Chapter 12 Risk Attitude and Utility Theory
 Utility
Theory  Maximize Expected Utility
 Motivation
 Rescale all values to between 0 and 1 based on risk attitude
 Certainty Equivalent
 Manage
Risk – Utility Theory explains
 Insurance
 Partnership
 Risk Aversion
assessment
 Standard function with parameters
 Direct assessment
 Problems with assessment
 Critique
Chapter 12
Utility Theory: Paradox and Prospect Theory
Chelst & Canbolat
Value Added Decision Making
03/06/12
1
Utility Theory - Overview
 Incorporates
decision-maker’s risk attitude  Value of
alternatives cannot be captured by E(X) because risk attitude
 Certainty Equivalent (CE): The payoff amount we would accept
in lieu of under-going the uncertain situation, taking a gamble.
 Risk Premium: A situation’s risk premium (RP) is the difference
between expected payoff (EP) and certainty equivalent (CE)
 Risk Aversion: CE < E(X)  Concave function
 Profit – prefer sure profit that is less than E(X) of a profit gamble
 Cost – prefer sure cost that is higher than E(Y) of a loss gamble
 Risk
Prone: CE > E(X) Try for more money than average
 With high guaranteed minimum, may be will to try for home run even if
offered a value somewhat higher than the expected value
Chapter 12
Chelst & Canbolat
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03/06/12
2
TV show “Deal or No Deal” – Activate WEB GAME
Game Description and Risk Attitude








Chapter 12
Game starts with 26 suitcases, each with a dollar value ranging from $0.01 to $1M
Contestant picks one case as his to be opened at the end, and selects 6 cases to be
opened immediately. As they are opened, their stored dollar value is deleted from
the list.
After opening these six cases, the player is offered a sure amount or the option to
keep playing.
At each the step the number of boxes to open at this stage decreases until only
one at a time is opened each time.
For example, I played the game until there were 3 unopened boxes left ($25,
$50,000, and $1,000,000). One of these boxes I had selected as my box.
The offer was for $220,000.This is much less than the expected value
E(X) = (1/3)(25)+ (1/3)((50,000) + (1/3)(1,000,000) = (1/3) (1,000,025) =
$350,008
If you prefer to take less than the expected value  risk averse
Chelst & Canbolat
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3
Simple gamble (lottery) – Two Outcomes
Two boxes are left: $10,000 and $20,000.




You have a 50–50 chance of winning $10,000 or $20,000 depending upon what is
in your selected box.  E(X) = $15,000
Would you accept an offer of $12,000 or continue Yes __ or No __
Would you accept an offer of $14,500 or continue Yes __ or No __
What is the minimum you would accept to stop the game? ___  this is Certainty
Equivalent (CE) of the gamble
 If the CE is less than the expected value, you are a risk averse.
 Risk Premium is the difference between your CE and the expected value
 Assume you would accept $12,500
 Risk Premium = E(X) – CE = $15,000 - $12,500 = $2,500
 If the CE is more than the expected value, you are a risk prone.

Gamble is a set of uncertain outcomes with probabilities
 Not necessarily just 2 outcomes
 All outcomes may not have the same probability.
Chapter 12
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Value Added Decision Making
03/06/12
4
Expected Value is Inadequate
Generally Risk Averse
 Extremely
Rare Catastrophic Events
Law of averages no help for individual
Motivates insurance industry
Companies may self-insure up to extreme costs
Can tolerate moderate risks that are not devastating
Deductible on insurance
 Large
investments relative to size of company
Cannot afford the loss
Has need for certain profit more than high upside
potential  sell development rights
Chapter 12
Chelst & Canbolat
Value Added Decision Making
03/06/12
5
Determine function U(X)
 U(X)
function may be determined
Select from standard functional forms – exponential
or logarithmic and estimate parameters from
questions
Brute force graphing of the results of series of
Certainty Equivalent responses to gambles
 Assume
exponential U(X) = 1-e(-x/15000)
U(20,000) = 1-e(-20000/15000) = .7364
Chapter 12
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Value Added Decision Making
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6
Calculate Expected Utility  E(U(X)) and Not E(X)
Assume exponential utility function for this example
(0.5)
$10,000
E(X) = 0.5($10000) + 0.5($20000) = $12,500
(0.5)
$20,000
Assume U(X) = 1-e(-x/15000)
U(10,000) = 1-e(-10000/15000) = 0.4866
U(20,000) = 1-e(-20000/15000) = 0.7364
E(U(X)) = 0.5(0.487) + 0.5(0.736) = 0.6115
invert exponential function 
CE(0.6115) = $14,182
$14,250 would be preferred to gamble
$14,000 would not be preferred
Chapter 12
Chelst & Canbolat
Value Added Decision Making
(0.5)
0.4866
0.7364
(0.5)
03/06/12
7
Invert function U(X)  U-1(X)
 0.6115
= 1-e(-x/15000)
 e(-x/15000) =
 ln
of both sides  (-X/15000) = ln(0.3885) = -0.9455
X
= 15000 (0.9455) = 14,182
 CE
of 50-50 gamble of 10,000 and 20,000 is $14,182
 Risk
Chapter 12
1- 0.6115 = 0.3885
Premium = $15,000 - $14,182 = $818
Chelst & Canbolat
Value Added Decision Making
03/06/12
8
Risk Aversion

