Ch03.pdf

Chapter 3: Prospect Theory, Framing
and Mental Accounting
Powerpoint Slides to accompany Behavioral
Finance: Psychology, Decision-making and Markets
by Lucy F. Ackert & Richard Deaves
©2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or
posted to a publicly available website, in whole or in part.
1

Prospect theory
• Prospect theory was developed by Kahneman
and Tversky base on observing actual behavior.
• Experimental evidence says that people often
behave contrary to expected utility theory.
• Expected utility theory is normative.
– What people should do
• While prospect theory is positive.
– What people do
2

Risk aversion vs. risk seeking
• Prospect pair 1 -- choose between:
– A: (.8, 4,000)
– B: (3,000)
– Note: with certainty no need to show a probability
• Prospect pair 2 – choose between:
– A: (.8, -4,000)
– B: (-3,000)
• Results for 1: most prefer sure $3000 which is consistent with
risk aversion.
• Results for 2: most do not prefer sure -$3000 – this is
inconsistent with risk aversion.
• Implies people are risk seeking in negative domain (reflection
effect)!
3

Loss aversion
– A: no prospect
– B: (.5, $50, -$50)
• Most choose A.
• Despite risk aversion in positive domain and risk
seeking in negative domain, losses loom larger than
gains.
• This is called loss aversion.
4

Development of prospect theory
– These and other results led to prospect theory as an
alternative to expected utility theory.
– Key precepts:
• Value function is in terms of gains or losses
• Risk aversion in positive domain
• Risk seeking in negative domain
• Loss aversion
5

Prospect theory value function
6

Common value function functional form
– Function used often is:
v(z) = zα for z≥0, 0<α<1
v(z) = -λ(-z)β for z<0, >1, 0<β<1
– Kink at origin is from λ.
– Value function (not utility) so v is used.
– Ask people about 50/50 coin toss where loss is $50 and gain is
unknown.
– What gain would make people indifferent between gamble or
no gamble?
• Many say about $125, which implies value of 2.5 for λ.
• Value above one reflects loss aversion.
7

Common ratio effect
– A: (.9, $2000)
– B: (.45, $4000)
– A: (.002, $2000)
– B: (.001, $4000)
• Most choose 4A and 5B, but this contradicts
expected utility.
8

Common ratio effect cont.
• Invoke linear transformation rule:
– Set u(0) = 0 and u(4000) = 1
– 4A choice implies .9u(2,000) > .45
– 5B choice implies .002u(2,000) < .001
– A contradiction
• How does prospect theory reconcile observed
choices?
– Nonlinear weighting function can explain these choices
9

Lottery tickets
– A: (.001, $5,000)
– B: ($5)
• Most prefer A which is inconsistent with risk
aversion.
– Lottery effect
– People seem to overweight low-probability events
(which is why people buy lottery tickets)
10

Insurance
– A: (.001, -$5,000)
– B: (-$5)
• Most prefer B which is inconsistent with risk
seeking.
– Insurance need
– Once again, people seem to overweight low-
probability events (which is why people buy
insurance)
11

Certainty effect
– A: (.2, $4000)
– B: (.25, $3000)
– A: (.8, $4,000)
– B: ($3000)
• Most choose 8A and 9B, but they shouldn’t.
– Use exact same proof as above
• Why?
– Certainty is accorded high weight relative to near-certainty
12

Weighting function
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
probability
weight
13

Weighting function notes
• Instead of using simple probabilities as in expected utility,
prospect theory uses decision weights, which differ from
probabilities.
• This (displayed) mathematical function is:
(pr) = pr / [pr + (1- pr)](1/) where  = .65
• Weighting function for losses can vary from weighting
function for gains.
• Low probabilities are given relatively higher weights than
more probable events.
• And certainty is weighted highly vs. near-certainty.
• Using functions like this solves some earlier puzzles.
14

