A New Perspective of Market Behavior with
Spurious Herding
Rhea Tingyu Zhou, and Rose Neng LAI ∗
August, 2006
Abstract: Herding has been widely studied in the behavioral finance literature, mostly
using quarterly data. This paper tests herd behavior in a transparent, mature, and
order-driven market with daily data. Firstly, we propose to the literature (1) a change
in the definition of herding from the conventional clustering of investors to the
clustering of trades in a particular direction (whether buy or sell), and (2) a test of
herding due to fundamental analysis versus technical analysis. We find that herding is
more prevalent in small stocks, economic downturns, and when people perform
fundamental analysis. Secondly, and more importantly, to the best of our knowledge,
we are the first to show that the stock market is efficient even if there is herding. By
empirically separating herding into “spurious herding” and “intentional herding”, we
find that investors herd because they are equally informed, and they make decision for
the purpose of investing rather than simply doing what others do.
∗
Rhea Tingyu Zhou is graduate student of Faculty of Business Administration, University of Macau,
Macau, China.
Rose Neng Lai (Contact Author) is Associate Professor, Faculty of Business Administration, University
of Macau, Taipa, Macao, China. e-mail: [email protected]. Tel. No.: (853)-397-4744, Fax. No.:
(853)-838-320.
Abstract
of
A New Perspective of Market Behavior with Spurious
Herding
Herding has been widely studied in the behavioral finance literature, mostly using
quarterly data. This paper tests herd behavior in a transparent, mature, and
order-driven market with daily data. Firstly, we propose to the literature (1) a change
in the definition of herding from the conventional clustering of investors to the
clustering of trades in a particular direction (whether buy or sell), and (2) a test of
herding due to fundamental analysis versus technical analysis. We find that herding is
more prevalent in small stocks, economic downturns, and when people perform
fundamental analysis. Secondly, and more importantly, to the best of our knowledge,
we are the first to show that the stock market is efficient even if there is herding. By
empirically separating herding into “spurious herding” and “intentional herding”, we
find that investors herd because they are equally informed, and they make decision for
the purpose of investing rather than simply doing what others do.
1
1.
Introduction
“Herding” is referred to everyone doing what others do, even when their private
information suggests doing something quite different. In financial markets, it is
referred to buying (selling) simultaneously the same stocks as other investors buy
(sell). Herding has been a hot topic in behavioral finance over the past decade. Most
studies attempt to show that institutional investors in general herd because, as
Scharfstein and Stein (1990) comment, investment managers herd in order to share
the blame. In other words, it is better to be average, or wrong collectively, than be
right alone. Devenow and Welch (1996) further propose a distinction among three
models, which are (1) reputational model in that analysts and fund managers concern
their reputation more than real money return, (2) model with pay-off externalities with
which individuals forego an optimal decision only to coordinate and follow what
others in general do, and (3) cascade model which assume that investors have limited
information and that public visible actions by other investors are digested as another
part of their own information.
Most literature however finds virtually no herding among institutional investors when
using monthly, quarterly or biannual measurements. Lakonishok, Shleifer and Vishny
(1992) are among the first to propose a methodology (henceforth, the LSV model)
that is widely applied afterwards. In particular, while they use quarterly data and find
that fund managers do not herd in general, there is more herding in small stocks
“intentionally” because of less public information, and “unintentionally” because of
window dressing consideration; and that slightly more herding exists in past-winner
stocks (see also Wermers, 1999). Chang, Cheng and Khorama (2000) study Hong
Kong, the U.S., Japan, South Korea, and Taiwan markets and find no evidence of
2
herding in the more mature markets, but significant herding in the last two emerging
markets. Other markets have also been studied. For instance, Choe, Kho and Stulz
(1999) compare the herd behavior of foreign investors before and during the Asian
Financial Crisis in the Korean stock market. Wylie (2005) finds herd behavior in the
largest and smallest individual stocks in the U.K. data. Bowe and Domuta (2004) find
that foreign investors herd more than domestic investors in the Indonesian market
during the Asian Financial Crisis in 1997, while Voronkova and Bohl (2005) show
that pension fund investors in Poland tend to herd. Demirer and Kutan (2005)
conclude that there is no herding in the Chinese market both in the firm and sector
level.
In this study, we post and study two issues. Firstly, because most previous research
uses quarterly data, we ask the question, “Do investors herd in shorter periods in a
transparent, order-driven market?” To answer this, we study the Hong Kong stock
market, which is a well-developed international order-driven market. Using daily
horizon with intraday data, we compare herding behavior among stock groupings in
different industries, geographic origins, market capitalizations, past returns, and past
earnings per share. The rationale behind adopting the last two measures is that trading
based on past returns is considered as technical approach, while trading based on past
earnings per share is an act of performing fundamental analysis. It is therefore
interesting to see if investors follow fundamental analysis or otherwise whenever
there is herding. It is worth mentioning that former research also adopts a modified
definition of herding as the number of buys (or sells) rather than as the number buyers
(or sellers). The two methods are basically identical if the assumption that each buy
(or sell) is done by one individual trader holds in the former definition. We relax this
assumption in our context because we conjecture that an inclination towards one side
3
of trading is already evidence of herding; and there is no need to identify how many
traders are involved.
Secondly, and more importantly, we further empirically distinguish “spurious
herding” from “intentional herding”, which to the best of our knowledge is a first
attempt on the issue. “Spurious herding”, known as “unintentional herding” in
Lakonishok et al. (1992), is referred to all investors reacting identically to the same
piece of news, mostly for window dressing. Spurious herding may reflect either the
reaction of investors to commonly known public information or different opportunity
sets faced by investors. Particularly in crisis period, investors acting as a herd may
only reflect their perception of identical fundamental information of firms. On the
other hand, “intentional herding” can be perceived as taking an action that is common
to others and “sharing the blame” so as to avoid being alone with bad consequence,
especially when information about the stock is very scarce. Pure “intentional herding”
rarely exists, since the investors cannot be purely irrational. We propose that if we are
able to show that investors herd “spuriously” because they are equally informed, the
stock market is said to be efficient. Although Bikhchandani and Sharma (2001)
comment that it is difficult to distinguish between the two types of herding, we
attempt to empirically separate “spurious herding” from “intentional herding” by
applying the probability of information-based trading (PIN) due to Easley, Kiefer and
O’Hara (1996) from a market microstructure point of view. That is, we combine the
LSV and the PIN methodologies in the ground breaking papers by Lakonishok et al.
(1992) and Easley et al. (1996).
The remainder of the paper is organized as follows. The market nature, data and
methodology are described in Section 2. We then present our empirical results of
4
herding following the modified LSV model in Section 3. We further investigate
spurious and intentional herding (implicitly implied by measurement of herding
among informed traders and uninformed traders) via the probability of
information-based trading in Section 4. Finally, Section 5 concludes.
2.
The Market, Data and Methodology
2.1.
The Hong Kong Stock Market
Classified by the International Finance Corporation (IFC) as a developed market, the
Hong Kong stock market is ranked the second largest in Asia and the eighth largest in
the world by market capitalization. In this pure order-driven market (see Ahn et al.,
2001 for details), the trading system is extremely transparent (making our intraday
study more convincing) and with considerably low cost.1
In addition, a pronounced
characteristic of Hong Kong stock market is the dominance of institutional investors.
Nofsinger and Sias (1999) suggest that institutional herding impacts prices more than
herding by individual investors.
In this paper, the 200 constituent stocks in the Hang Seng Composite Index (HSCI)
from January 2003 to December 2004 are studied. HSCI, established on 3 October
2001, aims to cover 90% of the market capitalization of stocks listed on the Main
Board2 of the SEHK, and is therefore a good proxy of the overall Hong Kong stock
1
See O’Hara, M. (1995) for more detailed explanation about the impact of market transparency on
trading strategies.
2
The Hong Kong stock exchange, like most stock exchanges, has a Main Board and a second board,
which is called the Growth Enterprise Market (GEM). The entry requirement for the GEM is generally
lower than the Main Board.
