# Testing Weak Form Efficiency for Indian Stock Markets

#### This paper attempts to seek evidence for the weak form efficient market hypothesis using the daily data for stock indices of the National Stock Exchange, Nifty, and the Bombay Stock Exchange, Sensex, for the period of 1999-2004. The random walk hypothesis for the Nifty and the Sensex stock indices is rejected. Both the stock markets have become relatively more inefficient in the recent periods, and have high and increasing volatility. Non-parametric tests also indicate that the distribution of the underlying variables are not normal and the deviation from normality has become higher in recent years. Both the indices show a negative autocorrelation at lag 2, indicating over-reaction one day after information arrival, followed by a correction on the next day. The study suggests immediate dissemination of information on foreign institutional investor trades and equity holding and the need to improve free float of equity to move towards efficiency.

KHAN MASOOD AHMAD, SHAHID ASHRAF, SHAHID AHMED

n an efficient market where information is freely available, the price of a share approximates to its intrinsic value. If there is gradual flow of new information, then successive price changes will be dependent. However, if the adjustment to information is almost instantaneous, successive price changes will be random. Market efficiency has an influence on the investment strategy of an investor because, if the market is efficient, trying to pick up winners will be a waste of time. Given their risk in an efficient market, there will be no undervalued stock offering higher than expected returns. On the other hand, if markets are not efficient, excess returns can be made by correctly picking the winners.The efficient market hypothesis (EMH) states that stock prices reflect all available information so that prices are near their intrinsic values. According to Jensen (1978) a market is efficient with respect to information set θ, if it is impossible to make economic profits by trading on the basis of information set θ. 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.

The Indian capital market are represented by the National Stock Exchange (NSE) and the Bombay Stock Exchange (BSE). This paper is an attempt to seek evidence for the weak form efficient market hypothesis using the daily data of stock indices of NSE and BSE for the period of 1999-2004.The remainder of this paper is organised as follows: Section I reviews major features in the Indian stock market and its development over time. Section II discusses the concept and different forms of the EMH. Section III provides a review of literature. Section IV explains various tests for market efficiency. Section V presents empirical results. Finally, concluding remarks are given in Section VI.

#### I Recent Developments in the Indian Stock Market

The Indian stock market started its operation in Mumbai in 1875. Trading was through open outcry and settlements were paper based. Regulations were not very effective and disclosure norms by companies were inadequate. Finally in 1992, Securities and Exchange Board of India (SEBI) was established to reform and regulate the Indian stock market. NSE was set up with tight disclosure norms and electronic trading was established. The Depository Act, 1996 paved the way for setting depositories for trading in dematerialised form. The recommendations of the L C Gupta Committee (1996) on derivatives trading was accepted and passed by Parliament in December 1999, which expanded the definition of securities to include derivatives. Thus, trading on index futures and options, as well as futures and options of individual stocks, commenced from 2000 onwards. This was expected to improve the liquidity and efficiency in the market. The newly created derivatives market turnover now exceeds the cash market and market capitalisation as a ratio of GDP has improved from lows of 10 per cent to around 50 per cent currently.

SEBI reconstituted the governing boards of the stock exchanges, introduced capital adequacy norms for brokers and made rules for segregating client and broker accounts. Stock exchanges with screen based trading systems were allowed to expand their trading terminals to other locations and with the introduction of internet trading, physical boundaries ceased to exist. Trading on the stock exchanges shifted to the rolling settlement for major stocks in July 2001 and for all stocks in January 2002. The rolling settlement cycle was reduced from T+5 to T+2. This is attractive because on the settlement date all open positions are settled and systematic risk is reduced when the delay between trade date and settlement date is small [Shah and Thomas 2004]. An important step was bringing government-owned mutual fund, the Unit Trust of India (UTI), under the regulatory jurisdiction of SEBI. Permission was given to set up private mutual funds. SEBI also vets initial public offer (IPOs) documents to ensure that disclosure norms have been met by the company. The Indian capital market went global with permission for companies to issue Global Depository Receipts (GDRs) traded largely in Europe and American Depository Receipts (ADRs) traded on the US market.

Till the early 1980s there was no index to measure the movements of the stock prices. The BSE came out in 1986 with the Sensex, a basket of 30 stocks with the base year 1978-79. The Sensex was initially calculated on full market capitalisation but from September 2003 was shifted to the free float market capitalisation. The NSE launched the S&P CNX Nifty in April 1996 based on 50 stocks. The NSE Nifty is calculated from the base period November 1995 on the market capitalisation weighted method. Both the BSE and NSE have introduced other popular and sectoral indices. They have over time changed the constituents of the indices to reflect liquidity and market capitalisation. Every time a trade takes place the indices calculations are updated giving a fresh value. Non-synchronous trading, which lead to spurious autocorrelations becomes less important when the indices have highly liquid components [Shah and Thomas 1998]. In the early 2000s a rogue trader bulldozed the operations of the Indian capital market putting it into a period of crisis. An important structural defect in the stock market had persisted till 2001. It featured leveraged futures style trading on the spot market called “badla” in the local jargon. This led to a mismatch between the extent of leverage and the risk management. All variants of badla transactions were stopped from July 2001 [Shah and Thomas 2004].

