1. INTRODUCTION:

The term market ‘efficiency’ is used to explain the relationship between information and share prices in the capital market literature.

Market efficiency has influenced the investment strategy of an investor because in an efficient market, there will be no undervalued or overvalued stocks. This implies that stocks will not offer higher than deserved expected returns, given their risk. On the other hand, if the market is not efficient, excess returns can be made by correctly picking the stocks.

In this study, an analysis of share prices of sample banks listed in S and P BSE Bankex of Bombay Stock Exchange (BSE) was carried out to test the efficiency of Indian Stock Market and the randomness of stock price movements in the Indian stock market.

Fama established that information is the basis for efficiency. He defined efficiency of market as “A market, in which prices always fully reflect available information, is called Efficient” (Fama, 1970 p.383).

In 1970, Fama developed his ideas of efficient markets and divided the market into three different levels of efficiency. This extension of the definition was based on an earlier study made by Roberts in 1959. The capital market efficiency is classified into the three categories based on the information set (Fama, 1970).

They are

a) Weak Form Market Efficiency.

b) Semi-Strong Form Market Efficiency and

c) Strong Form Market Efficiency.

The focus of the present paper is on Weak Form Market Efficiency which is detailed below.

i) Weak Form Market Efficiency:

In the weak form, stock prices reflect all the information in the past series of stock prices. In this level, prices follow a random walk and it is impossible to gain superior returns by looking for patterns in historical stock prices. Tests of this form of efficiency have their origins in what has come to be known as the random walk theory. In tests of this kind, only historical data of stock prices are considered. Serial Correlation Tests, Filter Rule Test, Cyclical Tests and Volatility test are some of the most common used tests for assessing the weak form efficiency.

The nature of information does not have to be limited to financial news and research alone. Indeed, information about political, economic and social events, combined with how investors perceive such information, whether true or rumored, will be reflected in the stock price. According to the EMH, as prices respond only to information available in the market and because all market participants are privy to the same information, no one will have the ability to outdo anyone else in making profit. In efficient markets, prices become not predictable but random and therefore no investment pattern can be discerned. A planned approach to investment, therefore, cannot be successful. This "random walk" of prices, commonly spoken about in the EMH school of thought, results in the failure of any investment strategy that aims to beat the market consistently.

ii) S and P BSE Bankex:

The S and P BSE Bankex comprises the constituents of S and P BSE 500 that are classified as members of the bank sector. It was launched on 23^rd June 2003. The S and P BSE Bankex is designed to measure the performance of companies in the banking sector. It is calculated using a modified market-cap-weighted- methodology, the index has more than 10 years of history. The Index tracks the performance of leading banking sector stocks which are listed on the Bombay Stock Exchange India Ltd. It is based on the free-float methodology of index construction which considers 1^st January 2002 as the base date for computation of index. The base value for Bankex is 1000 points. 12 stocks which represent 90% of the total market capitalization of all banking sector stocks listed on Bombay Stock Exchange are included in the Index. The Index is disseminated on a real-time basis through BSE’s Online Trading (BOLT) terminal.