5
market. The 200 constituent stocks are selected and substituted periodically in terms
of average market capitalization over each of the two years in the sample.3
The HSCI is further divided into geographical and industrial indexes. Geographical
indexes comprise Hang Seng Hong Kong Composite Index (HSHKCI) (also
constituting Hang Seng HK LargeCap, MidCap and SmallCap Index) and Hang Seng
Mainland Composite Index (including Hang Seng China-Affiliated Corporations
Index). Constituent stocks classified in HSHKCI derive the majority of their sales
revenue from Hong Kong or places outside the mainland China. Within the HSHKCI,
companies are ranked by their market capitalizations into three classes: LargeCap (top
15), MidCap (16th to 50th) and SmallCap (51st and below). The Hang Seng Mainland
Composite Index (HSMLCI) includes HSCI constituents which generate at least 50%
of their sales revenue from mainland China. The selection criteria of Hang Seng
China-Affiliated Corporations Index (HSCCI) are (1) non-H-shares4 in the Hang Seng
Mainland Composite Index, and (2) at least 30% shareholding directly held by either
(i) Mainland entities that include state-owned organizations, provincial or municipal
authorities in mainland China; or (ii) companies which are controlled by Mainland
entities as in (i) above.
3
From 1 January, 2003 to 31 December, 2004, there are altogether eight changes of constituent stocks
on 3 March 2003, 4 August 2003, 8 September 2003, 6 October 2003, 8 March 2004, 5 July 2004, 9
August 2004 and 6 September 2004. In order to make our sample stocks consistent during the whole 8
quarters in two-year sample period, we make two yearly adjustments by setting our 200 constituent
stocks equivalent to the lists after the historical changes in HSCI in 3 March 2003 and 8 March 2004.
This adjustment has minor effects on our result due to the following. First, although there are eight
changes in the two-year period, only four changes, which include the changes on 3 March 2003 and on
8 March 2004, substitute over three constituent stocks. Second, the other two big changes on 8
September 2003 and 6 September 2004 only have effect on the last 3 months of the whole year. Third,
from our calculation, the market capitalizations of the deleted constituent stocks are not significantly
smaller than the added constituent stocks.
4
A-, B- and H- shares are three types of shares issued by Chinese firms. A-shares’ trading is restricted
to domestic investors. B-shares can only be traded by foreign investors until February 2001. Offshore
stocks listed and traded in the Hong Kong Stock Exchange (SEHK) but are issued by companies that
operate and have headquarters in mainland China are H-shares.
6
The HSCI industry index is to classify the 200 constituent stocks into nine broad
industrial groups, namely oil and resources, industrial goods, consumer goods,
services, utilities, financials, properties and construction, information technology and
conglomerates. The assignment of stocks to an industry group depends on the
definition that can fit most closely to the description their major business.
2.2.
The Data
The two-year sample period is considered reasonably representative due to the
intraday data we used. Furthermore, the sample period from 2003 to 2004 is selected
for the consideration of the impact of business cycle on the behavior of investors.
After the outbreak of the Severe Acute Respiratory Syndrome (SARS) in March and
April, 2003, the Hang Seng Blue-Chip Index (constituting 33 stocks with largest
capitalization) dropped below 9,000 index points. By the end of 2003, it surged to
12,575.9, near a two-and-a-half year high. Afterwards, it rose steadily from below
12,000 in April of 2004 to 14,230.14 towards the end December of 2004. Adopting
the period of 2003 to 2004 therefore covers a clear business cycle from trough to
recovery.
Table 1 depicts the composition of the HSCI and the total trading volumes in each of
the eight quarters in the sample period. It can be clearly seen that the total number of
trades for HSCI constituents in the first quarter of 2004 is more than double of that in
the first quarter of the previous year. While the trading volume in the constituents of
HSHKCI has not much change, constituents of HSMLCI tripled their trading volume
in the first quarter of 2004, compared with the same period of previous year. This
increase may stem from a rush of initial price offerings (IPOs) by mainland
companies. At industry level, property and construction stocks have been traded
7
actively along the recovery period of the property market, doubling its trading volume
in the sample period. The trading volume of oil and resources industry stocks surge to
more than triple at the end of the sample period.
There are totally 523 trading days in our two-year sample. We obtain the bid and ask
records as well as the trade records from the Hong Kong Stock Exchange (SEHK) for
the period. The bid and ask record is a collection of data files containing intra-day bid
and ask information recorded by the Exchange for both the Main Board and growth
enterprise market (GEM) stocks at 30 second intervals. The lack of price information
within the 30 second interval creates certain limitation in our study. The trade record
is a collection of all trades in securities listed on both the Main Board and the GEM.
Upon selecting the sample stocks, we delete all the trades that are non-automatched5 ,
and are not executed in Hong Kong dollar to avoid the inconsistency and errors. As
each bid and ask record is provided at 30-second intervals, each trade will fall within
the 30-second intervals. Within the interval, we use the bid and ask quotes with its
timing nearer to the trade to classify the trade direction (that is, buy or sell direction).
Usually in a market-making system where the monopolistic market maker who can
trade within posted spreads, the Lee and Ready’s (1991) method will be applied. In
other words, if a trade price is larger (smaller) than the midpoint of the corresponding
bid-ask spread, that trade is defined as a buy (sell). When a trade is executed at a price
equivalent to the midpoint of corresponding bid-ask spread, that trade will be defined
by the “tick test.” That is, a trade settled at a price higher (lower) than its previous
5
The definition of an automatched trade is a trade completed through the automatic order matching and
execution system (AMS) by automatic matching of buy and sell orders submitted by Exchange
Participant(s). See the explanation from the Hong Kong Stock Exchange for detailed information of
other trade types.
8
trade price is defined as a buy (sell). If a trade is dealt with at the same price as the
previous one, it is compared to the next most recent trade price, and the procedure is
continued until the trade direction is classified. However, since such a market maker
is absent in an order-driven market, trade direction becomes apparent without
applying Lee and Ready’s method.
2.3.
Methodology
2.3.1.
Modified LSV Model
Most empirical studies apply the approach proposed by Lakonishok et al. (1992) to
reveal herd behavior among institutional investors, especially fund managers.
Formally, the LSV measurement of herding of stock i in period t is
H i ,t =
⎡B ⎤
⎡B ⎤
B
− E ⎢ i , t ⎥ − E i , t − E ⎢ i ,t ⎥
N i ,t
N i ,t
⎣⎢ N i ,t ⎦⎥
⎣⎢ N i ,t ⎦⎥
Bi ,t
(1)
where Bi ,t ( Si ,t ) is the number of net buyers (sellers), who are defined as fund
managers that increase (decrease) their holding in stock i in period t, and
⎡B ⎤
N i ,t = Bi ,t + Si ,t is the total number of traders in the stock-period.6 E ⎢ i ,t ⎥ is the
⎢⎣ N i ,t ⎥⎦
adjustment factor which represents the expected proportion of number of managers
buying in that period relative to the total number of active managers. It differs from
period to period but not from stock to stock. Bi ,t follows a binomial distribution with
⎡B ⎤
⎡B ⎤
B
E ⎢ i ,t ⎥ of success. Under the null hypothesis of no herding, E i ,t − E ⎢ i ,t ⎥ is
N i ,t
⎢⎣ N i ,t ⎥⎦
⎢⎣ N i ,t ⎥⎦
the adjustment factor under the assumption that Bi ,t follows a binomial distribution.
6
A stock-quarter means a given stock in a given quarter. Hence, the number of “stock-day”, to be used
later in the paper, implies the number of stocks times the number of days considered in our sample.
9
Given the number of participants in a given stock-period, N i ,t , and the probability of
net buyers in that period, pt , the adjustment factor in equation (1) can be calculated
as:
Ni ,t
∑
Bi ,t = 0
Bi ,t
Bi ,t + Si ,t
− pt pt i ,t (1 − pt )
B
Ni ,t − Bi ,t
(2)
which means that the expected value is the sum of all the possible proportion of net
buyers given Bi ,t (where 0 ≤ Bi ,t ≤ N i ,t ), multiplied by its probability. The herding
measure, H i ,t , is then the simple average of the measure over all stocks in the periods.
