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Chapter 4
Behavioural Finance
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Behavioral psychology
Behavioral psychology tries to bring
answers to certain anomalies observed in
financial markets/investor behaviours and
which cannot be explained by using
financial theory.
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Behavioural finance
Behavioural finance integrates aspects of
social science; mainly psychology and
sociology to explain the behaviour of
investors and the evolution of financial
markets.
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Explain why individuals do not always take
decisions that maximize their expected
utility OR why the evolution of stock prices
cannot be explained by EMH
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Behavioural finance
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ec on : xpec e yTheory and prospect theory
Expected utility theory assumes that
investors always act in a rational manner,
by respecting the axioms of cardinal utility
(comparability, transitivity, independence,measurability, and ranking) and by
maximising expected utility.
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To verify whether the maximisation of
expected utility criteria is always applied
when individuals take decisions insituations of uncertainty, experiments
have been carried out. These experiments
consist in asking a sample of individuals tochoose between several lotteries. Through
the experiments, it was proved that
individuals do not always apply themaximisation of expected utility criteria.
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Choose between L1 and L2
L1 L2
3000
0
1
00
40000.8
0.2
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Results of the experiment show that:
80% of the individuals choose L1; i.e. L1
> L2
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Choose between L1 and L2
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Choose between L3 and L4
L3 L4
3000
0
0.25
0.750
40000.2
0.8
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Experimental results
Choose between L1 & L2
80% of the individuals participating to
experiment choose L1; i.e. L1 > L2
Choose between L3 & L4
65% of the individuals participating toexperiment choose L4; i.e. L4 > L3
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L3 = 0.25L1 + 0.75L5L
4
= 0.25L2
+ 0.75L5
With L5 = (0,1)
According axiom independence:If L1 > L2 then L3 > L4
From experiments: L4 > L3
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Conclusion
Individuals do not alwaysbehave in a rational manner.
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How to choose between lotteries: L1 & L2 OR L3
& L4 ?? Use expected utility theory
E.g. assume utility function: U (X) = X
Concave
EU (L1) = 1*3000 + 0 = 54.7723
EU (L2) = 0.8*4000 + 0 = 50.5964
EU (L3) = 0.25*3000 + 0 = 13.6931
EU (L4) = 0.2*4000 + 0 = 12.6491
L1 > L2
L3 > L4
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E.g. assume utility function: U (X) = X2
Convex
U (L1) = 1*30002 + 0 = 9 000 000
U (L2) = 0.8*40002 + 0 = 12 800 000
U (L3) = 0.25*30002 + 0 = 2 250 000
U (L4) = 0.2*40002 + 0 = 3 200 000
Maximisation of expected utility criteria not
respected
L4 > L3
L2 > L1
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Attitude of the majority of individuals
participating to the experiment:
- L1 > L2
Same decision as experiment is obtained from
utility function U (X) = X (concave);
therefore individuals are averse towards risk.
- L4 > L3
Same decision as experiment is obtained from
utility function U (X) = X2 (convex); therefore
individuals are attracted towards risk.
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According to expected utility theory, an individual
will have only one utility function, either:- Concave or Convex or Linear
However from the experiment, it is demonstratedthat depending upon the lotteries, the same
individual/s can adopt different attitudes towards
risk.Therefore the same individual/s will have
different utility functions.
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High probability associated with gains and
low probability to losses:
averse towards risk
Low probability associated with gains and
high probability associated to losses:Attracted towards risk
Shows that individuals are less willing togamble will gains (averse to risk) than with
losses (attracted to risk).
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Prospect theory
Because of contradictions in the expected
utility theory, other methods were
developed to enable individuals take
decisions in situations of uncertainty.Among these methods, one of the most
popular is prospect theory, which was
developed by Kahneman and Tversky in1979.
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It is a theory developed by psychologists,
which is being applied in finance. In
expected utility theory, there is only one
utility function to evaluate the utility of alloutcomes (gains/losses).
In prospect theory, there are two utility
functions, one function for gains andanother for losses.
