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Unformatted text preview: THE JOURNAL OF FINANCE • VOL. LIX, NO. 5 • OCTOBER 2004 Correlated Trading and Location
LEI FENG and MARK S. SEASHOLES∗
ABSTRACT
This paper analyzes the trading behavior of stock market investors. Purchases and
sales are highly correlated when we divide investors geographically. Investors who live
near a firm’s headquarters react in a similar manner to releases of public information.
We are able to make this identification by exploiting a unique feature of individual
brokerage accounts in the People’s Republic of China. The data allow us to pinpoint
an investor’s location at the time he or she places a trade. Our results are consistent
with a simple, rational expectations model of heterogeneously informed investors. OVER THE PAST DECADE, financial economists have become increasingly fascinated
with the trading decisions of investors. Does a welldefined subset of investors
tend to buy or sell the same security en masse? What drives this behavior? Are
investors choosing their investment strategies by observing the investment
decisions of others around them? Are investors driven by some sort of group
psychology? Does the presence of a herd mentality affect asset prices?
Alternatively, investors might simply be reacting to the dissemination of information. If subgroups of investors react similarly, financial economists would
also measure correlated trading behavior. In this alternative view, it is possible
that stock prices and trading patterns are jointly determined as equilibrium
outcomes.1
This paper addresses the above questions by employing a new data set that
is uniquely suited for studying correlated trading. We examine accountlevel
data from the People’s Republic of China (or PRC). In the PRC, brokerage rules
require that an individual place all of his or her trades through the branch
office where he or she opens the account. Individuals are not allowed to open
multiple accounts. Our sample consists of trades from seven branch offices.
Four are located within the same province of the PRC and three are thousands
of kilometers away in another municipality. In addition, our data allow us to
∗ McKinsey & Co. and University of California, Berkeley, respectively. We thank Ken Froot,
Rick Green, Terry Hendershott, Narasimhan Jegadeesh, Terry Odean, Robin Greenwood, Andrei
Shleifer, Jeremy Stein, and an anonymous referee for helpful comments. Also, we are grateful to
seminar participants at the AEA 2003 Meetings, University of Alberta, Arizona State University,
H.E.C Paris, Texas Finance Festival, University of California, Berkeley, and the Utah Winter
Finance Conference. ThuyUyen Dam provided some excellent research support. Any mistakes are
ours alone.
1
Many empirical studies of herding simply attempt to detect correlated trading and do not consider an equilibrium model of trading and stock returns. Some examples in international markets
include Choe, Kho, and Stultz (1999), Kim and Wei (2002a, 2002b), Oehler and Chao (undated),
and Lobao and Serra (undated). 2117 2118 The Journal of Finance track the stock trading behavior of individual investors at a daily frequency.
Existing studies typically use monthly or quarterly data.
This PRC brokerage rule is key to our study. It allows us to identify welldefined groups of individuals who are in the same room at the time they are
trading.2 The layout of a typical PRC brokerage office allows for open conservation between investors. Investors congregate in front of an enormous digital
display that provides a constant update of stock prices (see Figure 1). Hertz
(1998) describes the large amount of social interaction in her ethnographical
study of the Shanghai stock exchange. Thus, we expect ex ante to find significant “withinbranch” trading patterns.
If investors engage in herd behavior due to animal spirits or group psychology, we would expect the trades of two isolated groups to be uncorrelated. The
probability that two isolated groups choose to buy or sell a particular stock on
the same day is almost zero. Surprisingly, the first result of this paper shows
that isolated groups of investors engage in highly correlated trading behavior.
The correlation of net trades (buys minus sells) is positive between two groups
in the same region of the country. The correlation of net trades is negative between two groups in different regions of the country. The correlation of total
trades (buys plus sells) is positive for any two isolated groups—regardless of
location. Thus, there appears to be a lot of evidence of marketwide shocks to
trading and little evidence of branchlevel (grouppsychology) effects.
We then consider the predictions of a rational expectations model with heterogeneously informed investors. The model assumes that investors who live
near a firm’s headquarters have more precise information about future dividends than investors who live far away. The model predicts that the arrival of
public information induces trade as investors at different locations adjust their
demands for a risky asset by different amounts. As a result, realized returns
should be negatively (positively) correlated with the net trades of the “near”
(“far”) investors. We show that trading patterns in our data are consistent with
these predictions. We also show that net trades of “near” investors load positively on the first principal component of aggregate order f low, while the net
trades of “far” investors load negatively on the same factor. Finally, we perform
a number of robustness checks.
This paper contributes to our understanding of trading behavior in three
main areas. First, we document that the trades of individuals are significantly
correlated (contemporaneously), much like the trades of mutual fund managers.
The correlation becomes apparent when we condition on location. Second, we
2
Consider an individual investor who opens an account at the 3 Fuxing Road branch of Huatai
Securities in Beijing. This investor is not allowed to place trades at other branches of Huatai
Securities (even in Beijing). If the investor travels to Guangdong province, he or she must telephone
back to the branch at 3 Fuxing Road in Beijing to place a trade (assuming the investor has phone
privileges). If telephoning is not an option, the investor must wait until he or she is back in Beijing
before physically going to the office and trading. We concentrate on these physically placed trades,
since we know the investor is actually standing in the home branch office when the trade is placed.
We know other investors who use the same branch. Therefore, the brokerage rules, combined with
the high frequency of our data, allow us to identify isolated groups of investors. Correlated Trading and Location 2119 terminals
back office
rooms front
doors chairs for
investors large digital
stock display back office
rooms back office
rooms cashier windows
Figure 1. Layout of a typical branch office. This figure presents a schematic drawing of a
typical brokerage office. Stock prices are shown on a large, electronic board that covers a good
portion of one side of the room. Individual investors can place trades in one of two ways. Some
investors place trades through terminals that are located around the edge of the branch office.
Investors are able to “log in” by simply swiping a magneticstrip card at the terminal and then
entering a password. Investors enter electronic limit orders. A computer blocks any buy order for
which the investor doesn’t have sufficient credit or any sell order when the investor does not own
the shares. Some margin buying is possible. Other investors place trades at a cashier window after
they fill out an order firm. The cashier then enters the buy or sell order into a computer. Again,
the computer blocks nonconforming attempts to trade. show that what has been called “herding” in past studies can be described
as trade between asymmetrically informed investors. We outline a simple, rational expectations model and employ an assumption that investors who live
near a company’s headquarters receive (on average) more precise information
about the company than those who live far away. The relationship between the
net trades of various groups of investors and stock returns is consistent with
predictions of the model. Thus, understanding investors’ prior distributions of 2120 The Journal of Finance future payoffs is an important element in understanding trading behavior. Finally, we measure correlated trading behavior at a much higher frequency than
most other papers. This allows us to rule out some recently proposed theories
of information diffusion.
Brief Review of Related Empirical Work
Before moving on to our actual tests, we brief ly review related empirical
work.3 Early studies of herding in financial markets have a hard time detecting
either (i) correlated trading or (ii) a relationship between correlated trading and
asset returns. Lakonishok, Shleifer, and Vishny (1992) examine the impact of
institutional trading in the United States on stock prices. The authors find
that if money managers of taxexempt funds are equally likely to buy or sell
a stock in a given quarter, 52.7% of the managers tend to buy (sell) during a
quarter while 47.3% do the opposite. This (slight) imbalance of 2.7% could be
potentially destabilizing to stock prices, but the authors find little evidence of
this. The words “potentially destabilizing” relate to the authors’ search for a
causallink from trading behavior to returns. Grinblatt, Titman, and Wermers
(1995) find only “weak evidence that funds [tend] to buy and sell the same
stocks at the same time.”