The larger the value of H i ,t , the higher is the level of herding.
The LSV model investigates herd behavior among fund managers. If a manager
increases the number of stock i within the period t, s/he is defined as a net buyer. On
the contrary, if a manager decreases the number of stock i within the period t, s/he is
defined as a net seller. Bi ,t and Si ,t in equation (1) are defined as the total number
of net buyers and net sellers, respectively. In other words, fund managers are said to
herd if some of them tend to trade a given stock in the same direction more often than
would be expected under the assumption of random and independent trading. Some
former research such as Choe et al. (1999) modifies the definition of the above
variables as the number of buys and number of sells (rather than number of buyers
and sellers) for a particular stock within a particular period. In fact, both definitions
are identical under the assumption that each trade is done by an individual investor.
However, we propose to relax this assumption in our study. While it is doubtless that
our pool of data includes millions of small investors and a few large institutional
investors and we have no information about who has increased his or her shares of a
10
particular stock within that specific period, we adopt the second definition for a
different rationale as explained below.
In our model, we investigate the behavior of “sheeple”7 without regarding to their net
change (which is nevertheless unavailable information) over stock-periods. It is
possible for a market participant, to buy one thousand shares of a stock ten times but
sell twenty thousand shares in one time during a given period. In LSV model, this
market participant will be defined as a net seller because s/he decreases the net
holding of the stock in that period. However, in our study, the number of buys in the
stock-period is larger than the number of sells in that stock-period. The LSV model
describes that herding does not exist when the whole market is considered because
there is always a sale to cancel a purchase. We instead conjecture that since financial
abilities differ from person to person as well as from time to time, an inclination
towards one side of trading is already evidence of herding; and there is no need to
identify how many traders are involved.
It should be noted that the methods due to Christie and Huang (1995) and Chang et al.
(2000) are then next widely adopted models after the LSV models. The former uses
cross-sectional standard deviation (CSSD) of returns while the latter uses
cross-sectional absolute deviation of returns. Both are constructed under the belief
that individual stock returns will diverge from the average market return during
periods of large market movements in the absence of herding because the sensitivity
of each stock to the overall market return is expected to be different. However, if herd
behavior exists, individual stock returns will not deviate too much from the market
average (see also Gleason, Mathur and Peterson, 2004). These two methods are
7
Sheeple, often used as a synonym of herd, is created by combining the words “sheep” and “people.”
11
nevertheless prone to some criticisms. For instance, Bikhchandani and Sharma (2001)
mention that failure from showing the existence of herding by the CSSD method does
not imply its absence because the method functions for only particular forms of
herding. We therefore do not consider this method.
2.3.2.
“Spurious Herding” versus “Intentional Herding”
In financial markets, the number of times that a stock has been bought is significantly
larger than that has been sold if the stock price has risen, and thence herding, may be
a consequence of two factors. First, the increase in stock price either reflects the
fundamental price or otherwise. Second, investors are either informed or uninformed.
Both informed and uninformed investors may buy the stock if the increase in stock
price reflects a fundamental price. Uninformed investors may still buy the stock if the
increase in stock price does not reflect the fundamental price. Informed investors
would only buy for liquidity purpose. In this regard, the possibility of herding among
uninformed traders is expected to be larger than that among informed traders unless
the price is fundamental.
The issue is how we can extract informed from uninformed traders. We adopt the
method of Easley et al. (1996). For each stock in the HSCI during a particular period,
we estimate the probability of information-based trading. Brockman and Chung (2000)
apply the same model in the SEHK and propose that “de facto market-makers on the
SEHK are likely to provide liquidity in much the same fashion as ‘scalpers’ on
floor-based futures exchanges.” 8 The original model used to obtain maximum
likelihood estimates for a given day is as follow:
8
Brockman and Chung (2000). p. 128.
12
L(( B, S ) α , δ , ε b , ε s , µ ) = (1 − α )e −εb
+α (1 − δ )e
ε bB
B!
− ( µ +ε b )
e−ε s
ε sS
+ αδ e −ε b
ε bB
B!
B!
S
S
( µ + ε b ) −ε ε s
e
S!
S!
e − ( µ +ε s )
(µ + ε s )S
S!
(3)
where α is the probability of a private information event, δ is the probability of
bad news given the occurrence of a private information event, ε b is the order arrival
rate of uninformed traders submit buy orders, ε s is the order arrival rate of
uninformed traders submit sell orders and µ is the order arrival rate of informed
traders. With the data set D = ( Bt , St )Tt =1 over T days, the likelihood function is the
product of T daily likelihoods under the assumption of independence of information
events across days,9
T
L( D α , δ , ε b , ε s , µ ) = ∏ L (α , δ , ε b , ε s , µ Bt , St )
(4)
t =1
Upon obtaining the parameter vector ( α , µ , δ , ε b and ε s ) by maximizing the
likelihood function, the probability based on estimated parameters in a tree diagram of
the trading process is calculated as
10
PIN =
αµ
αµ + ε b + ε s
3.
Empirical Results
3.1.
Overall Levels of Herding
(5)
We form equally weighted portfolios according to the list of constituents for each
index and take average across each portfolio. Table 2 exhibits the overall levels of
9
See Easley et al. (1993) for a detailed explanation of the test of independence of information events.
See Easley et al. (1996) for more details.
10
13
herding measures of the 200 constituents of HSCI in the two-year sample period. The
number of stock-day is depicted in the parentheses. The herd measures are interpreted
as follows. The 11.85% for HSCI constituents as a whole in 2003 means that there are
11.85% more trades in one direction than would be expected under the assumption of
random and independent trades.
Over the 523 trading days, there are 97,242 stock-day herd measurements, in which
96,381 are positive, and the remaining are negative. Negative herd measurement
arises when few numbers of trades in a stock-day generates less variation in the
distribution of buy and sell trades than that is expected under the binomial distribution
assumption. These negative herd measurements indicate no apparent herding behavior.
A hurdle of five trades occurring in a stock-day is applied to eliminate a high
sensitivity of the herd measurement to few trades and to qualify the concept of herd
more reasonably.11 This rationale stems from the reality that only few trades in the
same direction do not reasonably represent a herd.
The herding measures presented in Table 2 can be considered high relative to those of
Lakonishok et al. (1992) and Wermers (1999). Notice however that they look at the
measures over a quarter, which are different from our time horizon. When our herding
results in daily measure are compared to Choe et al. (1999), our findings are
obviously smaller. During their sample period, most of their herding measures in the
Korean market are larger than 20%, compared to around 10% of our sample results in
the overall level.
11
Wermers (1999) proposes the hurdle of five funds trading in a given stock-quarter and finds in his
study that the hurdle of one funds trading in a given stock-quarter generates no significant difference in
results.
14
In general, herding is stronger in 2003 than in 2004. A decrease in the measures
accompanied with an increase in trading volume suggests that herding is negatively
correlated with the business cycle. This phenomenon also suggests a real upward
trend of investors’ confidence in a recovery of the Hong Kong economy, in which the
active financial and property sectors play a dominated role. Furthermore, herding
among stocks in the Hong Kong Composite Index (HSHKCI) is slightly stronger than
that in the Mainland Composite Index (HSMLCI). Within the HSHKCI index, the
herding measures of constituents in SmallCap Index are the largest, while those of
constituents in LargeCap Index are the smallest, and those in MidCap Index in
between. On average, herding among SmallCap stocks are five percent more than
herding among LargeCap stocks. This finding is consistent with most theories that a
higher herding exists among small stocks and/or high growth stocks. It is also worth
noting that the HSMLCI constituents, which derive at least 50% of their sales revenue
from mainland China, generally have much larger market capitalizations (that is,
equivalent to Large Cap), and hence less herding.
