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FRM Exam Part II · Netting, Close-out and Related Aspects

Netting Benefits and Exposure Calculation Explained

Updated 11 October 2026 · Fact-checked

Netting lets you offset positive and negative trade values with one counterparty, so exposure is the larger of the net sum and zero, not the sum of positive values. Gross exposure = Σ max(Vi, 0). Net exposure = max(ΣVi, 0). Net ÷ gross is the netting factor, and lower correlation gives more benefit.

Understand Netting Benefits and Exposure Calculation

Exposure is what you lose if a counterparty defaults today, before recovery. If there is no netting agreement, you must treat each trade on its own. Trades with positive value are claims you lose. Trades with negative value are debts you still owe the defaulted estate. So you count only the positive ones.

With an enforceable close-out netting agreement, all trades are combined into one single net amount at default. Gains on some trades absorb losses on others. If the net value is positive, the counterparty owes you that amount. If it is negative, your exposure is zero.

That gives the key comparison. Gross exposure = Σ max(Vi, 0). Net exposure = max(ΣVi, 0). Net is never more than gross. The two are equal only when all trades are positive or all are negative (or zero).

The benefit depends on how the trade values move together. If trade values are perfectly positively correlated, they move in the same direction and netting gives no benefit in expectation. If correlation is low or negative, one trade tends to be positive when another is negative, so netting removes more exposure. This is why netting matters most for diversified books of derivatives.

For the exam, you need two things: the arithmetic of net vs gross for given values, and the netting factor formula for n identical exposures with a common correlation. Netting is only recognised if it is legally enforceable in the relevant jurisdictions.

Key formulas to remember

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.

How to solve Netting Benefits and Exposure Calculation questions

Use this order for any numerical question on netting benefit or exposure.

  1. 1Check whether a legally enforceable netting agreement covers the trades. If not, use gross exposure.
  2. 2List each trade value with its sign, from your point of view.
  3. 3Compute gross: add only the positive values.
  4. 4Compute net: add all values, then set to zero if the total is negative.
  5. 5Compute benefit = gross − net, or the ratio net ÷ gross.
  6. 6If the question gives n, ρ and equal volatilities, use √(n + n(n − 1)ρ) ÷ n for the netting factor.
  7. 7Interpret: state whether netting helps more or less, and link to correlation.

Quickest way: Fast netting check

When to use it: Use when options are numerical and time is short.

  1. Sum the positives for gross and the whole sum for net.
  2. If the total is negative, net is zero.
  3. For the correlation formula, test the extremes: ρ = 1 gives 1, ρ = 0 gives 1/√n. Any answer outside that range is wrong.
  4. Compute n + n(n − 1)ρ first, take the square root, then divide by n.
  5. Sanity check: net ≤ gross, and a lower ρ gives a lower factor.

Common mistakes in Netting Benefits and Exposure Calculation

  • Netting negative values into gross exposure.

    Students sum all trades for both measures.

    Fix: For gross, floor each trade at zero before adding. Only net adds first and floors after.

  • Reporting a negative net exposure.

    Forgetting the max(·, 0) floor.

    Fix: Exposure is never negative. If the sum is below zero, net exposure is zero.

  • Applying the netting factor with the square root missing or misplaced.

    Mixing up variance and standard deviation of the sum.

    Fix: Portfolio standard deviation is √(n + n(n − 1)ρ) times one trade's volatility. Divide by n, the gross scale.

  • Assuming netting helps when ρ = 1.

    Believing netting always reduces exposure.

    Fix: At ρ = 1 the factor is 1, so no expected benefit. Benefit grows as ρ falls.

  • Ignoring legal enforceability.

    Treating netting as a purely arithmetic effect.

    Fix: Netting is recognised only where close-out netting is legally enforceable. Otherwise use gross.

Worked examples

Example 1

A bank has four OTC trades with one counterparty with mark-to-market values (USD million): +12, −5, +8, −20. Compute gross exposure, net exposure, the netting benefit and the netting factor, assuming enforceable netting.

Show the solution
  1. Gross = 12 + 8 = 20.
  2. Sum of all values = 12 − 5 + 8 − 20 = −5.
  3. Net = max(−5, 0) = 0.
  4. Benefit = 20 − 0 = 20.
  5. Netting factor = 0 ÷ 20 = 0.

Answer: Gross USD 20 million, net USD 0, benefit USD 20 million, netting factor 0 (a 100% reduction).

Example 2

A bank holds 4 trades with a counterparty. Exposures are normal with equal volatility, zero mean, and pairwise correlation 0.25. What is the ratio of netted to gross expected exposure?

Show the solution
  1. n = 4, ρ = 0.25.
  2. n + n(n − 1)ρ = 4 + 4 × 3 × 0.25 = 4 + 3 = 7.
  3. √7 = 2.6458.
  4. Factor = 2.6458 ÷ 4 = 0.6614.

Answer: About 0.66, so netting cuts expected exposure by about 34%.

Exam tips

  • Read the sign convention: values are usually from the bank's side.
  • Always floor at zero for net exposure; options often include a negative number as a trap.
  • For the correlation formula, check extreme cases first to eliminate options.
  • Expect interpretation questions: lower correlation or more trades gives more benefit, perfect correlation gives none.
  • Watch for legal wording: without enforceable netting, gross applies.

Practice questions from Netting, Close-out and Related Aspects

Netting Benefits and Exposure Calculation: frequently asked questions

What is the difference between netted and gross exposure?

Gross exposure adds only the positive trade values. Netted exposure adds all values first and floors the total at zero. Netted exposure is never above gross.

What is the netting factor formula in FRM Part II?

For n exposures with equal volatility, zero mean and common correlation ρ, netted EE ÷ gross EE = √(n + n(n − 1)ρ) ÷ n. It equals 1 when ρ = 1 and 1 ÷ √n when ρ = 0.

How does netting affect expected exposure?

It lowers expected exposure because gains on some trades offset losses on others. The reduction is larger when trades are less correlated and when there are more of them.

Does netting always reduce exposure?

It never increases exposure, but it may not reduce it. If all trades are positive, or perfectly correlated, the benefit is zero. It also relies on legal enforceability.