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Prospect theory
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Utility functions under prospect
theory The utility function for gains will be
concave and the utility function for losses
will be convex. This shows that individuals
are averse towards risk when gains areconsidered and attracted towards risk
when losses are considered.
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or osses n v ua s are
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or osses n v ua s areattracted towards risk.
E.g. two individuals must choose from a setof risky investments/lotteries. One
individual has just undergone a loss and
the other a gain; the individual who hasmade the loss would normally be more risk
averse as compared to the other individual
who has made a gain. The risk averse
individual could allocate more importanceto the losses as compared to the gains
when analysing the investments21
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E (L) = 900000
CE = 850000 (accepts)
Risk averse
1000000
0
0.9
0.1
E (L) = -900000
CE = -850000 (refuses)
Risk attracted
-1000000
0
0.9
0.1
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Prospect Theory (Kahneman and Tversky)
Initial wealth/amount paid to participate to lottery
= Rs1000 (reference point)
Lottery = (500, 1500; 0.5, 0.5)
Therefore Rs500 would be a loss and Rs1500
would be a gain.
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Two utility functions:
- One utility function for gains [U+(xi)];
Defined as a concave utility function;
showing aversion towards risk.
- Another utility function for losses [U (xi)]Defined as a convex utility function,
attracted towards risk.
Probabilities converted to weights: w(p1), w(p2)
...
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Evaluating lottery with expected utility theory:
E U(L) = p1U(x1) + p2U(x2) + p3U(x3) + ...
Lottery = (500, 1500; 0.5, 0.5)
E U(L) = 0.5U(500) + 0.5U(1500)
Evaluating lottery with prospect theory:
V (L) =
V (L) = w(0.5) U (500) + w(0.5) U+ (1500)
)()()()(11
i
m
niii
n
ii xUpwxUpw
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By applying prospect theory it can be proved
that for the sets of lotteries in the example:
V (L1) > V (L2) L1 > L2 and
V (L4) > V (L3) L4 > L3
Therefore prospect theory is able to explain the
choice of investors under uncertainty.
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Section 2: Efficient Market
Hypothesis and anomalies
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According to Market efficiency, stock prices
should move in a random manner over
time; as all information available is being
integrated in stock prices at all instants.
Information relative to past events or
anticipated future events (e.g. in the past
company had good financial results and itis anticipated that the future performance
will be good: increase in stock price) and
actual situation within the company oreconomy are integrated in the stocks
prices
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There are also unanticipated future events,
which are integrated in stock prices andmake them move in a random manner.
Market efficiency also implies that stocks
are fairly priced (stock value = market
price of stock) and no investor can make
gains in a consistent manner.
To test whether market are really efficient,
3 forms of market efficiency have been
defined29
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Weak form
Weak form: If past stock prices could beused to predict future stock prices, then
there should be a pattern in the evolution of
the stock prices.
Serial correlation of stock/security prices:
Studies (Fama 1965) have shown that
there is a very small positive correlation
(approaching zero) between daily stockprices. That is the stock price at time (t+1)
is not related to the stock price prevailing at
time t. 30
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Semi-strong form
Semi-strong form: public information, (e.g.company publishes earnings figures or
dividend payments) should be integrated
in the stock price at the moment it isreleased.
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Semi-strong form
Event study: researches have taken
similar events (e.g. merger
announcements; dividend payments)
and studied how the stock prices of thecompanies had been affected by the
events. If public information is instantly
reflected in stock prices, then around theannouncement date of the information an
impact should be noted on stock price.
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Strong-form
Strong-form: public and private information
(internal information which is possessed by
those who manage the company) must be
reflected in stock prices.
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Efficacy of professional investors (e.g.
mutual funds who are in possession of
internal information on the company):
researches have shown that they do notgenerate superior returns to market
indices. As private information is already
integrated in stock and cannot be used byprofessional investors to make gains.