Recent empirical papers are more successful at detecting correlated trading.
Wermers (1999) provides an extensive analysis of the mutual fund industry.
Like Lakonishok et al. (1992), he finds more correlated trading in small stocks
than in the average stock. He also finds that “stocks that herds buy outperform
stocks that they sell by 4% during the following 6 months.” The title of his paper,
“Mutual Fund Herding and the Impact on Stock Prices,” signifies the author’s
belief that causality runs from trading behavior to asset prices. Kumar and
Lee (2002) find a “buysell imbalance in individual investors’ trades” just like
our paper does. However, the authors find the imbalance is correlated with
small stock returns at a monthly frequency. They conclude “these findings are
broadly consistent with the predictions of a noise trader model in which the
systematic activities of individual investors affect the returns of those stocks in
which they are concentrated.” This interpretation also attributes a causallink
from trades to returns. Finally, in a recent working paper, Barber, Odean, and
Zhu (2002) confirm that individual investors (in aggregate) typically have a net
trade imbalance.
In other words, is causality running from the purchasing/selling decisions
of investors to stock returns? Wellknown papers in this area of finance essentially assume this causallink exists—as is obvious from the papers’ titles:
“The Impact of Institutional Trading on Stock Prices” by Lakonishok et al.
(1992) and “Mutual Fund Herding and the Impact on Stock Prices” by Wermers
(1999).
3
There is a large theoretical literature about herding and information cascades that we will not
cover here. For review articles on the entire literature see Devenow and Welch (1996), Hirshleifer
and Teoh (2003), and Bikhchandani and Sharma (2000). Correlated Trading and Location 2121 There are a few other papers that offer some insights into a possible link between trading behavior and location. Coval and Moskowitz (2001) present one
regression that is similar to tests in our paper. The authors regress a herding
measure on ownership variables and find “there is a strong inverse relationship between herding activity and geographic proximity.” Both our tests and
our results differ markedly from theirs, and we discuss these differences later
in Section III. Hong, Kubik, and Stein (2002) propose the idea that wordofmouth communication inf luences investors’ trading decisions. Like this paper
does, the authors show that buying/selling is highly correlated within a region. Their data are quarterly and concentrate on mutual fund managers. The
authors suggest that an epidemic model explains correlated trading decisions.
That is, information diffuses throughout a population. We show that public
information shocks can explain a large fraction of observed trading behavior,
even at frequencies that are too high to allow diffusion. We also discuss these
issues in Section III, along with other robustness checks. Finally, Grinblatt
and Kelojaru (2001) show Finnish investors are more likely to trade stocks of
Finnish firms that are located near them. The authors are also able to examine the marginal effect of language and culture. Unfortunately, our data do not
separate language and distance. The authors consider trading volume as measured by the number of buy orders and the number of sell orders. Our paper
concentrates on the relation between stock returns and direction of trade (buys
minus sells). In this way, the papers provide complementary results.
We now proceed as follows. Section I discusses the data used in this paper;
Section II presents our methodology and result; Section III explores alternative
hypotheses; and Section IV concludes.
I. Data
We use accountlevel data to investigate correlated trading in financial markets. Our data come from individual brokerage accounts in the PRC and are
uniquely suited for the task at hand. The data represent trades placed between
May 4, 1999 and December 4, 2000.
A. Brokerage Accounts in the PRC
Brokerage accounts in the PRC are both similar to, and different from, what
we are used to in the United States. A brokerage firm (the firm) has branch
offices (branches) throughout the country, region, or city. Many brokerage firms
are regionally focused. Individuals open accounts at a branch office and then
place all of their trades through this one branch. Thus, there is a critical difference in our study between brokerage firms (our data are from one firm) and
branch offices (our data come from seven different branches).
A branch office may have a number of ways for investors to place trades: terminals in the branch, cashier windows, telephone service, and computer links.
Computer links from private computers are uncommon at this time, effectively
leaving three channels with which to place a trade. Consider a brokerage firm 2122 The Journal of Finance with five regional branches in the country’s largest cities. An individual who
opens an account at the Beijing branch must place all his or her trades with
the Beijing branch. Even if the individual visits Shanghai, he or she may not
place trades at the local Shanghai branch. Instead, he or she must call Beijing
to place a trade (and may only do so if the account has previously been set up
to allow phone trades).
B. Individual Investor Data
While investors in the PRC have a number of options for placing trades, we
focus on trades that are actually placed at the branch office. We intentionally
look at groups of investors who are physically standing near each other during
the trading day and, for the time being, do not consider trades that are calledin.
We later use telephone trades as a means to recheck our results. We also limit
ourselves to secondary trading of shares and do not look at trades relating to
IPOs, secondary offerings, or warrants. Our data contain completed trades and
not orders that have been submitted and later withdrawn.
Some stocks in the PRC trade infrequently. The highestvolume stock (measured by total value traded in RMB from 1999 to 2000) trades 120.84× more
than the lowestvolume stock, 7.96× more than the onehundredthranked
stock, and 3.14× more than the seventhranked stock. The extreme skewness
in trading volume can be seen in Figure 2: a graph of the distribution of the 1.00
0.90 Distribution (CDF) 0.80
0.70
0.60
0.50 Volume per
stock (RMB) 0.40
0.30 Log Normal
Distribution 0.20
0.10
0.00
20.0 21.0 22.0 23.0 24.0 25.0 26.0 ln (Volume)
Figure 2. Trading volume in the PRC. The figure graphs the distribution of the natural log of
trading volume per listed company. Trading volume is defined as the total value of stock traded (in
RMB) for a given company over the 2year period from 1999 to 2000. The data come from the both
the Shenzhen Stock Exchange and the Shanghai Stock Exchange. Correlated Trading and Location 2123 natural log of trading volume. Since it is infeasible to measure correlated trading in stocks with low volumes, we choose to look only at trades in active stocks.
For simplicity, we limit ourselves to stocks that are listed in Guangdong (on the
Shenzhen Stock Exchange) with the company headquarters also in Guangdong.
We only look at stocks that are denominated in local currency (RMB). We initially consider the 25 highestvolume stocks as measured by total value traded
in 1999 and 2000. We base our selection on total market volume and not insample volume. We have rechecked our results using the 100 highest volume
stocks and by forming portfolios of stocks. Neither of these twists inf luences
the results in a meaningful way.
Finally, we treat one investor who makes five trades on a given day differently from five different investors making one trade each on the same day. The
difference in treatment seems natural when studying correlated trading among
investors. We sort our data to include only unique buy and sell orders. That is,
if an individual investor makes multiple purchases of a stock on a given day,
we count this as one purchase and call it a “unique trade.”
C. Overview of the Data
Table I presents an overview of the data. We have collected data from seven
branches of one brokerage firm. Panel A shows the total trades before we control
for investors who break up their trades over the course of 1 day. We can see that
the average number of trades per year is 6.03, which is higher than in the United
States.4 Panel B shows only unique trades (defined above) by filtering trades
that are brokenup over a day. Panel C shows unique trades that are physically
placed in a branch office. The data in Panel C are primarily used throughout
this study. The difference between Panel B and Panel C comes from investors
who place telephone trades. Table I (Panel C, column (ii)) shows there are 18,575
unique buytrades placed in branch offices over the 17month period (80 weeks
or 388 trading days) in our sample. The number of sell orders in column (iii) is
about 9% less and totals 16,905 trades.
