When is Inter-trade Time Informative? A Structural Approach. Tao Chen a*

Transcription

1 When is Inter-trade Time Informative? A Structural Approach Tao Chen a* Abstract This paper reinvestigates the role of inter-trade time in price discovery. The GH model (Glosten & Harris, 1988), the VAR model (Hasbrouck, 1991a), the MRR model (Madhavan et al., 1997), and the HS model (Huang & Stoll, 1997) are extended by the parameterization (Dufour & Engle, 2000) to analyze a cross-sectional sample of 472 composite stocks of the NIKKEI 500 on the Tokyo Stock Exchange (TSE). My results indicate that the price impact is negatively related to inter-trade time without model selection bias. Additionally, I find that the inter-trade time effect reveals an inverse U-shaped intraday pattern. Keywords: Information Content, Inter-Trade Time, Trading Intensity, Tokyo Stock Exchange JEL Classification: C32, G12, G14 * Corresponding author. Lee Shau Kee School of Business & Administration, Open University of Hong Kong, 30 Good Shepherd Street, Homantin, Kowloon, HK. Tel: Fax: address: tchen@ouhk.edu.hk 148

2 1- Introduction Central to a variety of studies on finance microstructure is the concept that, in a market full of asymmetrical information, trades initiated by informed agents release information and therefore impact security prices. In light of the previous literature on the critical determinants of price formation, a series of studies attach importance to inter-trade time, which accordingly sparks the interest of empirical researchers as to whether inter-trade time results in the attainment of efficient stock market prices. Numerous studies exist (Bagehot, 1971; Copeland & Galai, 1983; Diamond & Verrecchia, 1987; Easley & O Hara, 1992) that provide competing evidence in support of the important role inter-trade time plays in disseminating information. In particular, the presence or absence of trades imparts valuable information to market participants. Even though the findings of the above-cited literature conclude that inter-trade time matters as an information source, the research conclusions are still at odds with each other in terms of the association between inter-trade time and information-based trading. After taking into account the influence of short-sale restrictions on informed traders, Diamond & Verrecchia (1987) interpret non-trading as an indicator of bad news. Admati & Pfleiderer (1988) show that noise traders are discouraged from participating in share trading when evidence of informed trading exists. As a result, informed trading leads to a relatively longer inter-trade time. Nevertheless, from the perspective of Easley & O Hara (1992), the increase in the number of trades is driven by information events because these events, particularly related to short-lived information, enable the prompt trading of informed traders, thereby allowing them to realize the profit as soon as possible. Thus, information events are associated with a shorter inter-trade time. Interestingly, the empirical literature in this regard likewise offers conflicting evidence (Ghysels & Jasiak, 1998; Grammig & Wellner, 2002). For instance, Dufour & Engle (2000) find that the increase in the size and speed of price adjustment to trade-related information is correlated with the decrease in inter-trade time. This result is the effect of inter-trade time on stock liquidity and market quality. Consequently, the more intense the trading, the richer information content trades carry. Conversely, a stark opposite relationship is documented by Peng (2001) and Beltran et al. (2005), which indicate a significant and positive interaction between the information 149

3 content and inter-trade time. These inconsistent findings make vain attempts to answer the question raised by the theoretical model. Because the above studies infer an ambiguous association between the inter-trade time and information content and fail to obtain consensus, a suitable and reliable model for such interdependence must be identified. So far, the microstructure models in widespread use, such as the GH model (Glosten & Harris, 1988), the MRR model (Madhavan et al., 1997), and the HS model (Huang & Stoll, 1997), ignore the impact of inter-trade time on price changes, but the research conducted by Peng (2001) is an exception. To address the concern of the lack of inter-trade time, I introduce the variable of inter-trade time into the model by a parameterization approach proposed by Dufour & Engle (2000), who extend Hasbrouck s (1991a) VAR model to explore the price impact of inter-trade time using the same method. In contrast to prior studies, this paper complements a rich literature on time s role in price changes in the following aspects. First, in addition to the framework developed by Dufour & Engle (2000), my empirical section involves three more classical models (GH, MRR, and HS) modified through the coefficient parameterization. These four alternative models cross-validate the empirical findings from different perspectives. Moreover, the explanatory power of the above microstructure models are compared and examined in the same dimension. Second, the competing evidence for the duration/return relation presented in the literature depends on a limited number of stocks traded in the U.S. market. However, in this article, I seek out-of-sample evidence on the interaction between the price impact and inter-trade time for the component stocks of the NIKKEI 500 index on the Tokyo Stock Exchange (TSE), a typical order-driven market. In line with Dufour & Engle (2000), my finding indicates that a longer inter-trade time imposes a lower impact on price changes, which accordingly displays an inverse U-shape intraday pattern. Further, the simulated P-value generated by the bootstrapping technique confirms the significant role that time plays in the VAR model. Third, although inter-trade time is usually divided into two parts: deterministic and stochastic (Dufour & Engle, 2000), various studies treat only the deterministic component as the intraday periodicity, which basically is due to the trades occurring in different spans over the trading 150

