Inferring Trader Behavior from Transaction Data: A Simple Model

Transcription

1 Inferring Trader Behavior from Transaction Data: A Simple Model by David Jackson* First draft: May 08, 2003 This draft: May 08, 2003 * Sprott School of Business Telephone: (613) Ext Carleton University djackson@sprott.carleton.ca 710 Dunton Tower 1125 Colonel By Drive Ottawa, Ontario K1S 5B6

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3 Inferring Trader Behavior from Transaction Data: A Simple Model Abstract A model is presented that uses trade counts to characterize the arrival of news and the propensity of informed and uninformed traders to transact. Our model has extremely low data requirements, is very fast to estimate and is adaptable for different research applications. The model is used to investigate changes in the bid / ask spread in conjunction with trades. We develop and estimate an innovative extension of the model that relaxes the assumption that news is independent from day to day.

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5 Introduction In 1987, Easley and O Hara (EO) introduced a discrete-time, sequential trade microstructure model 1 that shines a light on the flow of information about an asset and reveals some characteristics of subsequent informed and uninformed trading. A strength of the EO model is its limited data requirements. Transaction counts of buying and selling, along with counts of non-trading periods are enough to estimate the probability that informed traders are active in a given asset market. Because most data sets do not provide the buy / sell direction of trades, EO use the Lee and Ready algorithm 2 to classify trade direction. The idea underlying the Lee and Ready method is to use both transaction and quote data to infer trade direction. A transaction price above the mid-quote is classified as buy-initiated; a transaction price below the mid-quote is classified as sell-initiated. As implemented in EO s published papers, no allowance is made for the uncertainty introduced by estimating trade direction. In effect, a researcher using the Lee and Ready algorithm in this way assumes more precise information than is available. Trade classification schemes have been shown to classify trades imperfectly, 3 however, raising questions about test outcomes that are dependent upon estimates from the EO model. In this paper, we derive a sequential trade model that uses trade counts only. There is no use of the unobserved trade direction, removing any concerns about misclassification of trades and understated standard errors. Our model, thus, has very low data preparation Easley and O Hara, Journal of Financial Economics, Lee and Ready, Journal of Finance, Theissen, Journal of International Financial Markets, Institutions & Money, 2000.

6 requirements, is extremely fast to estimate and is adaptable to different research applications. Ours is an example of models in which a subset of traders have private information about the value of the asset. These traders act to profit from their information at the expense of uninformed liquidity traders and the market maker. The directed trading behavior of the informed enables the market maker and other uninformed market observers to make inferences about the true value of the asset. Glosten and Milgrom provide an early sequential trade, asymmetric information model. 4 Sequential trade models allow only one trader at a time, and place some limit on the size of an individual trade. Because informed traders must wait their turn and because trade size is limited, informed trading is not instantly revealing. Thus, sequential trade models have the potential to show time series patterns in learning about the asset s value. Indeed, the process of learning by the market maker is a primary focus of the Easley and O Hara BSN model upon which our TNT model is based. The richness of information provided by buy and sell counts enables the BSN model to infer a bid / ask spread time series that reflects the parameters of the news process and the balance of informed and uninformed trading activity. By using trade counts only, the TNT model gives up the ability to infer the spread. Our contribution is to provide a model is very easy to work with and that does not suffer from possible misclassification of trade direction. We will demonstrate our trade / no-trade (TNT) model and briefly compare our parameter estimates with those provided by the EO buy / sell / no-trade (BSN) model. Both the TNT and BSN models assume day-to-day independence of information. We will 2

7 test this assumption and extend our model to allow for information that is not revealed to the public for two days. Finally, we present a generalisation of the TNT model that we use to investigate whether or not market makers change their quoted spreads in response to trading activity. This paper is organised as follows. Section 1 presents the EO buy / sell / no-trade (BSN) model and our trade / no-trade (TNT) model. The TNT model makes no assumptions about trade direction. In Section 2 the data is described. In Section 3 the model is estimated, and some robustness and goodness of fit tests are performed. Section 4 generalizes the model to estimate the propensity of market makers to change spreads around informed and uninformed trades. In Section 5 we summarise what we have demonstrated. 1. Two Discrete-Time Sequential Trade Models In a world with a single, risky asset, we model sequential trade between investors and a market maker. A key feature of the models considered here is that news about the value of the asset is generated intermittently. On any given day, there is uncertainty about whether or not the value of the asset has changed since the previous day. Before the start of trading, news about the end-of-day value of the asset is generated with a probability,. Any such news is bad with probability and good with probability 1 of each trading day, the news becomes publicly available.. At the end The market maker is risk neutral and faces competition, so quotes are set at the expected value of the asset, conditional on the trade direction of the next transaction. There are 4 Glosten and Milgrom, Journal of Financial Economics,

