FRM Part II · FRM Exam Part II

Liquidity Risk: formula sheet

Full chapter guide

Key formulas

Quoted spread: Quoted spread = Ask − Bid; Absolute cost of a round trip for one unit.
Mid-price: Mid = (Ask + Bid) ÷ 2; Used as the reference fair price.
Relative (proportional) spread: S = (Ask − Bid) ÷ Mid; Allows comparison across assets with different prices.
Effective spread: Effective spread = 2 × |Trade price − Mid| (for a buy: 2 × (Trade − Mid)); Use the mid-price at the time of the trade. Measures the actual cost paid.
Cost of liquidation (one-way): Cost = ½ × S × Position value; Assumes you trade at the bid or ask, and S is the relative spread.
Dimensions of liquidity: Tightness, depth, resiliency (plus immediacy); Know which dimension a scenario describes.
Liquidity cost (constant spread): LC = ½ × S̄ × P; S̄ is the mean relative spread (spread ÷ mid-price). P is position value. You pay half the spread when closing out.
LVaR, constant spread: LVaR = VaR + ½ × S̄ × P; Add the cost to VaR at the same confidence level and horizon. Use the same currency for both.
LVaR, exogenous spread: LVaR = VaR + ½ × (S̄ + k × σS) × P; σS is the standard deviation of the relative spread. k is the multiplier for the confidence level, e.g. 2.33 for 99% under normality.
Parametric VaR (input): VaR = z × σ × P; σ is return volatility over the horizon. Scale daily σ by √T for T days. z is 1.645 at 95% and 2.33 at 99% (one-tailed).
Liquidity-adjusted VaR as a ratio: LVaR ÷ VaR = 1 + liquidity cost ÷ VaR; Useful to state the percentage uplift from liquidity.
Leverage ratio: Leverage = Assets ÷ Equity; Higher leverage means a smaller price fall wipes out equity and triggers forced selling.
Haircut and margin: Haircut = (Asset value − Loan) ÷ Asset value; The haircut is the share of the asset funded by the borrower's own capital. A higher haircut cuts the loan available per unit of asset.
Borrowing capacity: Loan = Asset value × (1 − Haircut); When the haircut rises, the same assets support less funding, so the firm must sell or post more cash.
Leverage and haircut link: Maximum leverage = 1 ÷ Haircut; A 5% haircut allows at most 20 times leverage on that asset. Margin spirals reduce this ceiling.
Spiral rule: Loss spiral: price ↓ → equity ↓ → forced sales → price ↓. Margin spiral: volatility ↑ → haircut ↑ → forced sales → price ↓; Know which trigger starts each spiral. They reinforce each other.
Net cash flow in a bucket: Net cash flow = Inflows − Outflows; A negative value is a liquidity gap (shortfall) in that bucket.
Cumulative gap: Cumulative gap(t) = Σ net cash flow from bucket 1 to t; Compare it with the buffer at each horizon, not only at one date.
Stressed outflow: Stressed outflow = Balance × run-off rate; Apply run-off to deposits and wholesale funding; apply draw-down rate to undrawn commitments.
Buffer value after haircut: Buffer value = Market value × (1 − haircut); Only count unencumbered assets. Haircuts are larger for riskier or less liquid assets.
Survival horizon: Survival horizon = Buffer ÷ stressed net outflow per period; Valid when daily outflow is roughly constant; otherwise deplete the buffer bucket by bucket.
Liquidity surplus or shortfall: Surplus (shortfall) = Buffer − cumulative stressed net outflow; A negative result means the CFP must supply extra funding.
Liquidity Coverage Ratio: LCR = Stock of HQLA ÷ Total net cash outflows over next 30 days ≥ 100%; HQLA must be unencumbered and measured after haircuts and the Level 2 caps.
Net cash outflows: Net outflows = Total stressed outflows − min(Total stressed inflows, 75% × Total stressed outflows); Each outflow = balance × run-off rate. Each inflow = balance × inflow rate.
HQLA composition limits: Level 2 ≤ 40% of HQLA; Level 2B ≤ 15% of HQLA; Level 1 has no cap. Level 2A haircut is 15%. Level 2B haircuts are larger.
Net Stable Funding Ratio: NSFR = Available stable funding (ASF) ÷ Required stable funding (RSF) ≥ 100%; Horizon is one year. Both sides are weighted sums of balance sheet items.
ASF and RSF weighting: ASF = Σ (liability or capital × ASF factor); RSF = Σ (asset or off-balance-sheet item × RSF factor); High ASF factor means stable funding. High RSF factor means illiquid asset.

Quick revision

Market liquidity risk is the cost or difficulty of trading; funding liquidity risk is the inability to meet cash obligations when due.
Relative spread = (ask − bid) ÷ mid-price.
Cost of liquidating a position = position value × half the relative spread.
LVaR = VaR + liquidity cost, where the cost comes from the spread assumption given.
Wider or more volatile spreads raise the LVaR add-on.
Ordinary VaR ignores the cost of exiting a position, so it understates risk for illiquid holdings.
Liquidity spirals: falling prices raise margins and haircuts, forcing sales, which push prices down further.
Maturity mismatch between assets and liabilities is the core source of funding liquidity risk.
A contingency funding plan sets triggers, responsibilities and funding sources for a stress event.
LCR = high-quality liquid assets ÷ total net cash outflows over a 30-day stress period; the minimum is 100%.
NSFR = available stable funding ÷ required stable funding over a one-year horizon; the minimum is 100%.
LCR addresses short-term resilience; NSFR addresses structural funding over a longer horizon.

Common mistakes

Using the full spread as the cost of a single sale. Fix: One-way cost is half the spread. Use the full spread only for a round trip.
Calculating effective spread as the trade price minus mid, without doubling. Fix: Effective spread = 2 × |trade − mid|, so it is comparable with the quoted spread.
Using the full spread instead of half the spread Fix: A mid-price valuation is half a spread away from either the bid or the ask. Use ½ × spread.
Using an absolute spread with a relative formula Fix: Either use half the absolute spread × number of units, or convert to a relative spread first. Do not mix them.
Treating funding liquidity and market liquidity as the same thing. Fix: Funding liquidity is about meeting obligations with cash or borrowing. Market liquidity is about trading an asset without price impact. Then explain how they interact.
Saying a margin spiral starts with a price fall and a loss spiral starts with a margin rise. Fix: The loss spiral works through losses and lower capital. The margin spiral works through higher margins or haircuts, often due to higher volatility.
Using the market value of buffer assets without haircuts. Fix: Apply the haircut first: value × (1 − haircut). Then compare with outflows.
Counting encumbered assets as part of the buffer. Fix: Include only unencumbered assets that can be sold or repoed promptly.
Counting all inflows against outflows in LCR. Fix: Cap inflows at 75% of outflows. Net outflows are at least 25% of gross outflows.
Ignoring the 40% and 15% limits on Level 2 assets. Fix: Test the caps after haircuts every time. Excess Level 2 assets do not count.

Exam tips

Read carefully whether the question asks for the full spread or the half-spread cost.
Check whether the effective spread uses the mid-price at the time of trade, not the closing price.
Match scenario wording to the dimension: price gap is tightness, order size is depth, recovery speed is resiliency.
In stress scenarios, expect spreads to widen and the link between funding and market liquidity to feed back on itself.
Keep currency units consistent and state the answer in the format the options use.
Questions often give VaR already. Do not recompute it; add the half-spread cost.
Look for the word 'exogenous' or 'constant' to pick the formula. Endogenous wording signals a conceptual question about position size.
Check units: percentage spreads must be turned into a currency cost using position value.