# Prospect Theory

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```					                                           10/8/08

Prospect Theory

Sendhil Mullainathan
Economics 2030
Fall 2008

Outline of Talk
• What is Prospect Theory?
• Empirical Evidence for Prospect Theory
• Experimental Challenges
• Theoretical Work and Important
Application Areas
• Big Picture Observations

Outline of Talk
• What is Prospect Theory?
• Empirical Evidence for Prospect Theory
• Experimental Challenges
• Theoretical Work and Important
Application Areas
• Big Picture Observations

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10/8/08

What is Prospect Theory?
• A collection of extremely clever
experiment that illustrate a few core ideas.
• So presentation of this theory will be less
“theory” and more “experiment”
• One of the two stalwarts of behavioral
economics (present bias/hyperbolic
discounting/self-control is the other)

Some Evidence
• [8] Choose between two bets
– A : (.25 \$6000)
– B : (.25 \$4000; .25 \$2000)

Some Evidence

• [8’] Choose between two bets
– A : (.25 -\$6000)
– B : (.25 -\$4000; .25 -\$2000)

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Some Evidence
• [8] Choose between two bets (N=68):
– A : \$6000 at 25% chance (18% chose)
– B : \$4000 at 25% chance and \$2000 at 25% chance
(82% chose)
• [8’] N=64 people were asked to choose
between two bets:
– A : -\$6000 at 25% chance (70% chose)
– B : -\$4000 at 25% chance and -\$2000 at 25%
chance (30% chose)

Prospect Theory
Subjects who have already been given \$1000 are
• a certain reward of \$500            (84%)
• or a 50% chance of earning \$1000    (16%)

A different sample of subjects are given \$2000, and asked
to choose either
• a certain loss of \$500                 (31%)
• or a 50% chance of losing \$1000        (69%)

• a certain reward of \$1500
• a 50% chance of earning \$1000 and a 50% chance of
earning \$2000

General Lesson
• Losses vs. Gains matters
• Risk seeing in losses, risk averse in gains
• Losses and gains can be framed

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Some Evidence
• [9] (N = 152). Imagine that the US is preparing for the
outbreak of an unusual Asian disease which is expected to kill
600 people. Two alternative programs to combat the disease
have been proposed. Assume that the exact scientific estimates
of the consequences of the programs are as follows:
– A : If program A is adopted 200 people will be saved
– B : If program B is adopted there is a one third probability that 600
people will be saved and a two-thirds probability that no people will be
saved.
• Which of the two programs would you favour?

Some Evidence
• [9] (N = 152). Imagine that the US is preparing for the
outbreak of an unusual Asian disease which is expected to kill
600 people. Two alternative programs to combat the disease
have been proposed. Assume that the exact scientific estimates
of the consequences of the programs are as follows:
– A : If program A is adopted 200 people will be saved (72%)
– B : If program B is adopted there is a one third probability that 600
people will be saved and a two-thirds probability that no people will be
saved. (28%)
• Which of the two programs would you favour?

Some Evidence
• [10] (N = 155). Imagine that the US is preparing for
the outbreak of an unusual Asian disease which is
expected to kill 600 people. Two alternative programs
to combat the disease have been proposed. Assume
that the exact scientific estimates of the consequences
of the programs are as follows:
– C : If program C is adopted 400 people will die
– D : If program D is adopted there is a one third probability
that nobody will die and a two-thirds probability that 600
people will die.
• Which of the two programs would you favour?

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Some Evidence
• [10] (N = 155). Imagine that the US is preparing for
the outbreak of an unusual Asian disease which is
expected to kill 600 people. Two alternative programs
to combat the disease have been proposed. Assume
that the exact scientific estimates of the consequences
of the programs are as follows:
– C : If program C is adopted 400 people will die (22%)
– D : If program D is adopted there is a one third probability
that nobody will die and a two-thirds probability that 600
people will die. (78%)
• Which of the two programs would you favour?