CONCAVE for Negative (Cost)
 Prefer to PAY More than expected value to be sure Cost does not get
too large.
 50-50 COST Gamble $90,000 or $10,000 => prefer sure $60,000 cost
 Basis for Insurance Industry

CONCAVE for Maximization (Profit)
 Prefer to EARN less than expected value to be sure of earning at least
that profit.
 50-50 PROFIT Gamble $90,000 or $10,000
===> would prefer sure $40,000 profit to the gamble.
 Basis for Selling off bank Debts such as mortgages
Chapter 12
Chelst & Canbolat
Value Added Decision Making
03/06/12
9
Risk Aversion – Concave Curve
Profit
Cost
Risk Aversion - Cost
1.2
1.2
1
1
0.8
0.8
0.6
Series1
Utility
Utility
Risk Aversion - Profit
0.6
0.4
0.4
0.2
0.2
0
0
20000
40000
60000
80000
0
100000
-100000
Profit
-80000
-60000
-40000
-20000
0
Cost
0.5 for $10,000 or 0.5 for $90,000
E(X) = $50,000
Accept $40,000 = CE  U(40000)=.5
Risk Premium $10,000
Chapter 12
Utiltiy
0.5 for -$10,000 or 0.5 for -$90,000
E(X) = -$50,000
Accept -$60,000 = CE  U(60000)=.5 Risk
Premium $10,000
Chelst & Canbolat
Value Added Decision Making
03/06/12
10
Activity – Risk Aversion
Pay to avoid loss
___________________________________________
___________________________________________
 Accept less profit but be sure (or more certain) of profit
___________________________________________
___________________________________________
 Other Examples
___________________________________________
___________________________________________
___________________________________________
___________________________________________

