The Effects of Information-Based Trading on the Daily Returns and Risks of. Individual Stocks

Transcription

1 The Effects of Information-Based Trading on the Daily Returns and Risks of Individual Stocks Xiangkang Yin and Jing Zhao La Trobe University First Version: 27 March 2013 This Version: 2 April 2014 Corresponding author, Department of Finance, La Trobe Business School, La Trobe University, Bundoora, Victoria 3086, Australia. Tel: , Fax: , j.zhao@latrobe.edu.au. The authors would like to thank Xiaozhou, Zhou, Rong Wang and participants of 2014 MFA Annual Conference, 26 th Australasian Finance and Banking Conference, and seminars at La Trobe University, Audencia Nantes School of Management and Monash University for constructive comments. 1

2 The Effects of Information-Based Trading on Daily Returns and Risks of Individual Stocks ABSTRACT This paper investigates the dynamic relation between information-based trading of a stock and its daily return and risk. It develops a theoretical model to motivate the regression specifications for empirical analysis. Based on two samples of stocks, we demonstrate that the expected trading imbalances of a stock determine its daily return while the expected trades determine its volatility. Trading imbalance arisen from private information plays a dominant role in determining return but trading due to disputable public information is the dominant contributor to risk. Publicinformation trading is closely associated with idiosyncratic risk rather than systematic risk. JEL Classification: D82, G12, G14 Keywords: Information-based trading, Return volatility, Systematic risk, Idiosyncratic risk 2

3 The important role played by information in securities trading is well recognized. A common theme of information-based trading is the adverse selection issue caused by private information as analyzed by seminal works of Grossman (1976), Glosten and Milgram (1985), Kyle (1985). Because uninformed market players are at the risk of trading with privately informed speculators, they require an information risk premium to compensate for their potential loss to informed traders. In this sense, information risk is likely to be a risk factor determining asset return differentials in a cross-section. Easley, Kiefer, O Hara, and Paperman (1996) develop the concept of PIN (Probability of INformed trading) to measure trading motivated by privately informed investors. Since then, PIN measure has been widely adopted in the literature and Easley, Hvidkjaer and O Hara (2002, 2010) show that PIN is priced and can explain the crosssectional difference of securities returns. 1 Duarte and Young (2009) introduce Symmetric Order-flow Shocks (SOSs) to securities trading into the original PIN model and define PSOS (Probability of SOS) to isolate the illiquidity component of PIN. 2 It is found that PSOS measure is also a risk factor explaining cross-sectional difference of stock returns. This paper studies a related but different issue. It focuses on the effects of informationbased trading of an individual stock on its daily return and risk. Similar to Duarte and Young (2009), we consider two types of information-based trading. The first type of trading is originated from privately informed traders, who observe some private signals of the stock and thus have superior information over other market players. They take this informational advantage to buy or sell the stock to maximize their profits. The second type is caused by 1 Mohanram and Rajgopal (2009) replicate Easley, Hvidkjaer and O Hara s (2002) work and show that although PIN is priced for the sample period it does not constitute a risk factor for the period of Symmetric Order-flow Shock (SOS) has two explanations in Duarte and Young (2009). One cause of an SOS is the occurrence of a public information event. Because traders have different opinions or interpretations about the public information, both buy and sell orders increase when the public information is released. The other cause of an SOS is that traders simply coordinate trading at particular times to reduce trading costs. This paper inclines to the first interpretation. We will call trading activities induced by disagreement on a piece of public information disputable-public-information-induced trading or simply SOS trading. 3

4 different opinions or beliefs of a public information event such as an earnings announcement or disclosure of a new investment opportunity. Investors who are optimistic of the news buy the asset while those who are pessimistic sell it. Our main findings can be summarized as the following. First, the expected amounts of net buy orders (i.e., the expected trading imbalances from various sources) determine daily stock return, while the expected amounts of trades (including both buys and sells) determine return risk. Second, privately informed trading dominates SOS trading in both marginal and total effects on stock return, 3 while SOS trading dominates privately informed trading in return risk. Third, SOS trading or trading induced by disputable public information has a significant effect on total risk (return variance) of individual stocks and idiosyncratic risk but its effect on systematic risk (market beta of stock return) is mild. 4 Fourth, the of a firm matters in the sense that smaller firms provide stronger supporting evidence to the first three findings. The intuitions behind the findings, particularly the first finding, are straightforward. For a trading day with good (bad) news of a stock, privately informed speculators will quietly buy (sell) it, which pushes the stock price up (down) and leads the market to end up with a high daily return. Such one-d trading moves price in one direction and it does not necessarily cause excess volatility of return. On the other hand, a piece of disputable information can trigger a surge in both buy and sell order flows. Such symmetric order-flow shocks lead price and return to fluctuate but they do not substantially move return in one direction. We formalize these ideas in a theoretical model based on Brennan, Chordia, and Subrahmanyam and Tong (2012), which 3 The marginal effect is defined as the change of dependent variable caused by one unit change of explanatory variable. The total effect is measured by the average of the absolute values of the marginal effect times the daily explanatory variable over the estimation window divided by the average of the absolute values of dependent variable over the same time period. 4 Idiosyncratic risk is measured by the standard deviation of return residuals obtained through a market model of intraday return. 4

