### Test the Efficiency of Chinese Stock Market

Introduction

## 1. Background

Osborne (1959) proposed that the movements of stock price are similar to the “Brownian motion” in the area of chemistry which mentions the never-ending and disorder movement of the particles that suspended in liquid or gas. Since the feature of “random walk”, the path of the share price is unpredictable. Fama also recognized that the return of stock price has no “memory”, according to Fama (1965, 1970), the share prices in the stock markets are following the random walk, which indicates that in efficient stock market, the current share prices reflect all of the available and relevant information immediately and rationally. In that case, the current share prices in a financial market will be equal to the optimal forecasts using all available information (Fama, 1970).

Based on the “random walk theory”, Fama proposed “Efficient market hypothesis”, it implies that in the condition of efficient stock market, investors cannot predict future trends of the share price by using the historical data, thus no abnormal return exist in the efficient market since the prices reflect all the relative information immediately (Fama, 1970). According to Fama’s efficient market hypothesis, there are three levels of efficient market, weak form efficiency; semi-strong form efficiency and strong form efficiency (Fama, 1970).

Based on Fama’s theory, in the recent years there are many researches are related to the stock returns in financial economics. There are also a vast number of empirical researches of the stock price in both developed and developing countries. The tests had different results, for instance, most early research is supportive of the weak and semi-strong forms of the efficient market hypothesis in developed capital markets (see, e.g., Osborne 1962; Granger and Morgenstern 1963; Fama 1965; Ball and Brown 1968). Recent research, however, has reported that stock market returns are predictable (Poterba and Summers 1986; Fama and French 1988; Lo and MacKinlay 1988). The empirical evidence is also mixed for the developing countries. These studies 2 on emerging stock markets can be divided into two groups depending on findings. Researches who finds the evidence to support the weak-form efficiency (e.g., Urrutia 1995; Ojah and Karemera 1999; Abrosimova et al. 2005; Moustafa 2004), and others shows the evidence of predictability or rejection of the random walk hypothesis in stock returns (e.g., Huang 1995; Poshakwale 1996; Mobarek and Keasey 2002; Khaled and Islam 2005).

1.1.1 Chinese stock market

According to the above results, and considering the fastest economic gowning in China and the rapid development of Chinese stock market in recent years, a motivation to test the emerging stock market, namely Chinese stock market is emerged.

China has two stock markets—Shanghai stock market and Shenzhen stock market, and both of the markets classified stocks into A-share and B-share that are available for Chinese residents (Ma, 2004). The Shanghai Stock Exchange was found on 26th November 1990 and the Shenzhen Stock Exchange started on 3rd July 1991 (Liu, 2010). Since 2000, the government of China made the market-oriented policies, under the effective organization, both of the stock markets expanded rapid and have operated in an increasingly regulatory circumstance. Indeed, as the second large capital market in Asia, Chinese stock market is one of the most rapid growing emerging markets (Chung, 2006).

There are previous researches related to the test of the efficiency of Chinese stock market and the other emerging markets. (e.g.,Harvey 1993, Laurence et al. 1997; Mookerjee and Yu 1999; Lima and Tabak 2004, Ma 2004, Chung 2006, Liu 2010). Despite some studies shown that the emerging markets are not as nonrandom as thought, most of the studies indicated that the emerging markets are less efficient than the developed markets, even most of the researches explained the prices change in the Chinese stock markets are nonrandom walk. However, most these studies are concentrated on the initial years of the Chinese stock markets established. With the rapid development of the stock market in the recent years, under the circumstance of increasingly privatization and liberalization, nowadays Chinese stock market should be more than weak form efficiency, this study attempted to test the weak form efficiency and also semi-strong form efficiency of Chinese stock market using a vast number of indexes and data of both Shanghai stock market and Shenzhen stock market.

### 1.2 Objectives of the study

### 1.3 Scope of the study

### 1.4 Limitations of the study

## 2. Theoretical and empirical review

### 2.1 Concept of the efficient market hypothesis (EMH)

According to Fama (1965, 1970), in an efficient market, the stock price accurately reflect all of the available and relevant information instantaneously, in that case, investors in the efficient market could only receive normal return since the stock price change immediately with the information.

Fama’s paper “Efficient Capital Markets: A Review of Theory and Empirical Work” in 1970 be viewed as the earliest formal foundation of efficient market hypothesis and in the paper he pointed out three conditions of the existence of efficient market, no transaction costs, free information and all participants have the same preference in front of profit maximization, risk aversion, and sufficient acknowledge of the market and mentioned that in the circumstance of efficient market, the current price “fully reflect” all of the available information correctly and immediately (Fama, 1970).

Fama’s theory on efficient market hypothesis is concentrating on how market using information, while some other ideas keep on the relationship between investors and share prices (Chung, 2006). There are also some critical voices to the efficient market hypothesis, such as Leroy (1989) view efficient market hypothesis as empty and tautological since it did not point out how to use all of the information to determine share price. Despite that, the Fama’s theory of efficient market hypothesis is commonly acceptable in the research of determining the efficiency of the market.

Based on the assumption of “fully reflect” all of the available information, and all investors are rationally enough, the model of the efficient market can be explained as follow:

(Mishkin and Eakins, 2009)

= the current prices

= the optimal forecasts using all available information

Fama (1970) pointed out the three forms of market efficiency, which are weak form efficiency, semi-strong form efficiency and strong form efficiency. There are relationship among the three types of market efficiency, the weak form efficiency is included in the semi-strong form efficiency, while the strong form efficiency conclude both of weak form and semi-strong form efficiency (Fama, 1970).

2.1.1 Weak form efficient hypothesis

Weak form efficiency is the lowest level of the market efficiency, in a weak form efficient market, share prices full reflect all of the information regarding to the historical movement of the price (Fama, 1970). In other words, in the condition of weak form efficiency, future price of the stock could not be predicted by tracing the past path of the price, investors could not obtain abnormal profits by analyzing the historical prices information (Samuelson, 1965).

Based on the theory of weak form efficiency, to test whether the technical analysis of the past prices could make abnormal return could test whether the market is weak form efficiency. There are some specified methods that can be used to test whether the market is weak form efficiency, such as the filter approach and test the random walk hypothesis (Ma, 2004). The Historical evidence on weak form of market efficiency are as follow.

**Evidence from tests of the random walk hypothesis**

In order to test the weak form market efficiency, the serial correlation between the security’s current return and its historical return are applied in the investigations (Fama, 1965).

Bachelier (1900) performed a research about the French government bonds and found that the bonds follow a random walk, which seemed to be the first test of the random walk. Kendall (1953) had researched the British securities’ by tested correlation of weekly prices and got the independent time series of prices. Roberts(1959) used the weekly change of Dow Jones Industrial Average (DJIA) to examine whether the share prices can be replicated in assumption of the prices are following random walk, and the result of his study support the random walk theory. Osborne (1959) attributed an economic rationale behind the random walk, he views that individuals have separately ideas when facing the information, which is the reason of securities prices’ independently change. Cootner (1962) found that since the information appears independent, so the share prices changed with the information following the random walk. Granger and Morgenstern (1963) studied the independence of the successive share prices movements and the outcome also verified the similar result about the random walk. In the year of 1965, Fama had tested 30 securities’ daily return in Dow Jones Industrial Average between 1957 and 1962 by using serial correlation test, run test and Alexander’s filter rules. The result is a very small positive correlation coefficients and his test is also support that share price following random walk (Fama, 1965). Poterba and Summers’ (1988) further study presented that share returns are positive correlated in short period and negative correlated during the long period by studying the share returns from the New York Stock Exchange and 17 other stock markets.

On the other hand, there are also some evidences appear contrast with the weak form efficient hypothesis. Timothy (1993) shows his finding which is against the hypothesis of weak form efficiency since the transaction costs delay the timing of price adjustment and cause the correlation of share returns. Richard and Starks (1997) argued that the professional investors’ correlated trading pattern is the reason of the autocorrelation of share returns.

** Evidence from tests of trading strategies **

With the purpose of test the weak form efficiency, some trading strategies are used in the researches. The filter approach as one of the essential trading strategy is usually designed to track the essential movement of share prices on the base of any percentage (Kisor and Messner, 1969). For instance, selling a share once it falls 5 percent of its previous high point, and buying a share if it rises 5 percent from the previous low point. If use such a strategy, the investors could receive excess profits, it could be suggestive of weak form inefficiency (Kisor and Messner, 1969).

Alexander (1961) applied filer rule methodology to test the random walk, by analyzing the prices changes from 5 percent to 50 percent, Alexander tested Dow Jones Industrial Average from 1897 to 1929 and the Standard and Poor’s index of S&P 500 between 1929 and 1959. The consequence of his studies is that such trading strategy can not generate higher return than simple buy-and hold strategy after transaction fees were taken into account. Fama and Blume (1966) tested 30 securities in Dow Jones Industrial Average by using 24 different filters ranging from 5 to 50 percent. They found that the 5 percent of filter strategy can obtain much higher than buy-and hold strategy, however, after the transaction costs taken into account, the profit is lower than buy-and hold strategy. Consequently, the outcome of their examination is that no matter what size of filter be used, no extra returns can be generated by using filter strategy. Ball (1978) had added the condition of risk into consideration when testing the Melbourne Stock Market and the conclusion of his test is also consistent with the weak form efficiency.