Implications
• Losses and gains can be created by the
framing of the question

Some Evidence
• [11] (N = 86). Choose between
– A : 25% chance to win \$240 and 75% chance to
lose \$760
– B : 25% chance to win \$250 and 75% chance to
lose \$750

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Some Evidence
• [11] (N = 86). Choose between
– A : 25% chance to win \$240 and 75% chance to
lose \$760 (0%)
– B : 25% chance to win \$250 and 75% chance to
lose \$750 (100%)
• In Problem [11] it is easy to see that option B
dominates A, and all respondents chose
accordingly.

Some Evidence
• [12] (N = 150). Imagine that you face the following
pair of concurrent decisions. First examine both
decisions, then indicate the options you prefer:
– Decision (i). Choose between:
• C: A sure gain of \$240
• D: 25% chance to gain \$1000 and 75% chance to gain nothing
– Decision (ii). Choose between:
• E: A sure loss of \$750
• F: 75% chance to lose \$1000 and 25% chance to lose nothing

Some Evidence
• [12] (N = 150). Imagine that you face the following
pair of concurrent decisions. First examine both
decisions, then indicate the options you prefer:
– Decision (i). Choose between:
• C: A sure gain of \$240 (84%)
• D: 25% chance to gain \$1000 and 75% chance to gain nothing (16%)
– Decision (ii). Choose between:
• E: A sure loss of \$750 (13%)
• F: 75% chance to lose \$1000 and 25% chance to lose nothing (87%)

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Implications
• Losses loom larger than gains

• Value function implied
– Concave in gains
– Convex in domain of losses
– Loss curve around zero is steeper than gain
curve

The Hypothetical Value Function
Value
Concave in gains

Loss curve
steeper than gains
Losses                                      Gains

Convex in losses

Beliefs in Prospect Theory

The Creation of Decision Weights
From Probabilities

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Beliefs in Prospect Theory
• EU: Probabilities enter linearly
• Prospect theory: Probabilities enter as “decision
weights” by means of a function

Some Evidence
• [1] Consider the following choice put to N = 66
people:
– A : \$6000 at .45 chance [EV = 2700]
– B : \$3000 at .90 chance [EV = 2700]

Some Evidence
• [1] Consider the following choice put to N = 66
people:
– A : \$6000 at .45 chance [EV = 2700] (14% chose)
– B : \$3000 at .90 chance [EV = 2700] (86% chose)

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Some Evidence
• [1] Consider the following choice put to N = 66
people:
– A : \$6000 at .45 chance [EV = 2700] (14% chose)
– B : \$3000 at .90 chance [EV = 2700] (86% chose)
• [1’] Now consider the following problem put to N
= 66 people
– A : \$6000 at .001 chance [EV = 6]
– B : \$3000 at .002 chance [EV = 6]

Some Evidence
• [1] Consider the following choice put to N = 66
people:
– A : \$6000 at .45 chance [EV = 2700] (14% chose)
– B : \$3000 at .90 chance [EV = 2700] (86% chose)
• [1’] Now consider the following problem put to N
= 66 people
– A : \$6000 at .001 chance [EV = 6] (73% chose)
– B : \$3000 at .002 chance [EV = 6] (27% chose)

Some Evidence
• [2] Consider the following choice put to N = 72
people:
– A : 5000 at .001 chance [EV = 5] (72% chose)
– B : 5 at 1 (certainty) [EV = 5] (28% chose)
• [2’] Also consider the following choice put to N = 72
people
– A : -5000 at .001 chance [EV = -5] (17% chose)
– B : -5 at 1 (certainty) [EV = -5] (83% chose)

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Evidence for Certainty Effect
• [3] Zeckhauser asked respondents to imagine that they were
forced to play Russian Roulette. However, in this game they
were given the opportunity to purchase one bullet from the
– [A] How much they would be willing to pay for the chance to reduce the
number of bullets from four to three
– [B] How much they would be willing to pay for the chance to reduce the
number of bullets from one to zero?
• Most respondents were willing to pay much more for [B] the
reduction of the chance of death from 1/6 to zero than for [A]
the chance to reduce the probability of death from 4/6 to 3/6

More Evidence

• [4] Consider the following two stage game put to N =
85 people. In the first stage there is an 85% chance to
end the game without winning anything, and a 25%
chance to move to the second stage. If you reach the
second stage, you have a choice between:
– A : a sure win of \$30 [EV = 30] (74% chose)
– B : 80% chance to win \$45 [EV = 36] (26% chose)
i.e., before the outcome of the first stage is known.