5 builds up a relation between order flow and price change. We enrich the model by assuming that order-flows arrive at the market following independent Poisson processes (Easley, Hvidkjaer and O Hara (2002), and Roşu (2009)). Following the model s predictions, our empirical analysis concentrates on the effects of expected trading imbalances caused by privately informed traders and SOS traders on return and the effects of expected trades from these traders on stock risk. Inspired by the concepts of PIN and PSOS, 5 we use expected numbers of buy and sell orders from different types of traders to characterize information-based trading. We use two sets of measures. The first set includes expected numbers of net buy orders from informed traders and SOS traders and expected numbers of trades from these traders. The second set adopts relative measures; that is, all these expected numbers are scaled by the expected number of total orders submitted by all investors. 6 The measures based on expected numbers perfectly match variables used in the theoretical model and they in general lead to better performance of regression models. But the scaled measures are unit-free, which facilitate comparison across stocks. Standard PIN and PSOS are time invariant over the estimation window such as a couple of months to a year. Since we intend to investigate stock return and risk at daily level, we require dynamic or daily measures of information-based trading. To this end, we adopt the Hidden Markov Model (HMM) approach developed by Yin and Zhao (2014), which can estimate various expected numbers of buy orders and sell orders at daily level or even at a higher frequency. Their simulation and empirical analyses demonstrate the HMM approach can generate quite accurate estimates measuring information-based trading. 5 PIN is usually defined as the ratio of the expected number of buy and sell orders stemming from informed traders to the expected total trades, while PSOS is defined as the ratio of the expected number of trades from SOS traders to the expected total number of trades. Thus, they are our scaled measures of total orders from privately informed trading and SOS trading, respectively. 6 Our theoretical model and empirical analysis include a third type of trading, which is motivated by liquidity needs and is irrelevant to private or public information. 5

6 This paper is closely related to the growing literature on the PIN model and its variants as we have mentioned. But instead of the effects of information on the cross-sectional differentials of expected stock returns, we focus on how information drives the evolution of daily return and risk of each individual stock. Our premise is that stock price is continuously adjusted to private and/or disputable public information through trading dynamics. This evolution dictates the level and variation of daily return of each stock. Informed trading may lift average return over a long period up because of adverse selection, negative private information should drive return down in the short-run. More importantly, it can be shown that it is disputable public information rather than private information that dominates the effect on the total risk and idiosyncratic risk of stock return. This is to a certain extent consistent with Duarte and Young s (2009) argument that it is systematic order-flow shock (SOS) rather than private information that is decisive to the differential of expected returns across stocks. This paper is also related to Chordia and Subrahmanyam (2004), who investigate the relation between order imbalance and daily return of individual risky assets. Their findings are consistent with ours in the effect of trading imbalance on daily return, although they are more interested in revealing how market makers dynamically accommodate autocorrelated imbalances emanating from large traders, in order to explore the positive relation between lagged imbalances and return. Their key explanatory variable, order imbalance, is daily observation of the difference between buy and sell orders, which differs from our measures in two ways. First, our order imbalance is measured by the difference of expected buy and sell orders rather than observed numbers. This treatment enables us to filter the noise in daily observations. Second, we decompose order imbalance according three trading movies while Chordia and Subrahmanyam (2004) do not consider such decomposition. By separating trading types, we are 6

7 able to specify which type of trading is the dominant contributor to the level of daily return. Moreover, Chordia and Subrahmanyam (2004) do not consider the risk of stock return. Instead, we address total risks, systematic risks and idiosyncratic risks of individual stocks. Our finding of the strong link between dispersed beliefs on stock value and total risk is supportive to Banerjee and Kremer s (2010) the prediction that a jump in the difference of opinions leads to an increase in return volatility. On the other hand, our finding of the insignificant relation between SOS trading and systematic risk for most sample stocks is related to Patton and Verardo (2012). They propose a model where investors can use public information to extract information of the aggregate economy and find that daily realized market beta is higher on earnings announcement days but it declines on post-announcement days to a level below its non-event average. Thus, the relation between market beta and trading due to disputable public news over a period could be quite ambiguous, which is consistent with our finding. Rees and Thomas (2010) note that forecast dispersion proxies for idiosyncratic uncertainty about future cash flows during earnings announcements, which is in line with our empirical result that disagreement on public news is positively related to idiosyncratic risk. The remainder of this paper is organized as follows. Section I develops a theoretical model of the relation between return dynamics and trading activities. Section II introduces the approach of estimating the daily measures of information-based trading. Data and samples are described in Section III. Section IV examines the effects of different types of trades on daily return and total risk, while Section V studies the dynamic relationship between informationbased trading and systematic or idiosyncratic risk. Further tests and robustness checking are briefly reported in Section VI. The concluding remarks are provided in the last section. 7

