Journal of Financial Risk Management
2013. Vol.2, No.4, 87-91
Published Online December 2013 in SciRes (http://www.scirp.org/journal/jfrm) http://dx.doi.org/10.4236/jfrm.2013.24015
Open Access 87
The Herd Behavior of Risk-Averse Investor
Based on Information Cost
Guangming Deng
College of Science, Guilin Univ ersity of Technology, Guilin, China
Received November 11th, 2013; revise d D e cember 11th, 2013; accepted December 18th, 2013
Copyright © 2013 Guangming Deng. This is an open access article distributed under the Creative Commons At-
tribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the
original work is properly cited.
In this paper, the traditional model of herd behavior was improved and extended. The herd behavior of
risk-averse investor based on information cost was studied in the financial market. By refining the con-
cept of Bayes equilibrium and the analysis of the behavior of investors, it was discovered that the herd
behavior of the second risk-averse investor did not produce until the first risk-averse investors chose to
buy information.
Keywords: Risk Avoidance; Information Cost; Herd Behavior
Introduction
Herding behavior of financial markets refers that the majority
of individual investors tend to take the same or similar invest-
ment strategy with the others when making investment deci-
sions. Causes of herd behavior include information asymmetry,
the concern for the reputation and rewards programs (Sharma &
Bikhchandani, 2000), where the information asymmetry caused
by the spread of information is an important reason for herd
behavior. Banerjee (1992) was first proposed based on asym-
metric information model of herd behavior. Bikhchandani, Hir-
shleifer and Welch (1992,1998) also studied the relevant herd
behavior model, although both models are different, they all
believe that information diffusion is the cause of herd behavior.
As BHW model assumes that investors can get free private
information, Cui Wei (2008) for the real market, raised the cost
of herd behavior based on the information model, However,
BHW model also assumes that investors are risk neutral, in
which most investors in financial markets do not match the
characteristics of risk aversion. In this paper, BHW model was
further extension studied, and we analyzed the risk-averse in-
vestor herd behavior based on information costs, and by refin-
ing the concept and inductive method of Bayesian risk aversion
of investors so as to get the optimal decision-making behavior.
The Model of Risk-Averse Investor Herd
Behavior Based on the Information Cost
In this paper, the traditional basis of BHW model, the intro-
duction of investor risk aversion in financial markets and the
presence of the characteristics of information costs, with a
negative exponential utility function is the risk aversion of in-
vestors, the cost of herd behavior based on the information
model. Basic model assumptions are as follows:
1) The investment result 

1,1vV
1 in the beginning is determined randomly. represents investment result is
well and represents investment result is bad. is
equally likely to take on the values of and .
v
1 v v
1 1
c
2) Each of the investors chooses whether to buy private sig-
nal before making a decision. Let i denote the cost that in-
vestment purchase information, assuming .
c
i01
i
3) Let


1,1
i
sS
1s denote that private signal investor
receives. i

denotes a good signal, denotes a bad
signal. Conditions in the investment result, the investor’s pri-
vate signal is independent.
1s
4) i
p
stands for the accuracy of the investor i acquires
private signal, it is a function of the information cost , de-
i
c
noted as


i
ppci and 11
2i
p

. Accuracy refers to the
probability of signal correct on the conditions given investment,
and


0pc

,

1
02 p

. It is assumed that the information
cost can be observed. The following investors can infer signal
accuracy according to information cost the previous investors
paid for.
5)


0,1
i
aA
1adenotes the investment decisions of inves- tors.

stands for the decision to invest and 1a

 for
decision not to invest.
6) The information set of investor is observed in front of
all his investment decisions i


12 1ii
of investors
and their private information. Section of the public belief
,,haa
i,a



1
ii
, that investment in the historical conditions
, we get the probability of good investment results.
Pv h  
i
h7) Investors using negative exponential utility function, the
choice to buy private information, risk aversion returns to in-
vestors depends on information costs, investment decisions and
investment results , defined as follows:


,,e
ii i i
uacv c
 i va


In the case of uncertain future, investors expected return is
conditional expectation of


,,
iii
uacv under the condition of
the information set.

