Discussion Paper No. 34

Examining Investors Trading
Performance ThroughBrokers Network
Hongwei Chuang
February, 2015

Data Science and Service Research
Discussion Paper

Center for Data Science and Service Research
Graduate School of Economic and Management
Tohoku University27-1 Kawauchi, Aobaku
Sendai 980-8576, JAPANExamining Investors Trading Performance ThroughBrokers Network
Hongwei Chuang
Graduate School of Economics and Management, Tohoku University27-1 Kawauchi, Aoba Ward, Sendai 980-8576, Japan
hongwei@econ.tohoku.edu.tw

Abstract
Institutional investors play an important role in determining the stock returns.
However, not so many research conduct the empirical research to investigate their
behaviors because of the lankness of dataset. This paper, by using the unique dataset
which contains all daily buy and sell information in each broker, I explore the applications of multivariate vector autoregression (MVAR) models in constructing thefinancial networks of stock market. In the spirit of Granger causality, the proposed
methodology provides a direct way with statistical significance and economic meaning to describe the mutual interconnectedness of brokers. A financial network I analyzed illustrates as the structure properties for the underlying interactions among
institutional investors.
Key words: Financial Network; Vector Autoregression Model; Multivariate Time
Series Analysis.
JEL classification: C3; G2

1. Introduction
Networks have long appeared in almost every aspect of science and technology.
Researchers in economics, sociology, physics and computer science 1 have developed theoretical models for extracting the insights from networks and haveproposed many practical applications based on their empirical studies. The
PageRank algorithm of Google is an example. However, the impact on market quality of investors’ trading behaviors within a financial network remains
less developed. Hence, the purpose of this paper is to study the underlying
interactions among brokers in order to investigate the relationship between
investors’ trading profits and the brokers’ financial network.
1

For economics, more detail can be found in Schweitzer, Fagiolo, Sornette, VegaRedondo, Vespignani, and White (2009); For sociology, more details can be foundin Wasserman (1994); For physics and computer science, more details can be foundin Easley and Kleinberg (2010).

1

To construct a financial network, it is necessary to define the node (vertex) and link (edge). In this study, I analyze the dynamic interactions among
brokers, therefore, it is natural to represent the brokers as the nodes. As such,the definition of links would be problematic since the definitions of links infinancial network literature usually describes the links from the trading motives for each pair of investors. That is, if two investors trade the same stockin the same direction (buy or sell) in a short time period, the two investors aretreated as being connected. However, this definition is not applicable to thisstudy because a broker can be represented as a group of investors. In this case,
it is much easier to link a pair of brokers if they trade the same stocks, than
it is to compare a pair of investors. Comparing the brokers usually results ina fully connected financial network. In other words, the financial network is acomplete graph 2 .
Hence, I propose to use a statistical methodology to counter this problem–
instead of defining the links by using the trading motives, such that the definition of links can catch up to the trading behaviors of the brokers. The principle
is that if we consider the portfolio holdings of one broker during a period oftime and denote it by ~v1 . If ~v1 is Granger caused by other brokers’ portfolio
holdings, say ~v2 , ..., ~vk where k ≤ N (N is the total number of brokers) ina multivariate time series sense, then brokers v2 , ..., vk are going to connect
with v1 . Based on this principle, I adopt the multivariate vector autoregression (MVAR) models in constructing the brokers’ financial network to find theGranger causality among the brokers’ portfolio holdings. In fact, the proposed
methodology works not only for the brokers’ financial network, but also for
those networks with a sparse trading matrix.
The first contribution of this paper is the discovery that the links are
directional and the interconnectedness is a system-wide concept. The measurement of interconnectedness concerns the multivariate time series relationships which reflect a generous structure financial network, not only a pairwise
mutual connection, as in Billo, Getmansky, Lo, and Pelizzon (2012). The directional linkage is considered because the brokers trading network in which also
contains the institutional investors trading behaviors in the market. Usually,
these institutional investors are more informative than other individual investors. Their past trading information can affect the institutional/individual
investors in other broker firms. It is necessary to identify who are leaders
and who are followers in the market. Moreover, MVAR models can not only
implement the principle and measure the daily time-varying interconnectedness among brokers, but also can implement the Granger-Causality test to
determine the magnitude of interconnectedness.