8 assumed to be a fixed number of trading periods during the day, with one trade possible during any one period. All trades are for one unit of the asset, with all buys occurring at the ask and all sells at the bid. In each trading period, one potential trader arrives at the market. This trader observes any news with probability. If news is observed, this (informed) trader always trades, buying on good news and selling on bad. If news is not observed, this (uninformed) trader makes a liquidity trade with probability or chooses not to trade with probability 1. Similarly, on days, with no news, each trader must be uninformed and trades with probability or chooses not to trade with probability 1. Uninformed trades are equally likely to be buys or sells. The market maker can learn from periods of non-trading because they are more likely on days with no information than on days with good or bad news. 1.1 The EO BSN Model The EO trading structure is depicted in Figure 1. Note that a draw from the news generating process (no news, good news, bad news) occurs once during the day, whereas only the first of many trading periods is represented in Figure 1. For a given day, the probability of observing B buys, S sells, and NT no-trade periods, given the model parameters is Pr BSNT,,,,, BS B S NT B S NT NT 4

9 Day-to-day news events are assumed to be independent, so the likelihood function for many days is the product of the daily probabilities. The log-likelihood function for D trading days is D LBSN log Pr Bd, Sd, NTd,,, d 1 B S NT 2 2 B S NT log NT log 1 BS 1.2 The TNT Model The BSN model relies upon counts of buys and sells. Since trade direction is not provided in most transaction databases, it is useful to consider a model that depends only upon counts of trades. This simplified trade model is depicted in Figure 2. Because trade direction is not observed, the TNT model does not distinguish between days with good or bad news. Similarly, the propensity of uninformed traders to buy rather than sell becomes irrelevant. What this model captures is the intuition that trade will tend to be more intense on news days than on no-news days. A news day should have a higher count of trades and fewer no-trade periods than a day with no news. For a given day with T trades and NT no-trade periods, the likelihood function is T T NT NT Pr T, NT,, The log-likelihood function for D trading days is 5

10 L TNT D log Pr T, NT,, d 1 T NT T NT log Data Transaction and quote data is obtained from the TORQ database. The TORQ database provides quotes, orders and associated transaction prices for 144 NYSE securities from November 01, 1990 through to January 31, The securities in TORQ were chosen randomly so as to be distributed evenly among NYSE size quintiles. In order to remove securities that may have different trading practices and timing of information effects than common shares, we eliminate all REIT s, units, and closed-end funds. Because the model requires a certain level of trading activity to estimate meaningful parameters, we eliminate all common stocks that have many days with no market order transactions, including at least one stretch of more than five trading days with no transactions. This study uses 20 of the remaining 98 common stocks. For each stock, trade price and trade size for all market order transactions after the open are saved. Bid-ask spread and midquote price are calculated from the ask and bid quote time series. To allow for imperfect synchronisation between the quote and transaction time clocks, a quote must be in effect 5 seconds before a trade execution. Buy and sell direction of each transaction is inferred following the Lee and Ready (1991) algorithm. Following EO (1997), a 5 minute window without a trade is counted as a non-trading period. EO (1997) use data for 60 trading days to estimate the parameters of their model. For this study, we use the 60 trading days from November 06, 1990 through to January 31,

11 Table 1 lists summary statistics of counts of trades, no-trade periods and inferred buys and sells for the 20 stocks. The overall stock market increased sharply over the three months covered by the TORQ data. This is the probable explanation for the excess of buys over sells in Table 1. The mean daily trade count varies by a factor of nine from GLX to EMC, but the mean daily no-trade count varies only by a factor of two. This suggests that trades tend to cluster, rather than be uniformly distributed through the trading day. 3. Model Estimation Estimating the TNT Model Table 3 presents maximum likelihood estimates for 20 NYSE firms from the TORQ database. Daily trade counts for 60 trading days are used along with a five minute notrade interval. The log likelihood function is well behaved. Estimation is very fast and 60 days of data is sufficient to get significant estimates of all three parameters of the model:, the probability of a news day,, the probability that on a news day a given trader is informed, and, the probability that an uninformed trader chooses to trade. The model parameters,,,, can be used to calculate the probability of an informed trade, PI 1. Table 3 reveals a fair degree of cross-sectional variation in all four parameters. For example, over this period, the probability of an informed trade, PI, varies from 6.5% for FFB to 52.7% for HAN. Comparing the BSN and TNT Models Is the TNT model simply a restricted version of the BSN model? For example, are similar parameter estimates obtained if one uses the BSN model, but does not assume that 7

12 buy/sell direction is observable? Let us compare the TNT model to a version of the BSN model in which one half of the total number of trades are assigned to be buys and the other half are assigned to be sells. Further, set the probability of bad news,, equal to one half. Pr BS T 2, NT,,, 1 2 T T 1 T NT NT Compare this to the TNT equation. T T NT NT Pr T, NT,, The restricted BSN model does not reduce to a multiple of the TNT model. Since the two equations differ in their first term, the two equations will give different estimates for the parameters,,. None the less, does the BSN model give parameter estimates close to those of the TNT model? Table 3 presents estimates for Ashland Oil, 5 the firm used by Easley, Kiefer and O Hara (1997) to demonstrate the BSN model. The 95 percent confidence intervals for,, overlap. Since one model is driven by buy and sell counts and the other model is driven by their sum, we would hope to find consistent parameter estimates. Notice that is estimated with much less precision than and. Since there are many trading opportunities during a day, but 5 Thirty trading days of buy / sell / no-trade counts for Ashland Oil come from Table 1 in Easley, Kiefer and O Hara, Review of Financial Studies,

