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A.  Data

Our data are from the Pacific Basin Capital Market Research Center (PACAP) database maintained by the University of Rhode Island. We collect daily market returns and individual stock returns, monthly trading activity, and yearly market capitalization from PACAP for all Japanese securities listed on the Tokyo Stock Exchange (TSE) over the sample period from January 1979 to December 1998. We use market capitalization at the end of the previous year as our proxy for size. We use two measures of trading activity: trading volume, which we measure as the yen value of shares traded, and turnover, which we measure as the number of shares traded during the period divided by the number of shares outstanding at the beginning of the period. Market return is the return on TOPIX, a value‐weighted market index of all shares listed on the First Section of the TSE.

Most of the previous literature on cross‐autocorrelation patterns in short‐horizon stock returns uses weekly data. Using weekly returns helps to mitigate market‐microstructure‐related problems such as nonsynchronous trading. Therefore, we focus our empirical tests on weekly, size‐based portfolio returns.

We construct the size portfolios as follows. In December of each year t, we rank all stocks based on their market capitalization and divide them into five (quintile) portfolios. In forming these portfolios, we exclude stocks with missing size data at the end of year t and stocks with less than five monthly turnover data points in year t. Quintile 1 portfolios (S1) make up small‐size stocks, and quintile 5 portfolios (S5) make up large‐size stocks. We keep the composition of the portfolios over the next year (January to December of year ) and calculate the equal‐weighted weekly portfolio returns for each size‐sorted portfolio. We repeat this procedure to generate weekly returns from January 1979 to December 1998. We follow the standard convention of calculating weekly returns from Wednesday close to the following Wednesday close.

Since we want to examine the correlations conditional on the market state, we classify the state as UP or DOWN depending on whether the lagged market return over the previous L weeks is positive or negative. Longer horizons for L would better capture dramatic shifts in the market state, but using longer horizons also has the offsetting effect of increased clustering of UP and DOWN states. On the other hand, a short conditioning horizon may be unduly influenced by weekly fluctuations in market returns. Since there is no theoretical guide on L, we use the return on the value‐weighted market index, TOPIX, over the previous 12 and 26 weeks to determine the market state. At the beginning of each week, if the lagged 12‐week (or 26‐week) market return is positive (negative), we classify the state as an UP (DOWN) state.

B.  Descriptive Statistics

Our sample is composed of more than 1,500 stocks traded on the Tokyo Stock Exchange. This large size provides us with a sufficient cross section to perform portfolio tests. Panel A of table 1 presents the descriptive statistics for the equal‐weighted size quintile portfolios for the sample period of January 1979 to December 1998. We compute the summary statistics as average values in the year following the portfolio ranking period. As expected, the returns on the smallest firms is associated with the highest mean of 0.34% per week and volatility of 3.20%, compared to 0.13% and 2.32%, respectively, for the largest firms. We also observe a monotonic decline in the first‐order return autocorrelations (AC1) as we move from the smallest size to the largest size quintile. The autocorrelation function declines rapidly as we look at longer lags of from 2 to 4 weeks for all portfolio quintiles. Because the autocorrelations at lag 4 and beyond are statistically insignificant, we base all our subsequent analysis of portfolio autocorrelations on autocorrelations of up to four lags. On average, larger firms have higher yen volumes than smaller firms. The relation between turnover and firm size is less obvious. The summary statistics also indicate that there is stability in the firm characteristics between the ranking and test periods.

Table 1 Descriptive Statistics and Autocorrelation Matrices for Size Portfolios

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Panel B of table 1 presents the cross‐autocorrelation matrices for the size quintile portfolios. Although we report the full cross‐autocorrelation matrices at lag 1 ( ), to conserve space we report only the results for the extreme portfolios (S1 and S5) at lag 2 ( ) to lag 4 ( ). Panel B shows that there is evidence of asymmetry in the cross‐autocorrelations in size‐sorted portfolio returns. The correlation between the returns on lagged large‐firms portfolio (R_r,t) and current small‐firms portfolio (R_1,t) of 0.24 is higher than the correlation between returns on lagged small‐firms portfolio (R_1,t−1) and current large‐firms portfolio (R_5,t) of 0.02. Panel B also shows that the cross‐autocorrelations decay rapidly at longer lags of 2–4 weeks. We find that the amount of return autocorrelations and the asymmetry in cross‐autocorrelations in the size‐sorted portfolios in table 1 are comparable to those reported for the U.S. data (e.g., Lo and MacKinlay 1990).