2

A complete graph is a simple undirected graph in which every pair of distinct
vertices is connected by a unique edge.

2

The second contribution of this study is the unique dataset I have collectedfrom the Taiwan Stock Exchange (TSE), which consists of all brokers’ daily
trading information on all trading days from November 6, 2001 to March
2, 2011. There are a total 95 brokers and 1,330 stocks being traded during
the sample period. The dataset contains order types (buy or sell), daily total
trading amounts, and average prices for stocks that are traded by each broker.
The financial network analysis is based on brokers’ data instead of accountlevel data, because most stock market investors are illiquidity traders. Tracking
their trading behaviors would become confusing and possibly be irrelevant toconstructing a financial network. Even worse, it could result in an estimation
bias. 3 In this paper, I show that analyzing the brokers’ financial network could
prevent this issue.
Finally, my empirical findings provide substantial support for a positive
relationship between investors’ gains and losses and brokers’ financial network
centrality. When a broker has more connections with other brokers, whichmeans the lagging investors are more central in the network, these investors
are more profitable in the market. This is also shown in the conjecture of thetheoretical model in Walden (2013). This empirical finding can also be supported by recent studies on the effect of social networks on decisions madeby investors, which indicate that the central investors in the network tend
to access more information and trade earlier in the right direction than the
peripheral investors. In my regression analysis, I find that one standard deviation increase in rescaled centrality of a group of investors leads to a 0.1 to
2.7% increase in returns over the short-term. For the long-term, there is a 0.1
to 2.0% increase in returns .
The remainder of the paper is organized as follows: Related literature
review is in Section 2. Section 3 describes the details of the data and mymethodology to construct the Granger-Causality network. Section 4 illustrates
my main empirical results. Section 5 concludes the paper.
2. Related Literature
My study follows up on mainstream interests in investigating the equilibrium
analysis of information diffusion within a population of investors. For example,
Shiller and Pound (1989) survey 131 NYSE investors and ask what prompted
their initial interest in their most recent stock purchase or sale. The survey
reveals that for the majority of investors, discussion with peers prompted theaction. Ivkovi and Weisbenner (2007) find similar empirical evidence for households. Hong, Kubik, and Stein (2005) document that mutual fund managers
in a given city tend to have trading behavior that correlate more strongly
with other managers in the same city, as opposed to with managers in dif3

As shown in Gomez-Rodriguez, Leskovec, and Krause (2012), the exact maximum
likelihood estimation is not feasible for large networks.