(Consistent manner)
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Strong-form
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Over the years, many researches have
studied the efficiency of stock markets
and through the tests performed (asdetailed above); they have been able to
prove in many cases that markets are
really efficient. However there exist a fewevents in financial markets which cannot
be interpreted by using the efficient
market hypothesis.
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Crashes and Anomalies
ras an e o com
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ras an e o .comBubble
On 19th October 1987, the Dow JonesIndustrial Average (DJIA index) fell by %in one day.
Other indexes in the world also had sharp
decreases.
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Why sharp fall in the indexes?
EMH: an unfavorable information beingintegrated in the stock prices would cause
decrease in stock price and index.
However on the 19th of October, there was
no few fundamental information to justify the
sharp falls in the indexes.
EMH not able to justify the market crash.
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Dot.com Bubble
Between 1995 and 2000, the NASDAQ
Composite Index rose by 580%.
In November 2001 the index fell by 64%.
What caused this sharp increase???Behavioural finance:
- It is the optimism of individuals on the future
of the stocks that caused the index to rise.
- As the individuals generated profits, their
optimism was further increased.
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The sharp rises and subsequent sharp
decrease in indexes could not be
explained by efficient market hypothesis.The economic and financial conditions
prevailing when the crashes occurred (no
consequent rise in gross domestic
product or corporate profits) could not be
used to explain the evolution of the stock
prices within the indexes.
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NASDAQ is composed of technology
stocks. It has been put forward as
argument that it is the enthusiasm of theinvestors about the future of the
technology stocks, which could have
caused the relatively high increases in the
index. As potential investors observed
other investors who had made profits from
technology stocks, they were motivated
into investing in these stocks, thus drivingtheir prices up.
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Anomalies
According to EHM stock prices follow a
random walk; therefore it should be
impossible to predict changes in stock
prices based on publicly availableinformation and on past price behaviour.
According to market efficiency (weak
form), there should be no pattern in theevolution of stock prices. However in
reality some patterns have been noted.42
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January stock returns higher than in any
other month.
Returns
Monday effect: stock prices tended to go
down on Mondays.
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Anomalies
J ff t
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January effect
Studies carried out in several stockmarkets have shown that for no particular
reason, the return offered by stocks during
the month of January is superior as
compared to the other months. For
example a study carried out on the NYSE
over several years has shown that the
average return for January is equal to3.5% and the average return for the other
months is equal to 0.5%.44
J ff t
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Investors who are aware of this fact would
be willing to buy and hold stocks e.g. in
December, so as to benefit from the high
returns in January.
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January effect
M d Eff t
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Monday Effect
As stock prices move in a random manner,that is there is an equal probability of
increase and decrease in stock price on
any particular day of the week. The
expected return (obtained from the change
in stock prices; e.g. stock bought today (at
S0), its return over period t would be [(st -
S0)/ S0]) on a given stock should be thesame for Monday as it is for the other days
of the week.46
M d Eff t
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Studies have shown that the average
return on Monday was much lower than
the average return on other days. A study
done on the NYSE of a certain number ofyears have shown that on Mondays the
average return was equal to -0.2% and on
the other days the average return waspositive (e.g. Tuesday = 0.02%;
Wednesday = 0;1%...).
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Monday Effect
Holida effect
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Holiday effect
A study found that average stock returns
on trading days before public holidays are
abnormally high (9/14 times higher than
daily average return).
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ew exp ana ons rom
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ew exp ana ons romBehavioural finance
Investors are not identical and would notrespond in the same manner to the same
set of information, unlike what is assumed
by efficient market hypothesis. Several
theories have been developed, mainly
based upon human psychology, to explain
anomalies observed in financial theory.
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Examples of a few theories:
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Examples of a few theories:
Individuals usually give more weight to
recent events and give less importance toother information, when taking investment
decisions.
Biased expectations: people tend to be
overconfident in their predictions of future
stock prices.
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People also tend to hold stocks that are
generating losses for a longer time,
expecting that the stock prices may
improve. They also have a tendency to sellstocks that are generating gains too early
out of fear that stock prices may start to
decrease.
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