2. REVIEW OF LITERATURE:

An article entitled, “Empirical Testing for Weak form hypothesis of Emerging Capital Markets: A comparative study of Jordan’s ASE and Turkey’s BORSA IST” by Abdul Aziz Farid Saymeh (2014), empirically tested the weak efficient form hypothesis for two emerging stock indices of Jordan and Turkey for the period 2000-2011 using Ljung Box Autocorrelation, Runs Test, Dickey Fuller Test and Variance ratio test. The results rejected the random walk hypothesis for both the markets. Ankita Mishra et al (2014) in their working paper entitled, “The Random- Walk Hypothesis on the Indian Stock Market”, tested the random walk hypothesis, using nineteen years monthly data of six indices of NSE and BSE. Unit root test, with two structural breaks, were used to identify the market efficiency. The results of the study suggested that heteroskedasticity was an important factor when testing for a random walk. An article by Asma Mobarek and Angelo Fiorante (2014) on, “The Prospects of BRIC Countries: Testing Weak- form Market Efficiency”, examined the weak form efficiency of BRIC nations from September 1995 to March 2010, using Variance ratio test. Daily index data were collected from Data Stream. Serial Correlation Test results indicated that BRIC markets were fairly weak-form efficient. Mohammad Shafi (2014)in the article entitled, “Testing the Market Efficiency in the Weak form taking CNX Nifty as a Benchmark Index: A study”, made an attempt to examine the weak form efficiency in Indian Capital Market using the daily return of Nifty stocks. The tools used for analysis were Runs test and Autocorrelation test. The results evidenced that Indian Capital Markets were inefficient in the weak form. Kapil Jain and Paryul Jain (2013) analyzed the randomness of BSE SENSEX, using Runs Test, Autocorrelation and Dickey Fuller Test, in the paper “Empirical study of the Weak form of EMH on Indian Stock Market”. The results of Autocorrelation revealed randomness in index values whereas Runs Test and Dickey Fuller Test supported the random walk hypothesis for the Indian Stock Market. “Testing Weak form Efficiency of BSE Bankex”, a paper by Shikha Mahajan and Manisha Luthra (2013), examined the random walk in BSE Bankex for the monthly returns from January 2002 to September 2013 which were examined using Serial Correlation Test, Runs Test and Augmented Dickey Fuller Test. The results found that BSE Bankex was weak form efficient during the study period. Tariq Zafar S.M (2012) in his paper entitled, "A systematic study to test the EMH on BSE Listed Companies before Recession" analyzed the Bombay Stock Exchange Efficiency during the pre recession period from 4th January 2008 to 24th December 2008.The results evidenced that market was efficient in the weak form. An article entitled, "Does BSE Random Walk Randomly? An Innovative Investment Approach”, by Totala N.K et al (2012), examined the weak form efficiency for BSE Bankex companies, by using Unit root test, Runs Test and Autocorrelation. The daily prices of the scripts and value of Bankex for a period of 1st April 2006 to 31st March 2011 were collected from BSE website. All the fourteen banking companies listed on the Index, were selected as the sample. The results of the study suggested that the share prices of Bankex companies in BSE were located between inefficiency and weak form of market efficiency. The paper entitled, “Weak Form Efficiency in Indian Stock Market”, by Rakesh Gupta and Parikshit K. Basu (2007), tested the random walk hypothesis for the two major equity markets in India i.e. NSE and BSE, for the period 1991 to 2006. The study used three different tests, namely, ADF, PP and KPSS tests. The results of the NSE and BSE were influenced by volatility spillovers and the results showed significant difference if the changes in the settlement systems were incorporated in the analysis.

The above literature provided the results of the share price movements and tested the efficiency of the stock market at national and international level. The studies were carried out in different stock exchanges in India, specifically NSE and BSE as well as in the world scenario at different periods. Most of the studies observed that there were large variations in stock returns and the market was inefficient, which did not support the Random Walk Hypothesis during their study period. In some cases, the study results found that the markets supported the weak form efficiency. An attempt has been made in this study to test the weak form efficiency of Indian capital market by taking the models already used in the above studies. The present study would focus on analyzing the stocks traded at S and P BSE Bankex during the study period.

3. METHODOLOGY OF THE STUDY:

a) Statement of the Problem:

The capital market, being a vital institution, facilitates economic development. It is true that so many parties are interested in knowing the efficiency of the capital market. The small and medium investors can be motivated to save and invest in the capital market only if their securities in the market are appropriately priced. The random walk hypothesis of stock prices is concerned with the question of whether one can predict future price from past prices. Few studies have examined the daily returns, weekly returns and monthly returns of the stock market, with respect to Indian stock markets. There are studies which carried out to test the efficiency of the different sectors of a stock exchange in the Indian context. The results of the study were mixed. The present study is an attempt to find the efficiency of Indian stock market with respect to banking companies share prices listed at S and P BSE Bankex.

b) Need for the Study:

The study would provide an understanding of the efficiency of the Indian Capital Market. The study would provide ample data for benchmarking of banking companies stocks at S and P BSE Bankex. The study would be useful to the investors and technical analysts to make investment decisions and understand the market conditions relating to the performance of Banking Sectors. Further, the study would bring new methodological innovations to identify the weak form in the Indian capital market.

c) Objectives of the Study:

1. To analyze the stationarity in the daily share prices returns of sample Banking companies listed at S and P BSE Bankex.

