The 5th International Conference on Behavioral, Economic,
and Socio-Cultural Computing (BESC 2018)
http://besc-conf.org/2018/

Effect of Increasing Horizontal
Shareholding with Index Funds
on Competition and Market Prices
Investigation by Agent-Based Model
Takanobu Mizuta

SPARX Asset Management Co., Ltd.
Mail: mizutata[at]gmail.com
HP: http://mizutatakanobu.com

Note that the opinions contained herein are solely those of the authors anddo not necessarily reflect those of SPARX Asset Management Co., Ltd. andNomura Research Institute, Ltd.

You can download this presentation material fromhttp://mizutatakanobu.com/201811.pdf

1Table of Contents of Today’s Talk

(1) Introduction(2) Artificial Market Model(3) Simulation Results(4) Conclusion

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2

(1) Introduction(2) Artificial Market Model(3) Simulation Results(4) Conclusion

You can download this presentation material fromhttp://mizutatakanobu.com/201811.pdf

3Competition among Companies held by Different Investors
Investor A
Holding only
Com. 1A

B

Earn
from Dividends
Rising Stock Price

Encourage
Competition

Company 1
Make & supply

Low Price
High Quality
More
consumers

WIN

Lose
by No Dividends
Droping Stock Price

Encourage
Competition

Competition

Company 2

Price, Quality
Some
Industry
Consumer can choose
better Goods/Service

LOSE
So So Price
So So Quality
Less
consumers

Price/Quality Competition by Separated Companies
Benefits to Consumers

4Competition among Companies held by SAME ONE Investors (All Shares)
Perfect Horizontal Holdings
Always lose by looser company
C-> No Motivation to Encourage
from Dividends
Earn
Rising Stock PriceNO
Encouragement
Company 1
Make & supply

High Price
Low Quality
Consumers

When Comp.1 win,Comp.2 loose.
-> C does not earn
Investor C lose
from looser Comp.

NO Competition Company 2
Maintain High Price
Practically Monopoly

Might leads more earnings for Inv. C

Some Industry
Consumers
消費者には
have
NO Choice
逃げ場がないHigh Price
Low Quality

By anti-trust (anti-Monopoly) act

Prohibited Perfect Horizontal Holdings due to disadvantage consumers
It has long been considered that there is NOT practically monopoly
among Listed Companies (held by diversified shareholders)5Heavily Increasing INDEX FUNDS

From [Fichtner 17]

Index Funds are managed a return becomes same as a market index, e.g., the Dow Jones industrial averageIndex Funds horizontally shareholding all companies in Index

Index Funds
4 trillion US$
Only in USA

Most of 4 trillion US$, BIG3(Index Funds management company) managing
This means only 3 fund manager groups exists

6

Therefore, most companies held by same shareholders
From [Fichtner 17]

BIG3 constitute the largest shareholder with 40% of all listed US companies
7
BIG3 hold 15% of all shares of all companies

Many Empirical Studies

BIG3

Show existing Practically Monopoly
by horizontal shareholdings?????

Funds are limited holding only
one company for one industry?
[Elhauge 16]
lessening of hiring competition-> economic inequality?
[Elhauge 16]

Many private engagements
Pressure maintaining Price? [Fichtner 17]
Existing Silent Pressure? [Elhauge 16]

Company 1

Hypothesis of[Piketty 13]
is wrong?

Company 2

Most important study

Airline ticket prices are
3-7% higher? [Azar 14]
due to horizontal shareholding,compared with a counterfactual
world in which companies are
separately owned.

US Airline Ind.
No rising wage,
Rising commodity Price?
[Elhauge 16]

Already, Violate Anti-Monopoly act？[Elhauge 16]

However, there are many arguments against,
so no conclusion has been reached yet.

8Positive Feedback Process in horizontal shareholding

Decisionto Trade
Stock
Changing
Market
Price

leads

This System includes

Changing
intrinsic value ofcompanies(fundamental
value)

Positive
Feedback
Process

Changing
Shareholder
Composition

Changing
Business
Strategy

The Positive Feedback Process makes the System heavily Complex

Horizontal Shareholding induces Heavily Complex System 9

Difficulty of Empirical Study
Difficulty of Empirical Study such discussion on the mechanism between the micro-macro
feedback of certain types of investors is very difficult
 cannot be conducted to investigate situations that havenever occurred in actual financial markets, such as ones inwhich passive investors are more than present cannot be conducted to isolate the direct effect of changing
the distribution of investor types on price formation because
so many factors cause price formation in actual markets

