Why do Active Funds that Trade Infrequently Make a Market　more Efficient? -- Investigation using Agent-Based Model

1111
Why do Active Funds that Trade Infrequently
Make a Market more Efficient?
-- Investigation using Agent-Based Model
2017 IEEE Symposium on Computational Intelligence
for Financial Engineering & Economics (IEEE CIFEr'17)
http://www.mizutatakanobu.com/CIFEr2017.pdf
You can download this presentation material from
Note that the opinions contained herein are solely those of the authors and do not necessarily
reflect those of SPARX Asset Management Co., Ltd. and Nomura Research Institute, Ltd.
SPARX Asset Management Co., Ltd.
Nomura Research Institute, Ltd.
Takanobu Mizuta*
Sadayuki Horie
* Mail: mizutata[at]gmail.com
HP: http://www.mizutatakanobu.com/
http://www.ele.uri.edu/ieee-ssci2017/CIFEr.htm

2222
(1) Introduction
(2) Artificial Market Model
(3) Simulation Results
(4) Conclusion and Future Work
Table of Contents of Today’s Talk

3333
(1) Introduction

4
Active/Passive Managed Funds
where a manager chooses
stocks expected to raise
their prices and invests in
them
where a manager chooses
stocks expected to raise
their prices and invests in
them
where a manager expects a return
the same as a market index, e.g.,
Dow Jones, and replicates the
components of the index
where a manager expects a return
the same as a market index, e.g.,
Dow Jones, and replicates the
components of the index
Passive FundsActive Funds
Assets: Increasing
☆ Some empirical studies ［French 08, Bogle 14］ argued that
The average return of active funds lost that of passive funds.
☆ Recent regulations have made fund sellers accountable for
fund costs especially in the United States. ［A.T.Kearney 16］
（Costs of passive fund are cheaper than those of active,
since passive funds need not research companies.）
☆ Some empirical studies ［French 08, Bogle 14］ argued that
The average return of active funds lost that of passive funds.
☆ Recent regulations have made fund sellers accountable for
fund costs especially in the United States. ［A.T.Kearney 16］
（Costs of passive fund are cheaper than those of active,
since passive funds need not research companies.）
Assets: Decreasing
There are two types of portfolio management strategies for funds that invest in stocks,
Recently,
Because

☆ trade on the fundamental value measure precisely
☆ trade infrequently earn more
☆ trade on the fundamental value measure precisely
☆ trade infrequently earn more 5
Function and Goodness of Active Funds
Infrequent trades seem to not impact market prices?
☆ discover the fundamental value (intrinsic value of companies)
☆ leads to market prices converging with the fundamental price
(make a market more efficient)
☆ play an important role in allocating capital, which is an
important function in capitalism
☆ discover the fundamental value (intrinsic value of companies)
Good Active Funds
Active Funds have very Important function in capitalism
［Cremers 16］
［Wurgler 10］
Inconsistent? ［Suominen 11］
Important to discuss whether active funds trade infrequently make a market
more efficient or not, if so, to investigate the mechanism of how they do so.
By the way,
At first glance, there are

☆ trade infrequently earn more☆ trade infrequently earn more 6
Our CONTRIBUTION
Though the trading volume of active funds was low
throughout the whole period, the volume increased a lot
only when the market became less efficient, and these
trades then made the market efficient.
Good Active Funds
Important function in capitalism of Active Funds
［Cremers 16］
［Wurgler 10］
CONSISTENT!!
Our Result
Indicate

 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 have never
occurred in actual financial markets, such as ones in which 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
 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 have never
occurred in actual financial markets, such as ones in which 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
Artificial Market Simulation
Difficulty of Empirical Study
7
Difficulty of Empirical Study

8
Agents (Artificial Investors)
＋
Price Mechanism (Artificial Exchange)
Complete Computer Simulation needing NO Empirical Data
Virtual and Artificial financial Market built on Computers
Artificial Market Simulation (Agent-Based Model)
 can discuss on the mechanism between the micro-macro feedback
 can be conducted to investigate situations that have never occurred
in actual financial markets
 can be conducted to isolate the direct effect of changing the
distribution of investor types on price formation
 can discuss on the mechanism between the micro-macro feedback
 can be conducted to investigate situations that have never occurred
in actual financial markets
 can be conducted to isolate the direct effect of changing the
distribution of investor types on price formation
Agent
(Investor)
Order
Price
Mechanism
(Exchange)
Determination market price
Each Agent determines an
order by some rules,
Price Mechanism gather
agents orders and
determines Market Price
Models
Include

