypothesis under
both assumptions was rejected for Nifty Jr. at all intervals. Contrastingly, it was
accepted for Nifty through all intervals while SENSEX and FTSE 250 accepted null
hypothesis at all intervals other that 2. BSE 100 and FTSE 100 accepted null
hypothesis under both assumptions at lags 8, 12, 16 and 2, 12, 16 respectively.
Variance ratios for all indices accepting null hypothesis do not increase progressively,
thus adding to evidence for efficiency.
In sub period 3, the SENSEX, the Nifty and the FTSE 250 accepted null hypothesis
under homoscedasticity and heteroscedasticity at all intervals except 2. The Nifty Jr.
rejected null hypothesis under both assumptions, similar to sub period 2. BSE 100
rejects null hypothesis under homoscedasticity at all intervals and heteroscedasticity
at 2 and 4, thus being inefficient throughout this sample period similar to Nifty Jr.
Apart from interval 16, FTSE 100 accepted null hypothesis under both assumptions
at all remaining intervals.
Conclusive findings based on the variance ratio test indicate that the only the FSTE
250 of all 6 indices was efficient In the long run, thus proven that none of the two
markets were weak-form efficient. However, in the short-run, the SENSEX and
NIFTY were efficient in each sub-periods. The BSE 100 lost its efficiency towards the
end while the FTSE 100 and FTSE 250 became efficient from sub-period 2 onwards.
The NIFTY JR. was the most inefficient index. Significance in most indices were due
to either homoscedasticity or heteroscedasticity, which implies that these indices
fulfilled some requirements of random walk if not all.
Our evidence is consistent with those of Borges (2008) with the rejection of null
hypothesis for the U.K. markets although Worthington and Higgs (2004) had
contrasting results. We believe that our results are inconsistent with those of
Worthington and Higgs (2004) as this study integrates the period from 2002-2010
during which the markets were highly volatile as a result of the recession which
emerged in the U.S. Furthermore, our results are consistent with previous findings
related to emerging markets e.g. Worthington and Higgs (2005) and Nisar and Hanif
(2012) based on examination of Indian markets.

47

Table 5.5.1 Results of Variance Ratio Test
Results of variance ratio test for returns of all 6 indices for full period and three sub periods are indicated
below. Variance ratio values are denoted by VR (q). Asymptotic normal tests statistics under
homoscedasticity and heteroscedasticity are denoted by Z (q) and Z*(q) respectively. Estimates of VR
(q), the statics of Z (q) and Z*(q) for q intervals, i.e. 2, 4, 6,8,12 and 16 are reported below. Asterisks **
denote that the absolute value of the test statistics and p-value exceed the respective critical and
significant values and thus reject null hypothesis.
Sample Period: Full Period. Holding Period - (q)
Time Series. n 2 4 8 12 16
BSE1

Sensex 3391 VR(q) 1.064 1.078 1.094 1.128 1.170

Z(q) 3.776** 2.454** 1.870 1.991** 2.250**

Z*(q) 2.269** 1.519 1.175 1.256 1.426
BSE 100 3391 VR(q) 1.078 1.115 1.156 1.203 1.252

Z(q) 4.570** 3.609** 3.074** 3.166** 3.338**

Z*(q) 2.672** 2.185** 1.917 1.999** 2.128**
NSE1

Nifty 3391 VR(q) 1.061 1.075 1.100 1.131 1.170

Z(q) 3.606** 2.360** 1.977** 2.044* 2.260**

Z*(q) 2.069** 1.405 1.222 1.283 1.435
Nifty Jr. 3391 VR(q) 1.124 1.214 1.271 1.343 1.421

Z(q) 7.276** 6.6727** 5.350** 5.334** 5.571**

Z*(q) 3.800** 3.629** 3.112** 3.234** 3.471**
LSE1

FTSE 100 3391 VR(q) 0.963 0.875 0.788 0.757 0.737

Z(q) 2.118** 3.888** 4.164** 3.764** 3.474**

Z*(q) -1.175 2.069** 2.121** -1.900 -1.751
FTSE 250 3391 VR(q) 1.073 1.078 1.039 1.016 1.026

Z(q) 4.302** 2.443** 0.777 0.249 0.348
Z*(q) 2.871** 1.579 0.479 0.150 0.209
Sample Period : Sub Period
1
BSE1

Sensex 1303 VR(q) 1.065 1.037 1.106 1.146 1.195

Z(q) 2.366 0.714 1.295 1.406 1.605

Z*(q) 1.004 0.334 0.678 0.789 0.944
BSE 100 1303 VR(q) 1.088 1.069 1.155 1.192 1.230