Therefore, in this study,
I implemented a competition model, in which horizontal
shareholding changes the business strategy of companies andlessens competition among companies, into the artificial market
model of [Mizuta and Horie 2018].
I investigated the effect of increasing horizontal shareholding withindex funds on competition and market prices

10Artificial Market Simulation (Agent-Based Model)
Virtual and Artificial financial Market built on Computers
ModelsIncludeAgents (Artificial Investors)＋
Price Mechanism (Artificial Exchange)
Order

Price
Mechanism(Exchange)

Agent(Investor) Each Agent determines
an order by some rules,
Price Mechanism gather
agents orders anddetermines Market Price
Determination market priceComplete Computer Simulation needing NO Empirical Data can discuss on the mechanism between the micro-macro feedback can be conducted to investigate situations that have neveroccurred in actual financial markets
 can be conducted to isolate the direct effect of changing the11
distribution of investor types on price formation

Previous Contributions of Artificial Market Simulations
Many studies have investigated the effects ofseveral changing financial regulations andrules by using artificial market,
Reduction of Tick Size, Up-Tick Rule,
Price Variation Limit, Dark Pool, Frequently Batch Auction,
Contribution of HFTs for share competition among Exchanges,
Suitable Latency of Exchange System, VaR Shock,
Chain Bankruptcy of Banks,
Regulations and Rules to prevent Financial Crush Mizuta (2016) A Brief Review of Recent Artificial Market Simulation
Studies for Financial Market Regulations And/Or Rules, SSRN Working
Paper Series http://ssrn.com/abstract=2710495

12

NATURE/SCIENCE articles argued Importance of Simulations
 Farmer and Foley (2009) NATURE, Vol. 460, No. 7256, pp. 685-686.
https://www.nature.com/articles/460685a
In today’s high-tech age, one naturally assumes that US President Barack Obama’s
economic team and its international counterparts are using sophisticatedquantitative computer models to guide us out of the current economic crisis. They
are not. There is a better way: agent-based models.
 Battiston et al. (2016) SCIENCE, Vol. 351, Issue 6275, pp. 818-819.
http://science.sciencemag.org/content/351/6275/818
Traditional economic theory could not explain, much less predict, the near collapseof the financial system and its long-lasting effects on the global economy. Since the2008 crisis, there has been increasing interest in using ideas from complexity
theory to make sense of economic and financial markets.

Traditional economic theory could not explain, muchless predict, the near collapse of the financial system
Agent-Based Model is needed13

Practical Persons have began to use Agent-Based Modelto solve Urgent Real Problem
Regulators, Central Bankers, Stock Exchanges
JPX Working Papers Series
JPX(Tokyo Stock Exchange) shows Working Papers,
6 papers of all 23 are Agent-Based Studies
Reduction of Tick Size, Frequently Batch Auction,
Suitable Latency of Exchange System, and so on
https://www.jpx.co.jp/english/corporate/research-study/working-paper/

So many Examples,Working Paper by Bank of Japan
Toshiyuki Sakiyama and Tetsuya Yamada Market Liquidity and Systemic Risk in Government Bond
Markets: A Network Analysis and Agent-Based Model Approach
http://www.imes.boj.or.jp/research/abstracts/english/16-E-13.html
Project by EU
Integrated Macro-Financial Modelling for Robust Policy Design Work Package 7: Bridging agent-based
and dynamic-stochastic-general-equilibrium modelling approaches for building policy-focused macrofinancial models http://www.macfinrobods.eu/research/workpackages/WP7/wp7.html

14

(1) Introduction(2) Artificial Market Model(3) Simulation Results(4) Conclusion

You can download this presentation material fromhttp://mizutatakanobu.com/201811.pdf

15

Model of this study
model of [Mizuta and Horie 2018]
succeeded to model agents who trade infrequently
on the basis of the fundamental value
They constructed an artificial market model that is assimple as possible having these characteristics
The simplicity of the model is very important for this study because
unnecessarily replicating macro phenomena leads to models that areover-fitted and too complex.

The agent feature is same as Active funds encouraging
Companies Competition in Real Financial Market

Therefore, in this study
I implemented a competition model among 2 companies, inwhich horizontal shareholding changes the business strategy ofcompanies and lessens competition among companies, into theartificial market model of [Mizuta and Horie 2018].

