Decision analysis part ii

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Decision Analysis- Part II

Apr 15, 2023 2Data Analytics | Execution | Deployment | Training | QinT

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


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


Decision Analysis- Part I



• Maxmin

• Maxmax

• Minmax



• Probabilistic models• Decision-making under risk





Decision Analysis- Part III

Application and comparisons of:

• Criteria Based Matrix

• Decision analysis tools


Decision Analysis- Part I



• Maxmin

• Maxmax

• Minmax


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%


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%


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%


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


Case Study

States of nature

>1000 points 300-1000 +/-300 -300 to -

1000<-1000 points


Alternatives

Bonds 9% 7% 6% 0% -1%

Stocks 17% 9% 5% -3% -10%



Regret Matrix

States of nature

>1000 points 300-1000 +/-300 -300 to -

1000<-1000 points


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%)


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

Alter

natives

Bonds 8% 2% 1% 7% 8% 8%

Stocks 0% 0% 2% 10% 17% 17%

Fixed deposit 10% 2% 0% 0% 0% 10%



• Probabilistic models• Decision-making under risk





Expected Value Approach

• Neutral approach to find optimal decision

• The probability estimate for the occurrence ofeach 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


Case Study

States of nature

>1000 points 300-1000 +/-300 -300 to -

1000<-1000 points


Alternatives

Bonds 9% 7% 6% 0% -1%

Stocks 17% 9% 5% -3% -10%


Probability 25% 20% 40% 10% 5%


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

Alternativ

es

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%)


States of nature

>1000 points 300-1000 +/-300 -300 to -

1000<-1000 points


Alternatives

Bonds 9% 7% 6% 0% -1%Stocks 17% 9% 5% -3% -10%


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


• Uses Bayes’ theorem to calculate refined probabilities

Expected Value of Additional Information


Positive 80% 70% 50% 40% 0%

Negative 20% 30% 50% 60% 100%


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%


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%


States of nature

>1000 points 300-1000 +/-300 -300 to -

1000<-1000 points


Alternatives

Bonds 9% 7% 6% 0% -1%Stocks 17% 9% 5% -3% -10%


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


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…


Summary

States of nature

>1000 points 300-1000 +/-300 -300 to -

1000<-1000 points


Alternatives

Bonds 9% 7% 6% 0% -1%

Stocks 17% 9% 5% -3% -10%


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%


References

• University of Baltimore: http://home.ubalt.edu/ntsbarsh/opre640a/partIX.htm

• John Wiley & Sons

http://home.ubalt.edu/ntsbarsh/opre640a/partIX.htm




Thanks!!!

Date post:	06-Aug-2015
Category:	Business
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Decision analysis part ii

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