session 4 prospect theory
TRANSCRIPT
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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..