At industry level, there is more herding in financial and property and construction
industry stocks, especially in 2003. The herding differences between these two
portfolios and the others shrink towards the end of 2004. In other words, it is save to
conclude that herding in stocks from these two back-bone industries are more
sensitive to movement along a business cycle. This phenomenon reflects the
hypothesis that the investors’ sentiments are highly reliant on the dominant industries.
Their uncertainties about the profit and cash flows of the dominant industries become
higher when the market performances become poorer. In order to play save, they will
follow other investors in determining the trading decisions.
15
3.2.
Herding by Past Performance
In this section, the sample stocks are divided according to past performance indicators,
namely past return and past earnings per share (EPS). These two indicators reflect
different grounds on which investors make investment decisions. Trading following
past return suggests technical analysis, while trading on past earnings per share
implies fundamental analysis.
We study herding and past performance by firstly dividing the 200 constituents into
five past return quintiles in ascending order, and calculating the average stock-day
herding measures every month. Each quintile comprises 40 stocks and is rebalanced
every month. As revealed by the studies of Lakonishok et al. (1992), Choe et al. (1999)
and Voronkova and Bohl (2005), we fail to obtain strong evidence to support the
hypothesis that herding is more prevalent in stocks with high or low past return.
Results shown in Table 3 suggest that herding apparently does not depend on past
returns. Contradictory to the hypothesis, herding in some quarters is even the most
prevalent in the medium return quintile.
On the contrary, when we use earnings per share (EPS), the herding measures as
presented in Table 4 decrease with an increase in EPS quintile almost monotonically.
The highest herding measures appear in the smallest EPS quintile throughout the
sample period, while the smallest herding measures appear in the largest EPS quintile.
The insight is interesting. Investors under public information that stocks become less
attractive may act simultaneously to reduce their holdings; that is, they herd more on
stocks with poor performances. Given this, it is safe to conclude that they trade more
likely on fundamental level than on technical level. In the next section, we can see
that “spurious herding” echoes the finding here.
16
3.3.
Herding by Market Capitalization
Similar to the comparison between herding measures and past performance, stocks are
again segregated into five quintiles, ranked in ascending order and rebalanced every
month. Table 5 presents the results. Panels A and B show the monthly average in 2003
and 2004 respectively, while Panel C depicts quarterly average in the two-year period.
It is easy to see that there is a monotonic reverse relationship between market
capitalization and herding measures. Herding in the smallest quintile amounts to
almost twice as that in the largest quintile. This result is consistent with previous
empirical findings in subsection 3.1 that investors will herd on stocks with smaller
market capitalization because there is less public information. Interestingly, we can
also relate this phenomenon to literatures in market microstructure. For instance,
Easley et al. (1996) find that the probability of information-based trading is lower for
high volume stocks. It is common that stocks with high trading volumes are also
having high market capitalization. In this regard, investors herd less in stocks with
high market capitalization but more in stocks with a high probability of
information-based trading. In other words, investors herd when they have equally
scant information about a stock with low market capitalization.
4.
Herding and the Probability of Information-Based Trading
In empirical estimation, we apply the factorization of the joint likelihood function
recommended by Easley, Hvidkjaer and O’Hara (2005) to facilitate numerical
maximization in SAS nonlinear programming procedure
17
T
L(( Bt , St )Tt =1 α , δ , µ , ε b , ε s ) = ∑ [ −ε b − ε s + M t (ln xb + ln xs ) + Bt ln( µ + ε b ) + St ln( µ + ε s ) ]
t =1
T
+ ∑ ln ⎡⎣α (1 − δ ) e − µ xsSt − M t xb− M t + αδ e − µ xbBt − M t xs− M t + (1 − α ) xsSt − M t xbBt − M t ⎤⎦
t =1
(6)
where
M t = (min( Bt , St ) + max( Bt , St ))
xb =
xs =
εb
µ + εb
εs
µ + εs
Since the maximum likelihood estimates are sensitive to the initial values of numeric
procedure, we use Newton-Raphson method with the line search algorithm and adopt
the algorithm proposed by Yan and Zhang (2006) to avoid boundary solutions. They
construct 125 sets of initial values by assigning each value of the three variables, α i ,
δ j and γ k , from one of the five fractions (0.1, 0.3, 0.5, 0.7, 0.9). The 125 initial
value sets with the data of daily buys and sells of the stock can be obtained from
B − ε b0
α = α i , δ = δ j , ε = γ k ⋅ B, µ = 0
, ε s0 = S − α 0 ⋅ δ 0 ⋅ µ 0
0
α (1 − δ )
0
0
0
b
0
(7)
After eliminating the initial value sets with negative values of ε s0 , we run the
maximization procedure and choose the set of parameters which generates the highest
value of the objective function among the non-boundary solutions.12
12
See Yan and Zhang (2006) for a more detailed explanation of the estimation algorithm.
18
Following the requirement of a minimum of 60 trading days to generate reasonably
precise estimation of the parameters proposed by Easley et al. (1993), we calculate the
PIN for each stock on a quarterly basis using equation (6) with initial value setting in
equation (7). Furthermore, a hurdle of at least 50 trading days is applied to each
quarter. A quarterly basis ensures estimated parameters sufficiently robust, as well as
enables direct comparisons of our findings with most other research that adopts
quarterly basis. There are totally 1,532 available sets of estimated parameters after
deleting those that would generate boundary solutions and those without sufficient
trading days. Table 6 reports the mean, median and standard deviations of parameter
estimates by quarter in the sample period.
It should be noted that our estimated parameters are bounded with large standard
deviations when compared with the summary statistics of Easley et al. (1996). This
however is due to a remarkably wide variation of stock trading frequencies rather than
imprecise estimation of parameters. To see this, we group the constituent stocks into
five volume quintiles in ascending order in each quarter and find that the magnitude
of PINs decreases as the trading volume increases. The F-statistics in one-way
ANOVA for equality in the means across the five quintiles are significant even at the
1% level. More importantly, the standard deviation in each quintile is considerably
smaller. In other words, our results are consistent with the findings of Easley et al.
(1996) when the trading volumes are considered (lengthy results have been omitted
and can be provided upon request).
Previous empirical studies in financial market microstructure apply the PINs to study
the effect on spread. Our purpose of applying PINs is fundamentally different from
theirs. Our estimated parameters are much smaller than those in Brockman and Chung
19
(2000). This discrepancy may stem from different sample stocks in different periods.
They use over 500 companies and cover about one year sample period. In our case,
the frequently traded 200 constituent stocks have already occupied over 90% market
capitalizations in the SEHK, and should not lose much robustness by not including the
rest. In fact, low estimated PINs are associated with high trading volumes.
Since people with the intention to copy the behavior of other investors are mostly less
informed and are therefore less likely to involve into information-based trading, by
ranking the estimated PINs, “spurious herding” will simultaneously be distinguished
from “intentional herding”. In other words, we assume that the general investors will
take the opportunity to make money under private information. On quarterly basis, we
rank all the stocks in HSCI by their probabilities of information-based trading from
the smallest to the largest and compute the corresponding measurements of herding.
Table 7 displays the results. In all the eight quarters, the herding measures reveal an
upward trend with highly significant t-statistics. The relationship is almost monotonic
beginning from less than 10% in the smallest PIN quintile to larger than 15% in the
largest PIN quintile. Given that previous research finds that stocks with high trading
volume have low PINs, our result is in line with the hypothesis that investors herd less
(more) in the frequently (infrequently) traded stocks. In other words, by linking the
LSV model to the Easley et al. (1996) probability of information-based trading, our
findings suggest that a stock market is efficient even if there is herding. By
empirically separating herding into “spurious herding” from “intentional herding”, we
find that investors herd because they are equally informed (or uninformed), and they
make decision for the purpose of investing rather than simply doing what others do.
20
This is also agreeable with the conclusion that investors make their decision based on
fundamental analysis as discussed in Section 3.2.
The above finding can also be explained by the cascades model proposed by Avery
and Zemsky (1998). In this model, investors face both public information relevant to
everyone, and private but imperfect information about the results of their actions.
