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Outline the building blocks of a robust stress-testing framework within financial institutions, plus recommended practices for conducting stress tests.

FRM® Part II · Operational Risk and Resilience · Integrated Risk Management · FRM2.ORR.7.c

The idea

A robust stress-testing framework has several building blocks. These are clear governance with board and senior-management ownership, defined objectives, scenario design, models and methodologies, data and IT infrastructure, documentation, independent validation, and reporting that feeds decisions. Scenarios should be severe but plausible and cover historical, hypothetical and reverse approaches. Sensitivity analysis shocks one risk factor, while scenario analysis moves many factors consistently within a narrative. A reverse stress test starts from an outcome such as breaching capital minimums or failure, and works back to the events that could cause it. Good practice covers the whole firm and all material risks. It captures interactions and feedback effects, and it is realistic about management actions in stressed markets. Results should be tied to capital, liquidity, limit and strategy decisions. Stress tests complement VaR rather than replace it, and they are only useful if they change decisions.

Formulas

Stressed CET1 ratio

stressed CET1 ratio = (CET1 − L) ÷ stressed RWA

CET1
common equity tier 1 capital before the stress
L
the stress losses charged against CET1
stressed RWA
risk-weighted assets after the stress, including any rise from downgrades

Assumes losses reduce CET1 one for one. Both numerator and denominator move; leaving RWA at its pre-stress level overstates the ratio.

A practice question

From the question bank, with the reason each wrong option is wrong.

A reverse stress test starts from:

  1. A historical crisis, such as a past market collapse, that is replayed on the firm's current positions.Why not: This describes a historical scenario, which starts from a past event.
  2. A shock to a single risk factor, such as a parallel rate move, with all other factors held constant.Why not: This is sensitivity analysis, which moves one factor and observes the result.
  3. The firm's 99 percent VaR, which is then scaled up by a fixed multiple to give a stress loss.Why not: Scaling VaR is not a scenario method and does not search for the events behind a failure.
  4. A defined failure, such as breaching minimum capital, from which the causing scenarios are identified. - correct

Reverse stress testing works backwards from a predefined failure or breach to find plausible scenarios that would produce it, which exposes vulnerabilities that forward scenarios may miss.

A harder one

A risk manager moves the yield curve up 200 basis points in parallel and revalues the portfolio, holding every other risk factor constant. This is best classified as:

  1. Sensitivity analysis, because one factor is shocked. - correct
  2. Scenario analysis, because a narrative describing the economy is applied.Why not: A scenario moves several risk factors consistently within a narrative; here only one factor changes.
  3. Reverse stress testing, because the shock is large.Why not: Reverse tests start from a failure outcome, not from a shock size.
  4. Historical simulation, because the shock is a fixed number.Why not: Historical simulation uses actual past changes in the factors, not a chosen hypothetical shock.

One factor moved with all else held constant is a sensitivity test. A scenario would also move equity, credit spreads, FX and so on in a coherent, linked way.

The hardest tier

A bank starts with CET1 capital of USD 24 billion and RWA of USD 200 billion. The adverse scenario produces pre-tax losses of USD 9 billion, which reduce CET1 one-for-one with no tax or earnings effect, and downgrades raise RWA to USD 220 billion. The projected CET1 ratio at the end of the stress is closest to:

  1. 6.8 percent - correct
  2. 7.5 percentWhy not: Deducts the loss but leaves RWA at 200, ignoring the rise in RWA from downgrades.
  3. 10.9 percentWhy not: Uses the higher RWA of 220 but forgets to deduct the loss from capital.
  4. 2.7 percentWhy not: Deducts the loss twice, as 24 - 18 = 6 over 220, instead of once.

Stressed CET1 = 24 - 9 = 15. Stressed ratio = 15 / 220 = 6.8%, down from 12%. Both the numerator (losses) and denominator (RWA inflation) move in a stress test.

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