We look at 80 weeks, 25 stocks, and 7 branches, which gives 14,000 groupings
(there are 67,900 groupings if we separate trades into 388 trading days instead
of 80 weeks). Panel C, column (iv) shows there are 35,480 total unique trades
that are physically placed. If trades are spread evenly over time, across stocks,
and across branches, we should see an average of 2.53 trades per week in a given
stock at a given branch (or 0.52 trades per daystockbranch). However, trades
are not spread evenly over time, across stocks, and across branches. We refer
to 2.53 trades per week per stock or 0.52 trades per day per stock as the “data
density.” A low density is similar to having noisy data and biases estimates of
correlated trading to zero. We address this by forming portfolios of stocks, using
panel data, or grouping stocks by region. We doublecheck at all times that our
results are consistent regardless of what form we put the data in. 4 Note: 6.03 = (73, 953/7, 973) × (52/80), since we have 80 weeks in our sample. 2124 The Journal of Finance
Table I Overview of Data
This table presents overview statistics of the data used in this study. Data represent stock (equity)
trades placed by individual investors in the PRC between May 4, 1999 and December 4, 2000.
Trades, or orders, are placed at one of seven brokerage offices that are responsible for maintaining
the investors’ account data. There are four branches in Guangdong (A, B, C, and D) and three
branches in Shanghai (E, F, and G). We concentrate on a sample of buys and sells of highvolume
stocks that are listed and headquartered in Guangdong (listed on the Shenzhen Stock Exchange).
Panel A shows the total number of trades placed in a particular brokerage branch office during our
sample period. We take into account that some individual investors may “breakup” their trades
throughout a day. Panel B considers a “unique trade” to be one or multiple trades in the same stock
by a single investor on the same day. Panel C considers only trades placed by investors who are
physically standing in a particular branch office at the time the trade is placed (by terminal or
cashier window). Branch
Office (i)
# of
Accts (ii)
# of Buy
Orders (iii)
# of Sell
Orders (iv)
Buy + Sell
Orders Panel A: Total Trades in Data Set
A
B
C
D
E
F
G 1,386
1,538
1,514
1,775
662
751
365 8,487
7,367
8,889
7,552
2,901
2,401
1,646 8,141
6,504
7,878
6,803
2,224
1,695
1,465 16,628
13,871
16,767
14,355
5,125
4,096
3,111 Total 7,973 39,243 34,710 73,953 Panel B: Unique Trades in Data Set
A
B
C
D
E
F
G 1,368
1,538
1,514
1,775
662
751
365 6,003
5,316
5,887
6,348
2,091
1,791
1,183 5,483
5,059
5,818
5,973
1,763
1,346
1,078 11,486
10,375
11,705
12,321
3,854
3,137
2,261 Total 7,973 28,619 26,520 55,139 Panel C: Unique Trades That Were Physically Placed in a Branch Office
A
B
C
D
E
F
G
Total 957
943
971
963
449
588
263 4,011
3,152
3,851
3,540
1,602
1,490
929 3,659
2,943
3,693
3,179
1,377
1,170
884 7,670
6,095
7,544
6,719
2,979
2,660
1,813 5,134 18,575 16,905 35,480 Correlated Trading and Location 2125 II. Methodology and Results
We begin our empirical investigation by documenting that investors have
highly correlated trades when we condition on location. We then present a
simple rational expectations model with a number of testable hypotheses. We
show that our data is consistent with the model. Section III offers a number of
robustness checks that help reassure the reader that our interpretation of the
results is correct. A. Correlated Trading across Branches
Do investors within an isolated branch behave differently from investors at
other, isolated branches? Or, is there a common pattern to the buying and selling
behavior of all investors?
To answer these questions, we measure the total trades (buys plus sells) and
the net trades (buys minus sells) at each of the seven branches in our sample. We
only consider “unique trades” and, for this first test, we form weekly portfolios
that consist of all stocks in our sample. Table II presents our initial results.
In Panel A, we see the average correlation of total trades between any two Table II Regional Trading Correlation
This table presents overview statistics of crosslocation (branch) trading activity. Data represent
stock (equity) trades placed by individual investors in the PRC between May 4, 1999 and December
4, 2000. This time period represents 80 weeks. Trades are placed at one of seven brokerage branch
offices. We concentrate on a sample of buys or sells of highvolume stocks that are listed and
headquartered in Guangdong (listed on the Shenzhen Stock Exchange). Panel A: For each branch
office, we form a weekly portfolio of unique total trades (buys plus sells) across all stocks in our
sample. We then measure the pairwise correlation of these net trades between branches. There are
four branches in Guangdong (A, B, C, and D), or six pairs. There are three branches in Shanghai
(E, F, and G), or three pairs. There are 12 crossregion pairs. Panel B: We repeat the procedure
described above, but use net trades (buys minus sells). We use the asymptotic approximation of the
standard error of the correlation coefficient (see text).
Guangdong Shanghai Panel A: Total Trades (Buys + Sells) Average Correlation across Branches
Guangdong
(zstat)
Shanghai
(zstat) 0.7128
(22.22)
0.4784
(16.86) 0.2512
(4.15) Panel B: Net Trades (Buys − Sells) Average Correlation across Branches
Guangdong
(zstat)
Shanghai
(zstat) 0.3439
(8.01)
−0.2067
(−6.54) 0.1457
(2.27) 2126 The Journal of Finance branches is positive. All results are statistically significant at conventional
levels.5
In Table II (Panel B), we see the average correlation of net trades between
branches in Guangdong is positive. In fact, all six correlationpairs between the
four Guangdong branches are positive. The average correlation of net trades between branches in Shanghai is also positive. Again, all three pairs are positive.
Notice the average correlation of net trades between a branch in Guangdong
and a branch in Shanghai is negative. All 12 pairs are negative. Results are
significant at all conventional levels.
Table II presents some strong evidence that group psychology does not determine net buying/selling behavior at the branch level. If group psychology
were the main determinant, we would expect the net trades between any two
isolated branches to be uncorrelated. Clearly, this is not what we see. Instead,
there appear to be three important facts. First, Table II (Panel A) shows that
trade volume (buys plus sells) is a marketwide phenomenon. There is no evidence that Guangdong investors trade Guangdong stocks amongst themselves.
Second, there is clear evidence of correlated trading within a given region of the
country. Intraregion correlations are positive between pairs of isolated investorgroups (branch offices). Third, when one region of the country is buying, the
other is selling. This third fact is consistent with marketwide shocks to volume.
These three facts are not consistent with a grouppsychology effect that causes
one office to herd on one stock and another office to herd on another stock.
Given the results presented in Table II, we now turn to understanding the
economics behind correlated trading.
B. A Simple Rational Expectations Model
In this section, we review the predictions of a noisy, rational expectations
model. We then test the implications of such a model with our data. The model
is given in Appendix A.6
Brief overview of the model: In the model, there are three periods 0, 1, 2
and a continuum of investors who maximize end of period2 wealth. There is a
risky and a riskless asset. The risky asset pays a (random) dividend at the end
of period2. In period0, investors receive an endowment of the risky asset, a
public signal about the dividend of the risky asset, and a private signal about
the dividend.
At this point, we make one assumption about the precision of the private
signals that investors receive. The precision of the private signal is assumed to
5 To test for statistical significance, √ use the asymptotic approximation of the standard error
we
1 − ρ2
of the correlation coefficient: SE(ρ ) = √ N − 2 .