More Evidence

• [4] Consider the following two stage game put to N =
85 people. In the first stage there is an 85% chance to
end the game without winning anything, and a 25%
chance to move to the second stage. If you reach the
second stage, you have a choice between:
– A : a sure win of \$30 [EV = 30]
– B : 80% chance to win \$45 [EV = 36]
i.e., before the outcome of the first stage is known.

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More Evidence

• [5] Consider a problem put to N = 81 people.
Which of the following options do you prefer?
– C : 25% chance to win \$30 [EV = 7.5]
– D : 20% chance to win \$45 [EV = 9]

More Evidence

• [5] Consider a problem put to N = 81 people.
Which of the following options do you prefer?
– C : 25% chance to win \$30 [EV = 7.5] (42%)
– D : 20% chance to win \$45 [EV = 9] (58%)

Non-monetary evidence of certainty effect

• [6] N=72 people asked to choose between
– A : 50% chance to win a three week tour of England,
France and Italy (22% chose)
– B : A one-week tour of England with certainty (78% chose)
• [6’] N=72 people asked to choose between
– C : 5% chance to win a three week tour of England, France
and Italy (67% chose)
– D : A 10% chance of a one-week tour of England (33%
chose)

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Undervaluing intermediate probabilities
• [7] Suppose you are considering buying insurance
against flooding, but are hesitating because of the
with an alternative offer. You can have the insurance
at less than half the premium and you will be fully
covered if the flood takes place on an even numbered
day, but not covered at all if the flood takes place on
an odd numbered day. Would you take this revised
offer?
• Most people reject this offer of probabilistic
insurance

Hypothetical Probability Weighting
Function
1.0
1. Discontinuity
(Certainty
Decision                                            Effect)
Weight:                                             2. Underwighting
(p)                                               Intermediate
probabilities
.5
3. Overweighting
Very small
probabilities

.5

1.0
Stated Probability: p

Summary of Prospect Theory
• Editing phase
– Organizes options into relevant values, reference points and
probabilities. Bracketing
• Evaluation phase
– Maps real probabilities of bracketed prospect to subjective
“decision weights” through a “ ” function
– Maps objective “values” into a function defined in terms of
losses and gains from reference point
– Choose the prospect of highest value

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Editing Operations
• Coding as gain or loss
– People normally perceive outcomes as “gains” or “losses”. The
decision as to whether a gain or loss is involved in a prospect depends
on the reference point, which the statement (“framing”) of prospect can
affect
– Ex: 50/50 chance to gain 100 or lose 100 versus nothing?
• Segregation
– Riskless components of a prospect are segregated from risky
components
• Simplification
– Complex prospects are simplified to more manageable prospects
• These are by far the weakest part of prospect theory.

Summary of Prospect Theory
• Value Function
– Losses vs. gains
– Risk averse in gains; risk seeking in losses
– Loss aversion
• Probability weighting function
– Certainty effect
– Underweighting intermediate probability
– Overweighting very small probabilities
• Bracketing matters
– Value function: Narrow bracketing and framing of reference points
– Weighting function: pooling of events and p vs. 1-p

More Evidence
• Endowment Effect

• Risk aversion in small gambles

• Mental Accounting

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Kahneman-Knetsch-Thaler
• Observed numerous experiments showed
willingness to pay-willingness to accept
disparity in survey questions.

Experiment
• Subjects given tokens or not with valuations
– Each owner and non-owner provided willingness to
pay/accept.
– Demand and supply curves mapped out. Market
clearing price determined. Transactions implemented
• Half subjects given mugs
– All examined mug, either own or neighbors
• Again, market set.
• How many trades do you expect?

