Excess comovement and investor attention in Japan*

Toshifumi Tokunaga†
Musashi University
t-tkng@cc.musashi.ac.jp

Rei Yamamoto
Mitsubishi UFJ Trust Investment Technology Instituteyamamoto@mtec-institute.co.jp
First Draft: February 20, 2014
Abstract
This study investigates the monthly excess comovement of three groups
categorized by two industry classifications from May 1985 to December 2013. We
define excess comovement as a correlation between two stocks beyond what would bejustified by the Fama–French three factor model. We find that 42% of excess
comovement for the group of stocks within the same sectors in the 33 sector
classification can be explained by from nine to eleven variables, including the attention
measurement, short-term interest rate, market liquidity, market-wide uncertainty,
information heterogeneity, and lagged dependent variables. Our results support the
hypothesis that excess comovement among stocks within the same sectors correlates
positively with the corresponding investor attention.
JEL classification: D82; G12; G14
Keywords: daily individual stock return; monthly correlation; limited attention; sector;
turnover ratio*

We would like to thank Takashi Misumi, Katsuhiko Okada, and Hideaki Kato, participants at the2012 Association of Behavioral Economics and Finance meetings, and 2012 finance seminar
participants at the Nagoya University for our previous paper, “Time-series analysis of the structureof excess comovement in Japanese stock returns” (in Japanese). The authors would like to thankEnago (www.enago.jp) for the English language review.
†
Corresponding author.

Excess comovement and investor attention in Japan
1. Introduction
Excess comovement among financial asset returns is one of the existing anomalies regarding thecovariances between asset returns. Many researchers have challenged the question of why excess
comovement exists among various asset classes and countries using diverse and abundant data sets
since Shiller (1989) and Pindyck and Rotemberg (1990). However, the relevant relationship among
financial assets remains open to debate.
Theoretically, for example, assuming a Capital Asset Pricing Model (CAPM), the covariance
between two assets is expressed by the product of the market betas for each asset and market variance.
That means that the relationship between two assets can be completely expressed by a relationship withthe market. However, many empirical studies report another factor not theoretically captured in therelationship between two assets. Specifically, empirical evidence has discovered that assets exist in a
relationship greater than that indicated by the theory. Pindyck and Rotemberg (1990) call this evidence“excess comovement” and find that strong excess comovement exists in the U.S. commodity market.
Before discussing the sources of excess comovement, “a certain problem” that occurs whenanalyzing excess comovement must be re-examined. Many previous papers use residual correlations(or covariances) to determine the existence of excess comovement. Situations in which residual
correlations may occur include (1) overlooked factors when calculating the residual series, (2) incorrect
formulation for the true structure of the data of interest, and (3) true “excessive” comovement between
different assets that researchers require.
The inevitable decision about analyzing excess comovement is how we define this excessivenessand extract it from the data. For the stock market, fortunately, the theoretical models (e.g., CAPM) for1

evaluating asset pricing exist. Therefore, though the possibility of (1) and (2) exists, previous studies’
assertion that the model residual series based on a theory is applied to situation (3) seems to have gonethus far uncontested.
Although early studies concentrated on finding excess comovement among various markets(Pindyck and Rotemberg, 1990, 1993; Karolyi and Stulz, 1996; Deb, Trivedi, and Varangis, 1996), thenumber of papers analyzing the background has recently been increasing (for the early works, seeBarberis and Shleifer, 2003; Barberis, Shleifer, and Wurgler, 2005). Kallberg and Pasquariello (2008)
analyze excess comovement using 82 industry indexes in the U.S. stock market to make clear its
time-series characteristics. Defining excess comovement as the squared correlation between two stocks
adjusted by fundamental factors, they find that the excess comovement correlates positively to proxies
for information heterogeneity and to U.S. monetary and real conditions but correlates negatively tomarket volatility and the short-term interest rate.
During the past several years, a research stream has attempted to explain the generating mechanismof excess comovement theoretically by incorporating limited investor attention into a popular basicmodel. Peng and Xiong (2006) propose a model in which investors have both limited attention inlearning about asset fundamentals and overconfidence about their information processing ability. The
model describes an investor’s category-learning behavior of tending to process more market and sector
information than firm-specific information. The consequences of limited attention and overconfidence
suggest (1) the existence of excess comovement, (2) lower correlations between firms within a sector
with a higher information-processing efficiency, and (3) correlations weakened over time with the2development of information technology. Peng and Xiong (2006) mention that although suchphenomena had so far been reported empirically, it seems difficult to explain them using standard
rational expectations models.
Mondria (2010) is similar to Peng and Xiong (2006) because both papers are based on Sims’ (2003)
rational inattention1. However, Mondria (2010) offers a rational expectations model of asset prices withinformation processing constraints, without employing any parameters expressing investor
overconfidence as in Peng and Xiong (2006)2. He suggests that when investors receive private signals
such as linear combinations of two asset returns to update information about two asset returns, changes
in one asset affect both asset prices and generate excess comovement by information processing
constraints even if returns are essentially uncorrelated.
In contrast, a number of recent studies have documented the empirical evidence that limited
investor attention affects the time-series and/or cross-section of asset prices. A great difficulty inanalyzing investor attention empirically is how to extract that attention from available data3. Corwin
and Coughenour (2008) measure individual NYSE specialist attention from her portfolio. On the basisof their belief that the attention increases with the number of transaction and absolute return, they
analyze how the attention given a stock affects the prices and liquidities of the remaining assigned

1

Hirshleifer and Teoh (2003) and Hirshleifer, Lim, and Teoh (2011) model theoretically attention to accounting
information.
2
Mondria (2010) refers to two differences from Van Nieuwerburgh and Veldkamp (2009) regarding model
assumptions.
3
Mondria, Wu, and Zhang (2010), Da, Engelberg, and Gao (2011), and Garcia (2013) use the search frequency on theInternet as a proxy variable for attention. Mondria and Wu (2010, 2013) and Mondria and Quintana-Domequez (2013)use the quantity of news. Also see Hirshleifer, Hou, Teoh, Zhang (2004) and DellaVigna and Pollet (2007, 2009) for
empirical studies.

3

stocks within her portfolio. Interestingly, the results indicate that even the professional investor is
influenced by information processing restrictions.
The present study’s main purpose is to evaluate the relationship between limited investor attention
and a stock return’s excess comovement at monthly intervals on the basis of daily data. Specifically, weinvestigate the hypothesis that the information processing capability for an investor with limited
attention causes excess comovement between two stock returns within the same sectors but not
between stocks belonging to different sectors. Hou (2007) finds that the lead-lag relations among stock
returns are more dominant in an intrasector relationship than in a cross-sector relationship. This finding
suggests that the information diffusion processes differ between intra- and cross-sector relationships.
Our hypothesis is based on the idea of transposing “NYSE specialists” and “their remaining
assigned stocks,” which were used by Corwin and Coughenour (2008), to “investors” and “otherstocks within the same sectors,” respectively. We find that although investors allocate their attention totheir more active stocks during periods of increased activity, they are not as interested in improving
prices for other inactive stocks within the same sector. Our result could be interpreted similarly to
Mondria (2010), who demonstrates theoretically that when investors receive private signals such as
linear combinations of two stock returns, information processing constraints cause excess comovement.
In the case of two stocks belonging to different sectors, in contrast, investors seem to have difficulty inreceiving any signal from the combination of the two. Therefore, the price change of one stock does
not affect the other stock price. As a result, the relationship between the two stocks cannot be easily
affected by information processing restrictions.

4We find, however, that excess comovement among stocks belonging to different sectors positively
correlates to information heterogeneity among investors used by Kallberg and Pasquariello (2008),
with no relationship to limited investor attention. This result could be interpreted similarly to Peng andXiong (2006), who demonstrate theoretically that excess comovement results when overconfident
investors concentrate their attention excessively on market information, resulting from lower priority
for processing firm-specific information. Therefore, excess comovement between stocks belonging todifferent sectors correlates to investor category-learning behavior and overconfidence.
Kallberg and Pasquariello (2008) define excess comovement as the excess square correlation
between two stocks beyond what would be justified by fundamental factors. In contrast, we define it as
the correlation between two residual series adjusted by the Fama–French three factor model. Moreover,though Kallberg and Pasquariello (2008) calculate weekly excess comovement by overlapping the data,
we calculate monthly excess comovement by not overlapping the data, instead using daily data.
The paper proceeds as follows. In Section 2, we explain how to measure monthly excess
comovement. In Section 3, we describe the data and sample characteristics. In Section 4, we present
our empirical evidence from the calculations of the various regression models for the Japanese stock
market. In Section 5, we conclude the study.

2. Measuring monthly Excess Comovement
When empirically analyzing excess comovement, certain problems should be considered. First, as
discussed in the Section 1, excess comovement’s existence depends on the model setting. Fortunately,

5

finance theory offers CAPM, a widely recognized theoretical model explaining financial asset pricefluctuation, including comovement. Next, we must decide how to apply the selected model to data. As
in previous papers, our choice is usually either to estimate the parameters during the entire sample
period, using daily, weekly, or monthly data, or to estimate them by rolling several terms. Although thelatter method is adopted for analyzing the time-series characteristics of excess comovement, thedata-overlapping problem should be treated carefully as in Kallberg and Pasquariello (2008).
In this study, we define monthly excess comovement using daily individual stock returns to avoid
being restricted by the data-overlapping problem. At month t, we can obtain the monthly comovement
between stock i and stock j by calculating the daily sample correlation of the OLS residuals from the
Fama–French three factor model as follows:
,

=

,

=

where

Where

̂, , =

,

,

,

1
−1
, ,

−

,

, = 1, … ,

̂, ,
−

,

̂, , ,,, ,= 1, … , ,

(1)

≡

(2)

−

is the number of firms at month t,

, ,
,

∀, ,
, ,

−

,

, , .

is the number of days at month t,return of stock i for a riskless return at day d in month t, and, , ,, , , and(3)
, ,is the excess, ,are themarket (“market return minus risk-free rate”), size (“Small minus Big” for market values of firms), andvalue (“High minus Low” for book-to-market ratios), respectively, in the Fama–French three factor
model. To adjust the skewed distributions of correlations, we apply Fisher’s Z transformation to the6correlations:= 0.5 × ln 1 +,,/ln 1 −,.

