Decision Making Under Risk and Uncertainty
Decision Making
Decision Making Under Risk and Uncertainty
Syllabus tag: KASNEB CPA | Advanced Level | CA34S3 Advanced Management Accounting | Topic 9 Decision Making Under Risk and Uncertainty
Lesson objectives
By the end of this topic, you will be able to:
- Construct a payoff table
- Apply the maximin, maximax and minimax regret criteria
- Compute expected values where probabilities are available
- Compute the value of perfect and imperfect information
- Explain how attitude to risk shapes the decision
Why this matters
The same set of figures supports different decisions depending on the criterion applied. An examiner gives one payoff table and asks for several criteria precisely to see whether a candidate understands that the technique chosen embodies an attitude to risk.
One payoff table throughout
Chui Ltd must choose a plant size. Payoffs in KES millions:
| Decision | Low demand (0.25) | Medium (0.45) | High (0.30) |
|---|---|---|---|
| Small | 8 | 12 | 14 |
| Medium | 2 | 20 | 26 |
| Large | (6) | 16 | 42 |
Criteria without probabilities
Maximin — the pessimist. Take the best of the worst outcomes.
| Decision | Worst outcome |
|---|---|
| Small | 8 |
| Medium | 2 |
| Large | (6) |
Choose Small. Suits a company that cannot survive a bad outcome.
Maximax — the optimist. Take the best of the best outcomes.
| Decision | Best outcome |
|---|---|
| Small | 14 |
| Medium | 26 |
| Large | 42 |
Choose Large. Suits a risk-seeker, and ignores the possibility of a 6 million loss entirely.
Minimax regret — the avoider of hindsight. Regret is what you forgo by not having chosen the best option for the state that occurred.
Best payoff in each state: Low 8, Medium 20, High 42.
| Decision | Low | Medium | High | Maximum regret |
|---|---|---|---|---|
| Small | 0 | 8 | 28 | 28 |
| Medium | 6 | 0 | 16 | 16 |
| Large | 14 | 4 | 0 | 14 |
Choose Large, minimising the worst regret.
Expected value, where probabilities exist
| Decision | Expected value |
|---|---|
| Small | 11.60 |
| Medium | 17.30 |
| Large | 18.30 |
Choose Large.
Four criteria, three different answers. Maximin says Small, maximax and minimax regret and expected value say Large. None is wrong; they encode different attitudes to risk, and a candidate should state the assumption each carries rather than presenting one as correct.
:::checkpoint A family company with limited reserves faces this table. Explain which criterion its directors should apply and why the expected value answer could be the wrong advice for them specifically. :::
The value of information
Expected value with perfect information — knowing the state in advance and choosing the best decision for it:
(0.25 × 8) + (0.45 × 20) + (0.30 × 42) = 23.60
Best expected value without information = 18.30
EVPI = 23.60 − 18.30 = KES 5.30 million
That figure is the maximum worth paying for a perfect forecast. Since no forecast is perfect, it sets a ceiling on the price of any market research: a study costing 7 million cannot be worthwhile, whatever it promises.
Imperfect information is worth less. Its value is computed by revising the probabilities using the research findings — Bayes' theorem — recomputing the expected value, and comparing with the position without the study.
Attitude to risk
- Risk averse — prefers a certain outcome to a gamble with the same expected value. Maximin reflects this
- Risk neutral — indifferent, and therefore guided by expected value alone
- Risk seeking — prefers the gamble. Maximax reflects this
The expected value criterion is risk neutral, and that is its main weakness for a one-off decision. An expected value of 18.30 is an average over many repetitions, and the company will run this decision once.
The size of the exposure relative to the business is what should govern. A company that would not survive the 6 million loss should not take the Large option however attractive its expected value, because there is no long run for a firm that fails in the short one.
:::checkpoint Market research costing KES 6 million is offered, claiming to identify demand correctly 90% of the time. Using the EVPI above, say what you can conclude immediately and what further work would be needed. :::