Transcending time is no longer the sole concern of people seeking spiritual progress. The ‘time-transcendence’ principle seems to have seeped into the more mundane, The more we read about the stock markets being efficient, the more convinced we become about the general consensus about efficiency that even in the weakest form of its efficiency the stock market leaves little room for analyzing the past to predict the future. Two out of three dimensions of time would be rendered quite futile if the current stock prices are supposed to reflect all the information that is contained in the history of prices and volumes. As such, the past would be utterly futile in predicting the future. In other words, even a weakly efficient stock market would be beyond time. Kendall (1953) has indeed, among others, notes that there is no predictable pattern in stock prices; stock prices behave randomly irrespective of what has happened in the past.

Stock market efficiency has remained an issue that raises continuous debate in financial literature as is evident from Fama (1970), Haugen (1997)

and Huber (1997). For the sake of ease in comparison, stock market effi- ciency has been classified into three types, depending upon the type of infor- mation represented by each one of them: the set of historical price informa- tion, the remaining publicly available information and the ‘inside’ informa- tion. It is from these three information subsets, that the three degrees of effi- ciency have evolved namely; weak, semi-strong and strong. The weak form of market efficiency hypothesis postulates that present prices fully reflect information content of the price sequences in the past. The semi-strong form of the efficient market hypothesis contends that prices should reflect all the public information, and in its strongest form of efficiency, all the informa- tion, both public and non-public, is considered to be incorporated in the cur- rent prices. It follows that in order to be efficient in the semi-strong or strong form, the market must be efficient in its weak form.

The efficiency hypothesis rests on the presumption of a rapid infor- mation processing mechanism which would deny the market participants an opportunity of earning an abnormal return on a consistent basis because the changes in price would be serially uncorrelated and would follow a ‘random walk’,

One way of testing the ‘random walk model (RWM)’ is through the application of the Augmented Dickey Fuller Test (ADF), which tests for the presence of unit root ina time series and the Autocorrelation functions (ACF), which determine whether the first differences of a series indicate white noise. For a purely white noise series, the autocorrelations at different lags would stay close to zero, indicating stationarity. Time series econometrics postu- lates that the presence of a unit root is indicative of non-stationarity in the series. The terms non-stationarity, unit root and random walk are treated syn- onymous.

Vaidyanathan and Gali (1994) have tested the weak form of market efficiency in the Indian Capital Market. They have computed 208 autocorrelation functions, out of which only 19 are found significant, provid- ing support to the weak form of efficiency. Martin Laurence, Francis Cai and Sun Qian (1997) have examined the weak form efficiency and causality in Chinese stock markets by using Unit root test and autocorrelation functions. They conclude that market for “A” shares is weakly efficient but not the market for “B” shares. Ramasastri (1999) has used unit roots to test the mar- ket efficiency in India and finds that the hypothesis of random walk in the Indian stock market can not be rejected. Kleiman, Payne and Sahu (2002) have studied the random walk hypothesis by using stock market indices of real estate share prices for three geographical regions: Europe, Asia and North America. The Augmented Dickey-Fuller and Phillips-Perron unit root tests determine that each of these markets (as well as associated broader stock

Marker Efficiency And Integration: An Examination Of Indian Stock Market markets) exhibit random walk behavior. Similar findings have also been re- ported by Nassir (1991) in his results on the efficient market hypothesis in the Kuala Lumpur Stock Exchange.

It can be deduced, therefore, that unless the movements in a stock market were to respond to the movements in a more broadly defined market proxy and / or other informatory variables, there would exist no scope for earning super-normal profits and the market would be efficient. If, however, the causation is reverse, such integration would come at cross-roads with the tenets of market efficiency. Examining such integration would, in a way, in- vestigate the semi-strong form of market efficiency. In the past, market inte- gration has been studied by using correlation coefficients between two mar- kets. A high coefficient of correlation has been used as a supporting proof for market integration. One such study in the context is that by Uri and Rifkin (1985) on geographic markets, causality and railroad deregulation. However, the presence of autocorrelation and /or non-stationarity may dilute the utility of using simple correlation coefficients as indicators of integration. Granger and Newbold (1974) point out that if two variables were integrated of the order | [I(1)], - that is, they become stationary after first differencing, the basic assumptions of the ordinary least square estimation would be violated and the correlation would be spurious. Johansen (1988) suggests a procedure for determining the number of co-integrating vectors that could accommo- date more than two variables in the system.

