The Studies on Behavioral Finance with Agent-based Approaches

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The Studies on Behavioral Finance with
Agent-based Approaches

• Dr. Wei Zhang
• School of Management, Tianjin University, China
• Tianjin University of Finance and Economics, China

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Agenda

• Introduction
• Case I Excess volatility and learning frequency
• Case II Performance under different investment
  strategies
• Case III Time series predictability from simple
  technical rules perspective
• Research in the future

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Introduction

• At the cross of the century, it was declared that
  Behavioral Finance would be a redundant concept
  in the future because no other finance will exist
  (Thaler, 1999)
• Though Behavioral Finance has the ability to
  explain a bunch lots of market anomalies and
  improved the theories of financial economics,
  there are still quite a lot questions waiting for
  answers
• However, it is very difficult to give these
  answers only by the traditional approaches in
  finance

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Introduction
Common Market Information
Information Feedback
Market Restrictions
Equilibrium Price
Heterogeneous Individual Information
Ex ante Beliefs
Ex post Beliefs
Individual Choice
Objective Function
Individual Restrictions
Risk Preference
Price formation process
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Introduction

• Each box of the above chart could be a Hot
  Button.
• When being pressed to change the standard
  assumptions, it will deliver different price
  dynamics
• However, by only applying the traditional
  approaches, it is unimaginable to obtain a
  beautiful close-form model when the classical
  assumptions are relaxed
• We need to try some new approaches

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Introduction

• Hopefully, agent-based modeling (ABM) can help us
  out to explore some of these questions
• As a new approach, ABM is able to compensate for
  the shortcomings of the traditional
• Since 2000, studies of behavioral finance with
  ABM have achieved great progress in the world
• Here wed like to share some examples of our
  works in the past three years to show the ability
  and advantages of ABM for behavioral finance
  studies

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Case I Excess volatility and learning frequency

• Although learning is a common behavior among
  investors, it is rare in the literature that
  attribute the excess volatility of asset price to
  learning frequency
• A modified SFI-ASM model is developed with
  different dividend processes to observe the
  impact of learning frequency on the excess
  volatility of asset price.

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Case I Excess volatility and learning frequency

• Experimental Design
• (1) All experiments are without short-sale,
  which imitates the particular regulation in China
  stock market, although this might not quite true
  since the first Monday of Oct., 2008
• (2) Two kinds dividend processes are applied
• an AR(1) process with non-negative bounds
• a bounded geometric Brownian motion process

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Case I Excess volatility and learning frequency

• (3) Learning frequency is set as
• k250 (agents use GA every 250 periods)
• k 1000 (agents use GA every 1000 periods)
• Then all experiments are classified into
  four subgroups

k1000 k250
AR(1) ARL ARH
Geometric Brownian Motion GBL GBH
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Note The abscissa is experiment period, with
origin from the 100,000th period. The ordinate is
difference between price and its average. The
dotted line indicates actual price difference and
the solid one denotes theoretical price
difference by Shiller (1981).
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Case I Excess volatility and learning frequency

• The Theoretical Price
• Shillers (1981) approach is used to calculate
  the theoretical price by discounting the
  dividends every 100 periods
• where rf is risk-free rate, d denotes the
  dividend, and p represents the price

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Case I Excess volatility and learning frequency

• Samples
• (1) At first, artificial stock market
  operates 100,000 periods per run to ensure GAs
  effect
• (2) Then recording data of the next 10,000
  periods
• (3) For each experiment group, 25
  independent runs were done with different random
  seeds

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Case I Excess volatility and learning frequency

• Statistical results
• We use the panel data from the 25 runs for
  each subgroup
• By applying variance analysis, the F statistics
  shows the significant difference between the
  theoretical and experimental data, which means
  that the equilibrium prices from the experiments
  indicate excess volatility

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Case I Excess volatility and learning frequency

• Findings
• (1) Either dividend process follows AR(1) or
  geometric Brownian motion, the higher the agents
  learning frequency is, the higher volatility of
  price will be
• (2) Also, it is found from the recorded
  experimental data that when the agents learning
  frequency is lower, more fundamental rules will
  be used while when the frequency is higher, the
  agents are more likely to apply technical rules
  in making decision

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Case II Performance under Different Investment
Strategies

• The performance of various investment strategies
  is an interesting topic in behavior finance
• The works by BSV (Barberis, Shleifer Vishny,
  1998) and DSSW (De Long, Shleifer, Summers
  Waldmann, 1990) are two well-known analytical
  model referring to investment performance. The
  BSV model designed the BSV strategy, and the DSSW
  model provided noise trading strategy and
  rational expectation strategy. Both gave us some
  important theoretical results about price
  dynamics
• However, when the investors with the strategies
  respectively present in the same market, how each
  of them will perform?