3

ferent cities. Cohen, Frazzini and Malloy (2008, 2010) demonstrate that past
educational connections facilitate information transmission from managers tosecurity analysts, and examine educational connections between mutual fundmanagers and corporate board members to identify information transfer via
social networks. Ozsoylev, Walden, Yavuz, and Bildik (2013) study the trading behavior of investors by using an account-level dataset of all trades on the
Istanbul Stock Exchange in 2005. They find the central investors earn higher
returns and trade earlier than peripheral investors with respect to information events. Walden (2013) introduces a dynamic noisy rational expectations
model to explore agents’ trading behavior and finds that agents who are moreclosely connected will have more period-by-period trades. Their profits canbe determined by the measure of centrality of the network. Han and Yang
(2013) also analyze a rational expectations equilibrium model to explore theimplications of information networks for the financial market.
This study also links to other financial network literature which focuses on
the allocation purpose of investors. The main concept is that the two nodes ina financial network can be connected because they implement similar investing strategies and thus hold the same financial assets in their portfolios. For
example, Ibragimov, Jaffee, and Walden (2011) show that the recent financial
crisis has revealed significant externalities and systemic risks arising from theinterconnectedness of financial intermediaries’ risk portfolios. Negative externalities arise because of intermediaries’ actions taken to diversify their risks.
Billo, Getmansky, Lo, and Pelizzon (2012) propose econometric measures toinvestigate the monthly returns of the 25 largest companies in the four sectors(hedge funds, banks, broker/dealers, and insurance) in the U.S. stock market.
They find that all four sectors have become highly interrelated over the past
decade, likely increasing the level of systemic risk in the financial and insurance industries through a complex network of relationships. The two nodes are
more likely to share information and implement similar investing strategies sothat they can also hold the same financial assets and diversify their risk in themarket.
Haldane (2013) argues that financial innovation, in the form of structured
products, increases further network dimensionality, complexity, and uncertainty. Certain financial instruments, including RMBS, ABS, CDO, and CDS,
have created a series of gross claims among financial entities which far exceed
their capital bases. For example, Lehman had gross CDS exposure approximately eight times its balance sheet in August 2007. This occurred because
financial innovation in the form of structured credit also had the consequenceof creating a network structure, which was non-hierarchical. Financial engineers created products in which elements of a loan portfolio were reassigned
to a higher order subassembly. Thus, an automatic dependence was createdamong almost every substructure.
4

The financial network analysis is not only used in examining the stock
market, but also in other financial assets markets. Allen and Gale (2000)
studied how the banking system responds to contagion when banks are connected under different network structures. Their study showed that incomplete
networks are more prone to contagion than complete ones. Better connected
networks are more resilient because the proportion of losses in one bank’s
portfolio is distributed among more banks via interbank agreements. May,
Levin, and Sugihara (2008) discuss the similarities in analyzing financial networks and ecosystems, especially as regards their vulnerabilities. The system
includes over 8,000 banks, but 75% of the value is distributed among 66 banks.
Flows between large money center banks are seen as links with higher weights.
3. Data and Methodology
Taiwan Stock Market
The dataset for my empirical study is collected from the TSE, whichis the world’s 12th largest financial market. During my sample period, themarket operated from 9:00 AM to 1:30 PM. Buy and sell orders interacted todetermine the executed price, subject to applicable auto-matching rules, every
90 seconds. Orders were executed in strict price and time priority. A daily pricelimit of 7% held in each direction and a trade-by-trade intraday price limit of
two ticks from the previous trade price was in effect. The commission fee for
TSE was 0.1425% of the trading value and there was a transaction tax on stock
sales of 0.3%. Capital gains were not taxed, whereas cash dividends were taxed
at ordinary income tax rates for domestic investors and at 20% for foreign
investors. Corporate income was taxed at a maximum rate of 25%, whereas
personal income was taxed at a maximum rate of 40%. The accumulated
investor account number at securities companies was approximately 16 million
in 2011, almost 76% of the total population.
Brokers’ Daily Trading Information
Instead of using account-level data, I use all daily trading information of
brokers from November 6, 2001 to March 2, 2011 to carry out my empirical
study covering the financial crisis in 2007. My reason for using the brokers’
trading data set is that the majority of investors in a market trade infrequently. Tracking infrequent investors’ trading behavior and identifying theirmutual interactions could easily create distraction and would be irrelevant toa study of investors’ trading behavior via networks. Most important, without
this irrelevant information, my analysis of the size of the brokers’ financial network will be more stable over time. The sample used records order types (buyor sell), trading total amounts, and average prices for stocks traded by eachbroker every day. Therefore, I can investigate the trading behavior of groups
of investors within a financial network in a market. Further, these brokers can5be categorized into these finance types: Banking (13 brokers), Bills FinanceCorporations (1 broker), Specialized Brokerage Firms (32 brokers), Integrated
Securities Firms (31 brokers), and Foreign Financial Institutions (18 brokers).
During the sample period, a total of 95 brokers and 1,330 stocks had complete trading information. The average trading amount of these brokers isapproximately 97% of the entire market’s total daily trading amount.
Short- and Long-term Trading Gains and Losses
Based on the unique dataset, the first step of my analysis is to calculate
each broker’s daily buy and sell portfolios to mimic a group of investors’
net daily purchases and sales over a period of time. I use a method similar
to Barber, Lee, Liu, and Odean (2009), but focus on brokers’ trades overthe short- and long-term in order to evaluate groups of investors’ trading
gains and losses, which are denoted by the vectors Gt = (g1,t , ..., gn,t )0 and
Lt = (`1,t , ..., `n,t )0 at time t respectively. For example, consider one of thebrokers “Yuanta Securities.” On March 29, 2002, it buys 900 shares of HTC
and sells 700 shares. It makes 200 net shares of HTC, adding to the buy
portfolio, whereas no HTC shares are added to the sell portfolio. The purchaseprice is then recorded as the total value of buying 900 shares minus the total
value of selling 700 shares divided by the net shares of 200. Moreover, I consider
the shares being included in the mimicking portfolios for a fixed horizon, z,
where the short-term period is z = 5 (one week) and the long-term period isz = 20 (one month) trading days.
z
The volume-weighted (VW)-realized trading gains, gi,t, can be calculated

