Value a share by weighting several scenarios by their probabilities
The idea
A single forecast hides how uncertain the outcome is. Scenario analysis builds several internally consistent cases, typically base, bull and bear, each with its own revenue, margin and investment assumptions, values the share under each, and weights the values by their estimated probabilities. With values of 30, 45 and 20 and probabilities of 0.5, 0.2 and 0.3, the expected value is 15 + 9 + 6 = 30. The weighted figure is the central estimate, but the spread matters too: two shares with the same expected value can carry very different downside. Probabilities are judgements rather than facts, so analysts should say how they were set and test how sensitive the answer is to them.
A practice question
In scenario analysis, the probability-weighted value of a share is calculated as:
- the sum of each scenario value times its probability — correct
- the value in the most likely (base) scenarioWhy not: Ignores the other scenarios; if outcomes are asymmetric, the base case differs from the weighted value.
- the simple average of the scenario valuesWhy not: Weights every scenario equally, disregarding the probabilities the analyst assigned to them.
Expected value = Σ (probability × scenario value), which reflects both the range of outcomes and their likelihood.
A harder one
Scenario values for Gorsey Health are 90 (bull, 20%), 60 (base, 50%) and 30 (bear, 30%). The share trades at 50. The expected return implied by the probability-weighted value is closest to:
- 20.0%Why not: Weights the scenarios equally, giving 60, which ignores the higher probability of the bear case.
- 14.0% — correct
- 26.0%Why not: Swaps the bull and bear probabilities, giving a weighted value of 63.
Weighted value = 0.2 × 90 + 0.5 × 60 + 0.3 × 30 = 18 + 30 + 9 = 57. Expected return = 57 / 50 − 1 = 14.0%.
The hardest tier
An analyst's two scenarios for Wyncote Energy give values of 70 (bull) and 40 (bear). If the current price of 48 equals the probability-weighted value, the market-implied probability of the bull case is closest to:
- 26.7% — correct
- 73.3%Why not: Solves for the bear-case probability and reports it as the bull-case probability.
- 68.6%Why not: Divides the price by the bull value, which is not how probability weights combine two outcomes.
48 = p × 70 + (1 − p) × 40, so 30p = 8 and p = 8 / 30 = 26.7%.
In the app: 6 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.
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