If the prices of small firms adjust to common information at a slower rate than do the prices of large firms, then price increases in large firms in period t should be followed by price increases in small firms in period . Therefore, positive cross‐autocorrelations are consistent with smaller firms adjusting slowly to common information. However, this simple analysis does not control for own autocorrelation effects. In addition, our primary hypothesis is that these correlations change over time, depending on market conditions. Our analysis in the next section formally controls for own return autocorrelations effects and also tests for the impact of the market state.

C.  Vector Autoregressions

To formally test for evidence of significant cross‐autocorrelations in size portfolios, we perform vector‐autoregressive regression (VAR) tests. We adopt the bivariate unconditional VAR procedure used in Brennan et al. (1993). To test for lead‐lag relation between returns on the smallest and largest size quintile portfolios, S1 and S5, we estimate the following equations: where ( ) is the current return (return at lag ) on the small‐firm portfolio (S1) and ( ) is the current return (return at lag ) on the large‐firm portfolio (S5).

In the VAR setting, measures how well the lagged returns on portfolio S5 can predict the returns on portfolio S1 beyond the information contained in S1. Under the null hypothesis that there is no lead‐lag relation between large and small firms, we expect the sum of coefficients = 0. This test corresponds to the standard Granger causality test for a lead‐lag relation between the portfolios. The absence of any reverse lead‐lag relation between the two portfolios implies that . Brennan et al. (1993) show that the idea that the lagged return on the rapidly adjusting portfolio predicts the current return on a slowly adjusting portfolio can be tested by the cross‐equation hypothesis: .

Our primary hypothesis is that cross‐autocorrelations depend on market conditions. To test this prediction, we add two dummy variables to the VAR model, and , which correspond to the UP and DOWN market states in period t−K, respectively. We estimate a bivariate conditional VAR for the size portfolios using the following specification:

We perform the VAR tests separately for the UP and DOWN states. For instance, we test whether portfolio S5 responds faster than S1 to common information following the DOWN state in equations (3) and (4) by performing a cross‐equation test, .

Since the portfolio autocorrelations die out beyond a lag of 4 weeks, we estimate the VAR models for the two extreme size quintiles, S1 and S5, with 4‐week lags . The first two panels in table 2 report three sets of estimates: unconditional VAR estimates using equations (1) and (2) (in panel A), the conditional VAR results where the UP and DOWN lagged market condition is defined using lagged 12‐week market return (in the upper part of panel B), and the lagged 26‐week market return (in the lower part of panel B).5

Table 2 Vector Autoregressions for Size Portfolios

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Panel A of table 2 shows that, after we control for the effects of its own lagged returns, lagged large‐firm returns significantly affect the returns on small firms ( ). The lagged returns on large‐ and small‐firm portfolios together explain about 9% of the variation in the weekly returns of the small‐firm portfolio. As expected, the lagged small‐firm returns do not predict large‐firm returns ( ).6 The unconditional VAR tests suggest a lead‐lag pattern in size‐sorted portfolio returns that is similar to that of U.S. stocks.

