Understanding the decisional phenomenon in the modern capital markets is impossible nowadays without the psychological component of the investor’s attitude. A large number of the behavioural finance theories are based on a limited number of psychological biases, in order to build the foundation of the investor decision. In this context, the proposed paper uses the entropy law (one of the universal laws applicable in informational field beginning from 1870) as a way to approach the investor’s attitude.entropy theory, behavioural finance, investor's attitude

Aurora MURGEA

English

Research Papers in Economics

196                                                                       Finance – Challenges of the Future   
THE ENTROPY THEORY IMPLICATIONS IN 
BEHAVIOURAL FINANCE 
 
Lect. Aurora MURGEA, PhD  
West University of Timişoara 
 
 
I. Introduction 
 
A short look over the last decade 
capital markets’ evolutions allows us to 
see that the multiple financial crisis which 
have shaken the financial system, could 
be hardly explained using the traditional 
models where the rational investors 
determine the asset prices to reflect the 
net present value of the generated cash-
flows. In these conditions, one could 
include psychology (as methodology and 
results) as a solution in order to identify 
the potential causes of the financial 
crisis, the transmitting and contagions 
channels, and also to formulate some 
efficient ways to reduce their outcomes. 
As Statman [1999,p. 19] said:”...some 
believe that the behavioural finances 
introduced the psychology in Finance but 
psychology never been outside the 
finance. Even if the behavioural models 
are different they are all based on 
psychology”. 
  A large number of researchers 
centred their papers on the impact 
investor’s psychology has over the 
capital markets’ evolutions. In their 
seminal work, Tversky si Kahneman   
[1974] investigate the main heuristics 
used in incertitude conditions 
:representatives, availability, adjustability 
and anchoring. Despite the potential use 
of the heuristics as a probability valuator 
for uncertain events they can also 
generate some important systematic 
judgement biases.  Kahneman and 
Riepe[1998] are focusing their paper on 
the preferences and expectation biases 
which the financial consultants should 
know in order to be able to formulate 
recommendations to avoid them or their 
effects (systematic rationing errors: 
overconfidence, optimism, exaggerated 
reactions to events and others, 
preference errors :non-linear probability 
valuation, value function, the games form 
and attractiveness ; using buying price as 
a referential: narrow framing , short and 
long term vision; accepting the 
consequence of the own decisions:  the 
omission and engagement regret, risk 
assumption regret). In his book Shefrin 
[2000] extensively presents a sum of 
biases induced by heuristics 
(representatively bias, the law of small 
numbers, overconfidence, anchoring and 
adjustment, conservatism, ambiguity 
aversion, emotions and knowledge) and 
also frame dependence (loss aversion, 
mental accounting, emotional aspects, 
auto control, regret, money illusion). Also 
the main heuristics and the biases they 
generate are present in: Hirshleifer 
[2001] (proposes an detailed and unified 
version for the most known biases in the 
context of the investor’s psychology and 
asset valuation); Goldberg and Nitzsch 
[2001](define heuristics as information 
processing mechanisms used in order to 
determine a quick response, not 
necessary optimal, with reduce effort and 
divide them in two main categories: 
heuristics to reduce complexity and 
euristics for quick judgement); Barberis 
and Thaler [2003](describe main biases 
involved in the creation of investors’ 
preferences and opinions), 
(Altman[2006], Ko,K.,J, Huang,Z.[2006], 
Peterson[2007]. 
Despite the development of the 
behavioural theories, in the last decades, 
the potentially boundless set of 
psychological biases that theorist can 
use to build the imagine of the investors 
attitude and their decisional system make Year VIII, No.9/2009                                                                                                   197 
this imagine incomplete ( Chan, Frankel 
and Kothari [2002]).In this context since 
information is the reduction of entropy 
and all human activities are essentially 
entropy processes, it is natural to 
understand human psychology and 
market patterns from the viewpoint of 
entropy theory.  
The paper has four parts and the 
first one presents the informational 
entropy. The second one creates the 
connexion between entropy theory and 
the main features of the investors’ 
behaviour on the contemporary capital 
market and in the third one we are trying 
to validate some of the capital market 
patterns using this theory. Fourth part 
concludes.  
 