as:
z
gi,t
=

ni
X

#net shares of stock j purchased× rjt+1 ,
#net
total
sharespurchasedbybrokerij=1(1)where rjt+1 is the one-day return of the stock j after it was traded at timet and ni denotes the number of stocks that the broker i holds within z-days
holding period. An analogous calculation occurs for the VW-realized trading
losses, `zi,t , which are defined as`zi,t =

ni
X

#net shares of stock j sold× rjt+1 .
#net
total
sharessoldbybroker
i
j=1

(2)

z
The net profit, pzi,t is then defined as the difference between gi,tand `zi,t , thatis,z
− `zi,t .
(3)
pzi,t = gi,tIn the following study, I use the net profit time series data for brokers to
represent the profits of groups of investors to fit the MVAR models.
Multivariate Vector Autoregression (MVAR)
6

To construct the financial networks of 95 brokers, I use the MVAR models to empirically measure their mutual interconnectedness from a systemwide perspective so that the network structure can be inferred. The GrangerCausality test be used to investigate whether one time series can provide forecasting power to another, and determine the magnitude of interconnectedness
among these brokers. Hence, the interconnectedness I define can reflect both
statistical correlations and economic connections for the multivariate time series of groups of investors’ net profit. The definition of “link” in this study
is different from Ozsoylev, Walden, Yavuz, and Bildik (2013), who define theconnection between each pair of investors as if the two agents traded the same
stock in the same direction in a short-term period and also different from Pareek (2012), who defined it as two fund managers who allocate 5% or more of
their portfolio to the same stock being connected to each other.
MVAR model is defined as Yt = (y1t , ..., ynt )0 , t = 1, 2, ..., T, which denotes
a weak stationary multivariate time series of dimension n defined on a probability space (Ω, F, P). A p-th order vector autoregressive can be represented
in a simple form as
Yt = c +p
XΦk Yt−k + t ,

(4)

k=1

where c denotes an (n × 1) vector of constants and Φk denotes an (n × n)
matrix of autoregressive coefficients for k = 1, 2, ..., p. The t is a vector withΣ symmetric definite matrix. The stationary condition is satisfied if all rootsof |Φ(Z)| = 0 lie outside the unit circle.
For a large VAR model (n > 2), the Granger-Causality test can be used totest whether one variable is influenced by other variables in the model system.
Yt can be arranged and partitioned in subgroups Y1t and Y2t with dimensions
n1 and n2 (n = n1 + n2 ), respectively. VAR model can be represented as amatrix form:    
C1  Σ1 Φ11 (β) Φ12 (β) Y1t (5)  =   +  .
C2
Σ2
Φ21 (β) Φ22 (β) Y2t
The Wald statistic to test H0 : Cβ = c, where C is a s × (n2 p + n) matrix ofrank s and c is an s-dimensional vector can be obtained from√d0 −1
T (C β̂ − c)[C(Γ̂−1− χ2 (s).
(6)
p ⊗ Σ)C ] (C β̂ − c) →In this study, I set the significance level of Wald test as 1%, i.e., α = 0.01.
Granger-Causality Network
Based on the MVAR model, the financial network I construct followsa
concept similar to the Grange-Causality graph in Eichler (2007), and I denote
it as a “Granger-Causality” network. I define a network G = (N, E), where7