Panel B of table 2 presents the effect of the market state on the size portfolios. We define the market state by using the return on TOPIX over the previous 12 and 26 weeks. The cross‐autocorrelations between lagged returns on large firms and current returns on small firms is significant only in the DOWN market state, with = 0.72, and it is significantly higher than the coefficients in the UP state ( ).7 In other words, after controlling for the effects of own lagged returns, we find that a 1% decrease in the return on the large‐firm portfolio leads to a 0.72% (0.13%) decrease in the return on the small‐firm portfolio following the DOWN (UP) state. Furthermore, the predictable small‐firm return in the DOWN state is high relative to the unconditional mean weekly return of 0.34. This finding demonstrates that the magnitude of the lead‐lag effects is economically important in the DOWN market state. We find that the cross‐equation Wald test of the lead‐lag relation is significant only in the DOWN state. The VAR estimates that use the lagged 26‐week market return to define the market state produce identical results. These results and all subsequent findings are robust to the alternate definitions of market states.

Overall, the difference in the lead‐lag patterns in the UP and DOWN market states is striking. We find that the lead‐lag relation between large‐ and small‐firm portfolio returns is exclusive to the DOWN state. To the extent that cross‐autocorrelations reflect a slow diffusion of common information, our findings suggest that small firms are slower to respond to market‐wide bad news. Conversely, a recent market gain (UP market state) increases the relative speed of stock price adjustment for both large and small firms.

A.  Do Market Frictions Explain Our Results?

Technically, market microstructure effects such as the bid‐ask bounce, nonsynchronous trading, and stale prices can generate the lead‐lag pattern in returns (Lo and MacKinlay 1990; Bodoukh, Richardson, and Whitelaw 1994). Using weekly returns in forming the portfolios reduces the possibility that our findings are due to nonsynchronous trading. Further controls for nonsynchronous trading effects do not alter our main findings. For example, we obtain similar results (not reported here) when we reform the weekly returns using Wednesday to Tuesday prices, skipping a day between 2 consecutive weeks. The skip‐day weekly returns avoid the problems associated with bid‐ask errors. At the same time, these returns provide a stricter filter for nonsynchronous trading.

Ahn et al. (2002) suggest that portfolio autocorrelations and cross‐autocorrelations can be induced by stale prices associated with thin trading and that dollar volume is a better proxy to capture the effect of stale prices. To ensure that the cross‐autocorrelations reported in this article are not driven by stale prices, we first sort all stocks each year based on the yen volume of shares traded. We then eliminate the bottom 20% of stocks that have the lowest value of shares traded each year. We use the remaining 80% of stocks to form five size‐sorted portfolio quintiles, with yearly rebalancing. We repeat our VAR tests for the lead‐lag effects in UP and DOWN market states, using these more actively traded securities. Panel C of table 2 shows that our findings are robust to eliminating the extremely low‐volume stocks. We continue to find significant (insignificant) cross‐autocorrelations of 0.63% (0.06%) between lagged returns on large firms and current returns on small firms following DOWN (UP) state. We conclude that market frictions such as nonsynchronous trading, bid‐ask bounce, and thin trading effects cannot explain the relation between the market state and the lagged adjustment of prices to common information.

B.  Effect of the Magnitude of Market Return

We examine the definition of market state that incorporates the magnitude of lagged market return. If the higher DOWN state cross‐autocorrelations are due to smaller firms’ slower adjustment to negative information, the magnitude of the negative information event should matter in the detection of delays in information assimilation. We apply a threshold criterion to the definition of market variables. We define the market state as a DOWN (UP) state only if the cumulative lagged market returns over the past 12 weeks is less (more) than −3% (3%). If the market return is between −3% and 3%, then we define the market state as FLAT. If the market return is between zero and 3% and −3% and zero, respectively, then we further subdivide the FLAT market state into low positive and low negative return states, FLAT_POS and FLAT_NEG.8 This formulation allows us to assess if the slow incorporation of news persists in extreme negative market states.