Chapter 12
Chelst & Canbolat
Value Added Decision Making
03/06/12
11
Utility Function Assessment
Brute Force
 Series
of 3 lotteries
 Obtain Certainty Equivalent of utility values of .25, .5,
& .75
 Extrapolate over the range of 0 to 1.
 Create your own utility function for $0M to $10M
 set U(min) = 0 & U(max) = 1
 set U(0) = 0 & U(10) = 1
Chapter 12
Chelst & Canbolat
Value Added Decision Making
03/06/12
12
Decision tree Boss Controls automation investment
Need utility function for four values (0.8, 1.9, 8.5, 10)
40.0%
9.9
Take Rate
5.86
60.0%
50% Take
16.5
0
1.9
40.0%
13.8
Take Rate
6.32
60.0%
50% Take
23
0.4
0.8
30% Take
FALSE
Low
Automation Investment
-8
0
8.5
How Much
6.32
30% Take
High
Chapter 12
TRUE
-13
Chelst & Canbolat
Value Added Decision Making
0.6
10
03/06/12
13
Certainty equivalents
(0.5)
XL
≈ CE50
(0.5)
XH
(0.5)
XL
≈ CE25
(0.5)
(0.5)
CE50
XH
≈ CE75
(0.5)
Chapter 12
CE50
Chelst & Canbolat
Value Added Decision Making
03/06/12
14
BC automation investment certainty
equivalent for 0.50, 0.25, and 0.75 utility
(0.5)
0
(0.5)
(0.5)
(0.5)
(0.5)
(0.5)
Chapter 12
10
≈ CE50 = 3.6
0
≈ CE25 = 1.6
3.6
10
≈ CE75 = 6.2
3.6
Chelst & Canbolat
Value Added Decision Making
03/06/12
15
Utility assessment for BC automation
investment example
1
Utility Score
0.8
0.6
0.4
0.2
0
0
2
4
Dollars
6
8
10
Value
0
0.8
1.6
1.9
3.6
6.2
8.5
10
Utility
0
0.13
0.25
0.29
0.5
0.75
0.90
1
Table 12-4: Utility scores for BC automation investment
Chapter 12
Chelst & Canbolat
Value Added Decision Making
03/06/12
16
Decision tree for BC automation investment using
utility function
FALSE
40%
0
0.13
60%
0
1.0
40%
0.29
0.4
0.29
60%
0.9
0.6
0.90
30% Take Rate 0.13
Take Rate
0.652
High
50% Take Rate 1.0
Automation Investment
Decision
0.657
30% Take Rate
TRUE
Take Rate
0.657
Low
50% Take Rate
CE: $5.142 (0.652) vs. $5.196 million (0.657)
Chapter 12
Chelst & Canbolat
Value Added Decision Making
03/06/12
17
Utility Function: Simplify Interview
 Goal: simplify
interview process  One question for each
parameter
 Exponential U(x) = 1 – exp(-x/R)  Constant Risk Aversion
 Implies that the magnitude of cash on hand does not affect
attitude towards Risk
 R = Risk Tolerance
 R = Sum of Money about which you are indifferent between
a 50-50 chance of gaining the whole sum, R and losing the
half sum, R/2
Chapter 12
Chelst & Canbolat
Value Added Decision Making
03/06/12
18
Constant Risk Aversion
Risk Premium is Constant
R=35
Chapter 12
U(X) = 1 – exp(-x/35)
50-50 Gamble
Expected
Certainty
Risk
Between ($)
Value
Equivalent
Premium
10,40
25
21.88
3.12
20,50
30,60
40,70
35
45
55
31.88
41.88
51.88
3.12
3.12
3.12
Chelst & Canbolat
Value Added Decision Making
03/06/12
19
Determine R = Risk Tolerance
50- 50 gamble to determine R
Personal
Chapter 12
Win
Lose
$20
$200
$2,000
$20,000
$10
$100
$1,000
$10,000
Chelst & Canbolat
Value Added Decision Making
Would take
Gamble Y/N
03/06/12
20
Determine R = Risk Tolerance
50- 50 gamble to determine R
Corporate
Chapter 12
Win
Lose
$20,000
$200,000
$2,000,000
$20,000,000
$10,000
$100,000
$1,000,000
$10,000,000
Chelst & Canbolat
Value Added Decision Making
Would Corp.
Gamble Y/N
03/06/12
21
ENCO Project Selection
An energy company will select one of two projects. If the
company chooses Project A, it will undertake the development
of a new power plant in one developing country. The company
estimates that the investment cost will be $50 million and
total revenue for five-year after the operation cost will be $80,
$90, or $110 million. There is a 20% chance that the local
government will take over the plant once it is finished due to
some legal issues and just repay the original investment cost
($50 million). Project B also requires a $50 million investment.
Total revenue for five-year after the operation cost will be $66,
$80, or $90 million. In this second country, there is no chance
that the government will take over this project when it is
completed.
Chapter 12
Chelst & Canbolat
Value Added Decision Making
03/06/12
22
Maximize expected value
Decision tree for ENCO project selection
0.2
20.0%
Yes
0
50
TRUE
Project A
Government Take Project?
34.4
-50
30.0%
Low
80
43
0
40.0%
Medium
90
30.0%
High
110
Project
30
Revenue
80.0%
No
0.24
0.32
40
0.24
60
Project Decision
34.4
Low
Project B
FALSE
0
66
16
40.0%
0
80
30
30.0%
0
90
40
Revenue
28.8
-50
Medium
High
Chapter 12
30.0%
Chelst & Canbolat
Value Added Decision Making
03/06/12
23
Figure 12.11: Cumulative risk profile for ENCO project
selection Redraw diagram without student version
1
Cumulative Probability
0.8
0.6
Project A
Project B
0.4
0.2
Chapter 12
Chelst & Canbolat
Value Added Decision Making
70
60
50
40
30
20
10
0
-10
0
03/06/12
24
A utility score was calculated for each value.
R= $30 million
EU(Project A) = 0*20% + (0.632*30%+0.736*40%+0.865*30%)*80% = 0.595
EU(Project B) = 0.413*30%+0.632*40%+0.736*30% = 0.598
Chapter 12
Chelst & Canbolat
Value Added Decision Making
03/06/12
25
Decision tree for ENCO: using expected utility
Yes
Project A
FALSE
-50
20.0%
0
0.000
50
Government Take Project?
0.595
No
Project
80.0%
0
Revenue
0.744
40.0%
Medium
90
30.0%
High
110
0
0.632
0
0.736
0
0.865
Project Decision
0.598
Project B
Low
TRUE
-50
Revenue
0.598
Medium
High
Chapter 12
30.0%
80
Low
30.0%
66
0.3
0.413
40.0%
80
30.0%
90
0.4
0.632
0.3
0.736
Chelst & Canbolat
Value Added Decision Making
03/06/12
26
Impact of risk tolerance on certainty
equivalent
Certainty Equivalent
35.00
30.00
25.00
20.00
15.00
Project A
10.00
Project B
5.00
0.00
1
10
20
30
40
50
60
Risk Tolerance
Chapter 12
Chelst & Canbolat
Value Added Decision Making
03/06/12
27
Risk Sharing Strategies
 Buy
insurance
 Partnerships
Example: Transmission plant by GM and Ford
Joint ventures with foreign companies
 Diversification
Diversification with independent investments
Example: Dual sourcing, investment in different stocks
Diversification with dependent investments (Hedging)
Chapter 12
Chelst & Canbolat
Value Added Decision Making
03/06/12
28
Risk Sharing through Buy Insurance:
Project Selection