8 I. A Theoretical Model and Its Specifications for Empirical Analysis To motivate our empirical analysis, we develop a dynamic model associating asset return and its volatility with information-based trading, based on the formulation of Brennan, Chordia, Subrahmanyam, and Tong (2012), which originates from Glosten and Harris (1988). Let, denote the expected value of a risky asset, conditional on the public information available immediately after the th transaction of day t. Similar to Brennan et al. (2012), we assume that, evolves according to,,,,, (1) where, is the order of the th transaction of day t with, 0 corresponding to a buyerinitiated trade and, 0 a seller-initiated trade, and is the (inverse) market depth parameter. Thus,, in (1) reflects the revision in expectations upon an order arrival. It captures the adverse selection effect of a transaction on price because the transaction can potentially contain private information unknown to the market. Term, is the unobservable innovation between the 1 th and th transactions due to the arrival of public information, of which all market players have an unanimous view. Let, denote the direction of the th transaction of day t, i.e.,, 1 if, 0 and, 1 if, 0. Brennan et al. (2012) further consider a fixed component of transaction costs to account for inventory holding costs and fixed costs. Therefore, the transaction price of the th trade of day t,,, can be written as,,,. (2) Using (1) and (2), price change between two transactions is equal to Δ,,,,,,,. (3) If there are transactions on day t, the total return of that day can be represented in terms of aggregate trade-by-trade price changes, i.e., 8 Δ,. Our focus is how the expected

9 return and volatility are affected by information-based trading. For the simplicity of exposition, we assume the order of each transaction being constant and normalize it to one share so that,,. Such simplified assumption is widely adopted in theoretical analysis (see, for example, Glosten and Milgrom (1985)). It is also consistent with the concepts of PIN and PSOS measures in the empirical analysis, where the number of transactions rather than trading volume is considered. Based on trade directions of order flows, we can figure out the number of buyerinitiated orders on day t, min,,0. max,,0, and the number of seller-initiated orders, In the literature, it is widely assumed that the arrivals of buy orders and sell orders are independent Poisson processes (see for example, Easley, Hvidkjaer and O Hara (2002) and Roşu (2009)). Thus, we assume and follow Poisson distributions with parameters ; and ;, 7 respectively. A key innovation of our model is that it allows the distributions of buy and sell order flows to vary from day to day, as reflected by time-varying parameters ; and ;. For the total number of trades on day t,, it is also Poisson distributed with time-varying mean and variance ; ;. We then obtain the probability of an arriving order being buyerinitiated Pr, 1 ; ; ; and the probability of it being seller-initiated Pr, 1 ; ; ;. The first two moments of the distribution of the order flow become Ε, ; ; ; ; and Ε, 1, so that Var, 1 ; ;. Applying these results, we obtain the ; ; following proposition by routine computation. 7 The Poisson distribution is a one-parameter distribution with its mean (arrival rate) equal to variance. We will use order arrival rate and the expected number of orders interchangeably. 9

10 Proposition 1. If price response to order flows follows (3) and buy and sell orders arrive following independent Poisson processes with parameters ; and ; respectively, the expected total return and variance on trading day t are Ε ; ; E. (4) Var ; ; 2 1 ; ; Var ;, (5) ; where,. Proof: See Appendix A. Since ; and ; are the arrival rates and positive, there is ; ; ; ; 1. Therefore, ; ; is a higher-order small term and is negligible in comparison to other terms. On the ; ; other hand, reflects the fixed costs, which is small and is not the focal point of this study. If we model it zero, the second term on the right-hand side of (5) disappears. With these consideration, we rewrite (5) as Var ; ; Var Constant and higher-order terms. (6) In (4)-(6), represents the effects of non-disputable public news on day t, which is not associated with abnormal trading (see, for example, Llorente, Michaely, Saar and Wang (2002)). An important insight shed by the model is that the expected daily return of a risky asset is related to the expected trade imbalance, while the volatility of return is positively related to the expected total trade if the higher order effects are ignored. Moreover, expected daily return has direction in the sense that whether it is positive or negative depends on whether the expected amount of net buy orders of the day is positive or negative. This distinguishes the model from asset pricing 10

11 model where the focus is on the relation of expected long-term return and risk factors but return direction is not a concern. To study information-based trading, we should separate different types of transactions. We consider three trading motives as we mentioned in the Introduction. The first is the liquidity needs when investors want to adjust their portfolios to hedge their risks or rebalance their portfolios due to some exogenous shocks. The second type of trading activities is generated by speculative investors who have private information on the fundamental value of the asset. The third type of trades comes from symmetric order flow shocks, such as a disputable public news event, of which the occurrence induces some investors to buy the asset but others to sell. In Proposition 1, the numbers of buy orders and sell orders aggregate these three types of orders. Let ; ( ; be the arrival rate of liquidity buys (sells) on trading day t, ; ( ; the arrival rate of privately informed buys (sells), and ; ( ; the arrival rate of buys (sells) due to symmetric order flow shocks. Then, the means of and, ; and ;, can be decomposed into three components ; ; ; ;, ; ; ; ;. (7) Since liquidity trading constitutes the base of each day s trading activities, the associated arrival rates ; and ; are strictly positive for all trading days. The remaining two components in ; and ; can be zero if the trading day has no private information and/or disputable publication information. Moreover, we require that ; ; 0 since a private signal is either positive or negative, which induces informed traders either to buy or to sell. But for ; and ;, they are either both equal to zero if there is no disputable news event or both positive if there is such an event. Barclay and Warner (1993), Hasbrouck (1995), and Chakravarty (2001) document evidence of a disproportionately greater price impact that is attributable to informed 11

