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Editorial Board A Refereed Monthly International Journal of Management
Prof. B. P. Sharma
(Editor in Chief)
Prof. Mahima Birla
(Group Editor)
Dr. Khushbu Agarwal
(Editor)
Ms. Asha Galundia
(Circulation Manager)

 Editorial Team

Dr. Devendra Shrimali
Dr. Dharmesh Motwani
Mr. Jinendra Vyas
 

Testing Weak- Form Efficiency of Indian Stock Market using High Frequency Data

AUTHOR 1

Haritika Arora

Assistant Professor

C K D Institute of Management & Technology, Opp. Model Town, Near Railway Station, G.T. Road, Amritsar

Email: haritika.arora@gmail.com

Contact No.- 7814044556

Correspondence Address: 26, Krishna Square 2, Telephone Exchange Lane, Near Celebration Mall, Amritsar.

 

AUTHOR 2

Dr. Balwinder Singh

Associate Professor

Guru Nanak Dev University, Amritsar

Email: bksaini@gmail.com

Contact No. - 9417272232 / 8146082233

Correspondence Address: Department of Commerce, Guru Nanak Dev University, Amritsar

 

  1. I) INTRODUCTION

Eugene Fama in 1965 has discussed three forms of financial market efficiency: the weak form, the semi-strong form and the strong form efficiency. The weak form of efficiency is defined by the situation when current asset prices reflect all the information enclosed in the past price movement. Hence, future price movement cannot be forecasted by examining the past price movement. This also implies that it is not possible to obtain excess returns by studying the assets’ prices history. (Ahmad, Ashraf, & Ahmed, 2006). If financial market does not follow weak form efficiency, it becomes predictable in nature. (Bessembinder and Chan, 1995).  This predicable characteristics of the financial market  provides the opportunity to investors or traders to earn supernormal profits. Various scholastic studies found asset market's to be least weak form efficient (Bessembinder and Chan, 1995; Coutts and Cheung, 2001). These studies bring out the success of technical trading strategies based on this inefficiency to produce abnormal profits to investors.

Previous studies related to weak form efficiency have mostly used the daily data. However, problem associated with the daily data is that it is an average of last 30 minutes of the trade, consequently, it is not suitable to bring out the dynamics of complete trading session.  But, advent of high speed electronic technology available these days have made the high quality intraday data accessible. This high quality high frequency data is expected to reveal limitations related to efficiency of markets, thereby providing a way of (legally) making an excess return from trading (Goodhart and Hara, 1997). Therefore, the present study tries to re-examine the weak form efficiency of Indian Stock Market using the 5- minute interval intraday return data.

  1. II) REVIEW OF EXISTING LITERATURE

Majority of the previous studies provide an evidence for the financial markets to be weak form inefficient. However, some of the studies have found some markets to be weak form efficient which include Taiwan share market by Fawson et al. (1996); Hong Kong Stock market by Cheung & Andrew (2001); Hungary, Germany, Ireland, Portugal, Sweden and the United Kingdom markets by Worthington & Higgs (2003); Dhaka Stock Market  by Rahman et al. (2004); Australia and Taiwan markets by Worthington & Higgs (2005); Insurance sector of  Abu Dhabi Securities Market by Squalli (2006); Bahrain Stock Market by Asiri (2008). Table 1 depicts the existing literature that have examined weak form of efficiency in various financial markets.

The associated literature demonstrates various linear and non-linear dependencies in asset price behaviour. Nonlinear serial dependence has been recognized across various financial markets with different market structural systems (Al-Loughani & Chappell; 1997; Lim, 2009; Lim, Brooks, & Hinich; 2008). Various studies observed linear serial dependencies in financial data using simple serial correlation tests (Brown & Easton, 1989; Poshakwale, 1996; Laurence et al., 1997; Abrosimova et al., 2002; Hameed et al., 2006; Awad & Daraghma, 2009; Irfan et al., 2010; Gupta & Basu; 2011 etc.). Some studies used variance ratio test to investigate serial interdependence among various financial market asset's returns, return volatility, volume etc. (Urrutia, 1995; Cheung & Andrew, 2001; Buguk & Brorsen, 2003; Worthington & Higgs, 2003; Islam & Khaled, 2005; Worthington & Higgs, 2005; Squalli, 2006; Ntim, Opong, & Danbolt, 2007; Hamid et al., 2010). Various studies investigated weak form efficiency using GARCH models which include Milionis & Moschos (2000); Abrosimova et al. (2002); Ahmad et al. (2006); Hameed et al. (2006); Magnus (2008); Guidi et al. (2011); Alexeev & Tapon (2011); Mishra (2011) and Lean & Smyth (2015).

From table 1, it is clearly evident that most of the previous studies have used low frequency data (daily data) to test weak form efficient market hypothesis. With accessibility of high frequency data from few years have grabbed the attention of researchers to re-test the efficiency of financial markets. Few studies have tried to re-examine the weak form efficiency using high frequency data which includes Niarchos and Alexakis (2003); Strawinski and Slepaczuk (2008); Schulmeister (2009); Shmilovici et al. (2009); Wang and Yang (2010); Reboredo et al. (2012). Majority of these studies found financial markets to be weak form inefficient, except the study of Wang and Yang (2010) and Shmilovici et al. (2009). However, Wang and Yang (2010) have scrutinized the intraday efficiency of futures market using four major energy futures: crude oil, heating oil, gasoline, natural gas. Out of these four futures, crude oil and gasoline futures were found to weak form efficient. Commenting on weak form efficiency, Shmilovici et al. (2009) observed that intraday forex market tend to predictable above random. But, this predictability of the model is not enough to produce profitable trading strategy.