6
The model in this paper most closely follows Kim and Verrecchia (1991), although the assumption about information asymmetry is most similar to that in Brennan and Cao (1997). We fully
recognize that this model is not what is innovative about this paper. The application of information
asymmetry to an intranational setting (especially to explain correlated trading) is where this paper
contributes to the literature. Correlated Trading and Location 2127 vary across investors. This assumption is very similar to the one in Brennan
and Cao (1997), except we are looking at intranational instead of crossborder
(or international) information asymmetry. Investors who live near the headquarters of a traded stock company (the risky asset) are assumed to receive
more precise signals (on average) than those investors who live far away from
the headquarters. The motivation behind this assumption can be thought of as
follows: investors who live near the headquarters may have friends who work
for the company, there may be more news stories about the company in the
local paper, investors may use the company’s products more often, etc. In the
United States, it is not hard to imagine that investors read more about their
local telephone company than a telephone company across the country.
ASSUMPTION 1 (Location and Information; from Brennan and Cao (1997)): Investors can be divided into two groups, i ∈ {“near”,“ far” }, based on the distance
they live from a company’s headquarters. Investors who live near the headquarters of a ﬁrm receive (on average) more precise information than those who live
far away.
Trade takes place at the end of period0 so that prices and holding levels
are consistent with the investors’ beliefs. In period1, investors receive another
public signal about the dividend. Again, they are allowed to trade so the prices
and holding levels are consistent with their beliefs. The change in an investor’s
holdings of the risky asset from period0 to period1 represents the net trade
of that investor. Onehalf of the absolute value of the sum of all investors’
net trades is the volume or total trade in the risky asset. The change in the
equilibrium price from period0 to period1 represents the return of the risky
asset. These quantities (total trades, net trades, and return on the risky asset)
lead to a number of testable hypotheses when combined with the assumption
about location and information.
C. Implication Regarding Net Trades (Buys–Sells) and Stock Returns
When positive, public information about the risky asset’s dividend is released,
all investors raise their (posterior) valuation of the risky asset. However, all
investors do not necessarily start with the same priors. By Assumption 1, some
investors (“near”) have more precise priors than other investors (“far”).
When positive information is released, investors with the more diffuse priors
(“far”) update more than those with more precise priors (“near”). The shift in
equilibrium demands for the risky asset causes trade. For a positive signal,
“near” investors become net sellers and the “far” investors become net buyers.
Again, this happens because the “far” investors update more heavily than the
“near” investors (see equation (A7) in Appendix A.3). For a negative signal,
the “far” investors also update more heavily. This causes them to become net
sellers, while the “near” investors become net buyers.
HA (Net trade for “near” investors and returns). If Assumption 1 (location
and information) is true, investors who live near the headquarters of a
firm have net trades that are negatively correlated with stock returns. 2128 The Journal of Finance
Table III Regression Analysis of Trading and Stock Returns
This table presents regressions of returns on trading activity. Data represent stock (equity) trades
placed by individual investors in the PRC between May 4, 1999 and December 4, 2000. This time
period represents 80 trading weeks. Trades are placed at one of seven brokerage offices, and the
office is responsible for maintaining the investors’ account data. We concentrate on a sample of
buys or sells of highvolume stocks that are listed and headquartered in Guangdong (listed on
the Shenzhen Stock Exchange). Coefficients are estimated by generalized least squares with an
allowance for heteroskedasticity and crosssectional correlation between stocks. Every week, for
every stock, we aggregate net trades in each of the two regions of the country (Guangdong and
Shanghai). When then have 2,000 observations for the Guangdong investors and 2,000 observations
for the Shanghai investors. The number of observations equals 80 weeks times 25 stocks.
Investor Location
Guangdong (Near)
Dependent variable
Independent variable
ˆ
β
(zstat) Shanghai (Far) ri, t /σ i
Neti, t /σ Net, i
−0.1220
(−9.58) ri, t /σ i
Neti, t /σ Net, i
0.0431
(3.44) COROLLARY TO H A (net trade for “far” investors and returns): If Assumption 1
(location and information) is true, investors who live far from the headquarters
of a ﬁrm have net trades that are positively correlated with stock returns.
Table III provides a test of Hypothesis HA and its corollary. Table III offers
some of our strongest results. We regress the actual returns on the net trades
(buys minus sells) using a generalized least squares procedure that allows for
heteroskedasticity and crosssectional correlation between stocks. Every week,
for every stock, we aggregate the net trades in each of the two regions of the
country. We see that the net trades of the “near” investors are negatively correlated with returns. We see that the net trades of the “far” investors are positively correlated with returns. Both regression coefficients are significant at
conventional levels.
Hypothesis HA and its corollary are stated in terms of the correlation of
net trades and returns. While the regression framework of Table III clearly
measures correlation, some readers might appreciate a more direct test. In
Table IV, we measure the correlation of net trades and returns. The table
shows that the net trades of “near” investors are negatively correlated with
returns, while the net trades of “far” investors are positively correlated with
returns.
We conclude that our simple rational expectations model, combined with the
assumption of location and information, is consistent with our data. That is,
trading is the result of portfolio rebalancing. Investors rebalance in response to
public information about stocks. The decision by an individual investor to buy
or sell (in response to an information shock) is a function of the investor’s prior
valuation of the company and the new, marketclearing value of the company. Correlated Trading and Location 2129 Table IV Correlation Analysis of Trading and Stock Returns
This table presents the contemporaneous correlation of returns and trading activity. Data represent
stock (equity) trades placed by individual investors in the PRC between May 4, 1999 and December
4, 2000. This time period represents eighty trading weeks. Trades are placed at one of seven
brokerage offices, and the office is responsible for maintaining the investors’ account data. We
concentrate on a sample of buys and sells of highvolume stocks that are listed and headquartered
in Guangdong (listed on the Shenzhen Stock Exchange). Every week, we form three portfolios: (i) net
trades of Guangdong investors across the stocks in our sample; (ii) net trades of Shanghai investors;
and (iii) equalweighted returns across the stocks in our sample. We then measure the correlation
of net trades from our two groups of investors with returns. We then have 80 observations for the
Guangdong investors and 80 observations for the Shanghai investors. Statistical significance is
derived from the asymptotic approximation of the standard error of the correlation coefficient (see
text).
Region
Guangdong (Near)
Correlation coefficient
(net trades and returns)
(zstat) Shanghai (Far) −0.4946 0.2121 (−5.03) (1.92) We now turn to another econometric test that helps solidify our understanding
of correlated trading and location. D. Percent of Trading Explained by Location
We end this section by trying to estimate the fraction of trading behavior that
can be explained by location. Why is this important? The regression coefficients
in Table III and the correlation coefficients in Table IV give little intuition about
the economic importance of our findings. To address this question, we turn to
principal component analysis.
In the broadest terms, we can divide trading behavior into two parts: (i) the
part that can be explained by locationbased effects (common shocks or public
news); and (ii) the part that can be explained by other effects (withinbranch
effects). Examples of withinbranch effects have been discussed earlier and
include group psychology, insider trading, and white noise.
In order to estimate the fraction of trading that can be explained by locationbased effects, we extract a common factor (principal component) from our data.
We look at net trades across branches (i.e., across the isolated groups of investors in our sample).
