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City University Business School, Barbican Centre, London EC2Y 8HB, UK and ... stocks traded in the Athens Stock Exchange (ASE) are broadly not supportive ...
Applied Financial Economics, 2001, 11, 573 ± 579

A multivariate test for stock market eYciency: the case of ASE M A N O L I S G . K A V U S S A N O S * and E V E R T O N D O C K E R Y { City University Business School, Barbican Centre, London EC2Y 8HB, UK and Department of Accounting and Finance, Athens University of Economics and Business, 76 Patission Street, Athens 104 34, Greece. { Department of Economics, StaVordshire University, StaVordshire, ST4 2DF, UK

Market e ciency tests in developing markets display mixed evidence, in contrast to evidence on developed markets where the null hypothesis seems to be supported. Speci® cally, previous tests for market e ciency on the index and on samples of stocks traded in the Athens Stock Exchange (ASE) are broadly not supportive of the e cient market hypothesis. This paper introduces multivariate generalizations of the univariate Dickey± Fuller likelihood ratio tests to the class of Seemingly Unrelated Regressions, to investigate empirically the stock price e ciency of ASE. The method takes into account the contemporaneous correlation between stocks in the ASE, and avoids the sample biases which may result by considering only subsets of stocks listed in the exchange. Conclusively, the results con® rm that the ASE is informationall y ine cient, implying that past stock prices contain some information as to future price movements which investors may act on. I. INTRODUCTION The notion that a stock market is e cient, in the sense that stock prices quickly and accurately re¯ ect all available information, has long received considerable support in the ® nance literature. There is cumulative evidence in support of market e ciency of major industrialized countries’ stock markets such as the USA, the UK and elsewhere (see e.g. Fama, 1965, 1991; Dryden, 1969). The general consensus in these studies is that these markets are e cient in either weak-form or semistrong form.1;2 The issue of e ciency of smaller markets has also been undertaken by among others Hong (1978), Cooper (1982), Barnes (1986), D’Ambrosio (1980), Arrif and Finn (1989), Panas (1990), and Butler and Malaikah (1992). Thus, Barnes (1986) ® nds that the e cient market hypothesis could not be supported for the Kuala Lumpur stock market, Butler

and Malaikah (1992) unearth evidence of ine ciency in the Saudi Arabian stock market, though not in the case of the stock market of Kuwait, and Panas (1990) concludes that market e ciency could not be rejected for the Athens Stock Exchange (ASE). In weakly e cient markets investors are unlikely to make excessive pro® ts by exploiting information inherent in previous price changes. This is because, if information on prices is available to rational pro® t seeking market `agents’, arbitrage operations would ensure that security prices are at their equilibrium. A su cient condition for market e ciency is that the random walk hypothesis holds, which also suggests that stock price changes are unpredictable. Evidence of this, however, is questionable in view of the ® ndings on the predictability of stock market returns such as those of Fama and French (1988), Lo and MacKinlay (1988), and Jegadeesh (1990). Among the

* Corresponding author: E-mail: [email protected] 1 Notwithstanding, DeBondt and Thaler (1985, 1987), Lo and MacKinlay (1988), and Conrad and Kaul (1988) ® nd that some of the most developed stock markets in the world are in fact characterized by ine ciency. 2 Fama (1970) de® nes three forms of market e ciency: (a) Weak-form e ciency, under which historical market data are incorporated in current market prices, and are of no use in predicting future prices; (b) Semistrong form, under which all publicly available information, such as earnings and pro® ts/losses announcements, is quickly incorporated in prices; as a result no excess returns may be earned by investors; (c) Strong-form e ciency, under which stock prices fully re¯ ect all public and private information. Applied Financial Economics ISSN 0960± 3107 print/ISSN 1466± 4305 online # 2001 Taylor & Francis Ltd http://www.tandf.co.uk/journals DOI: 10.1080 /0960310001001300 6

