GSBA 509
Prospect Theory
An alternative to the expected utility maximization model
ƒ A model of choice under uncertainty
ƒ Is descriptive, empirical
ƒ Rejects strict optimization and rational cost/benefit
analysis
ƒ Rejects uniform analysis in favor of variations due to
factors such as framing and level of wealth
ƒ Focuses on gains and losses relative to a reference
point
ƒ Recognizes existence of heuristics and bias in decision
making
Prospect Theory
Kahneman and Tversky
Econometrica, 1979
1979 K&T Econometrica article
(one of the most widely cited papers in economics)
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Choices Under Uncertainty
Heuristics and Biases
• Uncertainty Examples
ƒ Medical operation
ƒ Plea bargain vs trial
ƒ Stock market investment
ƒ Outcome of a football game
ƒ Future price of oil
ƒ Pricing or product options
ƒ New product introduction
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• People commonly use decision making
short-cuts (heuristics)
• Heuristics lighten cognitive load, but lead to
greater biases and errors
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Prospect Theory
Risk Aversion
(Kahneman & Tversky, 1979)
• Would you be willing to pay $500 to enter a lottery with a
• Choose between:
50% chance of winning $1000 and 50% chance of $0?
ƒ A. A sure gain of $3000
ƒ B. An 80% chance of winning $4000 and a 20%
• Why not? It is a fair price: 0.5 x $1000 = $500
chance of winning zero.
• Bernoulli (1738): People are risk averse: they value the
1st dollar slightly more than the 2nd dollar, the 2nd more
than the third, etc...(diminishing marginal utility)
• Choose between:
ƒ A. A sure loss of $3000
ƒ B. An 80% chance of losing $4000 and a 20%
• So: The $500 it costs to enter is worth subjectively more
than the additional $500 you could win
chance of losing zero.
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Prospect Theory
Observed Behavior:
(Kahneman & Tversky, 1979)
• Choose between:
• People avoid risk when seeking gain, but
9 ƒ A. A sure gain of $3000
ƒ B. An 80% chance of winning $4000 and a 20%
chance of winning zero.
Most people show risk aversion here
choose risk to avoid a certain loss
• Choose between:
ƒ A. A sure loss of $3000
9 ƒ B. An 80% chance of losing $4000 and a 20%
chance of losing zero.
Most people prefer risk here
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Graphically
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Consider the two Choices Together:
(Choose A or B and choose C or D)
Utility
• Choose between:
ƒ A. A sure gain of $240
ƒ B. A 25% chance to gain $1000 and a
75% chance
h
tto gain
i nothing
thi
Losses
Gains
• Choose between:
ƒ C. A sure loss of $750
ƒ D. A 75% chance to lose $1000 and a
25% chance to lose nothing
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Consider the two Choices Together:
•
•
Losses Loom Larger than Gains
Choose between:
ƒ A. A sure gain of $240
ƒ B. a 25% chance to gain $1000 and a
75% chance to gain nothing
Choose between:
ƒ C. A sure loss of $750
ƒ D.
D A 75% chance to lose $1000 and a
25% chance to lose nothing
•
A and D: A 75% chance to lose $760 and a
25% chance to gain $240 – common choice
•
B and C: A 75% chance to lose $750 and a
25% chance to gain 250 – dominates
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• Consequences:
ƒ Framing matters
ƒ Conservative judgments (avoid risky change)
ƒ Endowment effect (things become more valuable
when already owned)
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Other K & T Examples
Framing Effects
• Imagine that California is preparing for the outbreak of
•
•
•
•
•
•
•
•
an unusual disease, which is expected to kill 600
people. Two alternative programs to combat the
disease have been proposed:
Framing
Bounded Rationality
Emotional Reaction
Action vs. Inaction
Endowment Effect
Availability
Optimism
Hindsight Bias
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• If program A is adopted, 200 people will be saved
• If program
p g
B is adopted,
p
there is a 1/3 p
probability
y that
600 people will be saved, and 2/3 probability that no
people will be saved.
• If program C is adopted, 400 people will die
• If program D is adopted, there is a 1/3 probability that
nobody will die, and 2/3 probability that 600 people will
be die.