16

Price Determination Model
100

Call Market (Batch Auction)

We employed

Supply Curve
Cumulative number of
Shares that sellers want
to sell over this price

Price

80
60 Market Price40
200

BUY (Bid)(Trade Price)

SELL (Ask)
Trading
Volume050
100
Cumulative number of Shares

Demand Curve
Cumulative number of
Shares that buyers wantto buy under this priceIn a call market, buy and sell orders are grouped together and then executedat specific times (rather than executed one by one continuously).
We determine Market Price and Trading Volume at the crossing point of supply
and demand curves.

17Our Agent Model: Common Setting for every Agent Types

Initial Holdings of Agents Determining Buy/Sell
One share or Cash 10,000 Holding One Share stock: SELL
← Half and Half of all agents
Holding no stock: BUY(Initial Market price=10,000)

Always place a BUY order
Holding NO Stock(No more than 2 shares, no negative no.)Always place a SELL order
Holding ONE STOCK

Matching
Buy/Sell
OrdersThe number of shares and buy or sell of orders are determined notdepending on Agent Types. Agent Types only differ in terms of how
an order price is determined. We can focus difference from the ways
determining order prices.

18

Our Agent Model: Three Agent Types
Agent Types only differ an Order Price
Noise Agents
Around Market Price Randomly

Technical Agents
Referring only Historical market prices
Corresponding

Fundamental
AgentsActive & Index Funds
In real financial market

They trade very infrequently thannoise and technical investors
Explain Details of Three Agent Types in Following some Slides

19

Noise Agents

Number of Agents = 1,000
𝑃𝑜 : Order Price
𝑃𝑡 : Market Price𝜂 : Constant (=10%)
𝜎𝑡,𝑗 : random variables

Order Price

𝑃𝑜,𝑗 = 𝑃𝑡 exp(𝜂𝜎𝑡,𝑗 )
Order
Price

Marke
t
Price

that follow a standard
normal distribution

𝑡: timej: Agent no.

They order around Market Price Randomly.
In this study, we handle a stock traded at a high enough volume.
We introduce noise agents to supply enough liquidity.
(Also, in real financial markets, there are such many liquidity suppliers)

20

Number of Agents = 100
Technical Agents
employ Momentum Strategy
𝑡𝑚𝑗 : reference term

Order Price

𝑃𝑜 = 𝑃𝑡
MarketPricegiven by random(1～100)for each agent

𝑃𝑡
𝑃𝑡−𝑡𝑚𝑗Order
Price
Momentum
Strategy

Expect continuing
historical return

Determine Order price Referring only historical market pricePrevious studies showed that such technical agents are needed toreplicate price formations observed in real financial markets

21

Number of Agents = 400

Fundamental Agents

𝑚𝑠 𝜇𝑗 : Margin of Safety
𝑚𝑠 = 10%
𝜇𝑗 : Uniform Random(0～1)±: when holding stock ”+”
when holding No stock ”-”

Order Price

𝑃𝑜 = 𝑃𝑓 exp 𝑑𝜎𝑗 ± 𝑚𝑠 𝜇𝑗
𝑃𝑓 = 10,000: Fundamental Price𝑑𝜎𝑗 : Difference estimatedfundamental price with true Pf
𝑑 = 10%, 𝜎𝑗 : SD Random

want to sell at a enough higher price thantheir estimated fundamental prices

MarketMargin ofPrice
SafetyEstimated
Fundamental
Price
Fundamental Price
They do not know TRUE Fundamental
Price but try to estimate

Holding ONE STOCK

Order
Price

Infrequent
TradesHolding NO STOCK

want to buy at a enough lower price thantheir estimated fundamental prices

Determine order prices by depending not on the market price,
but on the Estimated Fundamental Price with Enough Margin of Safety
22
which leads Infrequent Trades.

Competition Model

Previous empirical studies has showed no conclusion yet
Therefore, this Competition Model is strong assumption(for last 100 steps) No. of holders decides whether occur competition or not (by 100 steps)(Count for Only
Fundamental agents)

A Few Horizontal
Shareholdings Agents

Many Horizontal
Shareholdings Agents
Many agents
Holding both comp.