Next, we average adjusted excess correlations in a group as follows:

,

where

=

1

,

, ∈

,

,

= 1, … , ,is the set of stocks contained in theth group.

(4)

is the number of the groups, i.e., groups

containing the combinations of two stocks within the same sectors, the combination of two stocks
belonging to different sectors, and the combinations of all stocks.

3. Data and Sample Characteristics
3.1 Data Description
To calculate excess comovement in equation (1), we use the daily return data for all firms listed on
the Tokyo Stock Exchange (TSE) First Section from 1987 to 2013. We also calculate daily three factor
returns in equation (3), using this data set according to the procedure in Fama and French (1993).
We group the firms listed on the TSE First Section according to two types of sector classifications
to test our hypothesis. The first classification comprises 33 sectors based on the subclassification by
SICC (Securities Identification Code Committee), which has been used to compose the TSE industry
index and is one of the most popular classifications in Japan. The second comprises six sectors into
which we reorganize these 33 groups, referring to the main-classification (ten groups) by SICC. Table
1 Panel A presents the relationship between the six sectors and the 33 sectors.
This study’s main purpose is to demonstrate that excess comovement between two stocks within7the same sector relates to the relative gap of investor attention toward these stocks. Therefore, we
determine from the two types of classifications in Panel A whether two firms belong to the same sector.
Then, we construct three groups.
The first group consists of all the combinations of two stocks that belong to a same sector in the 33
sector classifications. This group should have a strong connection between stocks. We call a group ofsuch combinations “In33.”
The second group consists of all the combinations of two stocks that belong not only to the same
sector in the six sector classifications also to different sectors in the 33 sector classifications. This groupshould have a weak connection between stocks. We call a group of such combinations “In6Out33.”
The third group consists of all the combinations of two stocks that belong to different sectors in thesix sector classifications. Thus, this group contains all the remaining combinations of two stocks. This
group should have no connection between stocks. We call a group of such combinations “Out6.”
Table 1 Panel B summarizes the statistics for the number of combinations in each of the four groups
at the end of every month. In other words, it is the number of covariances and corresponds to the values
N (N − 1) / 2, where N is the number of stocks. On average, approximately 5% of all the combinationsof two stocks among all the stocks (“All”) has a strong connection between stocks through sectors, andapproximately 15% has a weak connection. If our prediction in Section 1 is supported, our data should
show that correlations between excess comovement and attention measurements are strongly
significant in the group In33, weak in the group In6Out33,” and insignificant in the group Out6, evenafter removing the influence of exogenous variables.

8

3.2 Hypothesis
In this study, we prepare proxy variables for investor attention through the following three steps.
First, we think that investor attention to each stock relates to the monthly means of daily trading
turnover ratios, the monthly standard deviations of daily stock returns, and those products. In otherwords, our monthly attention based on trading volumes, stock price changes, and those mixtures would
contain rich information.
Next, to measure relationships between investor attentions and return comovements, we define thegap between the attention to the i-th stock and the attention to the j-th stock as the relative attention
between two stocks. Assuming that this attention gap is expanded (i.e., if more attention is allocated to
one stock), evaluation of the stock with less attention is neglected or is inappropriately related with theevaluation of another stock with more attention even if both are essentially unrelated. In this study, we
think that the latter situation causes excess comovement. For simplicity, this attention gap is called“attention” in the following section.
Finally, to analyze whether excess comovement between two stocks in each group relates toattention gaps, we average the attention gaps for every group. Then, we propose the following
hypothesis:

Hypothesis: Excess comovement between two stocks within the same sectors (In33) correlates
positively with the corresponding investor attention. In contrast, excess comovement between two
stocks belonging to different sectors (Out6) is uncorrelated with the corresponding investor attention.

9

In the situation where investors are exposed to information processing restrictions, Mondria (2010)
demonstrates theoretically that investors observing a linear combination of stock returns as a private
signal causes excess comovement. Our measurements, such as attention gaps, correlate positively toinvestor information processing restrictions. However, we predict that although investors observe a
linear combination of returns for two stocks within the same sector, they tend to not observe a linear
combination of returns for two stocks belonging to different sectors. Probably, a portion of investors forwhom trading behavior changes stock price has very few opportunities to investigate stocks belonging
to different sectors simultaneously. For example, security analysts usually investigate stocks in a
specific sector.

3.3 Summary Statistics
Our attention measurements are inspired by Corwin and Coughenour (2008), who assert that
attention to a given stock increases with trading frequency and absolute return during a period. In theirempirical analysis, they arrange the number of trades, the absolute returns, and those products during
30-minute intervals based on intraday data. Furthermore, to test the Limited Attention Hypothesis(LAH) that implies a negative relationship between the provision of liquidity for a stock and the levelof specialist attention to other stocks in his portfolio, they use a new attention measurement(“PanelAttention”), defined for each stock as the sum of attention across all other stocks by the same
specialist panel, excluding the stock of interest. Thus, on the basis of Corwin and Coughenour’s (2008)
ideas, we define the three relative attention measures.

10

Table 2 reports summary statistics for excess comovement and the three attention measuresexplained in Panel B of Table 1. The categories “attention 1 (A1),” “attention 2 (A2),” and “attention 3(A3)” denote the logarithm of the absolute value of difference between two stocks regarding trading
turnover ratios, return standard deviations, and those products for stocks within a group, respectively.
Panel A presents the results for the entire combination (“All”). Excess comovement follows
distribution that has a positive mean and is skewed to the right. Autocorrelations of excess
comovement are strongly persistent. The mean and standard deviation of the attention measurement
A2 are small relative to those of A1. In other words, A1 and A2 are almost uncorrelated, whichsuggests that they include certain different information. Autocorrelations of all three attention measuresare very strongly persistent. Moreover, excess comovement and three attention measures correlate
positively.
Panel B reports the results for the combination of two stocks that belongs to a same sector in the 33
sector classifications (In33). The features of the shape of distribution and the pattern of autocorrelations
resemble those for the entire combination. However, the mean and standard deviation of excess
comovement are approximately 10 times larger. Most interestingly, the evidence that excess
comovement and the three attention measures are positively correlated, taking no account of influenceof other variables, is consistent with the study’s hypothesis.
Panel C reports the results for the combination of two stocks that belong not only to a same sector
in the six sector classifications but also to different sectors in the 33 sector classifications (In6Out33).
The features of the shape of distribution and the pattern of autocorrelations are more similar than those11

of the In33 group to those for the entire combination.
Panel D reports the results for the remaining combinations of two stocks (Out6). Excess
comovement follows a distribution with almost zero mean and a small standard deviation, comparedwith the other groups. Autocorrelations of excess comovement remain strongly persistent. Interestingly,
the evidence that excess comovement and two attention measurements (A1 and A3) are uncorrelated, if
taking no account of the influence of other variables, is consistent with the study’s hypothesis.

3.4 Relationship between Excess Comovement and Attention Measurement
Because excess comovement is strongly persistent as Table 2 reports, it is necessary to evaluate thetime series characteristics appropriately. Table 3 reports the results of regressions of excess
comovements on attention measurement and excess comovements with three lags. The Ljung–Box Q
tests for autocorrelation in the residual series with six lags (LB(6)) are not significant at the 5% level
for all cases, indicating that the time series characteristics of excess comovement are appropriately
adjusted by the auto-regressive (AR) terms of the dependent variable.
Interestingly, the coefficients of all three attention measures for the group In33 are positive andstatistically significant. However, those for the group Out6 are not statistically significant. These results
remain consistent with the study’s hypothesis as in Table 2’s results, if taking no account of theinfluence of other variables. In Section 4, we discuss the relationship between excess comovement andinvestor attention using the models described in Table 3 as the basic models.
In empirical analysis, it is important to remove the influence of any common factor likely to affect12

the relationship between stocks must be removed. We use the following twelve explanatory variables
expected to affect an excess comovement identified by Kallberg and Pasquariello (2008).
The variable “monthly market return with dividend” (symbol “Rm”) enables us to measure theeffect of market information. The variable “monthly rate of change of yen/dollar” (symbol “YD”)
seems to be an important macro variable because many Japanese firms depend strongly on export. The
variables “monthly CD rate (three month) at the end of the month” (symbol “CD”) and “monthly yieldspread between ten-year government bond yield and CD rate” (symbol “YS”) relate to the Japanesefinancial policy. The variables “monthly liquidity measure” (symbol “PS”) and “monthly illiquidity
measure” (symbol “IL”) are proposed by Pastor and Stambaugh (2003) and Amihud (2002),
respectively. Moreover, the variable “monthly trading value on TSE First Section” (symbol “TV”) is a
popular proxy for investors’ trading activity. The variables “bull markets for three months” and “bearmarkets for three months” (symbols “d+” and “d−”) are the dummy variables that equal to one if
sign,= sign,= sign,= + (−), and zero otherwise. The variable “market

uncertainty” (symbol “σm”) enables us to measure the level of market-wide information asymmetry.