9
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
Previous Contributions of Artificial Market Simulations
Many studies, including previous CIFEr papers, have
investigated the effects of several changing regulations and
rules by using artificial market,
Many studies, including previous CIFEr papers, have
investigated the effects of several changing regulations and
rules by using artificial market,
 Battiston et al. (2016) SCIENCE, Vol. 351, Issue 6275, pp. 818-819.
http://science.sciencemag.org/content/351/6275/818
 Farmer and Foley (2009) NATURE, Vol. 460, No. 7256, pp. 685-686.
https://www.nature.com/articles/460685a
NATURE/SCIENCE articles argued Importance of SimulationsNATURE/SCIENCE articles argued Importance of Simulations

10101010
(1) Introduction

（１） Agents are reflected the characteristics of investors
who trade infrequently
Real fundamental investors wait a market price reaching their target price.
←(previous) agents re-estimate buy/sell every time
（２） Focusing how an order price is determined
It easier to interpret the simulation results since the types of agents only
differ in terms of how an order price is determined,
and this allows us to build a model of agents who trade infrequently.
←(previous) agents determine target no. of shares, not order price
11
Our Modeling of Agents(Artificial Investors)
No previous model has these characteristics
We constructed an artificial market model that is as
simple as possible having these characteristics
We constructed an artificial market model that is as
simple 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 are over-fitted and too complex, and
such models would prevent us from understanding and discovering the mechanisms that
affect price formation because the number of related factors would increase.
Our Model is different from previous models where

1212
Price Determination Model Call Market (Batch Auction)
0
20
40
60
80
100
0 50 100
Price
Cumulative number of Shares
BUY (Bid)
SELL (Ask)
Market Price
(Trade Price)
Trading
Volume
Cumulative number of
Shares that sellers want
to sell over this price
Cumulative number of
Shares that buyers want
to buy under this price
In a call market, buy and sell orders are grouped together and then
executed at 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.
Supply Curve
Demand Curve
We employed

13
Our Agent Model: Common Setting for every Agent Types
Initial Holdings of Agents
One share or Cash 10,000
← Half and Half of all agents
(Initial Market price=10,000)
Deterring Buy/Sell
Holding One Share stock： SELL
Holding no stock ： BUY
(No more than 2 shares, no negative no.)
The number of shares and buy or sell of orders are determined
not depending 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.
Always place a BUY order
Holding NO Stock Holding ONE STOCK
Matching
Buy/Sell
Orders
Matching
Buy/Sell
Orders
Always place a SELL order

14
Our Agent Model: Three Agent Types
Agent Types only differ an Order Price
Noise Agents
Technical Agents
Fundamental
Agents
Around Market Price Randomly
Referring only Historical market prices
Referring only their Estimated Fundamental Price
with Enough Margin of Safety
Explain Details of Three Agent Types in Following some Slides

Noise Agents
They order around Market Price Randomly.
Order Price
Number of Agents = 1,000
𝑃𝑜,𝑗 = 𝑃𝑡exp(𝜂𝜎𝑡,𝑗)𝑃𝑜,𝑗 = 𝑃𝑡exp(𝜂𝜎𝑡,𝑗)
𝑃𝑜 : Order Price
𝑃𝑡 : Market Price
𝜂 : Constant (=10%)
𝜎𝑡,𝑗 : random variables
that follow a standard
normal distribution
𝑡: time
j: Agent no.Market
Price
Order
Price
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)
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) 15

Technical Agents
Order Price
𝑡𝑚𝑗: reference term
given by random(1～100)
for each agent
𝑃𝑜 = 𝑃𝑡
𝑃𝑡
𝑃𝑡−𝑡𝑚 𝑗
𝑃𝑜 = 𝑃𝑡
𝑃𝑡
𝑃𝑡−𝑡𝑚 𝑗
Momentum
Strategy
Contrarian
Strategy
Momentum Strategy
Determine Order price Referring only historical market price
𝑃𝑜 = 𝑃𝑡−𝑡𝑚 𝑗
𝑃𝑜 = 𝑃𝑡−𝑡𝑚 𝑗
Contrarian Strategy
Momentum and Contrarian exist
Half and Half of all Technical Agents
Previous studies showed that such technical agents are needed
to replicate price formations observed in real financial markets
Previous studies showed that such technical agents are needed
to replicate price formations observed in real financial markets
Number of Agents = 100
Market
Price
Order
Price
161616
Expect continuing
historical return
Expect going back
historical price