13 only one draw from the news process, we effectively have more observations for estimating, than. Are parameter estimates always so consistent for the two models? Table 4 presents 30 and 60 day parameter estimates for four NYSE firms that were selected to represent a range of trading activity. Given the relatively large standard errors, estimates for the probability of a news day,, mostly fall within the 95% confidence intervals. Such is not the case for other parameters, however. The estimates provided by the two models, for the probability that uninformed traders choose to transact,, and for the probability that a trader is informed on a news day,, differ significantly in many instances. Estimates of the probability of informed trading, PI, can be quite different too. This suggests some caution when using either model for research. Tests that rely upon absolute levels of the parameters may be sensitive to which model is chosen. Model Specification Sensitivity to Choice of No-Trade Interval A number of specification tests will now be presented. Looking first at parameter stability, Table 5 shows 60-day parameter estimates as the time specified for a no-trade period varies from one minute to 10 minutes. All estimates increase with the length of a no-trade period, especially for the 10 minute interval. Estimates of the probability of news,, are fairly consistent for different no-trade periods. This is expected, since reflects relative levels of trading from day to day, not relative levels of trading to nontrading. The probabilities that a trader is informed on a news day,, and that an uninformed trader chooses to transact,, both increase with the length of a no-trade 9

14 period. This is expected, since and reflect levels of trading relative to trading opportunities within each day. Two important composite measures of trade are, the fraction of informed trades on a new days and PI, the fraction of informed trades. We would like the model s estimates of and PI to reflect the flow of private information during a given period, without being sensitive to the choice of a no-trade interval. Table 5 shows that the increase in the estimates of and PI are proportional to the length of the no-trade period. The rate of increase is small, however, averaging 1.5% per minute for and 1.6% per minute for PI. Do Intermittent News and Private Information Help Explain Trade? The TNT model explains daily trade counts in terms of intermittent news events, captured by, and traders with different trading propensities on days with news than days without. One test of the model specification is to compare this model to one in which news is not intermittent, making trading propensity fixed from day to day. Which model is more likely given the data? The model restriction constrains the probability of news,, to be 1. With one parameter constrained, the likelihood ratio statistic is approximately distributed chi-squared, with one degree of freedom. We reject the restricted model for large values of the statistic. The five percent rejection value is Likelihood ratio statistics were calculated from 60-day estimates for the 20 NYSE firms. The smallest statistic from the 20 firms was 269, soundly rejecting the restricted model. The TNT model, with news on some days and no news on others better explains the data than a model in which each day is a news day. 10

15 Are News Events Independent from Day to Day? The two sequential trade models considered so far specify that any news about firm value is revealed at the end of each trading day. This specification results in a model with a very simple structure, but may be a poor representation of the information process driving trades. Easley, Kiefer and O Hara (EKO 1997), test and cannot reject the hypothesis that day-to-day news is independent for their one firm, Ashland Oil. One wonders whether or not this daily independence of news holds more generally. Although it is the quality of the predictions from a model that matters, not the realism of the assumptions, we will test for independence of day-to-day news events. Testing for independence is difficult because news events are not observed. Following EKO, we use the estimated probability of a news day,, to infer news events. Consider the firm, FPL, which has an of We assume that approximately of the trading days have news events. When FPL s daily trade counts are sorted, the twentysecond highest trade count is found to be 166. All days with trade count greater than 166 are categorized as news days; all days with a count less than 166 are categorized as nonnews days. Days with exactly 166 trades are ignored. For FPL there are n = 21 news days and m = 38 non-news days. Runs of news and non-news days are counted. Under the null of news independence, the number of runs is approximately normally distributed, with: mean 2nm n m 1 and 2 var iance 2nm 2nm n m n m n m

16 Table 6 presents the results of the runs tests on the 20 NYSE firms. The null hypothesis of independence is rejected in 11 of the 20 firms. We also look at trade autocorrelations. If news is independent from day to day, there should be no AR structure to daily trade counts. Table 7 gives the first four autocorrelations of daily trades for the 20 firms. The first order autocorrelation is significant for 13 of the firms. Higher order autocorrelations are significant for five of the 13. Together, the runs and autocorrelation tests suggest that news is independent from day to day for some firms, but not for others. The TNT model can be adapted to model news that lasts more than one day. Figure 3 depicts a generalisation of the TNT model that allows for news that is revealed to the public at the end of two days. A new parameter in the two-day model is, the probability that yesterday s news is observed today, given that there was news yesterday. becomes the probability that today s news is observed today, given that there is new today. It seems plausible that the probability of observing news that has been around for a while may differ from the probability of observing news that has recently been generated. Yesterday s informed trading may have lead to a search for yesterday s news, increasing the likelihood of it being observed. Alternatively, after yesterday s informed trading, much of the value of the news may already be incorporated into prices, reducing the incentive to search for the old news. Extending news beyond one day makes the two-day model considerably more complex than the one-day news model. In particular, the two-day model is dependent upon the order of days with and without news. Although it would be possible to write out the 12

