The document discusses decision analysis techniques for making decisions under uncertainty. It describes deterministic and probabilistic decision models, including decision-making under pure uncertainty using maxmin, maxmax, and minmax approaches. It also covers decision-making under risk using expected value returns, expected value of perfect information, and expected value of additional information through Bayesian analysis. A case study on investment decisions applies these techniques and calculates the expected values to determine the optimal decision.
1. Core Purpose: To Enable Organisations Become Happier
Decision Analysis- Part II
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What is Decision Analysis?
• A quantitative framework for making decisions
• Selection of a decision from a set of possible decision alternatives
when uncertainties regarding the future exist
• Goal is to optimize the resulting payoff in terms of a decision
criterion
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Decision Models
• Deterministic models
• Probabilistic models
• Decision-making under pure uncertainty
• Maxmin
• Maxmax
• Minmax
• Decision-making under risk
• Expected value returns
• Expected value of perfect information
• Expected value of additional information- Bayesian analysis
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Decision Analysis- Part I
• Deterministic models
• Probabilistic models
• Decision-making under pure uncertainty
• Maxmin
• Maxmax
• Minmax
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Decision Analysis- Part II
• Probabilistic models
• Decision-making under risk
• Expected value returns
• Expected value of perfect information
• Expected value of additional information- Bayesian analysis
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Decision Analysis- Part III
Application and comparisons of:
• Criteria Based Matrix
• Decision analysis tools
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Decision Analysis- Part I
• Deterministic models
• Probabilistic models
• Decision-making under pure uncertainty
• Maxmin
• Maxmax
• Minmax
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Case Study
States of nature
>1000
points
300-1000 +/-300
-300 to -
1000
<-1000
points
Large rise Small rise No change Small fall Large fall
Alternatives
Bonds 9% 7% 6% 0% -1%
Stocks 17% 9% 5% -3% -10%
Fixed
deposit
7% 7% 7% 7% 7%
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MaxMin
Pessimistic approach based on worst case scenario
1. Write min for each row
2. Choose max of the above
States of nature
>1000
points
300-
1000
+/-300
-300 to -
1000
<-1000
points
Large
rise
Small
rise
No
change
Small fall
Large
fall
Min
Alternatives
Bonds 9% 7% 6% 0% -1% -1%
Stocks 17% 9% 5% -3% -10% -10%
Fixed
deposit
7% 7% 7% 7% 7% 7%
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MaxMax
Optimistic approach based on best case scenario
1. Write max for each row
2. Choose max of the above
States of nature
>1000
points
300-
1000
+/-300
-300 to -
1000
<-1000
points
Large
rise
Small
rise
No
change
Small fall
Large
fall
Max
Alternatives
Bonds 9% 7% 6% 0% -1% 9%
Stocks 17% 9% 5% -3% -10% 17%
Fixed
deposit
7% 7% 7% 7% 7% 7%
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MinMax
Pessimistic approach to minimize regret or opportunity loss
1. Take the largest number in each coloumn
2. Subtract all the numbers in the coloumn from it
3. Choose maximum number for each option
4. Choose minimum number from step 3
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Case Study
States of nature
>1000
points
300-1000 +/-300
-300 to -
1000
<-1000
points
Large rise Small rise No change Small fall Large fall
Alternatives
Bonds 9% 7% 6% 0% -1%
Stocks 17% 9% 5% -3% -10%
Fixed
deposit
7% 7% 7% 7% 7%
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Regret Matrix
States of nature
>1000
points
300-1000 +/-300
-300 to -
1000
<-1000
points
Large rise Small rise No change Small fall Large fall
Alternatives
Bonds (17%-9%) (9%-7%) (7%-6%) (7%-0%) (7%+1%)
Stocks (17%-17%) (9%-9%) (7%-5%) (7%+3%) (7%+10%)
Fixed
deposit
(17%-7%) (9%-7%) (7%-7%) (7%-7%) (7%-7%)
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Regret Matrix
States of nature
>1000
points
300-1000 +/-300
-300 to -
1000
<-1000
points
Large rise Small rise
No
change
Small fall Large fall Max
Alternatives
Bonds 8% 2% 1% 7% 8% 8%
Stocks 0% 0% 2% 10% 17% 17%