With the relaxation of foreign institutional investor (FII) inflows, the FIIs have made their mark and 2004 has seen record inflows of over $8.5 billion to the Indian equity market. The Ashok Lahiri Committee [Lahiri et al 2004] was set up in regard to the investment limits for FIIs in different listed companies. The committee was reconstituted twice and had its last meeting in June 2004. A cautious approach has been proposed towards scaling up of FII investments in different sectors of the economy. The committee has suggested increasing investment caps in different sectors while pointing that there are difficulties in monitoring sector specific composite ceilings for diversified companies. Investment caps of 100, 74, 50, 49, 26, 20 per cent for FDI, FIIs and ADRs/GDRs confuses and builds in inefficiencies. It also ignores the derivatives market altogether, where the total daily transactions are more than the combined cash transactions of both NSE and BSE. Further, even with the introduction of modern technology, FII trades are released publicly after two days, the day of the trade and the next day. This is a vital source of information as FIIs have a significant influence in terms of equity holdings and turnover. Immediate dissemination of FII trades would help in accessing this information by all sections of market players thereby improving efficiency.

Finally an important issue is the level of free floats of company equity which may possibly affect the efficiency in the stock market. Free floats are the possible equity available for trading. Higher levels of free floats improve liquidity in the market. This seems to be lacking in the Indian stock market. For example, taking the top five companies in terms of market capitalisation, out of them three are government owned (ONGC, NTPC and Indian Oil). The Indian government has over 75 per cent equity holding in them. In case of the two private companies, Reliance’s 34 per cent equity ownership is not clear and promoter’s own over 85 per cent of Tata Consultancy Services (TCS). Further some of the major Nifty and Sensex constituents have low floating stocks like ONGC, SBI, Sail, Wipro, etc. The low free floats may possibly make price discovery and instantaneous adjustment to information difficult.

#### II Efficient Market Hypothesis (EMH)

The EMH relies on the efficient use of information by investors and is often referred to as “informational efficiency”. Fama (1970) defined three forms of market efficiency, namely, weak, semistrong and strong. Each one is concerned with the adjustment of stock prices to one relevant information subset. The weak form of the hypothesis states that prices efficiently reflect all information contained in the past series of stock prices. In this case it is impossible to earn superior returns simply by looking for patterns in stock prices, that is, price changes are random. The lower the market efficiency, the greater the predictability of stock price changes.

If by increasing the information set to include publicly available information (i e, information on money supply, exchange rate, interest rates, announcement of dividends, annual earnings, stock splits, etc) it is not possible for a market participant to make abnormal profits, then the market is said to be semi-strong efficient. Daily data on returns are a major boost for the accuracy of semistrong tests. When the announcement of an event can be dated to a certain day, daily data allow precise measurement of the speed of the stock-price response, the central issue for market efficiency.

If by increasing the information set to include private information, it is not possible for a market participant to make abnormal profits, then the market is said to be strong efficient. Under the strong form, the consideration is whether only some investors (i e, mutual funds) have access to information affecting stock prices. A precondition for the strong version is that information and trading costs are always zero. While operating in the stock market where information has a cost, it is difficult for markets to be informationally efficient [Grossman and Stiglitz 1980]. The extreme version of the market efficiency hypothesis is very unlikely to hold since there are positive trading and information costs.

Jensen (1978) points out that despite earlier evidence on the randomness of stock price changes there are pieces of evidence of anomalous price behaviour where certain series appeared to follow predictable paths. Due to these anomalies there is a necessity to carefully review both the acceptance of the efficient market theory and the methodological procedures. Subsequently Fama (1991) changed the categories and coverage of informational efficiency. According to him, the first category now covers the more general area of tests for return predictability, including work on forecasting returns with variables like dividend yields and interest rates. Further seasonalities in returns and volatility of security prices are to be considered under the rubric of return predictability. He further continues that semi-strong tests now be called event studies and strong form tests be called tests for private information. Fama (1998) suggests that apparent anomalies require new behavioural based theories of the stock market and the need to continue the search for better models of asset pricing.