4 day. My paper manifests its distinction from the above studies in that it extends the concept of the deterministic component to include the observed trading intensity, measured by the number of trades per day. This procedure allows me to go a step forward in the analysis for the pure stochastic effect. The arrangement of this paper is organized as follows. In the next section, I develop the model and empirical methodology employed in my study. Section 3 describes the institutional setting, the tick-by-tick transaction data, and the process of filtering the data on the TSE. In section 4, I present the empirical results of the regression analysis. Section 5 concludes the paper. 2- Model development 2.1 Basic model In the interest of brevity, I concentrate only on the reduced models that are ready to be estimated. First of all, the GH model (Glosten & Harris, 1988) is described as a two-component asymmetric information spread model, in which both the adverse selection and order processing components are presumed to be a linear function of trade sizes. P c x c ( q x ) z x z q x (1) t GH,0 t GH,1 t t GH,0 t GH,1 t t t where P t is the transaction price at time t, x t is the buy-sell trade initiator variable at time t, q t is the size of trade measured or number of shares traded, measured in multiples of minimum trading unit, and Δ is the first difference operator. μ denotes the average price change and ε t is the disturbance term capturing both the round-off error and public information innovation. According to the definition of the buy-sell initiator, if the trade is initiated by the buyer, the variable x t is equal to 1. If the trade is initiated by the seller, then the variable x t is equal to -1. Following Lee & Ready (1991), trades are categorized as buyer-initiated if the trade price is greater than the quote midpoint, and seller-initiated if the trade price is less than the quote midpoint. For trades at the quote midpoint, x t is assigned to be 0. In this model, the first two terms after μ reflect the temporary fraction of the price change attributable to a trade at time t. Second, the MRR model (Madhavan et al., 1997) deems that 151

5 changes in beliefs arise from two sources: (1) new public information announcements that are unrelated to trading; and (2) order flow, which may provide a noisy signal about the underlying value of the securities. Thus, the change in transaction price can be expressed as P z ( x x ) c ( x x ) (2) t MRR t t 1 MRR t t 1 t where P t and x t are the same as those in Equation 1. ρ stands for the first-order autoregressive coefficient in the trade indicator. Third, the HS model (Huang & Stoll, 1997) is developed under the assumption that the spread is constant and past trades are the normal size of one. The basic regression model is illustrated as P S ( x x ) 2 S x 2 (3) t HS t t 1 HS HS t 1 t where P t and x t are still identical to those in Equation 1. Equation 3 provides the estimate of the traded spread (S HS ), which reflects trades inside the spread but outside the midpoint and the sum of adverse selection and the inventory holding component (λ HS ). The GH, MRR, and HS models assume that the information content of a trade is promptly and completely incorporated into prices after each trade. No lagged information is taken into account. In fact, trades may have lagged price effect as well. Once the trading pattern is endogenously decided and lagged trades affect the current trades, the results produced by the GH, MRR, and HS models are biased and misleading. In view of the application of Hasbrouck s (1991a) VAR model in subsequent microstructure literature (Ahn et al., 2002; Spierdijk, 2004), all of the previous findings presume that summations in Equation 4 can be truncated at five lags. Consequently, I follow suit and specify the VAR model in this paper: Pt c 1 VAR, i Pt i z 0 VAR, ixt i i i 1t 5 5 t i 1 VAR, i t i i 1 VAR, i t i 2t x a P b x (4) 1 Empirically, Ljung-Box tests for serial correlation in the residuals fail to reject the null hypothesis that five lags is sufficiently long for all stocks in the sample. Changes in lag length in a few cases where rejection took place virtually had no impact on the results shown. 152

