Among the financial markets, studying the efficiency of stock markets is an important concept. It was clearly stated by Fama (1970) that market efficiency is used to study the relationships between the information and share prices prevailing in the market. Informational efficiency of the stock markets is an important parameter to determine the effectiveness of a financial system. It is evident that the level and trend of investment largely depends on flow of information in the market. Indian stock market also experiences the fluctuation in investment on the basis of information availability. Hence, this concept is placed highly in research studies. Therefore, at this juncture it becomes necessary to test the market movement by testing the weak form market efficiency.
The efficiency of the markets depends on the extent of absorption of information, the time taken for absorption and the type of information absorbed. Based on this, Fama (1970) classifies market efficiency into three categories namely, weak form, semi strong form and strong form. The Weak Form of market efficiency is considered if current prices fully reflect all information contained in historical prices, which implies that no investor can devise a trading rule, based solely on past price patterns to earn abnormal returns. Thus, under weak form, past data cannot be used to predict future prices. The Semi-Strong Form of the Efficient Market Hypothesis states that the current prices of stocks not only reflect all informational content of historical prices but also reflect all publicly available information. According to the Strong Form of stock market efficiency, the prices of securities fully reflect all available information both public and private. Information whether it is public or inside cannot be used consistently to earn superior investors return in the strong form.
In an efficient market, the prices of securities reflect the market's best estimate of their expected return and risk, this estimate takes into account all that is known about those securities. Therefore, there will be no undervalued securities. So, in an efficient market, a simple investment strategy based on the overall risk and return characteristics of the portfolio will be proved more rational. If markets are not efficient, and excess returns can be made by correctly picking undervalued shares, then it is worthwhile to spend time finding these undervalued securities. Market efficiency has an influence on the investment strategy of an investor because, if market is efficient, trying to pick up winners will be waste of time.
The lower the market efficiency, the greater will be the predictability of stock price changes. Since new information is deemed to come in a random fashion in an efficient market, changes in prices that occur as a consequence of that information will seem random. Thus, price movements in a weak-form efficient market occur randomly and successive price changes are independent of one another. In this regard, investors cannot expect to find any patterns in the historical sequence of security prices that will provide insight into future price movements and allow them to earn abnormal returns.
The random walk hypothesis of stock market prices states that price changes cannot be predicted from earlier changes in any meaningful manner. Successive price changes in individual securities are independent over time and price changes occur without any significant trends or patterns. Formally, the random walk model can be stated as:
pt = pt-1 + µt
Where pt is the price at time t, pt-1 is the price in the immediate preceding period and µt is a random error term.
This was highlighted by Ko and Lee (1991), "If the random walk hypothesis holds, the weak form of the efficient market hypothesis must hold, but not vice versa. Thus, evidence supporting the random walk model is the evidence of market efficiency. But violation of the random walk model need not be evidence of market inefficiency in the weak form".
Next section provides a brief review of the published literature, followed by the rationale and scope of the study, after that the objectives and hypotheses of the study are given, data and research methodology adopted is explained in the in later part, and at last empirical results are discussed, and the paper ends with the concluding remarks.
REVIEW OF LITERATURE
Market efficiency has been tested in many studies over the past 60 years. Various researchers have put forward their thoughts regarding different stock markets from diverse parts of the world. There are two schools of thought, formed from the results given by the researchers after examining the stock markets all over the globe. One school of thought asserts that there is existence of weak form market efficiency in some world markets; at the same time another school of thought did not find any evidence of random walk in same or the other stock markets in the world. The views of these researchers are summarized as under.
The first part of this section includes the studies which show the existence of weak form market efficiency in various stock markets around the world, while the second part depicts studies which do not show any sign of random walk in same or other parts of the world stock markets.