The present study endeavours to re-test the weak form efficiency using high frequency data in Indian Stock Market. High frequency literature is novel for Indian financial markets and have not yet been extensively researched. Therefore, this study contributes to the high frequency literature through re-testing basic weak form efficient market hypothesis in Indian financial markets.

Table 1: Empirical evidence for weak form of efficiency.

S. No.

Author

Market under study

Period of Study

Techniques used

Frequency of data used

Weak Form Efficient/ Inefficient

1

Brown & Easton (1989)

London Stock Market

1821-1860

Runs test, Serial correlation test

Low Frequency

Inefficient

2

Urrutia (1995)

Latin American emerging equity market 

1975-1991

Variance-ratio tests 

Low Frequency

Inefficient

3

Fawson et al. (1996).

Taiwan share market

 

1967 - 1993

Ljung-Box Q test, Binomial distribution test, Runs test and Unit root test

Low Frequency

Efficient

4

Poshakwale (1996).

Indian Stock Market

1987-1994

Kolmogorov Smirnov Goodness of Fit Test, Runs Test, Serial Correlation Coefficients Test

Low Frequency

Inefficient

5

Al-Loughani & Chappell (1997)

London Stock Market

1983-1989

GARCH- M model, BDS test

Low Frequency

Inefficient

6

Laurence et al. (1997)

Chinese Stock Market

1993-1996

Serial Correlations and Ljung-Box Statistics

Low Frequency

Inefficient

7

Milionis & Moschos (2000)

London Stock Market

1990-1997

GARCH-M model, Auto correlation function

Low Frequency

Inefficient

8

Mobarek & Keasey (2000)

Dhaka Stock Market

1988 - 1997

Non-parametric and run test and parametric test

Low Frequency

Inefficient

9

Cheung & Andrew (2001)

Hong Kong Stock exchange

1985-1997

Variance ratio tests

Low Frequency

Efficient

10

Abrosimova et al. (2002)

Russian Stock Market

1995-2001

Autocorrelation, variance ratio tests, ARIMA, GARCH

Low Frequency

Inefficient

11

Buguk & Brorsen (2003)

Istanbul Stock Market

1992 - 1999

Variance ratio test, Rank- and sign-based variance ratio tests

Low Frequency

Inefficient

12

Worthington & Higgs (2003) 

 16 developed and emerging stock markets

1986-2003

Serial correlation coefficient, Runs tests, KPSS test and MVR test.

Low Frequency

Hungary, Germany, Ireland, Portugal, Sweden and the United Kingdom are found to efficient rest inefficient

13

Niarchos, N. A. & Alexakis, C. A.(2003)

Greek Stock Market

June 1998-September 1998

ARCH test

High Frequency

Inefficient

14

Rahman et al. (2004).

Dhaka Stock Market

1990-2003

ADF and PP test

Low Frequency

Efficient

15

Onour (2004)

Saudi Stock Market

2003-2004

Mean square of successive difference test, Runs test

Low Frequency

Inefficient

16

Moustafa (2004).

Unites Arab Emirates (UAE) Stock Market

2001-2003.

Nonparametric runs to test for randomness

Low Frequency

Inefficient

17

Robinson (2005)

Jamaica Stock Market

1992- 2001

Auto-correlation test, Runs test

Low Frequency

Inefficient

18

Islam & Khaled (2005)

Dhaka Stock Market

1992 -2001

Variance Ratio Tests

Low Frequency

Inefficient

19

Worthington & Higgs (2005)

 10 emerging and 5 developed markets

1986-2003

Serial correlation coefficient, Runs tests, KPSS test and MVR test.

Low Frequency

Australia and Taiwan found to efficient, rest Inefficient

20

Ahmad Ashraf & Ahmed (2006)

Indian Stock Market

1999-2004

Auto-correlation Function, GARCH model, non parametric Kolmogrov–Smirnov test

Low Frequency

Inefficient

21

Squalli (2006)

Dubai and Abu Dhabi Securities Market

2000-2005

Runs test, Variance-ratio tests

Low Frequency

Insurance sector stocks in the ADSM is only weak-form efficient , rest Inefficient

22

Hameed et al. (2006).

Pakistan stock market

1998- 2006

Auto-correlation, GARCH(1,1)

Low Frequency

Inefficient

23

Rahman & Hossain (2006)

Dhaka Stock Market

1994 - 2005

Non-parametric tests and parametric-tests.

Low Frequency

Inefficient

24

Ntim, Opong, & Danbolt (2007)

Ghana Stock Market

1990- 2005

Variance Ratio Test

Low Frequency

Inefficient

25

Loh, E (2007)

Asian-Pacific stock markets

1990-2005

Break even cost test

Low Frequency

Inefficient

26

Mollah (2007)

Botswana Stock Market

1989–2005

Non-parametric and parametric test

Low Frequency

Inefficient

27

Elango & Hussein (2008)

GCC countries stock  markets

2001-2006

 Kolmogorov-Smirnov test, Runs test

Low Frequency

Inefficient

28

Asiri (2008)

Bahrain Stock Market

1990-2000

 ARIMA and Exponential smoothing methods

Low Frequency

Efficient

29

Magnus (2008)

Ghana Stock Market

1999-2004

Random walk test, GARCH(1,1)

Low Frequency

Inefficient

30

Lim, Brooks, & Hinich (2008)

10 Asian Stock markets

1992-2005

Hinich correlation and bicorrelation tests, Rank correlation, Tsay test, BDS test.

