# Utility Theory & Prospect Theory

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1012/2013Behavioral Finance

Chapter 6Prospect Theory

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Theory for decision making under risk

Normative Theory

Expected Utility Theory(von Neumann and Morgenstern, 1944)

Objective probability judgment

A set of intuitive axioms

Roots to be found in Bernoulli

(1738)

Descriptive Theory

Prospect Theory(Kahneman and Tversky, 1979)

Explicitly not normative

Positive application (summarizes

what people actually do)

Probably the most widely cited

(influential) social science paper

ever published

eike.kroll@ovgu.de

Advice how you should decide Prediction of what you will decide

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Prospect Theory

eike.kroll@ovgu.de

Editing Phase

Choice problem

Evaluation Phase

Probability

weighting Value Function

Decision

Prospect theory is strictly defined for choice

situations involving risk, although it has found its

way into other disciplines as well (e.g. marketing)

This is the preparation before options are evaluated.

Based on perception and psychological processes,

the presented information is organized.

This the link between observing information and

performing a choice. In contrast to expected utility

theory, risk is evaluated on two different dimensions.

(1) Probabilities and (2) payoffs

In contrast to normative choice theories, the goal of

prospect theory is to provide good prediction of

choices

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Editing Phase: Coding

In contrast to expected utility theory, decision makers do not consider their final

wealth. They consider gains and losses compared to a reference point.

During the editing phase, decision makers will decide what reference point to use

(e.g. opportunity cost, minimum wage requirement, etc.)

The payoffs of the lottery will then be coded as a gain or a loss

eike.kroll@ovgu.de

Choice Problem Modification

Option L

200.50

Option S

10

Expected

earnings in an

experiment

10

Option L

100.5-10

Option S

0

or

Reference Point

orEvaluation

Phase

Coding

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Editing Phase: Combination

In the evaluation phase, as in expected utility theory, only payoffs and

probabilities are considered

Therefore, probabilities of events with identical outcomes are combined

to one event.

eike.kroll@ovgu.de

Choice Problem

Option L

20E1(0.1)20E2(0.5)0

Option S

10

Option L

200.60

Option S

10

or

Reduction to Payoffs and Probabilities

orEvaluation

Phase

Combination

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Editing Phase: Simplification

People have difficulties to pick up small numerical differences in

probabilities and payoffs

For both, probabilities and payoffs, are modified to simpler numbers

eike.kroll@ovgu.de

Choice Problem

Option L

210.490

Option S

10

Option L

200.50

Option S

10

or

Rounding up/down to simpler numbers

orEvaluation

Phase

Simplification

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Editing Phase: Segregation

People perceive situations involving risk different than situations involving

sure outcomes (i.e. sure payoffs are not risky payoffs with probability 1)

Sure gains are segregated from the lottery, the same is true for sure losses

eike.kroll@ovgu.de

Choice Problem

Option L

300.2510

Option S

15

Option L

10 + 200.250

Option S

15

or

Disentangle safe from risky payoffs

orEvaluation

Phase

Segregation

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Editing Phase: Cancellation (Type I)

People focus on differences rather than similarities when evaluating

prospects

Equal payoffs of two options are therefore not considered when

performing a choice (are considered not to have an influence on wealth)

eike.kroll@ovgu.de

Choice Problem

Option L

200.250.5-5

Option S

200.2150.5-10

Option L

00.250.5-5

Option S

00.2150.5-10

or

Identical payoffs are not considered

orEvaluation

Phase

Cancellation

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Editing Phase: Cancellation (Type II)

In expected utility theory we have the Reduction of Compound Lotteries

axiom

In prospect theory: two-stage lotteries are reduced to the reduced form

If in the first stage one payoff is zero, the first stage is neglected all

together

eike.kroll@ovgu.de

Two-stage Lottery Neglecting of the first stage

Evaluation

Phase

Cancellation

0

20

000.25

0.75

0.8

0.2

20

00

0.8

0.2

h l

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Editing Phase

Note:

The sequence of editing

procedures may differ between

decision makers and choice

problems

The sequence of editingprocedures probably depends on

the task and framing of the

choice problem

The application of some editing

procedures may prevent othersfrom being applied

eike.kroll@ovgu.de

Coding

Combination

Simplification

Segregation

Cancellation

B h i l Fi

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Note down your decisions for the following scenario

Story: 600 people are attacked by a fatal disease

Choice: Which program would you prefer

Program A: Saving 200 lives for sure

Program B: Saving 600 lives with 1/3 probability

eike.kroll@ovgu.de

S1

B h i l Fi

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Note down your decisions for the following scenario

Story: 600 people are attacked by a fatal disease

Choice: Which program would you prefer

Program A: Losing 400 lives for sure

Program B: Losing 600 lives with 2/3 probability

eike.kroll@ovgu.de

S2

Behavioral Finance

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13012/2013Behavioral Finance

Note down your decisions for the following scenario

Story: Imagine that you have just been given 1000 Euro

Choice: Which option would you prefer

Option A: You receive 500 Euro for sure

Option B: You receive 1000 Euro with 50% chance

and nothing otherwise

eike.kroll@ovgu.de

S3

Behavioral Finance

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Note down your decisions for the following scenario

Story: Imagine that you have just been given 2000 Euro

Choice: Which option would you prefer

Option A: You have to pay back 500 Euro for sure

Option B: You have to pay back 1000 Euro with 50% chance

and nothing otherwise

eike.kroll@ovgu.de

S4

Behavioral Finance

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Framing effect

Story: 600 people are attacked by a fatal disease

Choice: Which program would you prefer

Live-saving frame:

Program A: Saving 200 lives for sure Program B: Saving 600 lives with 1/3 probability

Live-losing frame:

Program A: Losing 400 lives for sure

Program B: Losing 600 lives with 2/3 probability

Program A and B are identical in both scenarios.

Only the Frame of choice tasks changes

eike.kroll@ovgu.de

S1

S2

Blacked Out

To be revealed in the lecture

Behavioral Finance

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16012/2013Behavioral Finance

Framing Effect

Story: Imagine that you have just been given 1000 Euro

Choice: Which option would you prefer

Option A: You receive 500 Euro for sure

Option B: You receive 1000 Euro with 50% chanceand nothing otherwise

Story: Imagine that you have just been given 2000 Euro

Choice: Which option would you prefer

Option A: You have to pay back 500 Euro for sure

Option B: You have to pay back 1000 Euro with 50% chance

and nothing otherwise

Option A and B are identical in both scenarios.

Only the Frame of choice tasks changes

eike.kroll@ovgu.de

S3

S4

Blacked Out

To be revealed in the lecture

Behavioral Finance

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17012/2013Behavioral Finance

Evaluation Phase: Value Function

Three characteristics

Decreasing marginal utility for

gains (risk-aversi

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