Fewer agents holding Both comp.
only comp. 2

Many
agentsHolding
onlyComp.1more
Encourage
Competition

NO
Encouragement

fewer
Encourage
Competition

Company 1(Stock 1) Occurring
Competition

Company 2(Stock 2)

WIN

LOSE

UP

Down

Fundamental Price
Fundamental Price
price change width is 2500

NO
Encouragement

Encourage
Competition

Company 1(Stock 1)

NO
Competition

Encourage
Competition

Company 2(Stock 2)

NO Change
Fundamental Price23

Index Agent Model
Initial Holdings of Fundamental AgentsSome of 100, NFP
ofNo.=100 100

Holdstock1

Index Agents never trade
hold horizontal both stock forever

100

Hold
both stocks

Company 1(Stock 1)

Holdstock2

100

No Holdings

Company 2(Stock 2)

Changing NFP, I investigated the effect of increasing horizontal
shareholding with index funds on competition and market prices

24

(1) Introduction(2) Artificial Market Model(3) Simulation Results(4) Conclusion

You can download this presentation material fromhttp://mizutatakanobu.com/201811.pdf

25

Verification of Model
Stylized Facts In the case of No. of Index agents = 100

standard deviation of returns
kurtosis of price returns（Fat-Tail）

1.25%
1.29

autocorrelation coefficient for square returns（Volatility-Clustering）
lag
1
0.22
2
0.03
3
-0.09

Our model replicated the statistical characteristics(Stylized Facts), fat-tails, and volatility-clustering,observed in real financial markets.

26

Time evolution of market prices & fundamental prices
In the case of No index agents (NFP=0)
Market Price of Stock 1

Market Price of Stock 2

Fundamental Price of Stock 1

Fundamental Price of Stock 2

14000
13000

Price

12000
11000

10000
9000
8000
7000

900

800

700

600

500

400

300

200

100

0

6000
Time

The fundamental prices changed many times, and competition occurred
frequently. Furthermore, the two companies won alternately.

A mechanism that balances competition powers among corporations

25.0%

22.5%

20.0%

17.5%

15.0%

12.5%

10.0%

7.5%

5.0%

2.5%

9
8
7
6
5
4
3
2
1
0

0.0%

Frequency of Competitions

Frequency of competitions for various No. of Index Agents

No. of Index Agents/
No. of All Fundamental Agents

When the ratio >12.5%, competition never occurred.
Even when the existing ratio of index funds is not that large,
the funds lessen competition.

28

Time evolution (expanding from t=100-110) of market price minus
fundamental price and No. of Agents Holding only a Stock
Market Price - Fundamental Price of Stock 1
Market Price - Fundamental Price of Stock 2
No. of Agents Holding only Stock 1
No. of Agents Holding only Stock 2(market price falls deeper
than the company value)

400

Market Price - Fundamental Price

3000
2500
2000
1500
1000
500
0
-500
-1000
-1500
-2000
-2500
-3000

Stock 2 Prices:103Orvershooted

300
250
200
150
100
50

109

108

107

106

105

104

103

102

101

100

0

No. of Separate Holding Agents

350

Stock 2-> Undervalued
No. of agents holding
only Stock2 Increases-> Stock(Company) 2 isEncouraged Competition

Time

Overshoot leads to Buy Looser company

29

Mechanism to balance competition powers
In the case of .. Company

In the case of .. Company

Loser

WinnerFundamental Price

Overshoot-> Overvalued

Sharply
Drop

MarketPrice

SharplyGrow

Buy ->Encourage
Competition
ActiveActiveFunds

Sell -> NO

Encouragement

Company loosecompetitive power-> Drop
Fundamental Price

Fund

Overshoot-> Undervalued

Company gains competitive power-> Increase Fundamental PriceThis mechanism balances competition powers among corporations
Growing index funds may possibly weaken this balancing mechanism
30

(1) Introduction(2) Artificial Market Model(3) Simulation Results(4) Conclusion

You can download this presentation material fromhttp://mizutatakanobu.com/201811.pdf

31

Conclusion
 In this study, I implemented a competition model, in whichhorizontal shareholding changes the business strategy ofcompanies and lessens competition among companies, in theartificial market model of [Mizuta and Horie 2018]. I investigatedthe effect of increasing horizontal shareholding with index funds
on competition and market prices.

 The result shows that even when the holding ratio of index funds
is not that much, the funds lessen competition.
 When the value of a company unsuccessful at competition drops,
its market price falls deeper than the company value(overshoots), and the company becomes undervalued; then, thenumber of shareholders who encourage competition increases,
and the company gains competitive power, vice versa.
 My simulation result indicated that such a mechanism balancescompetition powers among corporations. Growing index funds
may possibly weaken this balancing mechanism.

