Current syllabus: Risk and uncertainty remain explicitly examinable in ACCA PM for September 2026 to June 2027. The syllabus includes information gathering, simulation, expected values, sensitivity analysis, maximax, maximin, minimax regret, decision trees and the value of perfect and imperfect information.
Management decisions are made now but produce results later. PM questions test whether you can organise possible outcomes, apply an appropriate decision rule and explain the limitations. The calculation is only part of the answer: different rules reflect different attitudes to risk.
1. Risk, uncertainty and attitude
Risk exists when several outcomes are possible and probabilities can be estimated. Uncertainty exists when probabilities are unavailable or too unreliable to support a probabilistic decision.
The usual decision attitudes are:
Risk neutral: focuses on expected value.
Risk seeking: may prefer the highest possible payoff, reflected by maximax.
Risk averse: gives greater weight to adverse outcomes; maximin is an extreme cautious rule.
Real managers may also consider cash constraints, survival, reputation, ethics and strategic fit. A mathematically attractive expected value can still be unacceptable if one possible loss threatens the organisation.
2. A payoff table for four decision rules
A company must choose a small, medium or large capacity plan. Profits are in $000:
Decision | Low demand | Medium demand | High demand |
|---|---|---|---|
Small | 30 | 40 | 40 |
Medium | 10 | 60 | 70 |
Large | (20) | 50 | 110 |
Interactive probability and EV lab
Change the three probability weights. They are normalised automatically, so they do not need to total 100. The legend recalculates every expected value and marks the best risk-neutral decision. The payoff bars themselves do not change.
Three quick experiments: weight low demand heavily, then high demand heavily, then use equal weights. Notice when the best expected-value decision changes—and why that still does not make the downside disappear.
3. Expected value
Expected value (EV) weights every payoff by its probability:
Small: (30 × 0.25) + (40 × 0.50) + (40 × 0.25) = 37.5
Medium: (10 × 0.25) + (60 × 0.50) + (70 × 0.25) = 50.0
Large: (-20 × 0.25) + (50 × 0.50) + (110 × 0.25) = 47.5
A risk-neutral decision maker chooses Medium because it has the highest EV of $50,000.
EV is a long-run average, not a prediction that this one decision will earn exactly $50,000. It is most persuasive for repeated decisions with reliable probabilities. It also ignores the decision maker's utility for money: a $100,000 loss may matter more than an equal-probability $100,000 gain.
4. Maximax, maximin and minimax regret
Maximax selects each decision's best outcome and then chooses the largest: max(40, 70, 110). It chooses Large.
Maximin selects each decision's worst outcome and then chooses the least bad: max(30, 10, -20). It chooses Small.
Minimax regret asks how much opportunity was lost by not choosing the best decision for the state that actually occurred. First build a regret table by subtracting each payoff from the best payoff in its column:
Decision | Low demand | Medium demand | High demand | Maximum regret |
|---|---|---|---|---|
Small | 0 | 20 | 70 | 70 |
Medium | 20 | 0 | 40 | 40 |
Large | 50 | 10 | 0 | 50 |
Choose the decision with the smallest maximum regret: Medium. Regret can never be negative, and the best payoff in each state always has zero regret.
Practise expected value and EVPI
Enter formulas in the yellow cells. Payoffs are in $000. Calculate each decision EV, then the value with perfect information and EVPI.
| Decision | Low p=0.25 | Medium p=0.50 | High p=0.25 | Your EV |
| Small | 30 | 40 | 40 | |
| Medium | 10 | 60 | 70 | |
| Large | (20) | 50 | 110 | |
| EV with perfect information | ||||
| EVPI |
5. Expected value of perfect information
Perfect information reveals the future state before the decision is made. Choose the best decision in each demand state:
EV with perfect information = (30 × 0.25) + (60 × 0.50) + (110 × 0.25) = 65.
Without information, the best EV is 50. Therefore:
EVPI = 65 - 50 = $15,000.
EVPI is the maximum worth of information before paying for it. Perfect information is rarely available; its value is an upper ceiling for any imperfect research. The expected value of imperfect information (EVSI) is calculated from the revised decision strategy after receiving possible research signals, less the current best EV. The research should be purchased only if EVSI exceeds its cost.
6. Decision trees
A decision tree is useful where choices and uncertain events occur in sequence:
A square is a decision point controlled by management.
A circle is a chance point with probabilities that sum to one.
Branches show alternatives, probabilities, cash flows and terminal outcomes.
Work from right to left. At a chance node, calculate the expected value. At a decision node, select the best available branch. Include costs at the point they are incurred and do not multiply a certain decision cost by a later probability.
Tree discipline: draw the chronological structure first, add probabilities second, add cash flows third, then roll back. This reduces double counting and keeps conditional probabilities attached to the correct branch.
7. Sensitivity analysis
Sensitivity analysis asks how much a key estimate can change before the decision changes. In investment-style questions the sensitivity of a variable is often:
Margin before decision changes / present value of the relevant variable × 100%.
The precise numerator and denominator depend on the requirement. The interpretation is consistent: a small percentage means the decision is sensitive and the estimate deserves attention. Sensitivity analysis changes one variable at a time, does not assign probabilities, and does not show how variables may move together.
8. Simulation and gathering information
Simulation models many possible combinations of uncertain inputs. A typical approach is to define probability distributions, generate random values, calculate the resulting outcome repeatedly and examine the distribution of results. It can show the probability of a loss and the range of outcomes, but the model is only as reliable as its assumptions, distributions and correlations.
Information may be gathered through market research, expert judgement, pilot tests, focus groups, historical data and data analytics. Consider relevance, sample bias, timeliness, cost and whether the information changes the decision. More data is not automatically better information.
9. Common exam errors
Using expected value when no probabilities are given.
Adding probabilities that do not total one without investigating the data.
Treating EV as the guaranteed outcome of a one-off decision.
Calculating regret across rows instead of down each state-of-nature column.
Subtracting research cost before calculating the value of the information itself, then subtracting it again.
Using unconditional probabilities where a tree gives conditional probabilities after research.
Recommending a number without discussing risk attitude or the possible downside.