G. M. DENG





,, ,
1,,,
1,,,
iii ii
ii iiiii
ii iiiii
Eu acvhs
PshEu acvhs
PshEu acvhs






 

1
1
where


1, 0
,,
e,, 1
ii
iii vii ii
ca
Eua c vEhsca
 
 








  


1
1
e,
1, e1, e
vii
ii ii
Ehs
Pv hsPvhs









 
Without purchasing information, the risk aversion of inves-
tors expected return is:


1, 0
,
e, 1
i
N
ii ivii
a
Eu avhEha
 





















e1e1
e1 e
ee e
vii i
ii
i
EhPvh Pvh

e

 








 
 

Risk-Averse Investors Decision Analysis
After comparing the purchase information and do not pur-
chase information expected return, risk averse investors before
deciding whether to buy information. This section uses the
Bayesian algorithm and the inductive method to analyze inves-
tors optimal information cost and make the optimal investment
decisions to maximize the expected return.
The First Risk Averse Investor’s
Investment Decisions A1
In order to analyze the first investor risk aversion A1 invest-
ment decisions, you first need to discuss the situation given
information costs, and then further discuss the best information
costs.
Case Given Information Costs
Information costs are assumed, the signal accuracy is. Ac-
cording to Bayes rule, in the purchase of information, the first
investor risk aversion investment results A1 update their beliefs
as:











11
11
11 11
1
11 1
1, 1
,11 1
,111,1 11
1,11
Pv hs
Phs v Pv
Phs v PvPhs vPv
pc
Pv hspc

 
 


(1)
If you get a good signal A1, then A1 investment results are
good update belief; if A1 get is bad signal, then the result is
good for investors A1 updated belief. A1 in getting a good sig-
nal and bad signal to make investment decisions after the ex-
pected benefits are:



 



  


11 1 11
11 1
1
11
1
11 1
1 1
11
1, ,,1
e,1
1, 1e
1,1e
e1 e
v
Eu acvhs
Ehsc
Pv hs
Pv hsc
pcpc c



 



 
 


 

 

1

 

(2)


 








111 11
11 1
1
11
1
11 1
1
1
11
1, ,,1
e,1
1,1 e
1,1 e
1e e
v
Eu acvhs
Ehsc
Pv hs
Pv hsc
pc pcc














 

 

1

 

(3)
There




111 11111 111
,, ,10,, ,1
E
uacvhsEua cvhsc


 

So ended the first A1 in investor risk aversion will not be a
bad signal for investment.
Proposition 1 Assume

1
11
2pc

,
then


111 111
,,, 11Eu acvhsc



.
Proposition 1 is true can guarantee a good signal was ob-
served after the first risk averse investor must invest A1. Oth-
erwise, regardless of the resultin g signal A1 is good or bad, A1
will not invest, so that investors behind the A1 will not be able
to grasp the behavior of their access to real information. The
second risk averse investors A2 and A1 will face the same situ-
ation, so A2 would not choose to invest, and after that all in-
vestors will not invest. Thus, if Proposition 1 is false, no one
making investment decisions, and no one involved in the deci-
sion-making model.
Proposition 1 is equivalent to

1
1e
ee
pc


 


Intuitively, since investors are risk averse, the accuracy of
the signal must be larger to ensure investors.
In the case of Proposition 1 is true, A1 will make investment
decisions according to its private signal, that is, while getting
good signal


11s

, A1 decided to invest in

11a


; For the
bad signal


11s

, A1 decided not to invest


10a

. A1 in
getting a good signal and bad signal the expected benefits re-
spectively is:










111 11
1
1
11
11
111 111
,,, 1
e1 e
eee
,, ,1 1
Eu acvhs
pcpc c
pc c
Eu acvhsc









1

 



 

(4)
Open Access
88

G. M. DENG
The first risk aversion investor, the probability of obtaining
good signals and bad A1 were 50%, therefore, A1 expected
return after purchase information is:










11111
11 11111
1
11
,, ,
1,,,1
1
1
22
ee e1
22
Eu acvhs
PshEu acvhs
c c
pc c

  






 


If A1 chooses not to purchase information, the A1 fo
ment results for the good faith is the public belief, i.e.
11 11111
11
1, ,,1
1
eee
PshEu acvhs
pc
 

  


 

(5)
r invest-
1
1
2


,
the A1 earnings should be:




11 1
ee
11
,e1
N
Eu avh








22 2



ee 2
4
 


Thus, when
 
11111111
,,Euacvh


, ,
N
sEu avh



Namely,






11
11
1
1
ee e1 ee2
22
ee
ee 20
2
21
0
ee2
pc c
pc c
c
pc
 








 

 
4

 