6 where P t, x t are defined the same as in Equation Parameterization with time In an attempt to yield insight into the role of time to play in price changes, I include the time between consecutive trades as an explanatory variable into the preceding basic models. From the perspective of economics, the private and public information is a potential impetus to move the price. Limit-order traders post their schedules based on information that contains the history of the trade and quote. Thus, the duration, or the inter-trade time, is an important information source typically observed by traders. Because inter-trade time releases information, Dufour & Engle (2000) extend the VAR model (1988, 1991a, 1991b) to allow the trade coefficients to vary with time, where the modified model becomes more general and flexible. In an effort to clarify whether inter-trade time affects the price adjustment in the quote equation, Dufour & Engle (2000) incorporate the time-variant trade coefficients in the functional relationship of Equation 4. Because they focus on the role of time to play, and in particular if it has any differentiable effect from the time-of-day effects, 2 time is decomposed into the deterministic and stochastic components. To separate these components, the parameterization procedure on z VAR,i is employed to reflect the individual effect, J r zvar, i i 1 j, id j, t i i ln( Tt i ) j (5) where T t-i is current or past inter-trade time, and D j,t-i are a set of dummy variables for intraday periodicities. In this paper, I split the trading day into nine half-hour sub-periods. Since the regression is run across these sub-periods respectively, to some extent it is able to remove the intraday periodicities as adding the dummy variables into the model. Thus the deterministic part of Equation 5 is deleted, and only the stochastic component remains in the model. Similar to 2 Intraday periodicities have been studied in an effort to describe the dynamic of several market variables: arrival of public information (Berry & Howe, 1994), transaction volume (Jain & Joh, 1988; Foster & Viswanathan, 1990), return (Harris, 1986; Wood et al., 1985), and time duration (Engle & Russell, 1998). 153

7 the procedure applied to the VAR model, I postulate that the adverse selection components of the spreads depend on time between trades captured by the parameter θ in the GH, MRR, and HS models. Following Grammig et al. (2007), the parameterization procedure is thus employed to each model. GH model: z GH,1 GH θ GH ln T t (6) MRR model: z MRR MRR θ MRR ln T t (7) HS model: λ HS HS θ HS ln T t (8) VAR model: z VAR,i VAR,i θ VAR,i ln T t i (9) 3- Institutional background and descriptive statistics 3.1 Institutional background Generally speaking, stocks are traded on four different boards on the TSE, which are the first section, the second section, the foreign section, and the Mothers section (market of the high-growth and emerging stocks). In simple terms, the first section is the marketplace for stocks of larger companies, while the second section is for stocks of smaller and newly listed companies. Stocks in the second section are reviewed at the end of each business year to assess whether or not they satisfy the criteria for transferring to the first section. Conversely, stocks in the first section are likely to be relegated to the second section. The NIKKEI 500 used in this study originates from the first section. Each trading day the TSE opens two sessions from 9:00 a.m. to 3:00 p.m., with a lunch break between 11:00 a.m. and 12:30 p.m. In addition, the TSE provides preopening quotes in the period prior to the opening auctions (from 8:20 a.m. for the morning session, and from 12:05 p.m. for the afternoon session). These quotes are the estimates of the expected opening prices, and only indicate a probability. The only exceptions are the first and last trading days of the year, when the TSE conducts only the morning sessions. Tick size is the increment by which prices move, and depends on the price per share. Hence, it is particularly 154

8 important when placing limit orders, as it determines the possible prices available. For example, if you wish to place an order for a price less than 2,000 yen, you can choose from prices at 1-yen intervals; but for prices between 2,000 yen and 3,000 yen, you may only choose prices at 5-yen intervals. 3.2 Sample source Nikkei Economic Electronic Database System (NEEDS), the most detailed and extensive dataset on the TSE, allows me to acquire the real-time trade and quote data on the Japanese stock market. All trades and quotes that take place on the TSE are recorded in the NEEDS database, so historical tick data for the code, date, time, price, and volume are easily found. In spite of being time-stamped to the nearest minute, a serial number that identifies the sequence of data within one minute is included. Additionally, the database has detailed indicators reflecting the state of each trade and quote, such as contract/quotation flags, morning/afternoon session flags, opening/closing trade flags, buy/sell flags, and special/warning quote flags. All trades and quotes of the component stocks of the NIKKEI 500 from January 1, 2005, to December 31, 2005, constitute the initial sample, which duly represents the Japanese capital market. 3.3 Filtering process In the original database of the composite stocks of the NIKKEI 500, 28 stocks are priced over 30,000 yen. In view of the tick-size rule on the Tokyo Stock Exchange, a significantly large tick size imposes a confounding influence over the empirical results. 3 Therefore, exclusion of these 28 samples ensures the quality of my findings. In an effort to obtain a clean, reliable, and accurate dataset for the empirical analysis, some filtering procedures are further applied to individual trades and quotes for the remaining 472 constituent stocks. In particular, three steps are taken. First, all off-hours quotes and trades are 3 Ahn et al. (2002) suggest that stocks priced greater than 30,000 yen should be eliminated to avoid possible confounding effects. 155

