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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

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

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

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

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

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 we’d 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

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.

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

Case I: Excess volatility and learning frequency

(3) Learning frequency is set as:

k=250 (agents use GA every 250 periods)

k= 1000 (agents use GA every 1000 periods)

Then all experiments are classified into four subgroups

ARH

GBL

GBH

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).

Case I: Excess volatility and learning frequency

The Theoretical Price

Shiller’s (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

Case I: Excess volatility and learning frequency

Samples

(1) At first, artificial stock market operates 100,000 periods per run to ensure GA’s 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

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

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

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?

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 ask—market price is the equilibrium price at period t

Case II: Performance under Different Investment Strategies

- Investor Preference：CARA 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 changetheir riskyasset positions.

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

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 agent’s wealth to 1000, and its risky asset position to 1 unit

Case II: Performance under Different Investment Strategies

The Results: Wealth Descriptive Characteristics

Rational > BSV > Passive > Noise

Furthermore, an ANOVA test is used to detect the significance of the above differences

Case II: Performance under Different Investment Strategies

a

Wealth ANOVA

Statistical Results:

(a) Rational = BSV

(b) Noise < Passive

(c) Noise < Rational

(d) Noise < BSV

b

d

c

Case II: Performance under Different Investment Strategies

Further experiment with 500,000 Periods

Wealth Figure

- Statistical Results:
- Rational = BSV
- Noise < Passive < Rational
- Noise < Passive < BSV

Case II: Performance under Different Investment Strategies

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

Wealth Figure

- Statistical Results:
- BSV < Passive < Rational
- On this specific situation, the Friedman(1953) Hypotheses is correct

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

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

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

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 Itis 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.

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

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 > lmat*(1+b) then s=”Buy”; if smat < lmat*(1-b) then s=”Sell”

- Fixed-length Moving Average (FMA):

if smat-1< lmat-1*(1-b) and smat > lmat*(1+b) then s=”Buy”

if smat-1 > lmat-1*(1+b) and smat < lmat*(1-b) then s=”Sell”

- Trading Range Break-out (TRB):

if Pt-1 > Pmax*(1+b) then s=”Buy”; if Pt-1 < Pmin*(1-b) then s=”Sell”

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

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%)

Case III: The predictability of simple technical rules

- Forecasting Ability of Technical Rules

Here, we take one example of TRB rules when investor’s proportion is 1:1 and chartist’s memory length is 50-periods

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.

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

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?

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

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

Case III: The predictability of simple technical rules

- Second, the effect of chartist’s 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

FMA

TRB

VMA

Figure. Returns under different chartist’s memory length

FMA

TRB

Case III: The predictability of simple technical rules- Third, the effect of investor’s proportions is also not significant. Especially, there is no obvious change at some points (such as 1:9, 1:5, 3:2, 5:1), which are from real market surveys (Frankel & Froot, 1987, 1990; Shiller, 1989)

Figure. Returns under different investor’s proportions

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.

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

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 investor’s behavior and trading mechanism. It provides an opportunity to explore its price dynamics with ABM

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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