Information-Based Trading and Autocorrelation in Individual Stock Returns

Transcription

1 Information-Based Trading and Autocorrelation in Individual Stock Returns Xiangkang Yin and Jing Zhao La Trobe University Corresponding author, Department of Economics and Finance, La Trobe Business School, La Trobe University, Bundoora, Victoria 3086, Australia. Tel: , The authors are grateful to Talis Putnins, the seminar participants at University of Bath, Shanghai University of Finance and Economics, Fudan University, Jiangxi University of Finance and Economics, University of Newcastle, and the 28 th Australasian Finance & Banking Conference for their constructive comments. The research is supported by funding provided by the Australian Research Council Discovery Projects (DP ). 1

2 Information-Based Trading and Return Autocorrelation in Individual Stocks ABSTRACT Applying a recently developed approach, this paper estimates the arrival rates of orders driven by private information and investor disagreement for each stock in a sample of NYSE-listed companies. Autocorrelations of these arrival rates are determinants of their return autocorrelation. Stock return tends to continue on consecutive days when privately-informed trading prevails, leading to positive return autocorrelation. However, return tends to reverse itself on days with continuous disagreement-driven trading, leading to more negative return autocorrelation. Contrarian trading strategies conditional on measures of investor disagreement can yield economically and statistically significant excess returns, after controlling for other determinants of return autocorrelation. JEL Classification: D82, G12, G14 Keywords: Information-based trading, return autocorrelation, private information, dispersion in beliefs 2

3 Autocorrelation in short-horizon stock returns is well documented in the literature and many studies find that autocorrelations in the returns of individual stocks are significant. 1 The evidence is fundamental to finance because it suggests predictability in stock returns and challenges the efficient market hypothesis. Why are stock returns serially correlated and what factors affect the correlation? This article addresses these questions from an information economics perspective. The premise of this study is that speculative trading triggered by the arrival of superior private information and order flows driven by investor disagreement in a stock are time-varying and serially correlated. 2 These correlations are profound factors in determining autocorrelation in stock returns and its variation. More importantly, these two types of information-based trading play very different roles in determining return autocorrelation. It is hypothesized that the propagation of private information in consecutive trading days increases serial correlation in stock returns and makes it positive, while dispersion in beliefs reduces the serial correlation and makes it more negative. The paper focuses on separately and jointly testing these hypotheses using both panel data and time-series data of individual stocks. It further demonstrates that the autocorrelation in trading of a particular motive has statistically and economically profound impacts. That results in the predictability of stock return to a certain extent and the profitability of investment strategies exploiting this autocorrelation. The link between privately-informed trading and return autocorrelation is intuitive. When an investor receives a negative private signal of the future payoff of a stock, she/he sells the stock and the price of the stock falls. However, this price usually only partially reflects the private information and the low return in the current period can be followed by a low return in the next 1 See, for example, Jagadeesh (1990), Lehmann (1990), Conrad, Kaul and Nimalendran (1991), Copper (1999), Gervais, Kaniel and Mingelgrin (2001), Avramov, Chordia and Goyal (2006), and Hendershott and Seasholes (2014). 2 We use investor disagreement and dispersion in beliefs interchangeably in this paper to account for investor heterogeneity because they receive differential information and/or have varied interpretations for the same public information. 3

4 period as the negative private information is further spread and impounded into the price. This intuition has been imbedded in theoretical analysis. For instance, Wang (1994), and Llorente, Michaely, Saar and Wang (2002) propose models in which returns generated by privately-informed trades tend to continue themselves. On the other hand, if some event, say the publication of a piece of disputable news, triggers dispersion in investors beliefs about the future value of a stock, 3 a pessimistic investor is willing to lower the price to sell the stock. Since there is no substantial change in the aggregate expectation of future stock payoff, a low return in the current period, as a result of the lower price pushed by a pessimistic seller, is more likely to be followed by a high return in the next period when an optimistic investor buys it. Thus, the disputable public news may make the price alternate between up and down from one period to another and manifest return reversal. The link between trades due to dispersion in beliefs and return autocorrelation has been explored using various theoretical models, 4 but it is Banerjee (2011) who first predicted that increased disagreement should reduce return autocorrelation if investors have rational expectations. Building on the theoretical foundations of prior studies, this paper analyzes return autocorrelation by characterizing the information environment of a stock s trading, i.e., its market state. To this end, we identify every trading day s information state for each stock in a sample of NYSE (New York Stock Exchange) stocks. Then, nonparametric analysis and regression analysis on pooled data and time series of individual stocks are conducted to estimate the contributions of continuous privately-informed trading and disagreement-induced trading to the serial correlation in individual stock returns. Consistent with theoretical predictions, it is found that returns on consecutive days tend to continue when trading stemming from informed speculators prevails on 3 For instance, Kim and Verrecchia (1994) model market participants processing earnings announcements differently, resulting in more information heterogeneity at the time of an announcement. 4 Harris and Raviv (1993) show that stock returns in their model are negatively autocorrelated. Shalen (1993) demonstrates that dispersion about futures prices contributes to the positive correlation between consecutive absolute price changes. 4

