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Applied Economics Letters, 1996, 3, 121–123

Testing the efficient market hypothesis using panel data, with application to the Athens stock market E. Dockery1 and M. G. Kavussanos2 1 Economics 2

Division, Staffordshire University, Leek Road, Stoke-on-Trent, UK and International Centre for Shipping, Trade and Finance, City University Business School, Frobisher Crescent Barbican Centre, London, UK Received 9 May 1995

This paper performs unit root tests using panel data to investigate empirically stock price efficiency of the Athens stock market. Our Wald test statistics reject the random walk hypothesis for stock prices, which is a necessary condition for market efficiency.

I. INTRODUCTION In recent times, there has been a growing body of empirical research on emerging capital markets, partly in response to the diversifying activities of multinational enterprises in these markets, and as a result of the growing interest shown by private and large institutional investors seeking to diversify their portfolios in international capital markets. Capital markets play an important role in allocating a nation’s capital resources; a natural way of assessing their efficiency is to examine the behaviour of stock prices. If markets are efficient, the resulting stock prices should offer no trace as to future changes in prices, otherwise there would be opportunities for investors to make considerable profits and thus markets would be imperfect (Fama, 1970, 1991). For this purpose, the Athens stock market is of particular interest for empirical work in view of the reforms of the late 1980s, aimed largely at liberalizing, restructuring and regulating the Athens Stock Market (ASM). Previous tests for market efficiency in the ASM are attributed to Panas (1990) and indirectly Koutmos et al. (1993), who test for weak-form efficiency, and Niarchos and Georgakopoulos (1986) who consider semi-strong form efficiency. Panas (1990) examines monthly data on ten stocks listed in the ASM and performs independence tests on successive stock returns along with separate tests for randomness and normality for each individual stock return, and concludes that the market is weakly efficient. In all of these studies, the tests employed may be criticized on several fronts. Firstly, in the study by Panas (1990) only ten stocks of ASM were examined. Thus it is possible that a ‘small’ subset of stocks may lead to false rejections of non-efficiency for the whole market. Also, it may be argued that testing for 1350–5851 © 1996 Chapman & Hall

efficiency on stocks individually is likely to be statistically less powerful, since no account is taken of cross stock correlations. The same criticisms apply to the work of Niarchos and Georgakopoulos (1986). Also, it is noticeable that their sample is non-random, which may well bias their results. Koutmos et al (1993), however, use the general ASM index to examine predictability of returns. Here, well-known stock market anomolies, such as thin and non-synchronous trading and the ‘size’ problem may also lead to spurious indications of return predictability in the general index. Overall, and apart from the ambiguity surrounding the evidence for rejection of market efficiency, these results suffer from selectivity bias and low statistical power. It is with regard to the latter that the present paper seeks to make a contribution to the literature, by presenting tests of the efficient market hypothesis for the ASM, which hopefully will go some way towards diminishing our earlier criticisms by drawing on the full sample of available monthly data of individual stocks, and by performing a joint test of efficiency over all stocks. Section II describes the econometric methodology, and section III discussed the data used and the main empirical results. Some conclusions are noted in the final section.

II. METHODOLOGY Consider the following regression model which is used to test the hypothesis of efficiency in the Athens stock market. Pit = α i + ρ i Pi , t −1 + ε it

(1) 121


Dockery and Kavussanos

for i = 1,K, N and t = 1,K, I ; where Pit and Pi,t−1 are the prices of stock i at time t and t−1 respectively, εit is a Gaussian error term which may exhibit contemporaneous correlation between stocks, and αi, ρ, are intercept and slope constants relating to individual stocks. The weak form of the efficient market hypothesis instructs us that the only reliable information at time t is the last observed price, that is, Pi, t - 1.From this, the argument follows that the null hypothesis of market efficiency is H0: ρi = 1 and αi = 0 , ∀ i in Equation 1. It is usually the case that stock prices are non-stationary, in which case in order to avoid inference problems stock returns are considered, and the model thus becomes: rit = αi + εit for i = 1,K, N , and t = 1,K, T


The null hypothesis of market efficiency now becomes Ho: αi = 0 , ∀ i. Equation 2 involves a system of N equations with cross equation correlations allowed in the residuals. Zellner (1962) calls these seemingly unrelated regression equations (SURE) and finds that they provide more efficient parameter estimates compared to ordinary least squares(OLS). Apart from the increased efficiency argument it allows one to test the joint hypothesis in a multivariate framework. A Wald test statistic using only the unrestricted model, Equation 2, may be used for our purposes. Let h(a)=0 describe the set of restrictions. Given a vector of estimates a, the associated covariance estimate V(a), and the covariance matrix of the restrictionsV(h(a))=(∂h/∂a)´V(a)(∂h/∂a), the Wald test statistic, evaluated at the unrestricted estimates a, is: W = h(a) V[h(a)]−1h(a)´


This test statistic follows asymptotically a chi-squared distribution with degrees of freedom equal to the number of restrictions.