17 likelihood function for the two-day TNT model, the path dependence means that the likelihood function is no longer a product of identical daily terms. We have implemented estimation of the model in a recursive routine. Estimation is fairly fast, but a linearisation of the log likelihood function is used to prevent overflow and underflow during the likelihood maximisation. Table 8 presents parameter estimates for the two-day TNT model. For firms in which news is independent from day to day, we would expect to see a low value of, because the probability of seeing yesterday s news today is zero if the news was revealed after one day. should also be smaller than the estimate for the oneday model, because we are weighting the case in which a trader sees yesterday s news yesterday. For firms in which news is not independent from day to day, we expect a nonzero, and because yesterday s news is explaining some of today s trading, we again expect to smaller than the estimate for the one-day model. 4. Extensions: Do Bid / Ask Spreads Respond to Trading? In their 1997 paper, Easley, Kiefer and O Hara (EKO) demonstrate an extension of the BSN model to test whether or not informed trades concentrate in larger trade sizes. EKO find no evidence that larger trades are more likely to be informed trades. In another paper, we intend to use the TNT model to give this intriguing result a thorough examination. In this article, we will demonstrate how the TNT model can be extended to study how market makers behave in changing the bid / ask spread. Do market makers increase the spread if they believe that informed traders are active? If so, are the spreads increased before or after the informed trading? Can market makers even distinguish informed from uninformed trades on average? To investigate these 13

18 questions, we will use quote data in addition to transaction data to count when there is a spread increase in conjunction with a trade and when there is no spread increase in conjunction with a trade. Figure 4 depicts the diagram of the trading process for this extended model. Two new parameters are added to the model. is the probability that the spread increases when there is an informed trade. is the probability that the spread increases when there is an uninformed trade. Table 9 presents 60-day estimates of the model for the 20 NYSE firms. The model parameters have been estimated twice for each firm for counts of spread increases before trade,,, and for counts of spread increases after trade,,. 6 Table 9 also shows SI, the probability of a spread increase when there is any trade. Look first at the question whether the spread tends to increase more often before or after trade. There is no evidence that differs from or that differs from. Spreads are not more likely to increase before a trade than after, whether that trade is informed or not. Look next at the question whether or not the spread tends to increase more in conjunction with informed than uninformed trading. The estimates of the probability of an increase with informed trades are generally smaller than the estimates for informed trades, but the difference is significant at the 5 percent level only for CPC, CMY, AL, FBO and FPC. These results are similar whether we consider spread changes before or after trades. It 6 The quote time series corresponds to bid and ask quotes in effect at the time of market order transactions. The spread is the ask minus the bid. A spread change is calculated as the spread in effect for the market order transaction at time t minus the spread in effect for the market order transaction at time t-1. Note that the spread may change more than once or not at all between market order transactions, it is the cumulative change that is calculated here. 14

19 would seem that spreads are less likely to increase in conjunction with informed than uninformed trading. This result is an interpretation of the data in the context of the model. News days are not observable. Days with relatively many trades are interpreted as days with news, and some of the trades on these days are interpreted as informed. Given this, we conclude that market makers prefer to increase spreads around uninformed trades. One might argue that this result makes little sense, in that it suggests that market makers have some ability to distinguish informed from uninformed trades, and that they prefer to increase the spread around the uninformed trades. A more likely interpretation is that the spread increases for uninformed trades are related to the lighter trading during days without news. At any time, proportional spreads tend to be higher for lower volume stocks. For many of the same reasons, one might expect to see time series variation in spread, reflecting differences in volume from day to day. 5. Conclusions We have demonstrated the viability and usefulness of the trade / no-trade (TNT) model that depends only upon transaction counts to infer features of market maker and trader behavior. The model s assumption of intermittent news performs well compared to one in which news arrives every day. The model s assumption of day-to-day independence of the news is not well supported for many firms. We have shown that the model can be extended to allow for news that lasts for one day. Using an extension of the basic one-day news model, we find that market makers are no more likely to increase the bid / ask spread before a trade than after. We do find that the 15

20 spread is more likely to increase around an uninformed trade than around an informed trade. This may simply reflect higher per share costs of market making under the lower trade volume of days with no news. 16