5 these days, while returns tend to reverse if investors beliefs are highly heterogeneous on these days. For instance, the first-order autocorrelation of close-to-close daily return is 0.089, on average, if there is no continuous information-based trading. This autocorrelation is increased by 0.16 (i.e., becomes 0.071) on days with speculative trading on private information but reduced by (i.e., becomes on days with trading from disagreeing investors. In fact, it is further demonstrated that return autocorrelation depends on the intensity of information-based trading in a dynamic manner. Return continuation increases with the intensity of continuous privatelyinformed trading, while return reversal increases with the intensity of continuous disagreementdriven trading. These findings are robust and remain qualitatively similar when we take stock illiquidity and turnover (Avramov, Chordia and Goyal, 2006), bid-ask bounce bias (Blume and Stambaugh, 1983) and contemporaneous order imbalance (Chordia and Subrahmanyam, 2004) into account in our analysis. When firm size is taken into consideration, it appears that the effect magnitude of information-based trading varies substantially. The connection between return autocorrelation and continuous privately-informed trading is stronger for smaller firms because to them information asymmetry is more likely to be a profound issue. On the other hand, the connection between return autocorrelation and continuous disagreement-induced trading is stronger for larger firms, which implies that sophisticated and confident investors who condition on prices and their own beliefs are more likely to trade large stocks. Since information-based trading, disagreement-driven trading in particular, is likely to be highly persistent, this makes it possible to predict current return based on return and informationbased trading on the prior day. We develop contrarian and momentum trading strategies to examine the statistical and economic significance of their profitability. When the contrarian strategy is coupled with criteria for the lagged information state, it yields significantly positive returns and 5

6 outperforms both equal-weighted (EW) and value-weighted (VW) market portfolios by substantial margins. For instance, the long-short zero-investment portfolio in our experiment generates cumulative raw returns of 37% to 57% over a 2-year sample period. They surpass the EW market portfolio by 3,095 to 4,973 basis points and the VW market portfolio by 1,989 to 3,713 basis points. The effect of disagreement-driven trading complements the determinants of return autocorrelation documented in the existing literature, as we find that our contrarian strategy is still highly profitable after controlling for firm size and commonly known determinants such as stock illiquidity, trading volume and liquidity provision. This paper contributes to the literature in four related research areas. First, because very different theoretical models can have similar implications for the time-series behavior of returns, trading volume is often used as additional data to stock return data for the identification problem. Regarding serial correlation in stock returns, the literature of volume-induced return reversal include Campbell, Grossman and Wang (1993), Conrad, Hameed and Niden (1994), Sias and Starks (1997), and Cooper (1999). However, the results are inconclusive. For instance, return reversal decreases with trading volume for relatively small Nasdaq stocks as shown in Conrad, Hameed and Niden (1994), but increase with trading volume for large NYSE stocks as shown in Cooper (1999). Trading volume alone seems unable to fully reveal the hidden determinants of return autocorrelation. Thus, we distinguish trades according to their trading motives and use proxies of different trading activities to characterize the information environment of a stock market. Our empirical evidence showing, firstly, the contrasting effects of the two types of informationbased trading on return autocorrelation, and secondly, the variation of these effects over firm size may explain the inconclusiveness of prior findings. The importance of distinguishing trading motives is also evidenced by further robustness tests which show these effects remain qualitatively unchanged after controlling for trading turnovers. 6

7 Second, Llorente, Michaely, Saar and Wang (2002) empirically demonstrate that the autocorrelation of a stock s returns increases in the proxy of the stock s information asymmetry such as bid-ask spread. However, their focus is not on directly estimating the magnitude of privately-informed trading s effect on return autocorrelation or ascertaining whether privatelyinformed trading makes this autocorrelation positive. 5 On the other hand, there is growing literature studying the impact of investor disagreement. 6 Banerjee (2011) is the first empirical analysis on the relationship between dispersion in beliefs and return autocorrelation. His empirical findings provide limited support for the theoretical prediction of a negative relationship between them. 7 Our analysis differs from prior empirical studies as we directly regress daily return on interaction terms of lagged return and daily measures of information-based trading. More importantly, the same regression includes both effects of private information and dispersion in beliefs, which not only quantitatively estimates these effects but also gauges their relative significance. Third, there has been widespread interest in short-run reversal strategies and their profitability since the discovery of short-horizon return reversals by Jagadeesh (1990) and Lehmann (1990). 8 For instance, Lehmann (1990) demonstrates that contrarian strategies exploiting the return reversals in individual stocks generate weekly abnormal returns of about 1.7%. Using internal NYSE data, Hendershott and Seasholes (2014) form long-short portfolios that yield returns 5 Their conclusion is achieved by a two-stage analysis, where the first stage is a time-series analysis of an individual stock, in which future return is regressed on current return and the interaction between return and trading volume, and the second stage is a cross-sectional analysis, in which the coefficient of the interaction term estimated from the first stage is regressed against a proxy of information asymmetry of the stock. 6 See Harris and Raviv (1993), Shalen (1993), Banerjee and Kremer (2010), Carlin, Longstaff and Matoba (2014). 7 More specifically, these results show that difference in return autocorrelation between high- and low-disagreement stocks is statistically significant (insignificant) when disagreement is proxied by trading volume (dispersion in analyst forecasts). Nevertheless, trading volume can be driven by other factors in addition to dispersion in investors beliefs, such as change in risk aversion (Campbell, Grossman and Wang (1993)) and private information (Kyle (1985)). In prior studies, the empirical relationship between trading volume and return autocorrelation has been investigated but the findings are inconclusive. 8 Conrad, Hameed and Niden (1994), Ball, Kothari and Shanken (1995), Copper (1999), Avramov, Chordia and Goyal (2006), and Hendershott and Seasholes (2014). 7