Low Frequency

Inefficient

31

Strawinski and Slepaczuk (2008)

Warsaw Stock Market

2003- 2008

Robust Regression

High Frequency

Inefficient

32

Lim, K. P. (2009).

Middle East and African stock market

1992-2005

McLeod–Li test, Engle LM test, BDS test, Tsay test, Hinich bicorrelation test, and Hinich bispectrum test

Low Frequency

Inefficient

33

Lim et al. (2009)

Shanghai and Shenzhen Stock Market

1991-2003

Linear and Non Linear Serial dependence test

Low Frequency

Inefficient

34

Awad & Daraghma (2009)

Palestinian Securities Market

1998-2008

Unit roost test, Runs Test and Autocorrelation test

Low Frequency

Inefficient

35

Schulmeister, S. (2009).

US spot and Futures Market

1983–2007

Based on success of technical trading strategies

High Frequency

Inefficient

36

Shmilovici et al. (2009).

Foreign exchange Market

Jan 2000- Dec 2000

Universal Variable Order Markov (VOM) test

High Frequency

Efficient

37

Hamid et al.(2010)

14 Asia-Pacific nation's stock market

2004-2009

Autocorrelation, Ljung-Box Q-statistic Test, Runs Test, Unit Root Test and  Variance Ratio

Low Frequency

Inefficient

38

Srinivasan (2010)

Indian Stock Market

1997-2010

ADF and PP test

Low Frequency

Inefficient

39

Korkmaz & Akman (2010).

Istanbul Stock Market

2003-2009

Unit root test

Low Frequency

Inefficient

40

Irfan et al.(2010)

Pakistan Stock Market

1999-2009

Unit root, Auto-correlation test, ARIMA model

Low Frequency

Inefficient

41

Wang and Yang (2010)

New York Energy Futures Market

2000-2007

Neural network, semiparametric functional coefficient model, nonparametric kernel regression, GARCH

High Frequency

Heating oil and natural gas futures- Inefficient. Crude Oil and Gasoline futures- Efficient

42

Gupta & Yang. (2011)

Indian Stock Market

1997-2011

Augmented Dickey-Fuller test, the Phillips-Perron test and KPSS test

Low Frequency

Inefficient

43

Guidi et al. (2011)

Central and Eastern Europe (CEE) equity markets

1999–2009.

Generalised Autoregressive Conditional Heteroscedasticity in Mean (GARCH-M) model

Low Frequency

Inefficient

44

Khan & Mehtab (2011)

Indian Stock Market

2000-2010

Non para-metric runs test

Low Frequency

Inefficient

45

Alexeev & Tapon (2011)

Toronto Stock Exchange

1980-2010

Pattern Recognition, EGARCH

Low Frequency

Inefficient

46

Gupta & Basu (2011)

Indian Stock Market

1991-2006

Durbin-Watson (DW) statistics

Low Frequency

Inefficient

47

Ntim et al. (2011).

African Stock Market

2000-2007

Variance‐ratio tests based on ranks and signs

Low Frequency

Inefficient

48

Mishra (2011).

8 emerging and developed stock markets

2007-2010

Unit root and GARCH(1,1)

Low Frequency

Inefficient

49

Ajao & Osayuwu (2012)

Nigerian Stock Market

2001–2010

Box-Ljung statistic, Runs test

Low Frequency

Inefficient

50

Gimba (2012).

Nigerian Stock Market

2005-2009

Variance Ratio test, Auto-correlation test, Runs test

Low Frequency

Inefficient

51

Stănculescu & Mitrică (2012).

Romanian capital market

1997-2000

Augmented Dickey-Fuller test, the Phillips-Perron test

Low Frequency

Inefficient

52

Al-Saleh & Al-Ajmi (2012)

Saudi Stock Market

1994-2007

Run test, and rank- and sign-based single and multiple variance ratio test

Low Frequency

Inefficient

53

Nisar & Hanif (2012)

South Asian markets

1997-2011

Runs test, Serial correlation, Unit root and Variance ratio test

Low Frequency

Inefficient

54

Patel (2012)

Asian Stock Markets

2000-2011

Runs Test, Unit Root Test, Variance Ratio, Auto Correlation test

Low Frequency

Inefficient

55

Al-Ahmad (2012)

Damascus Securities Exchange Market

2009-2011

 Variance Ratio, Auto Correlation test

Low Frequency

Inefficient

56

Reboredo et al. (2012).

US Stock Market

April 2006 -August 2006

Simple Random Walk model, Auto regressive model, Nonlinear regression models

High Frequency

Inefficient

57

Rabbani et al. (2013)

Pakistan Stock Market

1999-2010

Augmented Dickey-fuller test, Auto-correlation function test, Phillip Perron test and Runs test

Low Frequency

Inefficient

58

Shaker (2013)

Finnish and Swedish Stock Market

2003-2012

Serial Correlation test, Variance ratio test

Low Frequency

Inefficient

59

Mazviona & Nyangara (2013).