We measure this variable as monthly standard deviation of daily market returns within a month. The
variables “information heterogeneity” (symbols “H1” and “H2”) enable us to measure the degree of
information heterogeneity. We measure these variables as cross-sectional means of the standard
deviations of analysts’ EPS forecasts and the ratios of the differences between their highest and lowest
forecasts, respectively. Finally, the variable “the number of analysts” (symbol “N”) is added to
information asymmetry and heterogeneity. We measure this variable as the cross-sectional mean

13

number of analysts covering the forecast firms.
Table 4 reports the correlations between variables that are likely to affect excess comovement.
Following Kallberg and Pasquariello (2008), “σm,” “H1,” “H2,” and “N” are classified as proxies for
information asymmetry and heterogeneity. “CD,” “d+,” and “d−” are classified as proxies for liquidity
shocks. These values are utilized for variable selection in a multiple regression model. For example,
variables “IL” and “TV” or variables “H1” and “H2” are not simultaneously included in a model.
Table 5 reports the estimation results for the time-series simple regressions of excess comovement
on each explanatory variable. The variable “Rm” is positive and significant for the group In33 but notsignificant for the group Out6. In other words, market information causes excessive comovement ofstocks within the same sectors, even after removing the market factor from individual returns. The
variable “YD” does not affect excess comovement.
The variable “CD” can be interpreted in directly opposite ways, as summarized by Kallberg andPasquariello. On one hand, the trading activity by financially constrained investors generates the
positive correlation between interest rate and excess comovement (Shiller, 1989; Calvo, 1999; Kyleand Xiong, 2001; Yuan, 2005). On the other hand, the portfolio rebalancing activity by cost-sensitive
investors generates the negative correlation between interest rate and excess comovement (Fleming,
Kirby, and Ostdiek, 1998; Kodres and Pritsker, 2002; Pasquariello, 2007). The results in Table 5 are
more consistent with the latter interpretation, as are the results in Kallberg and Pasquariello (2008). The
variables “PS,” “IL,” and “TV” can be interpreted similarly to the variable “CD.” Naturally, therelationships with the variable “CD” are expected to be negative for the variables “PS” and “TV” but14

positive for the variable “IL.” The results reveal that the coefficients of the three variables in the case of
the group In33 satisfy the sign conditions. Especially, the coefficients of the variables “PS” and “IL”
are strongly significant. The variables “d+” and “d−” enable us to estimate the asymmetric relationshipbetween excess comovement and market conditions. Although Kallberg and Pasquariello (2008) find apositive correlation with excess comovement only in the U.S. bull markets, our results reveal asymmetric relationship for In33 and a nonrelationship for Out6.
The variable “σm” can be interpreted in directly opposite ways, as summarized by Kallberg andPasquariello (2008). On one hand, the inability to distinguish between idiosyncratic and systematic
shocks derived from greater market uncertainty generates a positive correlation between market
volatility and excess comovement. On the other hand, the improvement in the relative precision of
traders’ signals derived from greater market uncertainty generates a negative correlation between
market volatility and excess comovement. The result for In33 reported in Table 5 is consistent with theformer interpretation, contrary to the results in Kallberg and Pasquariello (2008). However, our results
reveal a nonrelationship for Out6. The variables “H1” and “H2” seem to be positively correlated toinvestors’ cross-inference regarding fundamentals. Pasquariello (2007) suggests that if information
heterogeneity increases, investors’ cross-inference becomes increasingly incorrect and causes excess
comovement. The results for Out6 demonstrate significantly positive correlations and are consistent
with Pasquariello (2007). However, the results for In33 demonstrate significantly negative correlations.
The results for the additional variable “N” demonstrate significantly positive correlations.

15

4. Empirical Results
Our main purpose in this study is to evaluate the relationship between excess comovement andinvestor attention correctly. In Section 4, we presented two important results. The first is that the sectors
to which the pair of stocks used for measurement of comovement belong exhibit different relationships
between excess comovement and investor attention. The second is that excess comovement has astrong relationship with certain exogenous variables.
In this section, we evaluate these results as a whole to support a conclusion regarding ourhypothesis. In the second half of this section, we verify that the results do not change, even taken into
consideration the influence of size. Finally, focusing on information heterogeneity, we empiricallyconsider the generating mechanism of excess comovement suggested by the theoretical model of Pengand Xiong (2006).

4.1 Explaining Excess Comovement by Explanatory Variables Related to the Stock Market
Table 6 reports the results for time series regressions of excess comovement on attention
measurement and explanatory variables with lagged dependent variables. The first four explanatory
variables reflect the results reported in Table 3. In other words, we take into consideration that excess
comovement is strongly persistent. The remaining explanatory variables reflect the results reported inTable 5. We fix four variables (interest rate (“CD”), liquidity (“IL”), information heterogeneity (“H2”),
and the number of analysts (“N”)) that have high explanatory power in the single regressions of thefour models. Next, although Model 1 and Model 3 include the market return variable (“Rm”), Model 216and Model 4 include the market condition variables (“d+” and “d−”) instead of market return.
Although Model 1 and Model 2 include market volatility (“σm”), the coefficient of which can bepositive and negative, Model 3 and Model 4 do not include it. Panel A presents the results for the entire
combination (“All”). The twelve regressions that comprise three attention measures and four regression
models demonstrate that all the adj

s exceed 40%.

Panel B reports the results for the combination of two stocks that belong to a same sector in the 33

sector classifications (In33). The twelve regressions reveal that the adj

s range from 39.44% to46.18%. The coefficients of the variable “attention” are positively significant except in Model 1 for
Attention 2, even taking into consideration the influence of explanatory variables. These results support
our hypothesis that excess comovement among stocks within the same sectors correlates positively
with the corresponding investor attention.
The coefficients of the variable “Rm” are positively significant as in the single regression results
reported in Table 5. The coefficients of the variable “CD” are positively significant in the multiple
regressions but are not significant in the single regression. This outcome means that the trading activity
by financial constrained investors causes excess comovement. Although the coefficient of the variable“IL” is negatively significant in the single regression, the influence on excess comovement weakens in
multiple regressions. The coefficients of the variable “d+” have more stable explanation power than thecoefficients of the variable “d−.” This outcome is similar to the results in Kallberg and Pasquariello(2008). It seems, however, that no clear asymmetric reactions occur under the market conditions. The
coefficients of the variable “σm” remain positively significant although the influence on excess

17

comovement slightly weakens. The coefficients of the variable “H2” are not significant in the multiple
regressions but are negatively significant in the single regression. This outcome means that othervariables absorb the influence of information heterogeneity. Although the coefficient of the variable “N”
is positively significant in the single regression, the influence on excess comovement weakens in
multiple regressions.
In summary, the results of the twelve regressions support our hypothesis. Furthermore, excess
comovement moves together with the market and especially increases with market uncertainty duringbull markets. Excess comovement also relates to trading activity by financially constrained investors.
Panel B reports the results for the combination of two stocks that belong not only to the same sector
in the six sector classifications but also to different sectors in the 33 sector classifications (In6Out33).
Although these results as a whole resemble those in Panel B, the explanation power of each variable
seems weaker, which may be attributed to the weak connections between stocks in this group.
Panel D reports the results for the remaining combination (Out6). The twelve regressions reveal thatthe adjs range from 27.07% to 27.97%. These outcomes are lower than the values for In33 (Panel

B). In other words, few variables have high explanation power. The coefficients of the variable“attention” remain insignificant, even taking into consideration the influence of explanatory variables.
These results support our hypothesis that excess comovement among stocks belonging to different
sectors is uncorrelated with attention.
Unlike the results for In33, the coefficients of the variables “Rm,” “IL,” “d+,” “d−,” “σm,” and “N”
are not significant. The coefficients of the variable “CD” remain negatively significant, which is similar18

to the results in Kallberg and Pasquariello (2008). This outcome means that the portfolio rebalancing
activity by cost-sensitive investors causes excess comovement. However, the positive coefficients forIn33 and the negative coefficients for Out6 make interpretation of the variable “CD” difficult. These
opposite results may suggest that excess comovement for the two groups follows different data
generating processes and that mutually different underlying factors exist. The coefficients of thevariable “H2” remain positively significant, which is similar to the results in Kallberg and Pasquariello(2008). Because the coefficients of the variable “H2” for In33 are not significant, such significance forOut6 provides us with a new subject of interest. In subsection 4.3, we discuss this subject.
In summary, the results of the twelve regressions support our hypothesis. Furthermore, excess
comovement relates to the portfolio rebalancing activity by cost-sensitive investors. Thus, the source ofexcess comovement changes with combination of the sectors to which stocks belong

4.2 Robustness Checks for Size-Sorted Groups
Today, many investors, especially institutional investors, invest with consciousness of sector
classification and/or investment style, such as small stocks, large stocks, value stocks, and growthstocks. In this subsection, we analyze whether excess comovement results from a size-related
investment style in addition to our sector-based groups. Of course, we remove the size-related factor
from individual stock returns in the first step to calculate excess comovement. Therefore, our focus iswhether a “size” category called affects irrational behavior among investors engaging in diversified
investment. Barberis and Shleifer (2003) and Barberis, Shleifer, and Wurgler (2005) examine the19relationship between investment style and price comovement.
The calculation procedure is as follows. First, each company is classified into one of five cohorts
according to market value at the end of each month. Next, the combination of two stocks (i.e., 25
types) is created. Finally, these types are divided into the three sector-related groups already used.
Table 7 reports the results for time-series regressions of excess comovement on attention
measurement and explanatory variables with lagged dependent variables based on Model 2 forsize-sorted groups. Symbols “L,” “M,” and “S” express the largest, middle, and smallest cohorts ofstocks, respectively, on the basis of their market values. Therefore, for example, “L–L” means thatlarge stocks constitute both cohorts.
Panel A reports the results for the combination of two stocks that belongs to the same sector in the
33 sector classifications (In33). The results as a whole resemble those in Table 6 Panel B, althoughwith weaker impacts of the coefficients of the variable “attention” in the case “Attention 2.” Moreover,
the adjusted coefficients of determination for combinations containing the smallest size are lower.
Panel B presents the results for the remaining combinations of two stocks (Out6) not belonging to theIn33 and In6Out33. The results as a whole resemble those in Table 6 Panel D, although some unstable
results appear similar to those in Panel A. Although the results as a whole do not offer a certain
systematic feature, certain results represent slight instability. We think that this outcome requires further
investigation, including the relationship with other investment styles.