N is a set of elements called nodes (N = 95 in this study) and E is a set of
directed edges which belong to the class{j → i|i, j ∈ V, i 6= j} ∈/ E ⇔ Φij (k) = 0 ∀k,(7)where Φ is the autoregressive coefficients matrix in Equation (4). A financial
network can be represented as an adjacency matrix A ∈ {0, 1}N ×N , with

Aij =



 1 if broker j is directly linked to i,(8) 0 otherwise.

Moreover, I assume that a broker is connected with himself; that is, Aii = 1
for all i. This class represents the directed edges corresponding to direct causal
relations among the components of Yt which can be identified by the Granger
Causality test as shown in Equation (6). For simplicity, I consider the case of
k = 1 and use a 180-day rolling window to estimate Φ in Equation (4).
An Illustration
As an example, if I take the following four-dimensional VAR(1) process,with Equation (4):Yt = ΦYt−1 + t
(9)with statistically significant parametersΦ11 0 Φ13 0  0 Φ22 0 Φ24 
.
Φ=



Φ
 31 0 Φ33 0 



0

(10)

0 Φ43 Φ44

Therefore, the adjacency matrix A of Equation (8) can be represented as1 0 1 00 1 0 1

.
A=

1 0 1 0





(11)

0011

Based on the above adjacency matrix, the autoregressive structure can bevisualized by the associated path diagram shown in Figure 1.
<Insert Figure 1 here>
Eigenvector Centrality
8

Once the network is constructed, to measure the relative importancewithin a network of a node, I calculate its centrality. Following the analysis of Ozsoylev, Walden, Yavuz, and Bildik (2013), I adopt the eigenvector
centrality which is defined as:
xi =

1X
1 X
xj =
Aij xj ,λ j∈M (i)
λ j∈G

(12)