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Framing Effects
Framing in Business Decisions
• Imagine that California is preparing for the outbreak of
an unusual disease, which is expected to kill 600
people. Two alternative programs to combat the
disease have been proposed:
72%: If program A is adopted, 200 people will be saved
• If pprogram
g
B is adopted,
p
there is a 1/3 p
probability
y that
600 people will be saved, and 2/3 probability that no
people will be saved.
• If program C is adopted, 400 people will die
78%: If program D is adopted, there is a 1/3 probability
that nobody will die, and 2/3 probability that 600 people
will be die.
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•
Assume you are the vice president of manufacturing in a Fortune
500 company employing over 130,000 people with annual sales
exceeding $10 billion. Due to a recession and structural changes in
your industry, one of your factories (with 600 employees) is faced
with either a complete or partial shutdown. You and your staff have
carefully narrowed the options to either:
•
a. Scale back now and keep a few production lines open.
Exactly 400 jobs will be lost (out of 600)
•
b. Invest in new equipment that may or may not improve your
competitive position. There is a one-third chance that no jobs
will be lost, but a two-thirds chance that all 600 jobs will be lost.
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Framing in Business Decisions
•
Frames of Reference
• The reference point is a point of comparison, a
Assume you are the vice president of manufacturing in a Fortune
500 company employing over 130,000 people with annual sales
exceeding $10 billion. Due to a recession and structural changes in
your industry, one of your factories (with 600 employees) is faced
with either a complete or partial shutdown. You and your staff have
carefully narrowed the options to either:
benchmark
•
a. S
Scale
l b
back
k now and
d kkeep a ffew production
d i lilines open.
Exactly 200 jobs will be saved (out of 600 threatened with layoff)
•
b. Invest in new equipment that may or may not improve your
competitive position. There is a one-third chance that all jobs
will be saved, but a two-thirds chance that none of the 600 jobs
will be saved.
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• Examples of reference points in an investment setting:
ƒ Purchase price (entry point)
ƒ Current price
ƒ Lowest price the stock reached after purchase
ƒ Highest price the stock reached after purchase
(Stock price path over time may influence reference
point)
• Prospect Theory does not dictate the reference point
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Other Framing Examples
Frames as an “Anchor”
• Increase in prices
ƒ Price increase vs. discontinuing a discount or rebate
• Credit card price difference
ƒ Cash discount vs. extra fee for use of credit card
• Tax Consequences
ƒ Exemptions for children vs
vs. higher tax if no children
• IBM and Fed Ex
ƒ Internet E commerce company vs. computer
Richard Thaler example:
In the following "before or after" problem the target date is chosen
randomly for each person. To do this, take the last three digits of your
student ID number and add 400. Insert the result in the first blank below,
where it reads [date].
The Huns under Attila invaded Europe and penetrated deep into what is
now France where they were defeated and forced to return eastward.
Did these events occur before or after AD _____ [date]?
manufacturer
ƒ transport company vs. package delivery
Before____
• How a stock performs is judged relative to a benchmark;
not its absolute performance
After____
In what year did Attila's defeat occur? ____
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Frames as an “Anchor”
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Framing and Anchoring
• Idea:
ƒ the way that options are presented affects
Results:
If [date] was between…
option selection or outcome
the average response was…
400 - 700
676 AD
701 - 1000
738 AD
1001 - 1200
848 AD
1201 - 1400
940 AD
• Example: Subjects were given 5 seconds to
estimate the following:
•
8x7x6x5x4x3x2x1
[correct answer: 451 AD]
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Bounded Rationality Example
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Example 1
• Please rank order the following statements by their
probability, using 1 for the most probable and 8 for the
least probable
• Linda is 31 years old, single, outspoken and
very bright. She majored in philosophy. As a
student she was deeply concerned with the
issues of discrimination and social justice,
and
d also
l participated
ti i t d iin anti-nuclear
ti
l
demonstrations.
