2017 IEEE Symposium on Computational Intelligencefor Financial Engineering & Economics (IEEE CIFEr'17)
http://www.ele.uri.edu/ieee-ssci2017/CIFEr.htm

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

SPARX Asset Management Co., Ltd.

Sadayuki Horie

Nomura Research Institute, Ltd.
* Mail: mizutata[at]gmail.com
HP: http://www.mizutatakanobu.com/

Note that the opinions contained herein are solely those of the authors and do not necessarilyreflect those of SPARX Asset Management Co., Ltd. and Nomura Research Institute, Ltd.

You can download this presentation material fromhttp://www.mizutatakanobu.com/CIFEr2017.pdf

1

Table of Contents of Today’s Talk

(1) Introduction(2) Artificial Market Model(3) Simulation Results(4) Conclusion and Future WorkYou can download this presentation material fromhttp://www.mizutatakanobu.com/CIFEr2017.pdf

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(1) Introduction(2) Artificial Market Model(3) Simulation Results(4) Conclusion and Future WorkYou can download this presentation material fromhttp://www.mizutatakanobu.com/CIFEr2017.pdf

3

Active/Passive Managed Funds
There are two types of portfolio management strategies for funds that invest in stocks,

where a manager chooses
stocks expected to raise
their prices and invests in
themwhere a manager expects a returnthe same as a market index, e.g.,
Dow Jones, and replicates thecomponents of the index

Active Funds
Assets: Decreasing

Passive Funds
Assets: Increasing
Recently,

Because☆ 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 forfund 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.）
4

Function and Goodness of Active Funds
Active Funds have very Important function in capitalism☆ 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［Wurgler 10］
At first glance, there are

Inconsistent?

［Suominen 11］

Infrequent trades seem to not impact market prices?
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,

Good Active Funds☆ trade on the fundamental value measure precisely［Cremers 16］☆ trade infrequently earn more

5Our CONTRIBUTION
Important function in capitalism of Active Funds☆ 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［Wurgler 10］

Our Result
Indicate

CONSISTENT!!

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☆ trade infrequently earn more

［Cremers 16］

6

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 have neveroccurred 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 manyfactors cause price formation in actual markets

Artificial Market Simulation

7

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 anorder 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 never occurredin actual financial markets✓ can be conducted to isolate the direct effect of changing the
distribution of investor types on price formation

8

Previous Contributions of Artificial Market Simulations
Many studies, including previous CIFEr papers, haveinvestigated the effects of several changing 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

NATURE/SCIENCE articles argued Importance of Simulations
 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

9

(1) Introduction(2) Artificial Market Model(3) Simulation Results(4) Conclusion and Future WorkYou can download this presentation material fromhttp://www.mizutatakanobu.com/CIFEr2017.pdf

10

Our Modeling of Agents(Artificial Investors)
Our Model is different from previous models where（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 priceNo previous model has these characteristics
We 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 are over-fitted and too complex, andsuch models would prevent us from understanding and discovering the mechanisms that
affect price formation because the number of related factors would increase.

11

Price Determination Model

Call Market (Batch Auction)

We employed

100

Price

80

60

BUY (Bid)

Market Price
40 (Trade Price)

SELL (Ask)
Trading
Volume2000Supply Curve
Cumulative number of
Shares that sellers want
to sell over this price

50
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 thenexecuted at specific times (rather than executed one by one continuously).
We determine Market Price and Trading Volume at the crossing point of
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supply and demand curves.

Our Agent Model: Common Setting for every Agent Types
Initial Holdings of Agents
Determig 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) (No more than 2 shares, no negative no.)ｍ
Always place a BUY order
Holding NO Stock

Always place a SELL order
Holding ONE STOCK

Matching
Buy/Sell
OrdersThe number of shares and buy or sell of orders are determined
not depending on Agent Types. Agent Types only differ in termsof how an order price is determined. We can focus difference
13
from the ways determining order prices.