#### III Review of Literature

The early studies on testing weak form efficiency started in the developed market. Empirical evidence on the weak form efficiency indicates mixed results. Kendall (1953) examined 22 UK stock and commodity price series and concluded that the data behave almost like wandering series. The near zero serial correlation of price changes came to be labelled the random walk model. Fama (1965), using 30 US companies of the Dow Jones found evidence of dependence in the price changes. The first order autocorrelation of daily returns were positive for 23 of the 30 companies and they were significant for 11 of the 30 companies. Fisher (1966) also suggests autocorrelations of monthly returns, it being positive and larger for diversified portfolios than for individual stocks. Conrad and Juttner (1973) applied parametric and non-parametric tests to daily stock price changes in the German stock market. They found that the random walk hypothesis is inappropriate to explain the price changes. Cooper (1982) studied world stock markets using monthly, weekly and daily data for 36 countries. He examined the validity of the random walk hypothesis by employing correlation analysis, run tests and spectral analysis. With respect to the US and UK, the evidence supported the random walk hypothesis. For all other markets, the random walk hypothesis was rejected. DeBondt and Thaler (1985, 1987) attribute inefficiency on the New York Stock Exchange (NYSE) to market over-reaction to good or bad news about the listed companies. Lo and Mackinlay (1988) find that weekly returns on portfolios of NYSE stocks show reliable positive autocorrelation. Panas (1990) demonstrated that the Athens stock market is efficient. Frennberg and Hansson (1993) examined the random walk hypothesis using Swedish data from 1919 to 1990. They found that Swedish stock prices have not followed a random walk in that period.

Seiler and Rom (1997) examined the behaviour of daily stock returns of the US market from February 1885 to July 1962, partitioned annually. Using Box-Jenkins analysis for each of the 77 years they indicated that changes in historical stock prices were completely random. Qi (1999) developed a recursive modelling procedure to examine the predictability of S&P 500 for the US market using linear regression and neural network model. He shows that a switching portfolio based on neural network earns higher risk adjusted returns than from the forecasts of the linear regression framework. Bacmann and Dubois (2002) for the US market during July 1962 to December 1998, show that the proportion of stocks exhibiting conditional heteroscedastic residuals is high. Lanne and Saikkonen (2004) analysed monthly excess US stock returns from January 1946 to December 2002. The results indicate the presence of conditional skewness in stock returns. This is because large pieces of news persist, which increases not only present but also future volatility. The evidence seems to suggest that there is informational inefficiency and stock prices can be predicted with a fair degree of reliability.

Literature for emerging markets is limited and the results are mixed. For example, Hong (1978) investigated the efficiency of the Singapore stock market and found evidence that it was efficient in the weak form. Another study made by Ang and Pohlman (1978) on far-east Asian stocks also found support for the weak form efficiency. Evidence for the inefficiency of markets was obtained by Ghandi et al (1980) in a study of the Kuwait stock market. Wong and Kwong (1984) examined the behaviour of the daily closing prices of 28 Hong Kong stocks. The results of serial correlation coefficients showed that the successive stock price changes were dependent random variables. Barnes (1986) reports the Kuala Lumpur stock market to be inefficient. Butler and Malaikah (1992) found evidence of inefficiency in the Saudi Arabian stock market, but not in the Kuwaiti market. Dickinson and Muragu (1994) found the Nairobi stock market as efficient. This is difficult to believe as the accumulating evidence seems to suggest that stock markets are inefficient.

For the Indian stock markets, Sharma and Kennedy (1977) compared the behaviour of stock indices of the Bombay, London and NYSE during 1963-73 using run test and spectral analysis. Both run tests and spectral analysis confirmed the random movement of stock indices for all the three stock exchanges. Barua (1981) and Gupta (1985) also found that the Indian stock market was weak form efficient. Studies by Kulkarni (1978) and Choudhary (1991) did not support this hypothesis. A detailed survey on empirical literature for market efficiency during 1980s and early 1990s is available in Barua et al (1994).

Looking at literature for more recent years, Bhaumik (1997) found that the stock prices closely represent a random variable. He tested the efficiency of Indian capital market using the Sensex data for only 115 days starting November 1996. Ramasastri (1999) tested Indian stock markets for random walk during 1990s using the Dickey-Fuller unit root test. He also did not reject the null hypothesis that stock price are random walk. Narayana (2001) attempted to estimate systematic risk of 50 different stocks comprising Nifty using daily data from November 1995 to May 2000. He showed that there was a strong possibility for the existence of a weak relationship between risk and return in the Indian stock market. Mohanty (2001) used the Sensex to estimate betas on monthly return data during the period 1994 to 2000. He showed that small stocks outperformed the large stocks in the sample period and the excess returns could be because the market for the small stocks was inefficient. Pant and Bishnoi (2001) tested the random walk hypothesis using Nifty, NSE-50, Sensex, BSE-100 and BSE-200 during the period April 1996 to June 2001. The unit root test strongly accepted the null hypothesis of random walk for all the indices, whereas it was rejected using heteroscedasticity corrected variance ratio test. The study also showed that there were significant first order autocorrelation in daily returns, which are in general absent in weekly returns. Nath and Reddy (2002) used Nifty for the period July 1990 to November 2001. They say that trends were apparent and the movement of stock prices did not follow a random movement.