Z(q) 3.207 1.332 1.903 1.851 1.892

Z*(q) 1.329 0.606 0.970 1.015 1.090
NSE1

Nifty 1303 VR(q) 1.077 1.047 1.119 1.147 1.191

Z(q) 2.810 0.918 1.463 1.422 1.567

Z*(q) 1.079 0.390 0.709 0.748 0.869
Nifty Jr. 1303 VR(q) 1.163 1.163 1.224 1.244 1.316

Z(q) 5.891 3.147 2.743 2.356 2.597**

Z*(q) 2.174 1.260 1.244 1.166 1.364
LSE1

FTSE 100 1303 VR(q) 0.932 0.859 0.718 0.694 0.680

Z(q) 2.428** 2.720** 3.429** 2.938** 2.619**

Z*(q) -1.618 -1.736 2.163** -1.859 -1.663
FTSE 250 1303 VR(q) 1.075 1.140 1.226 1.312 1.402

Z(q) 2.722** 2.720** 2.763** 3.007** 3.298**
Z*(q) 1.953 1.923 1.992** 2.208** 2.454**

48

Table 5.5.1 (continued)
Sample Period : Sub Period 2 Holding Period – (q)
Time Series. n 2 4 8 12 16
BSE1
Sensex 1044 VR(q) 1.062 1.089 1.070 1.106 1.161
Z(q) 2.030** 1.540 0.764 0.9166 1.185
Z*(q) 1.538 1.171 0.571 0.674 0.865
BSE 100 1044 VR(q) 1.071 1.130 1.138 1.195 1.263
Z(q) 2.321** 2.258** 1.510 1.688 1.935
Z*(q) 1.714 1.682 1.122 1.245 1.425
NSE1
Nifty 1044 VR(q) 1.049 1.078 1.068 1.105 1.158
Z(q) 1.610 1.357 0.749 0.909 1.164
Z*(q) 1.209 1.020 0.559 0.672 0.857
Nifty Jr. 1044 VR(q) 1.1000 1.237 1.284 1.384 1.476
Z(q) 3.245* 4.109** 3.106** 3.317** 3.497**
Z*(q) 2.244** 2.866** 2.236** 2.428** 2.592**
LSE1
FTSE 100 1044 VR(q) 0.960 0.852 0.800 0.784 0.774
Z(q) -1.261 2.551** 2.177** -1.854 -1.656
Z*(q) -0.800 -1.553 -1.264 -1.064 -0.949
FTSE 250 1044 VR(q) 1.077 1.072 1.043 1.009 1.011
Z(q) 2.492** 1.258 0.471 0.083 0.084
Z*(q) 1.992** 0.977 0.347 0.060 0.060
Sample Period : Sub Period 3
BSE1
Sensex 1042 VR(q) 1.070 1.106 1.151 1.177 1.184
Z(q) 2.280** 1.842 1.650 1.524 1.352
Z*(q) 2.018** 1.575 1.368 1.245 1.101
BSE 100 1042 VR(q) 1.083 1.141 1.208 1.255 1.277
Z(q) 2.706** 2.434** 2.273** 2.198** 2.037**
Z*(q) 2.373** 2.077** 1.891** 1.805 1.668
NSE1
Nifty 1042 VR(q) 1.074 1.111 1.166 1.199 1.211
Z(q) 2.410** 1.922 1.816 1.717 1.549
Z*(q) 2.109** 1.627 1.494 1.393 1.253
Nifty Jr. 1042 VR(q) 1.133 1.237 1.323 1.417 1.485
Z(q) 4.314** 4.098** 3.534** 3.593** 3.561**
Z*(q) 3.774** 3.595** 3.059** 3.084** 3.057**
LSE1
FTSE 100 1042 VR(q) 1.008 0.971 0.850 0.775 0.729
Z(q) 0.272 -0.497 -1.631 -1.930 -1.982
Z*(q) 0.214 -0.375 -1.196 -1.411 -1.450
FTSE 250 1042 VR(q) 1.066 1.054 0.904 0.830 0.813
Z(q) 2.132** 0.935 -1.044 -1.460 -1.370
Z*(q) 1.884 0.768 -0.824 -1.140 -1.068