Chapter 12
Buy insurance against a government takeover of project A.
$4 million premium the company will receive a $10
million payment if the government takes the project.
Add new decision branch to tree as part of Project A. (top
of next tree)
Chelst & Canbolat
Value Added Decision Making
03/06/12
29
ENCO: insurance reporting expected value
20.0%
Yes
FALSE
Buy Insurance
-4
0
6
60
Government Take Project?
32.400
30.0%
80
Revenue
39.000
Medium 40.0%
90
Low
80.0%
0
No
TRUE
Project A
-50
High
Insurance Decicion
34.400
20.0%
Yes
TRUE
Do Not Buy
0
50
Government Take Project?
34.400
30.0%
110
80.0%
0
Project Insurance
30.0%
80
Revenue
43.000
Medium40.0%
90
0.24
30
30.0%
110
0.24
60
High
Project Decision
34.400
Low
Project B
FALSE
-50
Revenue
28.800
Medium
High
Chapter 12
30.0%
66
0
16
40.0%
80
30.0%
0
30
0
40
Chelst & Canbolat
90
Value Added Decision Making
0
36
0
56
0.2
0
Low
No
0
26
03/06/12
0.32
40
30
ENCO : insurance option reporting CE
TRUE
Buy Insurance -4
Insurance Decision
27.630
Project A
TRUE
-50
FALSE
Do Not Buy
0
Project Decision
27.630
20.0%
0.2
60
6
Government Take Project?
27.630
30.0%
Low
80
80.0%
Revenue
No
0
36.830
Medium 40%
90
Yes
High 30.0%
110
20.0%
0
50
0
Government Take Project?
27.107
30.0%
Low
80
80.0%
Revenue
No
0
40.83040.0%
Medium
90
High
Project B
Chapter 12
FALSE
-50
0.32
36
0.24
56
Yes
Project Insurance
30.0%
66
Revenue
27.322
40.0%
Medium
80
30.0%
High Chelst & Canbolat
90
Value Added Decision Making
Low
0.24
26
0
16
0
30
0
40
30.0%
110
03/06/12
0
30
0
40
0
60
31
Decision Tree for Insurance company
Tree Not in Textbook
Yes
TRUE
Sell
20.0%
0.2
-10
-6
Government Take Project?
4
2
80.0%
No
0
Insurance Company
0.8
4
Decision
2
Do Not Sell
Chapter 12
FALSE
0
0
0
Chelst & Canbolat
Value Added Decision Making
03/06/12
32
Share Risk through Partnership
 Concept: Commit
to only a percentage of the cost
(liability) and accrue the equivalent percentage of
revenue
 Common amongst insurance companies to reinsure and
share risk of catastrophic event – Lloyd’s of London
 Decision Tree Method – reduce costs and revenues
proportionate to share and calculate new utility scores.
Chapter 12
Chelst & Canbolat
Value Added Decision Making
03/06/12
33
Share Risk through Partnership:
Project Selection