Herding may arise in the situation with a high probability when private information of
the appropriate course of action of an investor is influenced by and incorporated with
observable actions of other investors. The cascades model also proposes that such
behavior is considered rather fragile and idiosyncratic. Since infrequently traded
stocks are those with less public information revealed, they are also likely to be
herded.
5.
Conclusion
This paper examines herding behavior of general investors in a transparent,
order-driven market by applying intraday data. We modify the definition of herding
measure proposed by Lakonishok et al. (1992) to represent the number of trades in
one (buy and sell) direction on a daily basis. We find that herding is more pronounced
in the trough of an economic cycle. We also observe different patterns in herding
among geographical and industrial indexes. In geographical level, herding is stronger
in stocks listed by local companies and weaker in stocks listed by companies from
Mainland China. In industrial level, herding is consistently stronger in stocks in the
determinant industries such as the financial, and property and construction.
21
We further investigate herd behavior by past performance and market capitalization.
We propose that investors relies more on fundamental analysis than technical analysis
because herding is more apparent when using past earnings per share. The findings
with market capitalization are similar to previous literature in that investors tend to
herd more in stocks with smaller market capitalization. In our attempt to distinguish
“spurious herding” from “intentional herding”, we see that the herding measures are
positively correlated with the probabilities of information-based trading.
We contribute by firstly proposing a modified definition of herding measure, secondly
suggesting past EPS is a better assessment of herding than past returns, and lastly
separating spurious herding from intentional herding by finding the probability of
informed trading, and hence verifying that the Hong Kong stock market is after all
efficient and mature in terms of herding.
22
References
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from the Stock Exchange of Hong Kong. Journal of Finance 56, 767-788.
Avery, C., Zemsky, P., 1998. Multidimensional uncertainty and herd behavior in
financial markets. American Economic Review 88, 724-748.
Bikhchandani, S., Sharma, S., 2000. Herd behavior in financial markets: A review.
IMF working paper WP/00/48.
Bowe, M., Domuta, D., 2004. Investor herding during financial crisis: A clinical study
of the Jakarta Stock Exchange. Pacific-Basin Finance Journal 12, 387-418.
Brockman, P., Chung, D.Y., 2000. Informed and uninformed trading in an electronic,
order-driven environment. The financial Review 35, 125-146.
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Mass.
23
Scharfstein, D.S., Stein, J.C., 1990. Herd behavior and investment. American
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Wermers, R., 1999. Mutual fund herding and the impact on stock prices. Journal of
Finance 54, 581-622.
Wylie, S., 2005. Fund manager herding: A test of the accuracy of empirical results
using U.K. data. Journal of Business 78, 381-403.
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PIN. Working paper, University of Pennsylvania and Nanyang Technological
University.
24
Table 1 Composition of Hang Seng Composite Index (HSCI) Constituent Stocks and Trading Volumes in the Sample Period
Indexes
Number of
stocks
2003
Number of Trades
2004
2003
Overall
Q1
Q2
2004
Q3
Q4
Overall
Q1
Q2
Q3
Q4
Hang Seng Composite Index
200
200
15,095,589 2,496,598 3,314,537 4,605,457 4,678,997 18,096,365 5,946,135 4,232,438 3,720,135 4,197,657
Hang Seng Hong Kong Composite Index
115
109
7,796,227 1,381,558 1,780,496 2,364,032 2,270,141 7,938,917 2,526,511 1,798,225 1,640,411 1,973,770
Hang Seng HK LargeCap Index
16
16
3,606,112 686,528
868,165 1,020,451 1,030,968 3,307,860 1,088,758 831,436
665,193
722,473
Hang Seng HK MidCap Index
35
35
2,343,433 410,553
511,908
672,578
748,394 2,928,132 899,700
673,926
671,458
683,048
Hang Seng HK mallCap Index
64
58
1,846,682 284,477
400,423
671,003
490,779 1,702,925 538,053
292,863
303,760
568,249
86
92
7,299,362 1,115,040 1,534,041 2,241,425 2,408,856 10,157,448 3,419,624 2,434,213 2,079,724 2,223,887
28
27
2,837,648 453,214
635,069
838,127
911,238 3,020,521 937,789
680,680
663,657
738,395
Oil & Resources
9
11
1,224,417 154,830
224,796
393,532
451,259 2,000,586 768,764
452,751
377,357
401,714
Industrial Goods
21
19
1,617,570 224,534
317,377
505,220
570,439 1,881,626 536,121
508,606
436,098
400,801
Consumer Goods
37
41
2,244,293 404,134
531,559
655,770
652,830 2,175,256 648,389
513,865
505,660
507,342
Services
42
41
3,465,773 575,559
773,702 1,091,228 1,025,284 3,347,054 1,135,186 778,000
692,892
740,976
Utilities
8
10
155,776
174,752
217,907
234,016 1,082,778 287,356
299,409
249,131
246,882
Financials
21
22
1,911,867 310,290
370,846
546,373
684,358 3,078,899 1,167,012 707,364
577,963
626,560
Properties & Construction
33
29
1,553,773 276,967
365,302
510,626
400,878 2,162,766 640,359
483,622
433,326
605,459
Information Technology
14
11
94,034
160,418
212,068
181,020
171,308
116,206
111,748
121,672
Conglomerates
15
17
1,647,905 300,474
395,785
472,733
478,913 1,728,851 549,107
341,644
319,818
518,282
Hang Seng Mainland Composite Index
Hang Seng China-Affiliated Corporations Index
Hang Seng Composite Industry Indexes
782,451
647,540
520,934
25
Table 2 Mean Herding Measures for Constituent Stocks (in percentages)
The herding measures are in percentages. The number of stock-days is presented in parentheses.
2003
Indexes
Hang Seng Composite Index
Overall
2004
Quarter 1 Quarter 2 Quarter 3 Quarter 4 Overall Quarter 1 Quarter 2 Quarter 3 Quarter 4
11.85
13.17
12.27
10.74
11.29
11.39
10.42
11.00
12.00
11.85
(48,573)
(11,916)
(11,797)
(12,559)
(12,301)
(48,669)
(12,342)
(11,752)
(12,460)
(12,115)
12.79
14.02
12.92
11.45
12.21
12.07
11.38
11.86
12.47
12.40
(27,714)
(6,783)
(6,755)
(7,125)
(7,051)
(26,522)
(6,711)
(6,271)
(6,755)
(6,725)
8.49
9.20
8.46
8.30
8.02
8.40
8.02
7.73
8.67
9.09
(3,940)
(952)
(958)
(1,023)
(1,007)
(3,976)
(991)
(955)
(1,038)
(1,008)
10.88
12.77
11.66
10.02
9.19
10.58
10.04
10.41
11.05
10.85
(8,633)
(2,103)
(2,091)
(2,238)
(2,201)
(8,603)
(2,162)
(2,057)
(2,211)
(2,173)
14.91
15.91
14.72
13.08
