Más contenido relacionado La actualidad más candente (20) Similar a Chap16 decision making (20) Más de Uni Azza Aunillah (12) Chap16 decision making1. Statistics for Managers
Using Microsoft® Excel
4th Edition
Chapter 16
Decision Making
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-1
2. Chapter Goals
After completing this chapter, you should be
able to:
Describe basic features of decision making
Construct a payoff table and an opportunity-loss table
Define and apply the expected value criterion for decision
making
Compute the value of perfect information
Describe utility and attitudes toward risk
Statistics for Managers Using
Microsoft Excel, 4e © 2004
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Chap 16-2
3. Steps in Decision Making
List Alternative Courses of Action
List Uncertain Events
Possible events or outcomes
Determine ‘Payoffs’
Choices or actions
Associate a Payoff with Each Event/Outcome
combination
Adopt Decision Criteria
Evaluate Criteria for Selecting the Best Course
of Action
Statistics for Managers Using
Microsoft Excel, 4e © 2004
Chap 16-3
Prentice-Hall, Inc.
4. List Possible Actions or Events
Two
Methods of
Listing
Payoff Table
Statistics for Managers Using
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Decision Tree
Chap 16-4
5. A Payoff Table
A payoff table shows alternatives,
states of nature, and payoffs
Investment
Choice
(Action)
Profit in $1,000’s
(Events)
Strong
Economy
Large factory
200
Statistics for Managers Using
Average factory
90
Microsoftfactory 4e © 2004
Small Excel,
40
Prentice-Hall, Inc.
Stable
Economy
50
120
30
Weak
Economy
-120
-30
20
Chap 16-5
6. Sample Decision Tree
Strong Economy
90
Stable Economy
120
-30
Strong Economy
Statistics for Managers Using
Microsoft Excel, 4e © 2004
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-120
Weak Economy
Small factory
50
Strong Economy
Average factory
Stable Economy
Weak Economy
Large factory
200
40
Stable Economy
30
Weak Economy
20
Payoffs
Chap 16-6
7. Opportunity Loss
Opportunity loss is the difference between an actual
payoff for an action and the optimal payoff, given a
particular event
Investment
Choice
(Action)
Payoff
Table
Profit in $1,000’s
(Events)
Strong
Economy
Stable
Economy
Weak
Economy
Large factory
200
50
-120
Average factory
90
120
-30
Small factory
40
30
20
The action “Average factory” has payoff 90 for “Strong Economy”. Given
“Strong for Managers Using
Statistics Economy”, the choice of “Large factory” would have given a
payoff of 200, or 110 higher. Opportunity loss = 110 for this cell.
Microsoft Excel, 4e © 2004
Chap 16-7
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8. Opportunity Loss
(continued)
Investment
Choice
(Action)
Large factory
Average factory
Small factory
Payoff
Table
Profit in $1,000’s
(States of Nature)
Strong
Economy
200
90
40
Stable
Economy
50
120
30
Investment
Choice
(Action)
Statistics for Managers Using
Microsoft Excel, 4e © Large factory
2004
Average factory
Prentice-Hall, Inc.
Weak
Economy
Opportunity
Loss Table
-120
-30
20
Opportunity Loss in $1,000’s
(Events)
Strong
Economy
0
110
Stable
Economy
70
0
Chap
Weak
Economy
140
50
16-8
9. Decision Criteria
Expected Monetary Value (EMV)
Expected Opportunity Loss (EOL)
The expected profit for taking action Aj
The expected opportunity loss for taking action Aj
Expected Value of Perfect Information (EVPI)
The expected opportunity loss from the best decision
Statistics for Managers Using
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Chap 16-9
10. Expected Monetary Value
Solution
Goal: Maximize expected value
The expected monetary value is the weighted
average payoff, given specified probabilities for
each event
N
EMV( j) = ∑ x ijPi
i=1
Where EMV(j) = expected monetary value of action j
xij = payoff for action j when event i occurs
Statistics for Managers Using
P = probability of event i
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Chap 16-10
11. Expected Monetary Value
Solution
(continued)
The expected value is the weighted average
payoff, given specified probabilities for each
event
Profit in $1,000’s
(Events)
Investment
Choice
(Action)
Strong
Economy
(.3)
Stable
Economy
(.5)
Large factory
200
50
Average for Managers Using 120
90
Statisticsfactory
Small factory
40
30
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Weak
Economy
(.2)
-120
-30
20
Suppose these
probabilities
have been
assessed for
these three
events
Chap 16-11
12. Expected Monetary Value
Solution
(continued)
Goal: Maximize expected value
Payoff Table:
Profit in $1,000’s
(Events)
Investment
Choice
(Action)
Large factory
Average factory
Small factory
Strong
Economy
(.3)
Stable
Economy
(.5)
Weak
Economy
(.2)
200
90
40
50
120
30
-120
-30
20
Expected
Values
(EMV)
61
81
31
Maximize
expected
value by
choosing
Average
factory
Example: EMV (Average factory) = 90(.3) + 120(.5) + (-30)(.2)
Statistics for Managers Using
= 81
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Chap 16-12
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13. Decision Tree Analysis
A Decision tree shows a decision problem,
beginning with the initial decision and ending
will all possible outcomes and payoffs.