9 removed from the database. Second, the first and last trading days of the year 2005 on the TSE utilize only the morning sessions for trading, so the trades and quotes in these two days are completely deleted. Third, in light of the price location flags, each transaction is easily identified to be traded at the bid, at the ask, within the bid and ask, or outside the bid-ask bounce. Thus, I exclude all observations made either within or outside the spread. 3.4 Summary statistics Basic summary statistics including the cross-sectional mean, standard deviation, and median for a number of trading activity-related variables are documented in Table 1. For Group 4 stocks, the variables of trades per day, price, standard deviation of price change, daily volume in shares, daily volume in yen, trade size in shares, trade size in yen, and spread in yen are greater relative to other groups. This discrepancy is easily understandable as stocks with intense trading naturally possess higher prices, daily volumes, and trade sizes because of traders active participation. Conversely, an utterly different pattern is seen in inter-trade time and spread in percentage. With respect to frequently traded stocks, the corresponding spreads in percentage should be lower than those of less traded stocks. Table 2 presents the cross-sectional mean estimates of important market variables for the nine half-hour intraday intervals during the morning and afternoon sessions on the TSE. For all four groups of stocks over the course of the trading day, a familiar U-shape pattern is seen with trades per day, trade size in shares, and spread in percentage, which is in accordance with findings by Lehmann & Modest (1994), Hamao & Hasbrouck (1995), Madhavan et al. (1997), and Ahn et al. (2002). Even though a comparable conclusion cannot be drawn for each group in terms of share price, the closing price is lower in general than the opening price. The opening session likely overreacts to the information accumulated overnight. As the quotes and trades proceed, share prices gradually restore to their fundamental values at the close. Meanwhile, the evidence of hump-shaped inter-trade time implies that the lunch break induces lower inter-trade time in the opening half-hour of the afternoon session. In an effort to assess whether the change in inter-trade time is significant or not on an intraday level, I implement nonparametric tests to 156

10 Inter-Trade Time (Minutes) Table 1 Descriptive statistics of trading activity-related variables Trades Per Day (10 3 ) Price (10 6 ) S.D. of Price Changes Daily Volume in Shares (10 6 ) Daily Volume in Yen (10 9 ) Trade Size in Shares (10 3 ) Trade Size in Yen (10 6 ) Spread in Yen Spread in Percentage (%) All (N = 472) Mean S.D Median Group 1 (N = 118) Mean S.D Median Group 2 (N = 118) Mean S.D Median Group 3 (N = 118) Mean S.D Median Group 4 (N = 118) Mean S.D Median Note: This table presents cross-sectional descriptive statistics of 472 composite stocks of the NIKKEI 500 on the Tokyo Stock Exchange (TSE) from January 1, 2005, to December 31, According to the observed trading intensity, measured by trades per day, all samples are equally classified into four groups. Group 1 is the least active stock, while Group 4 is the most active stock. For all trading activity-related variables, inter-trade time, trades per day, transaction price, S.D. of price changes (standard deviation of price changes), daily volume in shares, daily volume in yen, trade size in shares, trade size in yen, spread in yen, and spread in percentage (the spread over the midpoint of the bid-ask price) are presented. These descriptive statistics cover the mean, standard deviation, and median. 157

11 Table 2 Mean estimates of trading activity-related variables by half-hour trading intervals Trading Interval 09:00-09:30 09:30-10:00 10:00-10:30 10:30-11:00 12:30-13:00 13:00-13:30 13:30-14:00 14:00-14:30 14:30-15:00 All (N = 472) Inter-Trade Time (Minutes) Trades Per Day (10 3 ) Price (10 3 ) Trade Size in Shares (10 3 ) Spread in Percentage (%) Group 1 (N = 118) Inter-Trade Time (Minutes) Trades Per Day (10 3 ) Price (10 3 ) Trade Size in Shares (10 3 ) Spread in Percentage (%) Group 2 (N = 118) Inter-Trade Time (Minutes) Trades Per Day (10 3 ) Price (10 3 ) Trade Size in Shares (10 3 ) Spread in Percentage (%) Group 3 (N = 118) Inter-Trade Time (Minutes) Trades Per Day (10 3 ) Price (10 3 ) Trade Size in Shares (10 3 ) Spread in Percentage (%)

12 Table 2 Continued Group 4 (N = 118) Inter-Trade Time (Minutes) Trades Per Day (10 3 ) Price (10 3 ) Trade Size in Shares (10 3 ) Spread in Percentage (%) Note: This table presents the cross-sectional mean estimates of the inter-trade time, trades per day, transaction price, trade size in shares, and spread in percentage during half-hour intraday trading intervals for 472 composite stocks of the NIKKEI 500 on the Tokyo Stock Exchange (TSE) from January 1, 2005, to December 31, According to the observed trading intensity, measured by trades per day, all samples are equally classified into four groups. Group 1 is the least active stock, while Group 4 is the most active stock. 159

