To further explore the implications of the STACD-PD model, the opening hours data are grouped into two distinct regimes according to lagged trade duration: (1) in the DG regime the past trade duration equals or exceeds the mean trade duration, and (2) in the DL regime the past trade duration is less than the mean trade duration. Consequently, the DG regime represents the longer trade duration regime, while the DL represents the shorter trade duration regime. Panel A of Table 5 illustrates the market microstructure characteristics of the four regimes.
Spreads and trading volume per second in the DG regime significantly exceed those in the whole opening hours while the volatility per second in the DG regime
12 Diamond and Verrecchia (1987) found that short sale constraints reduce the information adjustment speed during the downward market and increase the trade duration.
13 Easley and O’Hara (1992) posited that more frequent trading is related to the existence of more informed traders. Accordingly, they proposed that longer trade durations are associated with smaller price variation owing to infrequent trading.
Table 5. The Characteristics of the Opening Hours and Associated Two Regimes, and Estimation Results of the Logistic Regression
Panel A: The Characteristics of the Opening Hours and Associated Two Regimes
Spread Volume/s Volatility/s
Mean SE Mean SE Mean SE
Whole Opening Hours 0.0749 0.0490 1.2054 1.9249 0.3393 5.9002
DG 0.0800‡ 0.0502 1.4977‡ 2.2917 0.4786 6.7323
DL 0.0722 0.0481 1.0487 1.6755 0.2647 5.4011
Panel B: Estimation Results of the Logistic Regression with the DG as the Choice Regime
Intercept Spread Volume/s Volatility/s
-1.0119 a. Spread represents the difference between prevailing bid and ask prices. Volume/s represents the ratio of the
de-seasonalized transaction volume divided by the de-seasonalized trade duration. Volatility/s represents the ratio of the absolute change in the midpoint of prevailing quote divided by the de-seasonalized trade duration.
b. Mean represents the average. SE represents the standard error. The standard errors of parameter estimates are in parentheses.
c. † and ‡indicate that the number in the cell is significantly larger than of the whole data during opening hours at significance levels of 10% and 5%, respectively, under the Mann-Whitney-Wilcoxon mean test.
d. *, **, and *** represent significance levels at 10%, 5%, and 1%, respectively, when the corresponding mean is larger than of the whole data during opening hours.
e. (1) DG regime in which the lagged trade duration change equals or exceeds the mean of trade durations, and (2) the DL regime in which the lagged trade duration change is less than the mean of trade durations.
f. The numbers of observations are 6,276, 2,190, and 4,086 for the whole opening hours, DG, and DL, respectively.
g. The logistic regression is specified as follows:
is not significantly larger than in the whole opening hours. Fundamentally, spreads comprise order processing costs, inventory costs, and information costs (for example, Stoll, 1989 and van Ness et al., 2001). The DG regime does not display serious information asymmetry because of the insignificant volatility per second, while inventory and order processing costs are relatively higher owing to the significant trading volume per second. The higher inventory and order processing costs create higher spreads in the DG regime. Panel B of Table 5 shows the estimation results of a Logit Model with the DG regime as the choice regime, and
also confirms that wider spreads and larger trading volume per second significantly increase the probability of occurrence of the DG regime. The trading hour data are also grouped into four different regimes based on past price changes and lag two trade durations: (1) in the PGDG regime the past price change equals or exceeds zero and the lag two trade duration equals or exceeds the mean of trade durations, (2) in the PLDG regime the past price change is less than zero and the lag two trade duration equals or exceeds the mean of trade durations, (3) in the PGDL regime the past price change equals or exceeds zero and the lag two trade duration is less than the mean trade duration, and (4) in the PLDL regime the past price change is less than zero and the lag two trade duration is less than the mean trade duration. The PGDG and PGDL regimes are upward price change regimes, and the PLDG and PLDL regimes are downward price change regimes.
Meanwhile, the PGDG and PLDG regimes are longer trade duration regimes while the PGDL and PLDL are shorter trade duration regimes.
Panel A of Table 6 summarizes the market microstructure characteristics of the four regimes. Notably, compared to the whole trading hours data, the PLDG and PLDL regimes have significantly higher volatility per second. Consequently, the information asymmetry is more serious for the downward price regimes due to the higher volatility per second. Restated, when the price is trending downwards, the probability of trading against informed traders increases. The asymmetric findings for the upward and downward markets are consistent with a stylized fact in the finance literature. Generally, negative returns generate higher unexpected volatility than positive returns (for example, French et al., 1987, Schwert, 1989).