To implement the test, we modify VAR equations (3) and (4) to allow for four states of the market (UP, FLAT_POS, FLAT_NEG, and DOWN): where equals one if STATE is of type UP, FLAT_POS, FLAT_NEG, or DOWN, and zero otherwise. Panel A of table 3 presents our estimates of the above VAR specification for our sample period 1979–98. The cross‐autocorrelation between the current return on small firms and lagged returns on large firms is a significant 0.84 in the DOWN state compared to an insignificant 0.08 in the UP state. The cross‐autocorrelations of 0.58 and 0.33 in the FLAT_NEG and FLAT_POS market states are insignificant. We observe that the cross‐autocorrelation coefficients become monotonically weaker as we progress from the high negative market state to the high positive market state. Consistent with our expectations, the predictive ability of large‐stock returns is strongest following an extreme DOWN market state.

Table 3 Vector Autoregressions: Magnitude of Lagged Market Returns and Subperiod Analysis

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Figure 1 shows that the Japanese stock market index, TOPIX, experienced a run‐up during Japan’s stock market bubble period of 1980s. The bull market took the index from 450 in January 1979 to above 2,000 in 1990. This rise was followed by the bubble bursting in the 1990s, with the market index level dropping by almost half to about 1,100 in December 1998. We are interested in finding out if the effect of market states on return cross‐autocorrelations in Japan is due to differences in market conditions during the bubble versus the crash periods or if it reflects the general issue of reaction to positive versus negative common information. To test this alternate hypothesis, we split the sample into two subperiods, 1979–90 and 1991–98.

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Fig. 1.— Japanese Market Index (TOPIX). The sample period is 1979–98

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We perform the conditional VAR tests by using equations (5) and (6) for each subperiod, and the results are presented in panels B and C of table 3. We continue to find that the cross‐autocorrelations between lagged large‐stock returns and current small‐stock returns are significant only in the DOWN state in each subperiod. This evidence points to the asymmetric influence of market states in explaining the time‐series variation in the price adjustment process.

C.  Vector Autoregressions Using Volume Portfolios

Chordia and Swaminathan (2000) suggest that volume plays a significant role in their analysis of cross‐autocorrelations in stock returns. According to these researchers, low trading volume delays the price adjustment process so that prices of low‐volume stocks adjust to common information at a lag. We examine if there are significant cross‐autocorrelations in volume‐sorted quintile portfolios in UP and DOWN market states, controlling for firm size.

To construct the volume portfolios, we first follow the same procedure as before, forming the size portfolios to obtain five quintile portfolios (S1–S5). Then we rank all stocks in each of the quintile portfolios based on their average yen volume in year t and divide them into five volume‐based portfolios. In this way, we create 25 size‐volume portfolios.9 We then choose the two extreme volume quintile portfolios within each size quintile for further analysis.

Table 4 presents the VAR tests for the volume‐sorted portfolios within size quintiles 1, 3, and 5, using the specification in equations (5) and (6). For the sake of brevity, we report the coefficients corresponding to the UP and DOWN states only. Consistent with the findings in Chordia and Swaminathan (2000), we find that high trading volume increases the speed of assimilation of common information. More important, the results show that the cross‐autocorrelations between the lagged return on the high‐volume portfolio and the current return on the low‐volume portfolio are significant in all size quintiles but only in DOWN states. For example, among the largest firms, the return cross‐correlation between the lagged high‐volume portfolio and the current low‐volume portfolio is a significant (insignificant) 0.46 (0.03) in the DOWN (UP) market state. Although differences in trading volume contribute to the speed of adjustment of prices, low‐volume stocks experience slower adjustment in the negative market state.

Table 4 Vector Autoregression for Size‐Volume Portfolios

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D.  Cross‐Autocorrelations and Market Conditions in the United States

Several papers report significant asymmetric cross‐autocorrelations in size‐sorted portfolio returns in the U.S. markets (e.g., Lo and MacKinlay 1990; Mech 1993; McQueen et al. 1996; Chordia and Swaminathan 2000). We verify whether our findings extend beyond the Japanese market by repeating our analysis using the set of all ordinary common stocks traded on the American and New York Stock Exchanges over the period 1979–98. We form five size quintiles at the beginning of each year by sorting all firms in the Center for Research in Security Prices (CRSP) NYSE/AMEX stock file by their market capitalization at the end of December of the previous year. We follow the method outlined in Section II.B to compute Wednesday‐to‐Wednesday weekly returns. As we did in our analysis of the Japanese data, we use the cumulative return on the CRSP value‐weighted market index over the previous 12 weeks to determine if the market state is UP (positive) or DOWN (negative).10