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A Gamble
• What X makes you indifferent between (1, \$X)
and (.5 \$0; .5 \$20)

Interpreting this
• Expected utility theory
.5Eu(w + 20) + .5Eu(w) = Eu(w + x)
– What do you expect x to be?

• Prospect Theory. Could be:
.5v(20) + .5v(0) = v(x)
– Why do I write “could be”?
• Rabin’s calibration theorem

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Source : M. Rabin and R.H.Thaler (2001), Anomalies- Risk Aversion, Journal of
Economic Perspectives, pages 219-232

Rabin’s Calibration Theorem
• Intuition
– Use concavity to force the utility function to
get flatter and flatter
– Key is that you turn down the bet at many
wealth levels

Mental Accounting
• This illustrates importance of bracketing
• Mental accounting investigates at greater
length.
– Framing is not just about losses/gains
– It is also about which gambles are segregated
or integrated
– Elusive editing module of prospect theory

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Multiattribute Problem
• [13] N=88. Imagine that you are about to
purchase a jacket for \$125 and a calculator for
\$15. The calculator salesman informs you that
the calculator that you wish to buy is on sale
for \$10 at another branch of the store, located
20 minutes drive away. Would you make a trip
to the other store?
• 68% said “Yes”

Multiattribute problem
• [13’] N=93. Imagine that you are about to purchase a
jacket for \$125 and a calculator for \$15. The jacket
salesman informs you that the jacket that you wish to
buy is on sale for \$120 at another branch of the store,
located 20 minutes drive away. Would you make a
trip to the other store?
• Only 29% of N=93 respondents were willing to drive
to the other store to save \$5 on as \$120 jacket

Interpreting in Prospect Theory
• Implied Coding
• Costs t to save s
v g (g) + v\$ ( p) compared to v g (g) + v\$ ( p + s) + v t ( t)

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Which Account?
• [14] N = 200. Imagine that you have decided
to see a play and paid the admission price of
\$10 per ticket. As you enter the theatre, you
discover that you have lost the ticket. The seat
was not marked and the ticket cannot be
recovered.
• Would you pay \$10 for another ticket?

Which Account?
• [14] N = 200. Imagine that you have decided
to see a play and paid the admission price of
\$10 per ticket. As you enter the theatre, you
discover that you have lost the ticket. The seat
was not marked and the ticket cannot be
recovered.
• Would you pay \$10 for another ticket?
• Yes (46%). No (54%)

Which Account?, ctd
• [14’] N = 183. Imagine that you have decided
to see a play where admission is \$10 per ticket.
As you enter the theatre, you discover that you
have lost a \$10 bill.
• Would you still pay \$10 for a ticket for the
play?
• Yes (88%). No (12%).

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Which Account?, ctd
• [14’] N = 183. Imagine that you have decided
to see a play where admission is \$10 per ticket.
As you enter the theatre, you discover that you
have lost a \$10 bill.
• Would you still pay \$10 for a ticket for the
play?

Why might this be happening?
• Conjecture
Lost ticket v g ( play 20) vs v\$ ( 10)
Lost money v g ( play 10) + v\$ ( 10) vs v\$ ( 10)

Outline of Talk
• What is Prospect Theory?
• Empirical Evidence for Prospect Theory
• Experimental Challenges
• Theoretical Work and Important
Application Areas
• Big Picture Observations

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Empirical Evidence
• Labor Markets

• Asset markets

• Some examples of framing

Card Hyslop

Taxi Cab Drivers

Camerer Babcock Lowenstein Thaler

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Taxi Cab Drivers

Taxi Cab Driver Controversy
• Fail to find it for hot dog vendors in

• Farber’s reanalysis of other cab driver
data finds weak evidence

• What to think of the former?
– Latter is easy to understand

Field
• Law School Students
• Lottery to receive financial aid
• Must repay if they do not go into public interest law

• Waived if they go into public interest law

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Labor Markets
• Under-explored
– Ex: Do people search differently given their
last wage might be a reference wage?
– Do incentive/promotion schemes take into
account features of loss aversion? Bonuses?

