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Judge whether a bank's economic capital is adequate given the credit risk it carries.

FRM® Part II · Credit Risk Measurement and Management · Capital Structure in Banks · FRM2.CR.4.a

The idea

A bank's economic capital is adequate when the capital it actually holds covers the unexpected credit loss at the confidence level management has chosen. That level is usually tied to a target credit rating, such as 99.9 or 99.97 percent over one year. In the test, EC is economic capital and EL is expected loss. The bank compares capital available with the requirement, which is calculated as EC = loss at the chosen quantile − EL. Expected loss is not part of the requirement because it is priced into loan spreads and covered by provisions, so counting reserves as capital double counts them. Raising the confidence level, adding concentration or increasing correlation all raise the requirement. Economic capital is the bank's own view and can differ from the regulatory minimum, so meeting the regulatory minimum does not prove adequacy.

Formulas

Economic capital for credit risk

EC = Q − EL

Q
the loss at the chosen confidence level, such as the 99.97th percentile over one year
EL
the expected loss

Capital is adequate when capital held, excluding reserves, is at least EC. Counting reserves as capital double counts the expected loss.

A practice question

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

Which statement about the confidence level used to size economic capital for credit risk is correct?

  1. It is fixed by the loss distribution and cannot be chosen by management, so the required capital does not change with the target rating.Why not: Believes the confidence level is a statistical given; it is a policy choice tied to the target rating.
  2. It reflects the bank's target solvency standard, usually linked to its desired credit rating, so a higher level means more capital is required. - correct
  3. A higher confidence level lowers required capital because fewer scenarios are considered.Why not: Reverses the effect: a higher confidence level looks further into the tail, which raises capital.
  4. It is the probability that expected loss is exceeded, and is therefore close to 50 percent.Why not: Confuses the confidence level with the chance that EL is exceeded; the level is chosen near 99.9 percent or higher.

Management chooses the confidence level to match the credit rating it wants to protect; moving further into the tail raises economic capital.

A harder one

A bank's credit loss model shows an expected loss of USD 60 million and a 99.9 percent one-year loss quantile of USD 610 million. Loan loss reserves already equal the expected loss. The bank holds USD 480 million of capital, excluding the reserves. Judged against economic capital at 99.9 percent, the bank's capital is:

  1. adequate, with a surplus of USD 420 million over the expected loss.Why not: Compares capital with EL only and ignores unexpected loss.
  2. inadequate, with a shortfall of USD 130 million.Why not: Compares capital with the full loss quantile without netting the EL already covered by reserves.
  3. inadequate, with a shortfall of USD 70 million. - correct
  4. inadequate, with a shortfall of USD 190 million.Why not: Adds EL to the quantile instead of subtracting it.

Economic capital = quantile - EL = 610 - 60 = 550 million. Capital of 480 million falls short by 70 million.

The hardest tier

A bank's equity is USD 700 million, its regulatory credit capital requirement is USD 650 million, and its internal model gives an expected loss of USD 90 million and a 99.9 percent loss quantile of USD 890 million. Reserves cover the expected loss. Which conclusion about adequacy of capital for credit risk is best supported?

  1. It meets the regulatory minimum but is USD 100 million short of economic capital at the target confidence level. - correct
  2. It is adequate, because equity exceeds the regulatory requirement by USD 50 million and economic capital is only advisory.Why not: Treats the regulatory requirement as the test of adequacy, ignoring the bank's own tail-risk measure.
  3. It is USD 190 million short, because equity must cover the whole loss quantile.Why not: Fails to net the expected loss, which reserves already cover.
  4. It is USD 10 million short, because the expected loss is deducted twice, once for reserves and once for provisioning.Why not: Deducts EL twice from the quantile; economic capital subtracts it once.

Economic capital = 890 - 90 = 800 million. Equity of 700 million exceeds the 650 million regulatory figure but is 100 million below economic capital.

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