However, Bertoneche (1981) applied two strategies (spectral analysis and filter rules) to test the same stock markets (New York Stock Exchange and six European stock markets) during the same periods (from 1969 to 1976), the outcomes are opposite. Bertoneche (1981) concluded that the spectral analysis is not powerful enough and the stock markets are not weak form efficiency.

** Anomalous evidence of the efficient market hypothesis **

There are also some anomalies (such as day-of-week effect, month-of year effect, holiday effect) existing in the stock markets, De Bondt and Thaler (1985) analyzed some portfolios with better returns and worse returns in the interval of three years; they found that the superior portfolio were underperformed in the last three years and he viewed that there should be some implications by analyzing the past path of stock price.

The seasonal effect is the important anomalous which expressed as that stock returns change regularly in some special time, such as day-of-week effect and January effect (Ma, 2004). Fields (1931) tested Dow Jones Industrial Average from 1915 to 1930 and first found that there was day-of-week effect in the market. Cross (1973), French (1980), Jaffe and Westerfield (1985), Ball and Browers (1988) and some other scholars also verified the existence of the Monday effect in many stock markets. Wang (1997) found that the Monday effect had been disappeared in the U.S stock market by analyzed the data of the market during the period between 1962 and 1993. Wachtel (1942) first found the January effect which express as stock returns in January is higher than any other month. After that, Rozeff and Kinney (1976), Brown (1983), Tinic (1987), Reinganum and Shapiro (1987), Agrawal and Tandon (1994) Mookerjee and Yu (1999) found that in January, stock returns normally higher than the other months in most of the stock market.

Despite the existence of anomaly, it is hard for investors to get abnormal returns purely by analyzing the historical prices and most of evidence support that the stock markets are following random walk and the markets are weak form efficiency ().

2.1.2 Semi-strong form efficiency and tests

In the semi-strong form efficient market, the securities prices fully reflect all of the publicly available information, which include not only past prices but also technological breakthrough, earnings data, stock splits and dividend announcement (Fama, 1970). In case of the semi-strong form efficient market, no market participant has time to make superior returns based on analyzing the announcements, since the share prices had adjusted to the new information instantaneously (Fama, 1970).

** Historical evidence on semi-strong form of market efficiency **

The test on semi-strong form efficiency focuses on whether the securities prices adjust to the new public information fully correct and immediately, in other words, after the announcement of the information, whether the investors could benefit by analyzing the announced information (Fama, 1965). The pioneers of this field is Fama, Fisher, Jensen and Roll (1969), they examined 940 stocks in the New York Stock Exchange during the period from 1927 to 1959 and found that through the method of purchasing split securities after the announcement of split is announced could not increase the expected returns. The results support the semi-strong form efficiency. Brown (1970), Brown (1972), Brown, Finn and Hancock (1977) studied the Half-year and annual profit announcements and the evidence shows that share prices concluded all the published information immediately, the evidence supports the theory of semi-strong form efficiency.

On the other hand, there are also evidence shows that in some conditions, markets are not semi-strong form efficiency; Scholes (1972) tested the shares in New York Stock Exchange between July 1961 and December 1965 and found that superior returns existence as the corresponding to insiders’ block transaction. Ibbotson (1975) represented that in the first month of new issue, initial purchasers could obtain superior returns, and the return will lower to the average level in the third month. Kahenam and Tversky (1982) explained that for the reason of investors’ overreaction, a strategy that buying stock that undervalued and sell the stock which overvalued will accept over average profits. Rendleman, Jones and Latane (1987) tested the performance of the shares during the periods of announcements, he found that the prices adjusted before the announcement published and commonly overreact to the announcement, which is inconsistence with the semi-strong form efficiency. Lewellen and Shanken (2002) suggest that some variables such as interest rates, financial ratios could be used to predict the securities prices in stock markets.

2.1.3 Strong form efficiency and tests

In the strong form efficient market, securities prices correctly and fully reflect all of the available information, includes historical information, private information and public information (Fama, 1970). In such condition, all of the market participants, including the ones who monopolistic access the inside information, have no chance to get abnormal returns in the strong form efficient market since all the information have been incorporated into the share prices (Fama, 1970).

**Historical evidence on strong form of market efficiency **

In the assumption of strong form market efficiency, the average prices of the securities must be separated from the distribution of information and investors have the same value preference of the information (Ma, 2004).

If the insider has the chance to access the privilege information and buy the shares before the information publication and sell them after the price increase with the information, it will be viewed as the contradiction with the strong form efficiency (Fama, 1970).

Empirical tests of the strong form efficiency are focus on whether the managers, analysts, professional investors have chance to obtain the inside information and whether they could benefit from the inside information (Fama, 1970).

Jensen (1969) evaluated the fund managers’ performance by studying 115 mutual funds of the United States during the year from 1955 to 1964, he got the consequence that after the deduction of management fees and some other fees, the mutual funds did not outperform the average performance, the consequence support the strong form efficiency of the United States stock market. Diefenbach (1972) reported that the over average performance and superior profits of the professional investors is due to chance.

On the contrary, Niederhoffer and Osborne (1966) have mentioned that on the New York Stock Exchange, the specialists could obtain superior returns by using their monopolistic rights to get inside information. Jaffe (1974) found that insiders can get over average returns by investigating the inside trading of the 200 companies of the United States. Ippolito (1989) analyzed 143 mutual funds in the United States between 1965 and 1984, he found the returns of mutual funds were 0.83 higher than the Sharpe-Lintner market line and got the conclusion that there were inside trading.

### 2.2 Empirical work on efficiency

The stock markets around the world have different background and grown up with the different government, some of the stock markets are developed markets, such as the United Stated stock market, the United Kingdom stock market, the Japanese stock market, they are more liberal; on the other hand, there are also some emerging stock markets such as the Latin American stock markets, the Indonesia stock market, which present more restriction (Risso, 2009). Particularly, the efficiency of the stock markets expressed different and the developed markets normally performed more efficient then the emerging markets under the same circumstance (Risso, 2009). It is necessary to discuss the developed markets and the emerging markets separately.

2.2.1 Evidence from developed stock market

**Empirical test of the United States stock market**

As one of the most essential stock market, the efficiency of the United States stock market attracted many scholars attention. In terms of weak form efficiency, Fama (1965) researched the Dow Jones Industry Average in the period from 1957 to 1962 and the result supports to the weak form efficient hypothesis. Alexander (1961) developed the trading strategy of filter rules to test the Dow Jones Industry Average (DJIA) (1987–1929) and Standard and Poor’s index of 500 stocks (S&P 500) (1929–1959) and the result also support the random walk theory. The study of Fama and Blume (1966) about the Dow Jones Industrial Average (DJIA) by using filter rules also sustain the weak form efficiency. On contrary, Fields (1931) examined the Dow Jones Industrial Average (DJIA) from 1915 to 1930 found the day-of-week effects; similarly, Cross (1973), French (1980) also certificated the day-of-week effects in the Standard and Poor’s index of 500 stocks (S&P 500). Lo and MacKinlay (1988) also found significant positive serial dependence in the consequently weekly stock price indexes and single securities. Rozeff and Kinney (1976), Keim (1982), Sias and Starks (1997) and some others also represented evidence of the month-of-year effects in the U.S. markets. And Keim (1982) viewed there were relationship between the January effects and company size while Schultz (1985) explained the reason of the January effects in the U.S. as the result of tax regime. Field (1931) and Smidt (1988) found the pre-holiday effects in the U.S. since the stock prices increased significantly on the days in advance of public holidays.

Regarding to semi-strong form efficiency, Fama, Fisher, Jensen and Roll (1969) investigated the stock splits on the New York Stock Exchange from 1927 to 1959, and outcome to be semi-strong form efficiency. However, Scholes’s (1972) and Chan’s (1988) results show that the New York Stock Exchange failed to support the semi-strong form efficiency. Busse and Green (2002) also found that in the U.S. stock market, share prices react to positive announcement much quicker than the reaction to the negative announcement.

As to the strong form efficiency, Jensen’s (1969) and Diefenbach’s (1972) researches consistent with the strong form efficient hypothesis in the U.S. stock market. In contrast, more evidence appear that there are inside trading or abnormal return existing in the U.S. stock market, such as the results of Jaffe (1974), and Ippolito (1989).

** Empirical test of the European developed stock markets**

As the typical case of developed markets, European stock markets are tested by many scholars. As regards to the weak form efficiency, Kendall (1953) investigated the British stock market and concluded that British stock coincide with weak form efficiency. Bird (1985) tested the London Metal Exchange and viewed it is weak form efficiency. Hudson, Robert, Dempsey and Keasey (1996) represented trading strategy cannot bring abnormal return in the United Kingdom stock market and the market is consistent with the weak form efficiency. While according to the other scholars, such as Reinganum and Shapiro (1987) identified the existing of the January effects in the United Kingdom. The results of Jennergren (1975) and Hunter (1998) indicate that the trading strategies are useful in the stock transaction in Swedish market, and Jamaican Stock Exchange, separately. Al-Loughani and Chappel (1997) applied Dickey-Fuller unit root, Lagrange Multiplier (LM) serial correlation and Brock, Dechert and Scheinkman non-linear tests to investigate the United Kingdom stock market and the conclusion rejected the weak form efficient hypothesis.

