FRM Part II · FRM Exam Part II

Liquidity Stress Testing: formula sheet

Full chapter guide

Key formulas

Net cash flow in a period: Net cash flow = Cash inflows − Cash outflows; Stressed inflows are reduced and outflows are increased by scenario assumptions.
Cumulative liquidity position: Cumulative gap(t) = Liquidity buffer (after haircuts) + Σ net cash flows up to t; The first t where it turns negative is the survival horizon.
Buffer value after haircut: Haircut value = Market value × (1 − haircut); Use the stressed haircut, not the normal one.
Survival horizon: Survival horizon = number of days until the cumulative liquidity position falls below zero; Compare it with the horizon set by policy or regulation.
Survival horizon: Survival horizon = the first day on which cumulative net cash flow plus starting buffer falls below zero; Compare it with the minimum the bank's risk appetite requires.
Net stressed cash flow: Net stressed outflow = Stressed outflows − Stressed inflows; Apply run-off rates to liabilities and haircuts or delayed receipt to assets.
Liquidity buffer after stress: Buffer after stress = Σ (market value of asset × (1 − stressed haircut)); Include only assets that are unencumbered and can truly be monetised in that scenario.
Stressed run-off outflow: Outflow = Balance × run-off rate; Rates are higher for unsecured wholesale and uninsured funding than for stable retail deposits.
Scenario severity ordering: Idiosyncratic < Market-wide < Combined (typical severity for a given bank); A rule of thumb, not a law. Market-wide can be milder for a bank with little exposure to it.
Stressed outflow from deposits: Outflow = Balance × run-off rate; Use a different rate for each deposit category, then sum.
Credit line drawdown: Drawdown = Undrawn committed amount × drawdown rate; Apply to the undrawn part only. Drawn balances are already on the balance sheet.
Rollover shortfall: Outflow = Maturing funding × (1 − rollover rate); Only the part not renewed is a net cash outflow.
Stressed inflow: Inflow = Contractual inflow × (1 − haircut); Inflows are reduced because not all will be received in stress.
Net cash flow: Net = Stressed inflows − Stressed outflows (including collateral calls); A negative number is a funding need.
Cumulative gap and survival: Cumulative net flow + Buffer ≥ 0 at each bucket; Survival horizon is the last bucket where this holds.
Haircut-adjusted liquidity value: Liquidity value = Market value × (1 − haircut); Apply to each asset class separately. Cash has a haircut of 0%.
Counterbalancing capacity: CBC = Σ [Market value_i × (1 − haircut_i)] over unencumbered assets monetizable within the time bucket; Exclude encumbered assets. Include only assets that can be monetized within the bucket.
Stressed net cash outflow: Net outflow_t = Stressed outflows_t − Stressed inflows_t; Inflows are often capped or haircut. Use the supervisor's or the scenario's rates.
Cumulative liquidity position: Position_t = CBC available by t − Σ Net outflows up to t; The first t with Position_t < 0 marks the end of the survival horizon.
Approximate survival horizon (constant outflow): Survival days ≈ CBC ÷ daily stressed net outflow; Valid only if outflows are roughly even. Use the day-by-day method if they are not.
Liquidity Coverage Ratio: LCR = Stock of HQLA ÷ Total net cash outflows over next 30 calendar days ≥ 100%; Short-term, stress-based. HQLA is measured after haircuts and caps.
Total net cash outflows: Net outflows = Total expected outflows − MIN(total expected inflows, 75% of total expected outflows); Inflows are capped at 75% of outflows, so net outflows are never below 25% of gross outflows.
Net Stable Funding Ratio: NSFR = Available stable funding (ASF) ÷ Required stable funding (RSF) ≥ 100%; Structural, covers a one-year horizon. Each item is weighted by an ASF or RSF factor.
ASF and RSF weighting: ASF = Σ (liability or capital amount × ASF factor); RSF = Σ (asset or off-balance-sheet amount × RSF factor); Regulatory capital and liabilities of one year or more get a 100% ASF factor. Cash and central bank reserves get a 0% RSF factor in Basel's standard.
Outflow amount: Outflow = Balance × run-off rate; Stable retail deposits have a lower run-off rate than unsecured wholesale funding from financial institutions.
HQLA after haircut: Eligible HQLA = Market value × (1 − haircut); Level 1 has no haircut. Level 2A has a 15% haircut. Level 2B has haircuts of 25% or 50% depending on asset type.
Survival horizon: Survival horizon = the first day on which cumulative net outflows > liquidity buffer; Compare cumulative net stressed outflows with available buffer after haircuts. Report the number of days.
Liquidity surplus or shortfall: Surplus (shortfall) = Buffer after haircuts − Cumulative stressed net outflows; A negative result means the CFP must supply the gap.
Buffer after haircuts: Buffer value = Σ (market value × (1 − haircut)); Apply haircuts to each asset class before comparing with outflows.
Reverse stress test logic: Define failure → find scenario that causes it → judge plausibility → act; The starting point is the outcome, not the scenario.
Limit utilisation: Utilisation = Measured exposure ÷ Limit; Above 100% is a breach and triggers escalation.