where M (i) is a set of the neighbors of i and λ is a constant and Aij is definedin Equation (8).
Eigenvectors of adjacency matrices are useful as measures of centrality orof status. However, they are misapplied to asymmetric networks in which somepositions are unchosen (see Bonacich and Lloyd (2001)) and there will be manydifferent eigenvalues λ for which an eigenvector solution exists (see Spizzirri(2011)). The additional requirement that all the entries in the eigenvector bepositive, implies (by the Perron-Frobenius theorem) that only the greatest
eigenvalue results in the desired centrality measure. The i-th component of
the related eigenvector then gives the centrality score of the vertex i in the
network. Power iteration is one of many eigenvalue algorithms that may be
used to find this dominant eigenvector. I also use a more robust measure,rescaled centrality, to capture the information advantage than pure centrality
in an empirically estimated investor network. The rescaled centrality of node
i is as follows:
Centralityi(13)
In Degreei + Out Degreei
where In Degreei measures how many links from other nodes to i and Out Degreei
measures how many links from i to other nodes.
4. Empirical Results
Power Law Distribution
The distribution of centrality is intimately related to asset pricing dynamics, and therefore may be informative about the aggregate behavior of a stock
market as stated in Gabaix, Gopikrishnan, Plerou, and Stanley (2003). Oneof aggregate behaviors is that the degree distribution follows a power law inthe form ofP(X > x) ∼ x−α(14)
in the tail of the distribution. This is also called preferential attachment ofinvestors. In examining the phenomenon, I plot the centrality distribution ofa different z in Figure 2.
<Insert Figure 2 here>
In Figure 2, the black line is for z = 5 and the red dashed line is for z = 20.
9I find that the network centrality is followed by the power law distribution.
Trading Profits v.s. Financial Networks
The summary statistics and the main empirical results are represented inTable 1 and Table 2. Table 1 and Table 2 show short-term trading behavior(z = 5) and long-term trading behavior (z = 20) of groups of investors,
respectively. In both, I report the VW-realized trading gains, VW-realized
trading losses and net profits from all trades under the five types of brokers.
I also illustrate their centralities and rescaled centralities.
<Insert Table 1 here>
Table 1 illustrates the short-term trading behavior of groups of investors.
For the rescaled centrality, Table 1 shows the investors belonging to the broker
category Bankers are most connected with others, while investors belonging to
the broker category Financial Corporations are the least connected. Investors
trading in the broker category Integrated Securities firms are the most profitable, with a mean net profit of 2.4% during a one week period, while the investors trading in category Bills Finance Corporations are the least profitablewith a mean net profit of -1.7%. Table 1 also indicates that the VW-realized
trading losses are positively correlated to the rescaled centrality. When therescaled centralities increase, the VW-realized trading losses increase as well.
<Insert Table 2 here>
Table 2 illustrates the relationships of long-term trading behavior amonggroups of investor. For the rescaled centrality, Table 2 shows the investors
belonging to the broker category Integrated Securities Firms are the mostconnected with others, whereas the investors belonging to the broker category
Bills Finance Corporations are the least connected. Investors trading in the
category Integrated Securities Firms are the most profitable, with a mean net
profit of 1.0%, while investors trading in the category Specialized BrokerageFirms are the least profitable with mean net profit of -0.6%. Table 2 also showsthat the VW-realized trading gains are positively correlated to the rescaled
centralities. When the rescaled centralities increase, the VW-realized trading
gains also increase. We argue that the rescaled centralities of brokers canaffect the investors trading gains and losses could because one possibility isthat these brokerage firms provide better research reports to their clients, theresearch they provide could be correlated, which affect their client’s trades.
Regression Analysis
I further investigate the relationship between the rescaled centrality and10net profit via regression analysis. The models arec= αc + β c RCT RALci,t + i,t ,N P ROFi,t(15)cwhere c denotes the three levels profitability: low, medium, and high. N P ROFi,tcand RCT RALi,t indicate net profit and rescaled centralities for a group of investors in different categories. The regression results are shown in Table 3 andTable 4.

<Insert Table 3 here>
Table 3 is for z = 5. In Table 3, we can find that rescaled centrality
is important in determining the net profit of a group of investors. Rescaled
centrality can explain the high profitability of investors in the Integrated Securities Firms. We see one-standard deviation in the increase in the rescaled
centrality of the high profitability of investors belonging to the category Integrated Securities Firms, leading to a 14.3% in return. For brokers in Bills
Finance Corporations and Banking, rescaled centrality is also important indetermining profitability of investors. I find a one-standard deviation increase
in rescaled centrality of low profitability for investors belonging to Bills Finance Corporations and Banking, leading to 276.9% and 81.1% in returns,
respectively.
<Insert Table 4 here>
The regression results in Table 4 are for z = 20. Rescaled centrality can explain
the high-level profitability of investors belonging to category Foreign Financial
Institutions. We find one-standard deviation increase in rescaled centrality forthe high profitability of investors belonging to the category Foreign Financial Institutions, leading to 18.3% in return. In addition, we see one-standard
deviation increase in rescaled centrality of medium profitability for investors
belonging to the category Bills Finance Corporations and Specialized Brokerage Firms, leading to 206.8% and 22.8% in returns, respectively. In sum,
rescaled centrality can explain investors’ profitability.
5. Conclusions
Investors trading behaviors are more complicated than they appear. Therefore, the mechanisms needed in order to form links in a population in the market within a financial network structure are not readily apparent. In this study,
I use the multivariate time series models and perform a statistical test to directly identify the links. According to the property of the dynamic similarities
in portfolio holdings among a group of investors, I construct the GrangerCausality network to measure their relative importance within a brokers’ financial network. My empirical results show the net profitability of groups ofinvestors are positively correlated to their relative importance in the brokers’
11financial network.
My findings provide another viewpoint from which to study the trading
behaviors of investors from the perspective of brokers’ financial networks. The
results demonstrate the existence of empirical evidence to support the hypothesis of information diffusion via investors’ social networks which can affect their trading behaviors. Understanding the mechanism for forming links
among investors will be useful in future study. It is also interesting to apply
the network analysis to different financial assets.