Mitra (2000 a, b) disproved the random walk hypothesis by developing a neural network model, which performed very well in forecasting stock prices on the BSE. Samanta and Bhattacharya (2002) used weekly and monthly data of BSE-100 during January 1996 to December 2000. They pointed out that results were not conclusive for assessing the usefulness of the spread between E/P ratio and interest rates in explaining stock market returns. Though spread seems to have a reasonably strong causal influence on returns, the usefulness of spread in formulating a profitable business strategy was not clear. Pandey (2002) covered the period of January 1999 to December 2001 to analyse the empirical performance of the extreme value volatility estimators for Nifty and 10 constituent stocks. He concluded that the estimators could be used safely for estimating the volatility in these liquid assets.

Samanta (2004) carried out spectral shape tests for daily data on the BSE-100 from January 1993 to December 2001. He partitioned the entire period into 18 sub-periods and tested separately for each sub-period. The study showed that the market was considerably inefficient during each sub-period till June 1996. It achieved high level of efficiency during July 1996 to December 1999 and showed efficiency at a relatively lower level thereafter, except with some aberration during 2000. Nath and Dalvi (2005) examined the day of the week effect anomaly during 1999 to 2003 for Nifty. They found that market inefficiency exists. According to Dhankar and Chakraborty (2005) variance ratio test suggests dependency of the Sensex series, which violates the assumption of the random walk hypothesis. Using the ARIMA process they have developed a model for forecasting future returns to the Sensex.

Thus in the Indian context, except for some studies, the available evidence in general indicates that successive price changes are dependent and the random walk model may be inappropriate to describe stock behaviour. Research on the weak form of market efficiency with daily data and econometric tests have been attempted largely for the period 1992 onwards to 2002. It would be interesting to extend the analysis and compare the weak form of efficiency over a period of time. The period of analysis (i e,1999-2004) for the present paper has seen some major crises, scams, intense capital market activity and introduction of new financial instruments.

In the present study we used a long timeseries of daily data of NSE Nifty (nseindia.com) and BSE Sensex (bseindia.com) for the period of January 4, 1999 to August 30, 2004. The daily data consists of 1,425 observations for the total period which is a big sample size from the view of statistical inference. The series was further split into two equal periods 1999-2001 and 2002-04 to test whether or not the efficiency of the market improves over time. The first phase of the period incorporates the internet euphoria, rogue traders crisis and the stoppage of badla. The second period includes the introduction of rolling settlement, transactions in futures and options, the bull run and the highs in the indices, market capitalisation and FII inflows during 2004. A number of parametric and non-parametric tests have been used in the study for the overall and the sub-periods to check the robustness of the results.

#### IV Methodology for Testing Market Efficiency

The weak form of the EMH involves two separate hypotheses:

(a) successive stock price changes are independent, and (b) the price changes are identically distributed random variables. If successive stock price changes are independent of one another and are identically distributed random variables, then historical price changes cannot be used to predict future price movements in any meaningful way.

To illustrate what is meant by the notion of random walk, suppose that an asset price, yt , can be described by the following process

E(yt+1|θ) = yt ...(1)

t

The variable yt is said to be a martingale with respect to the information set θt–1. If we allow for a constant term in equation (1) the process is said to follow sub-martingale. Given the information set, θt–1, equation (1) says that the value of today is the best prediction for the value of tomorrow. If we parameterise equation (1) we can get the random walk model, y= y +ε...(2)

t+1 t t+1

where ε~ NID(0,σ2). Substituting backwards from yt–1, yt–2,

tetc, leads to

t −1

y =∑ε+y ...(3)

tt 0 t =1

where y0 is some initial value of yt. The first term on the right hand side represents the stochastic trend in yt. Expression (3) shows that any shocks will have permanent effects on the stock price in the future. Taking the first difference of (3) leads to a white noise process,

...(4)

Δ=ε

yt twhere Δdenotes the first difference of the series and εis a

yttwhite noise error term. Different tests can be used to check

whether yt is a random walk and thus ε~ NID(0, σ2).