Zimbabwe Stock Market

2009-2012

Auto-correlation, Runs test and the Q-statistic test

Low Frequency

Inefficient

60

Mobarek & Fiorante (2014)

Equity markets of BRIC countries

1995-2010

Serial correlation test, Variance ratio test

Low Frequency

Inefficient

61

Jiang, Xie & Zhou (2014)

West Texas Intermediate Oil Futures Market

1983-2012

De-trended fluctuation and De-trending moving average analysis

Low Frequency

Inefficient

62

Jamaani & Roca (2015).

Gulf Stock Market

2003-2013.

Augmented Dickey Fuller test, Variance Ratio test

Low Frequency

Inefficient

63

Lean & Smyth (2015).

Crude Palm Oil Future and Spot Market

1999-2014

ADF test, and GARCH model

Low Frequency

Inefficient

64

Guney & Komba (2016)

Tanzania Stock Market

2007-2014

Variance-ratio, Ranks and Sign test

Low Frequency

Inefficient

Where, ADF test- Augmented Dickey-Fuller (ADF) test, ARCH- AutoRegressive Conditional Heteroskedasticity, ARIMA - Autoregressive Integrated Moving Average models, BRIC countries -Brazil, Russia, India and China, EGARCH-exponential GARCH, GARCH- Generalized AutoRegressive Conditional Heteroskedasticity, GARCH- M - GARCH in mean,  GCC countries -Gulf Co-operation Council countries, KPSS tests - Kwiatkowski–Phillips–Schmidt–Shin,  MVR- multiple variance ratio, PP test- Phillips-Perron (PP) test

 

Source: Compiled from various research studies.

III) DATABASE AND METHODOLOGY

The sample used for the study is Nifty 50 and top 10 frequently traded stocks for the period 1st January 2009-31st March 2011 using 5-minute interval data for prices.  During the period of our study, the stock market in India have seen two major significant structural changes in stock trading which are as follows:

  1. On 1st January 2010: Advancement of trading hours (market opening changed from 9:55am to 9:00am).
  2. On 18th October 2010: Pre-opening session (Pre-auction period) launched. This pre-open session lasts for 15 minutes from 9:00 AM to 9:15 AM.

The intention of these major structural changes in the stock market is to make market more liquid, less volatile and more efficient. Therefore, with the prevalence of these changes in stock market, re-testing the market efficiency theories has become the need of an hour. Consequently, complete data period was divided into 3 parts

Sub period 1: 1st January 2009-31st December 2009 (Before the change in trading time)

Sub period 2: 1st January 2010-17th October 2010 (After the change in trading time/ Before the launch of pre-opening session)

Sub period 3: 18th October 2010-31st March 2011(After the launch of pre-opening session)

Further, out of top 50 frequently traded stocks only top 10 frequently traded stocks are selected based on following filters:

1)  Stocks whose prices are adjusted due to any corporate action such as issue of bonus shares, stock splits, merger or acquisition during the sample period are excluded.

2) Then top 10 stocks which have highest turnover (trading volume multiplied by share price) are included in the study.

Database for high frequency data for the Capital Market segment has been purchased from Dotex International Limited, a subsidiary of National Stock Exchange. This database is managed in two steps using software Visual Fox Pro:

1) Company Based Management: Data set includes complete transaction book for each trading date separately. In this step, the complete database is arranged company wise using Microsoft visual fox pro. Results output contains tick by tick information for each company separately.

2) Time Based Management: The second step of database management is time based management, in which proper interpolation rule is used to extract data at fixed intervals. Using nearest value and trading volume adjusted weighted average prices, desired companies or indices have been extracted at required fixed intervals (5-minute interval).

Statistical tests are applied in two steps, the first step includes preliminary analysis, which forms the basis of every time series statistical analysis. It includes the summary statistics using Mean, Standard Deviation, Skewness and Kurtosis. Unit Root test or Augmented Dickey Fuller (ADF) test has been used to check stationarity of the series. In a weak-form efficient market, there is no correlation between successive prices. Hence, the second step is applying the main time series statistics tools to check interdependence.

Various statistical analysis such as ARMA (Auto-regressive Moving Average) model and GARCH(1,1) is used to check presence of interdependence. An ARMA model is a special type of regression model in which the dependent variable has been stationarized and the independent variables are all lags of the dependent variable and/or lags of the errors.  The model consists of two parts, an autoregressive (AR) lags of the dependent variable part and a moving average (MA) part.

When the Intraday returns variances are dependent of time, then above models were adjusted to take into account these Autoregressive Conditional Heteroscedasticity (ARCH) effects. A natural extension of an ARCH(q) model is a Generalized Autoregressive conditional heteroscedastic (GARCH) model, which is widely employed in practice. From GARCH model volatility clustering can be observed. High persistent volatility clustering represent the inefficiency of a stock returns. GARCH (1,1) is employed in present study, which is represented as follows:

  1. IV) PRELIMINARY ANALYSIS

This section deals with preliminary analysis through unit root test and descriptive statistics.

  1. a) Unit Root Test

Present study deals with the time series data, it becomes the major concern if the time series data is non-stationarity. In the nonexistence of stationarity, outcome of time series statistical analysis will become spurious. In order to check the presence of unit root and determining the order of differencing required to bring stationarity, this study has used the Augmented Dickey-Fuller (ADF) test.

Table 2 reveals that all price series are non-stationary. The null hypothesis of a unit root for price series is not accepted at the 1%, 5% and 10% level of significance. However, null hypothesis of a unit root for price series at first difference is accepted at the 1% level of significance.

