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Chapter 3: Prospect Theory, Framing and Mental AccountingPowerpoint Slides to accompany Behavioral Finance: Psychology, Decision-making and Markets by Lucy F... Prospect theory• Prospect

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

• Expected utility theory is normative.

– What people should do

• While prospect theory is positive

– What people do

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

• Despite risk aversion in positive domain and risk

seeking in negative domain, losses loom larger than gains.

• This is called loss aversion.

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

Prospect theory value function

Common value function functional form

– Function used often is:

v(z) = z α 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

Common ratio effect

• Prospect pair 4 choose between:

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

– Once again, people seem to overweight

low-probability events (which is why people buy

insurance)

• 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

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

Valuing prospects under prospect theory

• Instead of expected utility we have:

V(P) = ( pr A ) * v(z A ) + (1 - pr A ) * v(z B )

• Steps:

– Convert probabilities to decision weights

– Calculate values of wealth differences

– Use above formula

Prospects 8 & 9 again

• Following probabilities are mapped on to this

Prospects 8 & 9 again cont.

• 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

Some more prospects

• Prospect pair 10 – you are given $1000 – then choose

• Results for 10: most prefer B.

• Results for 11: most prefer A.

• Problems are identical! People have chosen differently

An odder example

• You must make two lottery choices One draw will be in

morning; other in afternoon.

An odder example cont.

• But 12A and 13B combo leads:

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…

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)?

Integration vs segregation

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

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 2 nd question, integration is more likely because

both lost ticket and new ticket would be from same

“account.”

Opening and closing accounts

• Once an “account” is closed, you go back to