12 trading. Alexander and Peterson (2007) also note that trades resulting in greater proportional price impacts are more likely to have been made by informed traders than noise or liquidity traders. Therefore, we modify the impact of trading on price,,, by considering these three different types of orders empirical analysis. Furthermore, can be treated as an independent error term n empirical analysis. In light of Proposition 1, we estimate the following regression relations for each individual stock: ; ; ; ; ; ;, (8) ; ; ; ; ; ;, (9) where we use to denote realized volatility to proxy for the variance of return. We include a lagged term in the regressions to capture the persistence of dependent variables. The variables we used in measuring trading activities are expected numbers of buy and sell orders on a trading day. For instance, ; ; and ; ; are expected order imbalance and expected order originated from SOS traders. Such raw measures are not convenient for cross-sectional comparison if some stocks involving heavy trading while others are very light. To facilitate cross-sectional comparison, we scale these measures by the expected number of total trades (or the arrival rate of all orders), ; ;. Such scaling actually leads us to the PIN developed by Easley et al. (1996) and PSOS introduced by Duarte and Young (2009): ; ; ; ;, ; ; ; ;. (10) However, we would like to point out that the original PIN and PSOS measures are constant over the estimation window. The PIN and PSOS used in this paper are estimated by the Hidden Markov Model (HMM) approach (see the next section), which vary from day to day. We further 12

13 define the ratio of the expected number of net buys due to private information to the expected total number of trades as PNbIN (probability of net buys due to private information) and the ratio of the expected number of net buys due to SOSs to the expected total number of trades as PNbSOS (probability of net buys due to symmetric order flow shocks): ; ; ; ;, ; ; ; ;. (11) Then, we can estimate an alternative version of regression models (8)-(9):, (12). (13) In these regressions, measures of liquidity trading is not explicitly included for two reasons. First, ; ; ; ; 1 so that ; ; ; ; should not be included in (13). Second, the expected number of liquidity buys is expected to be similar to that of liquidity sells on average, ; ; ; ; is almost zero and negligible. 8 liquidity buy, ; ; ; ;, is also dropped in (12). To make (12) in the same format as (13), the expected net To preserve tractability, we analyze price change (total return) in the theoretical model, which is standard practice in the microstructure literature on informed trading (see for example, Hong and Stein (1999); Chordia and Subrahmanyam (2004)). However, in the empirical analysis, in order to preserve comparability in the cross-section, we analyze simple daily returns and report the associated results since the implications of the theoretical model hold to both price changes and simple returns. Total return and log return, as alternative measures to simple return, are considered in the robustness checks. 8 Some empirical studies actually presume ; ;, see for example Easley, Engle, O Hara and Wu (2008). 13

14 II. Daily Measures of Information-Based Trading In order to empirically test the effects of information-based trading on daily return and risk of an individual asset, we need to estimate the daily order arrival rates according to their trading motives to measure information-based trading. Although the estimation of the standard PIN and PSOS measures of Easley, Hvidkjaer, and O Hara (2002) and Duarte and Young (2009) has been discussed thoroughly in the literature, these conventional measures are constant over the whole estimation period, say a quarter, and it is difficult to use them to well capture shortterm variations in information-based trading. To overcome the difficulty, Yin and Zhao (2014) develop a new Hidden Markov Model (HMM) approach, which can estimate daily measures with satisfactory accuracy. This section briefly outlines the approach and the estimation process. The core of this approach is a Hidden Markov Model (HMM), which links the observable trading activities to the unobservable information state of the market of a risky asset. The information state is used to describe whether private and/or public information events of the asset occur or not, and if they occur, how intense they are. 9 More specifically, it is characterized by the expected numbers of buyer-initiated and seller-initiated orders arriving at the market. Each trading day is associated with a distribution of information states and its evolution portraits the trading process of the risky asset. Formally, the HMM consists of two parts: a two-dimensional unobservable stochastic process of state ;, ; : 1,,, satisfying the Markov properties; a bivariate state-dependent trading process, : 1,,. In this model, T is the time horizon being considered, indicates the hidden state at time t, and and represent the observable time series of buyer- and seller- initiated trades, respectively. The 9 For instance, informed investors may receive an extremely good signal of a company or it is just slightly better than the expected. The private signal can be observed by either a very limited number of investors or a relatively large amount of investors. For public information event, divergence in opinions can be either profound or mild. 14