.
The first risk averse investors A1 is willing to buy private
information.
Lemma 1
Assum



0pc,
ee 1
4
p
 




(ee 0, 4 c
 









),
if and only if

21
:0
ee2
c
cpc
 
 
,
the first risk aversion inves inform.
Proposition 2
, s. t.
tor A1 purchasesation
Assume c

21
0
ee2
c
pc
 


，
and
ee ee
0,c

, 1
44
p






.
Under the conditions in Lemma 1, Proposition 2 is true
guarantee of a risk averse investor A1 never buys a private
e. If A1 is not purchasing information, then the result is
investment belief is 0.5, the probability of investment
is 0.5. So, A1 investment decisions investors will not give back
any of the information transmitted, the second investor risk
aversion and A1 A2 facing the same situationmpathy, A2,
and behind all investors will not buy information, which model
lo
  


messag
good for
, e
ses significance
Optimal Cost of Information
While purchasing information, A1 faced with the expected
return on the following maximization problem:

 
1
11
1
0,1,0
ee 2pc c
 
1
1
1
21
max :ee 2
21
s.t.:
c
c
pc
c
pc
 


 

( 6)

A1 Optimal information cost *
1
c meet

*
1
2
pc ee

 
,

or


*
11pc

and
*
1
ee
04 c

 

 .
At the same time, the optim investmeal nt decision A1 is
make decisions according to their private signals, namely when
the it gains signal


*
11s

, A1 decidto invest ed


*
11a

;
when it gets bad ed not to invest.
The Second Investor Risk Aversion
A2 Investment Decisions
signal, A1 decid
The second risk averse investors A2 according to the optimal
information cost *
1
c of A1, can be speculated that A1 signal
accuracy.
First, assume that A1 decided to invest


*
11a, this
that the A1 has good signal s mean


*1s. So A2 in t
1h
t results, a
e purchase
lso is the information, update beliefs about investmen
second period public faith 2

:







**
1
 
ase if
exp
22 11
*
111
1e
Pv hPv apc
pc

  

 (7)
ee
So, in the absence of purchnormation, the second risk
avoidance investors A2 the optimal decision is a choice, and A2
after investment earnings areected to be:





*
22 21
1,e ee1
N
Eu avhpc
  


 

Then, the second risk aversion investor A2 in bu
mation and not to buy the expected return of the comparison. If
th
ying infor-
e given information for cost, when the A2 is a good sign, she
updated belief as the result of the investment:





22
1, 1Pvh s





   
 



22
*
12
**
12 21
,1 1 1
1.
2 12
Ph svPv
pc pc
pcpcpcpc
 

22 22
*
12
**
212 1
,1 11,1 11
11
Phs vPvPhs vPv
pc pc
pc pcpcpc

 

 


.


Open Access 89

G. M. DENG
Open Access
90
A2, therefore, decided to invest in.
When the A2 is bad signal, she updated belief as the result of the investment:














 





22
22
22 22
**
12 12
**
**
12 1
21 21
,11 1
1, 1,11 1,111
11
2
11
Ph svPv
Pvh sPh svPvPh svPv
pc pcpc pc
pcpcpcpc
pc pcpcpc
 
   
  
 


 
 
.
2
When




*
12
pc pc, the value is more than 1
2, A2 decided to invest in; Otherwise, not investment.
d bad, respectively is: The second risk aversion investor A2, the probability of obtaining good signals an









 



**
221221
**
22 1212
11 2
12
Pshpcpcpcpc
Pshpcpcpc pc

 
After the purchase information, A2 expected return is:










222222 2222222222222
,, ,1,, ,11,, ,1EuacvhsPshEuacvhsPshEu acvhs
 

 
  
where















 




1
1
222 222222222
,, ,1e,11,1 e1,1Eu acvhsEhscPvhsPvhs2
**
1212 1
12
22 22
e
e1 e
11
c
pc pcpcpcc
Ps hPs h







v   
  



 






22
Eu a

2 222
,,,1 1cvhs c




When





*
12
p
cpc, that is, the second risk aversion investor A2 signal is not the first risk aversion investor A1ignal accu-
rately s






*
222 2212
,,,eeeEu acvhspcc
  


 
 .