4.3 Additional Tests for Effects of Investor Overconfidence on Excess Comovement

20

In this subsection, we examine the effects on excess comovement of both investor
category-learning behavior and overconfidence, as suggested by Peng and Xiong (2006), among stocks
belonging to different sectors. In subsections 4.1 and 4.2, we reported that although excess
comovement among stocks within the same sectors correlates strongly to attention gaps, excess
comovement among stocks belonging to different sectors correlates to market-wide dispersions ofanalysts’ forecasts, not to relative information about individual paired stocks. To investigate the latter
finding further, we evaluate the combined effect of the forecast dispersions and investor
overconfidence. We expect that, during periods when analysts’ forecasts disperse, because investors
cannot process the firm-specific information correctly, they process market information more
preferentially by category-learning and, consequently, their overconfidence causes excess comovement.
The empirical evidence in Peng, Xiong, and Bollerslev (2007) is consistent with the hypothesis thatwhen market-wide uncertainty increases, investors shift their attention to processing market
information.
We use the magnitude of foreign investors’ buying and selling pressure as a proxy variable forinvestor overconfidence. This magnitude is measured as absolute values of monthly net trading values
that subtract “sales” from “purchases” for TSE First Section stock transactions by foreign investors. In
other words, we think that large net buying and net selling express investor overconfidence. Iihara,
Kato, and Tokunaga (2001) find that foreign investor herding affects stock prices, using twenty years ofownership data in the Japanese stock market. They conclude that foreign investors’ trades are related to
information.

21

Table 8 reports the results for time-series regressions that incorporate the influence of foreign
investors’ behavior on the coefficients of the information heterogeneity variable (H2) in Model M2 inTable 6. Model 2′ adds the absolute values of monthly net trading values (|F|) as a proxy variable forinvestor overconfidence to Model 2 of Table 6. The estimation results reveal that this additionalvariable does not have significantly linear relationships with excess comovement in any case,regardless of the sector.
Model 2″ allows the coefficients of information heterogeneity to vary with the level of investor
overconfidence. The estimation results reveal that the coefficients of the combined effect for the
cross-sector (“Out6”) correlate positively to excess comovement, but those for the intrasector (In33)
have no relationship. Furthermore, the coefficients of the information heterogeneity in the case of Out6
weaken. Nevertheless, the adjusted coefficients of determination for Model M2″ are higher than thosefor Model M2 in Table 6 by approximately 1%. These results mean that excess comovement amongstocks belonging to different sectors correlate more strongly positively with information heterogeneity
during periods of stronger investor overconfidence. Therefore, it is consistent with our hypothesis.

5. Concluding Remarks
This study investigates the monthly excess comovement of three groups categorized by two
industry classifications from May 1985 to December 2013. We define excess comovement as acorrelation between two stocks beyond what would be justified by the Fama–French three factor
model. We find that 42% of excess comovement for the group of stocks within the same sectors in the22

33 sector classification can be explained by from nine to eleven variables, including attention
measurement, short-term interest rate, market liquidity, market-wide uncertainty, information
heterogeneity, and lagged dependent variables. Our results support the hypothesis that excess
comovement among stocks within the same sectors correlates positively with corresponding investor
attention.
As a future study, we will analyze the relationship between excess comovement and various
investment styles moderated by limited investor attention. Further, future research should re-examine
firm size and redefine a proxy variable for investor overconfidence in the Japanese stock market.

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25

Table 1: Definition of groups and the number of the sample
Panel A. two types of sector classification
Type 1: 6 sectors
Type 2: 33 sectors (Tokyo Stock Exchange)
High-Technology Stock

Machinery, Electric Appliances, Transportation Equipment, Precision Instruments

Cyclical Stock

Mining, Textiles & Apparels, Pulp & Paper, Chemicals, Oil & Coal Products,
Rubber Products, Glass & Ceramics Products, Iron & Steel,
Nonferrous Metals, Metal Products, Marine Transportation, Wholesale Trade

Domestic-Demand Stock

Other Products, Land Transportation, Air Transportation,
Warehousing & Harbor Transportation Services,
Information & Communication, Retail Trade, Services

Finance & InsuranceBanks, Securities & Commodity Futures, Insurance, Other Financing Business

Defensive Stock

Fishery, Agriculture & Forestry, Foods, Pharmaceutical, Electric Power & Gas

Construction & Real Estate

Construction, Real Estate

Panel B. the number of combinations: N (N − 1) / 2
mean
min
All
1,046,425
583,740
In33
55,626(5.32%)
30,439In6Out33
163,655 (15.64%)
95,874Out6827,144 (79.04%)
457,427

1Q
759,528
40,142
117,785
601,601

median1,003,960
53,806
149,279
800,876

3Q
1,389,028
74,664
223,316
1,090,877

max
1,546,161
84,026
253,432
1,208,703

Note: “All” means the group of all the combinations of two stocks among all the stocks. “In33” means the group of all the
combinations of two stocks that belong to the same sector in the 33 sector classifications. “In6Out33” means the group of all
the combinations of two stocks that belong not only to the same sector in the six sector classifications but also to different
sectors in the 33 sector classifications. “Out6” means the group of all the remaining combinations of two stocks.

26

Table 2: Summary statistics for excess comovement and attention measurements

Panel A. All
excess comovement (EC)attention 1 (A1)attention 2 (A2)attention 3 (A3)
Panel B. In33
excess comovement (EC)attention 1 (A1)attention 2 (A2)attention 3 (A3)
Panel C. In6Out33
excess comovement (EC)attention 1 (A1)attention 2 (A2)attention 3 (A3)
Panel D. Out6
excess comovement (EC)attention 1 (A1)attention 2 (A2)attention 3 (A3)

lag = 1

autocorrelation
2

3

0.221
0.602
0.281
0.612

0.557
0.929
0.682
0.836

0.467
0.869
0.530
0.731

3.564
−2.348−0.590−1.527

1.687
0.613
0.269
0.632

0.474
0.939
0.686
0.851

0.858
−2.175−0.500−1.4130.734−2.125−0.539−1.356

0.607
0.608
0.271
0.613

−0.016−2.176−0.466−1.423−0.026−2.122−0.505−1.380

0.245
0.601
0.285
0.612

mean

medianstd. dev.

0.318−2.183−0.476−1.4290.273−2.135−0.522−1.3873.687−2.322−0.554−1.571

Correlation
with A1

Correlation
with A2

Correlation
with A3

0.421
0.821
0.445
0.662

0.446
−
−
−

0.269
0.016
−
−

0.463
0.898
0.413
−

0.353
0.886
0.529
0.753

0.353
0.844
0.448
0.691

0.625
−
−
−

0.055
−0.009
−
−

0.620
0.904
0.387
−

0.413
0.931
0.677
0.841

0.337
0.873
0.518
0.739

0.360
0.822
0.439
0.666

0.500
−
−
−

0.169
−0.001
−
−

0.514
0.899
0.393
−

0.432
0.928
0.683
0.833

0.376
0.866
0.532
0.727

0.300
0.818
0.446
0.658

−0.059
−
−
−

0.151
0.022
−
−

−0.047
0.898
0.419
−

Note: “All” means the group of all the combination of two stocks among all the stocks. “In33” means the group of all the combinations of two stocks
that belong to the same sector in the 33 sector classifications. “In6Out33” means the group of all the combination of two stocks that belong not only tothe same sector in the six sector classifications but also to different sectors in the 33 sector classifications. “Out6” means the group of all the remaining
combinations of two stocks. The attention measurement “A1” denotes the series of averaging the logarithm of the absolute value of the difference
between two stocks regarding trading turnover ratios for stocks within a group. The attention measurement “A2” denotes the series of averaging thelogarithm of the absolute value of the difference between two stocks regarding return standard deviations for stocks within a group. The attention
measurement “A3” denotes the series of averaging the logarithm of the absolute value of the difference between two stocks regarding the product oftrading turnover ratios and return standard deviations for stocks within a group.
27

Table 3: Time-series regressions of excess comovement on attention measurement with lagged dependent variables (ECs)
A1

All
A2

A3

A1

In33
A2

A3

A1

In6Out33
A2

A3

Constant

0.305(5.65)

0.163(5.71)

0.263(6.60)

6.110(10.44)1.643(5.94)

4.636(11.09)1.263(7.53)

0.497(5.97)

1.046(8.76)−0.045 0.012(−0.98) (0.52)−0.035(−1.13)

Attention

0.078(4.19)

0.120(3.34)

0.088(4.85)

1.392(8.79)

0.690(2.26)

1.292(9.20)

0.337(6.01)

0.348(3.18)

0.369(6.97)−0.018 0.039(−0.89) (0.89)−0.02(−1.03)EC(−1)

0.343(6.13)

0.371(6.66)

0.329(5.89)

0.182(3.36)

0.362(6.56)

0.189(3.57)

0.194(3.54)

0.274(5.02)

0.176(3.26)

0.311(5.53)

0.308(5.47)

0.311(5.54)

EC(−2)

0.129(2.20)