Fundamental Agents Various Number of Agents
𝑃𝑓 = 10,000: Fundamental Price
𝑑𝜎𝑗: Difference estimated
fundamental price with true Pf
𝑑 = 10%, 𝜎𝑗: SD Random
𝑃𝑜 = 𝑃𝑓exp 𝑑𝜎𝑗 ± 𝑚 𝑠 𝜇 𝑗𝑃𝑜 = 𝑃𝑓exp 𝑑𝜎𝑗 ± 𝑚 𝑠 𝜇 𝑗
Fundamental Price
Estimated
Fundamental
Price
𝑚 𝑠 𝜇 𝑗: Margin of Safety
𝑚 𝑠 = 10%
𝜇 𝑗: Uniform Random(0～1)
±: when holding stock ”+”
when holding No stock ”-”
Margin of
Safety Infrequent
Trades
Market
Price
Order
Price
Holding A STOCK
Holding NO Stock
Determine order prices by depending not on the market price,
but on the Estimated Fundamental Price with Enough Margin of
Safety which leads Infrequent Trades.
Determine order prices by depending not on the market price,
but on the Estimated Fundamental Price with Enough Margin of
Safety which leads Infrequent Trades.
Order Price
17
They do not know TRUE Fundamental Price
but try to estimate want to buy at a enough lower price than
their estimated fundamental prices
want to sell at a enough higher price than
their estimated fundamental prices

18181818
(1) Introduction

19
Our model replicated the statistical characteristics
(Stylized Facts), fat-tails, and volatility-clustering,
observed in real financial markets.
Our model replicated the statistical characteristics
(Stylized Facts), fat-tails, and volatility-clustering,
observed in real financial markets.
Verification of Model
standard deviation of returns 0.22%
kurtosis of price returns
（Fat-Tail）
2.37
autocorrelation coefficient for square returns
（Volatility-Clustering）
lag
1 0.18
2 0.14
3 0.13
4 0.15
5 0.12
Stylized Facts In the case of No existing Fundamental agents

20
Time Evolution of Market Prices for various No. of Fundamental Agents
Fundamental
Price
The higher the number of fundamental agents, the more
efficient the market became Market Prices oscillated in a
narrower range near the Fundamental Price.
The higher the number of fundamental agents, the more
efficient the market became Market Prices oscillated in a
narrower range near the Fundamental Price.

21
Market Inefficiency
Number of Fundamental Agents
0 10 20 50 100 200 500
Market
Inefficiency
7.7% 3.0% 2.2% 2.4% 1.4% 0.7% 0.6%
The higher no. of Fundamental Agents, lower Market
Inefficiency, the market became more efficient
The higher no. of Fundamental Agents, lower Market
Inefficiency, the market became more efficient
This indicates the possibility that a decrease in the number of
active investors makes a market less efficient, and this implies
that money moving from active funds to passive funds leads to
a market becoming less efficient.
𝑀𝑖𝑒 =
1
𝑡 𝑒
𝑃 𝑡
− 𝑃𝑓
𝑃𝑓
𝑡𝑒
𝑡=1
Directly measuring market efficiency
(Never observed in empirical studies)
Mie is always greater than zero, and
Mie=0 means a market is perfectly
efficient

22
The trading volume of fundamental agents was much
smaller than those of other type agents.
The trading volume of fundamental agents was much
smaller than those of other type agents.
Trading volume share Prices for various No. of Fundamental Agents
Trading volume
share
0 10 20 50 100 200 500
Noise (No.=1000) 97.3% 97.2% 97.2% 97.0% 97.0% 96.9% 96.9%
Technical (No.=100) 2.7% 2.8% 2.8% 3.0% 3.0% 3.1% 3.1%
Fundamental --- 0.002% 0.002% 0.006% 0.010% 0.011% 0.023%
To discuss why fundamental agents whose trading volume is
low make a market more efficient, we show three figures on
following slides.
(total volume of a type of agent/total volume of all types of agents)

Distribution of the frequencies of market price (Black) &
Of Trading volume of fundamental agents (Red) for various market price ranges
Fundamental agents traded (second) Frequently at 9800, far from
FP (Red), though here is rare case(Black).
They traded frequently only when the market became inefficient
(rare case) as Market Price moved farther away from FP.
Fundamental agents traded (second) Frequently at 9800, far from
FP (Red), though here is rare case(Black).
They traded frequently only when the market became inefficient
(rare case) as Market Price moved farther away from FP.
No. of Fundamental Agents = 500
Fundamental Price
Market Prices(Black):
Peek around FP
Far FP, lower Fq. rare
Trading Volume(Red):
Double Peek:
Second Peek is
Low Frequency
=> Rare Case
23