15 distributions of and depend only on the current state and not on previous states or trades, i.e., Pr Pr and Pr, Pr, where,,, and,,,. Although the Markov property implies that conditioning on the history of the process up to time t is equivalent to conditioning only on the most recent value of, there exists a dependence structure in the evolution of hidden states. The transition matrix of this 2-dimensional Markov chain can be written as where Γ γ, ;, γ, ;, γ, ;, γ, ;, γ, ;, γ, ;, γ, ;, γ, ;, γ, ;, γ, ;, γ, ;, γ γ,, ;, γ, ;,, ;, γ, ;, γ, ;, γ, ;, Pr ;, ; ;, ;, is the probability that state is, at time 1 conditional on it being, at time, and m and n are the ranges of the two components of hidden state. The unconditional probability of the hidden state being in state, at time t,, ; Pr ;, ;, is a key variable of any HMM. Denoting these probabilities by the row vector, ;,, ;,,, ;,,, ;,,, ;,, ;, we can deduce the distribution of states at time 1 from its distribution at time t by Γ. Moreover, the distribution of future information states, over a forecast horizon of h days, can be calculated by Γ. 15

16 Consistent with prior literature and the assumption in Section I, buy and sell order flows arrive at the market according to a bivariate independent Poisson process for state,. 10 Thus, given state being, the probability of observing buy orders and sell orders at time t, Pr ;, ;, is, where ; ;! and ; ;.! In the above expressions, λ ; and λ ; are the arrival rates of buys and sells, respectively, when buy state is i and sell state is j. The marginal distribution of observing, at time t can be calculated by Pr Pr ;, ; Pr ;, ;, where -diagonal matrix is defined by 0 1 and. 0 1 The HMM model also yields a probability distribution of states for each day, conditional on the history of observed trades: Pr ;, ;, for 1,2,,. (14) The parameters of the model include the initial distribution of states, transition matrix Γ and order arrival rates λ ; and λ ; ( 1, 2,,, 1, 2,,. They can be estimated by maximizing the following likelihood function as shown by Yin and Zhao (2014): 11 Θ Γ Γ Γ. 10 Although buys and sells are independent in a specific state, the observed daily numbers of buys and sells are contemporaneously and serially correlated because of correlation between states. 11 The details of parameter estimation of the HMM based on Expectation and Maximization Algorithm (see Baum, Petrie, Soules, and Weiss (1970)) are given in Appendix B.1. 16

17 The numbers of buy and sell states, m and n, are determined in model selection according to information criterion, such as Akaike information criterion (AIC) or Bayesian information criterion (BIC). After obtaining λ ;, λ ; and Pr ;, ; in the process of estimating the HMM, Yin and Zhao (2014) further develop a two-step approach to decompose the order arrival rates, λ ; and λ ; into three components ; ; ; ;, ; ; ; ;. (15) The first step applies k-means clustering together with the jump method (see Sugar and James (2003)) to all observed trade imbalances 1,2, in order to identify the arrival rates of trades due to private information for each hidden state. They argue that the states belonging to the cluster with the smallest mean of trade imbalances do not contain trades with private information. The rest states contain private information revealed by their substantial expected trade imbalances. After partitioning the states by this way, the estimates of arrival rates of trades due to private information, ; and ;, can be easily obtained as specified in Appendix B.2. The second step conducts a 2-means clustering analysis on the observations of balanced trades 1,2, to separate states with disputable public information from states without disputable public information. The estimation of arrival rates of trades due to disputable public information, ; and ;, is detailed in Appendix B.2. Therefore, we can obtain the estimates of the arrival rates of different types of trades at trading day t in the framework of the HMM approach, 17

18 ; ; ; ;, ;, ;, Pr ;, ;, ; ;, Pr ;, ;, ; ;, Pr ;, ;, ; ;, Pr ;, ;, Pr ;, ;, Pr ;, ;, (16) where the conditional probability of the hidden state Pr ;, ; is available after the estimation of the HMM as detailed in Appendix B.1. III. Data and Sample Description We use two samples of stocks for our empirical analysis. The first dataset is a sample of 120 stocks that were traded on the New York Stock Exchange (NYSE) in 2010 and It consists of 40 stocks randomly selected from S&P 500 Index, S&P MidCap 400 Index, and S&P SmallCap 600 Index, respectively. The ticker symbols of these sample stocks are detailed in Panel A of Table I. This dataset has been used by Yin and Zhao (2014), which demonstrates that the HMM approach can effectively measures information-based trading for all the sample stocks and performs better than prevailing approaches. In particular, both positive contemporaneous correlation between buys and sells and serial dependence of order flows are captured with high accuracy. Because the sample firms are selected from three indexes, they are representatives for a variety of industries and market capitalizations. This sample includes only NYSE stocks to avoid possible variation caused by differences in trading protocols. INSERT TABLE I HERE The second sample consists of all constituent stocks of S&P 500 Index in 2010 and We exclude the stocks added or removed from the index over the sample period and the final sample contains 451 stocks. S&P500 stocks are arguably the most actively traded stocks, capturing 75% coverage of U.S. equities in terms of market capitalization. This sample presents 18