Studies Supporting Weak Form Market Efficiency
Barnes (1986) and Annuar et al. (1991) found Kaula Lumpur Stock Exchange (KLSE) to be weak form efficient and concluded that the KLSE exhibit a high degree of efficiency in the weak-form. Though the findings suggest the market is generally weak form efficient, pockets of inefficiency are observed for shares that suffer liquidity problem. Lee (1992) examined the random walk process for the period 1967-1988 for weekly stock returns of the United States and ten industrialized countries and found that the random walk model is appropriate for majority of these countries. Urrutia (1995) investigated random walk for the four Latin American emerging markets using monthly data of index prices from the period December 1975 to March 1991 and based on results, he has concluded that the four Latin American emerging stock markets are weak form efficient. Similarly, Al-Loughani and Chappell (1997) studied the London stock market and could not reject the random walk hypothesis. Karemera et al. (1999) examined the random walk hypothesis for fifteen emerging stock markets and their results supported the evidence provide by Urrutia (1995) who finds Argentina, Brazil and Mexico to be weakly efficient.
Asiri (2004) examined the market efficiency in the Kuwait stock market for the daily stock prices over the period from 1991 to 2002 and the results of the studies strongly confirmed the weak-form of efficiency in the Kuwait stock market. Akinkugbe (2005) investigated the weak form of EMH in Botswana stock exchange using 738 weekly observations for the period of June 1989 to December 2003 and found stock markets in Botswana to be weak and semi-strong form efficient. Omran et al. (2006) investigated the validity of the random walk hypothesis and tests for calendar effects in five major Middle Eastern emerging markets, by applying a range of statistical and econometrics techniques. As a result, the Israel's TA-100 stock market shows greater support for the random walk hypotheses (RWH) compared with the other markets in the sample. Then, Asiri (2008) tested three random walk models for Bahrain Stock Exchange and found that the all stock prices follow random walk without a drift and a trend. Chigozie (2009) investigated whether the Nigerian stock market (from period 1984 to 2006) follows random walk. To carry out the investigation the GARCH was employed. The result shows that the Nigerian stock market follows a random walk and is therefore weak form efficient.
In India, Sharma and Kennedy (1977) compared the behavior of stock indices of the Bombay, London and NYSE during 1963-73 using run test and spectral analysis and both the tests confirmed the random movement of stock indices for all the three stock exchanges. The researches on BSE in India includes the study by Bhaumik (1997), Rao and Shankaraiah (2003), Samanta (2004) and Sharma and Mahendru (2009) and all of these studies concluded that the BSE is weak form efficient and returns of BSE follows random walk. Ramasastri (1999) and Pant and Bishnoi (2002) used unit root test to examine the random walk hypothesis for Indian stock market. The unit root test strongly accepted the null hypothesis and it was concluded that Indian stock market follow random walk and is weak form efficient.
Studies Not Supporting Weak Form Market Efficiency
The earliest studies on European Stock markets includes the research by Conrad and Juttner (1973), who applied both parametric and non-parametric tests to daily stock price changes in the German stock market found absence of random walk in the market. Similarly, Lo and MacKinlay (1988) provided evidence and strongly rejected random walk model, using a sample of 1216 observations of firms in the NYSE-AMEX over the period 1962-1985. Frennberg and Hansson (1993), who examined the random walk hypothesis using Swedish stock prices, found that the random walk was not present. Gandhi et al. (1980) and Al-Loughani (1995) used monthly data and weekly data for the Kuwait Stock Exchange and found that the hypothesis for weak-form efficiency was rejected. In the same way, Laurence (1986) tested both on the Kuala Lumpur Stock Exchange (KLSE) and the Stock Exchange of Singapore (SES) for the period of 1st June 1973 through 31st December 1978 and the results suggest that both markets are not weak form efficient.
