FRM Part II · FRM Exam Part II

Netting, Close-out and Related Aspects: formula sheet

Full chapter guide

Key formulas

Exposure without netting (gross): Gross exposure = Σ max(Vi, 0); Vi is the value of trade i to you. Only positive-value trades count; negatives are ignored.
Exposure with enforceable close-out netting: Net exposure = max(Σ Vi, 0); Sum all values in the netting set first, then floor at zero.
Netting benefit: Benefit = Gross exposure − Net exposure; Always ≥ 0. It equals zero when all trades have positive value (or all negative).
Net-to-gross ratio (NGR): NGR = Net exposure ÷ Gross exposure; Lower means more netting benefit. Defined when gross exposure is above zero.
Close-out net amount: Net close-out amount = Σ (close-out values of terminated trades) ± unpaid amounts; Positive means the defaulter owes the non-defaulting party. Negative means the reverse.
Net exposure with enforceable close-out netting: Net exposure = max(Σ MtM of all trades, 0); One payment is due on default. Positive and negative values offset across the whole netting set.
Gross exposure without netting: Gross exposure = Σ max(MtM of each trade, 0); Used when netting is not enforceable. Only positive trades count, since you still owe on the negative ones.
Netting benefit: Netting benefit = Gross exposure − Net exposure; It is never negative. It is zero if all trades have the same sign.
Netting ratio (NGR): NGR = Net exposure ÷ Gross exposure; Lies between 0 and 1. Lower means more benefit.
Single agreement rule: All trades under one Master Agreement = one contract; It blocks cherry picking and underpins close-out netting.
Gross exposure (no netting): Gross = Σ max(Vi, 0); Sum only the positive trade values. Negative values are ignored.
Net exposure (with netting): Net = max(Σ Vi, 0); Add all values first, then floor at zero.
Netting benefit: Benefit = Gross − Net; Always ≥ 0. Often quoted as a percentage of gross.
Netting factor (ratio): Netting factor = Net ÷ Gross; Lower means more benefit. Some texts quote 1 − this as the reduction.
Netting factor, n identical normal exposures: Net EE ÷ Gross EE = √(n + n(n − 1)ρ) ÷ n; Assumes n trades with equal volatility, zero mean, common correlation ρ. Holds for expected exposure under normality and zero expected value.
Limits of the factor: ρ = 1: factor = 1. ρ = 0: factor = 1 ÷ √n; At ρ = 1 there is no benefit. At ρ = 0 the factor is 1/√n.
Gross exposure: Gross exposure = Σ max(Vi, 0); Sum of positive trade values. This is what a cherry-picking administrator would aim to collect, while the solvent party must pay its out-of-the-money trades.
Net exposure with enforceable netting: Net exposure = max(Σ Vi, 0); Vi is the value of trade i to you. Valid only if close-out netting is legally enforceable.
Netting benefit: Netting benefit = Gross exposure − Net exposure; Never negative. It is zero when all trades have the same sign.
Net-to-gross ratio (NGR): NGR = Net exposure ÷ Gross exposure; Between 0 and 1 for positive gross exposure. Lower means more netting benefit.
Cherry-picking loss to solvent party: Loss = Σ max(−Vi, 0) paid in full − recovery on Σ max(Vi, 0); Here Vi is value to the solvent party. It pays its negative trades in full and recovers only a percentage on its positive ones. Loss is the amount paid in full on negative trades minus the recovery on positive ones, compared with the net claim.
Rule for capital recognition: Netting recognised only if legal basis is well founded in all relevant jurisdictions; Typically supported by written, reasoned legal opinions.
Collateral required (variation margin): Required = max(0, Net exposure − Threshold); Net exposure is the mark-to-market of the whole netting set. Use the threshold of the party that is owed.
Collateral call: Call = Required − Collateral held, if |Call| ≥ MTA; otherwise no transfer; The MTA applies to the change in collateral. Some CSAs also use rounding.
Haircut-adjusted collateral value: Value = Market value × (1 − haircut); Haircuts cover price volatility and FX mismatch of the collateral asset.
Exposure after collateral: Exposure = max(0, V(t+MPOR) − C(t)); V is net value at default close-out. C is collateral held at the last margin call.
Exposure with initial margin: Exposure = max(0, V(t+MPOR) − VM − IM); IM absorbs part of the MPOR move, so it reduces exposure.
MPOR scaling of volatility: σ(MPOR) = σ(daily) × √(MPOR in days); Assumes independent daily changes. Longer MPOR raises residual exposure by the square root of time.

Quick revision

Close-out netting: on default, all trades end, are valued and combine into one net amount.
Gross exposure = sum of positive-value trades only; net exposure = max(sum of all values, 0).
Netting never increases exposure; it cuts it or leaves it unchanged.
Benefit is greatest when trades have offsetting values with the same counterparty.
Netting only counts if it is legally enforceable in the relevant jurisdictions.
Cherry picking: a liquidator keeps profitable contracts and drops losing ones; close-out netting prevents it.
The ISDA Master Agreement sets common terms; the Schedule customises them.
The CSA covers collateral; it sits alongside the Master Agreement.
Exposure after collateral = max(net exposure − collateral held, 0), ignoring other frictions.
Thresholds and minimum transfer amounts leave some uncollateralised exposure.
Collateral brings its own risks: valuation gaps, liquidity and the margin period of risk.
Netting sets are defined by agreement and enforceability, not by product type alone.

Common mistakes

Confusing payment netting with close-out netting. Fix: Payment netting covers same-day, same-currency payments in normal operation. Close-out netting applies on default and involves termination and valuation of all trades.
Flooring each trade at zero before summing when netting applies. Fix: Under enforceable netting, sum first, then floor once per netting set.
Treating all termination causes as Events of Default. Fix: Events of Default are a party's fault. Termination Events such as illegality or tax events are not. Ask who is at fault.
Thinking the Schedule is a separate contract from the Master Agreement. Fix: The Schedule modifies the Master Agreement. Together with Confirmations they form one agreement.
Netting negative values into gross exposure. Fix: For gross, floor each trade at zero before adding. Only net adds first and floors after.
Reporting a negative net exposure. Fix: Exposure is never negative. If the sum is below zero, net exposure is zero.
Treating netting and set-off as identical. Fix: Remember close-out netting terminates and values all trades into one sum. Set-off is the right to deduct mutual debts, with conditions set by law or contract.
Assuming netting always works. Fix: Enforceability depends on insolvency law of the relevant jurisdictions. Always look for a legal opinion or a jurisdiction flag.
Calling collateral on each trade instead of on the netting set Fix: Net the trades first, then apply threshold and MTA once.
Treating the MTA as a deductible from exposure Fix: The threshold reduces required collateral. The MTA only blocks small transfers. Apply the MTA to the call, not to exposure.

Exam tips

Look first for the legal condition. Many questions turn on whether netting is enforceable.
Read whether the question asks for payment netting or close-out netting. The default trigger signals close-out.
Do not net across separate agreements; floor each netting set at zero.
Check that your net exposure is never greater than gross exposure.
Remember a positive net claim is still unsecured unless collateral exists.
Know which items are Events of Default and which are Termination Events. Examiners test the line between them.
If the question mentions a jurisdiction without a legal opinion, expect gross exposure to be the answer.
Link single agreement to cherry picking. It is the most common conceptual question.