Transformed series of 5-minute interval return data is taken as a logarithmic transformation of the price series is taken for further analysis. The returns are calculated as the difference of the

logarithmic prices i.e

Rp = Ln (Pt - Pt-1)

Where Rp= Returns, Pt= Price at interval t and Pt-1 =Price at interval t-1

  1. b) Descriptive Statistics

Descriptive statistics for entire sample are computed to study the distribution pattern. Descriptive statistics include analysis of mean, maximum values, minimum values, standard deviation, skewness and kurtosis. Further, normality has been checked by applying the Jarque bera test. Skewness and kurtosis helps to understand the characteristics of a distribution.

From table 3, 4 and 5, it is observed that mean returns are positive for complete sample in sub-period 1. In sub-period 2, mean returns are positive for Nifty, I C I C I Bank Ltd., State Bank Of India, Infosys Ltd., H D F C Bank Ltd., Axis Bank Ltd., D L F Ltd., Bharat Heavy Electricals Ltd., Hindalco Industries Ltd. However, NTPC Ltd. and Sesa Goa Ltd have negative returns for this period. However, in sub-period 3, negative returns are observed for complete sample. Standard deviation is a measure of the variability or dispersion of a statistical population. From descriptive statistics, it is clearly evident that all returns series have low standard deviation which depicts the fluctuation of a security around its mean or average return (the mean reverting behavior).

The coefficient of the Jarque-bera is significant at 1 percent for complete sample in three periods. It documents that the trading returns are asymmetric and do not have the normal distribution. Leptokurtic distribution (kurtosis>3) of all the trading returns for Nifty and all companies is evident.

Table 2: Unit Root test- Augmented Dickey-Fuller test statistic

 

Sub- Period 1

Sub- Period 2

Sub- Period 3

 

At Level

1st Difference series

At Level

1st Difference series

At Level

1st Difference series

Nifty

-0.713391

-126.9683*

0.080932

-126.026*

-1.398241

-96.32451*

I C I C I Bank Ltd.

-0.766293

-134.2486*

-0.436839

-133.7734*

-1.669042

-93.50274*

State Bank Of India

-0.402951

-136.7036*

0.959741

-132.8746*

-1.645768

-103.0971*

Infosys Ltd.

-0.402229

-141.2799*

-1.031055

-94.50739*

-1.79807

-94.68191*

H D F C Bank Ltd.

-0.804369

-141.2906*

-0.196054

-96.74844*

-1.868907

-96.77029*

Axis Bank Ltd.

-0.659084

-141.861*

-0.979043

-142.5101*

-1.87294

-92.90322*

D L F Ltd.

-1.001687

-137.6104*

-1.259605

-131.0396*

-2.092678

-92.95216*

Bharat Heavy Electricals Ltd.

-1.223485

-136.7467*

-2.785598

-139.3929*

-1.608481

-95.88289*

Hindalco Industries Ltd.

0.258444

-134.7131*

-0.302803

-139.9682*

-2.078518

-94.7373*

N T P C Ltd.

-1.599286

-102.5966*

-3.432994

-99.90094*

-1.843396

-98.03349*

Sesa Goa

0.566967

-141.7578*

-1.468415

-132.9205*

-2.425756

-94.36965*

* 1% significance level

 

 

Table 3: Descriptive statistics for period 1st January 2009-31st December 2009

 

 Mean

 Median

 Maximum

 Minimum

 Std. Dev.

 Skewness

 Kurtosis

 Jarque-Bera

 P-value of  Jarque-Bera

Nifty

3.43E-05

5.89E-05

0.11089

-0.03012

0.002322

6.783139

335.6882

75795022

0.000*

I C I C I Bank Ltd.

4.07E-05

3.33E-05

0.16806

-0.0692

0.004723

2.479522

122.7614

9824291

0.000*

State Bank Of India

3.27E-05

0.000

0.09115

-0.03609

0.003577

2.380227

66.91133

2799652

0.000*

Infosys Ltd.

5.18E-05

2.50E-05

0.04901

-0.04637

0.003012

0.0206

42.25659

1052109

0.000*

H D F C Bank Ltd.

3.28E-05

0.000

0.07495

-0.05699

0.003481

1.154628

53.30064

1732477

0.000*

Axis Bank Ltd.

4.03E-05

0.000

0.13293

-0.10944

0.004569

1.300141

99.78504

6410326

0.000*

D L F Ltd.

1.57E-05

0.000

0.17941

-0.1654

0.006161

0.411079

120.0274

9365278

0.000*

Bharat Heavy Electricals Ltd.

3.43E-05

0.000

0.0957

-0.03356

0.003234

2.226727

69.92403

3076146

0.000*

Hindalco Industries Ltd.

6.84E-05

0.000

0.07658

-0.08657

0.004833

-0.12941

29.81664

491812.5

0.000*

N T P C Ltd.

1.64E-05

0.000

0.16415

-0.06321

0.003137

8.017291

482.7048

1.58E+08

0.000*

Sesa Goa Ltd.

9.48E-05

0.000

0.16000

-0.11855

0.005426

1.099536

103.9483

6949431

0.000*

* 1% significance level

Table 4: Descriptive statistics for period 1st January 2010-17th October 2010

 

 Mean

 Median

 Maximum

 Minimum

 Std. Dev.