Panel A of table 5 presents the estimates of VAR equations (3) and (4) for the U.S. size‐quintile portfolio returns. The estimates are similar to those of the Japanese stocks: the cross‐autocorrelation between current returns on small stocks and lagged returns on large stocks exclusively follows DOWN market state. Furthermore, when we take into account the magnitude of the market state, our estimates continue to yield similar conclusions. Panel B of table 5 shows the estimates of the VAR specification in equations (5) and (6). The cross‐autocorrelation is low and insignificant at 0.14 following the extreme UP state; in contrast, it is high and significant at 0.85 following the extreme DOWN state. The cross‐autocorrelations are insignificant following the middle two FLAT market states. Overall, these findings not only reinforce our interpretation that there is a significant delay in price adjustment to negative common information but also confirm that the results are robust across both the Japanese and U.S. markets.

Table 5 Vector Autoregressions: U.S. Size Portfolios

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E.  Effect of the Length of the Conditioning Horizon in Japanese and U.S. Markets

We use long‐horizon returns (12 weeks or longer) to define the market state. However, McQueen et al. (1996) examine cross‐autocorrelations in size‐sorted portfolio returns in the U.S. markets when conditioned on large‐stock returns over the short horizon. The short‐horizon conditioning interval used in McQueen et al. (1996) has the same length as the horizon over which returns are predicted. Unlike the impact of long‐horizon market conditions, McQueen et al. find that positive large‐stock returns over the short interval increases the cross‐autocorrelations in returns in the U.S. market. They find that, when returns on large stocks are positive (i.e., when the market state is UP), small‐stock returns have a lower contemporaneous correlation with large‐stock returns but a higher cross‐autocorrelation with lagged large‐stock returns. Conversely, when returns on large stocks are negative, they find that small‐stock returns have a high contemporaneous correlation with large stocks but have insignificant cross‐autocorrelations with lagged large‐stock returns.

Chang et al. (1999) extend the McQueen et al. (1996) analysis by investigating monthly returns in several Asian markets, and they report that the directional asymmetry in McQueen et al. (1996) is not universal. When they condition on positive and negative short‐horizon monthly returns, these authors do not find evidence of asymmetry in the cross‐autocorrelation pattern in monthly Japanese stock returns. Apparently, the impact of market condition on cross‐autocorrelations depends on the horizon over which market condition is measured.

Here, we investigate whether the delayed price reaction to negative market‐wide news persists when we measure it over the long conditioning horizon, after controlling for the positive effect of short‐horizon market condition reported in McQueen et al. (1996) for U.S. stocks. To do this, we introduce a two‐stage, long‐ and short‐horizon market conditioning, where we measure the short horizon over the previous 4 weeks and the long horizon over the prior 12 weeks (as previously defined). Specifically, the two‐stage market state is defined as UP_UP (DOWN_DOWN) only if the cumulative market return is positive (negative) over the long horizon, from week t−16 to t−5, and also positive (negative) over the short horizon, from week t−4 to t−1. Similarly, the two‐stage market state is defined as UP_DOWN (DOWN_UP) if the cumulative market return is positive (negative) over the long horizon but negative (positive) over the short horizon. We modify the VAR setup in equations (3) and (4) to allow for variation in both short‐ and long‐horizon market conditions: where is equal to one if STATE is of type UP_UP, UP_DOWN, DOWN_UP, or DOWN_DOWN, and zero otherwise. The empirical estimates of the VAR equations (7) and (8) for the Japanese and U.S. size‐sorted weekly portfolio returns are reported in panels A and B of table 6, respectively.