Chapter 12
Outside investor shares 50% of cost and benefit of each
project.
By sharing the investment, the company can now be
involved in more projects. Let’s evaluate a 50% share. As a
result the company can invest in BOTH A and B.
Chelst & Canbolat
Value Added Decision Making
03/06/12
34
ENCO with 50% partnership reporting expected profit
Government takes away project A?
TRUE
34.400
-50 +
Project Decision
34.400
FALSE
Revenue
Project B
+
28.800
-50
30.0%
Low
33
20.0%
Revenue
from
B
Yes
14.400
25
40.0%
Medium
40
30.0%
High
45
FALSE
Government
takes
away
project
A?
50% of Both Projects
31.600
-50
Project A
Project - Diversification
0
8
0
15
0
20
30.0%
33
Revenue from B
29.400
40.0%
Medium
40
30.0%
High
45
Low
Low
No
Chapter 12
80.0%
0
30.0%
40
0
23
0
30
0
35
Revenue from A
35.900
40.0% Revenue from B
Medium
34.400
45 +
Revenue
from B
30.0%
High
44.400
55 +
Chelst & Canbolat
Value Added Decision Making
03/06/12
35
ENCO decision tree with partnership option
reporting certainty equivalent
Project A
Project - Diversification
FALSE
-50
Government Take Project?
+
27.107
FALSE
-50
+
Project Decision
29.450
Project B
Revenue
27.322
0.06
8
30.0%
33
Revenue from B
20.0%
Yes
14.032
25
Medium 40.0%
40
30.0%
High
45
Government Take Project A?
29.450
Low
50% of Both Projects
TRUE
-50
0.08
15
0.06
20
30.0%
33
Revenue from B
29.032
40.0%
Medium
40
30.0%
High
45
Low
Low
No
Chapter 12
80.0%
0
Chelst & Canbolat
Value Added Decision Making
30.0%
40
Revenue from A
34.966
Medium 40.0%
+
45
30.0%
High
+
55
0.072
23
0.096
30
0.072
35
Revenue from B
34.032
Revenue from B
44.032
03/06/12
36
Optimize PERCENT Share of Project
 Can optimize based on risk attitude
Percent share of option A
Percent share of option B
 Different companies with different risk attitudes
will have different optimum preferences
Chapter 12
Chelst & Canbolat
Value Added Decision Making
03/06/12
37
Phillips Petroleum and Onshore US Oil Exploration
Prospect Ranking: R equal to $25 million
Expected Value Basis
Prospect
Rank EV 100% share
Certainty Equivalent Basis
Rank
Optimal
Share
Certainty
Equivalent
South Louisiana
1
18.6
8
12.5%
0.6
Norphlet
2
16.5
6
12.5%
0.8
Wilcox
3
11.8
5
25%
0.8
Frio
4
10.8
7
12.5%
0.7
Vicksburg
5
4.0
4
75%
1.0
Yegua Deep
6
3.0
3
100%
1.0
Smackover
7
2.5
1
100%
1.8
Yegua Shallow
8
2.2
2
100%
1.1
Chapter 12
Chelst & Canbolat
Value Added Decision Making
03/06/12
38
Following two slides not in the textbook
 Impacts
of the target setting on the risk attitude
 Consistent with prospect theory
Chapter 12
Chelst & Canbolat
Value Added Decision Making
03/06/12
39
Risk Attitude and Targets
Component Cost Target $46 – Goal: Minimize Cost
You are near completion on a design and are almost certain that you will
be able to reach the variable cost target of $46. A suggestion comes
along that by changing materials the component should be easier to
manufacture with the cost dropping to $40 per part. However, time is
short and there is a concern that without proper testing of Design for
Manufacture the change could, in fact, increase the cost to $47 per
component and miss the target. Would you make the change assuming
the two outcomes were equally likely?
.5
$46
OR
.5
Chapter 12
$47
Chelst & Canbolat
Value Added Decision Making
$40
03/06/12
40
Risk Attitude and Targets
Component Cost Target $40
You are near completion on a design and are almost certain that you will
NOT be able to reach the variable cost target of $40 and that the part
will cost $42. A suggestion comes along that by changing materials the
part should be easier to manufacture with the cost dropping to $40 per
part. However, time is short and there is a concern that without proper
testing of Design for Manufacture the change could, in fact, increase the
cost to $47 per part and miss the target. Would you make the change
assuming the two outcomes were equally likely?
.5
$42
OR
.5
Chapter 12
$47
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Problems With Carrying Out Risk Aversion
Assessment in Real-World
 Managers
are uncomfortable with this abstract concept
 Managers are inconsistent -- Prefer ranges for CE and not
specific values
 People are inconsistent
risk prone for small values ( i.e. will buy lottery tickets)
risk averse for large values (i.e. buy insurance)
May be risk prone if values are negative but risk averse if all
values are positive and vice versa
Attitudes towards risk are influenced by artificial targets
Target secure – take no gamble to improve
Target at risk – take extreme gambles to reach target
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Risk Assessment In Practice
(Done Less than 10% of the time)
 Howard Rule of Thumb for R in major decisions:
 R = 6.4% of sales or 1.25 Net Income – Your company value?
 Example: R = $1 Billion dollar investment or purchase decision for
a company with over $15 Billion in sales.
 First
carry out analysis without Risk Aversion
 Display Comparative Risk Profiles and discuss
 Insert exponential function & determine whether or not
the optimal solution is Sensitive to Risk Tolerance Value
within a realistic range for your company.
 If optimal decision can change within a reasonable range
of R then assess actual utility function.
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Assumptions of Utility Theory
 Expectation: U(x1,p1;…;xn,pn)
= p1u(x1)+…+pnu(xn)
 Asset Integration: The domain of the utility function is final
states (which include one’s asset position) rather than gains
or losses.
 Risk Aversion: u is concave (u’’< 0)
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Critique of Utility Theory
 Expectation Assumption
- Allais paradox
Problem 1: Choose between
A: $1 Million with certainty
Problem 2: Choose between
X: $1 Million with probability 0.11
0 with probability
0.89
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B: $1 Million with probability 0.89
$5 Million with probability 0.10
0 with probability
0.01
Y: $5 Million with probability 0.10
0 with probability
0.90
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Critique of Utility Theory- Actual preferences
 Expectation Assumption
- Allais paradox
Problem 1: 82% choose A
A: $1 Million with certainty
B: $1 Million with probability 0.89
$5 Million with probability 0.10
0 with probability
0.01
Problem 2: 83% Choose Y
X: $1 Million with probability 0.11
0 with probability
0.89
Y: $5 Million with probability 0.10
0 with probability
0.90
Conclusion: People overweight “certain” outcomes more than merely probable
outcomes.
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Utility Function Stability and Accuracy
 Affected
by mood
 Quality of life QOL
 Assessment of QOL living with serious disease.
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Prospect Theory (Kahneman and Tversky)
Example not in textbook