HB (Correlated trading across branches). If the decision to buy or sell
a given stock is related to marketwide effects, then there is a common
component across N isolated groups of investors. In other words, the first
principal component across N branches explains more than (1/N ) of the
total variance. 2130 The Journal of Finance
Table V Principal Component Analysis of Trading Behavior
The table examines the variance of net trading activity. We define net trades as the number of
unique buy orders that are physically placed in a branch office, minus the number of unique
sell orders. Data come from the PRC between May 4, 1999 and December 4, 2000. This time
period represents 80 weeks. We concentrate on a sample of buys or sells of highvolume stocks
that are listed and headquartered in Guangdong (listed on the Shenzhen Stock Exchange). This
table shows results from a principal component analysis where we have normalized net trades
for each stockbranch by its standard deviation. Panel A shows the decision to buy or sell a given
stock is correlated across isolated groups of investors. zstats are calculated using MonteCarlo
methods and the empirical distribution of buys and sells within each branch. Panel B shows loading
coefficients that come from a regression of the net trades from a given branch on a constant and the
first principal component. Net trades in Guangdong branches load positively on the first principal
component, while net trades from Shanghai branches load in the opposite direction on the same
principal component. Tests of statistical significance use robust (White) standard errors.
Panel A: Principal Components
1st Comp
Percentage of variance explained
(zstat)
Cumulative % of variance explained 2nd Comp 3rd Comp 31.8326
(7.66)
31.8326 15.9632
(5.00)
47.7958 14.2197
(3.94)
62.0155 Panel B: Branch Loadings on the 1st Principal Component
Branch Loading on
1st component A
B
C
D 0.4825
0.1838
0.2188
0.5112 Guangdong average (zstat) 0.3491 E
F
G −0.1055
−0.4008
−0.5025 Shanghai average (7.25)
(3.23)
(4.70)
(7.44) (−2.30)
(−6.81)
(−3.28) −0.3363 Alternative to HB (uncorrelated trading across branches): If the decision
to buy or sell a given stock is not related to marketwide effects, then there
is no common component across N isolated groups of investors. In other
words, the first principal component across N branches explains (1/N ) of
the total variance, the first two principal components explain (2/N ) of the
variance in total, and so on.
Table V shows strong support for HB , rejects its alternative, and provides
additional support for locationbased trading. Table V (Panel A) shows that
the first principal component explains 31.83% of the variance of net trades
across branches (both Guangdong and Shanghai branches). In the strictest
interpretation of our model, we should only consider a single shock (factor) that Correlated Trading and Location 2131 drives trading and should only measure the first principal component. Thus, we
can say that 31.83% of correlated trading can be explained by a single common
component (which is public news in the model). The remaining 68.62% can be
thought of as within branch effects (including white noise). The first principal
component is significant at conventional levels.7
We can further bolster our findings by testing whether the first principal component actually represents locationbased trading in the way we hypothesize.
We regress the net trades from each branch on the first principal component.
Table V (Panel B) shows the rather striking results. The Guangdong branches
(A, B, C, and D) load heavily on the first component. The Shanghai branches
(E, F, and G) load heavily on the second component (but with an opposite sign).
Table V (Panel B) is another way to view the results presented earlier in the
paper. That is, when investors in Guangdong tend to be buying, investors in
Shanghai tend to be selling. There is clear indication of one common factor that
affects the entire universe of investors simultaneously (although the effect on
net trades depends on location).
To summarize the results up to this point, investors in our sample have
correlated trades that become dramatically clear when we condition on location.
That is, groups of investors within a region of the country tend to buy and sell
together even though the groups (branch offices) are separate and isolated.
The trading behavior is consistent with the “near” group of investors having
more precise information (than “far” investors) about the prospects of nearby
companies. Our interpretation of the results remains constant regardless of
which econometric test we use (correlation, regression, or principal component
analysis). We now explore a number of alternative hypotheses.
III. Robustness Checks
A. Implications Regarding Total Trades (Volume) and Stock Returns
We can use Assumption 1 to formulate specific hypotheses about the sign of
the correlation between total trades and stock returns (for details, please see
equation (A5) in Appendix A3). The intuition is straightforward. Public news
about the payoff of the risky asset causes investors to update their beliefs. When
investors update their beliefs and are allowed to trade, volume is correlated
with the absolute value of returns. This hypothesis regarding volume and stock
returns is by no means unique to our model. It is consistent with our model and
serves as a nice alternative check.
HC (Volume and stock returns). Volume is positively correlated with the
absolute value of returns.
The relationship between volume and returns holds for the market as a
whole. It also holds for both of our subgroups of investors {“near”, “far”} under
7 We estimate standard errors using a MonteCarlo simulation procedure that is explained in
Appendix B. 2132 The Journal of Finance Assumption 1. The reason the relationship holds for our subgroups is that (on
average) one group’s precision is high and one is low. Thus, neither match the
market as a whole.
To test this hypothesis, we regress the absolute value of returns on total
trades (buys plus sells). As we did earlier, every week for every stock, we aggregate total trades (buys plus sells) in each of the two regions of the country. We estimate a common coefficient using generalized least squares with an
allowance for heteroskedasticity and correlation between stocks. We find the
regression coefficients are significantly different from zero at all conventional
ˆ
levels. For “near” investors, the β coefficient is 0.0642 with a 5.19 zstat.8 For
the “far” investors, the β − hat coefficient is 0.0454 with a 4.47 zstat. It is clear
that the absolute value of returns is positively correlated with trading volume
(regardless of whether we look at the volume from “near” or “far” investors).
The results are available from the authors upon request and are presented in
a format similar to Table III.
B. Turning “Near” and “Far” Around
An obvious and very powerful test of our results can be carried out if we
simply f lip our definition of “near” and “far.” We now concentrate on companies
with a headquarters in Shanghai. We still consider stocks listed in Guangdong
(on the Shenzhen stock exchange) but now choose a new list of stocks (with
a headquarters in Shanghai) and repeat all of the work presented earlier. In
particular, we redo the results of Table IV. We calculate the correlation of net
trades with returns. For the Guangdong investors (now the “far” investors)
the correlation is 0.4904 and significantly positive with a 4.97 zstat. For the
Shanghai investors (now the “near” investors) the correlation is −0.1996 (and
significant at the 10% level) with a −1.80 zstat. The results are available from
the authors upon request and are presented in a format similar to Table IV.
C. HighFrequency Results
Another powerful test of our results is to look at frequencies higher than a
week. We choose to look at a daily frequency since this is the finest division of
stock returns we have available. We measure the correlation of net trades and
daily stock returns. We use the full sample of 50 stocks (25 with headquarters
in Guangdong and 25 with headquarters in Shanghai). “Near” investors is the
union of Guangdong investors trading in Guangdongheadquartered stocks and
Shanghai investors trading in Shanghaiheadquartered stocks. “Far” investors
is the union of Guangdong investors trading in Shanghaiheadquarterd stocks
and Shanghai investors trading in Guangdongheadquartered stocks.
Trades of the “near” investors are negatively correlated with returns with a
−0.0839 correlation coefficient and a −2.34 zstat. Trades of the “far” investors
are positively correlated with returns with a 0.0620 coefficient (and significant
at the 10% level) with a 1.73 zstat. The results are available from the authors
upon request and are presented in a format similar to Table IV. Correlated Trading and Location 2133 D. Feedback Trading
Papers such as Grinblatt and Keloharju (2000) and Nofsinger and Sias (1999)
study feedbacktrading strategies of various investor classes. It is possible that
we have misidentified the mechanism that appears to cause the contemporaneous correlated trading documented in this paper. It is possible that net trades
are actually a response to past price movements. To test if this is the case, we
redo Table III, but regress this week’s net trades on last week’s returns. Appendix C shows our results. We see that neither the “near” investors nor the
“far” investors appear to be following a feedback trading strategy. The relationship between net trades and lagged returns is insignificantly different from
zero.
