FRM Exam Part II · Capital Planning at Large Bank Holding Companies: Supervisory Expectations and Range of Current Practice

Loss, Revenue and Expense Estimation in Bank Stress Testing

Updated 11 October 2026 · Fact-checked

Banks project stressed losses, pre-provision net revenue (PPNR) and balance sheet items by linking each to scenario variables, usually with statistical models. Losses use PD, LGD and EAD or loss-rate models. PPNR is net interest income plus non-interest income minus non-interest expense. Overlays and judgment fill model gaps and must be documented and challenged.

Understand Loss, Revenue and Expense Estimation Methodologies

Capital planning asks one question: after a severe but plausible scenario, will the bank still hold enough capital? To answer it, the bank projects each driver of capital over the planning horizon, typically nine quarters. Post-tax net income plus changes in risk-weighted assets and capital actions give the capital ratio path.

There are three building blocks. Losses cover loan losses, securities impairments, trading and counterparty losses, and operational losses. Pre-provision net revenue (PPNR) is net interest income plus non-interest income minus non-interest expense, before provisions. Balance sheet items such as loan volumes, deposits and risk-weighted assets link the other two together.

For loans, banks commonly use either a loss-rate approach (stressed loss rate × balance) or a component approach (PD × LGD × EAD by segment). Models relate PD, LGD or loss rates to macro variables such as unemployment, GDP, house prices and interest rates. Trading losses often come from full revaluation of positions under shocked risk factors. PPNR is harder to model because it depends on volume, margin, fee income and expense behaviour, which have shorter and noisier histories than credit losses.

No model covers everything. Where data are thin, relationships break in stress, or a portfolio is new, banks use overlays (adjustments applied outside the model) and expert judgment. Supervisors accept these only if they are documented, justified, consistently applied, independently reviewed and tied to governance. A bank that leans on overlays without a clear rationale shows a weak process.

All of this is model risk. Supervisory expectations stress sound development, validation, effective challenge, and clear communication of limitations and uncertainty. Results should be shown with sensitivity analysis and not treated as precise point forecasts.

Key formulas to remember

PPNR: PPNR = Net interest income + Non-interest income − Non-interest expense; Measured before provisions for loan losses. Stress usually cuts income and may raise expense.
Expected loss (component approach): EL = PD × LGD × EAD; Under stress, PD and LGD rise and EAD can rise as credit lines are drawn.
Loss-rate approach: Projected loss = Stressed loss rate × Exposure balance; Applied by segment, often with loss rates driven by macro variables.
Pre-tax income: Pre-tax income = PPNR − Provisions − Other losses (trading, securities, operational); Tax effects then give net income, which feeds the capital ratio.
Capital ratio path: Capital ratio = Regulatory capital ÷ Risk-weighted assets; Capital changes by net income less capital actions. RWA changes with stressed balance sheet and risk weights.

How to solve Loss, Revenue and Expense Estimation Methodologies questions

Use this order for any question on loss, revenue or expense estimation. It keeps you from mixing up what is modelled, how, and how it is governed.

1Identify what is being estimated: credit losses, trading losses, PPNR component or balance sheet item.
2Note the scenario variables given and how they should drive the item (for example unemployment drives retail PD).
3Choose the matching method: loss-rate or PD/LGD/EAD for loans, revaluation for trading, volume × margin for net interest income.
4Do the arithmetic in the right order: segment by segment, then sum, then apply tax if asked.
5Check direction: stressed losses up, net interest margin and fees usually down, RWA often up.
6Ask whether a model gap needs an overlay or judgment, and what documentation and challenge it requires.
7Pick the answer that is consistent with supervisory expectations: documented, validated, conservative where uncertain.

Quickest way: Direction, method, governance check

When to use it: Use when a conceptual MCQ lists four plausible practices and you have under two minutes.

Eliminate options that treat PPNR as including provisions or that ignore the scenario link.
Eliminate options that use unadjusted historical averages with no stress linkage.
Prefer options with documented overlays, independent validation and sensitivity analysis.
For numbers, compute PPNR first, then subtract losses, and check the sign.

Common mistakes in Loss, Revenue and Expense Estimation Methodologies

Subtracting provisions when calculating PPNR.
Students mix PPNR with net income.
Fix: PPNR is before provisions. Subtract provisions and other losses afterwards to get pre-tax income.
Assuming credit losses alone drive capital depletion.
Credit losses get most attention in the syllabus.
Fix: Remember PPNR, trading and counterparty losses, securities impairments and RWA changes also move the capital ratio.
Treating overlays and judgment as a weakness in themselves.
Models sound more objective.
Fix: Overlays are acceptable when justified, documented, reviewed and governed. The weakness is unsupported or inconsistent use.
Applying a loss rate to the starting balance when the balance changes under stress.
Students ignore projected balance sheet paths.
Fix: Use the projected exposure for each period, including drawdowns and portfolio runoff, unless the question fixes the balance.
Assuming historical relationships hold unchanged in stress.
Model fit looks good in normal times.
Fix: Expect nonlinearity and structural breaks. Supervisors expect sensitivity analysis and consideration of model limitations.

Worked examples

Example 1

A bank projects, for one year of a stress scenario: net interest income $1,200 million, non-interest income $450 million, non-interest expense $1,000 million, provisions $500 million, trading losses $100 million. Ignoring tax, what is pre-tax income?

Show the solution

PPNR = 1,200 + 450 − 1,000 = $650 million.
Subtract provisions: 650 − 500 = 150.
Subtract trading losses: 150 − 100 = 50.

Answer: Pre-tax income is $50 million; PPNR is $650 million.

Example 2

A loan segment has a projected stressed exposure of $8,000 million. Stressed PD is 5%, LGD is 40%. What is the projected loss, and what happens to it if a validated overlay raises LGD to 45%?

Show the solution

Base loss = PD × LGD × EAD = 0.05 × 0.40 × 8,000 = $160 million.
With overlay: 0.05 × 0.45 × 8,000 = $180 million.
Increase = 180 − 160 = $20 million.
The overlay must be documented, justified and subject to independent challenge.

Answer: Base loss is $160 million; with the overlay it is $180 million, an increase of $20 million.

Exam tips

Read whether the question asks for PPNR or pre-tax income. The two differ by provisions and other losses.
In conceptual questions, the best answer usually stresses documentation, validation and effective challenge.
Check the sign of each driver under stress before calculating.
Expect case-style wording about weak data, short histories or new products. Think overlay plus judgment plus governance.

Practice questions from Capital Planning at Large Bank Holding Companies: Supervisory Expectations and Range of Current Practice

Loss, Revenue and Expense Estimation Methodologies: frequently asked questions

What is PPNR in bank stress testing?

PPNR is net interest income plus non-interest income minus non-interest expense, before provisions. It shows the earnings a bank can use to absorb losses. Supervisors review how it is projected because it is harder to model than credit losses.

Which methods do banks use to estimate stressed losses?

Common methods are loss-rate models and PD, LGD and EAD component models linked to macro variables. Trading losses use revaluation under shocked risk factors. Banks add overlays and judgment where models are weak.

Why are overlays and judgment a model risk issue?

They sit outside validated models, so errors or bias can go unnoticed. Supervisors expect clear rationale, documentation, consistent use and independent challenge. Without these, results are hard to rely on.

Why is PPNR harder to project than credit losses?

Revenue and expense depend on volumes, margins, fees and management actions, with shorter and noisier data histories. Relationships to macro variables are less stable. Banks therefore use more judgment and sensitivity analysis.