Table 6 Vector Autoregressions: Two‐Stage, Long‐Horizon and Short‐Horizon Conditioning

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In table 6, panel A shows that the weekly cross‐autocorrelations in Japanese stock returns are significantly positive in the DOWN_DOWN market states but not in the DOWN_UP states. In other words, the DOWN market states, in the short horizon as well as the long horizon, contribute to cross‐autocorrelations in weekly returns.

The empirical VAR estimates in panel B of table 6 that uses the U.S. weekly size‐based portfolio returns are slightly different. The cross‐autocorrelations are significant in both the DOWN_DOWN and UP_UP market states. Consistent with McQueen et al. (1996), the short‐horizon UP market state adds positively to weekly return cross‐autocorrelations.11 Nevertheless, after adjusting for the directional asymmetry due to the short‐term market conditioning reported in McQueen et al. (1996) for U.S. stocks, we continue to find that weekly cross‐autocorrelations are significant in the long‐horizon DOWN market state. A longer conditioning period minimizes the effect of high frequency fluctuations in the market and is more likely to capture delays in price adjustments due to trading restrictions, which is consistent with the findings of price adjustment delays in Hong et al. (2000) and Chen et al. (2002).12 An interesting extension would be to examine the economic sources of the differential effects of long‐ and short‐horizon market states; we leave that for future research.

F.  Abnormal Trading Volume and Market Conditions

If trading restrictions, such as short‐selling constraints, cause small firms to react slowly to negative market‐wide news, then trading activity would be lower following a DOWN state.13 To examine if there are significant changes in trading activity in each market state, we require some measure of increase or decrease in volume at the portfolio level. The following two measures of abnormal trading for portfolio s at time t are chosen: where is the aggregate weekly yen volume for size quintile s for week t and the benchmark weekly “expected” level of volume ( ) is computed as the average weekly volume for portfolio s over the previous 12 weeks, which corresponds to the number of weeks we use to define the long‐horizon market state; AVOL1 measures the change in volume relative to the expected level of volume; and AVOL2 measures the percentage change in volume. A positive AVOL1 (or AVOL2) implies an increase in aggregate trading volume relative to the portfolio’s expected trading volume.

In table 7, the average abnormal yen trading volume measures (AVOL1 and AVOL2) show a decrease (increase) in volume in the DOWN (UP) state, particularly for the smaller size quintiles. For example, the average volume for the smallest size quintile stocks drops by 11 billion yen in a DOWN state but increases by 7 billion yen in the UP state. In terms of percentage changes in volume (AVOL2), there is a 19% increase in volume for the smallest quintile in the UP states. The abnormal trading volume is significantly lower in the DOWN state than in the UP state for the smaller firms, indicating that the DOWN market state is associated with a drop in trading volume, particularly for the smaller stocks.

Table 7 Abnormal Trading Volume and Market Conditions

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Our earlier results indicate that the cross‐autocorrelations are influenced by market states in the long as well as the short horizon. We examine whether the abnormal trading volume is different when we condition on both long‐ and short‐horizon market states. The average abnormal trading volume (AVOL1) estimates using the two‐stage market conditioning are presented in panel B of table 7. The pattern in the average abnormal volume estimates suggests that both short‐ and long‐horizon DOWN states contribute to a drop in volume. However, for the smallest quintile, the drop in abnormal trading is significant in the DOWN_DOWN state. Consistent with our results for cross‐autocorrelations in table 6, the abnormal trading volume for the small firms in the DOWN_DOWN state is significantly lower than in the DOWN_UP state. In unreported results, we find that the estimates are similar when we use AVOL2 and when the long‐horizon market state is measured over 26 weeks. Overall, our results support the hypothesis that stock return cross‐autocorrelations relate to constraints in trading activity that impede the assimilation of bad news in small firms.

G.  Speed of Adjustment in Individual Stocks and Market Conditions

So far we have based our evidence on cross‐autocorrelations on measures derived from portfolio returns. Now we examine measures of delay in an individual security’s response to common news, taking into account the state of the market. We obtain the delay measure by regressing weekly individual stock returns on both current market returns and past and future market returns, conditioning on UP and DOWN market states. Our idea is to determine if the lagged response of individual stock returns to information in market returns is slower in a DOWN market state.