19 a more comprehensive picture of the market, particularly for large stocks. There are 40 stocks appearing in both two samples and serving as the bridge between the two samples. Transaction data of all sample stocks are taken from the Thomas Reuters Tick History (TRTH) transaction database over a two-year period from January 1, 2010 through December 31, For each sample stock, transactions and quotes that occur before and at the open are excluded, as well as those at and after the close. Quotes with zero bid or ask prices, quotes for which the bid-ask spread is greater than 50% of the price, and transactions with zero prices are also excluded to eliminate possible data errors. Data of 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 TRTH transaction data to determine the daily numbers of buys and sells. For each stock, we measure firm by the average daily market capitalization over the sample period. Panel B of Table I summaries the statistics of characteristics for the first sample of 120 stocks and its three -based groups. It indicates a positive relation between firm and the average daily total number of trades, and the average daily absolute trade imbalance. Consistent with prior studies, the subsample of S&P SmallCap 600 constituents has the largest sample mean of average percentage effective bid-ask spread and the smallest sample mean of average daily turnover (measured by the ratio of the number of shares traded to the number of shares outstanding). The summary statistics of the characteristics of the second sample of 451 stocks constituting S&P 500 index are provided in Panel C of Table I. For each sample stock i, we apply the HMM approach to estimate the arrival rates of different types of trades on each trading day as specified by (16) in the previous section. We 19

20 also estimate the scaled daily measures of information-based trading, i.e.,,,,,,,,, using (10) and (11). We consider two types of return series here, i.e., open-to-close daily returns and close-toclose daily returns. The close-to-close daily returns are obtained from the Center for Research in Security Prices (CRSP), while the open-to-close daily returns are calculated based on the open and closing prices taken from the Thomas Reuters Tick History (TRTH) transaction database. Total risk of returns is defined as return variance. As a common indicator of return variance, realized variance provides a relatively accurate measure (Andersen and Bollerslev (1998)) and reflects time variations in total risk. For a particular trading day, the realized variance is calculated as the sum of squared intraday returns. As the sampling frequency of intraday returns approaches infinity, realized variance is free from measurement errors (Andersen, Bollerslev, Diebold, and Labys (2001)). We choose sampling frequencies of 15-minute and 10-minute for intraday returns to balance the desire for reduced measurement error with the need to avoid the microstructure biases that arise at the highest frequencies. IV. The Effects of Information-based Trading on Return and Total Risk In this section, we empirically examine the effects of information-based trading on stock returns and their total risks. A. Descriptive Statistics and Nonparametric Tests To preserve comparability in the cross-section, Table II presents only descriptive statistics of the scaled daily measures of information-based trading, i.e., PIN, PSOS, PNbIN, and PNbSOS because their counterparts of non-scaled measures are hardly comparable across 20

21 sections.,,, and are the averages of their underlying daily measures over the sample period. As Panel A shows, the cross-sectional sample means of and are and respectively for the first sample of 120 stocks, reflecting the existence of substantial information-based trading in the market. On the other hand, the crosssectional means of and are close to zero. While each, is likely to be vary small and close to zero leading a close-to-zero mean, small indicates that the privately informed buys and sells offset each other over a long period when a sell is treated as a negative buy. INSERT TABLE II HERE In order to examine the daily return s relation with information-based trading, we separately calculate the averages of scaled daily measures for days with a positive return and for days with a negative return. 12 The results of their cross-sectional sample means are given in Panel A of Table II as well. Consistent with the theoretical prediction from our theoretical model, the cross-sectional mean of on trading days with positive return is 0.041, while that on trading days with negative return is It demonstrates that positive (negative) daily returns are associated with net privately informed buys (sells). In contrast, the difference between s on positive and negative return days is much smaller and equal to ( In order to further explore the contemporaneous link of return and information-based trading for sample stocks, we test the equality of the average, (,, or, ) on days with a positive return and that on days with a negative return. Using the 5% significance level, 13 we find only 13.33% of stocks whose PINs are significantly 12 We use close-to-close daily return here. In regression analysis in the next subsection, both close-to-close and open-to-close returns are used. 13 Throughout of the paper, the statistical significance level is at the 5% level if it is not specified. 21