32That’s ALL, Thanks!!
Reference
Empirical Study for Horizontal Shareholdings
 [Azar 14] Azar, S. M. C., Jose and Tecu, I.: Anti-Competitive Effects of Common Ownership, SSRN
Working Paper Series (2014), https://ssrn.com/abstract=2427345
 [Elhauge 16] Elhauge, E.: Horizontal Shareholding, Harvard Law Review, Vol. 129, No. 5, p. 1267
(2016), https://harvardlawreview.org/?p=4185
 [Fichtner 17] Fichtner, J., Heemskerk, E. M., and GarciaBernardo, J.: Hidden power of the Big
Three? Passive index funds, re-concentration of corporate ownership, and new financial risk,
Business and Politics, Vol. 19, No. 2, p. 298326 (2017), https://doi.org/10.1017/bap.2017.6
 [Piketty 13] Piketty, T.: Le Capital au XXIe siècle, Éditions du Seuil (2013),
https://www.msz.co.jp/book/detail/07876.html
Artificial Market Model (Agent-Based Model)
 Mizuta (2016) A Brief Review of Recent Artificial Market Simulation Studies for Financial Market
Regulations And/Or Rules, SSRN Working Paper Series http://ssrn.com/abstract=2710495
 [Mizuta 18] Mizuta, T. and Horie, S.: Mechanism by which active funds make market efficientinvestigated with agent-based model, Evolutionary and Institutional Economics Review
https://doi.org/10.1007/s40844-018-0102-0
Full Text: https://rdcu.be/7mVh

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33

Appendix

You can download this presentation material fromhttp://mizutatakanobu.com/201811.pdf

34

What is a role of Simulation Models?
This book answer the question.
And also answer “What is amodel?”

Simulation and Similarity Using Models to Understand the World, 2012https://global.oup.com/academic /product/9780199933662

35

Aim is not replicating nor forecasting real world
In time, those Unconscionable Maps no longer satisfied,
and the Cartographers Guilds struck a Map of the Empire
whose size was that of the Empire, and which coincided
point for point with it . . . In the Deserts of the West, still
today, there are Tattered Ruins of that Map, inhabited by
Animals and Beggars;
On Exactitude in Science Jorge Luis Borges* Modeling, (is) the indirect study of real-world systems via theconstruction and analysis of models.
* Modeling is not always aimed at purely veridical representation.
Rather, they worked hard to identify the features of these systems
that were most salient to their investigations.
* Textbook model of the cell is both abstract and idealized relative
to any real cell. It is abstract because it isn’t a model of any
particular kind of cell; it is a model of properties shared by all
eukaryotic cells. Relatedly, it is idealized because its generality
forces some parts of the model to be distorted relative to any realcell. I think these are both interesting properties,
36

Role of Model (in the case of Agent-Based Artificial Market Model)

InvestorA

Investor
B

Investor
C

Inherit Only Important Properties(Behaviors, Algorithms) for Investigating Phenomena

Other Investigating
Phenomena,
Other Important Properties,
Other Good Models

Never Real-Existing Investor
For Understanding Properties
of Real-Existing Investors

Model ofInvestors e.g.: Fashion Model: Understanding Closes
Model Home: Understanding Home

An Aim is to understand how Important Properties (Behaviors, Algorithms)
affect Investigating Macro Phenomena and play Roles in System.

It is NOT aim Replicating real-existing Investors A, B and C.
It is aim Understanding real-existing Investors.

Other Focusing Phenomena, Other Good Models
37What simulation(computational) model can do and mathematical model can not do* When one invokes a computational model to explain some phenomenon,
one is typically using transition rules or algorithm as the explanans. Schelling
explained segregation by pointing out that small decisions reflecting small
amounts of bias will aggregate to massively segregated demographics.
Neither the time sequence of the model’s states nor the final, equilibrium
state of the model carries the explanatory force; the algorithm itself isneeded.
Algorithms: The As want at least 30% of their neighbors to be As and likewise
for the Bs. An agent standing on some grid element e can have anywherefrom zero to eight neighbors in the adjoining elements.

38

We want know a relationship between
Micro Process:
Deciding Orders, Rules of Exchange& Macro Phenomena: Price Formation

Mathematical Model
Macro Model

Stock
MarketCountry Ａ
Bond
MarketCountry A
Stock
MarketCountry B

Replicate Only
Important Properties

can treat only this region

Model ofInvestors

Inherit Only
Important Properties

Role of Model (cont.)

Deciding
OrdersInvestorA
Investor
B

InvestorC

Model of (Algorithms)
Exchange
ChangePrice
Rules
Formation Matching(Simulation Orders
We want know
(Aggregation of
Result)a relationship
Algorithms)
between them39