The point regarding the market as a processor of information has been made earlier. The speed of such processing determines the efficiency of the market. This would, however be true only in case of a uni-directional causality, where the stock market explains the macro phenomenon, In case, the causality is the other way round, the ability of the market as a rational processor of information is questionable and the market would prove to be inefficient in that case because then it would be possible to derive meaning- ful forecasts for earning more than normal returns. The findings of Huang and Kracaw (1984) support this argument. The concept of causality is impor- tant as a mere relationship between two variables does not indicate the direc- tion of influence. Something similar is emphasized by Gary Koop (2002). According to him, “...time does not run backward. That is, if event A hap- pens before event B, then it is possible that A is causing B. However, it is not possible that B is causing A. In other words, events in the past can cause events to happen today. Future events can not,”

If the direction of causality indicates that the stock market is ineffi- cient, the nature of cause-effect can be profitably studied to develop a fore- cast. Specifically, an attempt can be made to determine how the market is related to the explanatory factor; in a linear or non-linear fashion.

Here we examine the issue of efficiency in the Indian stock market. The data for this purpose constitute the Indian stock price index and the Emerg- ing Markets Free Index (EMF index hereafter), both published by the Mor- gan Stanley Capital International (MSCI hereafter). The MSCI Price Index for India measures the market price performance. The index measures the sum of the free float-weighted market capitalization returns of all its con- stituents on a given day. The MSCI EMF Index is a free float-adjusted mar- ket capitalization index that is designed to measure equity market perfor- mance in the global emerging markets. As of April 2002 it consisted of the following 26 emerging market country indices: Argentina, Brazil, Chile, China, Colombia, Czech Republic, Egypt, Hungary, India, Indonesia, Israel, Jordan, Korea, Malaysia, Mexico, Morocco, Pakistan, Peru, Philippines, Poland, Russia, South Africa, Taiwan, Thailand, Turkey and Venezuela.

The paper is intended to address the issue of market efficiency in the emerging markets of South-East. Obaidullah (1994) in his work on Interna- tionalization of Equity Portfolios observes that the benefits of including coun- tries like India followed by Thailand and the Taiwanese markets are “too immense and clear cut to be ignored”. The choice of the India as a market for this paper has been prompted by this finding. Also, only a few studies have been carried out on stock market integration in the Indian context. Amanulla and Kamaiah (1995) have studied the market integration in India as a pos- sible alternative to test market efficiency. Jha and Nagaranjan (1999) have also made an attempt on similar lines but their focus is on short run dynam- ics. The emphasis has been largely the inter-exchange integration within the country or the high frequency data pertaining to some of the stocks traded on an exchange for a short period. In this paper, we intend to explore the effi- ciency of the Indian stock market taken in totality and to see if the market responds to a proxy with a broader gamut. Since India belongs to one of the major emerging markets of South-East Asia, the causal nature has to be ex- amined against a larger entity. The EMF index provides the larger picture. The monthly data for both indices from February 1999 to May 2003 have been used for this paper.

The paper is arranged section wise, Section 2 presents the descriptive characteristics of the time series under study to see whether the data needs to be transformed for further analysis. Specifically, the series is examined for normality. Though the series should be checked for stationarity as well, this exercise has been been postponed till section 3, where the stationarity check also reveals the randomness of movement in the stock price index of India. In Section 3, the findings regarding the testing of weak form of market effi- ciency in India are reported. Section 4 determines the direction of causality between the Indian Stock Price Index and the EMF Index. Section 5 studies

Marker Efficiency And Integration: An Examination Of Indian Stock Market the co-integration between the Stock price index of India and the EMF index leading to the study of cause-effect relationship in section 6. Section 7 con- cludes the paper.

The purpose of this section is to look into the descriptive statistics of both the stock price index for India and the EMF index. This is necessary to make sure that both time series can be used for classical normal linear regression (CNLRM), which is applied for determining the cause and effect relation- ship.

One of the prime assumptions of the CNLRM is that each distur- bance term u, is distributed normally with mean, E (w,) = 0, variance E [ u,- E(u) = é* and i i#j the covariance (u,. 4) = 0 andi#j. This assumption has to hold good especially in the case of small samples in order to lend credibil- ity to the ¢ and F tests.