tSeveral tests for establishing statistical independence in a stockprice time series are available. The following parametric tests, namely, unit root tests, the sample Autocorrelation Function (ACF), Ljung-Box (Q) statistic and GARCH model are used. Further, nonparametric Runtest and Kolmogorov-Smirnov (K-S) test are used to check the randomness and normality in a stock-price time series. The essence of these tests are briefly discussed as below:

##### Unit Root Tests

If ytis a random walk, then Δyt must be stationary. A data series must be stationary if its mean and variance are constant (nonchanging) over time and the value of covariance between two time periods depends only on the distance or lag between the two time periods and not on the actual time at which the covariance is computed. The correlation between a series and its lagged values are assumed to depend only on the length of the lag and not when the series started. A series observing these properties is called a stationary time series. It is also referred to as a series that is integrated of order zero or as I(0).

The unit root test checks whether a series is stationary or not. Stationarity condition has been tested using Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) tests [Dickey and Fuller 1979, 1981; Gujarati 2003; Phillips and Perron 1988; Enders 1995]. The ADF test makes a parametric correction in Dickey-Fuller (DF) test for higher-order correlation by assuming that the series follows an AR(p) process. The ADF approach controls for higher-order correlation by adding lagged difference terms of the dependent variable to the right-hand side of the regression. The ADF test has three alternative specifications as follows:

p

yy +∑γΔ + u ...(5)

#### Δ=λ y

tt−1 it−it i=1 p

yy +γΔ + u ...(6)

#### αλ yΔ= +

t 0 t −1 ∑it −it i=1 p

y αβ λ t +y +γy ...(7)

#### Δ=+ Δ+ u

t 00 t −1 ∑it −it i=1

To test for stationarity, the null hypothesis is:

H0: λ= 0

and alternative hypothesis is:

H1: λ< 0

In the present study, all the ADF equations to test the series for stationarity have been used. We found that the results are invariant to the model specification except minor differences in ADF values. Therefore, only the result of ADF test based on equation (5) is presented. Phillips and Perron (1988) proposed a nonparametric method for controlling higher-order serial correlation in a series. The PP test makes a correction to the t-statistic of the coefficient from the AR (1) regression to account for the serial correlation in ut. The advantage of the PP test is that it is free from parametric errors. In view of this, PP values have also been checked for stationarity.

##### Autocorrelation Function (ACF)

The ACF, Ik, is used to determine the independence of the stock price changes. This measures the amount of linear dependence between observations in a time series that are separated by lag k, and is defined as

nk

∑− (Y −Y )( Yk −Y )

tt + t =1 ...(8)

I k = n ∑(Yt −Y )2

t =1

where Ik is the autocorrelation coefficient for a lag of k time units and n is the number of observations. If the price changes of the stocks are independently distributed, Ikwill be zero for all time lags. An approximate formula for the standard error of Ik, SE(Ik), has been derived by Bartlett [Kendall and Stuart 1961] which is given below:

1SE(Ik) =

n

##### Ljung and Box (Q) Statistic

The Q-statistic is used to test whether a group of autocorrelations is significantly different from zero. Ljung and Box (1978) used the sample autocorrelations to form the statistic

m ⎛Iˆ2 ⎞

QLB =nn ( +2) ∑⎜ k ⎟~ χm 2 ...(10) k =1 ⎝−⎠

nk

Under H0: I1 = ..... = Ik = 0, where Q asymptotically follows the χm 2 distribution with m degrees of freedom. The high sample autocorrelations lead to large values of Q. If the calculated value of Q exceeds the appropriate χm2 values in a table, we can reject the null hypothesis of no significant autocorrelations. Rejecting the null hypothesis means accepting an alternative that at least one autocorrelation is not zero.

##### GARCH Model

Uncertainty is measured by looking at volatility in individual series. The volatility of individual series is tested by applying GARCH model (Generalised ARCH), introduced by Bollerslev (1986). In the standard GARCH (1,1) specification

2 =+δβ2 + 2 +t ...(11)

uˆxt uˆxt−1 γσ ε

where residual series are generated by regressing xt, and yt on constant. σt 2 is the one period ahead forecast variance based on past information called the conditional variance. The coefficient βis defined as ARCH(1) and γas GARCH(1). If both the coefficients are individually significant and their sum is close to one then the series is said to be volatile.

t−1

##### Non-Parameteric Tests

Run test: The Run test is another approach to test and detect statistical dependencies (randomness) which may not be detected by the autocorrelation test. The null hypothesis of the test is that the observed series is random variable. The number of runs is computed as a sequence of the price changes of the same sign (such as; ++, - -, 0 0) [Siegel 1956]. When the expected number of runs is significantly different from the observed number of runs, the test rejects the null hypothesis. 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. Either situation would suggest an opportunity to make excess returns [Poshakwale 1996].