II. The entropy theory of information 
 
The informational entropy measures the 
incertitude associated with a random 
variable or in other words the medium 
informational content the receptor looses 
when does not know the value of the 
random variable (Shannon[1948]). 
The value of information is a probability 
function with the following proprieties: 
-  the informational value of two 
events is higher than the informational 
value of each of them; 
-  if the two events are independent 
one from another, their  information value 
could be written as the sum of the two 
events’ informational values; 
-  the informational value of any 
event is non-negative. 
The only mathematic function which 
satisfies all this proprieties and which 
represents the level of incertitude (when 
a signal appears the incertitude 
decreases, as a result of the information), 
is: 
 
H(P)= -logbP                                   (1) 
 
where b is a positive constant. 
Let X be an random event with  n 
discrete states:x1, x2, x3,....xn, each with 
probability  p1, p2,p3,...pn. One could say 
that  the informational value of X is the 
average of the each state’s informational 
values. 
) log( ) (
1
j
n
j
j p p X H 

   
If the probability is 1 then -log 
P=0 because the value of the known 
information is zero. When probability 
approaches to zero the value of the 
information increases because the less 
people know it the more valuable is the 
information. 
 Even if the access to information 
is free the user does not always know to 
understand it and use it.. According to 
Shannon[1948] the information quantity 
someone receive could be written as the 
sent quantity minus the average value of 
the conditional entropy.  
 
R=H(x)-Hy(x)                                    (3) 
 
The conditional entropy 
measures the ambiguity average of the 
received signal and represents a 
quantitative estimator for the 
informational asymmetry .If x and y are 
independent   Hy (x)=H(x) and R=0 . No 
information can be transmitted between 
two independent objects. The deeper is 
relation between the receiver and the 
sender the larger amount of information 
is transferred. The informational entropy 
theory offers a useful method to quantify 
the informational asymmetry and shows 
that the cost of obtaining information is 
positively correlated with the 
information’s value in opposition with the 
former opinion which assumes the 
quantitative side of the informational 
asymmetry determined in an exogenous 
way.   
 
III. The entropy law’s influence in 
investor’s behavioural pattern 
 
Closed systems have by 
definition maximum entropy because by 
entropy law it is easier for a system to 
disintegrate than to maintain its structure. 
That is why it is very important to 
genetically code the main information 198                                                                       Finance – Challenges of the Future   
and knowledge into heuristics principles 
in order to reduce the cost of learning. 
The entropy law influences these 
heuristics and we will try to present below 
some of these influences: 
 
1. Conservatism 
Humans have the tendency to 
answer conservatively at any new 
information and they need a long period 
of time to adjust the risk aptitude to the 
new information. 
This heuristics is strongly 
connected with the adjustment and 
anchoring (as a result of these two 
heuristics the high individual probability 
events’ conjunction is overestimated and 
the low individual probability event’s 
disjunction is underestimated). 
All these three proprieties could 
be considered a result of the 
informational theory. From education 3 
one could notice that the receipted 
information is equal with the send 
information minus the conditional 
entropy. The last one decrease when the 
individual general knowledge regarding 
the subject increases. 
Conservatism and anchoring 
reflect the gradually decrease of the 
conditional entropy in the information’s 
receptor.   
 
2. Framing 
The individual reaction towards 
the information usually depends from the 
way we understand and frame it in a 
certain importance category. 
This category will determine the 
response’s nature and the amplitude at 
the received signal. One could ask why 
we are doing this. A potential answer 
could be offered starting from the Gibbs’s 
inequality: 
 
 
 
   (4) 
 
Correct only if qj=pj and 1 ≤ j ≤ n 
 
The left side represents the 
average uncertainty associated with the 
event and the right side the uncertainty 
we associate to the event. 
This concept could be also 
connected to the entropy law because 
when the access to information increases 
and the information is correctly framed 
the new information are easier processed 
and used leading to a reduction  in the 
conditional entropy, which in this case 
could be assimilated with some 
corrections with the difference between 
the two parts of the inequality. 
 
3. Herd behaviour 
The lack of some own 
experiences regarding the events makes 
us often in the position of using others 
experiences and relate to their decisions, 
in order to reduce the cost of learning. 
Usually repeating others experiences is 
almost impossible because the informal 
and motivational context which lead to 
this decisions does not exist. This 
heuristic will reduce the informational 
entropy because the response to the 
information is not the one generated by 
the limited power of the received signal 
but a copied reaction, starting from what 
a specialised user will do. 
The danger of a wrong choice in 
the decisional referential exist, case in 
which the entropy will increase, but 
usually the effect is in the entropy and 
informational asymmetry reduction. 
 