21 References Easley, D., S. Hvidkjaer, and M. O Hara, 2002, Is information risk a determinant of asset returns?, Working paper. Easley, D., N. Kiefer, and M. O Hara, 1996, Cream-skimming or profit-sharing? The curious role of purchased order flow, Journal of Finance, 51, Easley, D., N. Kiefer, M. O Hara, and J. Paperman, 1996, Liquidity, information and infrequently traded stocks, Journal of Finance, 51, Easley, D., and M. O Hara, 1987, Price, trade size, and information in securities markets, Journal of Financial Economics, 19, Easley, D., and M. O Hara, 1997, One day in the life of a very common stock, Review of Financial Studies, 10, Glosten, L., and P. Milgrom, 1985, Bid, ask, and transaction prices in a specialist market with heterogeneously informed traders Journal of Financial Economics, 13, Lee, C., and M. Ready, 1991, Inferring trade direction from intraday data, Journal of Finance, 46, Theissen, E., 2000, A test of the accuracy of the Lee/Ready trade classification algorithm, Journal of International Financial Markets, Institutions & Money, 11,

22 Appendix Informed Trader Sells Uninformed Seller Sells Bad News Uninformed Seller No-Trade Uninformed Buyer Buys Day With News 1-1- Good News 12 Informed Trader Buys Uninformed Buyer No-Trade Uninformed Seller Sells Uninformed Seller No-Trade Uninformed Buyer Buys Day With No News Uninformed Buyer No-Trade Uninformed Seller Sells Uninformed Seller No-Trade Uninformed Buyer Buys Before Start of Trading Day During Trading Day Uninformed Buyer No-Trade Figure 1 EO s Discrete-Time (BSN) Model: Trade Direction Observable Once each day, before trading starts, nature chooses either good news, bad news, or no news. is the probability of a day with news; is the probability that any news is bad. Every trading period during the day, the trader in line to trade may observe the news. If so, there is an informed trade. If not, the trader may or may not choose to make an uninformed trade. is the probability that the trade is from an informed trader, given a news day; is the probability that an uninformed trader chooses to trade. 18

23 Informed Trade 1- Uninformed Trade 1- Day With News No Trade 1- Day With No News Uninformed Trade Before Start Of Trading Day During Trading Day 1- No Trade Figure 2 Simplified Discrete-Time (TNT) Model: Trade Direction Not Observable Once each day, before trading starts, nature chooses whether or not to generate news. is the probability of a day with news. Every trading period during the day, the trader in line to trade may observe the news. If so, there is an informed trade. If not, the trader may or may not choose to make an uninformed trade. is the probability that the trade is from an informed trader, given a news day; is the probability that an uninformed trader chooses to trade. 19

24 Assume No News on Day 0 1- Informed Trade Uninformed Trade Uninformed No-Trade Uninformed Trade Uninformed No-Trade 2 Before Start of Trading Day During Trading Day 1 Days 2+ Represent by Informed Trade Uninformed Trade Uninformed No-Trade Informed Trade Uninformed Trade Represent by Informed Trade Uninformed Trade Uninformed No-Trade Uninformed Trade 1 1- Uninformed No-Trade 1- Uninformed No-Trade Figure 3 TNT Model For News That Becomes Public After Two Days Once each day, before trading starts, nature chooses whether or not to generate news. is the probability of a day with news. Every trading period during the day, the trader in line to trade may observe the news for today or the news for yesterday. If so, there is an informed trade. If not, the trader may or may not choose to make an uninformed trade. Given news today; is the probability that the trade is from an informed trader on today s news. is the probability that the trade is from an informed trader on yesterday s news. is the probability that an uninformed trader chooses to trade, given the opportunity. 2 To save space on the diagram, we define: 11 1 and If there is news today, then tomorrow s tree diagram has the form 1. If there is no news today, then tomorrow s tree diagram has the form 2. We assume that the first day of observations had no news on the (unobserved) previous day. 20

25 Informed Trade & Spread Increase 1- Informed Trade & Spread Non-increase Uninformed Trade & Spread Increase Day With News Uninformed Trade & Spread Non-increase No Trade 1- Uninformed Trade & Spread Increase Day With No News 1-1- Uninformed Trade & Spread Non-increase Before Start Of Trading Day During Trading Day No Trade Figure 4 TNT Model Extended to Track Increases in Bid / Ask Spread Once each day, before trading starts, nature chooses whether or not to generate news. is the probability of a day with news. Every trading period during the day, the trader in line to trade may observe the news. If so, there is an informed trade. If not, the trader may or may not choose to make an uninformed trade. Given a news day; is the probability that the trade is from an informed trader. is the probability that an uninformed trader chooses to trade, given the opportunity. Either immediately before or immediately after each trade, the market maker decides to increase the spread or not to increase it. Around informed trades, the market maker increases the spread with probability and around uninformed trades, the market maker increases the spread with probability. 21

