Risk, Uncertainty and the Management Accountant
P1 distinguishes risk (outcomes have known probabilities) from uncertainty (probabilities cannot be assigned). You must build pay-off tables, compute expected values, apply maximax, maximin and minimax regret, use decision trees, and test sensitivity - while recognising that expected value is not the same as a risk-adjusted decision.
Decision criteria
- Expected value: sum of probability × outcome; suits repeated decisions and a risk-neutral decision maker.
- Maximax: choose the highest possible payoff; optimistic.
- Maximin: choose the highest of the worst outcomes; pessimistic.
- Minimax regret: build a regret (opportunity-loss) table, find each option's maximum regret, choose the option with the lowest maximum regret.
Decision trees
A decision tree sequences decision and chance nodes. At chance nodes calculate expected values; at decision nodes choose the highest value, after deducting relevant costs. Work backwards from the branch ends.
Worked example
Two options, two states: good (probability 0.6) and poor (0.4). Option A pays £100,000 (good) or £50,000 (poor). Option B pays £160,000 or £10,000. EV(A) = 0.6 × 100,000 + 0.4 × 50,000 = £80,000. EV(B) = 0.6 × 160,000 + 0.4 × 10,000 = £100,000. EV favours B. Maximin: worst outcomes are £50,000 for A and £10,000 for B, so A is chosen. Maximax: best outcomes £100,000 vs £160,000, so B. Regret table: in the good state, best is £160,000, so regrets are £60,000 (A) and £0 (B); in the poor state, best is £50,000, so regrets are £0 (A) and £40,000 (B). Maximum regrets are £60,000 and £40,000, so minimax regret chooses B.
Sensitivity and risk measurement
Sensitivity asks how far one variable can change before the decision changes; it is one-variable-at-a-time and ignores interdependence. Standard deviation measures absolute risk; coefficient of variation = standard deviation ÷ expected value, allowing comparison across different-sized projects.
Traps
- Treating expected value as risk-free; it hides spread.
- Using payoffs instead of regrets in minimax regret.
- Reversing maximin and maximax.
- Forgetting that probabilities must sum to 1.
- Applying sensitivity analysis to several variables simultaneously.