Valuing prospects under prospect theory
• Instead of expected utility we have:
V(P) = (pr A) * v(zA) + (1 - prA) * v(zB)
• Steps:
– Convert probabilities to decision weights
– Calculate values of wealth differences
– Use above formula
15

Prospects 8 & 9 again
• Following probabilities are mapped on to this
weighting function:
– pr = .20;  = .26
– pr = .25;  = .29
– pr = .80;  = .64
– pr = 1;  = 1
• Say we use v(z) = z1/2.
• Prospect 8:
– A: .26*40001/2 = 16.44
– B: .29*30001/2 = 15.88
– A is preferred.
16

Prospects 8 & 9 again cont.
• Prospect 9:
– A: .64*40001/2 = 40.48
– B: 1*30001/2 = 54.78
– B is preferred.
– A vs. B flip-flop comes from weighting function.
17

Frames
• Essential condition for a theory of choice is
principle of invariance: different
representations of same problem should yield
same preference.
• Unfortunately this sometimes does not work
out in practice:
– People have different perspectives and come up
with different decisions depending on how a
problem is framed.
18

Some more prospects
• Prospect pair 10 – you are given $1000 – then choose
between:
– A: (.5, another $1000)
– B: ($500)
• Prospect pair 11 – you are given $2000 – then choose
between:
– A: (.5, -$1000)
– B: (-$500)
• Results for 10: most prefer B.
• Results for 11: most prefer A.
• Problems are identical! People have chosen differently
because of different frames.
19

An odder example
• You must make two lottery choices. One draw will be in
morning; other in afternoon.
• Prospect pair 12:
– A: ($2400)
– B: (.25, $10,000)
• Prospect pair 13:
– A: (-$7500)
– B: (.75, -$10,000)
• People prefer 12A and 13B.
20

An odder example cont.
• But 12A and 13B combo leads:
(.25, $2400, -$7,600)
• And 12B and 13A combo leads:
(.25, $2500, -$7,500)
• So people on average choose a gamble that is
dominated by the one that they turn down.
• Why? They have difficulty getting past frame.
21

Mental accounting
• Related to prospect theory and frames.
• Accounting is process of categorizing money,
spending and financial events.
• Mental accounting is a description of way people
intuitively do these things, and how it impacts
financial decision-making.
• Often tendency to use mental accounting leads to
odd and suboptimal decisions.
• A few highlights of mental accounting follow…
22

Prospect theory, mental
accounting and prior outcomes
• Problem with prospect theory is that it was set
up to deal with one-shot gambles – but what
if there have been prior gains or losses?
• Do we go back to zero (segregation), or move
along curve (integration)?
23

Integration vs. segregation
24
Integration
Segregation

Theater ticket problems
• 1. Imagine you have decided to see a play where
admission is $10. As you enter theater you discover
that you have lost a $10 bill. Would you still pay $10
for a ticket to the play?
• 2. Imagine that you have decided to see a play and
paid the admission price of $10 per ticket. As you
enter the theater 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?
25

Theater ticket problems cont.
• Nothing is really different about the problems.
• Is the ticket worth $10?
• Of respondents given first question, 88% said they
would buy a ticket.
• Of respondents given second question, 54% said they
would not buy a ticket.
• In 2nd question, integration is more likely because
both lost ticket and new ticket would be from same
“account.”
– Integration might suggest that $20 is too much for the ticket.
26

Opening and closing accounts
• Once an “account” is closed, you go back to
zero.
• Evidence that people avoid closing accounts at
a loss:
– Selling a stock at a loss is painful: disposition effect (to be
discussed).
– Companies rarely have low negative earnings but often have low
positive earnings:
• They manage earnings either pushing things to low positive…
• Or they “take a bath” and move to high negative
27

Ch03.pdf

Recommended

Recommended

More Related Content

Similar to Ch03.pdf

Similar to Ch03.pdf (20)

Recently uploaded

Recently uploaded (20)

Ch03.pdf