Goss (1983) represent the London Metal Exchange is semi-strong form efficiency.

**Empirical tests of the other developed markets**

There are various empirical tests of the efficient market hypothesis and as to the developed markets, the essential evidence as follow: Ball (1978) used filter rules tested the Australia stock market and his result was accordance with weak form efficiency. Laurence (1986) had examined Kuala Lumpur stock market and Singapore stock market and concluded that both markets are following random walk. Lee (1992) tested the U.S. market and 10 industrialized countries’ markets by using variance ratio test and the outcome of his research is consistent with random walk. Choudhry (1994) had studied seven OECD countries’ markets with the Augmented Dickey-Fuller and KPSS unit root tests and the consequence support the random walk in such markets. Cheung and Coutts (2001) confirmed the Hang Seng Index of Hong Kong was following random walk. Huang (1995) employed variance ratio statistics to test nine Asian stock markets (Hong Kong, Japan, Korea, Singapore, Malaysia, Indonesia, Thailand, Philippines and Taiwan), only Japan, Indonesia and Taiwan’s markets support random walk. Brown, Keim, Kleidon and Harsh (1983) found evidence of the month-of-year effect existed in Australian; Gultekin and Gultekin (1983) and Agrawal and Tandon (1994) also verified the existence of such effects in global markets. Ball and Bowers (1988) represented that despite the existence of month-of-year effects in the Sydney Stock Exchange index, the significance of the effects can be ignored; however, they verified the holiday effects in Australian stock market.

Brown (1970 and 1972), Brown, Finn and Hancock (1977) investigated the impacts of announcement in Australian and the conclusion indicated the Australian stock market was consistent with semi-strong form efficiency. Groenewold (1997) used cointegration and Granger causality tests examined the semi-strong form efficiency of the Australia and New Zealand stock markets and the outcome shown that both markets support semi-strong form efficiency.

Robson (1986) had researched the performance of the Australian mutual fund during ten years from 1969 to 1978 and the evidence accordance with the strong form efficiency.

2.2.2 Evidence from emerging stock markets

With the rapid development of the developing countries and the emerging markets, an increasing number of studies are focus on the level of efficiency in the emerging markets (Hasson, 2006). Sharma and Kennedy (1977) tested the Bombay Stock Exchange support weak form efficiency. Dickinson and Muragu (1994) supported the Nairobi Stock Exchange is weak form efficiency. Urrutia (1995) tested four Latin American emerging markets and the results support the weak form efficiency. Filer and Hanousek (1996) confirmed that the stock markets of the Czech Republic, Hungary, Poland and the Slovak Republic are consistent to weak-form efficient market hypothesis. Ojah and Karemera (1999) represented four Latin American markets and the result was three of them except Chile were following random walk, which is similar to Urrutia’s (1995) result. Rockinger and Urga (2000) reported that the Hungarian stock market index is unpredictable and it is following random walk. Abeysekera (2001) confirmed the weak form efficiency of the Colombo Stock Exchange in Sri Lanka and reported no seasonal effects to be found in Sri Lanka Stock Market. Gilmore and McManus (2003) confirmed that the central European countries’ stock markets are weak form efficiency. Abrosimova— (2005) tested Russian stock market and the conclusion of the investigation support the weak form efficient hypothesis. Recently, Tsukuda et al. (2006) also supported the evidence that the stock markets in the Czech Republic, Hungary and Poland are weak form efficiency. Chander, Mehta and Sharma (2008) tested the India stock market and the results signified that the prices change in the India stock market follow the random walk and trading strategies based on the past prices cannot obtain extra return.

On the other hand, Solnik (1973) and Jennergren and Korsvold (1975), they tested some European markets include less-developed markets, and the consequences were contrast to the random walk. Errunza and Losp (1985) investigated 10 emerging markets and found the emerging markets are less efficient than the developed markets. Similarly, Roux and Gilbertson (1978) found Johannesburg Stock Market was weak form inefficiency. Ghandi, Saunders and Woodward (1980) also viewed Kuwaiti Stock Market not weak form efficiency. Paekinson’s (1987) research rejected the weak form efficiency hypothesis in the Nairobi Stock Exchange. Wong, Neho, Lee and Thong (1993) confirmed the January effects in Malaysian stock markets. Harvey’s (1995) tested six Latin American, eight Asian, three European and two African emerging markets and the investigation consisted with the finding that most of emerging markets are failed to support weak form efficient market hypothesis. Claessens, Dasgupta and Glen (1995) investigated nineteen emerging markets and he voiced the emerging markets inconsistent with weak form efficient market hypothesis. Poshakwale (1996, 1997) reported the India Stock Market is not weak form efficiency. Coutts (2000) certificated the existence of day-of-week effect in Athens stock market. The research of the three Gulf countries—Saudi Arabia, Kuwait and Bahrain made by Abraham, Seyyed and Alsakran (2002) rejected weak form efficient hypothesis. Mobarek and Keasey (2002) certificated the weak form inefficiency of the Dhaka stock market by using runs and autocorrelation tests. Appiah- Kusi and Menyah (2003) tested eleven African stock markets and only five of them had the evidence to consistent with the efficient market hypothesis. Hassan and Maroney (2004) tested the Dhaka Stock Exchange and found that the current stock prices can be predict by analyzing the history price path, which rejected the weak form efficient market hypothesis. Consequently, most of the research accepted the view that most of the emerging stock markets are not as efficient as the developed stock markets. Moustafa (2004) had confirmed the inefficiency of the United Arab Emirates stock exchange with the evidence that individual stocks did not follow normal distribution. Tas and Dursonoglu (2005) confirmed that the Turkey stock market is inefficiency during the research period. Goldman and Sosin (1979) explained the inefficiency in emerging markets as the results of the barriers of information dissemination. Butler and Malaikah (1992) result the inefficiency to the institutional factors such as illiquidity, reporting delays, market fragmentation.

However, Akinkugbe (2005) found evidence to confirm that the Botswana Stock Market is consistent with semi-strong form efficient market hypothesis by using autocorrelation, Augmented Dickey-Fuller and Phillip-Perron unit tests.

### 2.3 Previous researches about Chinese stock market

Since the 1990s, with the rapid development of Chinese economy, the Shenzhen Stock Market and Shanghai Stock Market appeared. During nearly 20 years development, increasingly investors and scholars are interested in investigating whether China’s stock market efficiency and what level efficiency the Chinese stock market belong to.

2.3.1 Chinese stock market is weak form efficiency

Traced back to the year of 1994, Bailey firstly examined nine stocks from both Shanghai and Shenzhen Stock Markets, and the conclusion of Bailey was that B-shares of China’ stock market was consistent with the weak form efficient hypothesis. Groenewold —-(2001) confirmed weak form efficiency of B-shares in Chinese Stock Market.

As to A-shares in Shanghai and Shenzhen stock market, the conclusions are conflicting among the researches. Song (1995) tested 29 securities in Shanghai Stock Market and found Shanghai stock market is weak form efficient. Wu (1996) applied serial correlation test on both Shanghai and Shenzhen Stock Markets during the period from June 1992 to December 1993 and concluded that both of the stock markets are weak form efficiency (Seddighi and Nian, 2004). Laurence, Cai and Qian (1997) tested Shanghai A-shares, B-shares and Shenzhen A-shares and B-shares with serial correlation tests, and got the results that except both A-shares presented negative correlation and both B-shares represented positive correlation, and the magnitude of the correlation became decreased since the year of 1994, which indicated China’s stock markets were increasing efficient. Liu, Song and Romilly (1997) applied ADF unit root test to examine the Shanghai and Shenzhen stock markets and the consequence of the investigation was support that China’s stock markets were following random walk. Long, Payne and Feng (1999) tested A-shares and B-shares in Shanghai Stock Market and support the random walk. Ma and Barnes (2001) applied the serial correlation, the runs and the variance ratio tests to examine both of A-shares and B-shares in Shanghai Stock Market and Shenzhen Stock Market, the results of their study shown the inefficient condition of Chinese stock market, while by Fama’s (1965) standard, Chinese stock market was in consistent with the weak form efficient hypothesis. Lima and Tabak’s (2004) variance ratio test of Shanghai and Shenzhen stock markets between June 1992 and December 2000 certificated that Chinese stock markets were weak form efficient.

Yu (1994) tested the data of Shanghai stock market before 1994 and confirmed Shanghai stock market is weak form inefficient. Hsiao (1996) tested the Shanghai Stock Market and the result of the test rejected weak form efficient hypothesis. Mookerjee and Yu (1999) investigated Shanghai Stock Market (from December 19, 1990 to December 17, 1993) and Shenzhen Stock Market (from April 3, 1991 to December 17, 1993) by using the serial correlation test and the runs test, the test presented seasonal anomalies in both of stock markets, which in contrast with weak form efficiency. Darrat and Zhong (2000) employed the variance ratio test and a model-comparison method to test A-shares of the Shanghai Stock Market and the Shenzhen Stock Market, their results shown that the share prices in both stock markets did not follow random walk. Groenewold —-(2001) and Chen and Hong (2003) showed evidence of inefficiency in both Shanghai and Shenzhen stock market. Seddighi and Nian (2004) tested Shanghai Security Index and eight shares in Shanghai Stock Exchange from January 2000 to December 2000 by using Lagrange Multiplier test, the Dickey-Fuller test and ARCH test, and the consequence of the study also expressed as Chinese stock market was weak form inefficiency. Gao and Kling (2005) confirmed that the existence of seasonal effects in Chinese stock markets. Chung (2006) used four methods to test the weak form efficiency of Chinese stock markets and the results were that despite increasingly efficient, Chinese was not in consistent with weak form efficiency. Recently, Lim and Brooks (2009) employed a battery of nonlinearity tests to investigate Chinese stock markets and the results indicate China’s stock market was weak form inefficiency. Liu (2010) employed serial correlation test, unit root test, ARIMA, GARCH, artificial neural network tests, and the bootstrap test to obtained a result that Chinese stock market is weak form inefficient.