 Skewness

 Kurtosis

 Jarque-Bera

 P-value of  Jarque-Bera

Nifty

9.77E-06

5.84E-06

0.01175

-0.01751

0.001082

-0.69118

36.10491

712456.2

0.000*

I C I C I Bank Ltd.

1.56E-05

-1.08E-05

0.03257

-0.034

0.002126

-0.34396

36.47846

730654.3

0.000*

State Bank Of India

2.13E-05

-7.10E-06

0.02627

-0.0456

0.001722

-0.26168

58.577

2012663

0.000*

Infosys Ltd.

1.07E-05

0.000

0.03549

-0.0297

0.001725

0.263927

56.83744

1888776

0.000*

H D F C Bank Ltd.

2.17E-05

0.000

0.03454

-0.03512

0.001784

-0.25482

42.42539

1012900

0.000*

Axis Bank Ltd.

2.63E-05

0.000

0.03868

-0.03132

0.002172

0.410178

37.83964

791280

0.000*

D L F Ltd.

2.26E-06

-3.23E-05

0.03143

-0.03882

0.002528

-0.06218

22.00318

235355.6

0.000*

Bharat Heavy Electricals Ltd.

2.27E-06

0.000

0.02225

-0.02028

0.00163

0.207371

21.56959

224826

0.000*

Hindalco Industries Ltd.

1.75E-05

0.000

0.05848

-0.05769

0.002844

-0.06669

57.05449

1904230

0.000*

N T P C Ltd.

-9.76E-06

0.000

0.02481

-0.02274

0.001596

-0.43096

35.36726

683239.7

0.000*

Sesa Goa Ltd.

-5.64E-06

-3.09E-05

0.02590

-0.05886

0.002793

-0.99289

35.77561

702616.7

0.000*

* 1% significance level


 

Table 5: Descriptive statistics for period 18th October 2010-31st March 2011

 

 Mean

 Median

 Maximum

 Minimum

 Std. Dev.

 Skewness

 Kurtosis

 Jarque-Bera

P-value of  Jarque-Bera

Nifty

-5.57E-06

1.90E-05

0.01390

-0.02103

0.00141

-0.32273

20.1968

103046.6

0.000*

I C I C I Bank Ltd.

-7.86E-07

0.000

0.02413

-0.03062

0.00251

0.121985

16.20857

62167.54

0.000*

State Bank Of India

-1.62E-05

-6.88E-06

0.04024

-0.04204

0.00224

-0.82987

52.9939

875959

0.000*

Infosys Ltd.

6.26E-06

0.000

0.02282

-0.03182

0.00176

-1.27713

38.32065

446711.2

0.000*

H D F C Bank Ltd.

-5.49E-07

4.67E-06

0.01518

-0.02578

0.00210

-0.3955

12.33624

31275.58

0.000*

Axis Bank Ltd.

-6.02E-06

-8.06E-06

0.02290

-0.02397

0.00243

0.024135

12.42489

31642.27

0.000*

D L F Ltd.

-3.73E-05

-2.71E-05

0.02180

-0.0331

0.00291

-0.36293

14.40844

46549.1

0.000*

Bharat Heavy Electricals Ltd.

-2.37E-05

0.000

0.01650

-0.03203

0.00190

-0.60522

21.22814

118877.5

0.000*

Hindalco Industries Ltd.

-2.11E-06

0.000

0.04096

-0.0329

0.00288

-0.10208

20.6578

111079.8

0.000*

N T P C Ltd.

-6.70E-06

0.000

0.01926

-0.01568

0.00176

0.201118

13.6081

26452.47

0.000*

Sesa Goa Ltd.

-2.91E-05

0.000

0.0210

-0.02521

0.00268

-0.21432

14.57414

47783.38

0.000*

* 1% significance level

  1. V) TESTS FOR PRESENCE OF AUTOCORRELATION

The Auto-correlation coefficient depicts the relationship between the values of a random variable at time t and its value in the preceding period. Kendall (1953), Fama (1965), Nordhaus (1987), Chen (1996), Mobarek & Keasey (2000) and many more researchers applied autocorrelation test in a variety of speculative markets over diverse periods.

Auto Regressive Moving Average (ARMA) Model.

Auto-correlations are confirmed using ARMA Model. The auto-correlation (ACF) and partial auto correlation (PACF) functions are used from correlogram to recognize appropriate ARMA model. An ARMA model is a special type of regression model in which the dependent variable has been stationarized and the independent variables are all lags of the dependent variable and lags of the errors. Table 6 reveals significant AR and MA terms in returns of sample understudy. 

In 1st sub period, AR(1) is significant for Nifty, I C I C I Bank Ltd, H D F C Bank Ltd., Bharat Heavy Electricals Ltd returns. Whereas,  MA (1) is significant for State Bank Of India, Infosys Ltd. Axis Bank Ltd. D L F Ltd. Bharat Heavy Electricals Ltd. Hindalco Industries Ltd. N T P C Ltd. Sesa Goa Ltd. returns. Additionally, MA(2)  is also significant for D L F Ltd. under this study period.

In 2nd sub period, AR(1) is significant for Infosys Ltd. and H D F C Bank Ltd. returns, where as AR(2) and AR(3) is significant for Nifty returns. On the other hand MA(1) is significant for State Bank Of India, Infosys Ltd., H D F C Bank Ltd., Axis Bank Ltd., D L F Ltd., Bharat Heavy Electricals Ltd., Hindalco Industries Ltd., N T P C Ltd. and Sesa Goa Ltd.