0.163(2.78)

0.130(2.25)−0.017(−0.31)0.104(1.76)

0.009(0.16)

0.054(0.97)

0.127(2.25)

0.054(1.00)

0.200(3.48)

0.197(3.42)

0.201(3.49)

EC(−3)

0.109(1.97)

0.137(2.47)

0.111(2.03)

0.055(1.06)

0.191(3.44)

0.096(1.91)

0.139(2.61)

0.224(4.12)

0.161(3.12)

0.095(1.69)

0.088(1.55)

0.097(1.73)

Group:
Attention:

2

adj. R
LB(6)

A1

Out6
A2

A3

38.52% 37.30% 39.61%

40.78% 27.30% 41.88%

31.12% 25.55% 33.50%

23.20% 23.20% 23.27%

0.425

6.009

8.511

0.847

0.914

0.427

3.335

11.333

11.33812.557

1.056

0.792

Note: “All” means the group of all the combinations of two stocks among all the stocks. “In33” means the group of all the combinations of two
stocks that belong to a same sector in the 33 sector classifications. “In6Out33” means the group of all the combinations of two stocks that belong
not only to the same sector in the six sector classifications but also to different sectors in the 33 sector classifications. “Out6” means the group of all
the remaining combinations of two stocks. “EC” is excess comovement, and the number in parentheses is a lag of a month’s interval. t-statistics arereported in parentheses. “adj.R2” denotes the coefficient of determination adjusted by the degree of freedom. “LB(6)” denotes the Ljung-Box Q tests
for autocorrelation in the residual series with six lags.

28

Table 4: Correlation matrix of explanatory variables
Rm
YD
CD
YS
PS
IL
TV
d+

Rm

YD

CD

YS

1.00
0.15*
−0.08
0.04
0.20*
−0.15*

1.00
−0.05
0.04
0.00
−0.08

1.00
−0.66*−0.24*
0.22*

♦

0.08

0.01

0.33*

♦

d−

−0.38* −0.14

♦

0.02

−0.09

σm

−0.25* −0.16*

−0.06

−0.10

−0.06

0.07

H1
H2
N

−0.13
−0.12
0.00

♦

−0.05
−0.08
−0.03

1.00

−0.08

1.00
−0.17*

−0.10

d+

d−

H1

σm

H2

N

1.00

†

†

♦

TV

1.00
−0.55*

0.05

−0.13

IL

0.14
0.06

0.06

0.09

PS

0.25*

−0.28*

0.09

1.00

†

−0.20*

0.20*

0.07

−0.17*

1.00†−0.35*

0.19*

−0.01

−0.14

♦

0.35*

1.00

−0.08

0.24*

−0.03

−0.05

0.09

0.04

1.00

0.15*

0.10

†

0.73*

1.00

0.06

♦

−0.02

0.22*

−0.24*

0.18*−0.65*♦

0.13−0.15*
0.08

0.38*−0.35*

−0.05

−0.08

0.16*

♦

0.12

0.11

1.00

Note: “Rm” denotes monthly market return with dividend. “YD” denotes monthly rate of change of the yen/dollar. “CD” denotes
monthly CD rate (three month) at the end of the month. “YS” denotes monthly yield spread between short−term interest rate andlong−term government bond yield at the end of the month. “PS” denotes the liquidity measurement proposed by Pastor and Stambaugh(2003). “IL” denotes the illiquidity measurement proposed by Amihud (2002). “TV” denotes the monthly trading value at TSE 1st floor.
Note that “d+” (“d−”) is a dummy variable equal to one if sign , = sign ,= sign ,= + (−), and zero otherwise,
which are the same definitions used by Kallberg and Pasquariello (2008). Furthermore “σm” is proxy for market uncertainty measured
as the monthly standard deviation of daily market returns within the same month. “H1” and “H2” are proxies for the degree of
information heterogeneity based on the cross-sectional mean of the standard deviations of analysts’ EPS forecasts and ratios of thedifferences between their highest and lowest forecasts, respectively, which are the same definitions used by Kallberg and Pasquariello(2008). Finally, “N” is the cross-sectional mean number of analysts covering the forecasted firms. A “†,” “◆,” or “*” indicate
significance at the 10%, 5%, or 1% level, respectively.

29

Table 5: Time-series regressions of excess comovement on each explanatory variable
const.

All
slope

0.319
(25.55)0.319(25.50)0.389(27.97)0.314(15.93)0.348(23.13)0.413(20.91)
0.314(24.93)0.298(22.58)0.324(24.07)0.233(8.61)
0.274(7.87)
0.249(7.83)−0.358(−5.04)0.003(1.48)
0.000(−0.13)−0.042(−8.58)0.006(0.35)
0.610(3.33)−0.072(−5.94)0.096(2.18)
0.140(4.09)−0.035(−0.98)0.071(3.55)
0.416(1.39)
0.220(2.37)
0.103(9.65)

Group:
Rm
YD
CD
YS
PS
IL
TV
d+
d−
σm
H1
H2
N

adj R

2

0.37%
−0.31%
18.67%−0.28%
3.09%
9.79%
1.17%
4.73%
−0.01%
3.54%
0.29%
1.44%
22.56%

const.

In33
slope

adj R

2

3.676
0.048
2.34%
(39.11) (2.93)
3.682 −0.002 −0.32%(38.65) (−0.07)
3.743 −0.037 −0.07%(31.86) (−0.88)
4.106 −0.441 3.94%(27.98) (−3.74)
3.882
4.223
2.50%
(33.80) (3.01)
4.796−0.86 24.25%(34.81) (−10.11)
3.663
0.390
0.11%
(37.96) (1.16)
3.505
1.201
6.07%
(35.09) (4.63)
3.760 −0.561 1.00%(36.88) (−2.05)
3.085
0.498
2.91%
(14.91) (3.24)
4.329 −5.959 1.84%(16.46) (−2.63)
4.655 −3.079 5.61%(19.61) (−4.45)
0.981
0.412
5.97%
(1.65)(4.59)

In6Out33
2
const.
slope
adj R

const.

0.858(25.21)
0.859(25.14)0.937(22.56)
0.949(17.77)0.921(22.24)1.132(21.13)0.850(24.58)0.819(22.39)0.873(23.72)0.542(7.44)
1.168(12.48)1.138(13.21)−0.401(−1.92)−0.015(−1.08)−0.015(−1.09)0.053(3.33)−0.07(−3.26)−0.004(−0.25)−0.028(−1.21)−0.018(−1.26)−0.021(−1.42)−0.017(−1.13)−0.019(−0.62)−0.177(−4.73)−0.222(−6.71)−0.413(−4.78)0.011(1.79)−0.009(−0.82)−0.047(−3.20)−0.094(−2.18)1.296(2.57)−0.211(−6.36)0.185(1.53)
0.275(2.89)−0.097(−0.98)0.265(4.89)−2.85(−3.54)−0.882(−3.51)
0.192(6.11)

0.69%−0.10%
2.85%
1.17%
1.74%
11.10%
0.42%
2.28%−0.01%
6.75%
3.51%
3.46%
10.30%

Out6
slope

2

adj R
−0.001 −0.23%(−0.51)0.001 −0.30%(0.25)−0.041 14.26%(−7.32)0.057
3.04%(3.30)
0.232
0.09%(1.13)
0.010 −0.16%(0.70)
0.051
0.03%(1.04)
0.042
0.05%(1.07)
0.012 −0.29%(0.31)
0.003 −0.31%(0.14)
1.489
6.09%(4.63)
0.656
12.49%(6.79)
0.061
6.16%(4.66)

Note: The symbols for the explanatory variables are the same as in Table 4. t-statistics are reported in parentheses. “adj.R2” denotes thecoefficient of determination adjusted by the degree of freedom.

30

Table 6: Time-series regressions of excess comovement on attention measurement and explanatory variables with lagged dependent
variables
Model 1Panel A. Allconstant
0.234(1.94)
attention 0.118(3.36)
EC(-1)
0.258(4.57)
EC(-2)
0.072(1.24)
EC(-3)
0.052(0.93)
Rm
0.002(1.09)
CD−0.012(−2.04)IL
0.019(0.92)
d+H2
N
adj. R

2

Model 4Model 10.194
(1.63)
0.112(3.23)
0.249(4.43)
0.077(1.33)
0.058(1.05)

0.267(2.32)
0.142(4.44)
0.263(4.69)
0.073(1.26)
0.054(0.96)

0.126(1.21)
0.181(3.33)
0.267(4.74)
0.081(1.40)
0.052(0.93)
0.002(1.29)−0.007(−1.31)−0.045(−3.28)0.031(1.65)
0.179(1.98)
0.019(1.36)−0.011(−1.92)0.022(1.10)
0.045(1.58)
0.030(1.00)
0.041(2.20)
0.177(1.97)
0.020(1.49)

42.73%

43.63%d−σm

Attention 1 (A1)
Model 2 Model 3
0.291(2.51)
0.143(4.47)
0.267(4.74)
0.071(1.21)
0.048(0.85)
0.001(0.60)−0.011(−2.02)0.035(1.95)−0.011(−1.88)0.041(2.25)
0.035(1.22)−0.041(−1.43)0.182(2.00)
0.020(1.48)

0.180(1.99)
0.022(1.64)

0.001(0.04)
0.069(0.78)
0.030(2.19)

42.41%

42.92%

42.69%

Attention 2 (A2)Model 2 Model 3

Model 4Model 1

0.096
(0.93)
0.178(3.31)
0.256(4.58)
0.086(1.49)
0.057(1.03)

0.111(1.13)
0.196(5.02)
0.258(4.63)
0.085(1.48)
0.055(1.00)