In Appendix C (Panel B), we check whether feedback trading might be occurring at a frequency higher than 1 week. We now regress daily net trades (buys
minus sells) on lagged returns. Again, we show no significant relationship.
While we would like to look at trading and returns at a higher frequency
(intraday), we simply do not have the data to do that. In particular, we do
not have tick data from the Shenzhen Stock Exchange (it does not exist). We
make the following notes: (i) Our results at a daily frequency represent a 20times finer (approximately) examination of correlated trading than past studies
that use monthly data. (ii) We have shown in Table IV that net trades and
contemporaneous returns are correlated at a daily frequency. (iii) If feedback
trading exists, there might be a predictable pattern in stock returns (see De
Long et al. (1990)). We do not see such a pattern in PRC stock returns. (iv)
When examining data at a very high frequency, our definition of correlated
trading has to change. With tickbytick data, only two trades cross at a time.
One trade is a buy and one is a sell. No other trades happen at exactly the
same time. Therefore, we might have to look at orders f low (instead of executed
trades) to see if groups of investors are posting orders en masse. Unfortunately,
we do not have these order f low data either. E. Coval and Moskowitz (2001) Results
As mentioned in our introduction, Coval and Moskowitz (2001) present one
regression that is similar to tests in our paper. The authors regress a herding
measure on ownership variables and find “there is a strong inverse relationship between herding activity and geographic proximity.” Our results are quite
different. All trading decisions in our model are determined simultaneously
and “herding” does not depend monotonically on location. In fact, we should
see net trades (“herding”) in one direction by “near” investors and net trades
(“herding”) in the opposite direction by “far” investors. If we had investors from
a “middle” region, we would expect zero net trades.
Table II (Panel B) in our paper shows a higher correlation coefficient among
“near” locations than “far” locations. This result is opposite to that of Coval
and Moskowitz (2001) but only considers Guangdongheadquartered stocks.
Highfrequency analysis from part C (above) shows roughly similar magnitudes 2134 The Journal of Finance of correlation coefficients when we consider stocks with headquarters in both
Guangdong and Shanghai. Note the correlation coefficients are of opposite sign
(negative for the “near” locations and positive for the “far” locations). This result
is consistent with the intuition given in the paragraph directly above.
F. Epidemic Models and WordofMouth Communication
Economists have long been interested in how information spreads. We believe
that investors (primarily) react to public (common) information. A competing
view is proposed by Hong et al. (2002) who look at quarterly data and argue that
investors “spread information and ideas about stocks directly to one another
by word of mouth.” The authors suggest an epidemic model to explain their
findings. That is, trading decisions over the quarter are correlated, because
investors who live near each other pass information between themselves.
While an epidemic model may be consistent with a quarterly observation
interval, it may not be consistent with highfrequency data. We reach this conclusion, because we are able to shrink our observation interval from a weekly to
a daily frequency. Daily frequency is an important threshold. If wordofmouth
communication plays a part in investors’ decisions, then groups of investors
would have to meet (talk by phone) each evening (i.e., between trading hours).
We do not believe it is likely investors from the same region of a country compare notes after trading hours and spread information amongst themselves.
We make this point in part C (above), where we see that net trades within a
given region of the country are still significantly correlated with returns (in the
direction our model predicts), even at a daily frequency!
We extend the highfrequency tests and look at the daily correlation of total
trades (buys + sells). We find the market as a whole experiences shocks to total
trades at a daily frequency. The correlation of total trades within Guangdong
Province is 0.6883 (zstat is 45.76), the correlation within Shanghai Municipality is 0.2214 (zstat is 7.74), and the crossregion correlation is 0.3829 with
a 28.28 zstat. There is little evidence of trading spreading from one region
to the next.8 The results are available from the authors upon request and are
presented in a format similar to Table II (Panel A).
G. Telephone Trades as a Control Group
We previously exclude telephone trades from our study for two reasons. First,
we want to concentrate on investors who are physically standing in the same
8
In an earlier version of this paper, we performed yet another test to bolster our argument (not
reported). We reran a correlated trading test, but ignored trades that happened before 11:00 a.m.
each day. We found the same significant correlation patterns within a given region as we do at a
daily frequency. Our test ignores the first hour and a half of the trading day. Thus, we eliminate
the following scenario: investors go home each night, compare notes with investors who use other
branch offices, return to trade in the morning, and place trades that reflect information obtained
from the investors who use the other offices. As mentioned above, only tickbytick data could allow
a true intraday study (and these data do not exist in the PRC). This said, we are now very confident
that trades in our sample result from public information shocks. Correlated Trading and Location 2135 room. Second, had we found a grouppsychology effect, we planned to use the
telephone trades as control group. Generally, an individual is either a telephonetrader or a branchtrader.
Although not reported, we repeat tests of correlated trading using only trades
placed by telephone. There are few discernable differences between inbranch
trading and telephone trades as far as correlated trading is concerned. H. Possible Recommendations
A reader of this paper might hypothesize that brokers at the branch offices
make recommendations and these recommendations cause investors to trade
together. Such a hypothesis is extremely unlikely. First of all, all of the branch
offices in our sample are part of the same brokerage company. Therefore, the
same company would have to make different, and conf licting, recommendations in Guangdong and Shanghai. Second, the brokerage firm does not issue
recommendations. Third, we have observed trading and found no evidence of
recommendations. Fourth, the brokerage firm states that they do not issue recommendations. Finally, the staff on hand only advise investors on how to fill
out order forms. They do not offer investment advice. Again, the firm and our
own observations support our results. I. Table III Revisited—at the StockBranch Level
An earlier version of this paper presented a regression similar to those regressions in Table III, except data was at the stockbranch level instead of
the stockregion level. This disaggregated form runs into data density issues,
but gives qualitatively similar results. The regression coefficient (zstat) of the
“near” investors was −0.0295 (−5.03). For the “far” investors, the values are
0.0042 (0.63). Clearly the coefficients are smaller—undoubtedly, due to noise
inherent in the disaggregated form of the data. The sign of the regression coefficients remain the same. Statistical significance remains the same for the
“near” investors but disappears for the “far” investors (also, undoubtedly due
to data density issues). J. Extreme Behavior
Some readers have suggested that the branch offices are not truly isolated.
We believe they are, especially once we look at trading on a daily frequency
(and after cutting out the trades before 11:00 a.m.).
We rule out (and have found no evidence of) special communication links
between investor groups. Such links would have to consist of unheard of scenarios such as the following: one friend opens an account at one branch office,
while his friend opens an account at another branch office. The two friends go
every day to their respective branch offices armed with cellular phones. Each
stands in the middle of his or her branch office, talks loudly on the phone, and 2136 The Journal of Finance announces to everyone what the other friend is observing at the other branch
office. We find such explanations farfetched. K. Private Information Shocks
Some readers might think that private information shocks cause a group of
investors to buy or sell a stock at the same time. It has even been suggested that
our results could be the product of investment clubs whose members use (and
meet at) the same brokerage office. If private information shocks were causing
the observed trading, we would expect to see a positive correlation between
net trades and returns in each branch office in our sample. In other words,
as a group of investors demand liquidity, other market participants “agree” to
provide it only at a higher price. We do not see this. We only see a positive
correlation between net trades and returns at the “far” branches. We believe
investors in the “far” branches are the ones who are least likely to have private
information.