8 around 13 to 20 basis points at a one-day horizon. Unlike previous studies, our contrarian trading strategies explore the role of investor disagreement in determining return reversals. It shows that the profitability of reversal strategies is statistically and economically significant, and increases with trading intensity driven by dispersion in investors beliefs. Investor disagreement is demonstrated to be a driver additional to well-known factors which can enhance the profitability of the contrarian investment strategy. A fourth related literature examines the impacts of trading activities on price efficiency. The use of autocorrelation-based measures to test market efficiency dates back to early studies such as Fama (1970), who argues that substantial return autocorrelation reflects deviation from random walk pricing and is indicative of violations of an efficient market. Boehmer and Kelley (2009), and Saffi and Siguardsson (2010) establish institutional trading activity and short selling as sources of the improved short-horizon information environment. Our study complements the rich literature on the role of information-based trading in equity markets. We directly link information-based trading to return autocorrelation and find that stock prices on days with greater privately-informed trading more strongly resemble a random walk. It therefore suggests that continuous trades from privately-informed investors increase price efficiency. However, as consecutive trading driven by investor disagreement lowers the return autocorrelation or leads to a greater absolute value of serial correlation in returns, we infer such trading makes stock return deviate from a random walk further and the market less efficient. The remainder of this paper is organized as follows. Section I introduces the research methodology and hypothesis development. Data and sample are described in Section II. Section III demonstrates the opposite effects of privately-informed trading and disagreement-driven trading on autocorrelation in individual stock returns. Section IV documents the profitability of 8

9 information-based trading strategies that exploit return autocorrelation. The concluding remarks are provided in the last section. I. Research Methodology and Hypothesis Development Time-series behavior of stock returns, including the dynamics of return correlation, has long been the research interests of academics and practitioners. Wang (1994) recognizes private information as an important trading motive in addition to risk sharing. His theory shows that returns generated by risk-sharing trades tend to reverse themselves while those generated by informed trades tend to continue themselves. The theoretical model of Llorente, Michaely, Saar, and Wang (2002) also separates hedging trades from informed trades and more sharply predicts the dependence of a stock s return continuation on the intensity of information asymmetry. These models highlight the diffusion process of private information, which leads persistence of privatelyinformed trading. Abstracting this diffusion and trading persistence, stock prices can be martingales even with the presence of information asymmetry (Kyle (1982), and Glosten and Milgrom (1985)). Inspired by these theoretical works, our first hypothesis is that continuous privatelyinformed trading is related to return autocorrelation and a greater measure of this type of trading leads to a higher autocorrelation. Contrary to the existing literature, we directly measure daily information asymmetry of a stock market by estimating expected flows of buy and sell orders rather than use other proxies of information asymmetry such as bid-ask spread. We then isolate the effect of privately-informed trading as a component determining the serial correlation in stock returns. Another and perhaps more important aspect of our analysis is our measure of private information taking into account the impact direction of information asymmetry. Theory and intuition tell us that the fundamental reason for private information exerting a positive effect on return 9

10 autocorrelation is that the propagation of private information takes time so that the same piece of private information can induce return to go up or down in two consecutive periods. Thus, the hypothesis is tested through the continuation of privately-informed trading in the same direction. Our second hypothesis conjectures that continuous trading stemming from disagreeing investors has a negative effect on return autocorrelation and a greater measure of this type of trading results in a lower autocorrelation. In a model of trading based on announcements of public information, Harris and Raviv (1993) demonstrate that consecutive price changes exhibit negative serial correlation. Banerjee (2011) predicts that investor disagreement is related negatively to return autocorrelation if investors are rational and use price information to update their beliefs. The intuition for the relationship between investor disagreement and return autocorrelation is straightforward. If some information event triggers belief dispersion about the value of a stock, optimists will initiate purchases and push the price up while pessimists will initiate sales and push the price down. In this process, the price swings from one period to another, leading to a negative serial correlation of stock return. The market reaches a new equilibrium through this interaction process between optimistic and pessimistic investors. Disagreement is critical here because a piece of non-controversial information will induce all investors to unanimously revise their valuation and it will not be associated with abnormal trading (see, Llorente, Michaely, Saar and Wang (2002), Banerjee and Kremer (2010)). Similar to the case concerning information asymmetry, we also directly measure trading caused by investor disagreement at daily frequency and apply this measure to separate the corresponding component that determines the serial correlation of returns. Since the focus of this hypothesis is on the continuation of trading triggered by investor disagreement, we test this hypothesis by separating consecutive days with this type of trading from other trading days. 10