 

 In 3rd sub period, AR(1) is significant for Nifty, Infosys Ltd., H D F C Bank Ltd., Hindalco Industries Ltd. and Sesa Goa Ltd. AR(2) is significant for I C I C I Bank Ltd., H D F C Bank Ltd. and Axis Bank Ltd. AR(3) is significant for Axis Bank Ltd. and AR(17) is significant for D L F Ltd. On the other hand, MA(1) is significant for State Bank Of India, H D F C Bank Ltd., Bharat Heavy Electricals Ltd., N T P C Ltd. and Sesa Goa Ltd. MA(2) is significant for I C I C I Bank Ltd only. All AR and MA terms are significant at 1% or 5% significance level.

Various studies such as Mobarek & Keasey (2000) Abrosimova et al. (2002) Rahman & Hossain (2006) Mollah (2007) Asiri (2008) Irfan et al.(2010) applied ARMA model in a variety of financial markets over diverse periods. All of these studies observed various significant AR and MA terms and claimed various financial markets to be weak form inefficient. Corroborating the results of these earlier studies, findings of this study also found Indian markets to be weak form inefficient. In order to re-confirm and interpret dependency in return series of sample understudy, further investigation is required. This interdependence is further investigated by GARCH(1,1) model.

Table 6: Average (ARMA) terms in return series

 

1st January 2009-31st December 2009

1st January 2010-17th October 2010

18th October 2010-31st March 2011

 

AR terms

MA terms

AR terms

MA terms

AR terms

MA terms

Nifty

AR(1)

0.016046

(0.039)**

 

AR(2)

-0.0177

(0.0271)**

AR(4)

0.0247

(0.0021)*

 

AR(1)

-0.04694

(0.000)*

 

I C I C I Bank Ltd.

AR(1)

-0.03794

(0.000)*

 

 

MA(1)

-0.07005

(0.000)*

AR(2)

0.563832

(0.002)*

MA(2)

-0.54272

(0.003)*

State Bank Of India

 

MA(1)

-0.05217

(0.000)*

 

MA(1)

-0.06661

(0.000)*

 

MA(1)

-0.10123

(0.000)*

Infosys Ltd.

 

MA(1)

-0.10332

(0.000)*

AR(1)

0.4345

(0.000)*

MA(1)

-0.5046

(0.000)*

AR(1)

-0.02355

(0.029)**

 

H D F C Bank Ltd.

AR(1)

-0.06513

(0.000)*

 

AR(1)

0.11875

(0.027)**

MA(1)

-0.2605

(0.000)*

AR(1)

0.422996

(0.043)**

AR(2)

0.052032

(0.000)*

MA(1)

-0.46811

(0.025)**

Axis Bank Ltd.

 

MA(1)

-0.0851

(0.000)*

 

MA(1)

-0.12759

(0.000)*

AR(2)

0.0297

(0.006)*

AR(3)

0.0197

(0.068)***

 

D L F Ltd.

 

MA(1)

-0.056

(0.000)*

MA(2)

-0.01605

(0.040)**

 

MA(1)

-0.04469

(0.000)*

AR(17)

-0.02247

(0.038)**

 

Bharat Heavy Electricals Ltd.

AR(1)

0.334

(0.009)*

MA(1)

-0.383

(0.002)*

 

MA(1)

-0.1097

(0.000)*

 

MA(1)

-0.0348

(0.001)*

Hindalco Industries Ltd.

 

MA(1)

-0.0603

(0.001)*

 

MA(1)

-0.1005

(0.000)*

AR(1)

-0.0241

(0.025)**

 

N T P C Ltd.

 

MA(1)

-0.1775

(0.000)*

 

MA(1)

-0.2036

(0.000)*

 

MA(1)

-0.0557

(0.000)*

Sesa Goa Ltd.

 

MA(1)

-0.1124

(0.000)*

 

MA(1)

-0.0578

(0.000)*

AR(1)

-0.8218

(0.000)*

MA(1)

0.8014

(0.000)*

                     

* 1% significance level ** 5% significance level *** 10% significance level


  1. VI) TEST FOR VOLATILITY CLUSTERING USING GARCH (1,1).

Another important requirement of time series data is that error terms of this developed autoregressive moving average model for stock returns should exhibit constant variance. If error terms does not exhibit constant variance, they are said to be heteroscedastic. Table 7 depicts the test for Heteroskedasticity :ARCH effects.

Table 7: Heteroskedasticity Test: ARCH test

 

1st January 2009-31st December 2009

1st January 2010-17th October 2010

18th October 2010-31st March 2011

 

F-statistics

p-value

F-statistics

p-value

F-statistics

p-value

Nifty

46.65296

0.000*

100.7077

0.000*

48.47189

0.000*

I C I C I Bank Ltd.

62.00874

0.000*

727.4613

0.000*

58.13098

0.000*

State Bank Of India

1833.424

0.000*

374.0223

0.000*

764.8163

0.000*

Infosys Ltd.

1511.131

0.000*

815.8887

0.000*

387.002

0.000*

H D F C Bank Ltd.

1635.375

0.000*

2555.182

0.000*

62.5085

0.000*

Axis Bank Ltd.

3347.442

0.000*

1299.572

0.000*

195.6403

0.000*

D L F Ltd.