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 Funds
In real financial market

Referring only their Estimated Fundamental Pricewith Enough Margin of Safety
Explain Details of Three Agent Types in Following some Slides

14

Noise Agents

Number of Agents = 1,000

Order Price

𝑃𝑜,𝑗 = 𝑃𝑡 exp(𝜂𝜎𝑡,𝑗 )
Order
Price
MarketPrice

𝑃𝑜 : Order Price
𝑃𝑡 : Market Price𝜂 : Constant (=10%)
𝜎𝑡,𝑗 : random variables
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)

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Technical Agents
Order Price

Number of Agents = 100
Momentum and Contrarian exist
Half and Half of all Technical Agents

Momentum Strategy

Contrarian Strategy

𝑃𝑡

𝑃𝑜 = 𝑃𝑡−𝑡𝑚𝑗

𝑃𝑜 = 𝑃𝑡

𝑃𝑡−𝑡𝑚𝑗𝑡𝑚𝑗 : reference term
Order
Price

MarketPricegiven by random(1～100)for each agent

Momentum Expect continuing
Strategy historical return

Contrarian Expect going backStrategy historical price

Determine Order price Referring only historical market pricePrevious studies showed that such technical agents are needed16
to replicate price formations observed in real financial markets

Fundamental Agents

Order Price

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

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

Various Number of Agents
𝑚𝑠 𝜇𝑗 : Margin of Safety
𝑚𝑠 = 10%
𝜇𝑗 : Uniform Random(0～1)±: when holding stock ”+”
when holding No stock ”-”
want to sell at a enough higher price thantheir estimated fundamental prices

Holding A STOCK
Order
Price

Infrequent
TradesHolding NO Stockwant 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
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Safety which leads Infrequent Trades.

(1) Introduction(2) Artificial Market Model(3) Simulation Results(4) Conclusion and Future WorkYou can download this presentation material fromhttp://www.mizutatakanobu.com/CIFEr2017.pdf

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Verification of Model
Stylized Facts In the case of No existing Fundamental agentsstandard deviation of returns
kurtosis of price returns（Fat-Tail）

0.22%

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

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

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Time Evolution of Market Prices for various No. of Fundamental Agents
Efficient market(near Fundamental Price)
Fundamental
Price

Inefficient market(far from Fundamental Price)

The higher the number of fundamental agents, the more
efficient the market became Market Prices oscillated in anarrower range near the Fundamental Price.

20

Market Inefficiency𝑡𝑒𝑃𝑡 − 𝑃𝑓
1
𝑀𝑖𝑒 = ෍𝑡𝑒
𝑃𝑓
𝑡=1

Average of Absolute Difference
between Market Price and Fundamental Price0
MarketInefficiency

7.7%

Directly measuring market efficiency(Never observed in empirical studies)
Mie is always greater than zero, and
Mie=0 means a market is perfectly
efficient

Number of Fundamental Agents10
20
50 100 200
3.0%

2.2%

2.4%

1.4%

0.7%

500
0.6%

The higher no. of Fundamental Agents, lower Market
Inefficiency, the market became more efficientThis indicates the possibility that a decrease in the number ofactive investors makes a market less efficient, and this implies
that money moving from active funds to passive funds leads toa market becoming less efficient.
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Trading volume share for various No. of Fundamental Agents(total volume of a type of agent/total volume of all types of agents)

Number 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%

The trading volume of fundamental agents was muchsmaller than those of other type agents.
To discuss why fundamental agents whose trading volume is
low make a market more efficient, we show three figures onfollowing slides.
22

Distribution of the frequencies of market price (Black) &Of Trading volume of fundamental agents (Red) for various market price ranges
No. of Fundamental Agents = 500
Market Prices(Black):
Peek around FP
Far FP, lower Fq. rare
Trading Volume(Red):
Double Peek:
Second Peek is
Low Frequency=> Rare Case

Fundamental Price

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 inefficient23(rare case) as Market Price moved farther away from FP.

Average of the absolute returns (Blue)

Fundamental Price
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.
Though the trading was low throughout the whole period, the volume
increased a lot only when the market became less efficient, andthese trades then made the market efficient.