49

5.6 Summary of Test Results of Random Walk Hypothesis.
Table 5.6.1 indicates a summary of all tests and whether RWH in each test was
accepted or rejected.
Table 5.6.1 Summary of Results of RWH (accept/reject)
Test Index
BSE
SENSEX
BSE
100
CNX
NIFTY
CNX NIFTY
JR.
FTSE
100
FTSE
250
Full Period
Serial Correlations Reject Reject Reject Reject Reject Reject
ADF Unit Root Test Accept Accept Accept Accept Accept Accept
Runs Test. Reject Reject Reject Reject Accept Reject
Variance Ratio Test. Reject Reject Reject Reject Reject Accept
Sub-Period 1
Serial Correlations Reject Reject Reject Reject Reject Reject
Runs Test. Reject Reject Reject Reject Accept Reject
Variance Ratio Test. Accept Accept Accept Reject Reject Reject
Sub-Period 2
Serial Correlations Accept Accept Accept Reject Reject Reject
Runs Test. Accept Accept Accept Accept Accept Accept
Variance Ratio Test. Accept Accept Accept Reject Accept Accept
Sub-Period 3
Serial Correlations Accept Accept Accept Reject Accept Reject
Runs Test. Reject Reject Reject Reject Accept Accept
Variance Ratio Test. Accept Reject Accept Reject Accept Accept

50

Chapter 6 Conclusion
Based on theoretical framework of weak-form efficiency, this study examines the
Indian and the U.K. equity markets, with an aim of comparing efficiencies of emerging
and developed markets. To test Indian markets with a wider scope, the study used
four stock price index series from BSE and NSE and two from the LSE represent the
U.K. markets. The period of 2002-2014 was carefully selected with an aim to
integrate the boom, outbreak and recovery phase of the 2008 recession which
emerged due to the “housing bubble” in the United States. We believe that analysing
markets with accounting global fluctuations like 2008 will help in provide a clearer
picture of market efficiency. The study does not consider the period prior to 2002 as
the period 1995-2002 marked another economic downturn due to the collapse of the
Internet “dot-com” bubble. 2014 has been included to derive more recent evidence
relating to efficiency. The full sample period was divided into three sub-periods to
analyse whether the two markets provide evidence of increasing efficiency over time.
Four statistical tests were employed in this study, namely the serial correlations test,
the ADF unit root test, the non-parametric runs test and the stringent variance ratio
test.
Empirical results of the statistical tests proved that in the long run (2002-2014), all six
indices failed to accept null hypothesis of weak-form efficiency market hypothesis
and RWH. Existence of Unit Root was proved by the ADF test. Though, the FTSE
100 and FTSE 250 were found to efficient under runs and variance ratio test
respectively, this does not provide sufficient evidence of overall weak-form efficiency.
There is also evidence of positive autocorrelation in daily returns.
In the short run, evidence suggests that both markets have shown increased
efficiency. Variance ratio tests suggest that except for the NIFTY JR. all other Indian
indices supported weak-form efficiency, however the U.K. indices remained
inefficient. The most notable evidence of this study is that the period 2007-2010, the
SENSEX, BSE 100, NIFTY, FTSE 100 and the FSE 250 were consistent with the
weak-form efficiency hypothesis under the Runs test and the Variance ratio test. The
SENSEX, BSE 100, NIFTY were not serially correlated. This suggests that the Indian
and U.K. markets were highly weak-form efficient during the period of global

51

recession. This could be a result of the collapse of the “housing bubble” in 2007. It
provides evidence of a possible cross-border integration between emerging and
developed financial markets, which could be subject to further research. The results
of this study are consistent with those of Sharma and Kennedy (1997) who found
links between Indian, U.S and the U.K. markets. When compared, the Indian and the
U.K. markets showed almost identical behaviour during the global recession. This
further adds to the fact that Indian markets have gradually integrated with global
markets. The 2011-2014 period provides evidence of certain degree of inefficiency in
the Indian markets, unlike the U.K. markets. This can be attributed to the fact that
Indian markets still show characteristics of an informationally inefficient emerging
market. Inefficient markets unsettle investment states of a country since stocks do
not reflect their true values. This hampers capital mobilization for firms with lower true
value and obstructs the equity raising capacity of larger firms. According to
Mishra,Das and Pradhan (2009), even though inefficiency is a negative reflection of a
market, predictability could have a positive effect as expectation of abnormal profits
could stimulate short run investment which could lead to introduction of financial
products designed to exploit the market environment.
This study concludes that Indian and U.K markets were weak-form inefficient in the
long run. However, when analysed in the short run, both markets were highly
consistent with weak-form market efficiency hypothesis from 2007 to 2010
Further research can be conducted by analysing weekly or monthly data for broader
liquid indices of both markets for example the BSE 500, NSE 500 and the FTSE 500.
Comparison can be drawn between more than two markets and cross-border
integrations can be checked for with appropriate statistical tests. Tests can be
conducted to ascertain whether profitable investment strategies can be formulated by
using trading rules. Markets can also be tests for calendar anomalies.

52

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