III. DATA AND EMPIRICAL RESULTS The data used in this study consist of closing stock prices observed monthly from February 1988 through to October 1994 for a total of 73 out of a possible 150 companies quoted on the ASM1. The main criterion for sampling was the period of trading activity, so securities not traded during the entire period were excluded from the sample.

Stationarity tests on logarithms of individual share prices and return series (defined for each stock as the difference in the logarithms of today’s price minus last month’s price) are first examined by Dickey–Fuller(DF) and Augmented Dickey–Fuller (ADF) tests (Dickey and Fuller,1981). The results indicate that the null hypothesis of non-stationarity is clearly rejected for all individual return series while the share price series was found to be non-stationary.2The fact that stock returns are stationary allows us to proceed with testing for stock market efficiency, in a multivariate setting. SURE methods are used for estimation, which allow for cross equation correlations in the system. Table 1 gives the Wald statistic of Equation 3. The null hypothesis is strongly rejected, indicating that the ASM is not efficient. The economic interpretation of the results here is that the statistical evidence that stock prices on the ASM are not integrated does strongly suggest that the market has not been informationally efficient during the period 1988–1994. Two main reasons may be put forward: 1 first that the ASM is not as technically organized as well-developed capital markets, and therefore information about stock prices may only spread gradually through the financial community; and second that the ASM traded stocks are likely to be less liquid, and daily trading volume low and much more unsteady than one would otherwise find on the well-developed capital markets. Consequently, the market itself may take considerable time to adjust fully to relevant information than would otherwise be expected in a developed capital market. Thus, investors are able to compute forecasts based on conditional means of prices, and so stock prices cannot be relied upon to furnish the information that investors would require which, of course, is not one of the principal characteristics associated with the concept of a perfect capital market structure. In order to examine whether the results in Table 1 are sensitive to the number of stocks included (and how representative they are of the entire ASM) in the test, and to compare our method with other studies, we perform the multivariate Wald test by including 10, 25, 30, 40, 45, 60 and 70 stocks in the SURE system of Equation 2. The results are given in Table 2. We observe that by including 10 stocks, the same as Panas (1990), the null hypothesis is clearly rejected. The results are in direct contrast with those of Panas (1990), who finds an efficient ASM through his univariate tests on individual stocks. Similarly, employing the same sample size as Niarchos and Georgakopulos Table 1. Wald test statistic and p value χ2(72) theoretical value


p value


The sample of 73 stocks includes all the stocks traded over the entire period under examination. It is worth noting here that 77 new stocks have been introduced in the ASE over the past 7 years, amounting to about one new stock per month entering the ASE. 2 The test results are obtainable from the authors upon request. 1

Testing the efficient market hypothesis


Table 2. Wald test statistics and p values for various number of stocks. χ2 statistic

Number of stocks considered 10

χ2(9) = 5.25 2

p-value 0.74


χ (24) = 25.80



χ2(29) = 31.96






χ (39) = 54.51

likely to demonstrate a greater degree on non-randomness simply beause market traders are unable to remove it.


χ (44) = 108.91



χ2(59) = 217.13



χ2(69) = 510.48


(1986), we find again that the null hypothesis is strongly rejected. In fact, when the number of stocks in the sample exceed 40 the null hypothesis of market efficiency is rejected comprehensively throughout. The results indicate that as the number of stocks in the sample increase(thereby being increasingly representative of the whole market), market efficiency is rejected. The question that naturally follows is, whether one should expect the ASM to be informationally less efficient than well-developed capital markets? The underlying reason why we, a priori, expect the ASM to be informationally less efficient than well-developed capital markets is that stock prices in a small market are less likely to follow a random walk process. Moreover, given the thinness of the ASM, it is more than likely that attempts by traders to exploit any information about future prices contained in past price data may not be worth the effort. For it may be the case that only a small number of shares can be bought on the market before stock prices are influenced by the actual buying and selling of shares which may then give rise to further fluctuations in share prices. As a result, stock prices are

IV. CONCLUSION In this letter we have investigated the price-efficiency of the ASM using well known empirical tests for unit roots in the price series. Our Wald statistical test results lead us to reject overwhelmingly the random walk hypothesis for stock prices, which is, itself, a necessary condition for stock market efficiency. In summary, our results confirm the ASE as informationally inefficient which also implies that share prices tend to move systematically over time.

REFERENCES Dickey, D. A. and Fuller, W.A. (1981) Likelihood ratio statistics for auto regressive time series with a unit root, Econometrica, 49, 1057–72. Fama, E. F. (1970) Efficient capital markets: a review and empirical work, Journal of Finance, 25, 383–417. Fama, E. F. (1991) Efficient capital markets: II, Journal of Finance, 46, 1575–617. Koutmos G., Negakis, C. and Theodossiou, P. (1993), Stochastic behaviour of the Athens Stock Exchange, Applied Financial Economics, 3, 119–26. Niarchos, N. A. and Georgakopoulos, M. C. (1986) The effect of annual corporate profit reports on the Athens stock exchange: an empirical investigation, Management International Review, 26, 64–72. Panas, E. (1990) The behaviour of Athens stock prices, Applied Economics, 22, 1715–27.

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