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Account for the difficulties of projecting a bank's revenues, losses and balance sheet across the horizon of a stress test.

FRM® Part II · Operational Risk and Resilience · Stress Testing Banks · FRM2.ORR.17.c

The idea

Projecting a bank across a stress horizon means forecasting capital, not just losses. PPNR is pre-provision net revenue, which is net interest income plus fees minus non-interest expense. Ending capital is starting capital plus PPNR, minus credit and market losses and provisions, minus distributions. The ending capital ratio divides that by projected risk-weighted assets (RWA), so the ratio is Ratio = (Start + PPNR − Losses − Payouts) ÷ RWA. Losses are easier because banks hold long loss histories by segment. Revenue is harder because there are few stressed observations and it depends on strategy, pricing and the rate path. Provision expense equals charge-offs plus the change in the loan loss allowance, so a reserve build for losses beyond the horizon also hits capital. Balance sheets are either static, which is simple but ignores drawdowns, funding strains and management actions, or dynamic, which needs assumptions consistent with the scenario. Exam point: the denominator moves too.

Formulas

Ending capital ratio over a stress horizon

capital ratio = (C0 + PPNR − losses − distributions) ÷ RWA

C0
starting capital
PPNR
cumulative pre-provision net revenue
losses
credit and market losses and provisions
distributions
dividends and buybacks
RWA
projected risk-weighted assets at the end

Both numerator and denominator move: use the projected RWA, not the starting figure.

Pre-provision net revenue

PPNR = NII + fees − non-interest expense

NII
net interest income
fees
fee income
non-interest expense
operating costs

Earnings before provisions. Its stressed path must follow the scenario, not the business plan.

Provision expense over a stress horizon

provision = charge-offs + (ending allowance − starting allowance)

charge-offs
loans written off over the horizon
ending allowance
the allowance needed at the end for losses beyond the horizon
starting allowance
the loan loss allowance at the start

A reserve build for future losses hits capital within the horizon. Counting charge-offs alone understates the charge.

A practice question

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

In a bank stress test, pre-provision net revenue (PPNR) is best described as:

  1. net interest income minus provisions and charge-offs, before fee income and expenses.Why not: Deducts loan losses, which PPNR excludes, and leaves out fee income and operating costs.
  2. total revenue minus taxes, after provisions for loan losses.Why not: Provisions come after PPNR, and PPNR is a pre-tax measure.
  3. the change in risk-weighted assets over the stress horizon.Why not: Confuses PPNR, an income measure, with the balance-sheet denominator of the capital ratio.
  4. net interest income plus fees minus non-interest expense, before loan loss provisions. - correct

PPNR is the bank's loss-absorbing earnings before provisions: net interest income plus fees minus non-interest expense. Provisions and losses are then subtracted from it to reach capital.

A harder one

A bank starts with common equity of 60 and risk-weighted assets (RWA) of 600. Over the stress horizon it projects cumulative PPNR of 25, credit losses (provisions) of 45 and dividends of 5, and RWA rise to 700. What is its ending common equity ratio (closest to)?

  1. 5.0% - correct
  2. 5.8%Why not: Divides ending capital by the starting RWA of 600, ignoring the increase in RWA.
  3. 1.4%Why not: Leaves out the PPNR of 25, so the earnings that absorb losses are ignored.
  4. -2.1%Why not: Subtracts PPNR instead of adding it.

Ending capital = 60 + 25 - 45 - 5 = 35. Ratio = 35 / 700 = 5.0%. Both the numerator (PPNR, losses, distributions) and the denominator (RWA path) move.

The hardest tier

At the start of a stress horizon, a bank's loan loss allowance is 10. Charge-offs over the horizon total 40, and the allowance needed at the end to cover expected losses beyond the horizon is 25. What is the provision expense charged against earnings over the horizon?

  1. 40Why not: Uses charge-offs only and ignores the reserve build needed at the end of the horizon.
  2. 25Why not: Subtracts the allowance increase of 15 from charge-offs instead of adding it.
  3. 65Why not: Adds the full ending allowance of 25 instead of the change in allowance (25 - 10).
  4. 55 - correct

Provision = charge-offs + change in allowance = 40 + (25 - 10) = 55. The reserve build for losses beyond the horizon reduces capital within the horizon.

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