Decision Making in English

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 16-1
Chapter 16
Decision Making
Statistics for Managers
Using Microsoft®
Excel
4th
Edition

Statistics for Managers Using
Microsoft Excel, 4e © 2004
Prentice-Hall, Inc. Chap 16-2
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

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

List Possible Actions or Events
Payoff Table Decision Tree
Two
Methods of
Listing

A Payoff Table
A payoff table shows alternatives,
states of nature, and payoffs
Investment
Choice
(Action)
Profit in $1,000’s
(Events)
Strong
Economy
Stable
Economy
Weak
Economy
Large factory
Average factory
Small factory
200
90
40
50
120
30
-120
-30
20

Sample Decision Tree
Large factory
Small factory
Average factory
Strong Economy
Stable Economy
Weak Economy
Strong Economy
Stable Economy
Weak Economy
Strong Economy
Stable Economy
Weak Economy
Payoffs
200
50
-120
40
30
20
90
120
-30

Opportunity Loss
Investment
Choice
(Action)
(Events)
Strong
Economy
Stable
Economy
Weak
Economy
Large factory
Average factory
Small factory
200
90
40
50
120
30
-120
-30
20The 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.
Opportunity loss is the difference between an actual
payoff for an action and the optimal payoff, given a
particular event
Payoff
Table

Opportunity Loss
Investment
Choice
(Action)
(States of Nature)
Strong
Economy
Stable
Economy
Weak
Economy
Large factory
Average factory
Small factory
200
90
40
50
120
30
-120
-30
20
(continued)
Investment
Choice
(Action)
Opportunity Loss in $1,000’s
(Events)
Strong
Economy
Stable
Economy
Weak
Economy
Large factory
Average factory
0
110
70
0
140
50
Payoff
Table
Opportunity
Loss Table

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

Expected Monetary Value
Solution
 The expected monetary value is the weighted
average payoff, given specified probabilities for
each event
∑=
=
N
1i
iijPx)j(EMV
Where EMV(j) = expected monetary value of action j
xij = payoff for action j when event i occurs
Pi = probability of event i
Goal: Maximize expected value

 The expected value is the weighted average
payoff, given specified probabilities for each
event
Investment
Choice
(Action)
(Events)
Strong
Economy
(.3)
Stable
Economy
(.5)
Weak
Economy
(.2)
Large factory
Average factory
Small factory
200
90
40
50
120
30
-120
-30
20
Suppose these
probabilities
have been
assessed for
these three
events
(continued)
Solution

Investment
Choice
(Action)
(Events)
Strong
Economy
(.3)
Stable
Economy
(.5)
Weak
Economy
(.2)
Large factory
Average factory
Small factory
200
90
40
50
120
30
-120
-30
20
Example: EMV (Average factory) = 90(.3) + 120(.5) + (-30)(.2)
= 81
Expected
Values
(EMV)
61
81
31
Maximize
expected
value by
choosing
Average
factory
(continued)
Payoff Table:
Goal: Maximize expected value
Solution

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

Add Probabilities and Payoffs
Large factory
Small factory
Decision
Average factory
Uncertain Events
Strong Economy
Stable Economy
Weak Economy
Strong Economy
Stable Economy
Weak Economy
Strong Economy
Stable Economy
Weak Economy
(continued)
PayoffsProbabilities
200
50
-120
40
30
20
90
120
-30
(.3)
(.5)
(.2)
(.3)
(.5)
(.2)
(.3)
(.5)
(.2)

Fold Back the Tree
Large factory
Small factory
Average factory
Strong Economy
Stable Economy
Weak Economy
Strong Economy
Stable Economy
Weak Economy
Strong Economy
Stable Economy
Weak Economy
200
50
-120
40
30
20
90
120
-30
(.3)
(.5)
(.2)
(.3)
(.5)
(.2)
(.3)
(.5)
(.2)
EMV=200(.3)+50(.5)+(-120)(.2)=61
EMV=90(.3)+120(.5)+(-30)(.2)=81
EMV=40(.3)+30(.5)+20(.2)=31

Make the Decision
Large factory
Small factory
Average factory
Strong Economy
Stable Economy
Weak Economy
Strong Economy
Stable Economy
Weak Economy
Strong Economy
Stable Economy
Weak Economy
200
50
-120
40
30
20
90
120
-30
(.3)
(.5)
(.2)
(.3)
(.5)
(.2)
(.3)
(.5)
(.2)
EV=61
EV=81
EV=31
Maximum
EMV=81

Expected Opportunity Loss
Solution
 The expected opportunity loss is the weighted
average loss, given specified probabilities for
each event
∑=
=
N
1i
iijPL)j(EOL
Where EOL(j) = expected monetary value of action j
Lij = opp. loss for action j when event i occurs
Pi = probability of event i
Goal: Minimize expected opportunity loss

Expected Opportunity Loss
Solution
Investment
Choice
(Action)
Opportunity Loss in $1,000’s
(Events)
Strong
Economy
(.3)
Stable
Economy
(.5)
Weak
Economy
(.2)
Large factory
Average factory
Small factory
0
110
160
70
0
90
140
50
0
Example: EOL (Large factory) = 0(.3) + 70(.5) + (140)(.2)
= 63
Expected
Op. Loss
(EOL)
63
43
93
Minimize
expected
op. loss by
choosing
Average
factory
Opportunity Loss Table
Goal: Minimize expected opportunity loss