0.149(1.41)
0.106(3.51)
0.258(4.57)
0.071(1.23)
0.050(0.89)
0.002(1.03)−0.012(−2.06)0.007(0.41)−0.007(−1.20)−0.039(−2.78)0.049(1.71)
0.030(1.00)
0.011(0.48)
0.071(0.82)
0.032(2.30)
43.72%

31

0.127(1.29)
0.182(4.76)
0.267(4.76)
0.081(1.41)
0.052(0.93)
0.002(1.35)−0.007(−1.32)−0.045(−3.28)−0.006(−1.14)−0.039(−2.80)0.046(1.65)−0.061(−2.11)

0.068(0.79)
0.031(2.25)

0.065(0.76)
0.033(2.45)−0.003(−0.14)0.140(1.59)
0.026(1.90)

42.88%

43.86%

42.92%

Attention 3 (A3)Model 2 Model 3

Model 40.114
(1.09)
0.101(3.43)
0.248(4.43)
0.076(1.31)
0.056(1.02)

0.126(1.28)
0.109(5.11)
0.249(4.45)
0.074(1.29)
0.055(1.00)−0.011(−1.93)0.011(0.66)
0.045(1.58)
0.030(1.00)
0.009(0.36)
0.141(1.61)
0.027(2.01)
43.86%

0.144(1.45)
0.103(4.89)
0.258(4.58)
0.072(1.24)
0.051(0.91)
0.002(1.15)−0.012(−2.06)0.006(0.41)−0.011(−1.94)0.015(1.04)
0.043(1.54)−0.058(−2.01)0.140(1.59)
0.026(1.90)

0.142(1.62)
0.028(2.08)

43.10%

44.02%

Table 6 −Continued
Model 1Panel B. In33
constant
4.911(4.83)
attention 1.440(5.27)
EC(-1)
0.166(3.09)
EC(-2)−0.039(−0.74)EC(-3)
0.049(0.95)
Rm
0.041(2.99)
CD
0.151(3.46)
IL−0.022(−0.15)d+H2Nadj. R

2

Model 4Model 1

4.899
(4.87)
1.493(5.53)
0.141(2.64)−0.013(−0.25)0.058(1.13)

5.905(6.07)
1.865(7.50)
0.153(2.83)−0.02(−0.37)0.046(0.88)

1.818(2.18)
0.812(1.84)
0.226(4.16)−0.012(−0.22)0.092(1.75)
0.054(3.89)
0.113(2.49)−0.627(−5.43)0.422(2.99)
0.161(0.25)
0.105(1.02)

0.152(3.48)
0.058(0.39)
0.395(1.81)
0.225(1.00)
0.463(3.26)
0.164(0.25)
0.102(0.99)

44.98%

45.42%d−σm

Attention 1 (A1)
Model 2 Model 3
5.857(5.98)
1.804(7.28)
0.170(3.12)−0.038(−0.71)0.040(0.77)
0.029(2.17)
0.160(3.63)
0.199(1.49)

0.161(3.66)
0.269(1.96)
0.273(1.25)−0.45(−2.05)0.256(0.39)
0.119(1.14)

0.267(0.40)
0.119(1.14)

0.506(2.70)−0.817(−1.21)0.222(2.06)

43.56%

43.71%

40.65%

Attention 2 (A2)Model 2 Model 3

Model 4Model 11.809
(2.18)
0.966(2.21)
0.191(3.50)
0.021(0.38)
0.106(2.01)

2.490(3.11)
1.794(5.65)
0.204(3.71)
0.020(0.37)
0.105(1.97)

3.811(4.39)
1.266(5.50)
0.164(3.06)−0.037(−0.69)0.059(1.16)
0.039(2.92)
0.150(3.46)−0.158(−1.19)0.113(2.52)−0.566(−4.80)0.575(2.55)
0.234(1.00)
0.509(2.73)−0.924(−1.37)0.225(2.08)
40.89%

32

2.504(3.12)
1.660(5.33)
0.232(4.22)−0.007(−0.12)0.093(1.75)
0.043(3.22)
0.129(2.85)−0.62(−5.31)0.130(2.88)−0.568(−4.77)0.462(2.07)−0.594(−2.56)−1.139(−1.69)0.285(2.68)−1.223(−1.82)0.289(2.71)

0.009(0.05)−0.35(−0.55)0.188(1.84)

39.44%

39.64%

45.40%

Attention 3 (A3)Model 2 Model 3

Model 43.755
(4.38)
1.321(5.85)
0.138(2.61)−0.011(−0.20)0.069(1.36)

3.828(4.83)
1.274(8.14)
0.163(3.07)−0.037(−0.69)0.059(1.16)
0.039(3.08)
0.150(3.51)−0.154(−1.43)3.820(4.86)
1.351(8.54)
0.138(2.61)−0.011(−0.22)0.068(1.35)−0.349(−0.55)0.188(1.86)−0.355(−0.56)0.191(1.89)

45.58%

46.18%

0.151(3.51)−0.078(−0.59)0.400(1.85)
0.223(1.00)
0.034(0.19)−0.357(−0.56)0.189(1.86)
46.01%

0.153(3.58)−0.065(−0.58)0.391(1.85)−0.647(−2.97)

Table 6 −Continued
Model 1Panel C. In6Out33
0.616
constant(1.83)
attention 0.373(3.79)
0.154
EC(-1)(2.87)
0.026
EC(-2)(0.49)
0.133
EC(-3)(2.54)
Rm
0.010(1.90)
CD
0.008(0.52)
IL
0.090(1.52)
d+H2
N
adj. R

2

Model 4Model 10.667
(1.99)
0.404(4.11)
0.140(2.60)
0.028(0.52)
0.122(2.34)

0.987(2.97)
0.537(5.71)
0.164(3.00)
0.026(0.47)
0.123(2.31)

0.060(0.20)
0.270(1.71)
0.183(3.39)
0.048(0.88)
0.150(2.82)
0.013(2.53)
0.011(0.65)−0.097（−2.52)0.949(2.85)
0.520(5.63)
0.169(3.09)
0.025(0.46)
0.128(2.39)
0.004(0.79)
0.009(0.55)
0.192(3.57)

0.202(3.80)−0.472（−1.88)0.086(2.14)

0.008(0.52)
0.110(1.87)
0.054(0.64)
0.087(1.00)
0.206(3.81)−0.485（−1.93)0.090(2.21)−0.471（−1.84)0.100(2.44)

36.58%

36.35%

33.80%d−σm

Attention 1 (A1)
Model 2 Model 3

0.009(0.53)
0.200(3.63)
0.004(0.04)−0.051（−0.60)Attention 2 (A2)Model 2 Model 3

Model 4Model 10.089
(0.29)
0.316(1.99)
0.166(3.06)
0.054(0.99)
0.140(2.62)

0.326(1.12)
0.612(5.09)
0.179(3.26)
0.051(0.92)
0.147(2.72)

0.267(0.89)
0.277(3.26)
0.161(2.99)
0.030(0.56)
0.143(2.73)
0.011(2.01)
0.007(0.44)
0.030(0.58)−0.475（−1.85)0.100(2.44)

0.200(2.92)−0.647（−2.50)0.104(2.49)

0.011(0.67)−0.091（−2.31)0.106(1.26)
0.089(1.00)
0.193(2.81)−0.695（−2.68)0.109(2.58)

33.53%

34.24%

33.68%

33

0.308(1.06)
0.589(5.08)
0.190(3.47)
0.046(0.84)
0.154(2.86)
0.009(1.75)
0.018(1.07)−0.093（−2.37)0.018(1.05)−0.09（−2.24)0.064(0.76)−0.096（−1.10)−0.769（−2.97)0.129(3.12)−0.799（−3.08)0.131(3.14)

0.125(1.82)−0.583（−2.32)0.104(2.56)

32.63%

32.19%

35.84%

Attention 3 (A3)Model 2 Model 3

Model 40.295
(0.98)
0.305(3.60)
0.146(2.71)
0.033(0.60)
0.133(2.53)

0.454(1.58)
0.403(6.40)
0.149(2.76)
0.026(0.48)
0.134(2.54)

0.437(1.52)
0.385(6.31)
0.160(2.96)
0.025(0.46)
0.142(2.69)
0.007(1.49)
0.008(0.48)
0.087(2.14)

0.007(0.43)
0.048(0.94)
0.067(0.80)
0.087(1.00)
0.119(1.74)−0.608（−2.42)0.109(2.66)

0.008(0.48)
0.098(2.32)
0.036(0.44)−0.113（−1.32)−0.604（−2.40)0.115(2.85)−0.62（−2.46)0.119(2.92)

35.56%

35.35%

35.13%

Table 6 −Continued
Model 1Panel D. Out6
constant −0.069（−0.46)attention −0.013（−0.32)0.249
EC(-1)(4.37)
0.124
EC(-2)(2.12)
0.011
EC(-3)(0.20)
Rm−0.002（−0.95)CD−0.022（−3.01)IL−0.003（−0.10)d+

H2Nadj. R

2

Model 4Model 1−0.131（−0.89)−0.031（−0.75)0.243(4.27)
0.124(2.12)
0.013(0.22)−0.154（−1.09)−0.041（−1.08)0.241(4.26)
0.124(2.12)
0.013(0.22)

0.036(0.28)
0.098(1.49)
0.250(4.41)
0.120(2.07)
0.000（−0.01)−0.003（−1.35)−0.02（−2.75)−0.001（−0.06)−0.022（−0.96)0.298(2.55)
0.001(0.03)−0.021（−2.89)−0.008（−0.32)0.029(0.79)
0.037(1.00)−0.012（−0.53)0.297(2.54)
0.002(0.14)

