Transcript here

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
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 Prentice-Hall, Inc.
Chap 16-2
Steps in Decision Making
 List Alternative Courses of Action
 Choices or actions
 List Uncertain Events
 Possible events or outcomes
 Determine ‘Payoffs’
 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 Prentice-Hall, Inc.
Chap 16-3
List Possible Actions or Events
Two Methods
of Listing
Payoff Table
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Decision Tree
Chap 16-4
A Payoff Table
A payoff table shows alternatives,
states of nature, and payoffs
Investment
Choice
(Action)
Large factory
Average factory
Small factory
Profit in $1,000’s
(Events)
Strong
Stable
Weak
Economy
Economy
Economy
200
90
40
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
50
120
30
-120
-30
20
Chap 16-5
Sample Decision Tree
Large factory
Average factory
Small factory
Strong Economy
200
Stable Economy
50
Weak Economy
-120
Strong Economy
90
Stable Economy
120
Weak Economy
-30
Strong Economy
40
Stable Economy
30
Weak Economy
20
Payoffs
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-6
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)
Large factory
Average factory
Small factory
Payoff
Table
Profit in $1,000’s
(Events)
Strong
Economy
Stable
Economy
Weak
Economy
200
90
40
50
120
30
-120
-30
20
The action “Average factory” has payoff 90 for “Strong Economy”. Given
“Strong Economy”, the choice of “Large factory” would have given a
payoff of 200, or 110 higher. Opportunity loss = 110 for this cell.
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-7
Opportunity Loss
(continued)
Investment
Choice
(Action)
Large factory
Average factory
Small factory
Payoff
Table
Profit in $1,000’s
(States of Nature)
Strong
Economy
Stable
Economy
Weak
Economy
200
90
40
50
120
30
-120
-30
20
Investment
Choice
(Action)
Large factory
Average factory
Small factory
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Opportunity
Loss Table
Opportunity Loss in $1,000’s
(Events)
Strong
Economy
Stable
Economy
Weak
Economy
0
110
160
70
0
90
140
50
0
Chap 16-8
Decision Criteria
 Expected Monetary Value (EMV)
 The expected profit for taking action Aj
 Expected Opportunity Loss (EOL)
 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 Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-9
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
Pi = probability of event i
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-10
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)
Large factory
Average factory
Small factory
Strong
Economy
(.3)
Stable
Economy
(.5)
Weak
Economy
(.2)
200
90
40
50
120
30
-120
-30
20
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Suppose these
probabilities
have been
assessed for
these three
events
Chap 16-11
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)
= 81
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-12
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 Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-13
Add Probabilities and Payoffs
(continued)
Large factory
Strong Economy (.3)
200
Stable Economy (.5)
50
Weak Economy
Average factory
Small factory
-120
Strong Economy (.3)
90
Stable Economy (.5)
120
Weak Economy
Decision
(.2)
(.2)
-30
Strong Economy (.3)
40
Stable Economy (.5)
30
Weak Economy
(.2)
20
Uncertain Events
Probabilities Payoffs
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-14
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
-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
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
(.2)
20
Chap 16-15
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
(.2)
(.2)
-120
90
Maximum
120
-30
Strong Economy (.3)
40
Stable Economy (.5)
30
Weak Economy
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
(.2)
EMV=81
20
Chap 16-16
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 = opp. loss for action j when event i occurs
Pi = probability of event i
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-17
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
Example: EOL (Large factory) = 0(.3) + 70(.5) + (140)(.2)
= 63
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-18
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 Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-19
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)
Stable
Economy
(.5)
Weak
Economy
(.2)
200
90
40
50
120
30
-120
-30
20
Value of best decision
200
for each event:
120
20
Large factory
Average factory
Small factory
Example: Best decision
given “Strong Economy” is
“Large factory”
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-20
Expected Profit Under Certainty
(continued)
Profit in $1,000’s
(Events)
Investment
Choice
(Action)
 Now weight
these outcomes
with their
probabilities to
find the
expected value:
Large factory
Average factory
Small factory
Strong
Economy
(.3)
Stable
Economy
(.5)
Weak
Economy
(.2)
200
90
40
50
120
30
-120
-30
20
200
120
20
200(.3)+120(.5)+20(.2)
= 124
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Expected
profit under
certainty
Chap 16-21
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
(EVPI is the maximum you would be willing to spend to obtain
perfect information)
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-22
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
18.0
Stock B
14
8
12.2
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Expected
Return:
Stock A has a higher
EMV, but what about
risk?
Chap 16-23
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
18.0
336.0
18.33
Stock B
14
8
12.2
7.56
2.75
Expected
Standard
Return:
Variance: Deviation:
N
2
2
2
Example: σ   ( Xi  μ) P( Xi )  (30  18) (.7)  ( 10  18) (.3)  336.0
2
A
i1
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-24
Accounting for Variability
(continued)
Calculate the coefficient of variation for each stock:
CVA 
σA
18.33
 100% 
 100%  101.83%
EMVA
18.0
CVB 
σB
2.75
 100% 
 100%  22.54%
EMVB
12.2
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Stock A has
much more
relative
variability
Chap 16-25
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 Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-26
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
Return, Stock B has a much larger return to risk
ratio and a much smaller CV
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-27
Decision Making in PHStat
 PHStat | decision-making | expected
monetary value
 Check the “expected opportunity loss” and
“measures of valuation” boxes
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-28
Decision Making
with Sample Information
Prior
Probability
 Permits revising old
probabilities based on new
information
New
Information
Revised
Probability
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-29
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
Prior probabilities
from stock choice
example
E2 = weak economy = 0.30
P(F1 | E1) = 0.90
P(F1 | E2) = 0.30
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-30
Revised Probabilities
Example
(continued)
P(F1 | E1)  .9 , P(F1 | E2 )  .3
P(E1)  .7 , P(E2 )  .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
P(F1 )
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-31
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
Σ = 25.0
Revised
probabilities
Σ = 11.25
EMV Stock B = 11.25
EMV Stock A = 25.0
Maximum
EMV
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-32
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
Minimum
EOL
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-33
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
25.0
175.0
13.229
Stock B
14
8
13.25
3.94
1.984
Expected
Standard
Return:
Variance: Deviation:
N
2
2
2
Example: σ   ( Xi  μ) P( Xi )  (30  25) (.875)  ( 10  25) (.125)  175.0
2
A
i1
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-34
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 Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-35
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 Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-36
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 Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-37
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 Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-38
Three Types of Utility Curves
$
Risk Averter
$
Risk Seeker
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
$
Risk-Neutral
Chap 16-39
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 Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-40
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
 Addressed the concept of utility
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.
Chap 16-41