No decision comes with a guaranteed outcome. Sales may be higher or lower, costs may rise and a new product may fail. Case Study requirements often ask for the risks of a proposal and how to deal with them. This topic explains the difference between risk and uncertainty, risk preference, expected values, decision trees and the value of perfect information.
In 30 seconds
Uncertainty means there is too little information about the outcome. Risk means several outcomes are possible and their probabilities can be estimated. You can reduce uncertainty with more information, such as market research, but you cannot remove it, and risk cannot be removed from a situation, only analysed and judged. Managers may be risk averse, neutral or seeking.
Expected value weights each outcome by its probability, a decision tree handles multi-stage decisions, and the value of perfect information is the most worth paying to know the outcome in advance.
The nature of risk and uncertainty
Managers decide without perfect knowledge of the outcome. Often the result differs from what they expected, for better or for worse.
| Term | Meaning | Can it be analysed statistically? |
|---|---|---|
| Uncertainty | Too little information about the outcome of a decision, so estimates of sales or costs may be inaccurate | Not reliably, because probabilities are not known |
| Risk | Several outcomes are possible, and the probability of each can be assessed with reasonable accuracy | Yes, because the probabilities can be estimated |
Uncertainty comes from a lack of reliable information, so it can be reduced by getting more information that can be relied on. It cannot be removed entirely. For example, market research into the attitudes and buying intentions of customers gives better estimates of demand, but demand will never be known exactly. Risk exists in the situation itself and cannot be removed from a decision.
A manager can only analyse it and decide whether it is justified or acceptable.
Risk preference
When allowing for risk, managers consider both the expected incremental revenue, costs and profit and the risk or uncertainty around them. How they weigh the risk depends on their attitude to it.
| Type | Behaviour |
|---|---|
| Risk averse | Considers risk and will not choose a riskier option unless the extra expected return justifies it. This manager does not avoid all risk but needs a clearly higher return for taking more |
| Risk neutral | Ignores risk and picks the option with the highest expected return |
| Risk seeking | Considers risk but takes extra risk in the hope of a higher return |
It is usually assumed that managers are risk averse.
Expected values
Where probabilities can be given to outcomes, the expected value is the weighted average: multiply each outcome by its probability and add. The rule is to choose the option with the highest expected profit or the lowest expected cost. The advantage is that it takes account of both the likelihood and the size of each outcome.
Decision trees
A decision tree is used when a decision has two or more levels and the second depends on the result of the first. It shows all possible outcomes and their probabilities. You draw it from the root to the branches, then analyse it from the branches back to the root. It has decision points, where a choice is made, and outcome points, where an expected value is calculated.
In the Case Study you may be asked to use this technique for a management decision.
The value of perfect information
Managers may ask how much they should pay for information that would make the outcome certain. This is the value of perfect information: the expected value with perfect information less the expected value without it. Remember that real forecasts only reduce uncertainty. An expert can also be wrong, so a forecast is never perfect.
Worked example
Scenario (fictitious figures, ₦ million). A company may launch a product. Strong demand (probability 0.3) gives a profit of 80, moderate demand (0.5) gives 30 and weak demand (0.2) gives a loss of 40. Not launching gives zero. Advise the board, and find the most it should pay for a perfect forecast of demand.
- Expected value of launching.
(0.3 × 80) + (0.5 × 30) + (0.2 × −40) = 24 + 15 − 8 = ₦31 million. - Decision on expected value. 31 is higher than 0, so launch.
- Risk. There is a 20% chance of losing ₦40 million. A risk-averse board may want a pilot or a smaller launch.
- Value of perfect information. With a perfect forecast you would launch when demand is strong or moderate and not launch when it is weak.
Expected value with perfect information = (0.3 × 80) + (0.5 × 30) + (0.2 × 0) = ₦39 million. - Result.
The value of perfect information is 39 − 31 = ₦8 million.
That is the most the company should pay for a forecast that is certain.
A real forecast is less than perfect, so it is worth less.
Common mistakes
- Using “risk” and “uncertainty” as though they mean the same thing.
- Choosing on expected value alone and not commenting on the chance and size of a loss.
- Drawing the tree and analysing it in the wrong direction.
- Claiming that more information removes uncertainty.
- Listing risks without a way to manage each one.
Quick revision
- Uncertainty: too little information. Risk: known probabilities.
- More information reduces uncertainty but never removes it.
- Risk averse, neutral and seeking.
- Expected value: sum of outcome times probability. Highest profit, lowest cost.
- Decision tree: draw root to branches, solve branches to root.
- Value of perfect information: EV with minus EV without.
Practice questions
These are original questions in the style of the Institute of Chartered Accountants of Nigeria exam. Try each one before you open the answer.
Question 1. Market research is most likely to:
- Remove all uncertainty
- Reduce uncertainty about demand
- Remove risk from the decision
- Fix the probabilities
Show the answer
B. It improves estimates but cannot make them certain.
Question 2. A manager picks the highest expected return and ignores the risk. This manager is:
- Risk averse
- Risk neutral
- Risk seeking
- Risk free
Show the answer
B. A risk-neutral manager ignores risk entirely.
Question 3. Outcomes are profit ₦60 million with probability 0.4 and loss ₦20 million with probability 0.6. The expected value is:
- ₦12 million
- ₦20 million
- ₦40 million
- ₦6 million
Show the answer
A. (0.4 × 60) + (0.6 × −20) = 24 − 12 = 12.
Question 4. The value of perfect information equals:
- The expected value without it less the value with it
- The expected value with it less the expected value without it
- The cost of the forecast
- The highest profit
Show the answer
B. It is the most the manager should pay for certainty.
Question 5 (6 marks). Distinguish between risk and uncertainty, and explain whether either can be removed from a decision.
Model answer
Show the model answer to Question 5
Distinction (3 marks). Uncertainty is a condition where there is not enough information about the outcome, so estimates may be inaccurate. (1.5) Risk is a condition where several outcomes are possible and the probability of each can be assessed reasonably well, so it can be analysed statistically. (1.5)
Removal (3 marks). Uncertainty can be reduced by obtaining reliable information, such as market research, but never removed entirely. (1.5) Risk exists in the situation, so it cannot be removed. A manager can only analyse it and decide whether it is justified or acceptable. (1.5)
The next topic covers business and investment valuation.
Pathfinder on Risk and uncertainty in decision making: expected values, decision trees and perfect information
These are the ICAN Pathfinder questions that test this topic. ICAN owns the questions and the suggested solutions, so we point you to them and do not copy them. Open your Pathfinder, attempt each question under exam conditions, then check your answer against the notes above.
The requirement asks for the three key risks and the techniques to manage them. Use the risk and uncertainty headings, then give a response to each risk.
Revise first: The nature of risk and uncertainty
The finance director asked for advice on avoidable or manageable losses. Link each loss to a way of reducing its likelihood or its cost.
Revise first: Risk preference
Source: ICAN Pathfinder, Case Study. Diets covered: May 2015 and May 2017.
Spotted a mistake? Tell us and we will check it.