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Case II Performance under Different Investment
Strategies

• The Conceptual Model
• Asset
• A risk-free asset, which pays a fixed interest
  rate and is in perfectly elastic supply
• A risky asset, which is available in a limited
  and constant supply across time. This asset pays
  a bounded AR(1) dividend
• Trading Mechanism
• A continuous auction mechanism
• Market Clearing
• The total bid equals the total askmarket price
  is the equilibrium price at period t

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Case II Performance under Different Investment
Strategies

• Investor PreferenceCARA utility function
• Investor Type
• BSV investors their trading behavior are
  somewhat similar to chartists in real financial
  markets
• Noise traders whose trading are unpredictable
• Rational expectation investors who are smart
  arbitrageurs and always adopt genetic algorithm
  to find and make use of any opportunity in the
  market
• Passive investors who follow the Buy-and-Hold
  (BaH) strategy and never change their risky
  asset positions.

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Case II Performance under Different Investment
Strategies

• The Agent-based Model
• ASM Platform
• An ASM model, denoted as s-ASM, was developed
  based on the above conceptual model and SFI-ASM
  2.4, and run it on the open Swarm 2.2 platform in
  Linux
• The Modifications of SFI-ASM
• Adding BSV investor, noise trader and passive
  investor
• New clearing mechanism Calculating equilibrium
  price by bid-ask balance

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Case II Performance under Different Investment
Strategies

• Experimental Design
• 24 experiments are done with different random
  seeds of dividend generation. Each experiment
  consists of 250,000 periods
• After the rational expectation agents finish
  their training in the initial 150,000 periods,
  the s-ASM model equally resets each agents
  wealth to 1000, and its risky asset position to 1
  unit

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Case II Performance under Different Investment
Strategies

• The Results Wealth Descriptive Characteristics

Rational gt BSV gt Passive gt Noise Furthermore, an
ANOVA test is used to detect the significance of
the above differences
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Case II Performance under Different Investment
Strategies
a

• Wealth ANOVA
• Statistical Results
• (a) Rational BSV
• (b) Noise lt Passive
• (c) Noise lt Rational
• (d) Noise lt BSV

b
d
c
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Case II Performance under Different Investment
Strategies

• Further experiment with 500,000 Periods

Wealth Figure

• Statistical Results
• Rational BSV
• Noise lt Passive lt Rational
• Noise lt Passive lt BSV

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Case II Performance under Different Investment
Strategies

• Further experiment (without the Noise) for
  500,000 Periods

Wealth Figure

• Statistical Results
• BSV lt Passive lt Rational
• On this specific situation, the Friedman(1953)
  Hypotheses is correct

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Case II Performance under Different Investment
Strategies

• Findings
• Rational expectation strategy is the best in all
  four
• Noise traders create living space for all
  irrational investors including themselves
• Rational arbitrageurs cannot always eliminate
  the irrational investors defined by the BSV
  easily, even in the long run, when the noise
  traders exist in the market

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Case III The predictability of simple technical
rules

• The empirical work of Brock et al (1992) found
  that some simple technical rules have the
  predictability for the returns
• Others (such as Fifield et al, 2005) made further
  investigation on the potential factors which may
  have impact on this ability
• In this presentation, we try to figure out
  whether exists any factor other than the above
  which may alter the predictability

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Case III The predictability of simple technical
rules

• The TA-ASM Model
• Assets
• One risky asset, its supply is a positive
  constant
• One free-risk asset, which pays a fixed
  interest rate and is in
• perfectly elastic supply
• Market Clearing Mechanism
• Call auction market
• Similar to Arthur, Holland, LeBaron et
  al.(1997)
• Investors
• Preference CARA utility function
• Type informed trader and chartist

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Case III The predictability of simple technical
rules

• Informed Traders
• For representative agent i of informed
  traders, his expected price at period t is
• where ?t N(0, ?2) and ?t?-?, ?. It is a
  proxy of information on asset price, ?t is noise
  on information.
• 4 groups of experiments are made. In each
  of them, the information It is set to the closing
  price of A-share index and B-share index of
  Shanghai Stock Exchange, A-share index and
  B-share index of Shenzhen Stock Exchange
  respectively.

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Case III The predictability of simple technical
rules

• Chartists
• For representative agent j, his expected
  price at period t is
• where s is buy or sell signals according to
  simple technical rules, denotes the k-th
  element of memory array about signal s at period
  t, l is memory length

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Case III The predictability of simple technical
rules

• Chartists
• Simple technical rules are used by
  chartists, as in Brock, Lakonishok
  LeBaron(1992)
• Variable-length Moving Average (VMA)
• if smat gt lmat(1b) then sBuy if
  smat lt lmat(1-b) then sSell
• Fixed-length Moving Average (FMA)
• if smat-1 lt lmat-1(1-b) and smat gt
  lmat(1b) then sBuy
• if smat-1 gt lmat-1(1b) and smat lt
  lmat(1-b) then sSell
• Trading Range Break-out (TRB)
• if Pt-1 gt Pmax(1b) then sBuy if Pt-1
  lt Pmin(1-b) then sSell
• sma (or lma) short-period (or
  long-period) moving average price
• b band width.
• Pmax (or Pmin) local maximum (or minimum)
  price on the past certain periods