Engle and Ng (1993) demonstrated that a news impact curve has an asymmetric pattern in which negative return shocks increase predictable volatility more than positive return shocks. The reason for this asymmetric pattern during the upward and downward trends could be due to the leverage effect14 from stock price declines increasing financial leverage, and thus increasing the risk of a company going bankrupt. Zhang et al. (2001) found that the fast transaction regime with shorter past trade durations can be characterized as an informed trading regime involving a high likelihood of trading against informed traders. This study
14 Figlewski and Wang (2000) proposed that the leverage effect could be better labeled the downward market effect since their empirical evidence reveals only a weak direct relationship between the leverage effect and firm leverage.
Table 6. The Characteristics of the Trading Hours and Associated Four Regimes, and Estimation Results of the Logistic Regression
Panel A: The Characteristics of the Trading Hours and Four Regimes
Spread Volume/s Volatility/s
Mean SE Mean SE Mean SE
Panel B: Estimation Results of the Logistic Regression with the PLDL as the Choice Regime
Intercept Spread Volume/s Volatility/s
-1.2499
a. Spread represents the difference between prevailing bid and ask prices. Volume/s represents the ratio of the de-seasonalized transaction volume divided by the de-seasonalized trade duration. Volatility/s represents the ratio of the absolute change in the midpoint of prevailing quote divided by the de-seasonalized trade duration.
b. Mean represents the average. SE represents the standard error. The standard errors of parameter estimates are in parentheses.
c. † and ‡indicate that the number in the cell is significantly larger than of the whole data during trading hours at significance levels of 10% and 5%, respectively, under the Mann-Whitney-Wilcoxon mean test.
d. *, **, and *** represent significance levels at 10%, 5%, and 1%, respectively, when the corresponding mean is larger than of the whole data during trading hours.
e. (1) PGDG regime in which the lagged price change equals or exceeds zero and the lagged trade duration is equals or exceeds to the mean of trade durations, (2) the PLDG regime in which the lagged price change is less than zero and the lagged trade duration equals or exceeds the mean of trade durations, (3) the PGDL regime in which the lagged price change equals or exceeds zero and the lagged trade duration is less than the mean of trade durations, and (4) the PLDL regime in which the lagged price change is less than zero and the lagged trade duration is less than the mean of trade durations.
f. The numbers of observations are 68,801, 16,207, 7,508, 31,129, and 13,957 for the whole trading hours, PGDG, PLDG, PGDL, and PLDL, respectively.
g. The logistic regression is specified as follows:
complements the findings of Zhang et al. (2001) and indicates that informed trading regimes are associated with price declines and shorter past trade durations.
The estimation results obtained via a Logit Model with the PLDL regime as the choice regime in Panel B of Table 6 also confirm that higher volatility per second significantly increases likelihood of the PLDL regime occurring.
We also simulate 100 samples using a sample size of 50,000 for each regime of opening hours and trading hours to calculate the related moments of expected trade durations. These simulated moments are generated using coefficient estimates in Panel B of Table 3 and Panel C of Table 4, as well as empirical distributions15 of trade durations, price changes, and residuals. Table 7 lists the simulated moments of DG and DL regimes on the market opening. Generally, the DG regime has more positive skewness and highly excess kurtosis than the DL regime. Thus, the trade durations in the DG regime tend to exhibit a large proportion of extremely longer trade durations. Meanwhile, unlike the DL regime, the DG regime does not have symmetric trade durations. Therefore, during opening hours, past longer trade durations are more likely to lead to extremely long trade durations.
Table 8 shows that the PLDG and PLDL regimes have more positive skewness and higher excess kurtosis than the PGDG and PGDL regimes during trading hours. The first moments of the PLDG and PLDL regimes are slightly smaller than those of the PGDG and PGDL regimes. Combined with the higher volatility per second in the PLDG and PLDL regimes, the shorter trade durations are likely to be associated with higher volatility per second, particularly in the downward market. However, trade durations in downward price regimes are also found to be more asymmetric than in upward price regimes and, are more likely to have markedly longer trade durations.