24
Though the trading was low throughout the whole period, the volume
increased a lot only when the market became less efficient, and
these trades then made the market efficient.
Absolute return near 9800 was large (Blue)
this means market volatility (dispersion of returns) increased
Absolute return near 9800 was large (Blue)
this means market volatility (dispersion of returns) increased
Fundamental agents traded frequently when market prices sharply
declined and market volatility was excessive.
Average of the absolute returns (Blue)
Fundamental Price

25
Estimated Return = （Order Price－Market Price）/Market PriceEstimated Return = （Order Price－Market Price）/Market Price
Orders of fundamental agents prevent this amplification.
Increasing market volatility makes the order prices of momentum
strategy agents move further away from FP, and this leads to
amplifying market volatility more excessively.
Increasing market volatility makes the order prices of momentum
strategy agents move further away from FP, and this leads to
amplifying market volatility more excessively.
Average of Estimated Returns of Momentum Agents (Green)
Fundamental Price

26
In short, In the case of Sharply Falling Market Price (Rarely Occurred)
Market
Price
Fundamental
Agent
Fundamental
Price
Order
Price
SELL
Falling Market Price
→ Accelerate Falling Speed
Falling Market Price
→ Accelerate Falling Speed
BUY
Many Orders Prevent This Accelerations
Momentum
Agent
(Only when such the Rarely Occurred Case)

27
Comparing with Empirical Study
[Fact] Active Funds make Markets Efficient[Fact] Active Funds make Markets Efficient
［Reason, Mechanism］ Active Funds that perform
well measure fundamental value more precisely
［Reason, Mechanism］ Active Funds that perform
well measure fundamental value more precisely
Support
Different
［Albagli 15, Cremers 15］
[Fact] Funds trading infrequently do not make a market efficient[Fact] Funds trading infrequently do not make a market efficient
［Suominen 11］
［Pastor 16］
［Reason］the volume of active funds varies over time and
that funds earn when the volume is larger
［Reason］the volume of active funds varies over time and
that funds earn when the volume is larger
Consistent
Not
Support
Though the trading was low throughout the whole period, the volume
increased a lot only when the market became less efficient, and
these trades then made the market efficient.
These simulation results in short,

28
The averages of the profits for the fundamental agents was
higher than those of the other types of agents.
The averages of the profits for the fundamental agents was
higher than those of the other types of agents.
Averages of the profits of agents for various No. of Fundamental Agents
Averages of
the profits
0 10 20 50 100 200 500
Noise (No.=1000) -0.06% -0.07% -0.13%-0.18% -0.30% -0.52% -0.85%
Technical
(No.=100)
0.64% -0.09% 0.24%-0.31% -0.62% -0.80% -0.91%
Fundamental --- 8.36% 5.18% 4.22% 3.61% 3.02% 1.87%
Lower no. of Fundamental Agents, the fundamental agents
earn. There are more opportunities for fundamental agents
to earn when the market becomes less efficient.
(Again) Number of Fundamental Agents
0 10 20 50 100 200 500
Market
Inefficiency
7.7% 3.0% 2.2% 2.4% 1.4% 0.7% 0.6%

29292929
(1) Introduction

30303030
Conclusion
 We built a model of agents who trade infrequently in an artificial market
model and investigated the effects of active investors who trade
infrequently on market prices and whether they make a market more
efficient or not by using the artificial market model.
 The fundamental agents traded frequently in the rare situation that the
market becomes unstable and inefficient due to the market price moving
further away from the fundamental price. These trades, occurring only at a
necessary time, impacted the market prices and lead them converging with
the fundamental price. This lead to preventing the market from becoming
more unstable and less efficient.
 Though the trading volume of fundamental agents was low throughout the
whole period, the volume increased a lot only when the market became
less efficient, and these trades then made the market efficient.
 It is implied that money moving from active funds to passive funds leads a
market to become less efficient because these orders of active funds
decrease.

31313131
Future Work
 There are many types of Fundamental Investors. Especially
“patient” investors who rarely loss-cut and “impatient”
investors who frequently loss-cut are important because of
first one earns more than second one showed by empirical
study [Cremers 16]. Therefore, We should investigate the
case that money moving from “impatient” investors to “patient”
investors.

