Liquidity, Information Asymmetry, Divergence of Opinion and Asset Returns: Evidence from Chinese Stock market

Transcription

1 Liquidity, Information Asymmetry, Divergence of Opinion and Asset Returns: Evidence from Chinese Stock market Preliminary Draft (Do Not Quote) Guangchuan Li Lei Lu 1 November 6, Guangchuan Li, visiting student researcher in Haas School of Business, University of California at Berkeley and PhD candidate in Department of Economics and Management, Beihang University. lofen.lgc@gmail.com. Lei Lu, assistant professor at School of Finance, Shanghai University of Finance and Economics. lu.lei@mail.shufe.edu.cn. We acknowledge the helpful comments of Liyan Han, Professor in Beihang University, Terrence Hendershott, Associate professor in University of California at Berekely, Charles Lee, Visiting professor in Stanford University and MeiChen Lin, Professor in United National University. We also appreciate comments from attendants on 5th China Finance Annual Meeting. Of course, all errors are Ours.

2 Abstract We examine the independent and dominating effects of the liquidity level, the information asymmetry and the divergence of opinion on asset returns in an important emerging market, Chinese stock market. We use the variable ILLIQ from Amihud (2002) to proxy for the liquidity level, the variable P IN from Easley, Hvidkjaer, and O Hara (2002) to proxy for the information asymmetry and the variable OBS based on Næs and Skjeltorp (2006) to proxy for the divergence of opinion. We find striking evidence that stocks with a higher liquidity level, or a lower information asymmetry, or a lower divergence of opinion, experience significantly lower excess returns. More importantly, the explanatory power of the liquidity level on asset returns may only reflect those from either the information asymmetry or the divergence of opinion. Moreover, we find no evidence on the dominating effect between the information asymmetry and the divergence of opinion when examining their impact on asset returns. These further findings verify the fact that the information asymmetry and the divergence of opinion both affect the liquidity level and meanwhile, the asymmetric information seems only partly to explain the dispersed beliefs among investors in Chinese stock market.

3 1 Introduction It is widely recognized that market risk failed to give the whole picture of the behavior of asset returns. After the well known three factor model proposed by Fama and French (1992), an extensive literature focused on new factors that influence asset returns, three strands of it drawing attention on the liquidity level, the information asymmetry and the divergence of opinion, respectively. Despite the fact that the association between asset returns and these three factors have been studied in developed markets both theoretically and empirically, few work has been done in emerging markets. Moreover, most existing empirical studies only examined whether the factors have independent impact on asset returns, leaving unsettled the underlying question of whether the explanatory power of one factor on asset returns can be dominated by that of another. This paper conducts an empirical study on the effect of the liquidity level, the information asymmetry and the divergence of opinion on cross-sectional asset returns in an important emerging stock market, Chinese stock market. Specifically, we first construct the variable ILLIQ based on Amihud (2002), the variable P IN based on Easley, Hvidkjaer, and O Hara (2002) and the variable OBS based on Næs and Skjeltorp (2006) using transaction data and limit order book data from Chinese stock market. These variables proxy for the liquidity level, the information asymmetry and the divergence of opinion respectively in our paper. Then, We investigate whether each of them has independent impact on cross sectional asset returns by incorporating our estimates into a Fama and French (1992) asset pricing framework. Next, we examine whether one factor can dominate another in a pairwise contest by incorporating two of them each time into the model. We finally investigate the situation when all three variables appear in the model to verify the dominating effects among them. The reason that we focused on Chinese stock market is that, few studies draw direct attention on the determinants of cross-sectional asset returns in China, in sharp contrast with the rapid development of Chinese stock market in recent years. The number of listed stocks in China has increased from 13 in 1991 to 1, 434 by the end of 2006, and the aggregate market capitalization has risen from US$1.3 billion to more than US$1000 1

4 billion. According to 2006 annual report from World Federation of Exchanges(WFE), Shanghai stock exchange and Shenzhen stock change ranked No.1 and No.4 in domestic market capitalization gains in 2006 in the world, which increased by more than 220% and 95% respectively. Previous studies on asset returns in China mainly concerned with B shares discount(see, among others, Kalok, Albert, and Yang, 2008; Mei and Xiong, 2005; Karoyi and Li, 2003; Chen and Xiong, 2001; Fung, Lee, and Leung, 2000; Chakravarty, Sarkar, and Wu, 1998). Although a few authors have studied asset pricing factors in China, they usually attribute cross sectional variation in asset returns to traditional factors, such as market betas(e.g., Su, 1999), size(e.g., Cui and Wu, 2007; Wang and Xu, 2004) and fundamentals(e.g., Zhang, Tian, and Tony, 2007; Wang and Xu, 2004). Some of them and others also verify the association between the liquidity level and asset returns(e.g., Cui and Wu, 2007; Zhang, Tian, and Tony, 2007; Eun and Huang, 2007). None of analysis above, however, addresses the role of the information asymmetry and the divergence of opinion in affecting cross sectional asset returns in China in contrast with our work. Moreover, they left possible dominating effects among these newly developed factors unexamined, which is the main interest of this paper. We find striking evidence that the liquidity level, the information asymmetry and the divergence of opinion all have independent impact on asset returns in Chinese stock market. Specifically, we observe both the illiquidity premium and the information risk premium in the market, which implies stocks with less liquidity or more information asymmetry earns abnormal positive excess returns. These findings are consistent with those in developed markets. Meanwhile, we find stocks with a higher divergence of opinion experience significantly higher excess returns, which conforms to the argument that the divergence of opinion is also a risk pricing factor. More importantly, we document a significant dominating effect between the liquidity level and either the information asymmetry or the divergence of opinion when examining their effect on asset returns. Specifically, The explanatory power of the former factor on asset returns may only reflect those from the latter two ones. An reasonable explanation for this result may lie in the fact the information asymmetry and the divergence of 2