14.99
13.98
13.12
13.88
14.39
14.29
(15,141)
(3,728)
(3,706)
(3,864)
(3,843)
(13,943)
(3,558)
(3,319)
(3,522)
(3,544)
11.03
12.06
11.64
10.10
10.57
10.60
9.26
10.01
11.38
11.24
(20,859)
(5,133)
(5,042)
(5,434)
(5,260)
(22,250)
(5,540)
(5,421)
(5,707)
(5,582)
10.62
12.00
11.30
9.76
9.27
10.02
8.34
9.34
11.41
10.88
(6,792)
(1,688)
(1,666)
(1,751)
(1,687)
(6,638)
(1,627)
(1,603)
(1,713)
(1,695)
Hang Seng Hong Kong Composite Index
Hang Seng HK LargeCap Index
Hang Seng HK MidCap Index
Hang Seng HK SmallCap Index
Hang Seng Mainland Composite Index
Hang Seng China-Affiliated Corporations
Index
Continue…
26
(Table 2 Continued)
2003
Indexes
Overall
2004
Quarter 1 Quarter 2 Quarter 3 Quarter 4 Overall Quarter 1 Quarter 2 Quarter 3 Quarter 4
Hang Seng Composite Industry Indexes
Oil & Resources
Industrial Goods
Consumer Goods
Services
Utilities
Financials
Properties & Construction
Information Technology
Conglomerates
9.79
12.02
11.03
8.21
8.08
9.02
7.98
8.28
10.03
9.71
(2,229)
(549)
(537)
(576)
(567)
(2,715)
(671)
(655)
(700)
(689)
11.10
12.15
11.68
9.89
10.82
11.16
10.14
10.59
11.29
12.57
(5,071)
(1,238)
(1,201)
(1,324)
(1,308)
(4,649)
(1,170)
(1,109)
(1,192)
(1,178)
12.06
12.37
12.32
11.54
11.97
12.90
12.13
12.54
12.76
12.59
(8,898)
(2,189)
(2,173)
(2,309)
(2,227)
(9,494)
(2,470)
(2,331)
(2,365)
(2,328)
11.45
12.30
11.39
10.47
11.51
11.62
10.32
11.32
12.2
12.63
(10,438)
(2,525)
(2,538)
(2,860)
(2,695)
(10,068)
(2,532)
(2,409)
(2,586)
(2,541)
10.21
11.50
10.15
9.88
9.34
9.80
9.06
8.76
10.72
10.54
(1,981)
(486)
(479)
(512)
(504)
(2,447)
(614)
(591)
(635)
(607)
13.79
16.4
13.99
12.81
12.01
12.35
11.89
11.16
13.68
12.58
(5,007)
(1,249)
(1,231)
(1,271)
(1,256)
(5,419)
(1,355)
(1,293)
(1,389)
(1,382)
13.7
15.32
14.80
12.27
12.51
10.69
9.73
10.60
11.44
10.93
(7,560)
(1,873)
(1,850)
(1,973)
(1,864)
(7,105)
(1,778)
(1,711)
(1,829)
(1,787)
12.36
13.84
12.65
10.30
12.68
10.86
9.97
10.68
11.74
11.05
(3,433)
(841)
(829)
(890)
(873)
(2,683)
(661)
(648)
(686)
(688)
9.46
10.94
9.85
8.56
8.56
10.29
8.78
10.70
11.39
10.28
(3,708)
(905)
(899)
(960)
(944)
(4,206)
(1,050)
(1,008)
(1,079)
(1,069)
27
Table 3 Herding Measures by Past Return
The herding measure for a particular stock-day, in %, is taken monthly average within a certain past return quintile, which is rebalanced every month. The number of
stock-days is presented in parentheses, and the t-statistics for the means are presented below the number of stock-days. Panel C summarizes the results of Panel A and
Panel B by taking the quarterly average of the sample period. Since the sample size for each index is large enough, all the t-statistics are highly significant.
Panel A: Herding Measures in 2003
Past Return
2003
Quintile
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
1
15.11
13.42
12.32
12.56
14.71
12.09
13.21
12.97
10.64
11.37
13.00
13.79
(smallest)
(804)
(729)
(810)
(777)
(774)
(763)
(830)
(771)
(813)
(877)
(778)
(819)
53.19
47.86
52.76
88.26
57.03
48.13
75.45
94.91
72.59
64.39
52.87
91.98
13.02
13.76
12.74
13.72
11.79
12.14
12.87
11.73
8.54
11.85
12.44
12.74
(803)
(752)
(814)
(778)
(798)
(796)
(849)
(837)
(836)
(836)
(785)
(825)
84.32
85.20
77.14
65.42
74.76
56.84
66.18
57.65
93.57
76.61
66.71
78.62
13.51
15.22
12.64
12.16
11.52
11.18
9.72
11.78
10.03
10.02
11.21
12.31
(825)
(737)
(807)
(779)
(797)
(780)
(879)
(820)
(777)
(873)
(756)
(771)
84.37
81.86
74.41
56.06
56.69
77.78
75.03
54.20
80.69
74.43
54.35
57.54
12.45
12.53
15.19
13.57
11.16
11.60
9.92
9.45
9.52
9.25
10.65
11.66
(837)
(758)
(809)
(757)
(784)
(800)
(878)
(834)
(829)
(879)
(792)
(827)
84.05
86.94
70.77
63.99
86.87
81.61
81.19
88.44
55.81
82.60
65.22
64.76
5
10.71
12.60
12.46
13.03
10.91
10.83
11.51
10.01
9.81
9.96
10.36
9.25
(largest)
(826)
(745)
(800)
(765)
(798)
(797)
(868)
(837)
(838)
(849)
(786)
(839)
105.84
83.44
71.34
84.58
90.39
70.68
45.19
90.89
65.19
69.24
72.34
43.19
2
3
4
Continue…
28
(Table 3 Continued)
Panel B: Herding Measures in 2004
Past Return
2004
Quintile
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
1
9.59
10.96
9.35
9.14
12.53
10.94
13.73
12.24
12.31
10.12
12.91
12.76
(smallest)
(755)
(795)
(917)
(750)
(767)
(825)
(800)
(863)
(823)
(754)
(833)
(868)
47.29
83.65
79.72
60.11
66.32
56.32
70.84
68.08
81.88
65.80
101.77
87.50
10.48
10.37
10.87
9.78
10.59
11.40
12.12
12.39
12.40
12.04
12.90
13.26
(751)
(793)
(904)
(754)
(751)
(822)
(824)
(804)
(838)
(759)
(823)
(867)
27.40
28.16
30.07
27.46
27.40
28.67
28.71
28.35
28.95
27.55
28.69
29.44
10.64
10.81
11.86
10.49
11.14
11.93
13.79
14.07
11.64
12.15
12.21
12.59
(754)
(795)
(914)
(757)
(784)
(813)
(765)
(843)
(774)
(749)
(874)
(845)
27.46
28.20
30.23
27.51
28.00
28.51
27.66
29.03
27.82
27.37
29.56
29.07
10.16
10.83
10.67
11.84
10.87
10.87
11.72
11.73
10.70
10.96
9.77
12.09
(755)
(797)
(917)
(742)
(781)
(810)
(824)
(878)
(831)
(697)
(877)
(807)
27.48
28.23
30.28
27.24
27.95
28.46
28.71
29.63
28.83
26.40
29.61
28.41
5
8.70
9.07
11.44
12.43
10.16
10.62
10.70
10.65
9.76
13.14
10.46
10.90
(largest)
(774)
(815)
(906)
(772)
(780)
(844)
(848)
(892)
(853)
(762)
(896)
(896)
27.82
28.55
30.10
27.78
27.93
29.05
29.12
29.87
29.21
27.60
29.93
29.93
2
3
4
Continue…
29
(Table 3 Continued)
Panel C: Herding Measures in Quarters from 2003 to 2004
Past Return
2003
2004
Quintile
Q1
Q2
Q3
Q4
Q1
Q2
Q3
Q4
1
13.61
13.12
12.27
12.72
9.97
10.87
12.76
11.93
(smallest)
(2,343)
(2,314)
(2,414)
(2,474)
(2,467)
(2,342)
(2,486)
(2,455)
2
13.17
12.55
11.05
12.34
10.58
10.59
12.30
12.73
(2,369)
(2,372)
(2,522)
(2,446)
(2,448)
(2,327)
(2,466)
(2,449)
13.79
11.62
10.51
11.18
11.10
11.19
13.17
12.31
(2,369)
(2,356)
(2,476)
(2,400)
(2,463)
(2,354)
(2,382)
(2,468)
13.39
12.11
9.63
10.52
10.55
11.20
11.38
10.94
(2,404)
(2,341)
(2,541)
(2,498)
(2,469)
(2,333)
(2,533)
(2,381)
5
11.92
11.59
10.45
9.86
9.73
11.07
10.37
11.50
(largest)
(2,371)
(2,360)
(2,543)
(2,474)
(2,495)
(2,396)
(2,593)
(2,554)
3
4
30
Table 4
Herding Measures by Past Earnings per Share (EPS)
The herding measure for a particular stock-day, in %, is taken monthly average within a certain past Earnings per Share (EPS) quintile, which are rebalanced every
month. The number of stock-days is presented in parentheses, and the t-statistics for the means are presented below the number of stock-days. Panel C summarizes
the results of Panel A and Panel B by taking the quarterly average of the sample period. Since the sample size for each index is large enough, all the t-statistics are
highly significant.
