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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

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

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

Loss aversion

• Prospect pair 3 choose between:– 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.

Development of prospect theory

– These and other results led to prospect theory as an alternative to expected utility theory.

Prospect theory value function

Common value function functional form

– Function used often is:v(z) = zαfor z≥0, 0<α<1

v(z) = -λ(-z)βfor 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:– A: (.9, $2000)

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

• Prospect pair 7 choose between:

– A: (.001, -$5,000)– B: (-$5)

• Most prefer B which is inconsistent with risk seeking.

– Insurance need

– Once again, people seem to overweight probability events (which is why people buy insurance)

low-Certainty effect

• Prospect pair 8 choose between:

– A: (.2, $4000)– B: (.25, $3000)

• Prospect pair 9– choose between:

– 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

Weighting function

00.10.20.30.40.50.60.70.80.91

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:

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.

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.

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

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.

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

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 2ndquestion, 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 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…