Darrat and Zhong (2000) and Ma and Barnes (2001) examined whether stock prices follow a random walk in Shanghai and Shenzhen exchange and their results indicated that both Chinese stock markets do not follow a random walk. Abraham et al. (2002) studied weak-form efficiency in three major Gulf stock markets including Kuwait, Saudi Arabia, and Bahrain using the variance ratio and runs tests for the period October 1992 to December 1998. The results of both tests reject the random walk hypothesis in all markets. Likewise, Babaker (2004) has investigated the market efficiency of all Arab Stock Exchanges but the results show that emerging markets in the Arab countries are less efficient than developed markets. In addition, efficiency of stock markets varies over time. Few studies in African markets which do not supports random walk hypotheses includes the study by Parkinson (1987), who had tested the validity of the weak-form efficiency of the Nairobi Stock Exchange (NSE) using monthly prices of individual companies for the period 1974 to 1978. The hypothesis of random walk is rejected for these studies. The efficiency level of the Athens Stock Exchange (ASE) was tested by Filis (2006) for the years 2000-2002 and the result was that ASE was not an efficient market, suffering from volatility clustering. Mobarek et al. (2008) and Uddin and Khoda (2009) analyzed the weak-form efficiency for the Dhaka stock exchange and the showed that returns do not follow the random walk and rejected the null hypothesis of weak-form efficiency. Awad (2009) examined the efficiency of the Palestine Security Exchange (PSE) at weak-level and suggested the weak form inefficiency in the return series.
Among the number of researches on Indian stock markets which do not favors the weak form market efficiency few are marked hereunder. Rao and Mukherjee (1971) found no evidence contrary to random walk hypothesis by applying spectral analysis to weekly averages of daily closing quotations of just one company's share (Indian Aluminum) for the period 1955-70. Choudhari (1991) used the serial correlation and run test on the 93 actively traded shares on Bombay Stock Exchange for the period January 1988 to April 1990. The study concluded that the market was not weak form efficient. Similar results were given by Poshakwale (1996), who examined weak form efficiency and daily of the week effect on the Bombay Stock Exchange in India using daily BSE national data for the period January 1987 to October 1994. The results indicated that the distribution was not normal and therefore the prices on BSE did not follow random walk. Similar results were obtained by Ahmad et al. (2006) and Gupta and Basu (2007) on testing the weak form efficiency in framework of random walk hypothesis for the two major equity markets in India i.e. BSE and NSE.
The present study is a contribution to the existing body of literature. Research studies on the issue of Stock Markets Efficiency, must be longitudinal rather than cross sectional, so a continued research on the subject could help policy makers and practitioners. This study takes a step ahead in the same direction.
RATIONALE AND SCOPE OF STUDY
It is observed that the studies related to market efficiency are very few and far in case of Indian stock market which is also testified by the review of literature given in the preceding part of the paper. Since there are three forms of market efficiency as illustrated above i.e. weak form, semi strong form and strong form but working on all the three forms is not normally possible due to the reason that it requires information on both the accounts that is public as well as private or insider information. Since private information is not easily accessible so studying the strong form of market efficiency is a difficult phenomenon. Similarly, semi strong form of market efficiency is also not capable of testing the randomness of the market that's why this form of market is also not considered for studying the market movements. Since our objective is to test the randomness of the market which is only possible by testing the weak form of market efficiency. Therefore, the scope of this paper is kept limited to testing the weak form market efficiency.
Furthermore, the present research paper is an attempt to carry out a comprehensive study on Indian stock market for which the long data set is required. Hence, it is assumed that daily stock market data for the period of ten year is long enough to give clear picture of the market. Therefore, in order to study the market efficiency for Indian stock market the data set for ten years is considered for the present study and the data has been collected from NSE website for the period of ten years beginning from 1st January 2000 to 31st December 2009.
OBJECTIVE
As described in the rationale and scope part of the paper, it is difficult to check all the three forms of stock market efficiency. So, for the present study weak form of market efficiency has been tested to know the nature of the market.
Random walk in stock prices is possible, if market is efficient in weak form. So, the same can be verified by testing the weak form of market efficiency for stock markets. Hence, the objective of the present study is to check whether Indian stock market follows random walk or not which can only be verified by testing weak form of stock market efficiency.
HYPOTHESES
The following Hypotheses are framed for the purpose of testing weak form market efficiency:
H01 = Returns of S&P CNX Nifty and Nifty Junior are normally distributed.
H02 = Both Markets are efficient in weak form.
H03 = Both Markets follow random walk.
We first use the descriptive statistics to examine the normality and then use the parametric and non-parametric test to examine the stationarity and randomness of the sample distribution.