Panel A: Herding Measures in 2003
Past EPS
2003
Quintile
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
1
16.17
16.71
16.33
16.42
14.74
13.78
15.06
12.72
12.08
13.17
15.91
15.83
(smallest)
(794)
(725)
(786)
(742)
(769)
(745)
(796)
(767)
(793)
(845)
(757)
(798)
55.66
59.73
53.24
59.05
55.79
51.85
66.33
63.32
64.26
68.81
64.55
65.87
12.89
13.42
13.12
13.64
12.87
12.23
11.39
11.35
10.07
11.31
12.21
12.79
(830)
(756)
(824)
(772)
(795)
(796)
(878)
(825)
(793)
(832)
(753)
(795)
97.39
90.86
86.85
91.28
65.66
62.28
57.93
52.33
94.27
88.66
68.34
75.48
11.89
12.62
13.06
12.04
10.78
11.28
9.63
10.46
9.31
9.74
10.19
10.74
(819)
(750)
(824)
(785)
(798)
(800)
(877)
(839)
(838)
(879)
(796)
(830)
99.87
88.54
85.14
85.94
94.76
74.48
85.84
98.35
80.16
71.89
66.32
60.11
11.95
12.49
12.06
12.63
11.61
10.24
10.86
11.16
9.37
9.84
10.51
10.96
(830)
(750)
(814)
(782)
(800)
(797)
(874)
(839)
(839)
(880)
(798)
(829)
95.46
81.97
93.12
94.40
80.28
75.62
60.56
73.28
68.10
84.67
70.71
67.77
5
12.10
12.37
10.54
10.33
10.28
10.23
10.34
9.80
7.88
8.49
8.83
9.71
(largest)
(739)
(665)
(734)
(738)
(789)
(798)
(879)
(829)
(830)
(878)
(793)
(829)
63.53
69.02
72.34
67.19
74.06
82.78
66.81
81.22
77.25
75.73
72.35
80.09
2
3
4
Continue…
31
(Table 4 Continued)
Panel B: Herding Measures in 2004
Past EPS
2004
Quintile
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
1
10.62
11.21
11.85
12.52
12.91
13.33
14.33
14.72
12.90
14.09
12.49
13.74
(smallest)
(748)
(793)
(900)
(747)
(758)
(807)
(801)
(852)
(793)
(695)
(807)
(803)
53.18
75.53
74.40
66.30
59.88
59.75
75.72
74.68
68.18
68.28
112.56
83.65
10.33
10.63
11.40
12.24
11.66
12.24
12.79
12.39
12.17
12.19
12.97
13.08
(752)
(797)
(908)
(753)
(767)
(804)
(785)
(814)
(804)
(752)
(861)
(848)
59.62
63.60
62.75
58.16
67.29
65.35
80.22
67.85
79.83
77.03
79.87
87.62
9.97
10.28
10.83
9.78
10.52
10.54
12.70
11.71
11.24
11.09
11.25
12.35
(752)
(794)
(898)
(742)
(766)
(830)
(813)
(858)
(832)
(751)
(868)
(872)
66.84
64.15
73.16
65.87
72.13
72.90
78.16
80.81
83.79
82.77
110.14
94.97
9.22
9.79
9.67
9.25
10.38
10.07
10.97
11.61
10.07
10.73
11.16
11.86
(759)
(798)
(916)
(759)
(773)
(818)
(823)
(862)
(837)
(754)
(876)
(870)
71.36
82.59
95.51
64.47
69.82
57.84
76.86
67.22
92.65
76.19
81.58
90.67
5
9.13
9.61
10.46
9.95
9.84
9.65
11.25
10.66
10.49
10.59
10.34
10.71
(largest)
(531)
(558)
(936)
(774)
(799)
(855)
(839)
(894)
(853)
(769)
(891)
(890)
68.81
65.29
68.86
62.59
70.03
67.27
71.22
67.22
61.14
68.36
78.88
75.50
2
3
4
Continue…
32
(Table 4 Continued)
Panel C: Herding Measures in Quarters from 2003 to 2004
Past EPS
2003
2004
Quintile
Q1
Q2
Q3
Q4
Q1
Q2
Q3
Q4
1
16.41
14.98
13.29
14.97
11.23
12.92
13.98
13.44
(smallest)
(2,305)
(2,256)
(2,356)
(2,400)
(2,441)
(2,312)
(2,446)
(2,305)
2
13.14
12.91
10.93
12.10
10.79
12.05
12.45
12.75
(2,410)
(2,363)
(2,496)
(2,380)
(2,457)
(2,324)
(2,403)
(2,461)
12.52
11.37
9.80
10.22
10.36
10.28
11.89
11.56
(2,393)
(2,383)
(2,554)
(2,505)
(2,444)
(2,338)
(2,503)
(2,491)
12.17
11.50
10.46
10.44
9.56
9.90
10.88
11.25
(2,394)
(2,379)
(2,552)
(2,507)
(2,473)
(2,350)
(2,522)
(2,500)
11.67
10.28
9.34
9.01
9.74
9.82
10.80
10.55
(2,138)
(2,325)
(2,538)
(2,500)
(2,025)
(2,428)
(2,586)
(2,550)
3
4
5
(largest)
33
Table 5 Herding Measures by Market Capitalization
The herding measure for a particular stock-day, in %, is taken monthly average within a certain size quintile, which are rebalanced every month. The number of
stock-days is presented in parentheses, and the t-statistics for the means are presented below the number of stock-days. Panel C summarizes the results of Panel A and
Panel B by taking the quarterly average of the sample period. Since the sample size for each index is large enough, all the t-statistics are highly significant.
