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Spell out the meaning of mark-to-market, replacement cost, credit exposure, credit migration, recovery, recovery rate, default probability and loss given default.

FRM® Part II · Credit Risk Measurement and Management · Counterparty Risk and Beyond · FRM2.CR.15.d

The idea

Mark-to-market is the current fair value of a contract. Replacement cost is what it would cost to replace the contract with an identical one at today's market. This matters only if the value is positive to you. Credit exposure is therefore the larger of the mark-to-market value and zero, taken for each netting set. Negative values are not at risk. Credit migration is a change in a counterparty's credit quality, such as a downgrade, without default. Recovery is what is actually received after default. The recovery rate is that amount as a fraction of the claim. Default probability, PD, is the chance of default over a horizon. Loss given default, LGD, is the share of the claim that is lost. Exam point: LGD and the recovery rate are complements, and exposure is floored at zero. LGD = 1 − Recovery rate. Expected loss combines exposure, default probability and loss given default. EL = Exposure × PD × LGD.

Formulas

Loss given default from the recovery rate

LGD = 1 − recovery rate

recovery rate
the share of the exposure recovered after default, net of costs

The two are complements. Applying the recovery rate where LGD belongs is the classic slip.

Expected loss on a counterparty exposure

EL = Exposure × PD × LGD

Exposure
the positive exposure after netting and collateral
PD
the probability of default over the horizon
LGD
loss given default, one minus the recovery rate

Over several years use the cumulative default probability, built from survival: one minus the product of yearly survival probabilities.

A practice question

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

Which statement defines replacement cost in the context of counterparty risk?

  1. The notional amount of the contract, which the defaulting party must repay to the non-defaulting party in full at the moment it defaults, regardless of market prices or any collateral held.Why not: Notional is not the claim in default; the claim is the mark-to-market.
  2. The amount of collateral that the defaulting counterparty had posted before default.Why not: Confuses replacement cost with collateral held, which only reduces the net exposure.
  3. The expense of funding the initial margin on the contract until maturity.Why not: Describes a funding cost (MVA-type), not the cost of replacing the contract.
  4. The cost of entering a new contract with the same terms at current market prices after the counterparty has defaulted, which matters when the contract's value is positive to the non-defaulting party. - correct

Replacement cost is the loss of value from having to replace a contract at current market prices. If the contract is out of the money to you, replacing it gives you a gain you do not lose.

A harder one

A dealer has four trades with a counterparty and no netting agreement, so each trade stands alone. The mark-to-market values to the dealer are +8, +3, -6 and -2 (USD million). The dealer's credit exposure is:

  1. USD 3 millionWhy not: Sums the values (netting), although no netting agreement exists.
  2. USD 11 million - correct
  3. USD 19 millionWhy not: Adds the absolute values, counting negative trades as exposure.
  4. USD 8 millionWhy not: Takes only the largest positive trade rather than the sum of positive values.

With no netting, exposure = sum of max(MtM, 0) = 8 + 3 = 11. Negative values are not credit exposure, and gains cannot be offset by losses without netting.

The hardest tier

A bank has a constant exposure of USD 50 million to a counterparty for two years. The annual default probabilities, conditional on survival to the start of each year, are 10% in year 1 and 20% in year 2. The recovery rate is 40%. The expected loss over the two years is closest to:

  1. USD 9.0 millionWhy not: Adds the two annual probabilities (30%) instead of compounding survival, which overstates cumulative default.
  2. USD 5.6 millionWhy not: Uses the recovery rate of 40% in place of the loss given default of 60%.
  3. USD 5.4 millionWhy not: Uses only the unconditional year-2 default probability (0.9 x 20% = 18%) and omits the year-1 default.
  4. USD 8.4 million - correct

Survival = 0.9 x 0.8 = 0.72, so cumulative default probability = 28%. Expected loss = 50 x 28% x (1 - 40%) = 8.4.

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

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