We run the following time‐series Dimson beta regression for each stock i for the entire sample period: where R_i,t is the return on stock i and R_m,t is the return on the value‐weighted market index, TOPIX, at time t. equals one if STATE is of type UP or DOWN, and zero otherwise. The market state is defined as UP (DOWN) if the cumulative market return over the previous 12 weeks is positive (negative). If a stock adjusts slowly to common news, it will have a higher correlation with lagged market returns and a lower correlation with contemporaneous market return. The delay measure capitalizes on this intuition. For each firm, delay in the DOWN state is based on the sum of lagged betas in the DOWN state divided by the contemporaneous beta. We define DELAY_DOWN as a log transformation of the speed of adjustment ratio: where We define DELAY_UP in the same way. These measures of delay are closely related to the speed of adjustment used in Chordia and Swaminathan (2000). Delay measures how fast a stock reacts to common information, depending on the state of the market; the longer the delay, the slower is the speed of adjustment. Conditional on the state of the market, the value of delay depends on the extent to which the stock’s returns correlate with the lagged market return relative to its contemporaneous correlation with the market. The logit transformation of X_UP,iand X_DOWN,i dampens the effect of extreme values so that the values of DELAY_UP_i and DELAY_DOWN_i are, by construction, bounded between zero and one. A stock that adjusts slowly to information contained in lagged market returns will register DELAY closer to one. If the DOWN market state is associated with a slower price adjustment to common news, we expect the delay to be higher in the DOWN state.

To ensure that our results are robust to how we measure market states, we take into consideration the effect of the magnitude of market returns and the two‐stage market conditioning discussed in Sections III.B and III.E. First, we compute delay using the following modified regression: where equals one if STATE is of type UP, DOWN, or FLAT, and zero otherwise. The market state is defined as UP (DOWN) if the cumulative market return over the previous 12 weeks is more (less) than 3% (−3%). If the market return is between −3% and 3%, then the market state is defined as FLAT. We compute the average delay for firm i in each of the three market states: DELAY_UP, DELAY_FLAT, and DELAY_DOWN. Similarly, our regression specification to obtain estimates of delays in price adjustment in individual firms using the two‐stage market conditioning approach is thus as follows: where is equal to one if STATE is of type UP_UP, UP_DOWN, DOWN_UP, or DOWN_DOWN, and zero otherwise. The average delay for firm i in each of the four different market states is denoted as DELAY_UP_UP, DELAY_UP_DOWN, DELAY_DOWN_UP, and DELAY_DOWN_DOWN.

In panel A of table 8, the empirical estimates of the average delay in equation (11) decline as we move from small to large firms, which is consistent with the view that smaller firms take longer to adjust to common information. More interesting, there is a significantly higher delay in price adjustments in the DOWN state. For the smallest quintile, the average delay value is 0.79 in the DOWN state, compared to an average of 0.65 in the UP state. For the overall sample, delay is significantly higher in the DOWN state at 0.68 as compared to 0.59 in the UP state.

Table 8 Speed of Adjustment in Individual Firms and Market Conditions

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Panel B of table 8 reports similar results when we use equation (13) to determine the average speed of adjustment for the three market states. The results support our hypothesis that the average speed of adjustment in security prices is significantly higher in the DOWN state, particularly among the smallest firms. The average speed of adjustment gradually increases as the market state becomes more positive.14

Finally, our estimates of equation (14) using the two‐stage market conditioning in panel C of table 8 corroborate with the finding in table 6 that cross‐autocorrelations and price adjustment delays in small Japanese stocks follow the DOWN market state in both the short and long horizons. For example, the smallest size quintile firms display the highest price delay of 0.79 in the DOWN_DOWN market state, which is significantly different from delay in the DOWN_UP state. Hence, the speed of price adjustments is affected by short‐ and long‐horizon market conditions.