The normality of the series under consideration has been checked by computing the higher moments (along with their z staristic) of a normal dis- tribution, namely the coefficient of skewness (s) and kurtosis (kk). The condi- tion of normality is satisfied if the coefficient of skewness is 0 (close to 0) and the coefficient of kurtosis is 3 (close to 3), The z statistic of skewness is given by;

skewness

Z spewneny = where, nis the sample size (1)

A stationary stochastic process means that its mean and variance are constant over time and the covariance between two time periods is dependent only on the lag between them.

If ¥, is a stochastic process, then it is considered to be stationary if;

Mean E(¥) =u Variance var (Y)=E(Y-uP =o? Covariance ¥, SEY -WY,,- WI where, y, is the covariance at lag k between ¥ and Y,,, 31, The Autocorrelation Function

If a time series does not show the above characteristics, it is said to be non- stationary. As mentioned earlier, the stationarity of the time series is impor- tant for the forecasts to have some pragmatic meaning. It follows that when a series is non-stationary and consequently, no meaningful forecasts can be drawn, the behavior of the series in question is considered random and it would then indicate market efficiency. The random walk model dries up all possibilities of a consistently superior return from the market.

We have tested the stationarity characteristics of both the Indian stock price index and the EMF index by first using the simple Autocorrelation func- tion (ACF) for 24 lags. According to Gujarati (2003), “A rule of thumb is to compute up to one-third to one-quarter the length of the time series.” The ACF has been plotted against these 24 lags to obtain a Correlogram. The ACF at lag & is obtained by;

x P, — (4) Ya where, A, - sample Autocorrelation function y. - sample Covariance at lag k y, - sample variance A plot of the sample ACF against the lag k is the sample correlogram. E- views generates a correlogram the ACF and PACF (Partial autocorrelation function). The dotted line in the plot indicates two standard error limit, which

. , 42 , , : bud Evan, pig, is obtained by Fr Where nis the sample size. An ACF lying within this limit is not statistically different from zero at 5% significance level. In order to test the joint hypothesis that all P, up toa given lag are simultaneously not statis- tically different from zero, the Ljung-Box OQ statistic is computed by E-views which is of considerable importance in small samples. Q statistic is defined as;

m {Pet LB =n(n+2) x —!| =c'm (5) Nek

The LB @Q statistic follows the chi-square distribution with m de- grees of freedom. If the computed value of Q statistic exceeds the critical Q value from the chi-square distribution at the selected significance level, the null hypothesis of all r, being zero can be rejected,

can be observed that the autocorrelation coefficients for lags closer to the present time period are very high and decline steadily till the 12" lag. From 13" lag onwards they start increasing on the negative side. The Q statistic for up to 24" lag is 220.3 but the probability of obtaining this value under the null hypothesis that the sum of 24 squared sample ACFs is zero, is zero. It can be inferred, therefore, that the Indian stock price index is a non-station- ary time series, When we examine the correlogram of the first difference of the series in Table 3.2, it indicates the presence of only white noise as the autocorrelation coefficients never quite depart from zero significantly. The value of Q statistic is 26.29, The probability associated with this value is around 34% which, though not very high, indicates that the first difference of the time series are stationary when combined with the observation that only the autocorrelation coefficients at lags 6, 8 and 11 manage to cross the dotted line and that too, barely. Further, there is a clear visual evidence of absence of any pattern in their occurrence. It points out towards the series containing one unit root. This is typically true of a random walk series. Therefore, the Stock price index of India seems to follow a random walk and the stock market may be understood to be efficient in its weak sense.

The correlogram for the EMF index in Table 3.3 shows almost an identical pattern as that of the stock price index of India. The autocorrelation coefficients begin high and decline slowly till lag 12 after which they move over to the negative side. The Q statistic is 213 and the associated probability is zero, leading to the conclusion that the series is non-stationary. The correlogram obtained after first differencing the series for EMF index is shown in Table 3.4. When compared to the first difference series of the Indian stock price index, it provides much more forthcoming evidence that the series should be 1 (1) as the autocorrelation coefficients stay close to zero for all the 24 lags. Probability of achieving the Q statistic of 15.976 for up to 24 lags under the null hypothesis of zero simultaneous correlations at all lags is about 89%. In the market efficiency sense, therefore, the time series for EMF index also seems to follow a random walk and is non-stationary in nature.