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a) Linda is a teacher in elementary school
b) Linda works in a bookstore and takes Yoga classes
c) Linda is active in the feminist movement
d) Linda is a psychiatric social worker
e) Linda is a member of the League of Women voters
f) Linda is a bank teller
g) Linda is an insurance salesperson
h) Linda is a bank teller and is active in the feminist
movement
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Common Heuristics
Common Heuristics
Cunjunctive Fallacy
• 85% of people rate “h” as more likely than “f”
• Fallacy in reasoning: probability of “h” cannot
strictly be higher than “f”
f , since “h”
h is a subset
of “f”
Representativeness Heuristic: making
choices based on how similar or
representative a person or sample is,
rather than relying on calculated probability
ƒ Linda is regarded as “representative” of a
feminist, so most people rate “c” highly
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Example 2
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Common Heuristics
• Imagine urns filled with balls, of which 2/3 are one
Frequency Heuristic: making use of number
of occurrences, rather than probability of
occurrence, in probability judgments
color and 1/3 another (that is, there are twice as many
of one color as the other)
• Assume that you draw 5 balls, 4 red ones and 1 white
• Urn example: Most people select Urn B
one from Urn A.
Urn B has more white (8 vs.
vs 1),
1) but the sample
size is larger so the sample proportion should be
closer to the true .6667 than for Urn A.
• Also assume that you draw 20 balls, 12 red and 8
white from Urn B.
• Suppose that one of the Urns has more white balls
than red ones. Which of the two is more likely to have
more white balls, A or B?
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Actual Probabilities
Example 3
• P(x = 1, given n = 5 and p = .6667) = .04115
The frequency of occurrence of letters in the
English language was studied.
• P(x = 8, given n = 20 and p = .6667) = .00925
In typical texts, the relative frequency of letters in
the first and third p
position was tallied. Consider
the letter R.
People ignore the fact that large samples are less
likely to deviate from the mean, compared to small
samples
Is it more likely to appear in
- the first position?
(remember the Central Limit Theorem?)
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- the third position?
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Common Heuristics
Example 4
Problem A:
Availability Heuristic: using the most
available, easiest to remember, or apparent
answer to guide judgment
In four pages of a novel (about 2000 words), how many words
would you expect to find that have the form _ _ _ _ _ n _ ?
(seven letter words that have the letter n in the sixth position)
Problem B:
Results (Thaler):
… seven letter words ending in “ing”, i.e. _ _ _ _ i n g ?
Among 152 subjects, 105 judged the first position to be more
likely, even though in reality the third position is more frequent
(same for letters K,L,N,V).
Indicate your best estimate by circling one of the values
below:
0
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5-7
8-10
11-15
16+
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Emotional Reaction
The availability heuristic: frequency or
probability is estimated by the ease with which
instances or associations can be brought to
mind.
“What do you think is the ratio of the number of deaths
caused by car accidents to the number of deaths
caused by stomach cancer in a typical recent year in
the U.S.?”
•
Mr. A and Mr. B were scheduled to leave the airport on different
flights, at the same time. They traveled from town in the same
limousine, were caught in a traffic jam, and arrived at the airport 30
minutes after the scheduled departure time of their flights.
•
Mr. A is told that his flight left on time.
•
Mr. B is told that his flight was delayed, and just left five minutes
ago.
• Who is more upset, Mr. A or Mr. B?
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Emotional Reaction
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Exception vs. Routine
• Emotional reaction (regret, sympathy) depends
• Ms. Y was involved in an accident when driving home
after work on her regular route. Ms. Z was involved in
a similar accident when driving on a route she only
takes when she wants a change of scenery.
on:
• 1) Ease of undoing event
ƒ Missed airplane (Kahneman & Tversky)
ƒ Silver & Bronze medalists (Medvec, Madey, &
• Who is more upset, Ms. Y or Ms. Z?
Gilovich)
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Another Availability Example
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Action vs. Inaction
Emotional Reaction
• Mr. Smith owns shares in a company A. During the
• Emotional reaction (regret, sympathy) depends on:
• 2) Ease of undoing actions leading to the event
• Exception vs. routine
past year he considered switching to stock in company
B, but decided against it. He now finds that he would
have been better off by $1200 if he had switched to the
stock of company B. Mr. Jones owned shares in
company B
B. During the past year he switched to stock
in company A. He now finds that he would have been
better off by $1200 if he had kept his stock in company
B.
