Session 4 Prospect Theory

8/3/2019 Session 4 Prospect Theory

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An analysis of decision under risk


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Exercise


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After Russ Berrie & Co., USA acquired the companythat made Koosh Ball, it was Jack Smiths job to

improve sales and profit. The balls were made in Asia

so he began by flying to Hong Kong and meeting with

the manufacturer. But before the meeting, hecontacted another firm in Asia to get a competitive

price. They offered to make the balls for 3 cents less

per ball. Smith now knew there was room for cost

cutting with his primary manufacturer. In China, yourword really matters and the honor you give your

partner means everything.


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Utility

Utility functions give us a way to measure

investor's preferences for wealth and the

amount ofrisk they are willing to undertake in

the hope of attaining greater wealth.

A utility function measures an investor's

relative preference for different levels of total

wealth


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The non-satiation property states that utility

increases with wealth, i.e., that more wealth is

preferred to less wealth, and that the investor

is never satiated { he never has so much

wealth that getting more would not be at least

a little bit desirable).


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The marginal utility of wealth decreases as

wealth increases.

Consider the extra (marginal) utility obtained by

the acquisition of one additional dollar. For

someone who only has one dollar to start with,

obtaining one more dollar is quite important.

For someone who already has a million dollars,

obtaining one more dollar is nearly

meaningless. In general, the increase in utilitycaused by the acquisition of an additional

dollar decreases as wealth increases.


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Decision making under risk can be viewed as a

choice between prospects or gambles.

A prospect (x1, p1; . .. ;xn, pn,) is a contract

that yields outcome xi with probability pi,

where p1 +p2+ . . .+pn, = 1.


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Expected Utility Theory (EUT)

Decision maker (DM) chooses between risky or

uncertain prospects by comparing

Their expected utility values, i.e., the weightedsums obtained by adding the utility values of

outcomes multiplied by their respective

probabilities

Expectation: U(x1, p1 ~. ;. . ;xn, pn) =p1u(x1)+ . . .

+pnu(xn).

Where U is the overall utility of a prospect


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EXPECTED UTILITY THEORY has dominated the

analysis of decision making under risk.

It is assumed that all reasonable people wouldwish to obey the axioms of the theory, and

that most people actually do, most of the

time.


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Probabilities

Utility


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Prospect Theory

There are several classes of choice problems

in which preferences systematically violate the

axioms of expected utility theory.


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Certainty, Probability & Possibility

PROBLEM1: Choose between

A: 2,500 with probability 0.33

2,400 with probability 0.66

0 with probability 0.01

OR

B: 2,400 with certainty


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Results

N =72 A [18] B [82]*

In Expected Utility Theory, the utilities of the

outcomes are weighted by their probabilities


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CERTAINTY EFFECT

Peoples preference systematically violate

principle ofExpected Utility Theory

Tendency to overweight outcomes that areconsidered certain, relative to outcomes

which are merely probable


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PROBLEM2: Choose between

C: 2,500 with probability .33,

0 with probability .67;

OR

D: 2,400 with probability .34,

0 with probability .66


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Results

N=72 C [83]*D

[17]Problem 2 is obtained from Problem 1 by

eliminating 0.66 chance of winning 2400 from

both prospects under consideration.

The change produces greater reduction in the

desirability when it alters the character of the

prospect from a sure gain to a probable one,

than when both the original and the reduced

prospects are uncertain


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PROBLEM 3

A: (4000, 0.80) or B : (3000)

PROBLEM 4

C: (4000, 0.20) or D : (3000,0.25)


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Results

N =95 Problem 3 A [20] B[80]*

N=95 Problem 4 C [65]* D [35]

The substitution axiom of utility theory asserts that ifM is preferred over N, then any (probability)mixture (M, p) must be preferred to the mixture(N,p).

Thus, reduction of probability winning from 1.0 to0.25 has greater effect than the reduction from 0.8to 0.2.