According to Mookerjee and Yu (1999), Darrat and Zhong (2000), Liu (2010), the reasons of inefficiency in China’s stock markets should be the restricted supply of shares; thin trading; asymmetric information and the imperfection and partial implement of policies.

2.3.2 Chinese stock market is semi-strong form efficiency

Since the contradiction with the weak form efficiency of Chinese stock markets, only few scholars believe that Chinese stock market could reach the level of semi-strong form efficiency.

Haw, Qi and Wu (2000) found that the good information generally reported earlier than the bad news by investigating the A-shares of Shanghai Stock Market and Shenzhen Stock Market. Ma (2000) tested the prices movements after the announcement of information, such as dividend and bonus, and found Chinese stock was departure from semi-strong form efficiency since evidence shown that the existence of under-reaction and over-reaction in Chinese stock markets. Su (2003) viewed A-shares could not reflect all of the available information immediately and correctly while the B-shares performed better than A-shares. Ma (2004) tested the random walk, seasonal effects and the reaction of share prices to the announcement of dividends, bonus and rights issues, and concluded that Chinese stock market was not semi-strong efficient nor weak form efficient.

## 3. Methodology

As mentioned above, whether Chinese stock markets efficiency is still a controversy, in order to test the efficient level of Chinese stock markets, the following methods will be used in this paper.

### 3.1 Methods to test whether Chinese stock market weak form efficient

Based on the former scholar researches about the efficient market hypothesis, four main statistical methods are applied in the test of weak form efficiency in this essay; the Augmented Dickey-Fuller unit root test, the serial correlation tests, runs tests and variance ratio tests are used to test the random walk.

According to Campbell and Hamao (1989), random walk processes can be classified into three sub-hypothesis: random walk 1 (RW1), random walk 2 (RW2) and random walk 3 (RW3). The random walk 1 is the most restrictive one which requires the movements of share prices should be independent and identically distributed; the random walk 2 (RW2) only require the independent distribution; and the random walk 3 (RW3) further observes the opportunity of serial correlation in the squared increments that cause the existence of conditional heteroscedasticity (Campbell and Hamao, 1989).

**Unit root test**

The unit root test is a common approach that used to test the random walk nature of the price changes which is developed by Dickey and Fuller (1981) to test the stationary of a time series. The only requirement of the unit roots test is that the first and second moments are subject to fixed stationary values, while the covariance between and tend to the stationary value which depend on |t-s| (Davidson and MacKinnon, 2004).

The theory of the unit root test is based on testing the stationary of time series, to investigate the random walk, a series can be viewed as stationary if the mean and the auto-covariance independent for time, a very common non-stationary series is the random walk (Campbell and Ludvigson,1997). And the non-stationary time-serial process (random walk process) is as follow:

(Davidson and MacKinnon, 2004) (1.1)

y: the series;

: a stationary random disturbance term.

The series y has a constant forecast value, conditional on t, and the variance of the series is increase over time, the random walk here is a difference stationary series since the stationary of the first difference of y (Davidson and MacKinnon, 2004).

(Davidson and MacKinnon, 2004) (1.2)

The first differences of the series is I (0), a series which is integrated to order d is denoted by I (d), if the model has d unit roots and it must have d times difference of such a model before an I (0) series results(Davidson and MacKinnon, 2004). Generally, it is stationary when the d times difference of a process has d unit roots (Enders, 2003).

The efficiency of the price change can be resulted by testing whether the time series has a unit root. The most popular approach to do the unit roots test is the Augmented Dickey-Fuller (ADF) tests, which were first designed by Dickey and Fuller (1988), and based on the assumption that the error term follow an autoregressive (AR1) process of known order (Davidson and MacKinnon, 2004).

In order to test the efficient of the stock market, the Augmented Dickey-Fuller unit root test applies the tau-statistic for every estimated coefficient to examine the significant of the estimated coefficients (Davidson and MacKinnon, 2004). The tau-statistic can be calculated with the same way as the student’s t-statistics but they do not follow the same distribution (Davidson and MacKinnon, 2004). To test the random walk of the data, the comparing between the estimated tau-statistics value and the critical values, in the case that the estimated tau-statistics value is greater than the critical values, the null hypothesis will not be rejected at the conventional test sizes (Davidson and MacKinnon, 2004).

After that, the further Augmented Dickey-Fuller unit root test will base on the regression and hypothesis as follow:

(Enders, 2003)(1.3)

Formula above is the pure random walk model which has no constant and no time trend.

(Enders, 2003)(1.4)

This model adds the constant in the equation comparing with the first one (Chung, 2006).

(Enders, 2003)(1.5)

The last model includes both constant and time trend.

: first difference;

: the log of the price index;

: the constant;

: the error term which is assumed to be white noise;

the coefficient to be estimated;

the coefficient to be estimated;

t: the trend;

the estimated coefficient for the trend;

q: the number of lagged terms; (Enders, 2003)

According to the equations above, the null hypothesis can be obtained:

H0: =0, the time series is non-stationary or unit roots, in this condition, the hypothesis can be accepted and the market can be confirmed as following the random walk;

H1: =1, the time series is stationary or not unit roots, in this case, the hypothesis will be rejected and the test of the market will result as weak form inefficient.

The equation 3.7 examines the null hypothesis of random walk against stationary alternative, and the equation 3.8 tests the null hypothesis against a trend alternative (Enders, 2003).

The length of the lags should be selected appropriately since the critical values depend on the sample size, too few lags means that the regression residuals do not perform the white noise processes and the Augmented Dickey-Fuller unit root test may over-reject the null hypothesis; on the other hand, including too many lags may cause the loss of freedom level and reduce the power of the test to reject the null hypothesis of a unit root (Enders, 2003).

A useful rule to determine the maximum length of lag () is as follow:

(Schwert, 1989)(1.6)

With the finite length of leg, the result of Augmented Dickey-Fuller unit roots test would be accurately and functional (Ender, 2003).

Serial correlation coefficients

Serial correlation test is one of the most commonly and intuitive tests for the random walk (Chung, 2006). Under the circumstance of the weakest version of the random walk (RW3), there is no correlation at all leads and lags, the correlation coefficient () should be near zero (Fama, 1965). Serial correlation test measures the relationship between the value of a variable at time t and in the previous time, the complete linear independence is while the complete linear dependence is (Fama, 1965).

The model of the serial correlation coefficient is as follow:

(Ma, 2004) (2.1)

: the return of a single share or a portfolio at time t;

the autocorrelation coefficient of the time series ;

k: the lag of the period;

Cov(): the covariance between the return of time period (t-1, t) and the lagged return t-k periods before;

Var(): the variance of a securities return during the time period (t-1, t);

The In condition of large sample, the standard deviation can be estimated as:

(Chung, 2006) (2.2)

: the sample mean of series y;

k: time lag, ;

To test the random walk, hypothesis should be used:

H0:, the serial correlation coefficient is approximately zero; in this case, the hypothesis can be accepted and the market will be confirmed as following the random walk;

H1: , in such condition, the serial correlation is existing in the observations and the market is weak form inefficient.

In large sample, if the autocorrelation equal to zero, the mean and variance of the sample autocorrelation is zero and 1, respectively. Generally, 1%, 5% and 10% significant levels can be accept by the null hypothesis, and the critical values are 2.576, 1.96 and 1.64, respectively (Chung, 2006). A 99% confident interval is, a 95% confident interval is, while the 90% confident interval is the entire autocorrelation coefficient () falling inside the intervals are accepted, and the market is weak form efficiency, otherwise, the hypothesis will be rejected (Ma, 2004).

Box and Pierce (1970) made the Q-statistic to test whether all of the autocorrelation equal to zero. The formula of the Q-statistic is as follow:

Box and Pierce (1970)(2.3)

Q: asymptotically distribute as Chi-Square with m degree of freedom;

m: the maximum lag length;

n: the number of observations.

For small samples, LB-statistic is formed by Ljung and Box (1978) and the model is:

Ljung and Box (1978)(2.4)

Both of the statistics are designed to test whether the autocorrelations departure from zero.

For the purpose to test the random walk of Chinese stock market, it is necessary to test whether the daily returns are independence by using the autocorrelation coefficient and Ljung-Box statistic.