26 Table 1 Summary Statistics of Trade Counts for 20 TORQ Firms 60-Day Stats Daily Number of Trade Size Daily # of Trade Price Buys Sells Trades (Shares) No-Trades ($) GLX Mean $32.90 Std $1.34 FPL Mean $28.49 Std $0.62 FNM Mean $33.96 Std $2.77 DI Mean $20.41 Std $1.42 AMD Mean $5.22 Std $0.99 CPC Mean $78.44 Std $2.54 CL Mean $70.47 Std $2.24 FDX Mean $34.08 Std $2.73 CMY Mean $27.43 Std $1.40 HAN Mean $18.44 Std $0.66 CUE Mean $12.84 Std $1.18 AL Mean $18.81 Std $1.15 CYR Mean $30.99 Std $3.69 FBO Mean $17.97 Std $1.82 CYM Mean $17.13 Std $1.68 FFB Mean $16.84 Std $1.55 DCN Mean $26.27 Std $2.49 AR Mean $26.13 Std $1.53 FPC Mean $38.15 Std $0.43 EMC Mean $8.85 Std $0.99 This table presents summary statistics for 20 firms NYSE used to estimate the BSN and TNT sequential trade models. Statistics are based upon 60 days of trade data for November 6, 1990 January 31, 1991 from the TORQ database. Buys and sells are inferred from transaction and quote data using the Lee and Ready (1991) algorithm. A five minute window without any transactions is counted as a non-trading period. The number of buys and sells are summed to give the number of trades for each day. Firms are sorted by daily number of trades. 22

27 Table 2 Parameter Estimates: 60 Trading Days; 5 Minute No-Trade Interval Pr[News] Pr[Informed Pr[Uninformed Pr[Informed news] trade] Trade] PI GLX (0.067) (0.016) (0.007) (0.000) FPL (0.070) (0.020) (0.011) (0.000) FNM (0.092) (0.025) (0.012) (0.000) DI (0.053) (0.026) (0.007) (0.000) AMD (0.060) (0.020) (0.008) (0.000) CPC (0.078) (0.019) (0.012) (0.000) CL (0.043) (0.031) (0.007) (0.000) FDX (0.064) (0.023) (0.009) (0.000) CMY (0.059) (0.022) (0.008) (0.000) HAN (0.056) (0.027) (0.031) (0.000) CUE (0.060) (0.023) (0.009) (0.000) AL (0.074) (0.016) (0.011) (0.000) CYR (0.080) (0.015) (0.014) (0.000) FBO (0.081) (0.023) (0.012) (0.000) CYM (0.052) (0.023) (0.007) (0.000) FFB (0.039) (0.033) (0.007) (0.000) DCN (0.039) (0.023) (0.006) (0.000) AR (0.052) (0.022) (0.007) (0.000) FPC (0.102) (0.029) (0.010) (0.000) EMC (0.058) (0.019) (0.008) (0.000) This table presents maximum likelihood estimates for the TNT sequential trade model. Estimates are based upon 60 days of trade data for November 6, 1990 January 31, 1991 for 20 NYSE firms. Firms are sorted by daily number of trades. GLX averages 155 trades per day; DI averages 94 trades; FDX averages 66 trades; and EMC averages 19 trades per day. A five minute window without any transactions is counted as a non-trading period. Standard errors are given in parentheses. 23

28 Table 3 Comparing Parameter Estimates, with and without Trade Direction: Ashland Oil 30 Trading Days Ashland Oil BSN (Buy, Sell, No-Trade) TNT (Trade, No-Trade) Pr[News], (0.1033) (0.1956) Pr[News is bad News], (0.1121) Not in model Pr[Informed News], (0.0138) (0.0216) Pr[Uninformed Trade Chance], (0.0119) (0.0331) Pr[Informed Trade], PI () () Log-Likelihood This table presents maximum likelihood parameter estimates for the BSN and TNT sequential trade models. Asymptotic standard errors are given in parentheses. Estimation uses 30 days of trade data for Ashland Oil (October 1, 1990 November 9, 1990) as supplied in Table 1 of EO (1987). Buys and sells are inferred from transaction and quote data using the Lee and Ready (1991) algorithm. A five minute window without any transactions is counted as a non-trading period. The number of buys and sells are summed to give the number of trades for each day. 24