Under the null hypothesis that successive outcomes are independent, and assuming that N1 >10 and N2>10, the number of runs is asymptotically normally distributed with

2NN

Mean: 1 2 ...(12)

ER =

() +1

N

2NN (2 NN −N)

Variance: 2 1 2 1 2 ...(13)

σ=

R 2

()( N 1)

N − Where, N = total number of observations N1 = number of + symbols N = number of – symbols

2

R = number of runs

The null hypothesis of randomness is sustainable if R lies in the following confidence interval and reject the null hypotheses otherwise [Gujarati 2003]:

Prob(E(R) – 1.96σR ≤R ≤E(R) + 1.96σR) = 0.95

The run test converts the total number of runs into a Z statistic. For large samples the Z statistic gives the probability of difference between the actual and expected number of runs. If the Z value is greater than or equal to ±1.96, the null hypothesis is rejected at 5 per cent level of significance [Sharma and Kennedy 1977].

##### Kolmogorov-Smirnov (K-S) Test

The K-S test was originally proposed in the 1930s [Kanji 1999]. K-S is one of the best known and most widely used goodnessof-fit tests. It is based on the empirical distribution function and converges uniformly to the population cumulative distribution function with probability measure one. The one sample K-S test procedure compares the observed cumulative distribution function for a variable with a specifiedtheoreticaldistributionwhich may be normal, uniform, Poisson, or exponential. The K-S Z is computed from the largest difference (in absolute value) between the observed and theoretical cumulative distribution functions. This goodness-of-fit test checks whether the observations could reasonably have come from the specified distribution.

#### V Empirical Analysis

The empirical results are presented as below.

##### Unit Root Tests

One of the basic assumptions of the random walk model is that if the NSE Nifty and BSE Sensex indices exhibit random walk then they will be non-stationary series and their first differences will be a random variable.

The ADF and PP tests are conducted on Nifty and Sensex indices. They are found to be non-stationary. Their first differences (i e, dNifty and dSensex) are stationary, i e, they are I (1). The results are presented in Table 1. This is true for the whole period 1999-2004 as well as for sub-periods, 1999-2001 and 2002-04. Therefore, based on unit root tests, one may conclude that Nifty and Sensex indices exhibit random walk and NSE and BSE can be deemed to be efficient markets.

##### Descriptive Statistics and Test for Normality

To test the distribution of series the descriptive statistics of dNifty and dSensex are presented in Table 2. It is seen that the frequency distribution of dNifty and dSensex is not normal for all the periods. The skewness coefficient, in excess of unity is taken to be fairly extreme [Chou 1969]. High or low kurtosis value indicates extreme leptokurtic or extreme platykurtic [Parkinson 1987]. Generally values for zero skewness and kurtosis at 3 represents that the observed distribution is normally distributed.

During 1999-2001, dNifty does not have skewness but it is leptokurtic. However, it becomes highly negatively skewed and highly leptokurtic during 2002-04. On the other hand, dSensex is mildly negatively skewed and leptokurtic during 1999-2001 but highly negatively skewed and highly leptokurtic during 2002-04. Therefore, skewed and leptokurtic frequency distribution of dNifty and dSensex series indicate that the distributions are not normal. Jarque-Bera test also rejects the null hypothesis of normal distribution for both the series in all the periods under study. Further, the deviation from normality is much higher during 2002-2004 as compared to 1999-2001 for both the series.

##### ACF and Ljung-Box (Q) Statistic

The ACF of dNifty along with their Q statistic are presented in Table 3. The ACFs are significant at lags 1, 2, 4, 6, 10 and 23 during the period 1999-2004. Q test also rejects the joint null hypothesis of zero autocorrelations at 1 per cent level. The period 1999-2001 seems better because ACFs are significant only at lags 10 and 23 and the Q test accepts the joint null hypothesis of zero autocorrelations. However, in the second period ACFs are significant at lags 1, 2, 4, 6, 14, 15, 16 and 24 and the Q test rejects the joint null hypothesis of zero autocorrelation at 1 per cent level. Further ACFs of Nifty are highly autocorrelated and results are not shown in the text.

This exercise is repeated for dSensex and the results are presented in Table 4. The ACFs are significant at lags 1, 4, 6, 20 and 23 lags and the Q test rejects the joint null hypothesis of zero autocorrelations for the full period. During the period, 1999-2001, ACFs at lags 6, 7 and 20 are significant and the Q test rejects the joint null hypothesis of zero autocorrelation at 5 per cent level. In the second period, ACFs are significant at lags 2, 4 and 6 and the Q test rejects the joint null-hypothesis of zero autocorrelations at 1 per cent level. The ACFs of Sensex are also highly autocorrelated and results are not presented in the text.