5 opinion both affects the liquidity level 1. Besides, we find no evidence on the dominating effect between the information asymmetry and the divergence of opinion. This finding imply that the divergence of opinion among investors in Chinese stock market may be not only due to the the information asymmetry but also other possible reasons, such as diversified interpretation of the available information. The remainder of this paper proceeds as follows. Section 2 provides a short review on the theoretical and empirical literature on the association between asset returns and the liquidity level, the information asymmetry and the divergence of opinion. We also provide more details in selecting our proxies in this section. Section 3 introduces our empirical framework, including the calculation of the variables ILLIQ, P IN and OBS respectively and our empirical methodology. In Section 4, we introduce our sample and data. Section 5 discusses the main results of our paper. Section 6 concludes. 2 Literature Review Three parallel strands of literature have documented the association between crosssectional asset returns and the liquidity level, the information asymmetry and the divergence of opinion respectively. First, studies concerning the relation between the liquidity level and asset returns can be tracked back to Amihud and Mendelson (1986), which concludes that the average liquidity proxied by quoted bid ask spread is priced. Then, the authors use various measures of the liquidity level to examine their effects on asset returns, such as trading volume (Brennan, Chordia, and Subrahmanyam, 1998), turnover rate (Datar, Y. Naik, and Radcliffe, 1998), amortized effective spread(chalmers and Kadlec, 1998), trading activity (Chordia, Subrahmanyam, and Anshuman, 2001), ILLIQ(the daily ratio of absolute stock return to its dollar volume)(amihud, 2002) and price pressure(the proportion of zero daily returns)(bekaert, Harvey, and Lundblad, 2007). All studies above have documented a significant illiquidity premium effect. In other words, Investors do require higher expected returns in assets with a less liquidity. Among various measures, Hasbrouck (2006) finds Amihud s illiquidity measure, that 1 This argument will be discussed in detail in the following section. 3

6 is, ILLIQ, outperforms other candidates in proxying for the daily liquidity level. Thus, we use ILLIQ to proxy for the liquidity level in this paper, like many other studies (see, among others, Acharya and Pedersen, 2005; Avramov, Chordia, and Goyal, 2006). Second, a number of authors have addressed the possible influence of the information asymmetry on required returns. The literature on this issue is mainly built from rational expectations framework. For instance, Admati (1985) analyzes how an asset s equilibrium price is affected by asymmetric information in a multi-asset model. Both Wang (1993) and Easley and O hara (2004) examine the risk premium induced by the information asymmetry between two groups of investors: informed and uninformed. They argue that uninformed investors demand a compensation for the adverse selection problem that arises from trading with informed traders, which will increase the required returns. In particular, Easley and O hara (2004) proves that the information asymmetry affects cross-sectional returns, which has been verified by the companying and following empirical studies(see, Easley, Hvidkjaer, and O Hara, 2002; Easley, Hvidkjaer, and O Hara, 2004; Aslan, Easley, Hvidkjaer, and O Hara, 2007). Hughes (2005) generalizes the framework of Easley and O hara (2004) by considering diversification effect. In their model, private signals on information reflect both systematic factors and idiosyncratic shocks and only the former matters in affecting asset returns. Jones and Slezak (1999) provides an alternative approach. They argue that the information asymmetry may influence asset returns through its impact on the change of agents portfolio holdings. In this paper, we follow Easley, Hvidkjaer, and O Hara (2002) in which the variable named probability of informed trading, that is, P IN, is employed to directly proxy for the information asymmetry for each asset. This variable has been recognized as a good measure of asymmetric information in empirical microstructure literature and used in many other contexts, e.g., Easley, O Hara, and Paperman (1998), Vega (2006), Chen, Goldstein, and Jiang (2007), Duarte, Han, Harford, and Young (2008), among others. Last, an extensive literature has documented why and how the divergence of opinion influences asset returns both theoretically and empirically 2. On the theory side, Miller (1977)and its followers(see, among others, Jarrow, 1980; Morris, 1996; Viswanathan, 2 As a theoretical foundation, Hong and Stein (2007)summarizes three underlying mechanisms which may drive divergence of opinion. 4