29 Table 4 Comparing Parameter Estimates, With and Without Trade Direction: Selected TORQ Firms GLX TNT GLX BSN DI TNT DI BSN FDX TNT FDX BSN EMC TNT EMC BSN Pr[News] Pr[Bad News News] Pr[Informed News] Pr[Uninformed Trade Chance] Pr[Informed Trade] Days PI (0.091) n/a (0.026) (0.009) (0.000) (0.093) n/a (0.023) (0.010) (0.000) (0.067) n/a (0.016) (0.007) (0.000) (0.091) (0.277) (0.014) (0.008) (0.000) (0.091) (0.075) (0.015) (0.006) (0.000) (0.067) (0.033) (0.013) (0.005) (0.000) (0.132) n/a (0.046) (0.015) (0.000) (0.085) n/a (0.022) (0.011) (0.000) (0.053) n/a (0.026) (0.007) (0.000) (0.086) (0.079) (0.014) (0.010) (0.000) (0.086) (0.145) (0.023) (0.009) (0.000) (0.076) (0.076) (0.014) (0.007) (0.000) (0.067) n/a (0.039) (0.010) (0.000) (0.090) n/a (0.023) (0.011) (0.000) (0.064) n/a (0.023) (0.009) (0.000) (0.164) (0.343) (0.043) (0.014) (0.000) (0.081) (0.356) (0.018) (0.009) (0.000) (0.073) (0.385) (0.029) (0.009) (0.000) (0.074) n/a (0.025) (0.009) (0.000) (0.086) n/a (0.024) (0.011) (0.000) (0.058) n/a (0.019) (0.008) (0.000) (0.086) (0.127) (0.016) (0.009) (0.000) (0.105) (0.095) (0.016) (0.011) (0.000) (0.066) (0.076) (0.012) (0.007) (0.000) This table presents maximum likelihood parameter estimates for the BSN and TNT sequential trade models for four NYSE firms chosen to represent a range of trading activity. GLX averages 155 trades per day; DI averages 94 trades; FDX averages 66 trades; and EMC averages 19 trades per day. Estimation uses 60 days of trade data from the TORQ database (November 6, 1990 January 31, 1991).Estimates are shown for the full 60 days and for the two 30-day sub-periods. Buys and sells are inferred from transaction and quote data using the Lee and Ready (1991) algorithm. A five minute window without any transactions is counted as a non-trading period. The number of buys and sells are summed to give the number of trades for each day. Standard errors are given in parentheses. The parameters of the models are,, and. is the probability of a news day. Conditional on news, is the probability that the news is bad and is the probability that an informed trader comes forward to trade. is the probability that an uninformed investor chooses to trade, given the opportunity. 25

30 Table 5 Comparing Parameter Estimates for Different No-Trade Intervals GLX DI FDX EMC No-Trade Pr[News] Pr[Informed Pr[Uninformed Pr[Informed Pr[Informed Interval news] trade] Trade news] Trade] (Minutes) PI Maximum likelihood parameter estimates for the BSN and TNT trade models using different no-trade intervals. Respectively, a one, two, five or ten minute window without transactions is counted as a non-trading period. Results are shown for four NYSE firms chosen to represent a range of trading activity. GLX averages 155 trades per day; DI averages 94 trades; FDX averages 66 trades; and EMC averages 19 trades per day. Estimation uses 60 days of trade data from the TORQ database (November 6, 1990 January 31, 1991). Standard errors are given in parentheses. The model parameters are: is the probability of a news day, the probability that the current trader is informed and the probability that an uninformed investor chooses to trade. Derived parameter of the model are, 1 the fraction of informed trades on a news day and PI the fraction of informed trades. 26

31 Table 6 Runs Tests for Independence of News from Day to Day TNT Model Mean Number of Runs Under Null of Independence Actual Number of Runs GLX 30.5 (3.7) 12 * FPL 29.8 (3.6) 16 * FNM 28.3 (3.4) 24 DI 17.7 (2.1) 12 * AMD 23.5 (2.8) 16 * CPC 28.3 (3.4) 26 CL 11.8 (1.3) 10 FDX 21.4 (2.5) 16 * CMY 21.4 (2.5) 16 * HAN 16.3 (1.9) 13 CUE 20.2 (2.4) 20 AL 29.8 (3.6) 25 CYR 30.5 (3.7) 20 * FBO 24.5 (2.9) 22 CYM 17.7 (2.1) 18 FFB 08.5 (0.9) 6 * DCN 10.2 (1.1) 8 * AR 16.3 (1.9) 14 FPC 21.4 (2.5) 12 * EMC 22.5 (2.7) 8 * This table present runs tests for the hypothesis that news events are independent from day to day. Because the presence of news cannot be observed, estimates of the probability of news,, from Table 6 are used to categorize trading days as days with or without news. For each firm, daily trade counts are sorted. The 60 th highest trade count is taken as the demarcation point. Days with more than this number of trades are classified as news days (denoted by 1 s) and days with fewer trades are taken as no-news days (denoted by 0 s). Days with exactly this number of trades are ignored. Runs of 1 s and 0 s are totaled for the 60 trading days. Under the null hypothesis of day-to-day independence of the news, the number of runs has a normal distribution with: 2nm 2nm2nmnm Mean 1 and Variance 1, 2 n m nm nm1 where n is the number of news days and m is the number of no-news days. Estimates are based upon 60 days of trade data for November 6, 1990 January 31, 1991 for 20 NYSE firms. Firms are sorted by daily number of trades. GLX averages 155 trades per day; DI averages 94 trades; FDX averages 66 trades; and EMC averages 19 trades per day. Standard errors are given in parentheses. An asterisk indicates rejection of the null at the 5 percent level. 27