*
12
ee e
p
cc
  

 A2 buys private information after the expected return , less than expected earnings of not to buy pri-
vate information





*
22 21
,ee
N
Eu avhpce

 


 
 .
A2 will not buy private information, therefore, A2 will fully believe that the signal1 and follow A1 investment decisions. A




*
1
pc pc, When 2
 











 




**
12 22
2e eeepcpccc
  
 
Only when

**
1212 1
1
222 22222222
22 22
1
,, ,1e1e11
11
1e1
pc pcpcpc
Eu acvhsPshcPshc
Ps hPsh
pc p


 





  

 




 

 
22222 222
,, ,,
N
Eu acvhsEuavh
 



, that is




















**
1212222
2eee1e102eee1e 100pc pcpcpcccc
   
,
t deci-
sions. Obviously, A2 buate information conditions cannot be met.
So when
The second risk avoidance investors A2 will buy private information, and according to its private signal making investmen
y priv




*
12
pc pc
estor A1 bought th
, A2 will not purchase information. Synthetically the above two kinds of circumstances, if the first risk
aversion inve most accurate information and investment, then the second risk aversion investor A2 will follow A1
investment decisions.
Next, the discussion on the first risk-averse investors A1 do not invest. If the A1 is not investment so that she will get
the bad signal A similar analysis can get the condition of second risk averse investors A2 bue information is:

*
10a,
y privat

*
11s .














**
11 22
2ee1e 10pcpcpcpcc
  
2
e


   
Also shows that A2 can be not buy private information, A2 will follow A1’s decision and choose not to invest, the expected re
to turn A2.

222
0,
N
Eu avh

1

 .


G. M. DENG
whether the f
formation A2 can take full advantage of
A
Investment Decision No.N Risk
Averse Investors in AN
ehavior if the second risk averse
investors A2 not buy private information and imitate A1, A2
e
purchase of pri-
make the same deci-
irst risk averse investors
ill not buy private information.
T
Therefore,irst risk averse investors whether A1
investment, second risk averse investors A2 will not purchase
information, private in
1 buy, and follow A1’s investment decision.
We can use similar methods to analysis behind all the risk
averse investors. Investment b
bhavior cannot risk on the back of the investors to avoid any
information reveals the role of. Then, the third risk averse in-
vestors A3 is facing the same situa tion and A2, A3 and A2 will
make the same decision, which mimics the first risk averse
investors A1 investment behavior without the
vate information. Next, A4, A5… AN will
sion. So, all investors are behind the f
follow A1 behavior, and w
herefore, information diffusion and herding from second risk
averse investors A2 began.
Conclusion
This paper, based on the BHW model, considering the char-
acteristics of investors in financial markets, risk aversion, and
the introduction of information cost, discusses the risk investors
herd behavior based on information cost. Through the research
of risk averse investors found, only the first risk averse inves-
tors are willing to buy information, the optimal information
cost is *
1
c, and meet:

*
1
2
ee
pc

 

or and


*
11pc
*
1
ee
04 c

 


Starting from the second risk ainvestor, all the risk
aversion of investors behind will not purchase information,
version and
follow the first risk aversion of iavior. In addition,
the information cost and risk aversion of investors decision-
to happen.
Acknowledgements
This work was jointly supported by tal Social Sci-
ence Fund (No.1
V. (1992) A simple model of herd behavior [J]. The
Quarterly Journal of Economics. 107, 797-817.
http://dx.doi.org/10
nvestors beh
making model, information diffusion and herd behavior will
occur, and from the second risk avoidance investors are starting
he Nation
3BTJ009), and the Guangxi Key Laboratory of
Spatial Information and Geomatics (No.1207115-27).
REFERENCES
Sharma, S., & Bikhchandani, S. (2000). Herd behavior in financial
markets: A review [J]. IMF Workin g Paper.
Banerjee, A.
.2307/2118364
shleifer, D., & Welch, I. (1992)Bikhchandani, S., Hir. A theory of fads,
fashion, custom, and cultural change as informational cascades [J].
The Journal of Political Economy, 1 0 0, 992-1026.
http://dx.doi.org/10.1086/261849
Bikhchandani, S. Hirshleifer, D., & Welch, I. (1998). Learning from the
behavior of others: Conformity, fads, and the informational cascades
[J]. Journal of Econo1-170.
http://dx.doi.org/10.1mics Perspectives, 12, 15 257/jep.12.3.151
Cui, W. (2008). Information costs and herd behavior in financial mar-
kets—For the improvement and expansion of BHW model [J]. Eco-
nomic Science, 6, 91-99.
Open Access 91