7 2001; Chen, Hong, and Stein, 2002)state that a higher divergence of opinion should forecast lower future returns. Their argument lies in the fact that pessimists may be driven out of the market due to short selling constraints or any friction that prevents the revelation of negative opinions. Consequently, optimists passion will drive the market price upwardly biased and thus lower the future returns. Other authors (e.g., Varian, 1985), however, treat the divergence of opinion as risk. As a result, assets with a higher divergence of opinion should earn higher future returns. On the empirical side, a variety of proxies for the divergence of opinion has been used to test their ability in forecasting asset price or return behaviors by different authors, such as dispersion in analysts earnings forecasts (e.g., Diether, Malloy, and Scherbina, 2002; Doukas, Kim, and Pantzalis, 2006a; Doukas, Kim, and Pantzalis, 2006b), trading volume(lee and Swaminathan, 2000), idiosyncratic volatility(risk)(boehme, Danielsen, and Sorescu, 2006), investor based measure(goetzmann and Massa, 2005) and breadth of mutual fund ownership(chen, Hong, and Stein, 2002), etc. It is worth noting that empirical findings above are also mixed in light of the coexistence of two competing theories. All of these proxies, however, can hardly be employed in Chinese stock market due to two limitations. First of all, we find it almost impossible to collect data on analysts forecast, individual investors account and mutual fund holdings in today s Chinese stock market. Second, idiosyncratic volatility and trading volume usually are not clean or fail to proxy for the divergence of opinion. For example, idiosyncratic volatility may be a proxy for the liquidity premium according to Guo and Savickas (2004) and fail to predict returns across low short interest stocks according to Duan, Hu, and Mclean (2007). Meantime, trading volume is commonly used as a proxy for the liquidity level in literature. Recently, scholars claim that the heterogeneous beliefs among investors should be reflected in their order submitting strategies. Thus, the limit order book may convey important information on the divergence of opinion. So far, many different variables have been constructed from the limit order book to proxy for the divergence of opinion in various contexts, such as order imbalance(e.g., Chow, Lee, and Liu, 2004; Kim, 2008) and order book slope(e.g., Næs and Skjeltorp, 2006; Duong and Kalev, 2008). Although the effects of these variables on price volatility have been examined, few studies show interest in their ability in forecasting asset returns. This paper thus employ the order 5

8 book slope(obs) proposed by Næs and Skjeltorp (2006) as the proxy for the divergence of opinion to examine its impact on asset returns. We drop another candidate, order imbalance, due to its possible role in proxying the liquidity level (Fung, 2007). Although studies above have documented that the liquidity level, the information asymmetry and the divergence of opinion all have independent impact on asset returns, the interlinkages and thus possible dominating effects among them in affecting asset returns seem to have been ignored in the asset pricing framework. Existing literature, however, provides strong evidence on the close relations among these factors. For a start, an important conclusion from the models based on Kyle (1985) framework (see, among others, Holden and Subrahmanyam, 1992; Benos, 1998) is that market liquidity provided by market maker should be directly influenced by how much private information is at informed traders hand. The more the private information has not been incorporated into the price, which implies a higher information asymmetry, the lower market maker will set the market depth. This is because he faces a more serious adverse selection problem. This suggests that, other things being equal, stocks with higher information asymmetry should be accompanied with a lower liquidity. Easley, Kiefer, OHara, and Paperman (1996) empirically showed that infrequently traded stocks indeed experience a higher probability of informed trading. Besides, other authors, e.g., Brennan and Subrahmanyam (1996), also claim that adverse selection cost induced by information asymmetry plays a key role in affecting the liquidity level. In the next place, the information asymmetry comprises one of the important sources of the divergence of opinion. The argument is obvious and intuitive. When information is vastly distributed in either quantity or quality among investors, they will finally form different beliefs on assets payoff conditional on their own information. In fact, Hong and Stein (2007) points out that gradual information flow and limited attention comprise two important sources of the divergence of opinion 3. Either case, according to its definition, can be seen as one form of information asymmetry. Finally, the divergence of opinion may be connected 3 The alternative source of the disagreement among investors is the differential interpretation of available information, according to Harris and Raviv (1993), Kandel and Pearson (1995) and Hong and Stein (2007), etc. If we observe a positive correlation but no dominating effect between the information asymmetry and the divergence of opinion, it may suggest that Chinese investors disagree with each other not only because they posses asymmetric information but also share differential interpretation on public signals. 6

9 with liquidity patterns. On one hand, if the information asymmetry is indeed one of sources of the divergence of opinion, the latter might negatively correlates to the liquidity level. On the other hand, according to famous no-trade theorem (see, for example, Milgrom and Stokey, 1982; Fischer, 1986), if all investors are rational, endowed initially efficient, homogeneously informed and perceive their information correctly, then there will be very little trading activities. This statement means even with symmetric information, the trading activities can also be provided by heterogeneous beliefs 4. There exist evidences, however, showing that trading activities may negatively correlate to the liquidity level in Chinese stock market(see, for example, Zhang and Liu, 2006). Thus, the divergence of opinion may negatively correlates to the liquidity level even when the former can be explained by differential interpretation of available information. In a word, the underlying interlinkages among the liquidity level, the information asymmetry and the divergence of opinion contribute to a possibility that one factor may dominate another in affecting asset returns, the main interest of this paper. 3 Empirical Framework 3.1 Variables Liquidity Level: ILLIQ Amihud s illiquidity measure ILLIQ reflects the daily ratio of absolute stock return to its dollar trading volume, averaged over some period. This absolute (percentage) price change per dollar of daily volume can be interpreted as the daily price impact of order flow. Thus, daily ILLIQ can be calculated as R imd /V OLD imd. R imd is the return on stock i on day d of month m and V OLD imd is the respective daily volume in dollars. The cross-sectional study in this paper employs for each stock i the monthly average 4 Authors, e.g., Varian (1985) and Harris and Raviv (1993) build theoretical models on this issue, while Brockman and Chung (2000) provides an empirical evidence. 7

