Explain why stress testing programs and capital planning make use of scenario analysis.
The idea
Stress testing in ERM is built on scenario analysis. A stress test applies a severe but plausible adverse scenario, usually a coherent set of macroeconomic and market shocks over several periods, and projects its effect on losses, earnings, risk-weighted assets, liquidity and capital. Scenarios are needed because tail events are rare, history may not contain them, and shocks interact across credit, market and funding risk. Capital planning uses the results: compare post-stress capital ratios with the minimum and target levels, set buffers, decide on dividends, buybacks and contingency actions, and align with risk appetite. Reverse stress testing starts from a failure outcome, such as capital falling below the minimum, and works back to the scenarios that cause it. Typical errors are using only the last crisis, static balance sheets and a one-day horizon. The exam point is plausible severity, multi-period impact and integration with capital decisions.
Formulas
Post-stress capital ratio
post-stress CET1 ratio = (CET1 − stress losses) ÷ stressed RWA
- CET1
- common equity tier 1 capital before the stress
- stress losses
- cumulative losses over the scenario
- stressed RWA
- risk-weighted assets at the end of the scenario
Both the numerator and the denominator move: rating migrations raise RWA as losses cut capital. Compare the result with the minimum and target ratios.
A practice question
Why do stress testing programs rely on scenario analysis?
- Because scenarios assign the precise probabilities that capital regulation requires for the firm's tail losses.Why not: Scenarios typically carry no precise objective probabilities.
- Because they measure the firm's resilience to specified severe but plausible adverse conditions that may not appear in historical data. - correct
- Because regulators forbid statistical models in stress testing.Why not: Statistical models are widely used in projecting stress impacts; nothing forbids them.
- Because scenarios remove the need for management judgement about severity.Why not: Judgement is central to designing scenarios.
Tail events are rare and may be absent from history, so stress tests specify adverse conditions directly and trace their effects.
A harder one
A bank has CET1 capital of USD 60 billion and risk-weighted assets (RWA) of USD 500 billion. In its stress scenario, cumulative losses are USD 18 billion and RWA rise to USD 550 billion because of rating migrations. Ignoring any management actions, the post-stress CET1 ratio is closest to:
- 12.0%Why not: This is the pre-stress ratio; it ignores both the loss and the rise in RWA.
- 8.4%Why not: Deducts the loss but keeps RWA at the pre-stress level instead of the stressed level.
- 10.9%Why not: Raises RWA but forgets to deduct the stress loss from capital.
- 7.6% - correct
Post-stress ratio = (60 - 18) / 550 = 42 / 550 = 7.6%. Both the loss in the numerator and the RWA growth in the denominator must be reflected.
The hardest tier
A firm's capital stress test shocks its trading book instantaneously, holds the balance sheet static and measures the effect over one day. Why is this design weak for capital planning?
- Capital planning requires a one-day horizon applied to the whole firm but with a much larger shock size.Why not: The horizon for capital planning is typically several quarters, not a day.
- Capital planning should consider only credit losses and exclude trading, because credit losses are the largest driver.Why not: Excluding trading and other risk types ignores the interactions that scenarios are meant to capture.
- Capital planning needs multi-period projections across risk types, which a one-day static shock lacks. - correct
- Scenarios should not include macroeconomic variables, which are too uncertain.Why not: Macroeconomic variables are the core of coherent stress scenarios.
Capital adequacy depends on how losses, income, RWA and management actions evolve over time; scenarios therefore need to be multi-period, coherent and cover several risk types.
In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.
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