Behavioural Finance
Prospect Theory and Loss Aversion
Session 3:
Read Shefrin and Statman, 1984
Kahneman and Tversky, 1979
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Overview
Prospect theory
as an alternative to utility theory
attitudes towards risk might be different
under different circumstances
Loss aversion in financial behaviour
riding losers for too long
selling stocks with gains
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What would you do?
A real estate investment example:
Bill and his wife are in their early thirties and just had
their first child. A good friend James is an expert in
real estate. James can find underdeveloped property
that looks like mess but has great potential. After
purchasing James cleans it up, divides into parcels
and resells at substantial profit. During the past three
years he sold most of his properties to one to two
times what he has paid for them.Since he makes the
purchases with borrowed funds, James has been
earning a very high rate of return!
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What would you do?
A real estate example (cont’d)
Some years ago James has gone through some
personal problems and Bill was very helpful and
supportive during those times. James wants to repay
Bill for his kindness. So last year James
recommended Bill join him by investing in a small
rural tract and Bill did. This year James sold the tract
for a 75% profit. Bill and wife are very happy! They
bumped into James one evening and James is very
enthusiastic about another deal. Bill and his wife
want to set aside money for their baby doughter’s
future, particularly her university education
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What would you do?
A real estate example (Cont’d)
James tells them the details: Clear Lake is worth
$205,000. James will invest $102,500 and will be
equal partners will Bill and his wife and follow the
usual formula. Within a year he will sell all the lots for
$459,000. Bill and his wife have $17,500 in savings
and James assures them they can borrow the
remaining $85,000 at an attractive interest rate.
James is a great believer in leverage as it can offset
inflation and taxes.
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What would you do?
On a scale of 1 to 10, how would you rank
Clear Lake as an investment whose
purpose is to fund university education in
15 years?
10.…9….8.…7.…6.…5.…4.…3.…2.…1
10 extremely suitable ,1 entirely unsuitable
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What would you do?
A real estate example (Cont’d)
Bill is making the payments on the $85,000 loan and not earning
anything on the $17,000 savings. Three months later Bill sees
James and asks him how Clear Lake is doing. James says there
is a small problem. Apparently the property has not been
surveyed properly and lots can not be sold until the survey is
complete and the survey is taking more time than anticipated.
Moreover the original loan $85,000 has come due. Renewal is
no problem but the bank renews only $75,000. Bill has to come
up with the additional $10,000 himself. James is embarrassed
but remains upbeat about the success of the project. Bill and his
wife have saved exactly $10,000 in recent months.
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What would you do?
If you were in Bill’s or his wife’s position,
how would you react emotionally?
Worried or anxious?
Patient and believing?
If you were in Bills’ or his wife’s position
would you begin feeling regret?
Would you feel anyone should be blamed?
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What would you do?
If you answered yes
Who would you blame most?
James? Yourself? The situation?
How obvious does it seem to you that
it would have gone that way?
Answer on a scale of 1 to 10
1….2….3…..4….5….6….7….8….9….10
1 very obvious, 10 impossible to predict
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What would you do?
A real estate example (Cont’d)
Time passes…A year later James apologizes that it has taken so
long to get things moving. James says he will work things out so
that Bill and his wife will not have to make any more payments
on the loan. James will handle the financial details. To move up
sales he will put up a model home on one of the lots.
Next time Bill sees James there is good news and there is bad
news. Good news is the model home has been built and sold,
the bad news is this has not stimulated additional demand.
James says he feels terrible and proposes Bill to take over his
interest in Clear Lake. Bill thinks OK, if I accept the offer I will
avoid extra losses but if investment turns profitable I lose the
chance to lower my loss and make a positive return.
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What would you do?
Put yourself in Bill’s shoes.
If you sign over your interest to him you will have to come to
terms with your $27,500 loss. If you keep your interest you risk
losing more money, but you might also recover your investment!
Would you tell James you understand that he is trying to
help and come to terms with your loss and sign your interest
over to him?
Would you remind James that he said this would pay for
your child’s university education and you still expect to do
that (keep your interest)?
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What would you do?
 Six years have passed.James proposes that you sign
your interest to him. James also tells you that one of the
estate agents offers $35,000 for the unsold lots and
together with the sale of the lot with model home
($8,900) total amount received would be $43,900.
James says he has decided to accept the estate agent’s
offer.
Would you tell James you understand that he is trying to
help and come to terms with your loss and sign your interest
over to him?
Would you remind James that he said this would pay for
your child’s university education and you still expect to do
that (keep your interest)?
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Prospect theory
Kahneman and Tversky,1979
Utility theory is a normative model of choice
under uncertainty
systematic violations of axioms
Prospect theory as a descriptive model of
decision under uncertainty
risk aversion in gains
risk seeking in losses
inconsistent preferences when the same choice is
presented in different forms
over-weighting of low probabilities
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What would you do?
You toss a coin. If you lose you lose £100
What is the minimal gain that would make
this gamble acceptable?
What sure gain is as attractive as
50% chance to gain £1,000
50% chance to gain nothing
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Value Function
Value
Losses
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Gains
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What would you do?
You are facing the chance to win £20,000
Consider the following.
Are the differences significant to you?
Can you order them by their impact on your
preferences?
A. The probability is either 0 or 1?
B. The probability is either 41% or 42%
c. The probability is either 99% or 100%
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Non linear weighing of
probabilities
Rational choice
multiply utility by probability!
Probabilities have equal weighting!
People deviate
overweight low probabilities
underweight high probabilities
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Who is more upset?
Andy owns stocks he bought for £100.
The value of the stock was £160
yesterday and today it dropped to £150.
Becky owns stocks she bought for £200.
The value of the stock was £160
yesterday and today it dropped to £150.
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Purchase price as a
reference point
Disposition effect
reluctance to realize losses!
A will perceive as a reduction in gain
B will perceive as increased loss!
Odean, 1998
Investors are more likely to sell when price
increases
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What would you do?
Chose between
A sure gain of £2400
25% chance to win 10,000
75% chance to gain nothing
Chose between
A sure loss of £240075% chance to lose 10,000
75% chance to lose nothing
Chose between
25% chance to win 2,400
75% chance to lose 7,600
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25% chance to win 2,000
75% chance to lose 7,500
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Narrow framing
Investors consider decision problems
one at a time
do not adopt a broader frame
Narrow framing
is mainly due to multiple mental accounts
(details next week!)
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Prospect theory
Accounts for observed attitudes towards
risk
risk aversion in gains risk seeking in losses
Over-weighting of small probabilities
lottery tickets, insurance policies
Gains and losses defined with a reference
point
Framing (details next week!)
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Riding losers too long
Shefrin and Statman, 1985
Aversion to loss realization in financial
markets
tax considerations can not explain patterns in loss
and gain realization
a wider theoretical framework
• mental accounting
• regret aversion
• self control
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Riding losers too long
Research Design
Question: Do investors time the realization of
their losses differently from the realization of
their gains?
Data:
Individual Investors
• roundtrip duration of trades
• 1964-1970
Mutual Funds
• purchases and redemption of mutual fund shares
• 1961-1973
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Riding losers too long
Analysis
For all values of roundtrip duration (1 month
to 12 months) 40% of trades realize losses!
The ratio of redemptions to purchases in
gains is higher than that in losses!
Conclusion
Investors ride losers for too long!
Why?
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Summary
Prospect theory
Risk aversion in gains risk seeking in losses
Over-weighting small probabilities
narrow framing
loss aversion-reference points
Riding losers for too long
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