skills/valuation/references/modules/M050-scenario-sensitivity-and-probability-weighting.md

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<!-- Module: 050 | Title: Scenario, Sensitivity, and Probability Weighting -->

## PART X - VALUATION | MODULE 050

# Scenario, Sensitivity, and Probability Weighting

> Mission. Replace false precision with explicit bull, base, bear, stress, and thesis-break cases.

## Decision output

Objective: Replace false precision with explicit bull, base, bear, stress, and thesis-break cases. The completed work product must be reproducible from evidence, show the downstream financial or decision effect when material, state the strongest contrary case, and define a dated update rule.

## Explicit operating procedure

1. Define scenarios as coherent operating states with linked demand, price, mix, margin, working capital, capex, financing, share count, and valuation assumptions.

1. Create a base case, plausible upside, plausible downside, severe stress, and explicit thesis-break case when material; distinguish temporary delay from permanent impairment.

1. Use one- and two-way sensitivities only for variables that can vary independently enough to create economically possible combinations.

1. Show scenario values before assigning probabilities. Probability weights are judgments and should include rationale, base rates where available, and an update rule.

1. Calculate expected value only as a decision aid; never let probability weighting hide catastrophic liquidity/dilution outcomes or a wide distribution.

1. Track which scenario drivers actually occurred and use post-mortems to recalibrate future ranges and probabilities.

## Required evidence and model bridge

- Primary-source set: normalized forecasts, capital structure, market data, peer definitions, scenario assumptions. Preserve exact document/version, date, period, and source location for every material factual input used in scenario, sensitivity, and probability weighting.

- For each key concept - coherent operating cases, correlated drivers, tail case, path dependence, probabilities, sensitivity matrices - state whether it is a reported fact, analyst calculation, management claim, external estimate, or judgment. Quantitative concepts must retain raw components and units; qualitative concepts must retain the specific evidence and counterevidence.

- Map only economically relevant findings into the model or decision record. Process-control modules such as scenario, sensitivity, and probability weighting may have no direct valuation line; in that case document the downstream error or governance risk the control prevents.

## Metrics and calculation controls

| Metric / concept | Construction | Required validation |
| --- | --- | --- |
| expected value | Sum of scenario value × scenario probability across mutually exclusive, collectively exhaustive cases. | expected value: Document scenario definitions and probabilities; verify probabilities sum appropriately, inputs are independently sourced, and sensitivity is recomputed rather than manually overridden. |
| downside asymmetry | Expected or stress-case downside magnitude relative to base/upside, including probability, liquidity, dilution, and permanent-impairment effects. | downside asymmetry: Document scenario definitions and probabilities; verify probabilities sum appropriately, inputs are independently sourced, and sensitivity is recomputed rather than manually overridden. |
| sensitivity slope | Change in equity value divided by change in the tested assumption over a defined local range; report nonlinear breakpoints where material. | sensitivity slope: Document scenario definitions and probabilities; verify probabilities sum appropriately, inputs are independently sourced, and sensitivity is recomputed rather than manually overridden. |



## Scenario design laboratory

- Define scenarios by coherent operating states, not by changing only valuation multiples. A bear case should connect demand, price, mix, margin, working capital, capex, financing, and share count where those variables interact.

- Probability weights are judgments, not facts. Show unweighted cases, weighted value, downside to stress, and the assumptions that would justify changing the weights.

- Add two-way sensitivities only for variables that are economically independent enough to vary separately. Avoid grids that combine impossible states.

## Worked application

> Case: revenue falls but the first bear case incorrectly leaves margins and working capital unchanged.

- Reconstruct the relevant reported fact from primary evidence before interpreting the case. For scenario, sensitivity, and probability weighting, show the raw components rather than only the resulting ratio or narrative.

- Build the causal chain through coherent operating cases, correlated drivers, tail case, path dependence, then identify which link is directly observed and which link remains an assumption.

- Calculate expected value, downside asymmetry, sensitivity slope from sourced components under the reported/base interpretation and at least one skeptical alternative interpretation.

- Translate the difference between cases into the variable that matters for scenario, sensitivity, and probability weighting: evidence quality, revenue, operating profit/NOPAT, free cash flow, invested capital, financing/dilution, risk, or valuation. Mark non-applicable links instead of inventing them.

- Expert consistency test: change linked operating variables together and keep liquidity failure from being averaged away.

- Precommit the specific future filing, KPI, customer/supplier observation, regulator action, or market input that would materially invalidate the scenario, sensitivity, and probability weighting conclusion.

## Failure tests

- FAIL if coherent operating cases cannot be defined and reproduced from the source pack.

- FAIL if scenarios are arbitrary percentage haircuts rather than coherent operating states with causal driver interactions and observable evidence that changes probability.

- FAIL if the scenario, sensitivity, and probability weighting conclusion depends on an unstated assumption, unreconciled definition, or evidence that cannot be traced to its source/version.

- FAIL if evidence materially inconsistent with the scenario, sensitivity, and probability weighting conclusion is omitted, reclassified, or dismissed without a documented definition, materiality, causal, timing, and source-quality analysis.

## Completion test

A senior reviewer must be able to reproduce the scenario, sensitivity, and probability weighting conclusion, vary the most sensitive assumption independently, trace the change through the model, understand the strongest opposing case, and identify the next evidence that would force an update. If any link is missing, the module remains open.