12References
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14

Figure 1: An Illustration of Granger-Causality Network
The figure illustrates an example of Grange-Causality network according to the four-dimensional VAR(1) model with the adjacency matrix shown in Equation (11).

15

Figure 2: Preference Attachment Examination
The figure plots the centrality distribution of brokers’ financial network to examine the preference attachment theory as shown in Equation (14). The black line is for z = 5 and thered dashed line is for z = 20.

16

Table 1: Summary Statistics (z=5)
The table reports the summary statistics of z=5 for five types of brokers. “Std” and “VW” mean standard deviation and volume-weighted, respectively.

z=5

Statistics

VW realized gain

VW realized loss

Net profit

Centrality

Rescaled Centrality

I. Foreign Financial
Institutions(N=20750)

Mean
Std
Skewness
Kurtosis

0.066
1.588
-0.157
2.070

0.068
1.599
-0.1702.023-0.002
0.703
0.069
2.807

0.091
0.061
0.885
0.721

0.674
0.455
0.963
1.025

II. Integrated
Securities Firms(N=56025)

Mean
Std
Skewness
Kurtosis

0.087
1.643
-0.426
1.936

0.064
1.645
-0.445
1.950

0.024
0.411
0.094
8.951

0.090
0.061
1.140
2.142

0.668
0.458
1.216
2.510

III. Specialized
Brokerage Firms(N=66400)

Mean
Std
Skewness
Kurtosis

0.057
1.708
-0.428
1.840

0.065
1.697
-0.4531.862-0.0090.424-0.025
9.462

0.090
0.063
1.166
2.176

0.672
0.480
1.232
2.445

IV. Bills FinanceCorporations(N=2075)

Mean
Std
Skewness
Kurtosis

0.037
1.772
-0.432
1.597

0.054
1.766
-0.3981.620-0.0170.594-0.362
3.876

0.085
0.061
0.822
0.392

0.635
0.467
1.020
1.213

V. Banking(N=24900)

Mean
Std
Skewness
Kurtosis

0.064
1.638
-0.415
1.974

0.070
1.645
-0.4272.008-0.0060.458-0.120
5.261

0.096
0.065
1.273
3.056

0.711
0.486
1.259
2.835

17

Table 2: Summary Statistics (z=20)
The table reports the summary statistics of z=20 for five types of brokers. “Std” and “VW” mean standard deviation and volume-weighted, respectively.

