Decision analysis part ii
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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.
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Decision analysis part ii
- 1. Core Purpose: To Enable Organisations Become Happier Decision Analysis- Part II
- 2. Data Analytics | Execution | Deployment | Training | QinT7-Jan-15 2 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
- 3. Data Analytics | Execution | Deployment | Training | QinT7-Jan-15 3 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
- 4. Data Analytics | Execution | Deployment | Training | QinT7-Jan-15 4 Decision Analysis- Part I • Deterministic models • Probabilistic models • Decision-making under pure uncertainty • Maxmin • Maxmax • Minmax
- 5. Data Analytics | Execution | Deployment | Training | QinT7-Jan-15 5 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
- 6. Data Analytics | Execution | Deployment | Training | QinT7-Jan-15 6 Decision Analysis- Part III Application and comparisons of: • Criteria Based Matrix • Decision analysis tools
- 7. Data Analytics | Execution | Deployment | Training | QinT7-Jan-15 7 Decision Analysis- Part I • Deterministic models • Probabilistic models • Decision-making under pure uncertainty • Maxmin • Maxmax • Minmax
- 8. Data Analytics | Execution | Deployment | Training | QinT7-Jan-15 8 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%
- 9. Data Analytics | Execution | Deployment | Training | QinT7-Jan-15 9 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%
- 10. Data Analytics | Execution | Deployment | Training | QinT7-Jan-15 10 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%
- 11. Data Analytics | Execution | Deployment | Training | QinT7-Jan-15 11 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
- 12. Data Analytics | Execution | Deployment | Training | QinT7-Jan-15 12 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%
- 13. Data Analytics | Execution | Deployment | Training | QinT7-Jan-15 13 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%)
- 14. Data Analytics | Execution | Deployment | Training | QinT7-Jan-15 14 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%
- 15. Data Analytics | Execution | Deployment | Training | QinT7-Jan-15 15 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
- 16. Data Analytics | Execution | Deployment | Training | QinT7-Jan-15 16 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
- 17. Data Analytics | Execution | Deployment | Training | QinT7-Jan-15 17 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%
- 18. Data Analytics | Execution | Deployment | Training | QinT7-Jan-15 18 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%)
- 19. Data Analytics | Execution | Deployment | Training | QinT7-Jan-15 19 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
- 20. Data Analytics | Execution | Deployment | Training | QinT7-Jan-15 20 • 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%
- 21. Data Analytics | Execution | Deployment | Training | QinT7-Jan-15 21 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%
- 22. Data Analytics | Execution | Deployment | Training | QinT7-Jan-15 22 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%
- 23. Data Analytics | Execution | Deployment | Training | QinT7-Jan-15 23 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
- 24. Data Analytics | Execution | Deployment | Training | QinT7-Jan-15 24 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…
- 25. Data Analytics | Execution | Deployment | Training | QinT7-Jan-15 25 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%
- 26. Data Analytics | Execution | Deployment | Training | QinT7-Jan-15 26 References • University of Baltimore: http://home.ubalt.edu/ntsbarsh/opre640a/partIX.htm • John Wiley & Sons
- 27. Data Analytics | Execution | Deployment | Training | QinT Thanks!!! 7-Jan-15 27