Quick revision

Funding liquidity risk is the inability to meet obligations when due; market liquidity risk is the inability to sell assets without a large price impact.
A stress test needs a scenario, cash flow projections, assumptions, a buffer and a horizon.
Combined scenarios mix a firm-specific shock with a market-wide shock and are usually the most severe.
Deposit run-off depends on type: insured retail deposits run off less than uninsured or wholesale deposits.
Committed credit and liquidity lines create contingent outflows through drawdowns.
Counterbalancing capacity is the stock of assets that can be sold, repo'd or pledged to raise cash. Apply haircuts to it.
Survival horizon is how long the bank can meet net outflows before the buffer is exhausted.
LCR = stock of high-quality liquid assets ÷ total net cash outflows over 30 days, and it must be at least 100%.
NSFR = available stable funding ÷ required stable funding, and it must be at least 100%. It addresses a one-year structural horizon.
Net outflows in the LCR equal outflows minus the lesser of inflows and 75% of outflows.
Reverse stress testing starts from a failure outcome and works back to the scenarios that cause it.
Results should feed limits, the contingency funding plan and strategic decisions, with senior management and board oversight.

Common mistakes

Treating market and funding liquidity as the same thing Fix: Ask whether the problem is selling an asset (market) or obtaining cash (funding). Remember they interact through spirals.
Saying a liquidity stress test measures capital adequacy Fix: Liquidity tests look at cash flows and survival horizon. Capital tests look at losses and capital ratios.
Assuming assets can be sold at normal prices in a market-wide scenario. Fix: In market-wide and combined scenarios, apply higher haircuts and limit sales to the truly liquid assets.
Calling a combined scenario simply the sum of two mild shocks. Fix: A combined scenario is a bank-specific shock occurring during market stress, with interactions such as loss of access to wholesale funding when the bank cannot sell assets.
Applying the drawdown rate to the whole commitment instead of the undrawn part. Fix: Subtract drawn amounts first. Drawdown = undrawn × rate.
Using the rollover rate as the outflow rate. Fix: Outflow = maturing amount × (1 − rollover rate). A 70% rollover means 30% leaves.
Using market value instead of haircut value Fix: Always multiply by (1 − haircut) before adding assets. Do it first, every time.
Counting encumbered assets in the buffer Fix: Read the question for pledged, repo'd or collateral-posted assets and exclude them.
Mixing up horizons: calling the NSFR a 30-day measure. Fix: Remember: LCR = liquidity in a 30-day storm; NSFR = funding structure over a year.
Forgetting the 75% cap on inflows in the LCR denominator. Fix: Net outflows = outflows − MIN(inflows, 0.75 × outflows). Always compute the cap.

Exam tips

Expect scenario questions that ask you to label the risk as market or funding liquidity. Look for the trigger words.
Know the interaction: funding stress forces asset sales, which hit market prices and raise haircuts and margin calls.
For differences between tests, remember: cash and short horizon for liquidity, losses and capital ratios for solvency.
In numerical items, apply haircuts before adding flows and use stressed assumptions.
Be ready to name uses of results: buffer sizing, limits, early warning indicators and contingency funding plan testing.
Read the case for the funding model first. The right scenario usually follows from it.
If markets are described as frozen, assume asset sales are limited and haircuts are higher.
Check whether an option confuses LCR's 30-day stress with a required horizon for all stress tests.