11 Properly and accurately measuring information-based trading is challenging and we here adopt the Hidden Markov Model (HMM) approach of Yin and Zhao (2015). The most notable advantage of this approach is its ability to produce time-varying measures of information-based trading with satisfactory accuracy. Unlike static measures such as PIN (Easley, Kiefer, O Hara and Paperman (1996)) and PSOS (Duarte and Young (2009)), which remain constant over the estimation window (ranging from a couple months to a year), these dynamic measures are at the daily or even higher frequency. This dynamic nature is particularly valuable to the study of the dynamic properties of stock returns such as autocorrelation in returns at the daily frequency. Another outstanding feature of the HMM approach is its ability to capture not only highly positive contemporaneous correlations between buy and sell order flows, but also the serial correlations of buy orders and sell orders observed in transaction data. 9 The autocorrelations in information-based order flows are particularly valuable to this study as they are the determinants of the serial correction of stock return. Through extensive Monte Carlo simulation experiments and real transaction data analysis, Yin and Zhao (2015) demonstrate that the HMM is very effective in identifying the market state of stock trading. In comparison with other prevailing models, the HMM approach shows superior performance in estimating daily measures of information-based trading as well as cumulative estimates over any time interval. It has also successfully been applied to address issues related to earnings announcement and co-movement of stock returns. From a technical point of view, the flexibility of HMM facilitates the estimation of model parameters and 9 Duarte and Young (2009) raise a concern regarding the original PIN model because of its failure to generate positive contemporaneous correlations between buy and sell order flows. Thus, dynamic measures based on the PIN model, such as those developed by Easley, Engle, O Hara and Wu (2008), lack such contemporaneous correlations. Of course, static models of information-based trading exclude autocorrelation in buy or sell order flows because order arrival rates in these models are static over their estimation windows. 11

12 circumvents the computational overflow problem. This is a major technical difficulty when estimating the PIN model and its variants for stocks with large daily trades. 10 Consistent with our purpose of testing the two hypotheses, the HMM includes two motives of information-based trading on a stock market: firstly, trades originating from speculative investors who possess superior private information of the stock and take this informational advantage to buy or sell the stock to maximize their profits/utility; and secondly, trades originating from disagreeing investors because of their different interpretations of the same public information or because they receive differential information of the stock. In addition, the model also includes liquidity needs as the third trading motive, which is independent of information-based trading motives. The information state of the market reflects whether private information events and/or events triggering investor disagreement occur or not, and if they occur, how intense they are. Since these events lead to different trading patterns, the state is uniquely associated with two random variables: the numbers of buyer-initiated and seller-initiated order flows. More specifically, state, is characterized by the expected values of these two random variables, ; and ;. The different trading motives imply that both arrival rates of buy orders and sell orders under a particular state have three components that 11 ; ; ; ;, ; ; ; ;, 1,2,,, 1,2,,, (1) where ; and ; denote, respectively, the arrival rates of privately-informed buy and sell orders, ; and ; the arrival rates of disagreement-driven buy and sell orders, and ; and ; the 10 For stocks with large daily number of trades, direct computation of the likelihood function of the PIN model may result in a numerical overflow problem and make the convergence of the maximum likelihood estimation fail, see, for example, Easley, Engle, O Hara and Wu (2008), Duarte and Young (2009), Easley, Hvidkjaer and O Hara (2010), and Lin and Ke (2011). Using Expectation and Maximization Algorithm, the estimation of the HMM converges for all the sample stocks in this study. 11 We use the expected number of orders and the arrival rate of orders interchangeably throughout this paper because of the HMM approach s Poisson assumption. 12