2. To analyze the randomness in the movements of daily share price returns of selected Banking companies listed at S and P BSE Bankex.

3. To assess the efficiency of selected daily share price returns of selected Banking companies listed at S and P BSE Bankex.

d) Null Hypotheses of the Study:

H01: The stationarity in the daily share price of sample banking companies are not significant.

H02: The daily share price movements of the sample banking companies are not random.

H03: The daily share price returns of the sample banking companies are not efficient in weak form.

e) Sample Selection:

The criteria for choosing the sample companies are given below.

1 Based on the total market capitalization of the sample companies.

2 Availability of daily market prices was also considered for taking the samples.

Table-1 Details of Selected Sample Companies listed in S and P BSE BANKEX and their Market Capitalization

S.NO	NAME OF THE COMPANY	MARKET CAPITALIZATION (Rs. in Crores)
1.	HDFC Bank Ltd	1,51,321.2
2.	State Bank of India	1,10,242.33
3.	ICICI Bank Ltd	1,08,183.7
4.	Kotak Mahindra Bank Ltd	53,239.76
5.	Axis Bank Ltd	50,057.93

Source: Official Website of BSE

f) Sources of Data Collection:

The information relating to share price of sample companies, volume of indices for S and P BSE Bankex was obtained from bseindia.com. The other relevant information regarding the efficiency of the Indian Capital Market was extracted from various publications and BSE website.

g) Period of the Study:

To analyze the weak form efficiency of Banking Companies share prices listed in S and P BSE Bankex, a period from 01^st April 2007 to 31^st March 2013 were considered for analysis.

h) Statistical/Econometric Tools used for Analysis

Table 2 Statistical/Econometric Tools used for the Study

S.No

Statistical/

Econometric Tools

Formula

Purpose

Daily Returns

Where,Ri,t = Returns on security i on time t

Pt = Price of the security at time t

Pt-1 = Price at time t -1

To convert the raw data into logarithmic returns to arrive at reliable results

Descriptive Statistics

Mean

= Where,

= represents the mean.

=Symbol of Summation

xi =Value of the i^th item x, i= 1, 2, 3 ….n

n=total number of items.

To arrive at single numerical value that represents the entire data set.

Standard Deviation

Where,

standard deviation

X= random variable

µ= mean value

To measure the variation in the data set between the periods.

Skewness

Where, µ_Î is the Î_th central movement

To identify the degree of symmetry or asymmetry of the data distribution.

Kurtosis

Where, µ_Î denotes the Î_th central moment (and in particular, µ₂ is the variance).

To identify the peakedness of the data distribution. To know how far the data is deviated from normal distribution.

Augmented Dickey Fuller Test

∆y_t =α +βt+γy_t-1+δ∆y_-1+…+δρ∆y_t-t+ε

Where, $α$ = Constant,

$β$ = The coefficient on a time trend, and

$p$ = The lag order of the autoregressive process.

To test the Stationarity of the time series data.

Stationarity=

Mean=Variance=Co-Variance.

Runs Test

To assess the increase or decrease or no change in prices.

Autocorrelation

Where,

The sample autocorrelation function for the lag K.

The returns on the day.

The mean returns.

T The total number of observation.

Variance of the returns series.

Used for measuring the dependence of successive terms in a given time series.

Table 3 Summary Results of Descriptive Statistics for the daily share price returns of Sample Banks listed in BSE Bankex from 01.04.2007 to 31.3.2013