22 different on positive and negative return days and the corresponding future for PSOS is 17.75%. These figures indicate that PIN and PSOS are not good proxies for the determinants driving daily return. Although measure may be priced in long-term asset pricing tests as a risk factor, it does not distinguish privately informed buys with privately informed sells and has an ambiguous effect on contemporaneous daily returns. In particular, the cross-sectional mean of is on days with a positive return, which is very close to that on days with a negative return (0.135). Similarly, the cross-sectional mean of on days with a positive return is close to that on days with a negative return (0.350 vs ). However, there are 94.17% and 49.17% of stocks, respectively, whose and PNbSOS on days with a positive return are significantly different from those on days with a negative return. It implies that positive daily returns are significantly driven by contemporaneous net privately informed buys but to a less extent driven by net buys due to public information. This result is consistent with Alexander and Peterson (2007), who argue that trades resulting in greater proportional price impacts are more likely, on average, to have been made by informed traders than noise or liquidity traders. For total risk, we sort trading days into quintiles by its realized variance for each sample stock. 14 The cross-sectional mean of is for the trading days within the largest quintile (, while that is for the trading days within the smallest quintile ( ). The difference-in-means test shows that on trading days within is significantly different from that within for almost all sample stocks (i.e., 96.67% of 120 stocks), but the corresponding figure for drops to 66.67%. For the other two measures, i.e., and, the cross-sectional means for the trading days within are close to their counterparts within. It implies that excess total risk of returns is mainly determined by the number of 14 Realized variance is calculated based on a time interval of 10 minutes. Both 10- and 15minute frequencies are used in the regression analysis in the next subsection. 22

23 orders rather than order imbalance and it is more profoundly related to disputable public information than private information. Panel B of Table II presents descriptive statistics of the four measures for the three based subsamples of the 120 stocks, and the second sample of 451 stocks constituting S&P500 Index, respectively. The cross-sectional means of both and obtained by averaging over all trading days decrease with firm, which implies that information-based trading is more prevalent in the market of small firms than that of large firms. The results of Panel A hold for all three -based subsamples and the second sample. In particular, for almost all sample stocks, on days with a positive return is significantly different from that on days with a negative return, while on days within the largest quintile is significantly different from that on days within the smallest quintile. Monotonicity in firm can also been seen for difference-in-means tests of when days are sorted by daily return and tests of and when days are sorted by. We also note that although the descriptive statistics and nonparametric test results of the subsample of large group are similar to those of S&P500 sample, difference between the two still exist. This difference may reflect the fact the S&P500 includes both NYSE and NASDAK stocks while the subsample of large group concentrates on 40 NYSE stocks included in S&P500 index. In order to further investigate return and total risk in a simple nonparametric way, we sort the trading days of each sample stock in another way, i.e., sorting days into quintiles according to the value of one of daily measures of information based trading. We then take the averages of daily return and realized variance of each quintile over time and across section. The results are documented in Table III. Panel A shows that the average daily return is higher for the trading days with a larger measure of,, consistent with the theoretical prediction of our model. 23

24 Such phenomenon is strongest for small, less frequently traded stocks, where the average daily return is 1.1% for days within the smallest, quintile and 1.2% for trading days within the largest quintile. Meanwhile, the relationship of,,, or, with the contemporaneous daily returns are ambiguous. Although, distinguishes buys with sells, SOS traders do not possess private information about the value of the stock so that the profits of their trading activities cannot be assured in general. Panel B shows that the average daily realized variance is higher for trading days with a larger measure of,, which is again consistent with our theoretical prediction. The other three scaled measures of information-based trading, i.e.,,,, and,, do not have clear and consistent effects on the contemporaneous total risk of returns. INSERT TABLE III HERE In summary, both Table II and Table III show that net information-based buys are associated with positive contemporaneous daily returns and such effect is largely driven by privately informed trading rather than SOS trading. The conventional measures of PIN and PSOS do not distinguish buys from sells and thus cannot effectively reveal the short-term association of returns with information-based trading. Excess total risk of return can be induced by both buys and sells due to information arrivals, where the effect of trading due to disputable public information is much stronger than that of privately informed trading. It implies the differential effects of two-sided shocks and one-sided shocks on total risk. B. The Effects of Information-Based trading on Daily Return To quantify the relation between information-based trading and daily return, we examine regression model (8), where is measured by either open-to-close or close-to-close daily return 24

25 on day t. The averages of regression coefficients of (8) and autocorrelation-corrected t-statistics are reported in Panel A of Table IV. To see the direction of the effect of each explanatory variable, we count and report the percentage of sample stocks with regression coefficient being significantly positive or negative. While the coefficient of each explanatory variable proxies its marginal effect, we are also interested in the total effect of the variable. In order to examine the normalized total effect of each regressor in individual regressions, we consider a measure of effect, which is the ratio of average of the absolute total effects to the average of absolute values of dependent variable. For instance, the effect of ; ; on is calculated by ; ;. Panel A presents the results of the first sample of the 120 stocks, its three -based subsamples, and the second sample of the 451 stocks constituting S&P500 Index, respectively, for both open-to-close and close-to-close daily returns. Because the results are robust to the choice of daily return, we take open-to-close for example to discuss. First of all, the marginal impacts of different trades are quite different. In particular, the regression coefficient of the expected number of net buys due to private information, ; ;, is positive and significant for the majority of sample stocks. In contrast, the coefficient of the expected number of net buys due to disputable public information, ; ;, or liquidity needs, ; ;, is mostly positive but they are significant for no more than 32.50% of sample stocks. In terms of magnitude, the marginal effect of informed trading is also the largest among the three types of trades, as implied by its largest average regression coefficient of ; ;. The explanatory power of SOS trading or liquidity trading to daily return is relatively low. Previous literature (see for example Chakravarty (2001); Alexander and Peterson (2007)) note that trades resulting in greater proportional price impacts are more likely, on average, to have been made by 25