Use a square to denote decision nodes
Use a circle to denote uncertain events
Statistics for Managers Using
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Chap 16-13
14. Add Probabilities and Payoffs
(continued)
Strong Economy (.3)
Large factory
200
Stable Economy (.5)
50
Weak Economy
(.2)
-120
Strong Economy (.3)
Average factory
90
Stable Economy (.5)
120
Weak Economy
(.2)
-30
Strong Economy (.3)
Decision
Small factory
Statistics for Managers Using
Uncertain Events
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40
Stable Economy (.5)
30
Weak Economy
(.2)
20
Probabilities Payoffs
Chap 16-14
15. Fold Back the Tree
EMV=200(.3)+50(.5)+(-120)(.2)=61
Large factory
Strong Economy (.3)
200
Stable Economy (.5)
50
Weak Economy
EMV=90(.3)+120(.5)+(-30)(.2)=81
Average factory
Small factory
Statistics for Managers Using
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-120
Strong Economy (.3)
90
Stable Economy (.5)
120
Weak Economy
EMV=40(.3)+30(.5)+20(.2)=31
(.2)
(.2)
-30
Strong Economy (.3)
40
Stable Economy (.5)
30
Weak Economy
(.2)
20
Chap 16-15
16. Make the Decision
EV=61
Large factory
Strong Economy (.3)
200
Stable Economy (.5)
50
Weak Economy
EV=81
Average factory
Strong Economy (.3)
Stable Economy (.5)
Weak Economy
EV=31
Small factory
Statistics for Managers Using
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(.2)
(.2)
-120
90
120
-30
Strong Economy (.3)
EMV=81
40
Stable Economy (.5)
Maximum
30
Weak Economy
(.2)
20
Chap 16-16
17. Expected Opportunity Loss
Solution
Goal: Minimize expected opportunity loss
The expected opportunity loss is the weighted
average loss, given specified probabilities for
each event
N
EOL( j) = ∑ L ijPi
i =1
Where EOL(j) = expected monetary value of action j
Lij = Using
Statistics for Managers opp. loss for action j when event i occurs
Microsoft Excel, 4e © 2004
Pi = probability of event i
Chap 16-17
Prentice-Hall, Inc.
18. Expected Opportunity Loss
Solution
Goal: Minimize expected opportunity loss
Opportunity Loss Table
Opportunity Loss in $1,000’s
(Events)
Investment
Choice
(Action)
Large factory
Average factory
Small factory
Strong
Economy
(.3)
Stable
Economy
(.5)
Weak
Economy
(.2)
0
110
160
70
0
90
140
50
0
Expected
Op. Loss
(EOL)
63
43
93
Minimize
expected
op. loss by
choosing
Average
factory
Statistics for Managers Using
Example: EOL (Large factory) = 0(.3) + 70(.5) + (140)(.2)
Microsoft Excel, 4e © 2004
= 63
Chap 16-18
Prentice-Hall, Inc.