ƒ Accident after route change (K & T)
• Action vs. inaction
ƒ Keeping vs. switching to a losing stock (K & T)
ƒ Time course of regret for actions and inactions (Gilovich &
Medvec)
• Short term -- regret action
• Long term -- regret inaction
• Who is more upset, Mr. Smith or Mr. Jones?
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Endowment Effect
Endowment Effect Examples
•
It may be hard to sell a stock once it is safely in your portfolio
ƒ Is this why firms offer dividends? Owners get cash flow without having to sell
• Also called the “status quo effect”
shares.
•
• People demand more for something they already own
than they would be willing to pay for it.
•
Reluctance to rebalance investment portfolios
Worker’s reluctance to change jobs – do new hires make more than
existing employees?
• Cornel University: coffee mug vs.
vs chocolate bar
•
example
ƒ Minimum “sell” offer > maximum “buy” offer
ƒ For rational decision makers these would be equal
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Trial ownership (and other “try before you buy” offers)
ƒ Extended test drive offer for a car
ƒ Money back guarantee on tires if not satisfied
ƒ “Try my Norelco razor free for 30 days…”
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•
Rooting for hometown football team after you move away
•
Law: people may value rights they already have more than they
value rights they could acquire
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Other Cognitive Biases
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Example 4
• Our minds usually work very well.
Problem 1: Suppose we rank the students in this class in
terms of their overall grade performance on the quizzes
and exams. In what percentile do you expect your
performance to be?
• But sometimes the world leads us astray.
• Does this matter in markets?
90+ 89-80 79-70 69-60 59-50 49-40 39-30 29-20 19-10
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Overconfidence and Optimism
Overconfidence and Optimism
Two kinds of knowledge:
Optimism:
Primary: how much you know.
Secondary: how well you know your limits.
an excessive estimate of the probability of
a good outcome.
Are overconfidence and optimism useful for managers?
My opinion: for decision making purposes, it is best to
have accurate probability assessments.
Overconfidence: regardless of primary knowledge,
secondary knowledge is overestimated.
But, it is possible that overconfidence and optimism may
serve a beneficial motivational role.
• When asked to give a 90% confidence limit for some quantity,
people give ranges that include the right number only 70% of the
time.
What factors contribute to overconfidence?
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Hindsight Bias
Hindsight Bias
Three major findings:
Hindsight Bias: the tendency for people, once
they know an outcome, to believe that they
would have predicted the actual outcome of the
event.
1. Hindsight effects exist: discrepancies are found
between probability ratings for events in foresight and
hindsight.
2 Th
2.
The effect
ff t is
i unconscious.
i
S bj t are unaware off
Subjects
the effects of outcome knowledge on hindsight
judgments.
Also known as
3. There are altered representations of relevant
evidence: the predictive importance of events related to
the outcome changes in hindsight.
“Monday Morning Quarterbacking”
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Improving Decision Making
Hindsight Bias
Key Points
• Don’t generalize based on insufficient data.
• Don’t let something that is easy to recall bias your
Applications of hindsight bias:
1. Judge to Jury: "Please ignore that statement."
decision.
• Don’t base estimates of future values on recently
2. Independence of second medical opinions?
observed or unrelated numbers.
Physicians: Arkes, Wortman, Saville, & Harkness (1981) compared
the diagnoses of physicians who read an unlabeled case history
with those of physicians who were told they were reading a case
history of a specified medical condition. Hindsight bias was
found.
• Don
Don’tt let the fact the people hate losses more than they
value gains influence repeated decisions.
• Don’t let the reality of past losses lead to risky options to
try to break even.
• Don’t let ownership or possession of something
3. ''If I coach third base, I'll have no one thrown out, I'll
guarantee that.''
influence its perceived value.
• Don’t let a positive/negative frame influence your
Don Zimmer, in applying for the Yankees 3rd base coaching job
(as reported in the New York Times)
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decision.
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