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FRM Exam Part II · Stress Testing Banks

Modeling Stress Impacts on Capital, Losses and Revenue for FRM Part 2

Updated 11 October 2026 · Fact-checked

Stress testing a bank projects capital over a scenario horizon: starting capital plus pre-provision net revenue (PPNR), minus credit and other losses, minus taxes and distributions, divided by projected RWA. You find the ratio path, compare it to minimums and buffers, and then challenge model limits.

Understand Modeling Stress Impacts on Capital, Losses and Revenue

A bank stress test asks one question: after a severe but plausible scenario, does the bank still hold enough capital? To answer, you project three things over the horizon, usually nine quarters in supervisory tests: losses, revenue and risk-weighted assets (RWA).

Losses come from loans, securities, trading and counterparty exposures, and operational events. For loans, banks usually build models of PD, LGD and EAD linked to scenario variables such as unemployment, GDP, house prices and interest rates. Provisions are the accounting charge that recognises expected credit losses. Under a stress they rise sharply, and under expected-loss accounting they are front-loaded.

Pre-provision net revenue (PPNR) is net interest income plus non-interest income minus non-interest expense, before provisions. It is the first line of defence against losses. Net interest income reacts to rates, deposit betas, loan growth and spreads. Fee income reacts to market activity. Expenses are partly fixed, so they fall slowly. Operational risk losses and litigation costs are usually deducted separately.

RWA and capital. Capital ratios have a numerator and a denominator. Net income after provisions, taxes and planned dividends or buybacks changes common equity. Under stress, RWA often rises because ratings migrate and PDs increase (for IRB banks), and drawn amounts on credit lines go up. Deductions from capital, such as deferred tax assets, can also change. The result is a CET1 ratio path, and the minimum point (the trough) is what matters.

Limitations. Models are fitted on limited history with few severe downturns, so relationships may break in a crisis. PPNR is hard to model because it depends on management actions and customer behaviour. Models may miss feedback loops, second-round effects and risk interactions. Good practice is to use expert judgement, overlays, sensitivity analysis, validation and effective challenge, and to document assumptions clearly.

Key formulas to remember

PPNR
PPNR = Net interest income + Non-interest income − Non-interest expense
Measured before provisions and before taxes. Operational and other losses are usually shown as separate lines.
Pre-tax income
Pre-tax income = PPNR − Provisions − Trading and counterparty losses − Operational losses − Other losses
Losses on securities and fair-valued items may run through income or through other comprehensive income depending on accounting.
Ending capital
Ending CET1 = Starting CET1 + Net income − Dividends − Buybacks ± Other adjustments
Net income = pre-tax income − taxes. A loss reduces capital. Include deduction changes.
Capital ratio
CET1 ratio = CET1 capital ÷ RWA
Compute it each quarter. Compare the minimum with requirement plus buffers.
Expected credit loss
EL = PD × LGD × EAD
Used to project loan losses under each scenario path. Stress raises PD, LGD and often EAD.
Leverage ratio
Leverage ratio = Tier 1 capital ÷ Total leverage exposure
Does not use RWA, so it is unaffected by risk-weight migration.

How to solve Modeling Stress Impacts on Capital, Losses and Revenue questions

Use the same chain for any question on projecting capital under stress. Build it in order and watch the sign of each item.

  1. 1Identify the scenario and horizon, and which variables move (GDP, unemployment, rates, house prices, equity prices).
  2. 2Project losses: EL = PD × LGD × EAD for loans, then add securities, trading, counterparty and operational losses.
  3. 3Project PPNR: net interest income plus fees minus expenses, adjusted for rate, volume and spread changes.
  4. 4Compute pre-tax income = PPNR − provisions and other losses, then subtract taxes (or apply the tax effect) to get net income.
  5. 5Roll capital forward: starting capital plus net income minus dividends and buybacks, with any deduction changes.
  6. 6Project RWA under stress (migration, drawdowns, balance sheet growth), then compute capital ratio = capital ÷ RWA.
  7. 7Compare the lowest ratio with the minimum plus buffers and state the shortfall or surplus.
  8. 8If the question is about limitations, name the specific weakness (data, model risk, behaviour, feedback) and the matching mitigation.

Quickest way: Capital waterfall in one pass

When to use it: For numerical MCQs that give you income lines, losses, RWA and ask for the stressed ratio or shortfall.