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Odean
• Looks for direct evidence of prospect theory in
asset markets

• In investor behavior.

• How do they buy or sell stocks?

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Other asset markets
• Genesove-Mayer examine housing
markets

Interpretation
• Higher loss means higher selling price

• Other Facts
– Higher loss means longer time to sell

– But also higher sales price

– Interesting aside: Implied return on waiting
pretty high

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Outline of Talk
• What is Prospect Theory?
• Empirical Evidence for Prospect Theory
• Experimental Challenges
• Theoretical Work and Important
Application Areas
• Big Picture Observations

List’s Experiment
• Baseball Card Show
– Dealers and non-dealers
• Give them card A or card B (randomly)
– Examine willingness to switch

List

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Interpretation
• Does experience remove loss aversion?
• Observations:
– 95% of the subjects kept the final good. Why
is this odd?
– Note what prospect theory says
Keep B if v(A) + v( B) < 0
Keep A if v(B) + v( A) < 0
– Do you see a different way to explain the List
effect?
– How to reconcile with Odean?

Outline of Talk
• What is Prospect Theory?
• Empirical Evidence for Prospect Theory
• Experimental Challenges
• Theoretical Work and Important
Application Areas
• Big Picture Observations

Theoretical Work
• Careful application of prospect theory

• Where do reference points come from?

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Odean Revisited
• Barberis and Xiong
Stock drops in price v( pcurrent p purchase )
– Why does selling affect this?
– Ask whether utility only happens at realization
• Notice centrality of bracketing

Consumption Model
• Simple Euler equation

• What if there are multiple assets?

• How do we convert this to equity pricing?

Equity pricing model

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Calibrating this model
• Mehra Prescott, 1890-1979
–   Rate of return on equity is about .06
–   Std dev of consumption growth: .036
–   Std dev of stock market: .167
–   Correlation: .40
–   Covariance: .0024
• Implies:     =25

Benartzi Thaler
• Investors invest in stocks and bonds
• Observe performance of portfolio in time
intervals
• Loss averse investors
• What is the implication of variance now?
– Does it depend on frequency of observation?
• How different is this from traditional risk?
• Notice relation to Barberis and Xiong’s point

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Interesting findings
• At around evaluation of year, stock and bond
roughly equal

Barberis-Huang-Santos
• Observe that in calibrations this is not enough
– BT is not an equilibrium model.
– Does not produce enough stock return volatility.
• How to price risk in even more?

Barberis Huang Santos

• Standard utility function in consumption
• Utility over wealth
– Defined over current gains/losses (X)
– Impact of S, wealth, relative to lagged reference points captured in z.
Allows changing reference points (mental accounting)
– Key feature: Wealth movements matter independent of consumption
• Show they can calibrate such a model to explain equity

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Koszegi Rabin
• Reference Points

Koszegi Rabin

Koszegi Rabin
• How are reference points selected?
• Rational expectations
– Lottery over choice sets
– Individuals forecast what they would choose
in each choice set
– This forecast sets the reference point

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Koszegi Rabin

Koszegi-Rabin
• Implications:
– Multiple personal equilibria
– Stochastic price decrease can decrease sales
– Loss aversion may not manifest itself in some
market cases
• Note that this is already a prediction of PT. But it
was a vague prediction
• Observations:
– How to think about nominal wage rigidity?
– Does this explain List’s experiment?

Outline of Talk
• What is Prospect Theory?
• Empirical Evidence for Prospect Theory
• Experimental Challenges
• Theoretical Work and Important
Application Areas
• Big Picture Observations

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Big Picture Observations
• Notice less work on framing
• Notice centrality of reference points
– Empirical work
– Theoretical conceptualization
• Notice centrality of bracketing
– Very little understood theoretically or
empirically
– Experimental work has been hard going

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