10 of the daily ILLIQ as follows, ILLIQ im = 1 D im R imd, (1) D im V OLD t=1 imd where D im is the number of days in which data are available for stock i in month m. In order to keep independent variables in the same quantity magnitude, the variable ILLIQ is multiplied by It should be noted that ILLIQ measures illiquidity level of the stock. It means the higher the variable ILLIQ, the less liquid the stock Information Asymmetry: P IN The information asymmetry measure P IN, probability of informed trading, is initially proposed by Easley, Kiefer, OHara, and Paperman (1996), which describes the percentage of the trades based on private information in all observed trades. A higher value of P IN means a higher degree of information asymmetry. In this paper, we employ a generalized version of P IN constructed by Easley, Hvidkjaer, and O Hara (2002). We briefly summarize the model as follows. For an extensive discussion of the structure of the model please refer to the original paper. Consider a model which depicts trading as a repeated daily game between risk neutral competitive market makers and two types of traders: informed and uninformed. Market makers set buying and selling prices based on their conjectures on the underlying true value of an asset. P IN thus plays an important role in market makers conjectures, since they can only observe sequence of trades in the market cannot differentiate informed traders and uninformed ones. From the perspective of an econometrician, given a particular sequence of trades, P IN can be calculated through estimating a group of structural parameters in the model. Trade occurs over t = 1,..., T discrete trading days.at each trading day, a private information event occurs with a probability α, in which case the probability of bad news is δ and good news (1 δ). Traders informed of bad news sell and those informed of good news buy. All traders arrive at the market following independent poisson process. 8

11 If a private information event occurs, informed traders arrive at rate µ, and uninformed buyers arrive at rate ɛ b, and uninformed sellers arrive at rate ɛ s. If no information event occurs, the arrive rates of uninformed buyers and sellers stay unchanged. Given this simple model structure, the likelihood function for the total number of buys and sells on a single trading day is: L ((B, S) ω) = α (1 δ) e (µ+ɛ b+ɛ (µ + ɛ s) b) B (ɛ s ) S B!S! + αδe (µ+ɛ b+ɛ (µ + ɛ s) s) S (ɛ b ) B + (1 α) e (ɛ b+ɛ (ɛ s) b) B (ɛ s ) S, B!S! B!S! (2) where (B, S) represents the total number of buys and sells for the day and ω = (µ, ɛ b, ɛ s, α, δ) is the parameter vector. The joint likelihood function for T days is simply a product of the above daily likelihood due to the IID of variables across days in the model. We estimate the following factorized version of the joint likelihood function to facilitate numerical maximization, in the Spirit of Easley, Hvidkjaer, and O Hara (2004), ) L ((B, S) Tt=1 ω = + T t=1 T [ ɛ b ɛ s + M t (ln x b + ln x s ) + B t ln (µ + ɛ b ) + S t ln (µ + ɛ s )] t=1 ln [ α (1 δ) e µ x St Mt s x Mt b + αδe µ x Bt Mt b x Mt s + (1 α) x St Mt s ] x Bt Mt b, (3) where M t = min (B t, S t ) + max (B t, S t ) /2, x s = ɛs µ+ɛ s and x b = ɛ b µ+ɛ b. This factorization process is especially important in Chinese stock market, since it overcomes underflow or overflow problems induced by large numbers of buys and sells, which we have observed in our data. When estimating the likelihood function above, we employ a method introduced by Yan and Zhang (2006) to set initial values that are representative of the parameter space. The main purpose of this method is to avoid problematic boundary solutions. In particular, in the beginning we produce 125 groups of initial value for each stock in every estimating period(a quarter)using the method. We then run the maximum likelihood estimation of the likelihood function using each group of initial values, after omitting the unreasonable ones 5. Last, if all solutions are on the boundary, we choose the one 5 Some groups of initial value calculated provide a negative value of µ or ɛ s, either of which is supposed 9

12 with the highest value of the likelihood function as our maximum likelihood estimate of ω. Otherwise, we exclude the boundary solutions and choose the non-boundary one with the highest value of the likelihood function as our maximum likelihood estimate of ω. With the chosen estimate of ω, P IN can be calculated as: P IN = αµ αµ + ɛ b + ɛ s, (4) The P IN measure can only be estimated using a relatively long period of data, at least a quarter of daily data. In this paper, we estimate one P IN for each stock in each quarter across the sample period Divergence of Opinion: OBS The divergence of opinion measure OBS is proposed by Næs and Skjeltorp (2006), measuring the content to which investors disagreement on assets future payoff. A higher value of OBS means a lower divergence of opinion among investors. The core of the variable OBS is the elasticity q/ p describing how quantity (q) supplied in the order book changes as a function of the price (p). Specifically, the variable OBS will be the monthly average of daily elasticities in our asset pricing test. The daily elasticities can be calculated in the following steps: 1. First, we divide each trading day into eight time intervals, each of which lasts 30 minutes. We snapshot the limit order book when the last transaction occurs for each interval. For either buy or sell side, and for each interval, we aggregate demanded (supplied) number of shares at each price level. This leaves us with the total volume demanded (supplied) at that price or higher (lower). 2. Second, for each snapshot, the local order book slope is calculated for each price level and then averaged across all price levels for the buy and sell side separately (explained in more detail below). to be positive since either of them represents the arrival rate of a particular group of investor.see more details in Yan and Zhang (2006). 10