Based on the results of Tables 3 and 4, we can conclude that both the NSE and BSE are inefficient markets during the period of study and they become worse in the period 2002-04 as compared to 1999-2001. Another result for both dNifty and dSensex is that they have negative autocorrelations at lag 2 across all periods. A negative autocorrelation indicates a price reversal. This can be due to correction from the over-reaction that occurred during the first day of information arrival, which indicates that NSE Nifty and BSE Sensex indices exhibit over-reaction one day after information arrival followed by a correction on the next day. Such corrective measures are observed at higher lags in both the cases. Marisetty (2003) using the daily data for NSE and BSE for the period of 1996-2002 also found evidence of over-reaction followed by a correction next day. Similar results are also reported for other countries [De Bondt and Thaler 1985; Da Costa 1994].

##### GARCH Results

The GARCH estimates, as shown in Table 5, are highly significant across all the periods for both dNifty and dSensex. It is observed that the sum of ARCH (1) and GARCH (1) coefficients are close to unity. This implies that both the series are highly volatile. The second period is relatively more volatile as compared to the first period for both the dNifty and dSensex. The sum of ARCH (1) and GARCH (1) is 0.98 for dNifty and dSensex in the period 2002-04 as compared to 0.91 for dNifty and 0.95 for dSensex for the period 1999-2001. The highly

Table 1: Unit Root Tests on Indices

Variables ADF Test Statistics PP Test Statistics 1999-20041999-2001 2002-04 1999-2004 1999-2001 2002-04

Nifty -1.6092 -1.6204 -0.8779 -1.6730 -1.8470 -0.7991 Sensex -1.5568 -1.4484 -0.7572 -1.5500 -1.5559 -0.6776 dNifty -16.1672 -11.7688 -10.9283 -34.2261 -24.3861 -23.9427 dSensex -16.5451 -12.0914 -10.8871 -35.2943 -24.9248 -24.9819

Note: MacKinnon critical values for rejection of hypothesis of unit root test at 1 per cent are -3.4377, -3.4418, -3.4418 for respective sample sizes.

Table 2: Descriptive Statistics and Test for Normality

dNifty dSensex 1999-2004 1999-2001 2002-04 1999-2004 1999-2001 2002-04

Mean 0.5154 0.1042 0.9254 1.4743 -0.0990 3.0433 Median 1.4000 0.6000 1.8500 4.1850 3.8000 4.8000 Maximum 115.2000 111.7500 115.2000 371.8600 369.2900 371.8600 Minimum -193.6500 -106.6500 -193.6500 -564.7100 -361.4800 -564.7100 Std Dev 22.2336 23.7807 20.5840 72.8229 82.7858 61.3181 Skewness -0.6413 -0.0631 -1.4986 -0.4748 -0.1441 -1.1734 Kurtosis 10.2043 5.3632 18.3591 8.5338 5.2243 16.7182 Jarque-Bera Probability 3177.3450 165.9281 7275.220 1844.2090 146.936 5673.759

(0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000)

Table 3: Autocorrelation Function of dNifty

Lag Auto-Q-Stat Auto-Q-Stat Auto-Q-Stat correlation (25 df) correlation (25 df) correlation (25 df) (1999-2004) (1999-2001) (2002-04)

1 0.084* 9.969 0.067 3.172 0.105* 7.950 2 -0.097* 23.397 -0.044 4.587 -0.167* 27.785

1

SE =

0.0265 0.0375 0.0375n

Notes: * Significant at two standard errors. # Significant at 1 per cent level.

significant values of the sum of ARCH (1) and GARCH (1) There seem to be enough anomalies in the Indian stock market coefficients rejects the null hypothesis of a random walk of stock to justify the search for underpriced stocks. It provides market indices. The high and increased volatility in the period of our players the opportunity to predict future prices and brings the study suggests widening of arbitrage opportunity and extreme possibility of earning higher than expected returns. Future

mispricing as argued by Shlefier and Vishny (1997).

##### Non-Parametric Tests

Run Test: The results of the run test are presented in Table 6. The Z-statistic for dNifty and dSensex for the full period and sub-periods rejects the null hypothesis of random walk at 5 per cent level. Kolmogorov-Smirnov Test: The K-S Z-statistics indicates that the frequency distribution of the underlying series does not fit normal distribution. The results are presented in Table 7.

The results based on non-parametric tests also supports the earlier findings based on parametric tests. The run test rejects the null hypothesis of random walk. The K-S test confirms that the frequency distribution does not fit the normal distribution. It is important to mention that only the unit root test supports the hypothesis of random walk of stock indices whereas all other tests used in the study reject the hypothesis of random walk for the sample period.