DATA AND RESEARCH METHODOLOGY
As given in the scope, the data for the present study has been obtained from National Stock Exchange indices i.e. S&P CNX Nifty and Nifty Junior. The collected data has been analyzed by using different statistical techniques like Unit Root test (Augmented Dickey-Fuller test and Phillips-Perron test), Run test and Kolmogorov-Smirnov (KS) test and the computations in the present study is done by the use of famous softwares that is Eviews 5.1 and SPSS 16.0.
ANALYSIS AND FINDINGS
Descriptive Statistics
The descriptive statistics, as generated by the Eviews 5.1 software on the basis of daily closing prices of indices, are presented in Table 1 and the table exhibits that the values of skewness are same for S&P CNX Nifty and Nifty Junior i.e. 0.69 and the values of kurtosis are 2.19 and 2.58 respectively. These values suggest that stock returns are not normally distributed, which is also verified with the Jarque-Bera statistic. The hypothesis of normal distribution is rejected at the conventional 5 percent level. Moreover, the values of standard deviation are 1439.01 for S&P CNX Nifty and 2784.06 for Nifty Junior, which shows that Nifty Junior is more volatile market as compared to S&P CNX Nifty. Further non-parametric tests are also conducted to explore evidences, whether the sample distribution conforms to a normal distribution.
Table 1: Descriptive Statistics
S&P CNX NIFTY
CNX NIFTY JUNIOR
Mean
2512.46
4531.57
Median
1954.76
4018.55
Maximum
6287.85
13069.45
Minimum
854.2
1046.7
Std. Dev.
1439.01
2784.06
Skewness
0.69
0.69
Kurtosis
2.19
2.58
Jarque-Bera
265.88
215.38
Probability
0.00
0.00
Observations
2496
2496
Unit Root Test
The unit root test tests time series for stationarity and find out whether a time series variable is non-stationary. The most appropriate tests are the Augmented Dickey-Fuller (ADF) test and Phillips-Perron (PP) test. Both tests use the existence of a unit root as the null hypothesis. If the series is non-stationary and the first difference of the series is stationary, the series contains a unit root.
It appears in the Table 2that the null hypothesis of unit root cannot be rejected for both S&P CNX Nifty and Nifty Junior, using intercept terms in the test equation in the level form. But inversely, for the first difference of both S&P CNX Nifty and Nifty Junior, the null hypothesis of a unit root is strongly rejected. So it can be said that both S&P CNX Nifty and CNX Nifty Junior contain a unit root, that is, non-stationary in their level forms, but stationary in their first differenced forms.
Table 2a: Unit Root Test(ADF Test)
Level
First difference
Symbol
Lag length
ADF statistic
p-value
Lag length
ADF statistic
p-value
S&P CNX NIFTY
1
-0.279606
0.9255
0
-46.73294
0.0001
CNX NIFTY JUNIOR
1
-0.288648
0.9242
0
-42.99535
0.0000
Exogenous: Constant
Lag Length: Automatic based on SIC, MAXLAG=26
*MacKinnon (1996) one-sided p-values.
Deterministic terms: Intercept
Table 2a: Unit Root Test (PP Test)
Symbol
Level
First difference
Bandwidth
P-P test statistic
p-value
Bandwidth
P-P test statistic
p-value
S&P CNX NIFTY
6
-0.188438
0.9375
4
-46.68999
0.0001
CNX NIFTY JUNIOR
9
-0.190271
0.9373
4
-42.96778
0.0000
Exogenous: Constant
Bandwidth: Newey-West using Bartlett kernel
MacKinnon (1996) one-sided p-values
Deterministic terms: Intercept
Run Test
The run test, also called the Geary test, is non-parametric test and is independent of the normality and constant variance of data. The Run test is used to test and detect statistical dependencies (randomness) in share price movements and compares the expected number of runs from a random process with the observed number of runs. A run is defined as a series of identical signs that are preceded or are followed by a different sign or no sign at all i.e. given a sequence of observations. The run test examines whether the value of one observation influences the values taken by later observations. If there is no influence (the observations are independent), the sequence is considered random. It is assumed that the sample proportion of positive, negative and zero price changes are good estimates of the population's proportions. Run test shows cutting point, the number of cases below the cutting point, the number of cases greater than or equal to the cutting point, and the tests statistics Z with its observed significance level. The total number of runs is measure of randomness, since too many or too few runs, suggest dependence between observations.