19. Value of Information
Expected Value of Perfect Information, EVPI
Expected Value of Perfect Information
EVPI = Expected profit under certainty
– expected monetary value of the best alternative
(EVPI is equal to the expected opportunity loss
from the best decision)
Statistics for Managers Using
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Chap 16-19
20. Expected Profit Under Certainty
Expected
profit under
certainty
= expected
value of the
best
decision,
given perfect
information
Profit in $1,000’s
(Events)
Investment
Choice
(Action)
Strong
Economy
(.3)
Large factory
200
Average factory
90
Small factory
Value of best decision 40
for each event:
200
Stable
Economy
(.5)
Weak
Economy
(.2)
50
120
30
-120
-30
20
120
20
Example: Best decision
given “Strong
Statistics for Managers Using Economy” is
“Large factory”
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Chap 16-20
21. Expected Profit Under Certainty
(continued)
Profit in $1,000’s
(Events)
Investment
Choice
(Action)
Strong
Economy
(.3)
Stable
Economy
(.5)
Weak
Economy
(.2)
Now weight
Large factory
200
50
-120
these outcomes Average factory
90
120
-30
with their
Small factory
40
30
20
200
120
20
probabilities to
find the
200(.3)+120(.5)+20(.2) Expected
expected value:
Statistics for Managers Using = 124
profit under
Microsoft Excel, 4e © 2004
certainty
Chap 16-21
Prentice-Hall, Inc.
22. Value of Information Solution
Expected Value of Perfect Information (EVPI)
EVPI = Expected profit under certainty
– Expected monetary value of the best decision
Recall:
Expected profit under certainty = 124
EMV is maximized by choosing “Average factory”,
where EMV = 81
so:
EVPI = 124 – 81
= 43
Statistics for Managers Using would be willing to spend to obtain
(EVPI is the maximum you
Microsoft Excel, 4e © 2004
perfect information)
Chap 16-22
Prentice-Hall, Inc.
23. Accounting for Variability
Consider the choice of Stock A vs. Stock B
Percent Return
(Events)
Stock Choice
(Action)
Strong
Economy
(.7)
Weak
Economy
(.3)
Stock A
30
-10
Stock B
14
8
Statistics for Managers Using
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Expected
Return:
18.0
12.2
Stock A has a higher
EMV, but what about
risk?
Chap 16-23
24. Accounting for Variability
(continued)
Calculate the variance and standard deviation for
Stock A and Stock B:
Percent Return
(Events)
Stock Choice
(Action)
Strong
Economy
(.7)
Weak
Economy
(.3)
Stock A
30
-10
Stock B
14
8
N
Expected
Standard
Return:
Variance: Deviation:
18.0
Example: σ = ∑ ( Xi − Using
Statistics for Managers μ) P( Xi ) = (30 − 18)
i=1
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2
A
2
2
336.0
18.33
7.56
12.2
2.75
(.7) + ( −10 − 18 )2 (.3) = 336.0
Chap 16-24
25. Accounting for Variability
(continued)
Calculate the coefficient of variation for each stock:
CVA =
σA
18.33
× 100% =
× 100% = 101.83%
EMVA
18.0
CVB =
Stock A has
much more
relative
variability
σB
2.75
× 100% =
× 100% = 22.54%
EMVB
12.2
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Chap 16-25
26. Return-to-Risk Ratio
Return-to-Risk Ratio (RTRR):
EMV(j)
RTRR(j) =
σj
Expresses the relationship between the return
(expected payoff) and the risk (standard deviation)
Statistics for Managers Using
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Chap 16-26
27. Return-to-Risk Ratio
RTRR(j) =
EMV(j)
σj
RTRR(A) =
EMV(A) 18.0
=
= 0.982
σA
18.33
RTRR(B) =
EMV(B) 12.2
=
= 4.436
σB
2.75
You might want to consider Stock B if you don’t
like risk. Although Stock A has a higher Expected
Statistics for Managers has a much larger return to risk
Return, Stock B Using
Microsoft Excel, a much smaller CV
ratio and 4e © 2004
Chap 16-27
Prentice-Hall, Inc.
28. Decision Making in PHStat
PHStat | decision-making | expected
monetary value
Check the “expected opportunity loss” and
“measures of valuation” boxes
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Chap 16-28
29. Decision Making
with Sample Information
Prior
Probability
Permits revising old
probabilities based on new
information
New
Information
Revised
Probability
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Chap 16-29
30. Revised Probabilities
Example
Additional Information: Economic forecast is strong economy
When the economy was strong, the forecaster was correct
90% of the time.
When the economy was weak, the forecaster was correct 70%
of the time.