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574 price `anomalies’ documented are the excess positive January returns (Gultekin and Gultekin, 1983), the larger small ® rm returns (Banz, 1981), the low Monday /high Friday eŒects (Gibbons and Hess, 1984), etc. In the weak-form sense, absolute allegiance to market e ciency necessitates, among other conditions, freely available information, competition among investors as well as instant communications. Usual explanations for the less frequent ® ndings of market e ciency on smaller markets include low liquidity, investors trading on less accurate information, less stringent information disclosure requirements, and lower technical organization of markets where less information is released by ® rms. In regard to these, it may, of course, be easier for large traders in smaller markets to manipulate the market since privileged information channels are more likely than not to exist. For example, market thinness coupled with the infrequent trading of some shares is likely to make it increasingly di cult for traders to gain new information. The present study investigates e ciency in the ASE, particularly in view of the growing interest shown by private and large institutional investors seeking to diversify their portfolios in international ® nancial markets. In view of this, the present study lends itself to an assessment of the Greek stock market in light of the reforms of the late 1980s. These were aimed largely at the liberalization and restructuring of the ASE, in addition to new laws concerning the management, organization, and regulation of the exchange; more information on these is provided in the next section of the paper. These changes have so far removed nearly all of the main administrative, political and legal constraints, which once made the ASE di cult for international investors to invest in. As a result, the ASE is now more open to private and international investors, thus giving rise to a growing awareness of the investment potential of Greek stocks. It also emphasizes the role of the ASE as a source of funds and as a determinant of a ® rm’s value and borrowing capacity. Extant tests for market e ciency in this direction are to our knowledge limited to the works of Spyrou (1998), Koutmos et al. (1993) and Panas (1990) who test for weak-form e ciency, and Niarchos and Georgakopoulos (1986) who consider semistrong form e ciency. Spyrou (1998) examines the value weighted ASE index for weak form e ciency using variance ratio (random walk), seasonality and nonparametric (runs) tests. Using daily and monthly data he rejects market e ciency. Similarly, Koutmos et al. (1993) in examining the conditional mean

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M. G. Kavussanos and E. Dockery of weekly returns of the value weighted ASE index ® nd that weak-form e ciency, or equivalently the nonpredictability of returns is rejected, since past returns ± a dummy and the conditional standard deviation of returns ± can explain current values. Panas (1990) in examining monthly data on ten stocks listed in the ASE 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 weak-form e cient. For their part, Niarchos and Georgakopoulos (1986) in utilizing monthly data for a nonrandom sample of 25 stocks test for semistrong form e ciency and observe that investors tend to react slowly and gradually to accounting information, thereby rejecting market e ciency. The results from tests employed in all these studies may be improved upon. First, in the study by Panas (1990) only ten stocks of the ASE were examined. Hence, it is possible that the selection of only a `small’ subset of stocks may lead to false acceptance of e ciency for the whole market. Along the same lines, it may be argued also that testing for e ciency on stocks individually is likely to be statistically less e cient if there are signi® cant cross stock correlations. This paper proposes a test which can take these problems into account. The work of Niarchos and Georgakopoulos (1986) is also subject to similar criticisms. In their work, Koutmos et al. (1993) and Spyrou (1998) rely on the general ASE index in order to examine the predictability of returns. Here, we are mindful that well known stock market anomalies such as thin and nonsynchronous trading3 and the `size’ problem may also lead to spurious indications of return predictability in the general index. The present paper seeks to make a contribution to the empirical literature by using the Seemingly Unrelated Regression (SURE) approach to test the e cient market hypothesis for the Athens stock market. The full sample of available monthly data on individual stocks is used to perform joint tests of e ciency over all stocks, thus taking into account the possibility of cross equation correlation. The outline of the paper is as follows: Section II provides some institutional information on the Greek stock market. Section III outlines the econometric methodology for the analysis undertaken. Section IV discusses the data used and the main empirical results. A summary of the main ® ndings, conclusions, and implications is provided in Section V.

Nonsynchronous trading arises because small capitalization stocks trade less frequently than larger ones. Thus, new information is assimilated ® rst by larger capitalization stock prices and then into smaller capitalization security prices with a lag. This lag induces signi® cant positive correlation, say, in equally weighted indices. The problem is mitigated somehow when examining value weighted indices, as in the above studies.