24Average of Estimated Returns of Momentum Agents (Green)
Estimated Return = （Order Price－Market Price）/Market Price

Fundamental Price
Increasing market volatility makes the order prices of momentum
strategy agents move further away from FP, and this leads toamplifying market volatility more excessively.

Orders of fundamental agents prevent this amplification.

25

In short, In the case of Sharply Falling Market Price (Rarely Occurred)(Only when such the Rarely Occurred Case)

Many Orders Prevent This Accelerations
Fundamental
Price

Fundamental
Agent

BUY

Market
Price
Order
Price

SELL
Momentum
Agent

Falling Market Price→ Accelerate Falling Speed
26

Comparing with Empirical Study
These simulation results in short,

Though the trading was low throughout the whole period, the volume
increased a lot only when the market became less efficient, andthese trades then made the market efficient.

［Albagli 15, Cremers 15］
Support[Fact] Active Funds make Markets Efficient

Different［Reason, Mechanism］ Active Funds that perform
well measure fundamental value more precisely［Suominen 11］
Not[Fact] Funds trading infrequently do not make a market efficient
Support［Pastor 16］［Reason］the volume of active funds varies over time andConsistentthat funds earn when the volume is larger
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Averages of the profits of agents for various No. of Fundamental Agents
Number of Fundamental Agents
Averages ofthe 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
0.64% -0.09% 0.24% -0.31% -0.62% -0.80% -0.91%(No.=100)
Fundamental--8.36% 5.18% 4.22% 3.61% 3.02% 1.87%(Again)Number of Fundamental Agents
010
20
50 100 200500

Market
7.7% 3.0% 2.2% 2.4% 1.4% 0.7% 0.6%
Inefficiency

The averages of the profits for the fundamental agents washigher than those of the other types of agents.
Lower no. of Fundamental Agents, the fundamental agentsearn. There are more opportunities for fundamental agentsto earn when the market becomes less efficient.

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(1) Introduction(2) Artificial Market Model(3) Simulation Results(4) Conclusion and Future WorkYou can download this presentation material fromhttp://www.mizutatakanobu.com/CIFEr2017.pdf

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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 themarket becomes unstable and inefficient due to the market price moving
further away from the fundamental price. These trades, occurring only at anecessary time, impacted the market prices and lead them converging withthe 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 thewhole period, the volume increased a lot only when the market becameless efficient, and these trades then made the market efficient.
✓ It is implied that money moving from active funds to passive funds leads amarket to become less efficient because these orders of active funds
decrease.
30

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 thecase that money moving from “impatient” investors to “patient”
investors.

31

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, andMarket Frictions
 [A.T.Kearney 16] A.T.Kearney, : The $20 billion impact of the new fiduciary rule on the U.S. wealthmanagement 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

You can download this presentation material fromhttp://www.mizutatakanobu.com/CIFEr2017.pdf

32

Discussion for rising Passive funds is VERY VERY IMPORTANT

Active Funds
Discovering Fundamental Price
Taking Liquidity

Passive Funds
Not Discovering it
No Taking Liquidity

Both has strengths, weaknesses
Most important point we should discuss is

How much maximum existing rate of Passive
Not to destroy price discovery function
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What is a role of Simulation Models?
This book answer the question.
And also answer “What is a model?”Simulation and Similarity Using Models to Understand the World, 2012https://global.oup.com/academic/product/9780199933662

34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 whichcoincided point for point with it . . . In the Deserts of theWest, 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 thatwere 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 ofcell; 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
35
properties,

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

36What simulation(computational) model can do and mathematical model can not do* When one invokes a computational model to explain some phenomenon, one istypically 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 sequenceof 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 toeight neighbors in the adjoining elements.

37

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
Deciding
OrdersInherit Only
Important Properties

Role of Model (cont.)
InvestorA
Investor
B

InvestorModel of (Algorithms)
C
Exchange
ChangePrice
Rules
Formation Matching(Simulatio
We want know
Orders(Aggregation ofn Result)
a relationship
Algorithms)
between them38