z=20

Statistics

VW realized gain

VW realized loss

Net profit

Centrality

Rescaled Centrality

I. Foreign Financial
Institutions(N=20750)

Mean
Std
Skewness
Kurtosis

0.059
1.559
-0.192
2.249

0.062
1.558
-0.1742.142-0.003
0.424
0.003
3.128

0.089
0.067
1.202
1.965

0.663
0.500
1.261
2.287

II. Integrated
Securities Firms(N=56025)

Mean
Std
Skewness
Kurtosis

0.069
1.625
-0.444
2.066

0.059
1.626
-0.461
2.103

0.010
0.247
-0.02315.272

0.090
0.071
1.495
3.533

0.667
0.530
1.489
3.314

III. Specialized
Brokerage Firms(N=66400)

Mean
Std
Skewness
Kurtosis

0.053
1.680
-0.450
2.004

0.060
1.672
-0.4732.038-0.0060.214
0.034
11.417

0.085
0.065
1.189
1.954

0.632
0.489
1.228
2.100

IV. Bills FinanceCorporations(N=2075)

Mean
Std
Skewness
Kurtosis

0.037
1.729
-0.455
1.800

0.042
1.733
-0.4211.803-0.0050.287-0.122
4.546

0.078
0.064
1.035
0.573

0.584
0.494
1.155
1.000

V. Banking(N=24900)

Mean
Std Deviation
Skewness
Kurtosis

0.060
1.617
-0.428
2.136

0.062
1.625
-0.4502.144-0.0020.286
0.069
15.152

0.085
0.070
1.778
5.729

0.632
0.528
1.829
5.955

18

Table 3: Short-Term Profitability of Investors and Rescaled Centrality of Brokers
The table reports regression results of Equation (15) under three-level profitability of low, middle, and high for five types of brokers for z=5. It investigates the relationship between therescaled centrality and net profit via regression analysis. The regression models are
NPROFc = αc + βc RCTRALc+ε
where c denotes the three level profitability of low, medium and high. NPROF and RCTRAL indicate net profits and rescaled centralities for a group of investors in different types of brokers,
respectively. *, **, and *** are represented by the statistical significance of 0.1, 0.05, and 0.01. The standard errors are in parentheses.

z=5
I. Foreign Financial
Institutions

NPROF
Intercept
RCTRALIntercept
II. Integrated Securities Firms

RCTRALIntercept
III. Specialized Brokerage
Firms

RCTRALIntercept
IV. Bills Finance Corporations

RCTRALIntercept
V. Banking

RCTRAL

Low

MiddleHigh

0.000(0.018)0.232(0.506)-0.001(0.048)0.060(0.581)-0.011(0.031)-0.041(0.186)0.005(0.017)0.219(0.205)0.003(0.010)0.143(0.061)0.008(0.016)-0.229(0.197)-0.010(0.010)0.048(0.057)-0.116(0.120)1.227(1.457)-0.100(0.082)0.598(0.504)0.007(0.029)-0.057(0.347)-0.023(0.016)0.079(0.092)0.027(0.006)-0.116(0.181)***-0.019(0.006)0.168(0.164)***-0.107(0.044)2.769(1.270)**-0.037(0.011)0.811(0.299)

***
***

19

**

Table 4: Long-Term Profitability of Investors and Rescaled Centrality of Brokers
The table reports regression results of Equation (15) under three-level profitability of low, middle, and high for five types of brokers for z=20. It investigates the relationship between
the rescaled centrality and net profit via regression analysis. The regression models are
NPROFc = αc + βc RCTRALc+ε
where c denotes the three level profitability of low, medium and high. NPROF and RCTRAL indicate net profits and rescaled centralities for a group of investors in different types of brokers,
respectively. *, **, and *** are represented by the statistical significance of 0.1, 0.05, and 0.01. The standard errors are in parentheses.

z=20
I. Foreign Financial
Institutions

NPROF

Low

MiddleHighIntercept-0.009(0.010)0.254(0.353)0.000(0.026)-0.094(0.338)-0.030(0.015)0.183(0.088)0.009(0.005)0.000(0.028)RCTRALIntercept
II. Integrated Securities
Firms

RCTRALIntercept
III. Specialized Brokerage
Firms

RCTRALIntercept
IV. Bills FinanceCorporations

RCTRALIntercept
V. Banking

RCTRAL

0.013(0.003)-0.163(0.122)***0.010(0.009)0.038(0.116)-0.006(0.003)-0.051(0.092)**-0.023(0.007)0.228(0.095)0.001(0.017)0.217(0.608)-0.165(0.059)2.068(0.784)-0.003(0.005)-0.087(0.187)0.024(0.016)-0.294(0.211)

20

***
**

***

-0.006(0.005)0.004(0.027)0.049(0.040)-0.354(0.237)-0.010(0.009)0.037(0.050)****