13 3. Third, we average local order book slopes in two sides as one slope measure for each snapshot. 4. Finally, we average slope measures across eight snapshots for each day and then average daily slopes across each month to obtain our OBS measure. We calculate local order book slopes for buy and sell side in a similar way. So, we only provide the calculation for sell side in the following way 6 : SSt i = 1 { v S NS 1 1 N S p S 1 /p S vτ+1/v S τ S 1 }, (5) p S τ+1/p S τ 1 where SS i t represents the slope of sell side for interval i on day t. N S is the number of price levels containing positive orders. In this paper, N S is equal to 3, since our high frequency dataset provides information on the 3 best bid and ask prices and volumes of the order book. τ is the index of price levels, with τ = 0 (p S 0 ) denoting the bid ask midpoint and τ = 1 (p S 1 ) denoting the best bid or ask quote price and so on. V S τ represents the natural logarithm of accumulated share volumes at the price level τ (p τ ). Following step 3 and 4 discussed above, once we obtain local order book slope measures SS i t for sell side and BS i t for buy side, our monthly OBS measure can be calculated as follows: OBS = 1 M t=1 i=1 τ=1 M I t 1 ( ) SS i 2I t + BSt i t where I t is the number of snapshots in day t and M is the number of trading days in the testing month. The variable OBS is multiplied by 10 4 to be in the same quantity magnitude as ILLIQ and P IN. (6) 3.2 Empirical Methodology Our methodology follows the standard cross sectional regression method in spirit of Fama and MacBeth (1973). Following Fama and French (1992), three commonly used 6 It should be noted that in this equation, the first and second items are not measured in the same units. According to Næs and Skjeltorp (2006), however, this setting has tiny influence on testing results after examining alternative slope measures. 11

14 factors, i.e., market risk β, size M E and book to market value BM will always appear in our cross-sectional regressions. We calculate betas using a similar approach with that of Easley, Hvidkjaer, and O Hara (2002). Above all, we sort 40 portfolios every quarter based on pre-estimated betas 7. Pre estimated betas are calculated for each stock using at least 24 monthly, when possible, five years, return observations before the test period. We regress these returns on the contemporaneous and lagged value weighted Shanghai and Shenzhen composite index. Next, pre estimated betas are given as the sum of two coefficients in the regressions. 40 portfolios are then formed on the base of ranking these betas. Second, we calculate monthly portfolio returns as equal weighted averages of individual stock returns in each portfolio for the next 3 months. Last, post estimated portfolio betas are calculated from the full sample period.specifically, portfolio monthly returns are regressed on the contemporaneous and lagged value weighted Shanghai and Shenzhen composite index. The post estimated portfolio beta, ˆβp, is then the sum of the two regression coefficients. We finally allocate each portfolio beta to individual stocks in the corresponding portfolio. It is worth noting that the individual stock betas are not constant through the sample period because portfolio compositions change every year. The size measure ME is calculated as the logarithm of market value of equity at the end of each year. Book to market value BM is the logarithm of ratio of the book value of equity to the market value of equity at the end of each year. Following Fama French, we set BM values outside the and fractiles equal to these fractiles, respectively. Based on post estimated betas, ME, BM, ILLIQ, P IN and OBS, we run our cross sectional regressions in the following three main steps. In the first step, we add only one of ILLIQ, P IN and OBS into the regression equations. The purpose of these regressions is to examine whether three individual variables have independent effect on asset returns. For each month in the sample period, we run the following three cross- 7 In contrast, Easley, Hvidkjaer, and O Hara (2002) adjusts portfolios every year. We adopt a quarterly frequency due to the fact that the number of sample stocks varies substantially across quarters. A yearly frequency may cause problems of important sample information loss. 12

15 sectional regressions, R it = γ I 0t + γ I 1t ˆ β pt + γ I 2tME it 1 + γ I 3tBM it 1 + γ I 4tILLIQ it 1 + ε I it, (7) R it = γ P 0t + γ P 1t ˆ β pt + γ P 2tME it 1 + γ P 3tBM it 1 + γ P 4tP IN it 1 + ε P it, (8) R it = γ O 0t + γ O 1t ˆ β pt + γ O 2tME it 1 + γ O 3tBM it 1 + γ O 4tOBS it 1 + ε O it, (9) where R it is the log return of stock i(i = 1,..., N t ) of month l in the year t (l omitted), γ K jt (j = 0,..., 5, K = {I, P, O}) are the estimated coefficients for three equations accordingly and ε it is the mean-zero error term. It should be noticed here that for each stock, both ME and BM are constant through each year and both betas and P IN are constant through each quarter, while both of the rest two explanatory variables vary across months. Next, we add two of ILLIQ, P IN and OBS each time into the regression to form three equations below. The purpose of this step is to examine whether the explanatory power of one variable can be dominated by that of anther. If we found the coefficient of one explanatory become insignificant after another variable s being incorporated into the regression, we will conclude that the latter variable dominates the former in affecting the asset returns. The three regressions are listed below, R it = γ IP 0t + γ IP 1t βˆ pt + γ2t IP ME it 1 + γ IP 3t BM it 1 +γ IP 4t ILLIQ it 1 + γ IP 5t P IN it 1 + ε IP it, (10) R it = γ P O 0t R it = γ OI 0t + γ P O 1t + γ OI 1t βˆ pt + γ P O 2t ME it 1 + γ3t P O BM it 1 +γ P O 4t βˆ pt + γ2t OI ME it 1 + γ OI P IN it 1 + γ5t P O OBS it 1 + ε P it O, (11) 3t BM it 1 +γ OI 4t OBS it 1 + γ OI 5t ILLIQ it 1 + ε OI it, (12) Finally, all of ILLIQ, P IN and OBS are incorporated into the equation to examine whether the dominating relations among them in the above step still hold after estimat- 13