27.47%

27.17%d−σm

Attention 1 (A1)
Model 2 Model 3−0.112（−0.80)−0.032（−0.86)0.245(4.31)
0.124(2.13)
0.011(0.20)−0.001（−0.68)−0.022（−3.02)−0.015（−0.65)−0.021（−2.89)−0.014（−0.61)
0.032(0.89)−0.003（−0.08)0.296(2.54)−0.001（−0.04)0.296(2.53)
0.002(0.10)−0.058（−1.94)0.287(2.50)
0.002(0.13)

27.49%

27.34%

27.97%

Attention 2 (A2)Model 2 Model 3

Model 4Model 1−0.009（−0.07)0.074(1.13)
0.242(4.27)
0.122(2.09)
0.006(0.10)−0.068（−0.55)0.006(0.13)
0.241(4.25)
0.123(2.11)
0.012(0.21)−0.043（−0.33)−0.001（−0.04)0.250(4.38)
0.123(2.12)
0.011(0.19)−0.002（−1.02)−0.022（−3.01)
0.003(0.14)−0.02（−2.65)0.003(0.16)
0.014(0.40)
0.037(1.00)−0.044（−1.46)0.303(2.63)
0.003(0.16)
27.34%−0.043（−0.35)0.005(0.12)
0.246(4.32)
0.123(2.11)
0.009(0.16)−0.002（−0.79)−0.022（−2.99)−0.001（−0.07)−0.021（−2.83)0.003(0.20)
0.024(0.68)−0.008（−0.23)0.315(2.75)−0.004（−0.24)0.322(2.80)−0.002（−0.11)−0.025（−0.83)0.304(2.64)
0.000（−0.02)27.32%

27.07%

27.45%

Attention 3 (A3)Model 2 Model 3

Model 4−0.091（−0.69)−0.017（−0.47)0.243(4.28)
0.124(2.12)
0.014(0.25)−0.079（−0.64)−0.023（−0.94)0.246(4.33)
0.124(2.14)
0.013(0.23)−0.002（−0.78)−0.022（−3.01)−0.008（−0.47)−0.105（−0.85)−0.025（−1.00)0.242(4.27)
0.124(2.13)
0.015(0.26)

0.304(2.64)−0.002（−0.11)0.309(2.68)
0.000（−0.01)27.52%

27.30%−0.021（−2.87)0.000（−0.02)0.026(0.72)
0.037(1.00)−0.01（−0.34)0.309(2.68)
0.000(0.03)
27.09%−0.021（−2.88)−0.005（−0.26)0.028(0.81)
0.000(0.01)

Note: The symbols for the explanatory variables are the same as in Table 4. “EC” is excess comovement and the number in parentheses is a lag of amonth’s interval. t-statistics are reported in parentheses. “adj.R2” denotes the coefficient of determination adjusted by the degree of freedom.

34

Table 7: Time-series regressions of excess comovement on attention measurement and explanatory variables with lagged ECs: Model 2
for size-sorted groups
Attention 1 (A1)Size:
L−L L−M
L−S M−M M−S
S−S
Panel A. In33
constant 8.552 4.822 5.085 6.016 3.730 2.682(2.80) (3.26) (4.65) (5.01) (3.75) (2.65)
attention 2.320 1.010 0.851 1.500 1.089 0.504(3.79) (3.27) (3.78) (4.52) (3.81) (2.42)
EC(-1) 0.265 0.134 0.057 0.030 0.013 0.111(4.73) (2.43) (1.01) (0.57) (0.23) (2.00)
EC(-2) 0.164 0.082 0.093 −0.084 −0.03 −0.056(2.91) (1.50) (1.71) (−1.6) (−0.55) (−1.00)
EC(-3) 0.100 0.087 0.104 0.081 0.004 −0.029(1.82) (1.62) (1.97) (1.56) (0.08) (−0.53)
CD
0.409 0.235 0.074 0.099 0.084 0.057(3.23) (3.66) (1.57) (1.81) (1.66) (1.03)
IL−0.108 −0.246 0.022 −0.048 0.226 −0.189(−0.33) (−1.33) (0.14) (−0.25) (1.28) (−1.14)d+1.001 0.554 0.726 0.087 0.505 0.084(1.86) (1.92) (3.09) (0.30) (1.91) (0.29)
d−−1.068 −0.779 −0.268 −0.777 −0.377 −0.384(−1.90) (−2.57) (−1.08) (−2.63) (−1.38) (−1.26)σm
1.017 0.615 −0.073 0.692 −0.097 0.921(2.70) (3.13) (−0.46) (3.84) (−0.60) (5.25)
H2
0.345 −1.037 −0.767 0.505 0.500 0.217(0.21) (−1.18) (−1.08) (0.59) (0.63) (0.25)
N
0.196 0.013 −0.331 0.089 −0.077 0.060(0.67) (0.08) (−2.73) (0.68) (−0.63) (0.44)
adj. R2

62.28% 42.68% 26.15% 26.59% 9.70% 14.66%

L−L

L−M

Attention 2 (A2)L−S M−M M−S

S−S

L−L

L−M

Attention 3 (A3)L−S M−M M−S

S−S

0.729 1.158 2.581 3.691 2.374 3.079(0.34) (1.05) (2.94) (3.42) (2.49) (2.99)
1.329 −0.044 0.294 1.177 0.418 1.333(1.39) (−0.08) (0.82) (2.10) (0.99) (3.09)
0.303 0.168 0.080 0.059 0.024 0.112(5.43) (3.05) (1.41) (1.10) (0.43) (2.03)
0.198 0.113 0.117−0.06 −0.029 −0.047(3.48) (2.06) (2.13) (−1.12) (−0.52) (−0.84)
0.142 0.113 0.120 0.108 0.016 −0.034(2.59) (2.11) (2.21) (2.04) (0.28) (−0.63)
0.169 0.144 0.045 0.086 0.084 0.093(1.55) (2.44) (0.93) (1.52) (1.56) (1.64)−0.891 −0.615 −0.405 −0.688 −0.289 −0.483(−3.05) (−4.03) (−3.29) (−4.87) (−2.31) (−3.61)
1.165 0.656 0.762 0.236 0.710 0.173(2.11) (2.20) (3.17) (0.81) (2.68) (0.61)−0.957 −0.767 −0.238 −0.884 −0.422 −0.439(−1.67) (−2.49) (−0.94) (−2.92) (−1.51) (−1.44)
1.264 0.930 0.131 0.648 −0.019 0.644(2.70) (3.53) (0.76) (2.70) (−0.1) (3.17)−1.158 −1.246 −0.998 −0.638 −0.249 −0.615(−0.68) (−1.36) (−1.37) (−0.74) (−0.31) (−0.72)
0.671 0.205 −0.133 0.137 −0.106 0.018(2.35) (1.41) (−1.15) (0.99) (−0.84) (0.13)

6.554 3.764 4.216 4.875 2.820 2.315(2.55) (2.97) (4.31) (4.62) (3.07) (2.38)
1.926 0.799 0.675 1.311 0.939 0.595(3.99) (3.18) (3.59) (4.86) (3.85) (3.26)
0.261 0.135 0.061 0.025 0.018 0.111(4.68) (2.45) (1.09) (0.47) (0.32) (2.01)
0.167 0.089 0.099 −0.084 −0.026 −0.051(2.98) (1.63) (1.82) (−1.61) (−0.46) (−0.92)
0.107 0.095 0.111 0.082 0.012 −0.027(1.98) (1.78) (2.10) (1.59) (0.22) (−0.50)
0.385 0.224 0.071 0.103 0.086 0.065(3.17) (3.55) (1.52) (1.89) (1.70) (1.17)−0.282 −0.344 −0.096 −0.177 0.088 −0.206(−0.95) (−2.04) (−0.68) (−1.07) (0.58) (−1.39)
0.956 0.548 0.714 0.101 0.528 0.050(1.77) (1.89) (3.03) (0.36) (2.01) (0.17)−1.055 −0.778 −0.263 −0.795 −0.394 −0.396(−1.88) (−2.57) (−1.06) (−2.71) (−1.44) (−1.31)
0.315 0.359 −0.262 0.278 −0.367 0.740(0.66) (1.46) (−1.36) (1.25) (−1.88) (3.95)−0.523 −1.343 −1.081 0.072 0.041 −0.027(−0.32) (−1.53) (−1.52) (0.09) (0.05) (−0.03)
0.346 0.089 −0.259 0.171 −0.011 0.117(1.25) (0.62) (−2.24) (1.29) (−0.08) (0.86)

60.76% 40.67% 22.86% 22.79% 5.70% 15.66%

62.46% 42.57% 25.82% 27.30% 9.78% 15.94%

35

Table 7 −Continued
Attention 1 (A1)Size:
L−L L−M
L−S M−M M−S
S−S
Panel B. Out6
constant −2.131 −0.819 0.242 −0.190 0.476 −0.020(−4.70) (−3.04) (1.00) (−0.58) (1.77) (−0.05)
attention −0.450 −0.208 0.003 −0.025 0.193 −0.043(−4.52) (−3.16) (0.06) (−0.23) (2.49) (−0.49)
EC(-1) 0.196 0.072 0.075 0.084 0.141 0.153(3.47) (1.28) (1.35) (1.46) (2.56) (2.72)
EC(-2) −0.004 0.064 −0.040 0.077 0.010 0.017(−0.07) (1.13) (−0.71) (1.36) (0.18) (0.30)
EC(-3) 0.089 0.031 0.045 0.029 0.075 0.046(1.59) (0.56) (0.81) (0.52) (1.39) (0.83)
CD−0.019 −0.026 −0.014 −0.069 0.001 0.014(−1.06) (−2.23) (−1.24) (−3.84) (0.08) (0.61)
IL−0.085 −0.025 −0.026 −0.025 0.070 −0.128(−1.44) (−0.65) (−0.65) (−0.41) (1.40) (−1.86)
d+0.038 −0.058 0.057 −0.113 0.079 0.104(0.42) (−1.02) (1.00) (−1.32) (1.05) (0.87)d−−0.102 0.043 0.042 0.110 −0.106 −0.069(−1.05) (0.72) (0.69) (1.24) (−1.36) (−0.56)σm
0.088 0.006 −0.141 0.136 −0.207 0.418(1.42) (0.15) (−3.68) (2.44) (−4.40) (5.67)
H2
0.536 0.295 0.479 0.352 0.454 0.050(1.92) (1.68) (2.72) (1.32) (1.96) (0.14)N
0.090 0.044 −0.061 0.045 −0.055 0.056(1.98) (1.54) (−2.12) (1.13) (−1.55) (0.98)
adj. R2