13 arrival rates of liquidity buy and sell orders. As (1) shows, the HMM allows for buy states and sell states and they are determined and estimated through model estimation. The random number of daily buy (sell) orders is modeled as the mixture of the random numbers of buy (sell) orders of all states. Thus, trading day can be characterized by its probability distribution over all states,. The very nature of the Markov model implies that any two consecutive trading days are linked by a Markov chain so that Γ, where Γ is the transition matrix of the Markov chain, whose element gives the probability of day 1 being on a particular state conditional on day being on another (or the same) state. The parameters of the HMM include the initial distribution of states, transition matrix Γ and order arrival rates λ ; and λ ; ( 1, 2,,, 1, 2,,. They can be estimated based on observed numbers of daily buy orders and sell orders by maximizing the likelihood function (see Equation (A1) in Appendix A.1) through Expectation and Maximization Algorithm. The details of the HMM and its estimation can be found in Appendices A.1 and A.2 of this paper. After the aggregate arrival rates of buy orders and sell orders under all states (i.e., λ ; and λ ; have been estimated, we follow the HMM approach to apply the k-means clustering analysis together with the jump method of Sugar and James (2003) to identify the three types of trading in (1). We outline the basic idea of the estimation here and present its details in Appendix A.3. First, we look into observed daily trade imbalances (the absolute value of net daily buys) and group them into clusters according to their statistic properties. The clusters with a center strictly larger than the center of the most frequent cluster are classified as ones involving privately-informed trading, while those with a center smaller or equal to the center of the most frequent cluster are considered without privately-informed trading. The rationale for this classification is the insight that information asymmetry leads to one-sided trading and substantial trade imbalance (Kyle (1985), Easley, Kiefer, O Hara and Paperman (1996), Sarkar and Schwartz (2009)). The most frequent 13

14 cluster of trade imbalances is chosen to be the cutoff point, because it includes states which occur most often and it is plausible to assume that most trading days do not have private information dispersed on the market. Extensive simulation analysis has also demonstrated the validity of using the most frequent cluster of trade imbalances for the cutoff point. For state,, we take the absolute value of its expected number of net buys (i.e., λ ; λ ; ) as an out-of-sample observation and assign it to the cluster whose center is the closest to it. If the assigned cluster involves privately-informed trading, we estimate ; and ; by Equation (A3) in Appendix A.3. If the assigned cluster does not involve privately-informed trading, ; and ; are equal to zero. Similarly, we following the HMM approach and apply the k-means clustering analysis together with the jump method to daily observations of balanced trades (i.e., the sum of buys and sells minus the absolute value of net buys). Note that liquidity trading generates a normal level of two-sided trades but an information event causing dispersion in investors beliefs results in a surge in both buys and sells or a shock to balanced trading, as argued by Duarte and Young (2009) and Sarkar and Schwartz (2009). 12 Thus, clusters of balanced trades with a center strictly larger than the center of the most frequent cluster are classified as ones that involve disagreement-induced trading, while those with a center smaller or equal to the center of the most frequent cluster are the ones not involving disagreement. Again, the cutoff point is the most frequent cluster of balanced trades since information events that cause controversy among investors are not likely to occur at a very high frequency. The choice of this cutoff point is strongly supported by simulation analysis. For state,, the expected number of balanced trades λ ; λ ; λ ; λ ; is taken as an outof-sample observation and it is assigned to the cluster with the closest center to it. The state is 12 If investors reach a consensus on the public announcement of a stock, they should revise their valuations of the stock similarly so that the announcement does not lead to abnormal trading. 14

15 classified according to the cluster it is associated with and in turn order arrival rates ; and ; can be estimated by Equation (A4) in Appendix A.3. When arrival rates ;, ;, ; and ; are estimated, arrival rates of liquidity buy and sell orders, ; and ;, can be backed out by (1). Since we know the probability distribution of trading day over the state space through the estimation of the HMM, the arrival rate of the buy or sell order of a particular type of trading on day is obtained by averaging the corresponding arrival rates over the state space, weighted by the probabilities of the market states (see Equation (A5) in Appendix A.3). Moreover, the aggregate arrival rates of buy and sell orders on day, ; and ;, can be derived by the sums of their three components that ; ; ; ; and ; ; ; ;. (2) To facilitate cross-sectional comparison, we scale the components of information-based trading in (2) by the total order arrival rate, ; ;. To a certain extent, the scaling also acts as a controlling device for trading volume because the total number of order flows on day is a random number with a mean of ; ;. Such scaling actually leads to some well-known concepts in the literature. The scaled order arrival rate of privately-informed trading corresponds to the developed by Easley, Kiefer, O Hara, and Paperman (1996), while the scaled order arrival rate of disagreement-driven trading corresponds to the S introduced by Duarte and Young (2009). It should be noted, however, that the original and are constant over the sample period and obtained through completely different methods. Therefore, following the existing concepts in the literature and accounting for their dynamic nature we call the scaled measures (dynamic probability of informed trading) and (dynamic probability of symmetric order-flow shock) that ; ; ; ;, (3) 15