16 ing the following regression: R it = γ IP O 0t + γ IP O 1t +γ IP O 4t βˆ pt + γ IP O 2t ILLIQ it 1 + γ IP O 5t ME it 1 + γ3t IP O BM it 1 P IN it 1 + γ6t IP O OBS it 1 + ε IP it O, (13) All regression coefficients from seven cross sectional regressions above are averaged through time, using both the standard Fama and MacBeth (1973) and Litzenberger and Ramaswamy (1979) methodology. The former uses an equal weighted mean while the latter weights the coefficients by their precisions, and is essentially a weighted least square methodology. 4 Sample and Data Our datasets are comprised of three components. The first one is the high frequency tick by tick dataset in Chinese stock market, which is provided by Beijing SinoFin Information Services Ltd. The sample stocks in this dataset cover the period from 1 June 1999 to 31 December Each record in the dataset includes the stock code, the transaction price, volume, date and time, together with the best three quoted buying and selling prices and volumes at the time each transaction occurs. We use this dataset to estimate the variable P IN quarterly and calculate the variable OBS monthly. The second dataset, obtained from the flying fox trading analysis software, contains daily transaction data ranging from 1997 to Each record in the dataset includes the stock code, the daily opening price, the highest and lowest price, the closing price, the daily volume and dollar volume. This dataset is employed to calculate the variable ILLIQ and betas. In particular, the daily data between 1997 and 1998 are only responsible for calculating pre estimated betas due to our choice of sample period. The last one is China Listed Company Financial Indicator Analysis Database provided by GTA Information Technology Company. We extract market value and book to market value data from this dataset for each stock at the end of each year from 1999 to We proceed sample selection in the following way. First, all B shares are removed, 14

17 leaving only A shares to be estimated. Since our main purpose is to examine the determinants of asset returns, not those of the discount of B shares, the distinguished investor structure in B shares may cause serious bias in our results. Technically, the stocks listed in Shanghai Securities Exchange with the code of which the first three number is 600 or 601 and those listed in Shenzhen Securities Exchange with the code of which the first two number is 00 are kept in our sample. Second, in each quarter, only those stocks that have records at least two years ago are kept in the sample. This procedure guarantees that pre estimated betas can be calculated for each stock in each quarter through the sample period. Last, in each quarter, we remove all stocks whose records are less than 40, which ensures the variable P IN can be estimated efficiently for each stock. Table 1 presents summary statistics of the remaining sample stocks in each quarter across the sample period. We can observe an obvious increasing trend in the number of sample stocks, except a temporary decline from the end of 2005 to the beginning of (Insert Table 1 Here) Data pretreatment is then conducted before the estimation of the variable P IN. Specifically, we remove all data in the call auction period to avoid possible influence of different trading mechanism. Next, we treat all transactions with the same transaction time and price in each trading day as one transaction. Last, we follow the standard Lee Ready algorithm (see Lee and Ready, 1991) to classify transactions as buys or sells. 5 Empirical Results 5.1 Distribution of ILLIQ, P IN and OBS To obtain a comprehensive understanding of statistical characteristics of ILLIQ, P IN and OBS, we first report their distributions together with those of parameter estimates of P IN model in this section. 15

18 Both time series and cross sectional distributions of the variable ILLIQ are shown in Figure 1. The variable ILLIQ experiences relatively big changes in our sample period, both cross-sectionally and individually. This fact is consistent with the according substantial change of market liquidity during the sample period. Panel A shows the 5th, 25th, 50th, 75th, and 95th percentiles each month in the sample period for the crosssectional distribution of ILLIQ. The time series patterns of ILLIQ are quite consistent with the market behavior. In the sample period, the ILLIQ shows downward trends before June 2001 and after July 2005, during both of which investors experience bull markets. In contrast, ILLIQ stays in a relatively high level during the rest of sample period, that is, from July 2001 to June 2005 which has been recognized as a bear market period 8. On an individual stock level, Panel B depicts the cumulative distribution of relative changes (percentage) from month t 1 to month t of individual stock ILLIQ in four unoverlapped subperiods. In all subperiods, we find that more than 50 percent of relative changes are beyond 35 percentage points, while 90 percent are beyond 10 percentage points. Thus, individual stocks exhibit a relatively high variability in the ILLIQ across months. Furthermore, we find the individual ILLIQ shows the highest variability in the period, while the lowest in the period. It is interesting to note that the market moves from bull to bear in the former period and from bear to bull in the latter. Thus, it turns out that the liquidity of individual stocks experienced a sharp drop when the market crashes and a gentle rise when the market becomes bullish. Panel C further illustrates the distribution of the pooled monthly ILLIQ across stocks. It seems that the pooled ILLIQ follows an exponential distribution regardless of some extreme values. We also find the pooled ILLIQ varies in a wide range which confirmed the large cross sectional variability of the ILLIQ. (Insert Figure 1 Here) Distributions of parameter estimates of P IN model are shown in Figure 2. Panel A and Panel B show the 5th, 25th, 50th, 75th, and 95th percentiles each quarter in the sample period for the cross-sectional distribution of α and δ, respectively. Before 2002, the 8 Shanghai Stock Index of A Share reached its local peak at on 13th June, 2001 and then dropped slowly until touching the bottom at on 11th July, Since then, Chinese stock market has stepped into a new bull market period. 16