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Multivariate test for stock market eYciency I I . T H E S T R U C T U R E O F T H E A TH E N S S T O C K EX C H A N G E The Athens stock exchange is the only stock market in Greece, constituting a smaller, thinner, and less liquid stock market in comparison to the major stock markets of the European Union. Developed markets are, in the main, characterized by active trading, large turnover, timely disclosures, minimum barriers to entry, considerable opportunities for diversi® cation, and communication of more accurate information. Thus on the basis of these de® ning characteristics, the ASE may be regarded as a developing stock market which, since the late 1980s, has grown rapidly in terms of trading value.4 Since the late 1980s, the institutional setting is being liberalized with technical changes, which are aimed at improving the overall workings of the market. The major changes, by way of legal provisions, namely Law 1806 and Law 1969, provided the legal framework for the establishment of the Parallel Market and the Central Securities Depository, and paved the way for the modernization of the ASE.5 Other changes in this direction consisted of the introduction of brokerage companies, the clear delineation of their rights and obligations, tighter systems of management controls, stricter monitoring against insider dealing, and the introduction in 1992 of the Automated Exchange Trade System (AETS).6 Table 1 presents summary statistics on the ASE over the sample period 1988± 1994. The changes in regulation and liberalization of the market, coupled with the greater degree of transparency and, with it, more reliable information, increased interest in the ASE, resulting in companies entering the market since 1988 at an average rate of one per month. This brought about an increase in market value from US $4285 million to US $14 921 million over the period. In 1998 it represented 40% of the country’s GDP. The value of trading over the period increased from US $313 million in 1988 to US $5145 million by the end of 1994. From the above discussion, it is evident that, like most emerging capital markets, the ASE has many characteristics found in developing economies. It is relatively thin 4

Table 1. Yearly statistics for ASE 1988-1994 Year

Market value (US$ million)

Trading value (US$ million)

Number of listed ® rms

1988 1989 1990 1991 1992 1993 1994

4285 6376 15 228 13 118 9489 12 319 14 921

313 549 3924 2443 1605 2713 5145

119 119 145 126 129 143 216

Source: Adapted from Emerging Stock Market Factbook 1995, International Finance Corporation, Washington, DC.

(with low trading volume) and is subject to nonsynchronous trading resulting from the periodic trading by individual `agents’, largely as a result of information, decision, and transaction costs.7 The question, however, to both foreign investors and to the local economy is whether the changes taking place have a signi® cant impact on the e cient functioning8 of the ASE.

I I I . M E T H O D O L O G I C A L FR A M E W O R K In the ® nance literature, the question of market e ciency is most often examined by investigating whether prices in capital markets display patterns, which allow prices to be predicted and, thus, enable unusual pro® t opportunities on the market to be realized. For a market to be e cient such patterns should not be present and prices should follow a random walk process, or at least be a martingale. From this, it follows that given a cross section of stock prices over time a regression equation of the following order may be used to test the hypothesis of e ciency in the Greek stock market. Pit ˆ ¬i ‡ »i Pi;t¡1 ‡ "it

i ˆ 1; . . . ; N

t ˆ 1; . . . ; T

…1†

Where, Pit and Pi;t¡1 are the prices of stock i at time t and t ¡ 1 respectively, and "it is a Multivariate Normal

As well as stocks, securities traded on the ASE include bonds of domestic and foreign corporations that satisfy speci® c requirements. Corporations listing shares and bonds are required to have equity of at least 170 million drachmas and must be able to demonstrate operating pro® ts for the last ® ve ® nancial years. Firms listed and traded on the ASE are also required to publish ® nancial statements, which are themselves audited and approved by the committee. 5 This also included the creation of a capital market committee, whose remit also includes the expulsion of ® rms from the exchange, the approval of issuance of new securities, and decisions on the appointment of new brokers. 6 Prior to the introduction of AETS trading in shares operated through an open outcry system. Also, the market saw the establishment of 8% and 4% price limits for the more and less actively traded stocks, respectively; see Phylaktis et al. (1999) for the eŒect of these price limits on the volatility of the ASE index and stocks listed in the exchange. Recent developments in the ® nancial markets have seen the widening of price limits to 10% and the introduction of new investment instruments in the form of futures contracts. 7 These problems are, in the main, a consequence of nonsynchronous price behaviour in the Greek stock market, due to the ASE trading mechanisms. 8 An e cient market facilitates the allocation of scarce capital resources and the ensuing economic progress.