Run tests

The run test is a method that used to test the statistical independencies (RW1). Unlike the serial correlation test, the run test does not require the normal distribution of the time series (Chung, 2006). The run test is a non-parametric statistic that is applied to detect the whether the changes of share prices are independent (Ma, 2004). A run is a sequence of the price changes with the same signs, such as: ++, –, 00,which indicates price increase, decrease and not change, respectively (Campbell, Lo and Mackinlay, 1997). In the case of no change can be viewed as the mean of the distribution and increase stands for positive change of the prices and the return is greater than the average level; contrarily, decrease stands for the return is lower than average (Worthington and Higgs, 2004). The runs test assumes that the expected number of runs and the observed number of runs should be closely, if the runs departed from each other significantly, the test will reject the hypothesis of random walk (Campbell, Lo and Mackinlay, 1997).

According to Wallis and Roberts (1956), the formula of the expected number of runs can be explained as follow:

Wallis and Roberts (1956)(3.1)

M: expected number of runs;

N: the number of observations (n1+n2+n3);

n1: the number of prices positive changes;

n2: the number of prices negative changes;

n3: the numbers of prices do not change.

If the observed number of runs is R=M1.64 S.E. in the condition of 90% confident interval, R=M1.96 S.E. in the condition of 95% confident interval or R=M2.756 S.E. in the case of 99% confident interval, the market can be conformed as following random walk at 1%, 5% or 10% significant level (Chander, Mehta and Sharma, 2008).

According to Wallis and Roberts (1956), the formula of the standard error is:

= Wallis and Roberts (1956) (3.2)

As Fama (1965) mentioned, in the condition of large size of sample, the expected number of runs M is normally distributed. Take standard normal Z-statistic to express the difference between the actual and expect number of runs:

(Wallis and Roberts, 1956) (3.3)

R: actual number of runs;

: the correction factor for continuity adjustment; (Wallis and Roberts, 1956)

If R?M, the continuity adjustment (Z) is positive, if R?M, the continuity (Z) is negative (Wallis and Roberts,1956). The positive Z indicates negative serial correlation while the negative Z indicates positive serial correlation, both of the results violated to the random walk theory (Chander, Mehta and Sharma, 2008).

Hypothesis can be set up as follow:

H0: R=M, in this case, the market would be viewed as weak form efficient;

H1: R?M, if the result in consistent with this hypothesis, the market should be departure from random walk.

Under the condition that the absolute value of Z is less than the critical value, the null hypothesis will be accepted. Based on the significant value of 10%, 5% and 1%, the confident intervals are 1.64, 1.96 and 2.576, respectively (Ma, 2004).

In the case that the expected number of runs equal to the actual number of runs, the hypothesis should be accepted and the market is considered to be weak form efficient; otherwise, the hypothesis will be rejected (Ma, 2004). Accordingly, the run test will be applied in this dissertation to test the random walk of the share returns and exam whether the movement of share prices in Chinese stock markets are predictable.

Variance ratio tests

Variance ratio test was developed by Lo and MacKinlay (1988), this test based on the assumption that the increments in a random walk series are linear; specifically, the variance of the qthdifference of a random walk increases linearly with q. In other words, the variance of the qth difference variable would be q times variance than its first difference. It can be expressed as the following equation:

(Ma, 2004) (4.1)

q: the number of one-period intervals;

: the mean of one-period return in logarithm;

: the stochastic error in logarithm.

In the version of q-period, the equation is:

(Ma, 2004)(4.2)

: the return over q-period.

The variance ratio is designed to test the random walk in returns; and it is not only sensitive to correlated price changes, but also with respect to non-normality and heteroscedasticity of the stochastic disturbance term (Cheung and Coutts, 2000). According to Campbell, Lo and MacKinlay (1997), despite the Random Walk 1 can be tested by comparing the variance of rt+rt-1to twice the variance rt;it is very difficult to indicate linearity in the condition of Random Walk 2 and Random Walk 3 since the variances of increments change over time. Lo and MacKinlay’s (1988) variance ratio test provided a method to test the uncorrelated residuals in series with the assumption of homoscedastic and heteroskedastic random walk. The variance ratio test rely on both of the rank of series and the magnitude of the observations, it is consider to be a more functional technique to conduct the random walk test when facing the uncorrelated increments (Hassan and Chowdhury, 2008).

Generally, under the circumstance of random walk, the variance of q period returns should be q times bigger than the first period returns, and the general expression of the variance ratio is as follow:

(Chung, 2006) (4.3)

Var(): the unbiased estimator of 1/q of the variance of the q times difference of the logged security return ();

Var(): the unbiased estimator of the variance of the logged return ().

According to Lo and MacKinlay (1988), the estimators and Var() can be computed as:

(4.4)

(4.5)

Where (4.6)

: the first observation of the time series;

Pnq: the last observation of the time series;

Pt: the price of security at time t;

n: the number of observations.

And the equation of the variance ratio can be reduced as:

(Ma, 2004) (4.7)

Where

: the order autocorrelation coefficient of ;

In the case of RW1, when the stock returns are uncorrelated, the autocorrelation coefficients in lags one to q should equal to zero [] for all of the conditions of, and the variance ratio should equal to one [VR(q)=1]. Similarly, under the RW2 and RW3, the variance ratio must still be equal to one (Workington and Higgs, 2004).

Accordingly, the hypothesis of the variance ratio test can be drawn as follow:

H0: VR(q)=1, the time series are uncorrelated, the hypothesis should be accepted. Regarding to the stock returns, they follow the random walk and the stock market should be weak form efficiency;

H1: VR(1)?1, the time serial are correlated, the hypothesis should be rejected. As to the stock returns, they are serial correlated and departure from the random walk and the stock market should be weak form inefficiency.

The test will be conducted at the 1% 5% and 10% significant levels, the critical values are 2.576, 1.96 and 1.64, respectively. If the absolute value of the test-statistics is less than the given critical values of 2.576, 1.96 or 1.64, correspondingly, the null hypothesis can be accepted at the 1% or 5% significant level, the series of stock returns are uncorrelated and the stock market confirmed as weak form efficiency; if not, the null hypothesis will be rejected and the stock market are weak inefficiency (Lo and MacKinlay, 1988).

The first test statistics for the variance ratio test is designed under the assumption of homoscedasticity, the asymptotic variance of the variance ratio is , which is defined as follow:

(Lo and MacKinlay, 1988) (4.8)

nq: the number of observations.

The standard normal test-statistics Z(q) for the variance ratio under the assumption of homoscedasticity is:

(Lo and MacKinlay, 1988)(4.9)

The rejection of the random walk under the assumption of homoscedasticity may be for the reason of heteroscedasticity or the existence of autocorrelation (Worthington and Higgs, 2004). Therefore, in order to get the exactly result of variance ratio test, the assumption of heteroscedasticity should be conducted.

Since the continuously change of the volatilities, random walk were rejected for the reason of heteroscedasticity. In order to allow general form of heteroscedasticity, Lo and MacKinlay (1988) recommended the heteroscedasticity-consistent method, he derived a test statistic Z*(q) of the variance ratio test under the assumption of heteroscedasticity, the asymptotic variance estimator under such assumption is, and it can be defined as:

(Lo and MacKinlay, 1988) (4.10)

Where

(Lo and MacKinlay, 1988) (4.11)

nq: the number of observations;

: the heteroscedasticity-consistent estimator;

: the stock price at time t;

: the average return.

The standard normal test-statistics Z*(q) for the variance ratio under the assumption of heteroscedasticity is:

(Lo and MacKinlay, 1988)(4.12)

According to the null hypothesis, VR(q) should be equal to one. If the heteroscedastic random walk be rejected, it indicates the serial correlation (Worthington and Higgs, 2004). If the value of VR(q) is greater than one, it implies the positive serial correlation and the stock returns are predictable; and in the case of VR(q) less than one, it indicates the negative serial correlation (Darrat and Zhong, 2000).

## 4. Data and analysis

The primary data of this dissertation are drawn from the database, which based on the two stock markets and four official exchanges in China, gathered the six price indices during the range from 1st July 1993 to 31st May 2011, and the number of the observations is 4674. The tests performed in this study will be conducted on the indices which are daily price-weighted series of all of the shares on the two stock markets, specifically, there are Shanghai A Share Price Index, Shanghai B Share Price Index, Shanghai SE Composite Price Index, Shenzhen A Share Price Index, Shenzhen B Share Price Index and Shenzhen SE Composite Price Index.

### 4.1 Data and analysis for the unit root test

Since the importance of the unit root test for random walk, it is necessary to use the unit root to test the random walk of the Chinese stock market. As the popular method of the unit root test, the Augmented Dickey- Fuller unit root test is used here to examine the null hypothesis of a unit root (Chung, 2006). In order to obtain more accurate result, the length of lags should be order in finite length; in the Augment Dickey-Fuller unit root test of Chinese stock market, according to the Schwarz’s (1989) equation, the maximum length of Chinese stock markets are 31 for all of the indices (the Shanghai A and B Prices Indices, Shanghai Composite Index, Shenzhen A and B Share Indices, Shenzhen Composite Index). The following tables presented the results of the Augmented Dickey-Fuller unit root test in the condition of no constant or the time trend (table 1), with constant but no time trend (table 2), with constant and time trend (table 3), which corresponding with the three equations mentioned above, equation 1.3, 1.4 and 1.5, respectively.

Table 1 Result of the ADF test in level

The table explains the unit root results of the Shanghai and Shenzhen prices indices by using the Augmented Dickey-Fuller unit root test in level, and the period of the sample is range from 1st January 1993 to 31st May 2011, the number of observations is 4673 for each of the index. The optimal lag length for the Augmented Dickey-Fuller is selected with the Schwarz’s equation (1.6), the maximum lag is 31. The conditions are with no constant or time trend, with constant but no time trend and with both of constant and time trend, and based on the equation 1.3, 1.4 and 1.5.