16 ; ; ; ;. (4) Note that 0 if privately-informed trading exists on day t. Hence, does not indicate if the private signal is positive (inducing buyer-initiated orders) or negative (resulting in sellerinitiated orders). For empirical analysis, it is important to differentiate this trading direction. Thus, we define (probability of net buys due to private information) as ; ; ; ;. (5) II. Data and Sample Description Our sample includes common stocks listed on the NYSE in the two-year period from January 1, 2010 to December 31, From the Center of Research in Security Prices (CRSP), we obtain data on daily return, the numbers of shares traded and the number of shares outstanding. The following securities are eliminated from the sample since their trading characteristics might differ from ordinary equities: certificates, American Depository Receipts, shares of beneficial interest, units, companies incorporated outside the U.S., Americus Trust components, closed-end funds, preferred stocks, and real estate investment trusts. To permit a reliable estimation of return autocorrelation, we further require that stocks in the sample are traded on at least two-thirds of days. After this screening process, there are 1,249 stocks in the sample. 13 The transaction data source is Thomason Reuter Tick History (TRTH). For each stock, transactions and quotes that occur before and at the open are excluded, as well as those at and after the close. Quotes with a zero bid or ask price, quotes for which the bid-ask spread is greater than 50% of the price, and 13 We have also applied a screen criterion to exclude penny stocks, which refers to a stock having a minimum share price over the sample period being less than one dollar. This screen leads to a reduction of 2.24% of the sample size. Nevertheless our findings are virtually unchanged when these penny stocks are excluded from the sample. Moreover, penny stocks usually have small market capitalization. Since we are also interested in size-stratified subsamples, we report our findings by including these penny stocks to create a more complete picture. 16

17 transactions with a zero price are also excluded to eliminate possible data errors. Data for November 26, 2010 and November 25, 2011 are removed due to an early day after thanksgiving closing. The Lee-Ready (1991) algorithm is applied to the transaction data to determine the daily numbers of buys and sells. Two daily return series are considered in this paper: open-to-close returns and close-toclose returns. The close-to-close daily returns are obtained from CRSP, while the open-to-close daily returns from the TRTH transaction database. The three measures of information-based trading introduced in (3)-(5) are estimated by the HMM approach for each stock on each day. Panel A of Table I summarizes the descriptive statistics of the entire sample and its three subsamples stratified by average daily market capitalization over the sample period ( ). As illustrated by column 2, the average daily of a stock over the sample period,, falls with firm size. For example, the cross-sample mean of is for the small stocks but and for the medium and large groups, respectively. This is consistent with the idea that proxies for information asymmetry and smaller firms often have more private information in their stock trading (Easley, Hvidkjaer and O Hara (2002)). On the other hand, is quite similar across the three size-based subsamples. Although one may expect the availability of public information, such as media coverage or analysts following, to be related to firm size, reflects the magnitude of belief heterogeneity in public news rather than simply the occurrence of public news events themselves. The insignificant relationship between firm size and is likely to indicate that traders have fewer disputes on public news of larger firms or receive less differential information although their news events may occur more often. It is also consistent with the empirical finding of Banerjee (2011) that none of the disagreement proxies are strongly correlated with firm size. For our empirical analysis, a more important variable of measuring information asymmetry than is the probability of net buys due to private 17

18 information. Column 4 reports the cross-sample descriptive statistics of its daily average over the sample period ( ). The absolute mean values of for the entire sample and the three subsamples are much smaller than their counterparts of. INSERT TABLE I HERE For each stock, we calculate the first-order autocorrelations (ACFs) of the two series of daily returns and the three series of daily information-based trading measures. Their crosssectional summary statistics are presented in Panel B. As shown in columns 1 and 2, the median autocorrelation is in close-to-close returns ( ) and in open-to-close returns ( ). It implies that autocorrelation in daily returns is negative for most sample stocks and relatively weak in comparison with autocorrelations in information-based trading documented in the last three columns. However, the serial correlations of and are and 0.153, small in comparison with the serial correlation of which is This suggests that investors private information is relatively shorter-lived than investor disagreement. Daily trading activities due to private information are positively correlated through time for most sample stocks, which is consistent with the theoretical setting of Chordia and Subrahmanyam (2004) that traders split their orders over time to minimize their price impact. When examining the three size-stratified subsamples, it is clear that private information in the small firms is longer-lived, evidenced by its mean s of and values of and 0.179, respectively. This is probably because the greater information asymmetry in the small firms needs to be resolved by longer time. In contrast, stocks in the large group on average have a larger of than small and medium stocks. 18

19 III. The Opposite Effects of Continuous Privately-Informed Trading and Disagreement- Driven Trading on Autocorrelation in Individual Stock Returns Before rigorously testing the hypotheses developed in Section I, we sort trading days according to their characteristics of information-based trading or stock return to examine their validity. We first separate consecutive days with continuous trades driven by private information in the same direction from other days; that is, select trading days according to,, 0. We also separate consecutive days without privately-informed trading at least on one of the two days, i.e.,,, 0. We then calculate the sample of each stock s return for these two different kinds of trading days to identify the impact of continuous trading driven by private information. Rows (2) and (3) of Panel A in Table II indicate that the mean s of and for the days satisfying,, 0 are and 0.032, respectively, which are significant at the 1% level. On the other hand, for the days satisfying,, 0, the estimates of serial correlation are and 0.062, respectively, which are also significant at the 1% level. This evidence implies that private information has a substantial impact on stock returns and it can change return autocorrelation from significantly negative to significantly positive; that is, change stock return from reversal to continuation. This change is profound, as shown in the lower part of Panel A that the difference between the mean s over the two kinds of days, i.e., ACF(2) ACF(3) is significant at the 1% level. INSERT TABLE II HERE Alternatively, trading days can be distinguished based on whether there is consecutive trading due to disagreement among investors. Rows (4) and (5) show that the mean s of and on consecutive days with disagreement-driven trading are and 0.150, respectively. They are much more negative than those on days without consecutive disagreement- 19