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M. G. Kavussanos and E. Dockery

Gaussian error term which may exhibit contemporaneous correlation between stocks, and ¬i , »i are intercept and slope constants relating to individual stocks. Speci® cally, the weak-form version of the (E cient Market Hypothesis) EMH instructs that successive returns generated by an e cient market will be independent; essentially they will mimic a random walk.9 Here, the weak form of the e cient market hypothesis asserts that the only reliable information at time t is the last observed price, that is Pi;t¡1 . From this, the argument follows that for the null hypothesis of market e ciency to hold one would expect H0 : ¬i ˆ 0 and »i ˆ 1, 8i in Equation 1. Alternatively, the hypothesis may be formulated in terms of the following equation: ¢pit ˆ ¬i ‡ ¯i pi;t¡1 ‡ "it

i ˆ 1; . . . ; N

t ¡ 1; . . . ; T

…2†

where small p’s refer to logarithms of prices and ¢pit are ® rst diŒerences of these logarithms, indicating returns.10 The null hypothesis of market e ciency now becomes H0 : ¬i ˆ 0 and ¯i ˆ 0; 8i. Single equation methods for testing market e ciency take each individual stock and test the above null hypothesis, using the statistics suggested by Dickey and Fuller (1979, 1981). The statistics proposed by Dickey and Fuller were, among others, the t-statistic for a unit root on » (or equivalently ¯) and the likelihood ratio test of the joint hypothesis …¬; »† ˆ …0; 1†: This paper suggests a multivariate version of the above test in a setting which allows cross equation correlations between individual stocks. In particular, using matrix notation, denote the multivariate normal distribution of the vector error term in Equation 1 or 2 as: " ¹ MIN …0; § « IT †

…3†

where § is the N £ N contemporaneous covariance matrix, assumed to be positively de® nite and symmetric. The setting as described involves a system of N equations with cross equation correlations allowed in the residuals which Zellner (1962) refers to as Seemingly Unrelated Regression Equations (SURE), and which are known to provide more e cient parameter estimates as compared to Ordinary Least Squares (OLS). Aside from the increased e ciency argument, the SURE method also allows one to test the joint hypothesis within a 9

multivariate framework. In this connection, the appropriate statistic to use in this type of multivariate setting is a likelihood ratio test statistic which in fact is similar to the univariate test of Dickey and Fuller (1981), but has the following structure: ¡2 ln ¶ ˆ T ‰ln j§R j ¡ ln j§U jŠ

…4†

where §R and §U are the estimated restricted and unrestricted estimates of the residual covariance matrix §. Theoretically, the statistic in Equation 4 follows a chisquare distribution with 2N degrees of freedom. And just as in the univariate test of Dickey and Fuller (1981), the ® nite sample distribution of the statistic is unknown and should therefore be derived empirically. On this basis, Monte Carlo simulations are employed in order to derive critical values of the empirical distribution at the upper 10% , 5% and 1% levels. The simulation procedure is performed as follows. First, the data generation process is based on the autoregressive model of Equation 2 on the speci® c assumption that the null hypothesis is true …H 0 : ¬i ˆ 0 and ¯i ˆ 0, 8i ). The sample size is then chosen to equal the number of observations available, that is T ˆ 75, and the number of equations equals the number of stocks, N ˆ 64. In each simulation, N error terms are generated jointly T times from a multivariate normal distribution with mean 0 and a given covariance matrix, but with the latter corresponding to the variance covariance matrix of the actual stock returns. The procedure just described allows simulation of ¢pit from model (Equation 2) and computation of a sample value of the test statistic given in Equation 4. Each experiment is then replicated 250 times to generate a sample distribution of the statistic under H0 . Table 2 reports the critical values of the statistic at the upper 10% , 5% and 1% levels.