Panel A: Herding Measures in 2003
Market Cap
2003
Quintile
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
1
15.86
16.19
15.17
16.77
15.62
15.81
15.19
13.93
12.92
14.79
16.91
16.97
Smallest
(794)
(720)
(781)
(714)
(764)
(757)
(811)
(752)
(739)
(797)
(704)
(743)
57.81
61.58
58.84
59.72
55.81
61.92
63.38
52.87
70.21
80.82
73.58
71.79
13.83
15.29
15.80
14.61
12.08
12.27
12.09
12.09
10.46
11.66
13.52
15.03
(818)
(749)
(814)
(775)
(799)
(798)
(870)
(837)
(840)
(880)
(797)
(830)
102.87
89.43
71.81
106.38
84.44
75.43
65.45
96.36
85.63
92.73
98.65
90.78
13.75
13.85
13.50
13.46
12.42
11.03
12.47
11.59
10.49
10.66
11.48
11.70
(819)
(742)
(806)
(780)
(788)
(782)
(867)
(831)
(834)
(878)
(798)
(833)
84.05
84.14
86.99
98.57
91.57
75.89
78.40
73.25
79.43
76.29
63.87
83.30
11.55
12.38
11.82
11.39
11.13
10.56
9.79
9.85
7.92
8.57
9.00
8.85
(836)
(756)
(827)
(790)
(800)
(800)
(877)
(839)
(840)
(879)
(799)
(836)
91.22
95.18
119.05
98.96
79.64
92.24
75.10
106.16
111.48
120.95
94.80
98.06
5
9.81
9.75
8.84
8.96
8.74
8.04
8.13
8.26
7.06
7.42
7.09
7.86
Largest
(807)
(735)
(791)
(777)
(780)
(779)
(857)
(819)
(819)
(858)
(779)
(818)
84.14
93.01
93.17
80.17
93.51
95.20
66.96
101.43
90.99
105.34
83.24
86.33
2
3
4
Continue…
34
(Table 5 Continued)
Panel B: Herding Measures in 2004
Market Cap
2004
Quintile
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
1
12.04
12.96
14.53
14.36
14.41
15.20
16.74
16.19
15.23
15.09
14.56
16.07
Smallest
(743)
(788)
(899)
(740)
(740)
(772)
(756)
(798)
(802)
(728)
(829)
(839)
58.85
77.87
85.24
83.68
78.74
76.30
96.25
80.18
89.14
89.62
100.91
108.83
11.84
11.84
12.15
12.04
13.25
13.51
14.24
15.20
12.95
13.91
13.79
14.15
(755)
(796)
(893)
(748)
(767)
(830)
(819)
(860)
(824)
(738)
(864)
(866)
27.48
28.21
29.88
27.35
27.69
28.81
28.62
29.33
28.71
27.17
29.39
29.43
8.92
9.84
9.85
10.26
9.80
9.46
11.54
11.19
10.24
10.92
10.86
11.63
(755)
(798)
(919)
(758)
(777)
(835)
(833)
(879)
(838)
(755)
(877)
(854)
27.48
28.25
30.32
27.53
27.87
28.90
28.86
29.65
28.95
27.48
29.61
29.22
8.40
8.68
9.08
8.94
9.63
9.52
10.42
10.10
9.80
9.70
10.06
10.48
(758)
(794)
(916)
(751)
(781)
(830)
(826)
(879)
(836)
(760)
(877)
(868)
27.53
28.18
30.27
27.40
27.95
28.81
28.74
29.65
28.91
27.57
29.61
29.46
5
7.85
7.96
7.84
7.46
7.67
7.40
8.91
8.39
8.61
8.90
8.93
9.11
Largest
(702)
(739)
(840)
(702)
(719)
(772)
(766)
(801)
(756)
(683)
(791)
(792)
26.50
27.18
28.98
26.50
26.81
27.78
27.68
28.30
27.50
26.13
28.12
28.14
2
3
4
Continue…
35
(Table 5 Continued)
Panel C: Herding Measures in Quarters from 2003 to 2004
Market Cap
Quintile
1 (smallest)
2
3
4
5 (largest)
2003
2004
Q1
Q2
Q3
Q4
Q1
Q2
Q3
Q4
15.74
16.07
14.01
16.22
13.18
14.66
16.05
15.24
(2,295)
(2,235)
(2,302)
(2,244)
(2,430)
(2,252)
(2,356)
(2,396)
14.97
12.98
11.54
13.40
11.94
12.93
14.13
13.95
(2,381)
(2,372)
(2,547)
(2,507)
(2,444)
(2,345)
(2,503)
(2,468)
13.70
12.30
11.52
11.28
9.54
9.84
10.99
11.13
(2,367)
(2,350)
(2,532)
(2,509)
(2,472)
(2,370)
(2,550)
(2,486)
11.91
11.03
9.19
8.81
8.72
9.36
10.11
10.08
(2,419)
(2,390)
(2,556)
(2,514)
(2,468)
(2,362)
(2,541)
(2,505)
9.47
8.58
7.82
7.46
7.88
7.51
8.64
8.98
(2,333)
(2,336)
(2,495)
(2,455)
(2,281)
(2,193)
(2,323)
(2,266)
36
Table 6 Descriptive Statistics of Estimates of Maximum Likelihood Parameters
by Quarter
This table reports mean, median and standard deviation of estimated parameters. Maximum
likelihood estimation proposed by Easley et al. (1996) was performed for each stock on
quarterly basis. We use Newton-Raphson method with the line search algorithm and adopt the
algorithm proposed by Yan and Zhang (2006) to avoid the boundary solutions. The parameters
are estimated generated from the following likelihood function:
εB
εS
εB
(µ + ε s )S
L (( B, S ) α , δ , ε b , ε s , µ ) = (1 − α )e −ε b e − ε s + αδ e −ε b e − ( µ +ε )
b
s
B!
+α (1 − δ )e − ( µ +ε b )
b
s
B!
B!
( µ + ε b ) S −ε ε sS
e
S!
S!
S!
The probability of information-based trading (PIN) is calculated as PIN =
Parameters
α
2003
αµ
.
αµ + ε b + ε s
2004
Q1
Q2
Q3
Q4
Q1
Q2
Q3
Q4
Mean
0.2807
0.3061
0.3073
0.2863
0.3043
0.3558
0.2939
0.2945
Median
0.2825
0.3065
0.3125
0.2821
0.2956
0.3589
0.3114
0.2878
Std.dev
0.1093
0.1078
0.1046
0.1072
0.1130
0.1065
0.1072
0.0974
Mean
0.3949
0.3775
0.3524
0.3523
0.3757
0.4880
0.3811
0.4008
Median
0.3944
0.3636
0.3359
0.3334
0.3440
0.4931
0.3529
0.3999
Std.dev
0.2064
0.1996
0.1931
0.1883
0.2067
0.1986
0.2032
0.1991
δ
µ
Mean
130.4505 171.0715 213.1017 215.7668 237.7816 157.1424 177.4686 210.3888
Median
97.5250
Std.dev
110.8894 139.5253 175.5854 197.9801 254.7448 159.7589 182.8560 204.5459
Mean
69.8451
96.3371
124.4660 130.7431 152.0219 129.0774 103.4856 119.1082
Median
35.4350
55.0000
74.8900 73.8650
Std.dev
92.7501
120.4203 145.7598 154.0636 176.1264 170.5016 123.3958 135.7335
135.6750 167.6300 162.7800 173.9600 97.1400 113.1500 147.3600
εb
91.8900
59.7300
53.6500
66.0650
εs
Mean
79.1174
252.0976 137.4853 145.2966 169.3946 130.2110 111.7307 131.6501
Median
43.6600
65.1700
Std.dev
96.4937 1985.3542 140.3759 157.1756 188.6738 163.5685 134.2649 142.0276
Mean
0.0499
0.0261
0.0201
0.0194
0.0174
0.0379
0.0384
0.0245
Median
0.0147
0.0104
0.0070
0.0062
0.0049
0.0085
0.0086
0.0071
Std.dev
0.1091
0.0454
0.0457
0.0371
0.0390
0.0711
0.0802
0.0429
93.2800 91.9950 108.1900 64.9300
62.1800
79.4350
PIN
37
Table 7
Herding Measures by Probability of Information-based Trading
(PINs)
LSV herding measures, in %, of the 200 constituents of HSCI in two-year sample period was
presented in the table below. The herding measure for a particular stock-day is taken monthly
average within a certain PIN quintile, which are rebalanced every month. The number of
stock-days is presented in parentheses, and the t-statistics for the means are presented below
the number of stock-days.
PIN
2003
2004
Quintile
Q1
Q2
Q3
Q4
Q1
Q2
Q3
Q4
1
9.745
8.238
6.676
6.752
6.962
6.405
8.431
8.330
(smallest)
(38.00)
(38.00)
(38.00)
(38.00)
(39.00)
(39.00)
(39.00)
(39.00)
11.15
21.01
32.43
28.49
23.92
25.62
19.75
25.30
10.556
11.179
9.187
8.640
8.246
7.965
8.940
9.595
(38.00)
(38.00)
(38.00)
(38.00)
(39.00)
(39.00)
(39.00)
(38.00)
25.55
12.27
12.76
29.16
39.48
40.26
29.89
32.12
12.846
11.423
10.254
11.087
9.820
10.640
10.981
11.144
(38.00)
(37.00)
(38.00)
(38.00)
(39.00)
(39.00)
(39.00)
(39.00)
35.00
36.74
34.72
16.81
18.05
17.80
30.82
35.80
15.123
13.130
11.493
12.522
10.987
13.100
14.364
13.565
(37.00)
(38.00)
(38.00)
(38.00)
(39.00)
(38.00)
(39.00)
(39.00)
42.62
38.31
40.72
27.48
37.86
27.64
26.39
51.78
5
17.123
16.688
15.605
16.915
15.253
16.354
16.606
16.377
(largest)
(37.00)
(38.00)
(37.00)
(38.00)
(39.00)
(39.00)
(37.00)
(37.00)
28.54
22.08
31.15
37.39
34.97
30.92
29.14
28.98
2
3
4
38