		Name of the Bank
Period	Statistic	Axis	HDFC	ICICI	KMB	SBI
01.04.2007	Mean	0.0018	0.0013	-4.077	0.001	0.0018
to	Std.Deviation	0.0298	0.0259	0.030	0.0372	0.027
31.03.2008
31.03.2008	Minimum	-8.199	-6.315	-1.479	-1.541	-9.245
	Maximum	1.014	1.0262	1.058	1.254	8.374
01.04.2008	Mean	-2.607	-1.276	-3.455	-3.284	-1.666
to	Std.Deviation	0.046	0.0352	0.050	0.047	0.0365
31.03.2009
31.03.2009	Minimum	1.530	-1.194	-2.195	-2.322	-1.356
	Maximum	1.825	1.1995	1.548	1.316	1.116
01.04.2009	Mean	0.0042	0.0028	0.0043	0.0039	0.0027
to	Std.Deviation	0.0307	0.1969	0.0327	0.0341	0.027
31.03.2010
31.03.2010	Minimum	-9.322	-6.062	-1.063	-8.100	-8.98
	Maximum	1.852	1.517	2.071	1.681	1.843
01.04.2010	Mean	0.0007	0.0007	0.0006	-1.946	0.0011
to	Std.Deviation	0.0198	0.0152	0.0208	0.0443	0.0191
31.03.2011
31.03.2011	Minimum	-5.727	-5.130	-7.510	-6.388	-4.656
	Maximum	6.080	4.575	6.338	6.590	6.699
01.04.2011	Mean	-8.148	-6.045	-9.094	0.0006	-1.118
to	Std.Deviation	0.024	0.1029	0.0229	0.0204	0.022
31.03.2012
31.03.2012	Minimum	-6.207	-1.603	-5.160	-5.161	-8.241
	Maximum	7.870	4.992	7.377	6.679	5.893
01.04.2012	Mean	0.0005	0.0007	0.0006	0.0007	-8.409
to	Std.Deviation	0.018	0.0117	0.165	0.0142	0.0177
31.03.2013
31.03.2013	Minimum	-5.020	-3.194	-4.084	-4.089	-5.977
	Maximum	7.421	3.437	5.250	4.038	5.373
01.04.2007	Mean	0.0006	-2.815	0.0001	0.0002	0.0004
to	Std.Deviation	0.0296	0.0470	0.0308	0.0350	0.0258
31.03.2013
31.03.2013	Minimum	-1.530	-1.603	-2.195	-6.388	-1.356
	Maximum	1.852	1.517	2.071	1.681	1.843

Source: Collected from www.bseindia.com and Computed using SPSS

Table 4 Summary of Augmented Dickey Fuller Test Statistic for the Daily Share Price Returns of sample banks listed in S and P BSE BANKEX during the study period

		ADF t-Statistics			Test Critical Values
S.No	Bank	Level difference Significance	First difference Significance	Second Level Difference	1%	5%	10%	Prob.
1	Axis Bank	-37.723	-18.659	-18.357	-3.4346	-2.8633	-2.5677	<0.001
2	HDFC Bank	-38.375	-19.338	-17.806	-3.4346	-2.8633	-2.5677	<0.001
3	ICICI Bank	-35.059	-17.679	-18.694	-3.4346	-2.8633	-2.5677	<0.001
4	Kotak Mahindra Bank	-36.645	-19.351	-19.235	-3.4346	-2.8633	-2.5677	<0.001
5	State Bank of India	-34.524	-17.826	-17.384	-3.4346	-2.8633	-2.5677	<0.001

Source: Data collected from bseindia.com and computed using SPSS

The Median Base results of Runs Tests for S and P BSE Bankex listed companies are presented in the Table 5. It can be observed that for Axis Bank during 2007-08 (-1.454), 2009-10 (0.642), 2011-12 (-1.841) and 2012-13 (-0.634), the test statistical value falls within the range of critical values of ± 1.96; therefore the null hypothesis H02 is accepted. The overall analysis of Axis Bank reveals that the test statistic value falls outside the range of ± 1.96 which is an indication to reject the H02. Therefore the succeeding price changes do not move in an independent manner. In the case of HDFC Bank, for majority of the sample years, the test statistical value falls outside the range of ± 1.96. The overall study period analysis (-1.425) clearly indicates the test statistical value falls in the range of ± 1.96 which indicates to accept the null hypothesis H02 at 5% significance level. The results of ICICI Bank clearly shows that for the financial year 2009-10 and 2011-12, the test statistical value falls in the range of critical values of ± 1.96. But the overall analysis indicates that the calculated value (-2.927) falls outside the range of ± 1.96 which clearly indicates the rejection of null H02. The results revealed that the past prices followed future prices during the study period. Kotak Mahindra Bank results reveals that for the first half of the study period (2007-08 to 2010-11), the statistical value lies in the range of ± 1.96, therefore it becomes evident to accept the H02. The overall analysis indicates that the rejection of H0, as the calculated value falls outside the range of ± 1.96. Therefore the prices do not move independent each other. The results of State Bank of India proved that for all the years, the statistical value falls outside the range of ± 1.96 which clearly suggested rejection of null hypothesis H02. Therefore the prices followed randomly.