IV. DATA AND EMPIRICAL RESULTS The sample used in this study consists of closing Greek stock prices observed monthly from February 1988 through to October 1994 for a total of 64 out of a possible 216 companies quoted on the ASE.11 The main criterion for sampling was the period of trading activity, so securities

Speci® cally, the random walk theory assumes the current price of a security re¯ ects all available information, so that only the arrival of new information will cause the price to change. Notably, a random walk model assumes that successive one-period price changes are both independent and identically distributed; see Fama (1970, pp. 380± 90). 10 As in previous studies logarithms of price diŒerences are used because there is evidence to suggest that variance in price changes is a function of the price level. Moreover ln …Pt=Pt¡1 † is approximately the rate of return from continuous compounding over the time period t ¡ 1 to t. 11 The sample of 64 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 period 1988 to 1994, amounting to about one new stock per month entering the ASE, adding breadth and diversi® cation.

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Multivariate test for stock market eYciency Table 2. Multivariate likelihood ratio test statistic and critical values at the upper 10% , 5% and 1% levels of the sampling distribution, derived under the Null of market eYciency. 250 simulations. N ˆ 64 and T ˆ 75.

Table 3. Multivariate likelihood ratio test statistic and critical values at the upper 10% , 5% and 1% levels of the sampling distribution, derived under the Null of market eYciency ± 250 simulations. Sample period: 1988:2 ± 1994:10

Number of stocks

10%

5%

1%

LR

Number of stocks

10%

5%

1%

Statistic

64

312.91

345.11

401.29

485.56

10 20 30 34 35 36 37 38 39 40 45 50 60 64

54.98 110.09 168.65 191.96 194.99 205.59 210.06 217.32 221.13 220.60 245.78 279.93 310.50 312.91

58.02 115.20 176.95 201.07 203.15 217.39 219.06 223.05 231.55 233.29 255.77 292.26 340.39 345.11

64.69 120.97 185.74 213.94 216.46 241.32 234.37 240.10 244.03 262.40 274.32 326.13 373.79 401.29

32.41 73.58 153.40 187.07 203.95 210.75 222.57 226.87 248.68 245.49 319.69 321.75 456.23 485.56

44.76

48.54

53.17

54.66

not traded during the entire period were excluded from the sample. Stationarity tests on logarithms of individual share prices and return series (de® ned for each stock as the difference in the logarithms of today’ s price minus last month’s price) are ® rst examined by Dickey± Fuller (DF) and Augmented Dickey Fuller (ADF) tests; see for example Dickey and Fuller (1981) . The results indicate that the null hypothesis of nonstationarit y is clearly rejected individually for each return series, while the share price series was found to be nonstationary.12 As a consequence, SURE methods were used to estimate the 64 stocks jointly so as to allow for cross equation correlations in the system. The observed value of the statistic in Equation 4 is then calculated and the empirical distribution of the statistic and the upper 10% , 5% and 1% critical values are derived and reported in Table 2. The observed value of the statistic is 485.56 which is well above the derived critical values at all levels of signi® cance. Clearly, the null hypothesis is strongly rejected, indicating that the ASE is informationally ine cient. Hence, it may be argued that the regulatory and institutional changes which have been alluded to have, it would appear, not yet brought about more and better quality of information and perhaps better informed investors. For it would seem that poor quality information, institutional restrictions on trading and possibly uninformed investors appear to have resulted in ine ciency.

Sensitivity analysis In order to examine whether the above results are sensitive to the number of stocks included (and how representative they are of the entire ASE) in the test, the multivariate likelihood ratio test is performed and derive the critical values from its empirical distributions by including 10, 20, 30, 34 up to 40, 45, 50, 60 and 64 stocks within the SURE system of Equation 2. The results are reported in Table 3. It is observed that by including up to 34 stocks in the system, the null hypothesis of market e ciency is not rejected at all reported levels of signi® cance. But when 12