13 examine the equality of the mean and median of intraday duration for each stock. Table 3 presents the P-values of both tests. The null hypotheses for both tests represent zero differences in inter-trade time between two neighboring trade intervals, as well as throughout the whole trading day. With the exception of some insignificant results obtained from 10:00-10:30 a.m. and 10:30-11:00 a.m., and 1:00-1:30 p.m. and 1:30-2:00 p.m., almost all P-values are less than The tests around noon provide the evidence to support that the information released during the lunch break triggers more trades in the opening of the afternoon session. Presumably, the trades intended to take place at the end of the morning session are transferred to the beginning of the afternoon session. 4- Estimation and discussion I begin by examining the impact of inter-trade time on price changes without considering the disturbance of the deterministic component of time. For brevity, Table 4 presents only the summary statistics on the parameter estimates for the inter-trade time. The summary statistics include the cross-sectional mean, the median, the standard deviation, the standard error, and the percentage of significance for the estimated coefficients of inter-trade time for individual structural models. Coefficients in bold indicate statistical significance at a 5% level of confidence for the equality test of the mean and median. If neglecting the observed trading intensity, the mean- and median-estimated coefficients of the inter-trade time, denoted by θ, impose a significantly negative impact on price changes, regardless of which structural models I employ. After controlling the observed trading intensity, the findings in Group 1, Group 2, Group 3, and Group 4 are similar to the results reported by all samples. Relative to some insignificant contemporaneous terms, all lagged terms in the VAR model appear to be negative and different from zero at a 5% significant level, suggesting that the information emerging from the preceding periods matters to current price changes. Alternatively, as long as the information released by traders is not fully absorbed in the lagged periods, its carry-forward impact plays a somewhat important role in present price changes. If this is the case, the positive but insignificant mean estimates found in the GH model for Group 160

14 Null Hypothesis Table 3 Nonparametric tests on inter-trade time between different trading intervals 09:00-09:30 & 09:30-10:00 09:30-10:00 & 10:00-10:30 10:00-10:30 & 10:30-11:00 10:30-11:00 & 12:30-13:00 12:30-13:00 & 13:00-13:30 13:00-13:30 & 13:30-14:00 13:30-14:00 & 14:00-14:30 14:00-14:30 & 14:30-15:00 All Periods All (N = 472) Mean Median Group 1 (N = 118) Mean Median Group 2 (N = 118) Mean Median Group 3 (N = 118) Mean Median Group 4 (N = 118) Mean Median Note: This table presents the statistical test results for the null hypothesis that no difference exists in the estimates between two neighboring trading periods and throughout the whole trading day in terms of mean and median of intraday inter-trade time, respectively. The P-value for the t statistic (z statistic) is reported for the nonparametric tests for the equality of mean (median) inter-trade time. The sample is 472 composite stocks of the NIKKEI 500 on the Tokyo Stock Exchange (TSE) from January 1, 2005, to December 31, According to the observed trading intensity, measured by trades per day, all samples are equally classified into four groups. Group 1 is the least active stock, while Group 4 is the most active stock. 161

15 Table 4 Estimated coefficients for inter-trade time by four structural models GH MRR HS VAR θgh θmrr θhs θvar,0 θvar,1 θvar,2 θvar,3 θvar,4 θvar,5 All (N = 472) Mean Median S.D S.E Sig (%) RMSE Group 1 (N = 118) Mean Median S.D S.E Sig (%) RMSE Group 2 (N = 118) Mean Median S.D S.E Sig (%) RMSE Group 3 (N = 118) Mean Median S.D S.E Sig (%)

16 Table 4 Continued RMSE Group 4 (N = 118) Mean Median S.D S.E Sig (%) RMSE Note: This table presents the cross-sectional mean, median, standard deviation (S.D.), standard error (S.E.), and percentage of significance (Sig) of the inter-trade time estimate and root square mean error (RSME) of the corresponding regression for 472 composite stocks of the NIKKEI 500 on the Tokyo Stock Exchange (TSE) from January 1, 2005, to December 31, 2005, by four structural models. These models include the GH model (Glosten & Harris, 1988), the MRR model (Madhavan et al., 1997), the HS model (Huang & Stoll, 1997), and the VAR model (Hasbrouck, 1991a). The coefficient θvar,i (i=0,...,5) measures the impact of contemporaneous and lagged inter-trade time on price changes. Sig denotes the percentage of significance (5%) for each stock among all stocks inside each group. Bold format indicates statistical significance at a 5% level of confidence for the equality test of the mean and median. According to the observed trading intensity, measured by trades per day, all samples are equally classified into four groups. Group 1 is the least active stock, while Group 4 is the most active stock. 163