20 driven trading, and The difference between the mean s of ( ) over the two kinds of days, i.e., ACF(4) ACF(5), is ), significant at the 1% level. Thus, as expected, continuous trading caused by dispersion in investors beliefs does substantially enhance the negative serial correlation in individual stock returns. We further jointly examine the effects of private information and investor disagreement on return autocorrelation by considering four kinds of trading days in rows (6)-(9), which show substantial in return autocorrelation. The comparison between rows (6) and (7) reveals the effect of consecutive privately-informed trading when consecutive trading due to investor disagreement does not appear. The comparison between rows (8) and (9) reveals the effect when disagreement trading is effective on consecutive days. Once again, they demonstrate the significantly positive impact of continuous privately-informed trading on serial correlation in returns, but the joint effects of the two types of information-based trading lead to a negative correlation. On the other hand, the comparisons between rows (8) and (6) and between rows (9) and (7), respectively, illustrate the effect of investor disagreement on the consecutive trading days when privately-information trading is effective and ineffective. The negative effect of belief dispersion is obvious and statistically significant. Panel B of Table II looks at the association of serial correlation in returns with informationbased trading from another angle, where trading days are sorted based on whether the consecutive daily returns of a stock continue or reverse. Then we estimate the serial correlations of and on these two kinds of days. Rows (II)-(III) demonstrate that autocorrelation in ( ) on days with close-to-close return continuation is much larger (smaller) than that on days with return reversal. The difference is ( 0.057), which is significant at the 1% level. Similar results can be obtained for open-to-close return as shown in rows (IV)-(V) and the following mean-difference test. Thus, return autocorrelation is positively connected with privately- 20

21 informed trading on consecutive days but negatively connected with disagreement driven trading on consecutive days. We further conduct a similar nonparametric analysis to the three size-stratified subsamples. As shown in Panels C and D of Table II, the findings from Panel A and B qualitatively hold for the three subsamples. A new observation is that the effect of private information on return autocorrelation increases as stock size becomes smaller, as evidenced by the monotonicity of, and in stock size shown in Panel C. Moreover, the difference between the serial correlations of on days with return continuation and days with return reversal falls as stock size increases, as shown by in Panel D. Similar monotonicity can also be found in the difference between serial correlations of. In the subsections below, we confirm these observations through regression analysis. Following Campbell, Grossman and Wang (1993), we study the dynamics of stock return autocorrelation and the factors affecting the dynamics by estimating different forms of the regression model:,,,,, (6) where, is stock i s return on day t, the time-invariant individual effect, 14 and, the error term. In (6), autocorrelation is a linear function of factors,. 15 We begin by reporting the results based on panel data regressions for the entire sample and the three size-stratified subsamples. We also conduct time-series regressions for individual stocks so that we can examine more closely the individual stock level. Finally, we discuss the robustness of our empirical findings. 14 We report the results of panel regressions including firm fixed effects. If month fixed effects are also included, the results are qualitatively similar and the overall explanatory power of the regression model increases. 15 Vector, in (6) also includes variables of information-based trading on day. To simplify notations, subscript is omitted. 21

22 3.1 Panel regressions over the entire sample We first estimate the fixed-effect panel regression model (6) with the specification that,,,,,, (7) where dummy variable takes value 1 if the condition 0 is satisfied and zero otherwise. As mentioned before,,, 0 implies that on the two consecutive trading days private information leads trading activities in the same direction. Thus,,, is used to capture the scenario that price on day 1 only partially incorporates private information and there are continuous informed trades due to the same or similar private signal on day t as well. Similarly, dummy variable,, captures the continuation of investor disagreement on the market. Regression (6)-(7) resembles the feature of Campbell, Grossman and Wang (1993), who regress return on the interaction term of lagged return and trading volume to study the effect of trading volume on return autocorrelation. The first hypothesis proposed in the previous section conjectures that return continuation is larger on days with continuous privately-informed trades (i.e., 0 and the second hypothesis argues that return reversal is larger on days with continuous disagreement-driven trades (i.e., 0 ). To ensure the results robustness, the panel regressions are run for two return series, close-toclose return and open-to-close return, and they are documented in Table III. Column 1 in Panel B shows the testing results for close-to-close returns where only private information is taken into account. The regression coefficient is significantly positive at the 1% level, thus supporting the first hypothesis. In particular, return autocorrelation on days without consecutive informed trading is on average, but it increases by on days with continuous informed trading. The test on the lower part of the panel shows the difference is statistically significant at the 1% level. It suggests that continuously incorporating private information leads to positive autocorrelation in stock returns. Comparing this return autocorrelation with the overall 22