Also, we see that individuals at isolated offices (within the same region) buy
and sell together. It is possible that, on occasion, private information could be
impounded into stock prices by investors at two locations. But we see this happening time and time again. Remember, the correlation of net trades between
two branch offices from the same region is positive and statistically so. Thus,
our research design allows us to say, with a very high level of confidence, that
there is a common, contemporaneous factor affecting the trading of isolated
individuals. Calling this factor a “private information shock” simply does not
fit the facts. L. Our Model and Proﬁtability
There are two ways to think about the rational expectations model reviewed
in this paper. It is possible that nearby investors perceive they have more precise
information about local companies. This perception could possibly come from
overconfidence. If this were true, we would also see the same correlation of net
trades and stock returns detailed in HA and Table III. If the “overconfident”
investors disregarded feedback signals from the market (i.e., they were not
really better informed and did not actually outperform other investors), this
correlation pattern could persist indefinitely. There would be no relationship
between location and profitability.
If we believe the rational expectations model in the strictest sense, then we
might believe that the betterinformed investors should be better able to predict
future returns. To test this hypothesis, we regress current net trades on future
returns (i.e., current returns on lagged net trades). We use a generalized least
squares methodology that allows for contemporaneous correlation between the
stocks in our sample. Our results (not reported) show a positive correlation for
Guangdong (“near”) investors between net trades this week and returns next
week. The results are not statistically significant. However, correlation of net Correlated Trading and Location 2137 trades and future returns for the Shanghai (“far”) investors is significantly less
than zero. This result is consistent with Coval and Moskowitz (2001).
M. Relevance of the Results
We end this section with a discussion of the relevance of our results. Some
readers might believe that studying individual investors and/or PRC investors
does not help to understand financial markets in the United States. We beg to
differ.
As Hertz (1998) clearly describes, the PRC is a place where we, ex ante, expect
to find grouppsychology effects. If we fail to detect such effects in the PRC, it
seems unlikely we would find them in the United States. That is, it is unlikely
that individual and institutional investors in the United States are more prone
to grouppsychology effects than individuals in the PRC. More importantly,
existing studies in the United States look at mutual funds. If institutions currently hold approximately 60% of the shares of the largest companies in the
United States, then individuals hold approximately 40% of the shares. Suppose we divide investors in the United States into two groups (institutions and
individuals). As discussed earlier, studying the trading behavior of one group
can tell us about the other group if we believe the groups are systematically
different and trade “against” each other (i.e., mutual funds vs. individuals).
IV. Conclusion
This paper provides an indepth look at investor behavior. We show that individual investors engage in correlated trading behavior. We provide a number
of tests designed to give us insight about the cause of correlated trading. We do
this through experimental design. That is, we isolate groups of investors who
are physically in the same room at the time they place trades. We are able to
rule out group psychology as the predominant force driving investment decisions. If group psychology were important, then we would expect the trades of
one isolated group to be uncorrelated with trades of other isolated groups (i.e.,
there is extremely low probability that two isolated groups would choose to buy
a particular stock at the same time or sell a particular stock at the same time).
Instead, we see isolated groups of investors in one region of the country tend
to buy and sell together. Investors in another region of the country tend to buy
and sell together. When one region is buying, the other is selling.
We present the testable hypotheses from a rational expectations model. We
assume that investors who live near the firm receive more precise information
(than those who live far from the firm) about future dividends. This assumption gives rise to a negative correlation of net trades for “near” investors and
returns. Our data are consistent with such a negative correlation. The model
is also consistent with the observed (positive) correlation of net trades for “far”
investors and returns.
We use a principal component analysis to estimate the fraction of trading that
can be explained by locationbased effects. We show that trades from one region 2138 The Journal of Finance of the PRC load heavily on the main factor. Trades from another region load
heavily (but oppositely) on the same, common factor. These results support the
idea that public (or marketwide) information is a major determinant of trading
decisions. The decision to buy or sell depends on location (and we observe this
as a positive or negative loading on the factor). Our conclusions remain unchanged regardless of which methodology we use (correlations, regressions, or
principal component analysis). Finally, a number of alternative hypotheses are
explored.
We show what has traditionally been called “herding” in the finance literature
is consistent with trade between asymmetrically informed agents. Thus, this
paper gives insight into the structure of information in domestic stock markets.
It also helps us understand the determinants of investment decisions.
Appendix A
This section reviews a simple, rational expectations model.9 Our goal is to
show that the net trading in our data is consistent with the predictions of a
rational expectations model. We present an extremely sparse model and use
the assumption that investors who live near a company receive more precise information about that company than investors who live far away from
the company. The model and this one assumption provided a number of testable
hypotheses.
A. Setup of Model
The model has three periods, t = {0, 1, 2}, and a continuum of investors who
are uniformly distributed on the closed interval from zero to one. Each investor
maximizes the utility of his or her wealth at the end of period2:
˜
Ui (W2, i ) = −exp − 1˜
W2, i ,
γi where γ i is investor i’s risk tolerance. For now, we assume all investors have
the same risk tolerance, γ . The timing of the model is as follows. In period0,
investors receive an endowment of a riskless bond, eriskless, i , and a risky asset,
erisky, i ,. The riskless bond pays one unit of consumption in the final period.
Without loss of generality, we assume the riskless interest rate is zero and
the end of period price of the riskless bond is one: pt, riskless ≡ 1 for t = {0, 1, 2}.
The risky asset pays an amount u in the final period, where u ∼ N (u, 1/h). In
˜
˜
¯
order to avoid a fully revealing equilibrium, the aggregate endowment of the
risky asset is not known to investors: erisky ≡ i erisky, i d i and erisky ∼ N (0, 1/θ ).
˜
˜ 9
The model in this paper most closely follows Kim and Verrecchia (1991), although the assumption about information asymmetry is most similar to that in Brennan and Cao (1997). For those
interested in similar work, see Admati (1985) and Dvorak (2001). Correlated Trading and Location 2139 In period0, investors receive two signals about the future dividend of the risky
asset, a public signal y t =0 = u + ηt =0 and ηt =0 ∼ N (0, 1/η0 ) and a private signal
˜
˜˜
˜
z t =0, i = u + εi and εi ∼ N (0, 1/st =0, i ). It is assumed that the precision of the
˜
˜˜
˜
private signal, st=0, i , is positive and bounded. After receiving their endowments
and signals, investors trade so the price at the end of period0 is consistent
with their beliefs. In period1, investors receive only a public signal about the
future dividend of the risky asset, yt =1 = u + ηt =1 and ηt =1 ∼ N (0, 1/η1 ). After
˜
˜˜
˜
receiving the signal, investors trade. In the final period, the dividend of the
risky asset is revealed: prisky, t =2 = u.
˜
˜
At the end of the first and second time periods (when trading takes place),
investors solve for the optimal demand of the risky asset (xriskless, t, i and xrisky, t, i
for t = {0, 1}), given the information available to them at the time. We stack the
endowments, prices, and holdings of the assets for notational simplicity:
Ei ≡ [eriskl ess, i
Pt ≡ [ priskl ess, t
X t , i ≡ [xriskl ess, t , i erisky, i ]
prisky, t ]
xrisky, t , i ] . The final period wealth of an individual investor can be written
˜
˜
˜
˜
˜
W2, i = P0 Ei + ( P 1 − P0 ) X 0, i + ( P 2 − P 1 ) X 1, i . (A1) B. Location Information Assumption—from Brennan and Cao (1997)
The precision of the private signal (st=0, i ) is assumed to vary across investors.