17 1 and Group 4 are likely driven by their focus on current inter-trade time as well as neglecting past one. In addition, the percentages of significance for each stock within all samples in the MRR, HS, and VAR models are greater than 80%, in contrast to those in the GH model. Due to different estimation methods for different models, Table 4 also reports the RMSE (root mean square error), an important measure for data fitting, which compares the explanatory power of these structural models. The RMSE in Table 4 suggests that the VAR approach best explains considerable variation in price changes, followed by the GH, MRR, and HS models. Next, I seek to isolate the pure stochastic component from the total inter-trade time effect using the identical regression run on half-hour intraday trading intervals. The estimation results by four models and nine periods are summarized in Table 5. For ease of comparison, I report only the cross-sectional mean estimates of the inter-trade time coefficients, as well as the RMSEs of the corresponding regressions, for four alternative models over nine trading periods in the same table. The analogous empirical results are displayed in Table 5, further validating the foregoing conclusion that most θs remain significantly negative in the present or lagged periods for all models, in particular the HS model. With regard to the number of significant coefficients of the inter-trade time, the GH model reveals weaker results than the others, parallel to the preceding findings in Table 4. Moreover, the negative effect of inter-trade time is presumably strengthened as the trading intensifies. This argument is supported by the evidence of more significant coefficients in Group 4 than in other groups. So far, all of these results imply that a shorter inter-trade time increases the information content of a trade and therefore leads to a greater price impact, consistent with the theoretical model developed by Easley & O Hara (1992). In light of their predictions, an intensive trading conveys much more information than a thin trade. Additionally, my finding confirms the results of Dufour & Engle (2000) on the NYSE. Their VAR analyses indicate that a longer inter-trade time is associated with a lower price impact of a subsequent trade. However, Peng (2001) documents a positive impact on the effective spread if subsequent inter-trade time is long. Again, Beltran et al. (2005) find a positive relationship between the information content and inter-trade time. Dufour & Engle (2000) attribute the negative price impact of 164

18 Table 5 Estimated coefficients for inter-trade time by half-hour trading intervals and four structural models GH MRR HS VAR θgh RMSE θmrr RMSE θhs RMSE θvar,0 θvar,1 θvar,2 θvar,3 θvar,4 θvar,5 RMSE Group 1 (N = 118) 09:00-09: :30-10: :00-10: :30-11: :30-13: :00-13: :30-14: :00-14: :30-15: Group 2 (N = 118) 09:00-09: :30-10: :00-10: :30-11: :30-13: :00-13: :30-14: :00-14: :30-15: Group 3 (N = 118) 09:00-09: :30-10: :00-10: :30-11: :30-13: :00-13: :30-14: :00-14: :30-15:

19 Continued Group 4 (N = 118) 09:00-09: :30-10: :00-10: :30-11: :30-13: :00-13: :30-14: :00-14: :30-15: Note: This table presents the cross-sectional mean estimate of inter-trade time and root square mean error (RSME) of the corresponding regression for 472 composite stocks of the NIKKEI 500 on the Tokyo Stock Exchange (TSE) from January 1, 2005, to December 31, 2005, by four structural models across nine half-hour intraday trading intervals. These models include the GH model (Glosten & Harris, 1988), the MRR model (Madhavan et al., 1997), the HS model (Huang & Stoll, 1997) and the VAR model (Hasbrouck, 1991a). The coefficient θvar,i (i=0,...,5) measures the impact of contemporaneous and lagged inter-trade time on price changes. Bold format indicates statistical significance at a 5% level of confidence for the t test. According to the observed trading intensity, measured by trades per day, all samples are equally classified into four groups. Group 1 is the least active stock, while Group 4 is the most active stock. 166

20 inter-trade time to the participation of market makers. In their opinions, the market makers generally equate heavy and rapid trading with informed trading, so a short inter-trade time leads to a higher price change. However, the TSE is a typical and pure order-driven market without market makers. This explanation seems vain and is inapplicable in my study. As suggested by Kyle (1985), noise (liquidity) traders are important market participants who provide insights into this issue on the TSE. Generally, noise traders are afraid to enter the market once heavy trading occurs. Without these trading counterparts, the transactions cannot be executed. Thus, a short inter-trade time triggers a greater price impact, consistent with findings by Chen et al. (2008). Moreover, the RMSE in Table 5 yields the same conclusion as Table 4 in terms of the explanatory power. To ascertain the intraday movement of the inter-trade time impact, the graphs of locally weighted scatterplot smoothing are depicted for each group and each structural model in Figure 1, Figure 2, Figure 3, and Figure 4, respectively. However, these figures fail to reach a consensus on the intraday pattern of the inter-trade time impact. Specifically, both the GH and VAR models display the inverse U-shaped curves, while the HS and MRR models exhibit the U-shaped and inverse L-shaped patterns, respectively. Because most estimates are negative, the inverse U shape implies that the effect of inter-trade time is stronger at the opening and closing of the trading day. Presumably, this occurrence is due to the clustering of informed trading in those periods. On the contrary, the U shape reflects that informed traders tend to trade before and after the lunch break instead of at the opening and closing of each day s trading. However, the inverse L shape indicates that informed trading only occurs at the opening, and gradually declines over the remainder of the trading day. If taking into account the RMSE, an important statistic to show goodness of fit, the inverse U-shaped pattern reveals more plausible and reliable outcomes since the VAR and GH models possess higher explanatory power and better fit the data. In addition to accurately assessing the significance of the role played by the stochastic component of time duration in the VAR model, I perform a Wald test of the null hypothesis that time coefficients (θs) are jointly zero. The results of the Wald statistics are presented in Table 6, including the cross-sectional mean F-value and the percentage of 167