  1. Write PPNR first, then subtract all losses to get income.
  2. Apply tax only if told to; a loss with no tax benefit gets no credit.
  3. Add income to capital, then subtract distributions.
  4. Divide by stressed RWA, not starting RWA.
  5. Check which option you are asked for: the ratio, the shortfall in capital, or the change in percentage points.

Common mistakes in Modeling Stress Impacts on Capital, Losses and Revenue

  • Treating PPNR as net income after provisions.

    The name sounds like profit, and students forget the word 'pre-provision'.

    Fix: PPNR excludes provisions. Subtract provisions and other losses afterwards.

  • Dividing stressed capital by starting RWA.

    Students only stress the numerator.

    Fix: Re-estimate RWA under the scenario, then divide. Say which RWA you used.

  • Ignoring planned dividends and buybacks.

    The focus is on losses and revenue.

    Fix: Subtract distributions from capital unless the question assumes they are cut or the test sets them.

  • Assuming stress always cuts revenue.

    Students expect everything to worsen.

    Fix: Net interest income can rise or fall with the rate path and funding costs. Read the scenario.

  • Confusing a model's statistical fit with its reliability under stress.

    Good in-sample fit looks reassuring.

    Fix: Historical relationships may fail in tail events. Look for limited data, structural breaks and behavioural changes, and use overlays and challenge.

Worked examples

Example 1

A bank starts with CET1 capital of USD 50 billion and RWA of USD 500 billion. Over the stress horizon, cumulative PPNR is USD 20 billion, provisions and other losses are USD 45 billion, there is no tax effect, and dividends are USD 5 billion. Stressed RWA is USD 520 billion. What is the ending CET1 ratio?

Show the solution
  1. Pre-tax income = 20 − 45 = −25 billion.
  2. No tax effect, so net income = −25 billion.
  3. Ending CET1 = 50 − 25 − 5 = 20 billion.
  4. CET1 ratio = 20 ÷ 520 = 3.85%.

Answer: About 3.85%, down from 10.0% at the start.

Example 2

A bank's loan book has EAD of USD 200 billion. In the base case PD is 2% and LGD is 40%. In the stress case PD is 6% and LGD is 50%. Projected stress PPNR is USD 18 billion. Ignoring other items and taxes, what is the pre-tax income, treating expected loss as the provision charge?

Show the solution
  1. Stress EL = 6% × 50% × 200 = 0.06 × 0.5 × 200 = 6 billion.
  2. Check: 0.06 × 0.5 = 0.03, and 0.03 × 200 = 6.
  3. Pre-tax income = PPNR − EL = 18 − 6 = 12 billion.

Answer: USD 12 billion pre-tax income (base-case EL would be 0.02 × 0.4 × 200 = 1.6 billion, so stress adds 4.4 billion of loss).

Exam tips

  • Read each line for sign and timing: PPNR is positive, provisions and losses are negative, distributions reduce capital.
  • When a question asks about limitations, pick the answer that names a specific weakness such as limited data on severe downturns, rather than a generic statement.
  • Check whether the question wants the ratio, the capital shortfall or the percentage-point decline before you calculate.
  • Remember that leverage ratio ignores RWA, so RWA migration affects CET1 ratio but not the leverage ratio.
  • Expect questions on why PPNR is harder to model than credit losses: it depends on behaviour and management actions.

Practice questions from Stress Testing Banks

Modeling Stress Impacts on Capital, Losses and Revenue in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Modeling Stress Impacts on Capital, Losses and Revenue: frequently asked questions

What is pre-provision net revenue in stress testing?

PPNR is net interest income plus non-interest income minus non-interest expense, before provisions. It measures the earnings available to absorb losses. In a stress test it is projected under the scenario alongside losses.

How do banks model losses under stress scenarios?

They link PD, LGD and EAD or loss rates to macro variables such as unemployment, GDP and house prices. Separate approaches cover securities, trading, counterparty and operational losses. Expert overlays are common where data are thin.

What are the main limitations of stress testing models?

Limited history of severe events, relationships that break under stress, weak modelling of behaviour and management actions, and missing feedback effects. Model risk is managed through validation, sensitivity analysis and effective challenge.

What steps do I follow to project a capital ratio under stress?

Project losses and PPNR, compute net income, adjust capital for distributions, project stressed RWA and divide. Then compare the lowest point with requirements and buffers.