ADF test statistics (level)

Noneconstant only

constant and time trend

Shanghai A Share Price Index

-0.106163

-1.419864-2.161270

Shanghai B Share Price Index

0.286104

-0.868789

-2.027649

Shanghai Composite Index

-0.156947

-1.417401

-2.163617

Shenzhen A Share Price Index

0.181292

-1.018803

-2.173322

Shenzhen B Share Price Index

0.935258

-0.173399

-1.925926

Shenzhen Composite Index

Critical value 1%

Critical value 5%

Critical value 10%0.206099

-2.545657

-1.940892

-1.616654

-0.996620

-3.431568

-2.861963

-2.567038

-2.168668

-3.960003

-3.410767

-3.127175

***, ** and * indicate the statistical significance at 1%, 5% and 10% level, respectively.

According to the table above, under the three conditions of with no constant or time trend, with constant but no time trend, and with both constant and time trend, the test critical values of the 1% level significance are -2.545657, -3.431568 and -3.960003, the critical values at 5% significance are -1.940892, -2.861963 and -3.410767, and the values of 10% significance are -1.616654, -2.567038 and -3.127175, respectively. The Augmented Dickey-Fuller test statistics show that as to the level test, all of the statistics are greater than the corresponding critical values at all of the three significant levels, which indicates all of the indices have unit roots, and the null at conventional test sizes should not be rejected. Accordingly, the Chinese stock indices are confirmed as having unit roots and following random walk under the Augmented Dickey-Fuller unit root test in level.

Based on the results of the ADF test in level, the further test of Augmented Dickey-Fuller unit root test in first difference should be applied to continue testing the unit root of the Chinese stock markets. And the results of the Augment Dickey-Fuller unit root test in first difference are as the following table 2.

Table 2 Result of the ADF test in first difference

The table explains the unit root results of the Shanghai and Shenzhen prices indices by using the Augmented Dickey-Fuller unit root test in first difference, and the period of the sample is range from 1st January 1993 to 31st May 2011, the number of observations is 4673 for each of the index. The optimal lag length for the Augmented Dickey-Fuller is selected with the Schwarz’s equation (1.6), the maximum lag is 31. The conditions are with no constant or time trend, with constant but no time trend

ADF test statistics (first difference)

Noneconstant only

constant and time trend

Shanghai A Share Price Index

-30.85476***

-30.85919*** -30.85595***

Shanghai B Share Price Index

-61.69467***

-61.70136***

-61.70284***

Shanghai Composite Index

-30.82507***

-30.82953***

-30.82631***

Shenzhen A Share Price Index

-36.20082***

-36.21054***

-36.21177***

Shenzhen B Share Price Index

-37.14310***

-37.17002***

-37.18717***

Shenzhen Composite Index

Critical value 1%

Critical value 5%

Critical value 10%-36.24753***

-2.545657

-1.940892

-1.616654

-29.44279***

-3.431568

-2.861963

-2.567038

-29.44570***

-3.960003

-3.410767

-3.127175

and with both of constant and time trend, and based on the equation 1.3, 1.4 and 1.5.

***, ** and * indicate the statistical significance at 1%, 5% and 10% level, respectively.

Based on the outcomes of the Augmented Dickey-Fuller unit root test in first difference, the test critical values are the same as the test in level under the same conditions, which are -2.545657, -3.431568 and -3.960003 at the 1% significant level, -1.940892, -2.861963 and -3.410767 at 5% significant level, and -1.616654, -2.567038 and -3.127175 at the 10% significant level. All of the Augmented Dickey-Fuller test statistics in first difference are less than the critical values of the three confidence intervals significantly; therefore, the results are that the time series are stationary and all of the Chinese stock indices have no unit root, which indicates that for the given conditions the null at conventional test sizes should be rejected. As a result, in the case of the Augmented Dickey-Fuller test in first difference, the results indicate that the Chinese stock indices are departure from the random walk and reject the hypothesis that Chinese stock market is weak form efficiency.

As a consequence, under the three conditions of the Augmented Dickey-Fuller test, the results of the level test show that Chinese stock markets have unit root and follow the random walk, however, with regards to the first difference test, all of the results express that the Chinese stock indices are stationary and do not have unit roots and six of the indices are not following random walk. Synthesizing the results above, it can be concluded that despite the existing of random walk in the six indices of Chinese stock markets, there are also some evidences explain the existence of stationary. In other words, with the Augmented Dickey-Fuller unit root test by using the daily data around 18 years and 4674 observations, the stochastic components do not necessary to verify that the stock return in Chinese stock markets are unpredictable, there is no enough evidence to confirm the weak form efficiency of the Chinese stock market, and the further tests are required.

4.2 Data and analysis of the serial correlation

The serial correlation coefficient is normally used to test the whether the time series are auto correlated, in order to test the random walk of Chinese stock market, the serial correlation test is applied here to exam whether the daily returns in the six main indices are correlated. Based on the methodology mentioned above and the theory of the serial correlation test, the null hypothesis is that is not different from zero significantly, in this case, the stock markets are viewed as random walk; on the other hand, the alternative hypothesis is, which indicates the existence of autocorrelation in the time series and the stock markets are departure from random walk (Fama, 1965). The test here is considered at two significance levels 1%, 5% and 10%, and the critical values of the significant levels are 2.576 and 1.96 and 1.64 respectively. If the absolute values of x are greater than the critical values, or the p-values of the Q-statistic are bigger than 0.01, 0.05 or 0.10, the random walk hypothesis will be rejected at the 1%, 5% or 10% significant level. The results of the serial correlation test for the random walk in Shanghai stock market are represented in table 3, and the results for Shenzhen stock market are shown in table 4.

Table 3 Results of the serial correlation test for Shanghai Stock Market

The table expresses the results of the autocorrelation coefficient and the Ljung-Box statistics for the daily return of the three indices in the Shanghai stock market during the period from 1st July 1993 to 31st May 2011. Thevalue is the autocorrelation coefficient which is calculated with equation (2.2); Q-value stands for the Ljung-Box statistics that is gotten by equation (2.4). The total lags used here is 20.

Shanghai A Share Index Shanghai B Share IndexShanghai Composite Index

valueQ-value (p-value) valueQ-value (p-value) valueQ-value (p-value)

Lag 1

Lag 2

Lag 3

Lag 4

Lag 5

Lag 6

Lag 7

Lag 8

Lag 9

Lag 10

Lag 11

Lag 12

Lag 13

Lag 14

Lag 15

Lag 16

Lag 17

Lag 18

Lag 19

Lag 20-0.006

-0.021

0.075***

0.056***

-0.028*

-0.021

0.018

-0.033**

-0.020

0.027*

0.032**

0.041***

0.034**

-0.028*

0.058***

0.040***

0.007

-0.012

-0.018

0.034** 0.1934 (0.660)

2.1885 (0.335)

28.685*** (0.000)

43.169*** (0.000)

46.941*** (0.000)

48.983*** (0.000)

50.524*** (0.000)

55.606*** (0.000)

57.417*** (0.000)

60.892*** (0.000)

65.637*** (0.000)

73.635***(0.000)

79.001***(0.000)

82.691***(0.000)

98.574***(0.000)

105.99***(0.000)

106.24***(0.000)

106.94***(0.000)

108.48***(0.000)

113.81***(0.000)0.101***

-0.024

0.033**

0.037**

-0.012

0.065***

0.051***

-0.029*

-0.037**

0.002

-0.009

0.048***

0.036**

-0.051***

-0.018

0.005

0.003

0.032**

-0.009

0.01147.275*** (0.000)

50.001*** (0.000)

55.197*** (0.000)

61.523*** (0.000)

62.210*** (0.000)

82.077*** (0.000)

94.070*** (0.000)

98.030*** (0.000)

104.59*** (0.000)

104.61*** (0.000)

105.01*** (0.000)

115.68*** (0.000)

121.83*** (0.000)

133.92*** (0.000)

135.50*** (0.000)

135.62*** (0.000)

135.65*** (0.000)

140.36*** (0.000)

140.76*** (0.000)

141.37*** (0.000)-0.006

-0.021

0.075***

0.056***

-0.028*

-0.020

0.018

-0.033**

-0.020

0.027*

0.032**

0.041***

0.034**

-0.029*

0.058***

0.040***

0.007

-0.012

-0.018

0.033**0.1715(0.679)

2.1429(0.343)

28.757*** (0.000)

43.606*** (0.000)

47.390*** (0.000)

49.244*** (0.000)

50.845*** (0.000)

55.895*** (0.000)

57.803*** (0.000)

61.309*** (0.000)

66.125*** (0.000)

74.051*** (0.000)

79.584*** (0.000)

83.457*** (0.000)

99.277*** (0.000)

106.78*** (0.000)

107.03*** (0.000)

107.74*** (0.000)

109.22*** (0.000)

114.31***(0.000)

***, ** and * indicates the significance at 1%, 5% and 10% level, respectively.

Considering the autocorrelation coefficient in the table 3, it can be seen that in the first two lags of Shanghai A Index and Shanghai Composite Index and some other lags in three indices, the autocorrelation coefficients are nearly zero. While the highest value is at the first lag of the Shanghai B Index, and many other values are departure from zero, such as the lags 3, 4, 12 and 15 of Shanghai A Index, lags 6, 7, 12, 14 for Shanghai B Index and lags 3, 4, 12, 15 and 16 in Shanghai Composite Index, all of them are none-zero at 1% significant level. Some others are none-zero at 5% and 10% significant level as the table shown, for instance, lags 5, 10, 11, 13, 14 and 20 of Shanghai A Index, lags 3, 4, 8, 9, 13, 18 of Shanghai B Index and lags 5, 8, 10, 11, 13, 14 and 20 for Shanghai Composite Index.