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Case III The predictability of simple technical
rules

• Experimental Design
• Statistic
• The number of buy (or sell) trading, CB (or CS)
• The fraction of buy (or sell) returns greater
  than zero, PrbB (or PrbS )
• Standard t-ratios testing the difference of the
  means of buy return and sell return from the
  unconditional 1-period average for VMA, and
  10-periods average for FMA and TRB
• Technical Scenarios
• Ten scenarios for VMA and FMA, (1,50,0)?(1,50,1)?
  (1,150,0)?(1,150,1)?(5,150,0)?(5,150,1)?(1,200,0
  )?(1,200,1)?(2,200,0)?(2,200,1)
• Six scenarios for TRB, (50,0)?(50,1)?(150,0)?(150
  ,1)?(200,0)?(200,1)

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Case III The predictability of simple technical
rules

• Forecasting Ability of Technical Rules
• Here, we take one example of TRB rules when
  investors proportion is 11 and chartists
  memory length is 50-periods

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????
scenarios
Experiment 1
Experiment 3
mean
Experiment 2
Experiment 4
mean
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Case III The predictability of simple technical
rules

• Findings
• The difference of mean returns, rB-rS , of almost
  all the trades are positive, and ten of them are
  significantly positive
• In 20 scenarios of the 24, the number of buy
  trading is larger than the number of sell
• The fraction of returns greater than zero in buy
  trading is larger than the fraction in sell
  trading, the difference of them is at least
  13.33
• All these means that the buy suggestion by the
  technical rules are more effective than the
  sell ones.

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Case III The predictability of simple technical
rules

• Result Analysis
• The result shows that these technical scenarios
  can really gain excess returns to certain extent
• It means that the simple technical rules can
  detect some predictable part of returns series,
  just as Brock et al (1992) revealed in their
  empirical work with real world data

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Case III The predictability of simple technical
rules

• After Brock et al (1992), the impact of
  transaction cost, dividend, non-synchronous
  trading on the predictability is considered
  (Bessembinder Chan,1998 Day Wang, 2002
  Fifield, Power Sinclair, 2005), and it is found
  that these factors only have limited influence
• However, are there any other factors being able
  to alter the predictability of the technical
  rules?

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Case III The predictability of simple technical
rules

• According to the setting of our ASM model, there
  are several potential factors that may interfere
  in the VMA, FMA and TRB rules forecasting
  ability.
• They are market equilibrium mechanism, chartists
  memory length, and the proportion of different
  type of investors

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Case III The predictability of simple technical
rules

• Firstly, market equilibrium mechanism hardly
  affects the statistical characteristics, because
  that a lot of empirical researches (such as the
  above listed papers) have had quite similar
  results to our findings

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Case III The predictability of simple technical
rules

• Second, the effect of chartists memory length is
  not obvious. The change of average sell returns
  of all rules is not significant in different
  memory zones. In particular, average buy returns
  of all rules are almost invariable

VMA
FMA
TRB
Figure. Returns under different chartists memory
length
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Case III The predictability of simple technical
rules

• Third, the effect of investors proportions is
  also not significant. Especially, there is no
  obvious change at some points (such as 19, 15,
  32, 51), which are from real market surveys
  (Frankel Froot, 1987, 1990 Shiller, 1989)

Figure. Returns under different investors
proportions
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Case III The predictability of simple technical
rules

• Conclusion
• Data analysis in this case shows that the
  technical rules can gain excess returns
• Just as the previous indicated factors which only
  have mild impact on the predictability, it is
  also revealed that equilibrium mechanism, memory
  length, and investors proportions also only have
  limited impact on the predictability, by our ASM
  model.

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Case III The predictability of simple technical
rules

• Discussion
• Brock et al (1992) gave a guess on why the
  predictability exists, based on their empirical
  findings, that it is quite possible that
  technical rules pick up some of the hidden
  patterns
• Considering all the potential factors indicated
  by the literature, we constructed an ASM, in
  which chartist may really capture some of the
  hidden pattern and does gain excess returns by
  applying the rules

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Research in the future

• (1) Multi Asset/Market Research
• For example, behavioral portfolio (Shiller,
  2000), behavioral option pricing, behavioral
  interest term structure (Shefrin, 2005) are all
  very interesting and useful issues
• (2) Research under Special Market Condition
• E.g. China security market has great
  difference with other markets (such as NYSE,
  NASDAQ) in investors behavior and trading
  mechanism. It provides an opportunity to explore
  its price dynamics with ABM

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Research in the future

• (3) Dynamics Research under Psychology-based
  Learning
• Brenner(2006) believes that
  psychology-based learning is an important field
  in economics. In fact, psychology-based learning
  is also much related to behavioral finance.
  However, traditional approaches have difficulty
  in dealing with it.
• ABM should be a promising tool

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Thanks for your attention!

• Email weiz_at_tjufe.edu.cn
• zhangwei_at_nsfc.gov.cn
• Tele 86-022-27891308