The null hypothesis of the test is that the observed series is random variable. When the expected number of runs is significantly different from the observed number of runs, the test rejects the null hypothesis. Under the null hypothesis that successive outcomes are independent, the total expected number of runs are distributed as normal with the following mean:
and the following standard deviation:
where n is the number of runs of type i. The test for serial dependence is carried out by comparing the actual number of runs, ar in the price series, to the expected number µ. The null proposition is:
H0 : E(runs) = µ.
Poshakwale (1996) opined that a lower than expected number of runs indicates the market's over-reaction to information, subsequently reversed, while higher number of runs reflect a lagged response to information. The number of runs is a measure of randomness. Too many or too few runs, suggest dependence between observations.
Table 3: Run Test
S&P CNX NIFTY
CNX NIFTY JUNIOR
Test Value *
1.9548
4.0816
Cases <Test Value
1248
1248
Cases >= Test Value
1248
1248
Total Cases
2496
2496
Number of Runs
14
29
Z
-49.449
-48.849
Asymp. Sig. (2-tailed)
0
0
* Median
The results of the runs test are shown in Table 3. It can be seen that the total number of runs are 14 and 29 for S&P CNX Nifty and CNX Nifty Junior respectively. It also shows zero observed significance level. Therefore, the hypothesis of randomness for both the series is rejected.
Kolmogorov-Smirnov (KS) Test
Kolmogorov-Smirnov (KS) Test is a widely used goodness-of-fit non-parametric test. It determines that how well a random sample of data fits a particular distribution. It compares the observed cumulative distribution function for a variable with a specified theoretical distribution which may be normal, uniform, Poisson, or exponential. The KS one sample test goodness of fit test compares the cumulative distribution function for variable with a uniform or normal distributions and tests whether the distributions are homogeneous. It checks whether the observations have come from the specified distribution.
Table 4: Kolmogorov-Smirnov Test
S&P CNX
NIFTY
CNX NIFTY JUNIOR
Most Extreme Differences
Absolute
0.155
0.105
Positive
0.155
0.096
Negative
-0.129
-0.105
Kolmogorov-Smirnov Z
7.767
5.269
Asymp. Sig. (2-tailed)
0.00
0.00
Test distribution is Normal
As presented in Table 4, for the present series, it is assumed that sample behave like a normal distribution. The KS results indicate a 0.00 probability for the Z at the 5 percent level. Null hypothesis of normal distribution for S&P CNX Nifty and CNX Nifty Junior is therefore rejected.
CONCLUDING REMARK
The hypothesis of normal distribution is rejected at the conventional 5 percent level. Apart from this, it can be said that both S&P CNX Nifty and CNX Nifty Junior contain a unit root, that is, non-stationary in their level forms, but stationary in their first difference forms. It can further be noticed in the case of run test that the total number of runs are 14 and 29 for S&P CNX Nifty and CNX Nifty Junior respectively. It also shows zero observed significance level. Therefore, the hypothesis of randomness for both the series is rejected. The Kolmogorov-Smirnov Goodness of Fit Test (KS) shows probability as 0.00 for the Z at the 5 percent level. Therefore, Null hypothesis of normal distribution for S&P CNX Nifty and CNX Nifty Junior is rejected.
Therefore, we finally conclude that movement of market under study does not exhibit weak form of market efficiency and thus do not follow random walk.
The findings of the paper are particularly useful for portfolio managers, corporate executives, policy makers and individual or institutional investors for the appraisal and management of their existing portfolios as their portfolio management strategies may be, up to some extent, dependent upon such research work.
Regarding the future implications, these types of studies are continues in nature so studies done in particular period by the researcher become useful to the people who wish to work on the related areas on the different set of time period in future. Observations drawn from the studies conducted in one period of time may help in justifying the studies of future researchers. Moreover, the results of past studies are not expected to be same but different and contradictory in nature. This outcome may become interesting to the future researcher who will work in the related areas in future.