23 return autocorrelation of in Panel A, it shows that privately-informed trading not only increases return autocorrelation but also shifts it from overall negative to positive. This positive serial correlation in stock returns is consistent with what is reported in Table II through nonparametric analysis. Results of open-to-close returns in column 4 of Panel B are also supportive of the first hypothesis, as they exhibit even a greater degree of return continuation on days with continuous informed trading. INSERT TABLE III HERE Furthermore, columns 2 and 5 in Panel B show the corresponding testing results for the second hypothesis of the effects of dispersion in beliefs. The autocorrelation of close-to-close returns reduces by on days with continuous trades due to investor disagreement, and that of open-to-close returns reduces by 0.089, which confirm the findings in Table II that serial correlation in stock returns is more negative on trading days with consecutive disagreement-driven trading. Both tests support the second hypothesis with an estimated coefficient significant at the 1% level. We also jointly test the two hypotheses and report the results in columns 3 and 6 of Panel B. The regression coefficients remain significant at the 1% level. In particular the autocorrelation of close-to-close returns is on days without consecutive information-based trading, and it increases by 0.16 on days with continuous informed trading but reduces by on days with continuous disagreement trading. Open-to-close returns exhibit a similar pattern. Moreover, if we compare estimates of in columns (3) and (1) or in columns (6) and (4), and compare estimates of in columns (3) and (2) or in columns (6) and (5), we find that the changes in both estimates themselves and their t-statistics are not substantial. This implies that the effects of private information and belief heterogeneity on return autocorrelation are not considerably overlapped. 23

24 Overall, the regression results in Panel B show that return autocorrelation varies across days and depends on the information environment of the market trading the stock. Panel A of Table III reports the regression results with lagged return alone as the prime explanatory variable (i.e., (7) is collapsed to, ). On the one hand, we find that the return autocorrelation is negative on all trading days, ignoring the variation in a firm s information environment. On the other hand, lagged returns only explain 0.09% (0.03%) of the variance of close-to-close (open-to-close) return series as indicated by in Panel A. Nevertheless, when we distinguish days according to their associated types of information-based trading, lagged returns explain 1.19% (1.10%) of the return variance, as shown in column 3 and 6 of Panel B, which is improved over 12 (35) times compared to Panel A. Although the results of regression model (6)-(7) demonstrate there is a strong association between return autocorrelation of a stock and its information-based trading, we would like to further investigate how this association changes with the intensity of information-based trading in a dynamic manner. Thus, we introduce the interaction terms between lagged return and measures of information-based trading into regressions and consider the following specification:,,,,,,,,,. (8) Columns 1 and 4 in Panel C of Table III show is significantly positive at the 1% level, supporting the first hypothesis. That means return continuation increases with the intensity of continuous privately-informed trading. Columns 2 and 4 in Panel C confirm that return reversal is enhanced by the degree of continuous trading resulting from investor disagreement, since 0 and is significant at the 1% level for both return series. When we jointly test the two hypotheses in columns 3 and 6, the regression coefficients remain significant at the 1% level. 24

25 In the literature, return autocorrelation is used as a measure of price efficiency (see, for example, Fama (1970), Boehmer and Kelley (2009), and Saffi and Siguardsson (2010)). Both negative and positive return autocorrelations reflect deviation from random walk pricing and are indicative of violations of the market efficiency hypothesis. Our results therefore link informationbased trading to price efficiency as well. For both two return series, the autocorrelation is negative when there are no continuous information-based trades on two consecutive days as Panel B of Table III shows. When there are continuous trades due to investor disagreement, return becomes more negatively autocorrelated, but it becomes positively autocorrelated with a smaller absolute value when there are continuous trades due to private information. These findings indicate that privately-informed trading increases price efficiency. Prices on consecutive days with these trades more closely track the fundamental value of the stock and more closely resemble a random walk. However, consecutive trading triggered by investor disagreement increases the absolute value of return autocorrelation so that return deviates more from a random walk. 3.2 Panel regressions over size-stratified subsamples We estimate the fixed-effect panel regression model of (6) with specification (7) or (8) over the three size-based subsamples and report the results in Table IV. Overall, the earlier results of positive (negative) dynamic relationships between return autocorrelation and continuous privatelyinformed trading (trading because of dispersion in beliefs) are generally robust and obtained for all subsamples. However, the positive effect of private information is more substantial for small stocks, while the negative effect of investor disagreement is more profound for large stocks. Let us take column 3 of Panel B as an example. The estimate of declines from to and then to over the small, medium and large subsample, while the absolute value of estimate increases from to and then to The t-statistics of and display similar monotonicity patterns. 25