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 con