19 estimates of α stay in a higher level. This fact is consistent with the according less mature market condition then, which means a higher level of informed trading. Besides, the estimates of δ experience a higher variability. This may be resulted by both immature and highly volatile market condition, which make bad and good news alternate frequently. In a more mature market since 2002, both α and δ have become more stable and stayed in a lower level. Panel C shows time series patterns of the quarterly cross sectional mean of the trading frequency parameters, µ, ɛ b and ɛ s. The parameters exhibit a U shape trend to some extend, which well matches the market behavior during the sample period. Moreover, informed trading activities seems more stable than those of uninformed across time. This result illustrates that the uninformed is influenced more by the market trend than the informed. Panel D, Panel E and Panel F illustrate the distribution of the pooled quarterly parameter estimates of α, δ and OrderImbalance respectively across stocks. From the figure, we find α and, in particular, δ, are dispersed over the parameter space, while OrderImbalance, which depicts balance between uninformed buying and selling and calculated as (ɛ b ɛ s ) / (ɛ b + ɛ s ), is more tightly distributed around the mode The dispersed δ illustrates large variability of information context across stocks in the sample period. The skewness of OrderImbalance suggests uninformed traders are marginally more likely to sell over our sample period. (Insert Figure 2 Here) Both time series and cross sectional distributions of the variable P IN are shown in Figure 3. Comparing with ILLIQ, the variable P IN experiences less variability across the sample period, both cross-sectionally and individually. Panel A shows the 5th, 25th, 50th, 75th, and 95th percentiles each quarter in the sample period for the cross-sectional distribution of P IN. Although exhibiting a relatively high variability before mid 2001, the median of the variable P IN has varied mainly in a narrow range from 0.1 to 0.15 since then. On an individual stock level, Panel B depicts the cumulative distribution of relative changes (percentage) from quarter t 1 to quarter t of individual stock P IN in four unoverlapped subperiods. In all subperiods, more than 50 percent of relative changes are within 30 percentage points, while 90 percent are within 70 percentage points. This fact suggests the individual P IN shows a relatively low variability across 17

20 quarters. Meantime, we find the individual P IN exhibits the highest variability in the period, while the lowest in the period, which is consistent with the time series patterns of cross sectional P IN in Panel A. Although the market switches from bear to bull in the period, the P IN stays in an even lower level. For one thing, the market information context has been substantially improved. Besides that, the more important reason lies in the fact that uninformed trading activities increase remarkably while informed trading activities are relatively stable, as shown in Panel C of Figure 2. Panel C further shows the distribution of the pooled quarterly P IN across stocks. We find the pooled P IN is tightly distributed around the mode 0.14, which also supports the fact that the P IN is relatively stable. (Insert Figure 3 Here) We finally show time series and cross sectional distributions of the variable OBS in Figure 4. The variable OBS also indicates a relatively stability in our sample period, cross-sectionally and, in particular, individually. Panel A illustrates the same five percentiles as before each month in the sample period for the cross sectional distribution of OBS. We find an upward trend in the first bull market period, a downward trend in the bear market period and another slight upward trend in the second bull market period in the time series pattern of the cross sectional OBS. This may indicate investors have more dispersed opinion in bear market than that in bull market. However, as the case in the variable P IN, the variable OBS changes in a slight way after 2002, either in the downward or upward stage, and thus in fact shows a relatively low variability. On an individual stock level, Panel B illustrates the cumulative distribution of relative changes (percentage) from month t 1 to month t of individual stock OBS in four unoverlapped subperiods. In all subperiods, more than 50 percent of relative changes are within 13 percentage points, while 90 percent are within 33 percentage points, which suggests the individual OBS shows little month to-month movement. We also find individual OBS exhibits the highest variability in the period, while the lowest in the period. This fact suggests that the disagreement among investors changes more when the market switches from bull to bear than that from bear to bull. Panel C finally indicates the distribution of the pooled monthly OBS across stocks. From the figure 18

21 we conclude the pooled OBS indicates a relative stability, which is tightly distributed around the mode 0.7. (Insert Figure 4 Here) In summary, over our sample period, the variable ILLIQ exhibits a relatively high variability, while those of the variable P IN and OBS are relatively low. Moreover, the economic behaviors of all variables are consistent with the according market condition and evolution. 5.2 Correlations of Variables We next report simple correlations of explanatory variables before examining their effect on asset pricing. Summary statistics on these variables are first reported in Table 2. We find both the mean and median of the excess return are negative, which reflects the fact that investors experience bear market most of time over our sample period. The post estimated portfolio beta varies in a relatively narrow range between 0.83 to The large standard deviation of ILLIQ compared to the mean is consistent with the high variability shown in Figure 1, while those of P IN and OBS are reasonably small. (Insert Table 2 Here) The simple correlations of explanatory variables together with excess returns are presented in Table 3. We find the correlations between both excess returns and beta and all explanatory variables are relatively low, all absolute values of which are less than 0.1. This is not a surprising result compared to previous work(e.g., Easley, Hvidkjaer, and O Hara, 2002). Market size (M E) positively correlates to OBS with the largest coefficient. This fact implies the information asymmetry is an important source of divergence of opinion in Chinese stock market, since smaller firms usually disclose little information and thus indicates a high level of information asymmetry. The signs of correlations between market size and ILLIQ, P IN are also consistent with past studies, 19