With regarding to the Ljung-Box statistics, the near zero autocorrelation coefficients in the first two lags in Shanghai A Index and Shanghai Composite Index have been supported by the Ljung-Box statistics, however, all of the other near zero autocorrelation coefficients have been rejected by the Ljung-Box at 1% significant level.

Consequently, the serial correlation are confirmed at the first two lags of Shanghai A Index and Shanghai Composite Index, all the others express as reject the null hypothesis of independence.

Table 4 Results of the serial correlation test for Shenzhen Stock Market

The table express the results of the autocorrelation coefficient and the Ljung-Box statistics for the daily return of the three indices in the Shenzhen stock market during the period from 1st July 1993 to 31st May 2011. Thevalue is the autocorrelation coefficient which is calculated with equation (2.2); Q-value stands for the Ljung-Box statistics that is gotten by equation (2.4). The total lags used here is 20.

Shenzhen A Share Index Shenzhen B Share IndexShenzhen Composite Index

valueQ-value (p-value) valueQ-value (p-value) valueQ-value (p-value)

Lag 1

Lag 2

Lag 3

Lag 4

Lag 5

Lag 6

Lag 7

Lag 8

Lag 9

Lag 10

Lag 11

Lag 12

Lag 13

Lag 14

Lag 15

Lag 16

Lag 17

Lag 18

Lag 19

Lag 20 0.054***

-0.019

0.078***

0.045***

-0.043***

-0.036**

0.025*

-0.025*

-0.021

0.051***

0.019

0.025*

0.036**

-0.010

0.044**

0.017

-0.008

-0.019

-0.020

0.024*13.792*** (0.000)

15.460*** (0.000)

44.259*** (0.000)

53.891*** (0.000)

62.528*** (0.000)

68.502*** (0.000)

71.323*** (0.000)

74.271*** (0.000)

76.330*** (0.000)

88.658*** (0.000)

90.274*** (0.000)

93.167*** (0.000)

99.380*** (0.000)

99.872*** (0.000)

108.97*** (0.000)

110.32*** (0.000)

110.61*** (0.000)

112.23*** (0.000)

114.11*** (0.000)

116.73*** (0.000) 0.058***

-0.025*

0.053***

0.047***

-0.030**

0.017

0.028**

-0.024*

-0.033**

0.037**

0.002

0.009

0.032**

-0.039**

0.002

0.007

-0.002

-0.003

-0.004

0.043**15.678*** (0.000)

18.502*** (0.000)

31.828*** (0.000)

42.247*** (0.000)

46.406*** (0.000)

47.796*** (0.000)

51.401*** (0.000)

54.171*** (0.000)

59.180*** (0.000)

65.643*** (0.000)

65.663*** (0.000)

66.052*** (0.000)

70.886*** (0.000)

78.190*** (0.000)

78.203*** (0.000)

78.427*** (0.000)

78.449*** (0.000)

78.481*** (0.000)

78.541*** (0.000)

87.130*** (0.000) 0.054***

-0.020

0.078***

0.046***

-0.045***

-0.034**

0.024*

-0.025*

-0.020

0.052***

0.015

0.026*

0.038**

-0.013

0.045***

0.017

-0.009

-0.020

-0.017

0.025*13.619*** (0.000)

15.505*** (0.000)

43.926*** (0.000)

54.024*** (0.000)

63.665*** (0.000)

68.949*** (0.000)

71.731*** (0.000)

74.588*** (0.000)

76.450*** (0.000)

89.009*** (0.000)

90.068*** (0.000)

93.024*** (0.000)

100.13*** (0.000)

100.95*** (0.000)

110.32*** (0.000)

111.65*** (0.000)

112.05*** (0.000)

113.87*** (0.000)

115.27*** (0.000)

117.68*** (0.000)

***, ** and * indicates the significance at 1%, 5% and 10% level, respectively.

According to the autocorrelation coefficients and the Ljung-Box statistics showned in table 4. It can be seen clearly that despite there are some autocorrelation coefficients express as near zero, all of the value of Ljung-Box statistics rejected the independence hypothesis at 1% level for all of the three indices in the Shenzhen stock market. As a consequence, the daily return in Shenzhen A Index, Shenzhen B Index and Shenzhen Composite Index are not following random walk, the Shenzhen stock markets are weak form inefficiency.

4.3 Data and analysis for run test

The nonparametric run test as a functional approach that is used to exam the asymmetrically distributed data. The stock returns are asymmetrically distribution, in order to detect the random walk of the Chinese stock market, it is necessary to apply the nonparametric run test (Ma, 2004). As the theory of the run test shown, a run is a successive sequence which expresses as positive sign, negative sign and zero (Campbell, Lo and MacKinlay, 1997). A random walk time series should have the nature that the expected number of runs similar to the actual number of runs, if the difference between the expected number of runs and the actual number of runs is too big, the time series will be inconsistent with randomness (Campbell, Lo and MacKinlay, 1997). The normal distribution of the estimated Z-value is N (0, 1), at the 1%, 5% and 10% significant levels, the critical values of Z are 2.576, 1.96 and 1.64, the null hypothesis is Chinese stock markets follow random walk, when the absolute value of Z is less than the critical values, the null hypothesis of random walk should be accepted at the responded significant levels (Campbell, Lo and MacKinlay, 1997). Otherwise, the random walk hypothesis will be rejected and the market will be verified as inefficient market. The results of the run test of the six indices of the two exchanges in the Chinese stock market are represented at table 4. For the purpose to get the trend of the efficiency of Chinese stock markets, this study classify the whole period into three sub-periods, from 1st July 1993 to 09th June 1999, from 10th June 1999 to 22nd February 2006, and from 23 February 2006 to 31 May 2011.

Table 5: Results of the run test

This table expresses the result of run test of the random walk of the Chinese stock market with the full period and the three sub-periods, the test conducted the daily returns of six main indices in China: Shanghai A Share Index, Shanghai B Share Index, Shanghai Composite Index, Shenzhen A Share Index, Shenzhen B Share Index and Shenzhen Composite Index. The full period include 4674 observations, and the three sub-periods include 1550, 1750 and 1374observations respectively. Total cases mentions the number of observations, ‘cases?mean’ expresses the number of runs have positive signs and equal to mean, ‘cases

Time series

Total cases

Cases

Cases?mean

Number of runs

Z-statistic

p-value

Full period (from 1st July1993 to 31st May 2011 )

Shanghai A Share Index

Shanghai B Share Index

Shanghai Composite Index

Shenzhen A Share Index

Shenzhen B Share Index

Shenzhen Composite Index

4674

4674

4674

4674

4674

4674

2452

2557

2453

2405

2572

2424

2222

2117

2221

2269

2102

2250

2267

2107

2257

2162

2056

2138

-1.916*

-6.208***

-2.207**

-5.096***

-7.636***

-5.765***

0.055

0.000

0.027

0.000

0.000

0.000

First sub-period (from 1st July 1993 to 09th June 1999)

Shanghai A Share Index

Shanghai B Share Index

Shanghai Composite Index

Shenzhen A Share Index

Shenzhen B Share Index

Shenzhen Composite Index

1550

1550

1550

1550

1550

1550

840

874

842

840

910

850

710

676

708

710

640

700

780

664

770

725

631

703

0.484

-5.133***

-0.011

-2.331**

-6.367***

-3.372***

0.629

0.000

0.992

0.020

0.000

0.001

Second sub-period (from 10th June 1999 to 22ndFebruary 2006 )

Shanghai A Share Index

Shanghai B Share Index

Shanghai Composite Index

Shenzhen A Share Index

Shenzhen B Share Index

Shenzhen Composite Index

1750

1750

1750

1750

1750

1750

953

1032

952

786

1001

788

797

718

798

964

749

962

823

817

827

801

812

801

-2.220**

-1.523

-2.035**

-3.187***

-2.239**

-3.205***

0.026

0.128

0.042

0.001

0.025

0.001

Third sub-period (from 23rd February 2006 to 31st May 2011 )

Shanghai A Share Index

Shanghai B Share Index

Shanghai Composite Index

Shenzhen A Share Index

Shenzhen B Share Index

Shenzhen Composite Index

1374

1374

1374

1374

1374

1374

650

650

649

629

658

631

724

724

725

745

716

743

662

642

662

622

626

624

-1.300

-2.382**

-1.294

-3.322***

-3.286***

-3.230***

0.194

0.017

0.196

0.001

0.001

0.001

***,** and * express the significance at 1%, 5% and 10% levels, respectively.

As the table shows, for the full period (from 1st July 1993 to 31st May 2011), the Z values for all of the six indices express as against the random walk hypothesis. The estimated Z values against the null hypothesis at 1% significant level for Shanghai B Share Index, Shenzhen A and B Indices and Shenzhen Composite Index, and reject the random walk hypothesis at 5% significant level for Shanghai Composite Index, the null hypothesis for Shanghai A index has been rejected at 10% significant level. The evidence indicates that for the nearly 18 years’ period, the Chinese stock markets are weak form efficiency, and Shanghai A Share Index performed better than the others.