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PROBLEM 5

A : 50% chance to win a 3 week tour toEngland, France and Italy

or

B : A 1 week tour ofEngland with certainty


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N =72 A[22] B[78]*


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PROBLEM 6

C : 5% chance to win a three week tour ofEngland, France & Italy

OR

D : 10% chance to win a 1 week tour ofEngland


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N=72 C [67]* D[33]


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PROBLEM 7

A : (6000, 0.45) B : (3000, 0.90)

PROBLEM8

C : (6000, 0.001) C : (3000, 0.02)


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RESULTS

Problem 7 N=66 A[14] B[86]*

Problem 8 N=66 C [73]* D [27]

Conclusion

Where winning is possible but not probable(very minuscule 0.001 & 0.002) , most peoplechoose the prospect that offers the largergain.


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REFLECTION EFFECT

What happens when gains are replaced by

losses

PROBLEM

8

A : (-4000, 0.80) B : (-3000)

C : (-3000,0.90) D : (-6000, 0.45)


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RESULTS

Problem 8 N=95 A [92]* B[8]

N=66 C[8] D [92]*

Preference between negative prospects is the mirror

image of preference between positive prospects.

Thus, the reflection of prospects around 0 reverses thepreference order.

Thus, reflection effect implies that risk aversion in thepositive domain is accompanied by risk seeking in thenegative domain


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Framing Effect

Example 1

Problem 1 (Survival frame)

Surgery: Of 100 people having surgery 90 livethrough the post- operative period, 68 arealive

at theendof the first yearand 34 arealiveattheendof fiveyears.

Radiation Therapy: Of 100 people havingradiation therapyalllive through the treatment,77 arealiveat theendofoneyearand 22 arealiveat theendof fiveyears


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Problem 1 (Mortality frame) Surgery: Of 100 people having surgery 10 dieduring surgeryor the post-operative period,32 dieby theendof the first yearand 66 die

by theendof fiveyears. Radiation Therapy: Of 100 people havingradiation therapy, nonedieduring treatment,23 dieby theendofoneyearand 78 diebytheendof fiveyears


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Outcome

Theinconsequentialdifferencein formulationproducedamarkedeffect.

Theoverall percentageofrespondents who favoredradiation therapyrose from 18% in the survival frame

(N = 247) to 44% in themortality frame (N = 336). Theadvantageofradiation therapyover surgery

evidentlylooms larger when statedas areductionoftheriskofimmediatedeath from 10% to 0% ratherthanas anincrease from 90% to 100% in therateof

survival.

The framingeffect was not smaller forexperiencedphysicians or for statistically sophisticatedbusinessstudents than foragroup ofclinic patients


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Framing

Framing, a term used in media studies, sociology

and psychology, refers to the social construction of

a social phenomenon by a mass media sources or

specific political or social movements or

organizations.It is an inevitable process of selective influence over

the individual's perception of the meanings

attributed to words or phrases.A frame defines the packaging of an element of

rhetoric in such a way as to encourage certain

interpretations and to discourage others.


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Example

The initial response of the Bush Administrationto the assault of September 11, 2011 was to

frame the acts of terror as crime.

This framing was replaced within hours by a warmetaphor, yielding the War on Terror". The

difference between these two framings is in the

implied response. Crime connotes bringing

criminals to justice, putting them on trial and

sentencing them, whereas as war implies enemy

territory, military action and war powers for

government


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What are chances of winning a major prize in

instant scratchies ?


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If we return to our prospect theory we see

that framing of the offer becomes very

important in low probability situations.


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The people code the outcome of the lottery as

a gain by ensuring that it is right outside of

most peoples natural reference point (status

quo).


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Thus, although is generally desirable, it

appears that certainty increases aversiveness

of losses as well as the desirability of gains


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Prospect Theory

Major violations ofExpected Utility theory

Value function is concave for gains,

Value function is convex for losses, Steeper for losses than for gains

Nonlinear transformation of the probability

scale, which overweights small probabilitiesand underweights moderate and high

probabilities


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The journey continues..

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Session 4 Prospect Theory