21 GH model Time effect Time of day bandwidth =.8 Group 1 Time effect Time of day bandwidth =.8 Group 2 Group 3 Group Time effect Time effect Time of day bandwidth = Time of day bandwidth =.8 Figure 1 Intraday pattern based on the GH model Note: The inter-trade time coefficient of the GH model is estimated for each stock across nine half-hour intraday trading intervals, and then averaged across stocks for four groups, equally classified by the observed trading intensity, measured by trades per day. The graph of locally weighted scatterplot smoothing is also presented. The top, left figure displays the result for Group 1, which is the least active stock. The top, right figure shows the result for Group 2, and the bottom, left figure depicts the result for Group 3. The bottom, right figure plots the result for Group 4, which is the most active stock. The sample is 472 composite stocks of the NIKKEI 500 on the Tokyo Stock Exchange (TSE) from January 1, 2005, to December 31, The bandwidth=0.8 appearing in the figure means that 80% of the data are used in smoothing each point. 168

22 MRR model Group 1 Group Time effect Time effect Time of day bandwidth = Time of day bandwidth =.8 Group 3 Group Time effect Time effect Time of day bandwidth = Time of day bandwidth =.8 Figure 2 Intraday pattern based on the MRR model Note: The inter-trade time coefficient of the MRR model is estimated for each stock across nine half-hour intraday trading intervals, and then averaged across stocks for four groups, equally classified by the observed trading intensity, measured by trades per day. The graph of locally weighted scatterplot smoothing is also presented. The top, left figure displays the result for Group 1, which is the least active stock. The top, right figure shows the result for Group 2, and the bottom, left figure depicts the result for Group 3. The bottom, right figure plots the result for Group 4, which is the most active stock. The sample is 472 composite stocks of the NIKKEI 500 on the Tokyo Stock Exchange (TSE) from January 1, 2005, to December 31, The bandwidth=0.8 appearing in the figure means that 80% of the data are used in smoothing each point. 169

23 HS model Group Time effect Time effect Time of day bandwidth =.8 Group Time of day bandwidth =.8 Group Time effect Time of day bandwidth =.8 Group Time effect Time of day bandwidth =.8 Figure 3 Intraday pattern based on the HS model Note: The inter-trade time coefficient of the HS model is estimated for each stock across nine half-hour intraday trading intervals, and then averaged across stocks for four groups, equally classified by the observed trading intensity, measured by trades per day. The graph of locally weighted scatter plot smoothing is also presented. The top, left figure displays the result for Group 1, which is the least active stock. The top, right figure shows the result for Group 2, and the bottom, left figure depicts the result for Group 3. The bottom, right figure plots the result for Group 4, which is the most active stock. The sample is 472 composite stocks of the NIKKEI 500 on the Tokyo Stock Exchange (TSE) from January 1, 2005, to December 31, The bandwidth=0.8 appearing in the figure means that 80% of the data are used in smoothing each point. 170

24 VAR model Time effect Time of day bandwidth =.8 Group 1 Time effect Time of day bandwidth =.8 Group Time effect Time of day bandwidth =.8 Group 3 Time effect Time of day bandwidth =.8 Group 4 Figure 4 Intraday pattern based on the VAR model Note: The inter-trade time coefficient of the VAR model is estimated for each stock across nine half-hour intraday trading intervals, and then the sum of these coefficients are averaged across stocks for four groups, equally classified by the observed trading intensity, measured by trades per day. The graph of locally weighted scatterplot smoothing is also presented. The top, left figure displays the result for Group 1, which is the least active stock. The top, right figure shows the result for Group 2, and the bottom, left figure depicts the result for Group 3. The bottom, right figure plots the result for Group 4, which is the most active stock. The sample is 472 composite stocks of the NIKKEI 500 on the Tokyo Stock Exchange (TSE) from January 1, 2005, to December 31, The bandwidth=0.8 appearing in the figure means that 80% of the data are used in smoothing each point. 171