This study has attempted an econometric analysis on both the NSE Nifty and BSE Sensex. It is tempting, but we are hesitant, to comment on the relative efficiency (or inefficiency) of the indices. The empirical analysis based on ACF (Tables 3 and 4) seems to suggest that the BSE Sensex is a little less inefficient than NSE Nifty during the study period which is against the popular perception. The results based on Jarque-Bera normality test (Table 2) also suggest that deviations from normality is less in the case of the BSE Sensex than NSE Nifty. However, the other statistical tests do not substantiate the above results. A detailed econometric analysis using high frequency data (hourly or five minutes) may provide a definitive evidence of the relative efficiency of both the indices.

#### VI Concluding Remarks

The random walk hypothesis for NSE Nifty and BSE Sensex stock indices is rejected during the period of analysis. Both the stock markets are relatively more inefficient in the second period. There is high and increasing volatility in both the stock indices. The indices also show a negative autucorrelation at lag 2 indicating over-reaction one day after the information arrival followed by a correction on the next day.

The results seem to go against the recent efforts towards improving the functioning and transparency of the stock market. It seems certain anomalies still exist which may be making the stock market inefficient. These could be the dissemination of information regarding equity holdings and FII trades. The level of disclosures about equity holdings is fuzzy at times. The categories of equity holders, consisting of promoters and “persons acting in concert”, do not reveal the actual entities and their equity holdings in a company. FIIs investments have become the second largest owners of equity in most of the index based companies. In terms of trading and transparency immediate dissemination of their trades may help in improving informational efficiency. Along with this, any increase in the free float of equity in the listed companies would improve liquidity. It is also important that a clear roadmap for disinvestments be defined for piecemeal actions may distort the stock prices. This happens when disinvestments are announced and the government backtracks.

Table 4: Autocorrelation Function of dSensex

Lag Auto-Q-Stat Auto-Q-Stat Auto-Q-Stat correlation (25 df) correlation (25 df) correlation (25 df)(1999-2004) (1999-2001) (2002-04)

1 0.058* 4.663 0.057 2.326 0.056 2.251 2 -0.032 6.129 0.020 2.622 -0.129* 14.048

1

SE = 0.0265 0.0375 0.0375

n

Notes: * Significant at two standard errors. ** Significant at 5 per cent level. # Significant at 1 per cent level.

Table 5: Garch Estimates

dNifty dSensex 1999-2004 1999-2001 2002-04 1999-2004 1999-2001 2002-04

ARCH(1) 0.1424* 0.1391* 0.1372* 0.1072* 0.1002* 0.1426* (10.5241) (6.4463) (6.9112) (10.9626) (5.7616) (7.6233) GARCH(1) 0.8498* 0.8281* 0.8539* 0.8913* 0.8581* 0.8498* (69.4088) (41.9346) (39.5860) (104.3471) (47.2393) (69.4088)

Notes: Figures in parentheses are Z-statistics. * Significant at 1 per cent level.

Table 6: Estimates of Run Test

Variable Total Number of Runs Z-Test Assymp Sig (2-Tailed)

1999-2004 dNifty 641 -3.772 .000 dSensex 639 -3.359 .001

1999-2001 dNifty 327 -2.189 .029 dSensex 327 -1.922 .055

2002-04 dNifty 329 -2.116 .034 dSensex 321 -2.409 .016

Note: Z-statistics of the underlying variables reject the null hypothesis ofrandom walk.

Table 7: Estimates of Kolmogorov-Smirnov Test

Test Absolute Positive Negative K-S Z Asy Sig Distribution (2-tailed)

1999-2004 dNifty Normal .072 .063 -.072 2.711 .000 dSensex Normal .072 .060 -.072 2.679 .000

1999-2001 dNifty Normal .064 .050 -.064 1.702 .006 dSensex Normal .058 .049 -.058 1.539 .018

2002-2004 dNifty Normal .091 .082 -.091 2.419 .000 dSensex Normal .083 .078 -.083 2.217 .000

Note: Null hypothesis of normal distribution of the underlying variables arerejected at 1 per cent.

research needs to analyse the impact of FII trade and its dissemination, investment caps in companies and categories of equity holding by different entities on the behaviour of stock prices. The use of high frequency data along with sophisticated econometric models may possibly help towards a better understanding of the underlying movement of stock prices.

Email: mkhan_jmi@yahoo.com

[The authors gratefully acknowledge the helpful and constructive commentsof the anonymous referee. However, the authors alone are responsible forany remaining errors.]

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