4. Overconfidence and optimism 
Starting with the most far away 
moments in history the individual 
decisions, no matter of their kind, were 
influenced by overconfidence and 
optimist. Without them the humanity 
would not probably survived during the 
ages. 
From the entropy law point of 
view any biological system as a non-
equilibrium system is permanently 
confronted with a continuous dissipation 
process. In the absence of the 
overconfidence and optimism the 
necessary efforts done in order to Year VIII, No.9/2009                                                                                                   199 
maintain a non-equilibrium system would 
be unbearable. 
 
5. Goals 
The investment behaviour, 
similar with other behaviours could be 
considered as oriented to the investor’s 
financial and non-financial goals. 
If for economic agents the unique 
goal is profit maximization for the 
individual investors the motivational 
palette is increased including also: the 
social preferences, equity, altruism, 
revenge, social status seeking or 
survival. 
The way we understand and use 
the information is usually connected or 
determined by our goals because our 
reactions toward the same signal could 
be extremely different depending or what 
are our desires and goals. 
From the presented analysis one 
could notice that some of the patterns 
which lead to a certain decision (for 
instance: conservatism, adjustment and 
anchoring) reflect the constraint induced 
by the psychics law. Others as framing, 
herd behaviour or goals seeking are 
mental attitudes which help us 
processing better the information. Still 
others as overconfidence or optimism are 
mental attitudes which help us to survive 
the constant dissipation process endured 
by all non-equilibrium systems.  
 
IV. Conclusions 
 
Even if the Newtonian laws and 
mechanisms have been dominant even 
in the thinking of social sciences for 
many years life processes are 
thermodynamic processes instead of 
mechanical processes.  
Finance is a very distinct subject 
in social science with the main advantage 
the vast amount of available data offered 
by the financial markets. These allow us 
to test better various hypotheses 
comparing with other fields. This work 
shows how problems in finance, a data 
driven and highly technical subject, 
stimulate researches in much broader 
areas. 
 
 
 
 
 
 
 
 
Altman,M.   Handbook of Contemporary Behavioral Economics: Foundation and 
development, M.E. Sharp, Inc, 2006; 
Barberis,N.C., 
Thaler , R.H 
A survey of behavioral finance.In Handbook of the Economics of 
Finance, volumul 1, pg. 1053-1128, Elsevier, 2003; 
Chan,W., Frankel,R, 
Kothari,S.P 
Testing Behavioral Finance Theories using trends and sequences in 
financial peformance, 2002, disponibil pe http://papers.ssrn.com/; 
Goldberg, J.,von 
Nitzsch,R 
Behavioral Finance, John Wiley and Sons Ltd, 2001; 
Hirshleifer,D  Investor psychology and asset pricing, Journal of Finance, 56(4), 
pg.1533-1597, 2001; 
Hirshleifer,D.,Hou,K.
,Teoh,S.H 
The accrual anomaly:risk or mispricing?, 2006, disponibil pe 
http://papers.ssrn.com/; 
Kahneman D, 
Riepe, M.W 
Aspects of investors psichology. Journal of Portfolio Management, 
24(4), pg. 52-65,1998; 
Ko,K,J, Huang,Z  Arrogance can be a virtue: overconfidence, information acquisition, 
and market efficiency, 2006,disponibil pe http://papers.ssrn.com/; 
Peterson,R.L  Inside the Investor’s brain: the power of mind over money, John Wiley 
and Sons, Inc, 2007; 
Shannon,C  A mathematical theory of comunication, The Bell System Technical 
REFERENCES 200                                                                       Finance – Challenges of the Future   
Journal, 27,379-423,623-656; 
Shefrin H  Beyond Greed and Fear – Understanding behavioral Finance and the 
Psychology of Investing, Harvard Business School Press, 2000; 
Statman M.  Behavioral finance: Past battles and futures engagements.Financial 
Analysts Journal, 55(6),pg.18-27,1990; 
Tesfatsion,L., 
Terano,T 
Agent –based computational economics:a constructive approach to 
economic theory , Handbook of Computational Economics, volumul 2, 
capitolul 16, paginile 831-880, Elsevier, prima editie, 2006; 
Tversky,A, 
Kahneman D 
Judgement under uncertainity:Heuristics and biases, Science 185 
(4157),pg. 1124-1131, 1974. 
 

The entropy theory implications in behavioural finance

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