25 significance from the Wald test for each stock. Because the true distribution of the cross-sectional mean F-value is uncertain, I apply the bootstrapping technique to calculate a simulated P-value, which is deduced from a two-tail test based on 1,000 simulations. In summary, the null hypothesis is strongly rejected based on the simulated P-values. The more intense the trading activity, the higher the F-value of the Wald test. This finding confirms the preceding interpretation that the market participant infers a higher possibility of informed traders if the trades occur heavily. The existence of informed traders discourages uninformed or noise trading, thereby enhancing the ratio of informed to uninformed trading. In this scenario, the task of finding liquidity traders to complete the transactions is increasingly difficult, and so trades have a higher information content of the inter-trade time. Similar results are found in the percentage of significance of the Wald test for each stock, which is greater, on average, for heavily traded shares than thinly traded shares. To determine whether time affects short-run price variations or long-run price information adjustments, I also perform a Wald test of the null hypothesis that the sum of θ coefficients is equal to zero. The results in Table 6 suggest that inter-trade time causes the long-term price to move in the negative direction. This negative carry-forward effect begins with strong momentum, weakens gradually, and finishes with a rebound at the end of the trading day. The intraday pattern of the inter-trade time impact is inconsistent with the explanation by French & Roll (1986) and Stoll & Whaley (1990), who argue that informed traders play increasingly dominant roles in trading from the opening to the closing of the market. Their interpretation infers that the effect of inter-trade time is strengthened over the course of the trading day. 5- Conclusion This research makes an empirical contribution to the fast-growing literature on high-frequency data. The finding in this paper is of interest to market participants, as they shed light on how inter-trade time affects traders behavior, and how the participants read the market. In this study, I apply four alternative structural models to a large sample of 472 composite stocks of the NIKKEI 500 on the TSE. This application allows me to 172

26 Table 6 Significance of inter-trade time in the VAR model by half-hour trading intervals Trading Interval 09:00-09:30 09:30-10:00 10:00-10:30 10:30-11:00 12:30-13:00 13:00-13:30 13:30-14:00 14:00-14:30 14:30-15:00 Group 1 (N = 118) H0: All θvar,i=0 H0: θvar,i=0 Group 2 (N = 118) H0: All θvar,i=0 H0: θvar,i=0 Group 3 (N = 118) H0: All θvar,i=0 H0: θvar,i=0 Group 4 (N = 118) H0: All θvar,i=0 H0: θvar,i=0 F-value Sig (%) $82.20 $86.44 $91.53 $87.29 $90.68 $94.07 $90.68 $91.53 $94.07 Coefficient Sig (%) F-value Sig (%) Coefficient Sig (%) F-value Sig (%) Coefficient Sig (%) F-value Sig (%) Coefficient Sig (%) Note: This table presents the cross-sectional mean F-value of the Wald test on the inter-trade time coefficient, θvar,i (i=0,...,5), of the VAR model for 472 composite stocks of the NIKKEI 500 on the Tokyo Stock Exchange (TSE) from January 1, 2005, to December 31, 2005, across nine half-hour intraday trading intervals. There are two sets of null hypotheses for the Wald tests. One is H0: θvar,0=θvar,1=θvar,2=θvar,3=θvar,4=θvar,5=0, and the other is H0: θvar,0+θvar,1+θvar,2+θvar,3+θvar,4+θvar,5=0. Sig denotes the percentage of significance (5%) for each stock among all stocks inside each group in terms of the Wald test. Wald tests are adjusted using a heteroskedasticity consistent covariance estimator. F-values and sums of coefficients with simulated P-values are obtained with the bootstrapping technique. Bold format indicates statistical significance at a 5% level of confidence. According to the observed trading intensity, measured by trades per day, all samples are equally classified into four groups. Group 1 is the least active stock, while Group 4 is the most active stock. 173

27 demonstrate the important role inter-trade time plays in the process of price discovery. First, enlightened by the parameterization method in Dufour & Engle (2000), which address a similar problem on the NYSE, this paper promotes four structural models and examines whether the empirical results are driven by bias due to model selection, after controlling for the observed trading intensity and intraday periodicity. Specifically, I extend the GH, MRR, HS, and VAR models to allow the trading intensity to be time dependent. The analysis of all structural models indicates that faster trading generally leads to greater price impact. In addition, the VAR is found to be the most optimal model to explain the inter-trade time effect in terms of the RMSE, an important goodness-of-fit dimension, as it is able to capture information from both the contemporaneous and lagged periods. Further, the GH and VAR models suggest that the effect of inter-trade time exhibits the inverse U-shaped pattern on an intraday level. Overall, four alternative structural models provide strong and consistent evidence in support of the argument that inter-trade time contains information. The null hypothesis of no trade means no information fails to be rejected from a statistical and economic viewpoint. This finding is in line with the conclusion drawn by Easley & O Hara (1992) and Dufour & Engle (2000), but inconsistent with Admati & Pfleiderer (1988), who establish that the information content is positively related to inter-trade time. 174

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