32 Table 7 Autocorrelation of Trade Counts for the 20 TORQ Firms Order of Autocorrelation * GLX (0.0000) (0.0025) (0.0002) (0.0019) * FPL (0.0009) (0.2152) (0.3411) (0.8227) * FNM (0.0067) (0.5732) (0.0729) (0.6035) * DI (0.0000) (0.0408) (0.0053) (0.0071) * AMD (0.0000) (0.0097) (0.0335) (0.0142) CPC (0.1171) (0.5811) (0.5145) (0.3782) * CL (0.0398) (0.7908) (0.7686) (0.9149) * FDX (0.0169) (0.6190) (0.7954) (0.1958) * CMY (0.0015) (0.2281) (0.6227) (0.8529) HAN (0.1717) (0.5427) (0.6339) (0.2545) CUE (0.1471) (0.0360) (0.6117) (0.8977) AL (0.0591) (0.7590) (0.6487) (0.9293) * CYR (0.0006) (0.2596) (0.7321) (0.5624) * FBO (0.0258) (0.6750) (0.5677) (0.7686) CYM (0.2795) (0.9655) (0.7824) (0.5030) * FFB (0.0144) (0.6676) (0.8755) (0.7449) DCN (0.1177) (0.7995) (0.7118) (0.7454) AR (0.0686) (0.6748) (0.8887) (0.3280) * FPC (0.0010) (0.0318) (0.0059) (0.2818) * EMC (0.0000) (0.0000) (0.0029) (0.0701) This table presents autocorrelations of daily trade counts for 20 NYSE firms used to estimate the BSN and TNT sequential trade models. Autocorrelation estimates are based upon 60 days of trade data for November 6, 1990 January 31, Firms are sorted by daily number of trades. p-values are shown in parentheses. An asterisk indicates a first order autocorrelation that is different from zero at the 5 percent level. 28

33 Table 8 Parameter Estimates When News Becomes Public After Two Days Pr[News] Pr[Informed Pr[Informed Pr[Uninformed Pr[Informed News Today] News Yesterday] Trade] Trade] PI GLX () () () () FPL () () () () FNM () () () () DI () () () () AMD () () () () CPC () () () () CL () () () () FDX () () () () CMY () () () () HAN () () () () CUE () () () () AL () () () () CYR () () () () FBO () () () () CYM () () () () FFB () () () () DCN () () () () AR () () () () FPC () () () () EMC () () () () This table presents maximum likelihood estimates of the probability of a news day for the TNT sequential trade model. Estimates are based upon 60 days of trade data for November 6, 1990 January 31, 1991 for 20 NYSE firms. Firms are sorted by daily number of trades. GLX averages 155 trades per day; DI averages 94 trades; FDX averages 66 trades; and EMC averages 19 trades per day. A five minute window without any transactions is counted as a non-trading period. Standard errors are given in parentheses. 29

34 Table 9 Do Market Makers Increase Bid / Ask Spreads in Reaction to Informed Trading? Pr[Spread Increase] Before Pr[Spread Increase] After Informed Uninformed Any Trade Informed Uninformed Any Trade Trade Trade Trade Trade SI SI GLX (0.006) (0.006) (0.006) (0.006) FPL (0.008) (0.007) (0.008) (0.007) FNM (0.012) (0.006) (0.012) (0.006) DI (0.012) (0.006) (0.012) (0.006) AMD (0.011) (0.006) (0.011) (0.006) CPC (0.019) (0.009) (0.019) (0.008) CL (0.023) (0.007) (0.023) (0.007) FDX 0.181(0.021) (0.008) (0.019) (0.008) CMY (0.015) (0.012) (0.015) (0.012) HAN (0.019) (0.025) (0.019) (0.026) CUE (0.023) (0.009) (0.023) (0.009) AL (0.018) (0.011) (0.017) (0.011) CYR (0.019) (0.011) (0.019) (0.011) FBO (0.020) (0.007) (0.020) (0.007) CYM (0.018) (0.009) (0.018) (0.008) FFB (0.021) (0.008) (0.021) (0.008) DCN (0.018) (0.015) (0.018) (0.015) AR (0.018) (0.008) (0.018) (0.008) FPC (0.052) (0.019) (0.051) (0.017) EMC (0.016) (0.015) (0.016) (0.014) This table presents maximum likelihood estimates for the TNT sequential trade model as extended to estimate the probabilities of spread change before or after trade. is the probability of a spread change before an informed trade, is the probability of a spread change before an uninformed trade and PI 1 PI is the probability of a spread change before any trade., and are the respective probabilities for spread change after. Estimates are based upon 60 days of trade data for November 6, 1990 January 31, 1991 for 20 NYSE firms. Firms are sorted by daily number of trades. GLX averages 155 trades per day; DI averages 94 trades; FDX averages 66 trades; and EMC averages 19 trades per day. A five minute window without any transactions is counted as a non-trading period. Standard errors are given in parentheses. 30