Fixed
deposit
10% 2% 0% 0% 0% 10%
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Decision Analysis- Part II
• Probabilistic models
• Decision-making under risk
• Expected value returns
• Expected value of perfect information
• Expected value of additional information- Bayesian analysis
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Expected Value Approach
• Neutral approach to find optimal decision
• The probability estimate for the occurrence of
each state of nature can be incorporated to arrive at the optimal
decision
1. For each decision add all the payoffs
2. Select the decision with the best expected payoff
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Case Study
States of nature
>1000
points
300-1000 +/-300
-300 to -
1000
<-1000
points
Large rise Small rise No change Small fall Large fall
Alternatives
Bonds 9% 7% 6% 0% -1%
Stocks 17% 9% 5% -3% -10%
Fixed deposit 7% 7% 7% 7% 7%
Probability 25% 20% 40% 10% 5%
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Expected Value Calculation
States of nature
>1000
points
300-
1000
+/-300
-300 to -
1000
<-1000
points
EV
Large
rise
Small
rise
No
change
Small fall Large fall
Alternatives
Bonds 9% 7% 6% 0% -1% 6%
Stocks 17% 9% 5% -3% -10% 7.25%
Fixed
deposit
7% 7% 7% 7% 7% 7%
Probability 25% 20% 40% 10% 5%
EV(Bonds)= 25%x9% + 20%x7% + 40%x6% + 10%x0% + 5%x(-1%)
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States of nature
>1000
points
300-1000 +/-300
-300 to -
1000
<-1000
points
Large rise Small rise
No
change
Small fall Large fall
Alternatives
Bonds 9% 7% 6% 0% -1%
Stocks 17% 9% 5% -3% -10%
Fixed deposit 7% 7% 7% 7% 7%
Probability 25% 20% 40% 10% 5%
• ER(PI)= 25%x17% +20%x9% + 40%x7% + 10%x7% + 5%x7% = 9.9%
• Expected value of perfect information: 9.9%-7.25% =2.65%
Expected Value of Perfect Information
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• Uses Bayes’ theorem to calculate refined probabilities
Expected Value of Additional Information
Large rise Small rise No change Small fall Large fall
Positive 80% 70% 50% 40% 0%
Negative 20% 30% 50% 60% 100%
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Probability- Positive Growth
State of nature
Prior
probability
Probability
(State|Positive)
Joint
probability
Posterior
probability
Large rise 25% 80% 20% 34.5%
Small rise 20% 70% 14% 24.1%
No change 40% 50% 20% 34.5%
Small fall 10% 40% 4% 6.9%
Large fall 5% 0% 0% 0%
Probability (Forecast=Positive) = 58%
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Probability- Negative Growth
State of nature
Prior
probability
Probability
(State|Negative)
Joint
probability
Posterior
probability
Large rise 25% 20% 5% 11.9%
Small rise 20% 30% 6% 14.3%
No change 40% 50% 20% 47.6%
Small fall 10% 60% 6% 14.3%
Large fall 5% 100% 5% 11.9%
Probability (Forecast=Negative) = 42%
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States of nature
>1000
points
300-1000 +/-300
-300 to -
1000
<-1000
points
Large rise Small rise
No
change
Small fall Large fall
Alternatives
Bonds 9% 7% 6% 0% -1%
Stocks 17% 9% 5% -3% -10%
Fixed deposit 7% 7% 7% 7% 7%
P (Positive) 34.5% 24.1% 34.5% 6.9% 0%
P (Negative) 11.9% 14.3% 47.6% 14.3% 11.9%
• EV(Bonds|Positive)= 9%x34.5% +7%x24.1+ 6%x34.5% + 0%x6.9% + (-1%) x 0%= 6.86%
• EV(Bonds|Negative)= 9%x11.9% +7%x14.3+ 6%x47.6% + 0%x14.3% + (-1%) x 11.9%= 4.81%
Conditional Expected Values
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Positive
Forecast
Negative
Forecast
Alternatives
Bonds 6.86% 4.81%
Stocks 9.55% 4.07%
Fixed deposit 7% 7%
• Expected Return from Additional Information: 58%*9.55%+42%*7% = 8.48%
• Expected Value of Additional Information: 8.48%-7.25% = 1.23%
Conditional Expected Values Contd…
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Summary
States of nature
>1000
points
300-1000 +/-300
-300 to -
1000
<-1000
points
Large rise Small rise No change Small fall Large fall
Alternatives
Bonds 9% 7% 6% 0% -1%
Stocks 17% 9% 5% -3% -10%
Fixed deposit 7% 7% 7% 7% 7%
Probability 25% 20% 40% 10% 5%
• Expected Value Returns: = 7.25%
• Expected value of perfect information: 9.9%-7.25% = 2.65%
• Expected Value of Additional Information: 8.48%-7.25% = 1.23%
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References
• University of Baltimore:
http://home.ubalt.edu/ntsbarsh/opre640a/partIX.htm
• John Wiley & Sons
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Thanks!!!
7-Jan-15 27