3232323232
Reference
 [Albagli 15] Albagli, E.: Investment horizons and asset prices under asymmetric information, Journal of
Economic Theory, Vol. 158, Part B, pp. 787 – 837 (2015), Symposium on Information, Coordination, and
Market Frictions
 [A.T.Kearney 16] A.T.Kearney, : The $20 billion impact of the new fiduciary rule on the U.S. wealth
management industry, A.T. Kearney study, Perspective for Discussion, A.T. Kearney, No. October (2016),
https://goo.gl/SA2EM9
 [Bogle 14] Bogle, J. C.: The arithmetic of “ all-in ” investment expenses, Financial Analysts Journal, Vol. 70,
No. 1, pp. 13–21 (2014), http://www.cfapubs.org/doi/pdf/10.2469/faj.v70.n1.1
 [Cremers 15] Cremers, M. and Pareek, A.: Short-Term Trading and Stock Return Anomalies: Momentum,
Reversal, and Share Issuance*, Review of Finance, Vol. 19, No. 4, p. 1649 (2015),
https://doi.org/10.1093/rof/rfu029
 [Cremers 16] Cremers, M. and Pareek, A.: Patient capital outperformance: The investment skill of high active
share managers who trade infrequently, Journal of Financial Economics, Vol. 122, No. 2, pp. 288–306 (2016),
http://dx.doi.org/10.1016/j.jfineco.2016.08.003
 [French 08] French, K. R.: Presidential Address: The Cost of Active Investing, The Journal of Finance, Vol.
63, No. 4, pp. 1537–1573 (2008), http://dx.doi.org/10.1111/j.1540-6261.2008.01368.x
 [Mizuta 16] 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
 [Pastor 16] Pastor, L., Stambaugh, R. F., and Taylor, L. A.: Do Funds Make More When They Trade More?,
SSRN Working Paper Series (2016), http://ssrn.com/abstract=2524397
 [Suominen 11] Suominen, M. and Rinne, K.: A Structural Model of Short-Term Reversals, SSRN Working
Paper Series (2011), http://ssrn.com/abstract=1787270
 [Wurgler 10] Wurgler, J.: On the Economic Consequences of Index Linked Investing, Working Paper 16376,
National Bureau of Economic Research (2010), http://www.nber.org/papers/w16376

Discussion for rising Passive funds is VERY VERY IMPORTANT
Discovering Fundamental PriceDiscovering Fundamental Price Not Discovering itNot Discovering it
Passive FundsActive Funds
How much maximum existing rate of Passive
Not to destroy price discovery function
Taking LiquidityTaking Liquidity No Taking LiquidityNo Taking Liquidity
Most important point we should discuss isMost important point we should discuss is
To discuss this we should know mechanism how
infrequent trades of Active funds impact market prices
So, we emphasis that our study is a part of most important
discussion about the entire system of capitalism and market
mechanisms that facilitate an increase in the general welfare 33
Both has strengths, weaknesses

This book answer the question.
And also answer “What is a model?”
34
Simulation and Similarity Using Models to Understand the World, 2012
https://global.oup.com/academic/product/9780199933662
What is a role of Simulation Models?

35
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 the
construction 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 real cell. I think these are both interesting
properties,
Aim is not replicating nor forecasting real world

Role of Model (in the case of Agent-Based Artificial Market Model)
36
Investor
A
Investor
B
Investor
C
Model of
Investors
Inherit Only Important Properties
(Behaviors, Algorithms) for Investigating Phenomena
An Aim is to understand how Important Properties (Behaviors, Algorithms)
affect Investigating Macro Phenomena and play Roles in System.
Never Real-Existing Investor
For Understanding Properties of
Real-Existing Investors
e.g.: Fashion Model: Understanding Closes
Model Home: Understanding Home
It is NOT aim Replicating real-existing Investors A, B and C.
It is aim Understanding real-existing Investors.
Other Investigating
Phenomena,
Other Important Properties,
Other Good Models
Other Focusing Phenomena, Other Good Models

37
* 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 is needed.
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 anywhere from zero to
eight neighbors in the adjoining elements.
What simulation(computational) model can do and mathematical model can not do

Role of Model (cont.)
38
Investor
A
Investor
B
Investor
C
Stock
Market
Country Ａ
Bond
Market
Country A
Stock
Market
Country B
ReplicateOnly
ImportantProperties
Price
Formation
(Simulatio
n Result)
Mathematical Model
Macro Model
can treat only this region
(Algorithms)
(Aggregation of
Algorithms)
Change
Rules
Model of
Exchange
We want know
a relationship
between them
We want know a relationship between
Micro Process:
Deciding Orders, Rules of Exchange
& Macro Phenomena: Price Formation
Deciding
Orders
Matching
Orders
InheritOnly
ImportantProperties
Model of
Investors

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