From the overall analysis, it can be concluded that HDFC Bank was the only sample Bank where the prices were random during the study period. The other four Banks did not follow random walk i.e. the succeeding price movements do not move independent of each other. Therefore the H02: “The daily share price movements of the sample banking companies are not random” is accepted.

Table 6 Summary Results of Autocorrelation function of sample banks during the study period

Lag	Autocorrelation Values
	Axis Bank	HDFC Bank	ICICI Bank	KMB	SBI
1	.024**	.006**	.096**	.052**	.113**
2	-.021*	-.004*	-.027*	.025**	.000**
3	-.014*	.000**	-.017*	-.008*	-.018*
4	.010**	-.003*	-.010*	-.016*	-.020*
5	-.073*	-.008*	-.066*	-.042*	-.088*
6	-.017*	-.015*	-.095*	-.036*	-.046*
7	.025**	-.013*	.007**	-.031*	.027**
8	.034**	.021**	.051**	.017**	.056**
9	.025**	-.006*	.000**	.020**	.015**
10	.022**	.015**	.016**	-.043*	-.005*
11	.033**	-.006*	.021**	.011**	.013**
12	-.074*	.000**	.017**	.039**	.002**
13	-.008*	.004**	-.010*	.024**	-.038*
14	.028**	-.003*	.008**	.004**	-.008*
15	-.029*	.001**	.005**	.065**	.011**
16	-.014*	.011**	.024**	.062**	.049*
17	.040**	.010**	.023**	.023**	.043*
18	.009**	.006**	-.030*	-.018*	-.020**
19	-.020*	-.030*	-.004*	-.033*	.004*
20	-.022*	-.004*	-.038*	-.067*	-.008**
21	.024**	.018**	.003**	.031**	.014*
22	-.002*	.019**	.009**	-.013*	.001*
23	-.031*	-.014*	.006**	-.007*	-.020**
24	-.004*	-.004*	-.009*	-.018*	.023*

Source: Collected from bseindia.com, computed using SPSS

* *Positive significance and *Negative significance at 5% level

Table 6 shows the results of Autocorrelation function for the daily share price returns of sample banks during the study period from 01.04.2007 to 31.03.2013. With respect to Axis Bank, the first lag started with positive value and the succeeding two lags recorded negative significance. Lags seven to Eleven recorded positive lag values after which the lags obtained positive and negative significance alternatively. The last three lags showed that all the values recorded negative significance. Similarly, for HDFC Bank, the lags with positive significance include lags 1, 3, 8, 10, 12, 13, 15, 16, 17, 18, 21 and 22. The other lags recorded negative significance. Therefore it is evident that the share prices of HDFC Bank were volatile during the study period. It could be traced that for ICICI Bank, out of 24 lags, 14 lags obtained positive significance and other lags recorded negative significance. Lags 7 to 12 obtained positive values and the subsequent lags turned negative and from lags 14 to lag 17, there was continuous upward trend. Therefore, it becomes clear that the previous day's price had no significant impact on the next day's price. It is to be noted that, 12 lags were positively significant and the remaining lags were negatively significant for Kotak Mahindra Bank during the study period. The lag with high positive significance include lag 15(0.065) followed by lag 16 (0.062). It is evident that there were no continuous positive or negative movements. While observing the results of State Bank of India, the lags 7 to 9 recorded positive values. The immediate subsequent lag was negative and the next two lags observed positive lag values. There is no continuous upward or downward trend recorded in all lags. As there was no stable pattern in the movement of prices for all the sample banks, the null hypothesis namely H03: “The daily share price returns of the sample banking companies are not efficient in weak form” is rejected. Hence it is evident that the share prices were independent of each other.

5. CONCLUSION AND IMPLICATIONS OF THE STUDY:

The present study made an attempt to evaluate the dependency of share prices movements of sample banks listed at S and P BSE Bankex. It becomes evident from the results that the share prices of sample banking companies were found to be independent. Hence, the investors are advised to rely not only on technical analysis but also on fundamental analysis for taking investment decisions. It is also advised that the investors need to track the updates of Reserve Bank of India with respect to the policy decisions for investment in banking stocks.