26 informed traders than noise or liquidity traders. 15 Our findings are consistent with this claim. It in turn demonstrates the validity of the two-step approach in identifying the order arrivals of different types of trades detailed in Appendix B. The difference of total effects between the three types of trading is more impressive because of their s of expected net buys. As we can see that the total effect of ; ; ranges from 26.6% to 39.3%. On the other hand, the total effect of ; ; ranges from 9.96% to 13.3% and that of liquidity trading ranges from 7.6% to 12.9%. INSERT TABLE IV HERE The information-based trading could affect the contemporaneous returns of large and frequently traded stocks differently from small and infrequently traded stocks. We compare the results of the three -based subsamples of the 120 stocks reported in Panel A to explore such possibility. The -stratified results demonstrate that both marginal effect and total effect of privately informed trading on daily return decreases with firm. This implies that the price impact of private information depends the of stock market capitalization. All other things being equal, private informing moves price less effectively for a stock with larger market capitalization. The intuition behind this is straightforward. Large stocks usually trade more frequently and the private information is more easily to be hidden by the high transaction traffic. Thus, it is less possible for informed trades to be followed by other investors in the market. Moreover, the sheer of market capitalization of large stocks means that the resources owned by informed speculators are relatively small so that their role played in these markets is relatively small. Different from privately informed trading, neither marginal effects nor total effects of 15 Some papers in the literature (see for example Barclay and Warner (1993); Hasbrouck (1995); Chakravarty (2001); and Alexander and Peterson (2007)) document the presence of stealth trading by institutional investors and find that medium-d trades, more likely to be attributable to informed traders, tend to have a disproportionately greater aggregate price impact. 26

27 both liquidity trading and public-information induced trading appear to be monotonic in firm. Our model seem to perform better for small firms as the average R 2 of regressions decreases with firm from over 10% to less than 6%. The coefficient of lagged return is negative on average and the stocks with a significantly negative coefficient are much more that with a significantly positive coefficient. It implies that stock returns are more like to reverse themselves rather than continue their trends. The average effect of lagged return is smaller than that of ; ;, ; ; or ; ; for both samples and the three subsamples, which demonstrates the dominant role played by trading activities in explaining return dynamics. The results of testing regression (12) are documented in Panel B of Table IV in the same format as Panel A. For more than 90% of the sample stocks, daily return is positively and significantly associated with the probability of net buys due to private information. There is no sample stock with regression coefficient of or being significantly negative for either open-to-close or close-to-close return. The average regression coefficient of always exceeds that of by a substantial margin, implying larger marginal effect of private information than disputable public information on daily return. Regarding total effect, the average effect of is larger than 28.3% for all samples and subsamples considered, while that of is less than 8.31%. Although the scaled measures of information-based trading are adopted in (12) to explain daily return instead of their non-scaled counterparts, the results of Panel A discussed above qualitatively hold here. However, for seven out of 10 cases the average adjusted R 2 in Panel B is slightly smaller than that in Panel A, indicating regression specification (8) marginally better conforms to the prediction of theoretical model. But when scaled measures of information-based trading are adopted as regressors in (12), 27

28 we can do the cross-sectional comparison between the marginal effects of the regressors by performing a simple different-in-means test of equality of and for each sample and subsample. As reported in the last row of Panel B, all the hypothesis tests yield a p-value less than It shows that the marginal effect of on daily return is significantly larger in comparison to at the 5% level. C. The Effects of Information-Based trading on Total Risk of Return For total risk, we regress (9) using realized variance of intraday returns sampled at the 15- or 10-minute frequency. The results are presented in Panel A of Table V in the same fashion as Panel A of Table IV. Let us first look at the first sample of 120 stocks and the case where realized return variance is generated by 15-minute frequency. The regression coefficient of ; ; is positive and significant for almost all the stocks (95%), showing the substantial effect of SOS trading on the total risk of return. Meanwhile, the regression coefficients of ; ; and ; ; are significant and positive for only 16.67% and 8.33% of the sample stocks, respectively. In terms magnitude, the average regression coefficient associated of ; ; is also the largest, while the average coefficient of ; ; is marginally larger than that of ; ;. These results are consistent with the prior literature that information arrival may induce excess volatility. Our results, however, further show that the marginal effects of the two types of information-based trading are different. The strong relation between ; ; and reflects the substantial effect of belief divergence of public news on the volatility of stock price. When a public information event occurs, say an announcement of profitability outlook of a firm, investors may disagree about the implication of the event. Those with a positive view actively buy the stock and push its price up, while those with a negative view (the announcement 28