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)

Expected Profit Under Certainty
 Expected
profit under
certainty
= expected
value of the
best
decision,
given perfect
information
Investment
Choice
(Action)
(Events)
Strong
Economy
(.3)
Stable
Economy
(.5)
Weak
Economy
(.2)
Large factory
Average factory
Small factory
200
90
40
50
120
30
-120
-30
20
Example: Best decision
given “Strong Economy” is
“Large factory”
200 120 20
Value of best decision
for each event:

Expected Profit Under Certainty
Investment
Choice
(Action)
(Events)
Strong
Economy
(.3)
Stable
Economy
(.5)
Weak
Economy
(.2)
Large factory
Average factory
Small factory
200
90
40
50
120
30
-120
-30
20
200 120 20
(continued)
 Now weight
these outcomes
with their
probabilities to
find the
expected value: 200(.3)+120(.5)+20(.2)
= 124
Expected
profit under
certainty

Value of Information Solution
Expected Value of Perfect Information (EVPI)
EVPI = Expected profit under certainty
– Expected monetary value of the best decision
so: EVPI = 124 – 81
= 43
Recall: Expected profit under certainty = 124
EMV is maximized by choosing “Average factory”,
where EMV = 81
(EVPI is the maximum you would be willing to spend to obtain
perfect information)

Accounting for Variability
Stock Choice
(Action)
Percent Return
(Events)
Strong
Economy
(.7)
Weak
Economy
(.3)
Stock A 30 -10
Stock B 14 8
Consider the choice of Stock A vs. Stock B
Expected
Return:
18.0
12.2
Stock A has a higher
EMV, but what about
risk?

Stock Choice
(Action)
Percent Return
(Events)
Strong
Economy
(.7)
Weak
Economy
(.3)
Stock A 30 -10
Stock B 14 8
Variance:
336.0
7.56
Calculate the variance and standard deviation for
Stock A and Stock B:
Expected
Return:
18.0
12.2
0.336)3(.)1810()7(.)1830()X(Pμ)X(σ 22
N
1i
i
2
i
2
A =−−+−=−= ∑=
Example:
Standard
Deviation:
18.33
2.75
(continued)

Calculate the coefficient of variation for each stock:
%83.101100%
0.18
33.18
100%
EMV
σ
CV
A
A
A =×=×=
(continued)
%54.22100%
2.12
75.2
100%
EMV
σ
CV
B
B
B =×=×=
Stock A has
much more
relative
variability

Return-to-Risk Ratio
Return-to-Risk Ratio (RTRR):
jσ
EMV(j)
RTRR(j) =
Expresses the relationship between the return
(expected payoff) and the risk (standard deviation)

Return-to-Risk Ratio
jσ
EMV(j)
RTRR(j) =
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
982.0
33.18
0.18
σ
EMV(A)
RTRR(A)
A
===
436.4
75.2
2.12
σ
EMV(B)
RTRR(B)
B
===

Decision Making in PHStat
 PHStat | decision-making | expected
monetary value
 Check the “expected opportunity loss” and
“measures of valuation” boxes

Decision Making
with Sample Information
 Permits revising old
probabilities based on new
information
New
Information
Revised
Probability
Prior
Probability

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.
Prior probabilities
from stock choice
example
F1 = strong forecast
F2 = weak forecast
E1 = strong economy = 0.70
E2 = weak economy = 0.30
P(F1 | E1) = 0.90 P(F1 | E2) = 0.30

EMV with
EMV Stock A = 25.0
EMV Stock B = 11.25
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 Σ = 11.25
Maximum
EMV

EOL Table with
EOL Stock A = 2.25
EOL Stock B = 14.00
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 Σ = 14.00
Minimum
EOL

Stock Choice
(Action)
Percent Return
(Events)
Strong
Economy
(.875)
Weak
Economy
(.125)
Stock A 30 -10
Stock B 14 8
Variance:
175.0
3.94
Calculate the variance and standard deviation for
Stock A and Stock B:
Expected
Return:
25.0
13.25
0.175)125(.)2510()875(.)2530()X(Pμ)Xi(σ 22
N
1i
i
22
A =−−+−=−= ∑=
Example:
Standard
Deviation:
13.229
1.984
Accounting for Variability with

The coefficient of variation for each stock using the
results from the revised probabilities:
%92.52100%
0.25
229.13
100%
EMV
σ
CV
A
A
A =×=×=
(continued)
%97.14100%
25.13
984.1
100%
EMV
σ
CV
B
B
B =×=×=
Accounting for Variability with

Return-to-Risk Ratio with
With the revised probabilities, both stocks have
higher expected returns, lower CV’s, and larger
return to risk ratios
890.1
229.13
0.25
σ
EMV(A)
RTRR(A)
A
===
011.7
984.1
25.13
σ
EMV(B)
RTRR(B)
B
===

Utility
 Utility is the pleasure or satisfaction
obtained from an action.
 The utility of an outcome may not be the same
for each individual.

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.

Three Types of Utility Curves
Utility
$ $ $
Utility
Utility
Risk Averter Risk Seeker Risk-Neutral

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

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

Decision Making in English

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