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Outline how well netting cuts credit exposure across different scenarios.

FRM® Part II · Credit Risk Measurement and Management · Netting, Close-out and Related Aspects · FRM2.CR.16.c

The idea

Netting cuts exposure because a counterparty's claim is the net of positive and negative values, not the sum of the positive ones. Netted exposure is the larger of zero and the sum of all trade values. Un-netted exposure is the sum of the positive values only. The net-to-gross ratio (NGR) is current net exposure divided by current gross exposure, so a low ratio means a large benefit. The benefit depends on the portfolio. It is largest with many trades, offsetting directions and low or negative correlation, and it is zero when all trades have positive value or only one trade exists, as with purchased options. Take N identical normally distributed trade values, with correlation ρ between each pair. Then the expected exposure of the netted set, as a share of the un-netted figure, is Ratio = √(1/N + (1 − 1/N) × ρ). The usual mistake is to assume netting always helps by a fixed amount, and to forget that it only works where it is legally enforceable.

Formulas

Net-to-gross ratio

NGR = net exposure ÷ gross exposure

net exposure
the larger of zero and the sum of all trade values
gross exposure
the sum of the positive trade values only

A lower ratio means a larger netting benefit; 1 means none. Gross is the sum of positive values, not of absolute values.

Netting benefit for identical normal trades

Netted EE ÷ un-netted EE = √(1 ÷ N + (1 − 1 ÷ N) × ρ)

N
the number of trades in the netting set
ρ
the pairwise correlation between trade values

Assumes identically distributed, zero-mean normal values so expected exposure is proportional to the standard deviation. Forgetting the square root is the usual slip.

A practice question

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

How does the credit exposure of a bilateral netting set compare with the sum of the positive trade values in it, ignoring collateral?

  1. It is always strictly smaller than the sum of positive values, whatever the trade valuesWhy not: It equals the sum of positive values when no trade has a negative value, so it is not always strictly smaller.
  2. The larger of zero and the sum of all values, never above the sum of positive values - correct
  3. It is the sum of the absolute values of all trades, so it can be larger than grossWhy not: Negative values reduce the claim; they are not added as if they were positive exposures.
  4. It equals the largest single positive trade valueWhy not: Exposure is the net of all values, not the largest individual value.

Netted exposure = max(sum of values, 0); un-netted exposure = sum of max(value, 0). The first can never exceed the second.

A harder one

A netting set contains five trades valued to the bank at +40, +25, -30, -15 and +10 (USD million). Closest to the net-to-gross ratio is:

  1. 0.4 - correct
  2. 0.25Why not: Divides the net value by the sum of absolute values of all trades (120) instead of by the positive values.
  3. 0.60Why not: Reports the netting benefit (1 minus NGR) rather than the ratio.
  4. 2.50Why not: Inverts the ratio, dividing gross exposure of 75 by net exposure of 30.

Net = 40 + 25 - 30 - 15 + 10 = 30. Gross (positive values) = 40 + 25 + 10 = 75. NGR = 30 / 75 = 0.40.

The hardest tier

A netting set has four identically distributed, zero-mean normal trade values with pairwise correlation 0.25. Expected exposure is proportional to the standard deviation of the portfolio value. By roughly what percentage does netting reduce expected exposure compared with no netting?

  1. 56.3 percentWhy not: Uses the variance ratio (0.4375) and omits the square root when computing the reduction.
  2. 50.0 percentWhy not: Assumes independent trades (ratio 1 over the square root of 4) and ignores the correlation.
  3. 66.1 percentWhy not: Reports the netted-to-gross ratio of 0.66 as if it were the reduction.
  4. 34 percent - correct

Ratio = sqrt(1/4 + 0.75 x 0.25) = sqrt(0.4375) = 0.661. The reduction is 1 - 0.661 = 0.339, about 34 percent.

In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.

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