F1 = strong forecast
F2 = weak forecast
E1 = strong economy = 0.70
E = Managers Using
Statistics2forweak economy = 0.30
Microsoft Excel, 4e © 2004
P(F1 | Inc.
P(F1 | E2) = 0.30
Prentice-Hall,E1) = 0.90
Prior probabilities
from stock choice
example
Chap 16-30
31. Revised Probabilities
Example
(continued)
P(F1 | E1 ) = .9 , P(F1 | E 2 ) = .3
P(E1 ) = .7 , P(E 2 ) = .3
Revised Probabilities (Bayes’ Theorem)
P(E1 )P(F1 | E1 )
(.7)(.9)
P(E1 | F1 ) =
=
= .875
P(F1 )
(.7)(.9) + (.3)(.3)
P(E 2 )P(F1 | E 2 )
P(E 2 | F1 =
= .125
Statistics for Managers )Using
P(F1 )
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Chap 16-31
32. EMV with
Revised Probabilities
Pi
Event
Stock A
xijPi
Stock B
xijPi
.875
strong
30
26.25
14
12.25
.125
weak
-10
-1.25
8
1.00
Revised
probabilities
Σ = 25.0
Σ = 11.25
EMV Stock B = 11.25
EMV Stock A = 25.0
Statistics for Managers Using Maximum
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EMV
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Chap 16-32
33. EOL Table with
Revised Probabilities
Pi
Event
Stock A
xijPi
Stock B
xijPi
.875
strong
0
0
16
14.00
.125
weak
18
2.25
0
0
Σ = 2.25
Revised
probabilities
Σ = 14.00
EOL Stock B = 14.00
EOL Stock A = 2.25
Statistics for Managers Using
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Minimum
EOL
Chap 16-33
34. Accounting for Variability with
Revised Probabilities
Calculate the variance and standard deviation for
Stock A and Stock B:
Percent Return
(Events)
Stock Choice
(Action)
Strong
Economy
(.875)
Weak
Economy
(.125)
Stock A
30
-10
Stock B
14
8
N
Expected
Standard
Return:
Variance: Deviation:
25.0
Example: σ = ∑ ( Xi − μ) P( Xi ) =
Statistics for Managers Using (30 − 25)
i=1
Microsoft Excel, 4e © 2004
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2
A
2
2
175.0
13.229
3.94
13.25
1.984
(.875 ) + ( −10 − 25 )2 (.125 ) = 175.0
Chap 16-34
35. Accounting for Variability with
Revised Probabilities
(continued)
The coefficient of variation for each stock using the
results from the revised probabilities:
CVA =
σA
13.229
× 100% =
× 100% = 52.92%
EMVA
25.0
CVB =
σB
1.984
× 100% =
× 100% = 14.97%
EMVB
13.25
Statistics for Managers Using
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Chap 16-35
36. Return-to-Risk Ratio with
Revised Probabilities
EMV(A)
25.0
RTRR(A) =
=
= 1.890
σA
13.229
EMV(B) 13.25
RTRR(B) =
=
= 7.011
σB
1.984
With the revised probabilities, both stocks have
higher expected returns, lower CV’s, and larger
return to risk ratios
Statistics for Managers Using
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Chap 16-36
37. Utility
Utility is the pleasure or satisfaction
obtained from an action.
The utility of an outcome may not be the same
for each individual.
Statistics for Managers Using
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Chap 16-37
38. Utility
Example: each incremental $1 of profit does not
have the same value to every individual:
A risk averse person, once reaching a goal,
assigns less utility to each incremental $1.
A risk seeker assigns more utility to each
incremental $1.
A risk neutral person assigns the same utility to
each extra $1.
Statistics for Managers Using
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Chap 16-38
40. Maximizing Expected
Utility
Making decisions in terms of utility, not $
Translate $ outcomes into utility outcomes
Calculate expected utilities for each action
Choose the action to maximize expected utility
Statistics for Managers Using
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Chap 16-40
41. Chapter Summary
Described the payoff table and decision trees
Opportunity loss
Provided criteria for decision making
Expected monetary value
Expected opportunity loss
Return to risk ratio
Introduced expected profit under certainty and the
value of perfect information
Discussed decision making with sample
information
Statistics for Managers Using
Addressed
Microsoft Excel, 4e the concept of utility
© 2004
Prentice-Hall, Inc.
Chap 16-41