22 that is, larger firms usually show higher liquidity level and lower information asymmetry. Besides, significant and negative correlations between BM and ILLIQ, P IN are also found in our sample. Although some authors have documented the correlation between book to market ratio and liquidity level with the same sign as ours(e.g., Cui and Wu, 2007), other studies show an opposite relation between BM and P IN in contrast with our work(e.g., Easley, Hvidkjaer, and O Hara, 2002). We are in particular interested in correlations among ILLIQ, P IN and OBS. The absolute values, all of which are above 0.1, illustrates they do interlink with each other. The positive correlation between ILLIQ and P IN means the stock with a higher liquidity level experiences a lower probability of informed trading, which has been presented in Easley, Kiefer, OHara, and Paperman (1996). The negative correlation between P IN and OBS then consolidate the fact that the divergence of opinion is to some extent due to the information asymmetry. It is noted that a negative correlation between ILLIQ and OBS is observed. This fact has been forecasted in our discussion in literature review section, based on which we can not, however, decide on which source of the divergence of opinion drives this correlation. The interlinkages among ILLIQ, P IN and OBS found in our data strengthen our motive to examine the possible dominating effects when they affect expected asset returns. (Insert Table 3 Here) 5.3 Portfolio Test As a first and simple examination on whether each of ILLIQ, P IN and OBS relates to asset returns, a portfolio test is conducted in this section. We construct different portfolios independently based on ME and ILLIQ, ME and P IN, ME and OBS respectively 9. Specifically and taking sorting stocks by ME and ILLIQ for example, at the beginning of each month we independently sort stocks into three groups based on ILLIQ of the prior month (for P IN, stocks are first sorted by P IN of the prior quarter), ranging from the lowest one third to the highest one third, and five size deciles based 9 As pointed out in previous work, firm size (ME) is related to the liquidity level, the information asymmetry, the divergence of opinion and expected returns. Thus, the purpose of sorting stocks on it and including it in the following regression test is to control its possible effect on asset returns. 20

23 on ME at the end of prior month, ranging from the smallest one fifth to the largest one fifth. Portfolios of stocks based on ME and P IN, ME and OBS are sorted in a similar way. The results of sorting procedure are presented in Table 4. (Insert Table 4 Here) Panel A reports average excess returns of portfolios sorted by M E and ILLIQ, while Panel B reports the according average ILLIQ in each portfolio. From Panel A we find the excess returns basically show an upward trend as we move from low to high ILLIQ, in particular within smaller M E groups. Although exceptions occur from medium to high ILLIQ within the largest two size groups, the differences between excess returns are so small that can be ignored. This result implies lower liquid portfolios of stocks experience higher excess returns, which conforms to the previous findings on illiquidity premium. Besides, we also find an increase of excess returns when moving from small to large M E within the low ILLIQ group. Although this fact contradicts the small firm effect, it seems that this large firm effect only occurs in relatively high liquid stocks. From Panel B we see a reasonable fact that portfolios with a larger size generally show a lower illiquidity level, especially in the low and medium ILLIQ groups. Panel C reports average excess returns of portfolios sorted by ME and P IN, while Panel D reports the according average P IN in each portfolio. From Panel C we find that within each size group portfolios with a higher P IN generally experience higher excess returns with a slight exception. This fact illustrates the existence of the information risk premium. Meantime, the relations between M E and excess returns are uncertain, since we do not observe a uniform trend of excess returns when moving from small to large ME. From Panel D we find on one hand, the differences between P INs from small to large ME within each P IN group are relatively small, which justifies the stability of P IN. On the other hand, the negative correlation between ME and P IN observed in Table 3 is to some extent verified by a slight decrease of P IN as we move from small to large ME within each P IN group with two slight exceptions within the high P IN group. 21

24 Panel E presents average excess returns of portfolios sorted by M E and OBS, while Panel F presents the according average OBS in each portfolio. We observe a significant decrease of excess returns from low to high OBS within each M E group from Panel E. This conforms to Varian (1985) that the divergence of opinion is a risk factor and should be priced. Meanwhile, we also find an upward trend in excess returns from small to large ME, in particular within the low and high OBS groups. Finally from Panel F, we find portfolios with a larger size usually experience a higher OBS with a slight exception. This conforms to the findings in correlation test, which suggests that investors disagree more on smaller firms. It is worth noting that smaller firms usually disclose less information and thus verifies that the information asymmetry is one source of the divergence of opinion. Summarizing, the results from Table 4 show that the variables ILLIQ, P IN and OBS all relate to asset returns. Meantime, firm size seems to play an important role and should be controlled when examining the effect of ILLIQ, P IN and OBS on asset returns. Since we do not include market risk and book to market ratio in the portfolio test, they will be added in the following standard regression test. 5.4 Asset Pricing Test In this section, we report results of standard regression asset pricing test using the Fama French three factor framework. In the first step, we run the regression tests given by equation (7), (8) and (9), in which one of ILLIQ, P IN and OBS is included in the regression each time. The purpose of these regressions is to examine the independent impact of ILLIQ, P IN and OBS on expected asset returns. Table 5 reports results of time series averages of the coefficients in each equation using standard Fama and Mac- Beth (1973) methodology (F M) and Litzenberger and Ramaswamy (1979) methodology (L R). T values are given in parentheses. The results of intercept are dropped due to its irrelevant role in this paper. (Insert Table 5 Here) 22