The time plots for the both time series are presented in Exhibit 3.1 and Exhibit 3.2. It can be observed that the first difference series for both the EMF index as well as the stack price index of India have a tendency to return back to their mean whenever there is an away movement from their mean values of 0.41 and (0.029) respectively indicating that stationarity is achieved after first differencing.

In order to establish causation and its direction, we haye used the Granger's causality test (1969). The test strives to answer the question whether x causes y and to determine how much of the current y can be explained by past values of x. It goes further to find out whether adding lagged values of x can im- prove the explanation. y is said to be ‘Granger-caused’ by x if x helps in the prediction of y. In other words, . would ‘Granger cause’ y, if the coefficients of the lagged x values are statistically significant. If the reverse is true, then x is ‘Granger caused’ by y. In case of bilateral causality, both x and y ‘Granger cause’ each other.

The phrase that x or y ‘Granger cause’ each other does not imply that they are the effects of each other. Granger causality only measures prece- dence but by itself it does not indicate causality in the more common use of the term.

For determining from x fo y, two bivariate regressions are run as follows:

Unrestricted: = y,= 4, + &)x,) + d,X,, + +d, x, (12)

Restricted: y=, 4+ Gy) + GV, tee +d y (13)

nn

Similarly, reverse causation from y fo x is determined by the follow- ing two bivariate regressions:

Unrestricted: x -d,tG,x,,t A,xX,, t...... +4,X,, (14) Restricted: R= apt Ak p+ Gag + ace +4, x, (15)

The null hypothesis is that x does not Granger cause y in the first regression and y» does not cause x in the second regression, which is tested by the F statistic,

Since Granger causality test is very sensitive to lag length, it has been tested at varying lag lengths in this paper till some reasonably definite conclusion is reached. The errors in the original time series are autocorrelated as indicated by their stationarity characteristics. Therefore, the first difference series for the EMF index as well as the stock price index of India, have been used for the causality test.

Perusal of Table 4.1 indicates uni-directional causality from EMF Index to the Stock Price Index of India. Though there are hints of such cau- sality for smaller lags, the F statistic does not assume conclusive signifi- cance for either null hypothesis at lags 2 and 4. In fact, at lag 4, the signifi- cance of the F statistic seems to drop off from that at lag 2. However, at lags 8 and 16, the significance of the F statistic increases for the null hypothesis that EMF Index does not Granger cause the Stock Price Index of India.

In conclusion, a uni-directional causality is apparent since the null hypothesis that the Stock Price Index of India does not Granger cause the EMF Index can not be rejected. The second null hypothesis that EMF Index does not cause the Stock Price Index of India is rejected at higher lags. There- fore, the direction of causality is that EMF/Index Stock Price Index of India. This finding indicates towards the fact that perhaps, the Indian stock market is not very efficient in processing information in the semi-strong sense. The implication is that forecasting could be beneficial gainful, at least when the basis for forecasting is the EMF Index. Section 6 is devoted to a forecasting effort.

However, since the original series are both I(1), a regression forecast may be spurious unless their linear combination is I(0). In other words, the regression results of two non-stationary series would be meaningful only if they are co-integrated. Such a regression would be called the co-integrating regression, The following section evaluates this possibility.

In order to test whether the time series of Stock Price Index of India is co- integrated with the time series of EMF Index, two simple methods have been used. They are; 1) The Augmented Engle-Granger Test (1987) and 2) The Co-integrating Regression Durbin-Watson Test .

The study was undertaken to test the efficiency and integration of the Indian Stock market to find out the level of efficiency in the market and to see whether the Indian stock market is integrated with the emerging stock markets of the world. The proxy for the Indian market was the MSCI Price index and the emerging stock markets were considered: by using the MSCI EMF Index. Specifically, the intention was to study whether any gainful forecasting can be done in the context of the Indian stock market. The conclusions drawn are: First, the Indian stock market is efficient in its weak sense as it seems to follow arandom walk. Second, there exists causality between the MSCI Price Index of India and the MSC] EMF Index. Third, the direction of causality is uni-directional from the MSCI EMF Index to the MSCI Price Index of India, indicating that the Indian stock market is not efficient in the semi-strong sense. Fourth, due to the inefficiency of the Indian stock market in the semi-strong sense, publicly available information (the MSCI EMF index in this study), can be utilized to construct meaningful forecasts and there may be a possibil- ity to earn superior returns. Fifth, the simple linear regression model seemed to yield a reasonable forecast after having been tested for normality and stationarity of the series and adjusting the autocorrelation.