The current study could be extended by taking into account all the sample banking companies listed at S and P BSE Bankex. A comparative analysis of banking companies share prices listed at Bombay Stock Exchange and National Stock Exchange of India Limited could also be undertaken, so as to know the complete status of banking companies’ shares in India.

6. REFERENCES:

1. Abdul Aziz Farid Saymeh (2014). “Empirical Testing for Weak form hypothesis of Emerging Capital Markets: A comparative study of Jordan’s ASE and Turkey’s BORSA IST”. Interdisciplinary Journal of Contemporary Research in Business. Vol. 5, No. 9, pp.61-80.

2. Abdus Salam (2013). “Testing on Weak form market Efficiency hypothesis: The evidence from Dhaka Stock Market yearn2004-2012”. International Journal of Science and Research. Vol.2, Issue 12, pp.371-377.

3. Asma Mobarek and Angelo Fiorante (2014). “The Prospects of BRIC Countries: Testing Weak- form Market Efficiency”. Research in International Business and Finance. Vol.30. pp.217-232.

4. D. A. Dickey and W. F. Fuller (1979). “Distribution of the Estimators for Autoregressive Time Series with a Unit Root”. Journal of the American Statistical Association, Vol. 74, No. 366, pp. 427-431.

5. Eugene.F.Fama (1970). “Efficient Capital Markets: A Review of Theory and Empirical Work”. Journal of Finance, Vol. 25, No.2, pp. 383-417.

6. Kapil Jain and Paryul Jain (2013). “Empirical study of the Weak form of EMH on Indian Stock Market”. International Journal of Management and Social Science Research. Vol.2, No.11, pp.52-59.

7. Rakesh Gupta (2007). “Weak Form Efficiency in Indian Stock Market”. International Business and Economics Research Journal. Vol.6, No.3, pp. 57-64.

8. Shikha Mahajan and Manisha Luthra (2013). “Testing Weak form Efficiency of BSE Bankex”. International Journal of Commerce, Business and Management. Vol. 2, No.5, pp.270-273.

9. Tariq Zafar S.M (2012). “A systematic study to test the EMH on BSE Listed Companies before Recession”. International Journal of Management and Social Sciences Research. Vol. 1, No.1, October 2012.

10. Totala N.K et al (2012). “Does BSE Random Walk randomly?” Pacific Business Review International. Vol.5, Issue 2, pp.11-22.

Working Papers:

Ankita Mishra et al (2014). “The Random-Walk Hypothesis on the Indian Stock Market”. Monash University- Business and Economics Discussion paper 07/14.

Text Books:

Chris Brooks. (2008). Introductory Econometrics for Finance, (2^nd Edition), Cambridge University Press, The ICMA Centre, University of Reading, London.

Roman Kozhan. (2010). Financial Econometrics with E-Views. Ventus Publishing Aps, Denmark.

Donald.E.Fisher and Donald.J.Jordan (2001). Security Analysis and Portfolio Management, Prentice-Hall of India, New Delhi

Received on 07.02.2018 Modified on 11.03.2018

Asian Journal of Management. 2018; 9(2):939-946.

DOI: 10.5958/2321-5763.2018.00149.X

Name of the Sample Companies	PERIOD
Name of the Sample Companies	01.04.2007 to 31.03.2008	01.04.2008 to 31.03.2009	01.04.2009 to 31.03.2010	01.04.2010 to 31.03.2011	01.04.2011 to 31.03.2012	01.04.2012 to 31.03.2013	01.04.2007 to 31.03.2013
Axis Bank	-1.454	-0.578	0.642	-2.012	-1.841	-0.634	-2.513
HDFC Bank	-0.189	-0.321	-1.026	-0.377	-0.444	0.000	-1.425
ICICI Bank	-2.719	-2.764	-0.642	-0.251	-0.952	-0.127	-2.927
Kotak Mahindra Bank	-1.454	-1.735	-0.898	0.880	0.318	2.281	-0.492
State Bank of India	0.063	0.065	-0.385	-0.503	-2.222	-2.155	-2.409