Panas’ 8 Stocks

the number of stocks in the sample is greater than 34 the null hypothesis of market e ciency starts being rejected as the number of stocks increases, and moreover, at gradually smaller and smaller levels of signi® cance. In short, the results indicate that as the number of stocks in the sample increases (thereby being increasingly representative of the entire market), market e ciency is overwhelmingly rejected. In order to compare our result with previous work on the e ciency of the Greek Stock Market, the ® ndings are compared with those of Panas (1990). He alludes an e cient ASE through his univariate tests on ten stocks; we consider the same stocks included in his sample.13 First, univariate unit root tests do not reject the null hypothesis, which is in line with Panas’ results. However, when the joint test of Equation 4 is employed in the multivariate SURE system for the same securities, the statistic overwhelming rejects the null hypothesis of market e ciency. The most likely explanation for the results that the ASE has not been informationally e cient during the sample period 1988± 1994 may be because the ASE is not as technically organized as well developed capital markets, and thus information about stock prices may only spread gradually through the ® nancial community. Second, since stocks traded on the ASE are likely to be less liquid, and daily trading volume is low and much more unsteady than one would otherwise ® nd on the well developed capital markets of the European Union, the market may take con-

The test results are obtainable from the authors upon request. These are: National Bank of Greece, Bank of Crete, Commercial Bank, Ionian Popular Bank, Mortgage Bank, Credit Bank, General Cement, Titan (Cement Co). Piraiki-Patraiki has closed down since, and data for Chemical fertilizers could not be obtained. 13

578 siderably more time to adjust fully to relevant information than in developed markets. One additional and noteworthy feature of what has just been argued is that investors are only then able to compute forecasts based on conditional means of prices, and so stock prices cannot be relied upon to furnish the information that most investors would require which, of course, is not one of the principal characteristics that one would normally associate with the concept of a perfect capital market structure. The question that naturally follows from what has been argued hitherto, is whether one should expect the ASE to be informationally less e cient than well developed capital markets? The underlying reasons why, a priori, the ASE is expected to be informationally less e cient than well developed capital markets is that stock prices in a small market are less likely to follow a random walk process. Given the thinness of the ASE, and the infrequent trading of stocks it is more than likely that any attempts by traders to exploit any information about future prices contained in past price data would not be worth the eŒort. For, indeed, it may be the case that only a small number of shares can be brought on the market before stock prices are again in¯ uenced by the actual buying and selling of shares which may then give rise to further ¯ uctuations in share prices. In consequence, stock prices are likely to demonstrate a greater degree of non-randomnes s simply because market traders are unable to remove it.

V. C ONCLUSION This paper investigates the e cient functioning of ASE for the period February 1988 through to October 1994. It extends the univariate Dickey± Fuller test into a multivariate setting in a system of Seemingly Unrelated Regression Equations (SURE), which covers all stocks in the market. The use of SURE takes into consideration the cross equation correlation one would expect to ® nd between stocks listed in the same stock exchange. In addition, it discounts the possibility of results, based only on a sample of stocks, being sample speci® c, and examines instead the whole spectrum of stocks in the market in a more robust setting. Indeed, simulations of multivariate market e ciency tests, with only a subset of stocks included, indicate that results are biased if only part of the market is considered. This calls into question the reliability of results on weak and semistrong market e ciency on ASE reported in the literature. The tests suggest that the e cient market hypothesis cannot be con® rmed for the ASE. Rejection of e ciency implies the presence of unexploited pro® t opportunities for 14

M. G. Kavussanos and E. Dockery `agents’ participating in the market. The reasons for ine ciency are due, it is believed, to several micro market factors. These include, amongst others, the low liquidity of the market, the restricted supply of stocks14 and the limited transparenc y of information; the latter being a result of limited enforcement of disclosure regulations and the use of the open outcry system (in part of the sample). Thus, it appears that despite the changes to improve the overall functioning of the market, there still remain more structural and institutional problems that need correcting. The ® ndings have immediate implications for investors and policy makers alike. First, if not addressed, the ine ciency of the ASE could well limit the potential of the capital market to allocate funds to the most economically e cient and productive sectors of the Greek economy, and possibly repress long-term growth. Second, it could potentially slow the government’s plans to privatize some key industries, which is central to current plans to restructure and improve the performance of state owned enterprises. At the margin, there is clearly room for more deregulation, and more timely and accurate disclosures may well help to make the market more e cient.

ACKNOWLEDGEMENTS Comments of participants at the International Economics and Finance Society (IEFS) conference in London, April 1999, and of an anonymous referee have helped to improve an earlier version of this paper. The authors are also grateful to Spyros Malavazos for his help with the data.

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The major banks and large institutions continue to hold a large percentage of stocks.

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