26.58% 17.73% 8.35% 25.14% 15.85% 16.72%

L−L

L−M

Attention 2 (A2)L−S M−M M−S

S−S

L−L

L−M

Attention 3 (A3)L−S M−M M−S

S−S−0.803 −0.185 0.260 0.134 0.239 0.177(−2.22) (−0.87) (1.32) (0.44) (0.91) (0.43)−0.146 0.042 0.047 0.378 0.048 0.188(−0.99) (0.40) (0.56) (2.39) (0.41) (1.08)
0.248 0.097 0.072 0.076 0.154 0.149(4.36) (1.71) (1.30) (1.34) (2.77) (2.64)
0.034 0.092 −0.040 0.066 0.016 0.022(0.58) (1.63) (−0.72) (1.18) (0.29) (0.38)
0.128 0.054 0.043 0.015 0.079 0.040(2.24) (0.96) (0.79) (0.27) (1.45) (0.73)−0.028 −0.025 −0.012 −0.067 −0.001 0.023(−1.45) (−2.13) (−1.08) (−3.78) (−0.05) (0.97)
0.109 0.065 −0.032 −0.027 −0.025 −0.113(2.42) (2.42) (−1.18) (−0.72) (−0.73) (−2.14)−0.035 −0.095 0.054 −0.164 0.121 0.075(−0.37) (−1.62) (0.94) (−1.93) (1.63) (0.64)−0.112 0.042 0.041 0.107 −0.109 −0.073(−1.12) (0.69) (0.68) (1.22) (−1.39) (−0.59)
0.014 −0.069 −0.153 0.007 −0.182 0.361(0.17) (−1.36) (−3.73) (0.10) (−3.25) (4.20)
0.604 0.296 0.468 0.309 0.292 0.048(2.04) (1.63) (2.66) (1.20) (1.29) (0.14)
0.012 0.014 −0.059 0.062 −0.06 0.056(0.27) (0.52) (−2.16) (1.56) (−1.68) (0.99)−1.486 −0.533 0.223 −0.099 0.291 0.018(−3.77) (−2.29) (1.04) (−0.34) (1.15) (0.05)−0.285 −0.131 −0.005 0.053 0.114 −0.030(−3.58) (−2.39) (−0.11) (0.59) (1.69) (−0.39)
0.218 0.083 0.075 0.082 0.148 0.153(3.87) (1.47) (1.35) (1.42) (2.67) (2.72)
0.011 0.074 −0.040 0.074 0.013 0.016(0.19) (1.31) (−0.71) (1.31) (0.23) (0.29)
0.104 0.041 0.045 0.028 0.078 0.046(1.84) (0.74) (0.81) (0.49) (1.43) (0.83)−0.022 −0.025 −0.014 −0.070 0.000 0.014(−1.21) (−2.21) (−1.27) (−3.92) (0.00) (0.62)−0.015 0.013 −0.030 0.007 0.024 −0.119(−0.28) (0.36) (−0.87) (0.13) (0.55) (−1.93)
0.019 −0.066 0.059 −0.129 0.097 0.100(0.21) (−1.15) (1.02) (−1.52) (1.29) (0.84)−0.106 0.044 0.042 0.114 −0.108 −0.068(−1.07) (0.73) (0.70) (1.29) (−1.38) (−0.56)
0.161 0.033 −0.137 0.102 −0.228 0.425(2.02) (0.66) (−2.98) (1.43) (−4.02) (5.29)
0.640 0.335 0.478 0.386 0.349 0.075(2.25) (1.89) (2.74) (1.48) (1.55) (0.21)
0.050 0.025−0.06 0.051 −0.049 0.054(1.14) (0.91) (−2.17) (1.26) (−1.37) (0.95)

21.91% 15.08% 8.45% 26.50% 14.18% 16.98%

24.81% 16.60% 8.36% 25.22% 14.94% 16.7%

Note: Symbols “L,” “M,” and “S” express the largest, middle, and smallest cohorts of stocks on the basis of their market values, respectively. Therefore,
for example, “L–L” means that both cohorts are constituted by large stocks. The symbols for the explanatory variables are the same as in Table 4. “EC”
is excess comovement and the number in parentheses is a lag of a month’s interval. t-statistics are reported in parentheses. “adj.R2” denotes thecoefficient of determination adjusted by the degree of freedom.

36

Table 8: Time-series regressions incorporating the influence of foreign investors’ behavior into information heterogeneity in Model 2
Group:
Attention:
Model:
constant
attention
EC(-1)
EC(-2)
EC(-3)
CD
IL
d+
d−
σm
H2
|F|
H2*|F|
N
adj. R

2

In33
A2

A1
M2’
5.027
(4.71)
1.516(5.46)
0.138(2.57)−0.014(−0.26)0.058(1.13)
0.150(3.41)
0.057(0.38)
0.419(1.83)−0.649(−2.88)0.471(3.27)
0.165(0.25)−0.07(−0.36)M2”
4.997(4.77)
1.513(5.47)
0.139(2.57)−0.013(−0.24)0.058(1.12)
0.150(3.42)
0.056(0.37)
0.417(1.83)−0.65(−2.89)0.471(3.26)
0.263(0.37)

0.096(0.92)−0.212(−0.34)0.094(0.89)

45.45%

45.44%

M2’
1.655(1.93)
0.944(2.15)
0.194(3.54)
0.021(0.38)
0.105(1.98)
0.118(2.59)−0.546(−4.50)0.522(2.19)−0.705(−3.01)0.490(2.60)−0.895(−1.33)0.138(0.70)

A3

M2”
1.709
(2.01)
0.937(2.13)
0.193(3.53)
0.020(0.36)
0.106(2.01)
0.117(2.56)−0.548(−4.47)0.535(2.26)−0.704(−3.01)0.497(2.65)−1.061(−1.48)0.234(2.15)

0.349(0.54)
0.235(2.14)

40.99%

40.95%

M2’
3.820(4.23)
1.331(5.78)
0.137(2.56)−0.011(−0.21)0.069(1.36)
0.150(3.45)−0.081(−0.61)0.415(1.83)−0.658(−2.94)0.037(0.20)−0.362(−0.57)−0.044(−0.23)

Out6
A2

A1
M2”
3.830
(4.3)
1.336
(5.79)
0.136(2.55)−0.01(−0.19)0.069(1.35)
0.150(3.44)−0.083(−0.62)0.421(1.86)−0.66(−2.95)0.038(0.21)−0.27(−0.39)0.186(1.81)−0.201(−0.32)0.182(1.76)

46.02%

46.02%

M2’−0.204(−1.31)−0.043(−1.02)0.235(4.12)
0.117(2.00)
0.017(0.30)−0.02(−2.66)−0.008(−0.30)0.013(0.34)
0.005(0.13)−0.018(−0.75)0.305(2.61)
0.048(1.48)

M2”−0.213(−1.4)−0.047(−1.11)
0.229(4.02)
0.110(1.89)
0.017(0.29)−0.019(−2.65)−0.006(−0.25)0.007(0.17)
0.007(0.18)−0.02(−0.86)0.212(1.71)

0.006(0.38)

0.217(2.07)
0.010(0.59)

27.69%

28.19%

M2’−0.053(−0.40)0.069(1.05)
0.236(4.14)
0.116(1.98)
0.010(0.17)−0.019(−2.47)0.008(0.47)
0.000(−0.01)
0.005(0.13)−0.049(−1.62)0.315(2.73)
0.040(1.24)

A3

M2”−0.062(−0.47)0.061(0.92)
0.231(4.06)
0.110(1.89)
0.010(0.17)−0.018(−2.47)0.011(0.67)−0.006(−0.15)0.007(0.18)−0.05(−1.65)0.239(1.99)

0.005(0.32)

0.186(1.79)
0.008(0.48)

27.71%

28.09%

M2’−0.149(−1.09)−0.025(−0.69)0.235(4.13)
0.117(2.01)
0.019(0.32)−0.02(−2.66)0.002(0.09)
0.011(0.28)
0.005(0.14)−0.013(−0.43)0.320(2.77)
0.045(1.41)

M2”−0.158(−1.18)−0.029(−0.81)
0.229(4.03)
0.111(1.90)
0.019(0.32)−0.019(−2.64)0.003(0.16)
0.004(0.11)
0.007(0.19)−0.014(−0.47)0.231(1.91)

0.004(0.22)

0.211(2.01)
0.007(0.42)

27.56%

28.05%

Note: The symbols for the explanatory variables are the same as in Table 4. “EC” is excess comovement, and the number in parentheses is a lag of amonth’s interval. “|F|” denotes the absolute values of monthly net trading values by foreign investors. t-statistics are reported in parentheses. “adj.R2”
denotes the coefficient of determination adjusted by the degree of freedom.
37