For the first sub-period (from 1st July 1993 to 09th June 1999), there are 1550 observations and the results for Shanghai B Index, Shenzhen B Index and Shenzhen Composite Index are rejected the null hypothesis at 5% significant level, and the Shenzhen A Index against the random walk at 5% significant level. In contrast with the results of the full period, the Shanghai A Index and Shanghai Composite Index express as following the random walk; which suggest that at this period, the daily return of Shanghai A share and Shanghai Composite are weak form efficiency.

Regarding to the second sub-period (between 10th June 1999 and 22nd February 2006), 1750 observations are included, the outcomes show except the Shanghai B Index, all the others reject the random walk hypothesis at 1% (Shenzhen A Index and Shenzhen Composite Index) and 5% (Shanghai A Index, Shanghai Composite Index and Shenzhen B Index) significant level. The evidence confirms that in this period only the daily return in Shanghai B Index follow random walk.

As to the last interval (from 23rd February 2006 to 31st May 2011), the number of observations are 1374, the estimated Z value for Shanghai A Index and Shanghai Composite Index are insignificant, but for Shanghai B Share Index is significant at 5% level. All the indices in Shenzhen stock exchange reject the random walk hypothesis strongly (at 1% significant level). The results here show that for the recent years, the daily returns of Shanghai A Share Index and Shanghai Composite Index are following random walk, and two of the stock markets are weak form efficiency.

Consequently, the Shanghai A Share Index and Shanghai Composite Index are trending to weak form efficiency, and the Shenzhen stock exchange is far away from the random walk.

4.4 Data and result for variance ratio test

As Lo and MacKinlay (1988) mentioned, the variance ratio test is a powerful and reliable method to do the test of random walk. It is necessary to apply the variance ratio test in the efficient test of Chinese stock market. Since the variance ratio test is based on the assumption that in a random walk series of the sampling interval, the increments are linear, under the assumption of random walk for variance ratio test, the stock return should be linear in the given interval (Lo and MacKinlay, 1988). Consequently, the variance of the q days share return should be equal to the variance of the one day return multiplied by q. According to the theory of variance ratio test, the VR(q) represented the variance ratio, if it equal to one, the null hypothesis of random walk should be accepted (Worthington and Higgs, 2004). If the value of test statistics is greater than 1.64, 1.96 or 2.576, the null hypothesis will be rejected at the corresponding significant levels (Lo and MacKinlay, 1988). The results [VR(q), Z(q) and Z*(q)] of the variance ratio test of the six indices (Shanghai Composite Index, Shanghai A Share Index, Shanghai B Share Index, Shenzhen Composite Index, Shenzhen A Share Index, Shenzhen B Share Index) are presented in the table 3, the variance lags of q are selected as 2, 4, 6, 8, 12 and 16 days.

Table 6: Results of the Variance Ratio Test for Chinese Stock Market

The table represents the results of the variance ratio test of Chinese stock market, includes the statistics of the six indices and the dada are daily return in two of the Chinese stock markets, VR(q) is the estimated variance ratio that get from equation (4.7), Z(q) and Z*(q) are the asymptotic normal test statistics under the assumption of homoscedasticity and heteroscedasticity that calculated by equations (4.9) and (4.12), respectively. The number of the observations in each index is 4673, and the variance lags are 2, 4, 6, 8, 12 and 16 days.

Observations Nq=2

q=4

q=8

q=12

q=16

Shanghai composite

4673

VR(q)

Z(q)

Z*(q)

0.994264

-0.421183

-0.186676

1.008859

0.276389

0.157412

1.084171

1.870159

0.924652

1.089959

1.546813

0.779480

1.143448

2.113943**

1.062828

Shanghai A share

4673

VR(q)

Z(q)

Z*(q)

0.993891

-0.446718

-0.199497

1.008080

0.247958

0.144026

1.081853

1.816748

0.901864

1.086736

1.488327

0.753721

1.139803

2.057695**

1.038764

Shanghai B share

4673

VR(q)

Z(q)

Z*(q)

1.099979

6.802337***

2.366752**

1.144039

5.209453***

1.850407

1.257191

5.856619***

2.114500**

1.301437

5.384695***

1.981046**

1.339270

5.135609***

1.929068*

Shenzhen composite

4673

VR(q)

Z(q)

Z*(q)

1.054083

3.666273***

1.710281

1.100992

3.638553***

1.756957

1.164973

3.731872***

1.826443

1.171681

3.029903***

1.518085

1.221024

3.310991***

1.683501

Shenzhen A share

4673

VR(q)

Z(q)

Z*(q)

1.054431

3.689987***

1.721148

1.102958

3.710328***

1.791965

1.167742

3.795663***

1.859257

1.174176

3.075186***

1.542222

1.223767

3.353319***

1.706964

Shenzhen B share

4673

VR(q)

Z(q)

Z*(q)

1.056967

3.863333***

1.757122

1.086178

3.186986***

1.421876

1.173449

3.927151***

1.810759

1.196520

3.480673***

1.671895

1.221397

3.316740***

1.643621

***, ** and * indicate the 1%, 5% and 10% significant level, respectively.

According to the statistics above, the exactly results of the variance ratio test of the random walk for the Chinese stock markets are explained. As to the Shanghai Composite Index, the values of the estimated variance ratio [VR(q)] are nearly to one at all of the different variance lags, which indicates the null hypothesis can be accepted at this step. The standard normal test-statistics value under the assumption of homoscedasticity [Z(q)] is 2.113943 which is greater than the critical value of 5% significant level; therefore, the null hypothesis would be rejected at this level. All of the values of standard normal test-statistics under the assumption of heteroscedasticity [Z*(q)] are support to accept the null hypothesis. The result indicates the random walk of the daily return in the Shanghai Composite Index has been rejected at the 16 days variance lags under the assumption of homoscedaticity. Consequently, the evidence shows that the daily returns in the Shanghai Composite Index are departure from random walk.

Regarding to the daily return of the Shanghai A Share Index, the results above show that the heteroscedasticity [Z*(q)] and estimated variance ratio [VR(q)] are not rejected the null hypothesis for the Shanghai A Share Index, however, under the assumption of homoscedasticity, the null hypothesis has been rejected at 5% significant level in interval 16. The random walk hypothesis of Shanghai A Share Index is rejected correspondingly.

With regards to the daily return of the Shanghai B Share Index, the estimated variance ratio [VR(q)] do not reject the null hypothesis in any interval. In the case of the standard normal test-statistics under the assumption of homoscedasticity, the values of Z(q) are rejected the null hypothesis at the 1% significant level in all of the intervals. The values of Z*(q) rejected the null hypothesis of heterocedastic random walk at 5% significant level in the intervals 2, 8 and 12. As a result, the Shanghai B Share Index is departure from random walk hypothesis.

The results of the Shenzhen Composite Index show that the values of the estimated variance ratio [VR(q)] and the values of Z*(q) are support the null hypothesis of random walk and homoscedastic random walk; however, under the assumption of heteroscedasticity, the values Z(q) rejected the random walk hypothesis at 1% significance in all intervals. Therefore, the Shenzhen Composite Index is not following random walk as well.

The consequence in the Shenzhen A Share Index and Shenzhen B Share Index are similar with the result of the Shenzhen Composite Index, despite the estimated variance ratio [VR(q)] and the values under the assumption of heteroscedasticity [Z*(q)] are supporting the random walk hypothesis in each of the interval, the homoscedastic random walk hypothesis still be rejected at 1% significant level for all of the intervals examined. The consequence of the daily returns in the Shenzhen A Share Index and Shenzhen B Share Index are confirmed to be departure from random walk.

All in all, the estimated values of Z(q) and Z*(q) show the evidence to reject the random walk hypothesis for Shanghai B Share market strongly, and this finding indicates the reason for the rejection of random walk may be autocorrelation. The estimated values of Z(q) rejected the null hypothesis of homoscedastic random walk strongly for the Shenzhen Composite Index, Shenzhen A Share and Shenzhen B Share Indices, and also rejected the null hypothesis of homoscedastic random walk in the interval 16 for the Shanghai A Share and Shanghai Composite Indices. This evidence suggested the rejection may due to heteroscedasticity. The overall evidences suggest that the Shanghai A Share Index and Shanghai Composite Index are expressed more efficient than the others, and the Shenzhen A and B Share Index, Shenzhen Composite Index are far away from random walk.

Conclusion

Market Making and Reversal on the Stock Exchange Victor Niederhoffer and M. F. M. OsbornePage 897 of 897-916 Journal of the American Statistical Association

Vol. 61, No. 316, Dec., 1966

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Alfred Cowles 3rd

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Econometrica Published by: The Econometric Society

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John Y. Campbell & Yasushi Hamao, 1989. “Predictable Stock Returns in the United States and Japan: A Study of Long-Term Capital Market Integration,” NBER Working Papers 3191, National Bureau of Economic Research, Inc