Value Function
◦ Concave for gains and Convex for losses;
◦ Steeper for losses than gains (Loss Aversion)
v(x)
1200
800
400
0
-1200
-800
-400-400 0
v(x)
400
800
1200
-800
-1200
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Prospect Theory (Kahneman and Tversky)
Example not in textbook

Weighting Function (The impact of events on desirability
of prospects, not merely the likelihood of events)
◦ Overweight certainty and small probabilities;
◦ Underweight moderate and high probabilities;
1
0.8
0.6
w+(p)
w-(p)
0.4
0.2
0
0
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0.2
0.4
0.6
0.8
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Prospect Theory (Kahneman and Tversky)
Example not in textbook

Chapter 12
Fourfold risk attitude:
Small
Probabilities
Moderate or high
probabilities
Gains
risk seeking
risk averse
Losses
risk averse
risk seeking
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Remember The Goal of Analysis
Update Intuition of Decision Maker
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Where are we headed next?
 Analytic Tools
completed! YEAH! No more new software!
 Data input: forecasting biases  Structured expert interview
 Decision making biases  awareness
 Ethics Decisions
 Negotiations
 Strategic Decisions & Scenario Planning
 Final Projects
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TREES-A Decision-Maker's Lament
I think that I shall never see
A decision as complex as that treeA tree with roots in ancient days
(At least as old as Reverend Bayes);
A tree with flowers in its tresses
(Each flower made of blooming
guesses);
A tree with utiles at its tips
(Values gleaned from puzzled lips);
A tree with trunk all gnarled and twisted
With axioms by Savage listed;
A tree with stems so deeply nested
Intuition's completely bested;
A tree with branches sprouting branches
And nodes declaring what the chance is; A tree with branches in a tangle
Impenetrable from any angle;
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TREES-A Decision-Maker's Lament
A tree that tried to tell us "should"
Although its essence was but "would";
A tree that did decision hold back
'Til calculation had it rolled back.
Decisions are reached by fools like me,
But it took a consultant to make that tree.
Michael H. Rothkopf
with apologies to Joyce Kilmer and to competent,
conscientious decision analysts everywhere
Operations Research Vol. 28, No. 1,
January-February 1980
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