167.9396

0.000*

462.859

0.000*

110.1322

0.000*

Bharat Heavy Electricals Ltd.

642.7608

0.000*

1089.268

0.000*

91.41244

0.000*

Hindalco Industries Ltd.

1099.581

0.000*

2138.143

0.000*

61.07063

0.000*

N T P C Ltd.

46.42308

0.000*

1342.532

0.000*

128.5512

0.000*

Sesa Goa

1320.322

0.000*

176.5055

0.000*

220.033

0.000*

* 1% significance level

Figure 1: Plot of Returns residual from ARMA Model.

Table 8: Variance Equation of GARCH(1,1)

 

1st January 2009-31st December 2009

1st January 2010-17th October 2010

18th October 2010-31st March 2011

 

Constant

ARCH(1)

GARCH(1)

Constant

ARCH(1)

GARCH(1)

Constant

ARCH(1)

GARCH(1)

Nifty

2.10E-07

0.20

0.79

7.51E-08

0.25

0.73

1.26E-07

0.15

0.80

p-value

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

I C I C I Bank Ltd.

3.43E-07

0.13

0.86

8.63E-07

0.25

0.59

6.01E-07

0.19

0.74

p-value

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

State Bank Of India

2.01E-06

0.37

0.54

4.31E-07

0.29

0.61

3.78E-07

0.15

0.79

p-value

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

Infosys Ltd.

9.20E-07

0.35

0.64

3.25E-07

0.45

0.57

6.99E-07

0.22

0.59

p-value

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

H D F C Bank Ltd.

2.59E-06

0.48

0.41

6.82E-07

0.41

0.46

3.96E-07

0.17

0.75

p-value

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

Axis Bank Ltd.

7.06E-07

0.19

0.80

6.09E-07

0.27

0.64

5.17E-07

0.19

0.73

p-value

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

D L F Ltd.

1.20E-06

0.16

0.82

1.45E-06

0.17

0.66

8.60E-07

0.12

0.78

p-value

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

Bharat Heavy Electricals Ltd.

5.76E-07

0.22

0.77

5.23E-07

0.26

0.56

5.23E-07

0.27

0.63

p-value

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

Hindalco Industries Ltd.

3.34E-06

0.31

0.60

1.64E-06

0.24

0.60

6.58E-07

0.18

0.76

p-value

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

N T P C Ltd.

1.07E-06

0.59

0.40

4.16E-07

0.50

0.47

3.60E-07

0.18

0.71

p-value

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

Sesa Goa

7.57E-06

0.72

0.27

9.32E-07

0.23

0.69

1.10E-06

0.17

0.69

p-value

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

0.000*

* 1% significance level, Source: Author’s calculations.

Table 7 represents the nature of residuals of ARMA model, for which null hypothesis is that residuals are homoscedastic. It is clearly evident from the table that residuals are heteroscedastic at 1% level of significance. Heteroscedastic nature of residual is again observed in plot of return residuals from ARMA model in figure 1. From this plot it is clearly evident that the period of high volatility is followed by the period of high volatility and the period of low volatility is followed by the period of low volatility, this suggests that the residuals are conditionally heteroscedastic, can be represented by ARCH and GARCH model. 

Hence, GARCH (1,1) is employed to study the nature of the return residuals. From GARCH model volatility clustering can be observed. Variance equation depicts the nature of volatility or conditional variance of the return series. This variance equation of GARCH(1,1) have two terms: ARCH and GARCH. The sum of the coefficients (α1+ β) of these terms depicts high persistence in volatility clustering, if the value is very close to one. High persistent volatility clustering represent the inefficiency of a stock market (Hameed et al., 2006). Table 8 shows that sum of ARCH and GARCH coefficient are very close to 1 for complete sample under study. Thus, suggesting a high persistence of volatility clusters over the sample period in the market.  Similar volatility clustering was observed in Indian stock market by  Abrosimova et al. (2002) using the daily data.

VII) CONCLUSION

Financial market efficiency is an important issue for investors, researchers, analysts and regulators of emerging market like India. Evidence of weak-form inefficiency is an imperative signal of predictability, thus making traders to earn supernormal profits. Earlier studies investigating the weak form efficiency have used the daily data, however, re-testing the weak form of efficiency using high frequency data is required to capture the intraday predictability characteristics of the stock market.  Additionally, problem associated with the daily data is that it is an average of last 30 minutes of the trade, consequently, it is not suitable to bring out the dynamics of complete trading session.  Hence, this study tries to re-examine the weak form efficiency using high frequency data. Various statistical techniques are employed such as ARMA model and GARCH (1,1) for the return series. ARMA model confirms significant serial dependence in the 5-minute interval return series. GARCH (1,1) model symbolize high persistence in volatility clustering for the three sub-periods. The outcome of these statistical models present evidence for the nonexistence of the weak-form efficiency.

The results of this study do not hold up the validity of weak form efficiency for stock market returns for Nifty 50 and top 10 frequently traded stocks. Therefore, this gives an opportunity to traders to forecast future prices and earn abnormal profits. Hence, this study re-confirms the testable implications for traders and investors, so that they can exploit predictability of stock using the intra-daily data. On the other hand, this study also have an implications for the market regulators who have been introducing major structural changes in the stock market to improve liquidity, lessen volatility and improve efficiency. Results of the study shows that advancement of trading hours and introduction of pre-opening session have not improved weak form inefficiency. Hence, market regulators need to take some more stringent steps to improve the same.

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