We further assume that investors who live near the headquarters of a traded
stock company receive more precise private signals (on average) than those investors who live far away from the headquarters. The motivation behind this
assumption can be thought of as follows: investors who live near the headquarters may have friends who work for the company, there may be more news stories about the company in the local paper, they may use the company’s products
more often, etc. In the United States, it is not hard to imagine that investors read
more about their local telephone company than a telephone company across the
country.
ASSUMPTION 1 (Location and private information; from Brennan and Cao 1997):
Investors can be divided into two groups, i ∈ {“near”, “far”}, based on the distance
they live from a company’s headquarters. Investors who live near the headquarters of a ﬁrm receive (on average) more precise information (private signals in
the model) than those who live far away.
We can write the assumption more formally as
E [si  i ∈ near ] > E [si  i ∈ far]. (A2) 2140 The Journal of Finance C. Solution to the Model
A brief description regarding the solution to the model is given here.10 Investors make conjectures about the relationship between prices and information in the economy. In equilibrium, these conjectures are true. Prices of the
risky asset are conjectured to be a linear function of the expected dividend (and
all signals related to the dividend) as well as of the expected supply of the risky
asset. Investors also know the precision of their own information (called K i, t )
at time t. The average precision in the market at time t is written simply Kt .
D. Equilibrium Holding Levels
The equilibrium holding of investor “i” in the risky asset at the end of period0
is given by the expression below. Here s is the average precision of the private
signal across investors. We take out the “t=” in the subscripts and leave only
the time period for compactness:
xrisky,0, i = γ s0, i
˜ i + γ (s0, i − s)
K 0, i
[h(u − u) − η0 η0 + γ sθ erisky ] +
˜¯
˜
˜
erisky . (A3)
˜
K0
K0 And the equilibrium holding of investor “i” in the risky asset at the end of
period1 is given by the expression below.
xrisky,1, i = γ s0, i
˜
+ i + γ (s0, i − s)
[h(u − u) − η0 η0 − η1 η1 + γ sθ erisky ]
˜¯
˜
˜
˜
K1 K 1, i
erisky .
˜
K1 (A4) Once the equilibrium holdings level at time t = 1 and t = 0 are found, the
difference between these level is the net buying (selling) for investor “i” over
the period. The absolute value of the net buying or selling gives us the volume
for investor “i.” If we aggregate individual volumes across all investors, we get
an expression for total volume in the market. Note, the only event that causes
the volume and net trading in this model is the release of a pubic signal in
period1.
E. Volume of Trade
The volume of total trade in the whole market caused by the public signal in
period1 is
Volumerisky, t =0→1 ≡ 1
2 ˜
γ st =0, i − s di  P t =0→1 . (A5) We see that volume and contemporaneous price movement (returns) are correlated. Volume is also correlated with dispersion of beliefs within the economy.
10 For readers who are interested in a complete solution to the model and additional details,
please see Kim and Verrecchia (1991). Correlated Trading and Location 2141 This makes sense. If everyone has the same beliefs, then a release of public
information can cause prices to move, but does not induce trading.
F. Net Trade
The change in holdings of the risky asset, for investor “i,” caused by the public
signal in period1 is
Netrisky, t =0→1, i ≡ xrisky, t =0→1, i ,
˜ ˜
= −γ (st =0, i − s) P t =0→1 . (A6)
(A7) Again, s is the average precision of the private signal across investors and st=0, i
is the private signal of investor “i.” We see that an investor updates his or her
beliefs about the value of the risky asset only if the precision of his or her prior
information is below (or above) the average precision in the economy. Investors
with less precise information will tend to update more heavily than those with
more precise information.
Appendix B
Table V (Panel A) shows the results of a principal component analysis. We
see that the first principal component explains 31.83% of the variance of net
trades, the second component explains 15.96% of the variance, etc. In order to estimate the significance of these percentages, we use a MonteCarlo
method.
Our data represent net trades and are in an 80 × 7 matrix (80 weeks and
seven branch offices). If the net trades of each branch were uncorrelated with
those of other branches (i.e., no common component), then each principal component should explain (1/7) or 14.29% of the total variance. However, even under
the null of uncorrelated trading across branches, the first principal component
may explain more than (1/7) of the total variance (when using our actual data).
This is due to the fact that the percentage is bounded from below by (1/7) and
biased upward.
We simulate our data by drawing from the original data with replacement.
That is, we draw an 80 × 7 matrix of data where draws in the columnn come
from the branchn distribution of net trades. We then extract the first principal component and calculate the percent of variance explained. The empirical
distribution of trades and sample size of 80 lead to a simulated first principal component that explains 20.65% of the variance. Our finding of 31.83% is
significantly above this value.
We now filter out the first principal component and look at the significance
of the second component. Since the first principal component from our random draws explains 20.65% on average, we expect the second component to explain (1/6) of the remaining variance of 79.35%. This fraction is 13.23%. Again,
due to sample size, the percentage is actually bounded from below by (1/6) 2142 The Journal of Finance and is biased upward. Our second principal component is significantly higher
than this number. We continue in a similar manner for the remainder of the
components.
Alternative Methodology: We doublecheck our principal component results
using a maximum likelihood factor analysis implemented by STATA. This software package offers two statistical tests. The first is a chisquared test that
there are three factors vs. no factors. This test has a 0.0000 pvalue. The second
test is a chisquared test comparing three factors vs. more than three factors.
This test has a 0.9134 pvalue. We are reassured about the statistical significance presented in Table V (Panel A).
More importantly any rotation of principal components that STATA generates gives the factorloading pattern that we report in Table V. That is, the
Guangdong branches load one way on the first factor, while the Shanghai
branches load with the opposite sign on the same factor. Thus, we are confident about our economic interpretation of a common, marketwide shock.
Appendix C Feedback Trading and Stock Returns
This table presents a regression trading activity on past returns. Data represent stock (equity)
trades placed by individual investors in the PRC between May 4, 1999 and December 4, 2000. This
time period represents 80 trading weeks, or 388 trading days. Trades are placed at one of seven
brokerage offices, and the office is responsible for maintaining the investors’ account data. We
concentrate on a sample of buys or sells of highvolume stocks that are listed and headquartered
in Guangdong (listed on the Shenzhen Stock Exchange) and in Shanghai (listed on the Shanghai
Stock Exchange). Coefficients are estimated by generalized least squares with an allowance for
heteroskedasticity and crosssectional correlation between branches. We form portfolios across
branches within a given region. In Panel A, there are 3,950 observations for “near” trades and
3,950 observations for “far” trades. The number of observations equals 80 weeks times 50 stocks
(twentyfive from each region), minus 50 observations due to the lag. In Panel B, there are 19,350
observations for each of the two groups. The number of observations equals 388 days times 50
stocks (25 from each region), minus 50 observations due to the lag. Examples of “near” trades are
the net trades of Guangdong investors in Guangdong stocks. Examples of “far” trades are the net
trades of Guangdong investors in Shanghai stocks.
Investor Location
Near Far Panel A: Weekly Regressions
Dependent variable
Independent variable
ˆ
β
(zstat) Neti, t /σ Net, i
ri, t− 1 /σ i
−0.0082
(−0.52) Neti, t /σ Net, i
ri, t −1 /σ i
0.0181
(1.14) Panel B: Daily Regressions
Dependent variable
Independent variable
ˆ
β
(zstat) Neti, t /σ Net, i
ri, t−1 /σ i
−0.0083
(−1.15) Neti, t /σ Net, i
ri, t− 1 /σ i
0.0125
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 MichaelKearns

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