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Contrast economic capital with regulatory capital in terms of what each is and how it is used.

FRM® Part I · Financial Markets and Products · Banks · FRM1.FM.1.b

The idea

Economic capital is the bank's own estimate of the capital needed to absorb unexpected losses over a horizon, usually one year. The confidence level is chosen to match a target credit rating. A 99.97% level corresponds to a default probability of 0.03%, which is only illustratively about an AA rating, because the mapping depends on the agency and the horizon. Economic capital is measured as the loss at that confidence level minus the expected loss, because expected loss is covered by pricing and provisions. Banks use it internally to allocate capital to business lines, to price deals and to judge performance. A common measure is RAROC = (revenue − costs − expected loss) ÷ economic capital. Regulatory capital is the minimum the supervisor requires, calculated with prescribed formulas such as risk weights. It is a compliance constraint applied to every bank alike. The two can differ in either direction, and meeting the regulatory minimum does not prove that economic capital is sufficient. Exam point: economic capital is internal and risk-based, while regulatory capital is external and rule-based.

Formulas

Risk-adjusted return on capital

RAROC = (Revenue − Costs − EL) ÷ EC

Revenue
the business unit's revenue for the period
Costs
its operating costs
EL
the expected loss, covered by pricing and provisions
EC
the economic capital allocated to the unit

Used internally to compare business lines and set hurdles. The usual traps are leaving out the expected loss or the costs, which overstates the return.

Economic capital from a loss distribution

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 covers unexpected loss only. Reporting the quantile itself, or adding the expected loss to it, are the usual errors.

A practice question

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

Which statement best describes economic capital?

  1. The minimum capital that supervisors require the bank to hold under the Basel framework rules.Why not: This describes regulatory capital.
  2. The book value of shareholders' equity shown on the audited balance sheet at year end.Why not: Accounting equity is not a risk-based estimate.
  3. The bank's own estimate of capital needed to absorb unexpected losses at a chosen confidence. - correct
  4. The capital held to cover expected losses, which is funded through loan-loss provisions.Why not: Expected losses are covered by pricing and provisions; capital covers unexpected losses.

Economic capital is an internal, risk-based estimate of the buffer against unexpected losses over a horizon at a confidence level tied to the bank's target rating.

A harder one

A business unit generates annual revenue of USD 12 million, with costs of USD 4 million and expected credit losses of USD 2 million. The economic capital allocated to it is USD 40 million. Its RAROC is closest to:

  1. 20%Why not: Ignores the expected loss: (12 - 4) / 40.
  2. 25%Why not: Ignores the costs: (12 - 2) / 40.
  3. 30%Why not: Divides revenue by economic capital without deducting costs or expected loss.
  4. 15% - correct

RAROC = (revenue - costs - expected loss) / economic capital = (12 - 4 - 2) / 40 = 6 / 40 = 15%.

The hardest tier

A bank's credit portfolio model gives a one-year loss distribution with an expected loss of USD 30 million and a 99.97th percentile loss of USD 180 million. The bank defines economic capital as the capital needed to cover unexpected loss at that confidence level. Economic capital is closest to:

  1. USD 150 million. - correct
  2. USD 180 million.Why not: Uses the total quantile loss and does not subtract the expected loss that is covered by provisions.
  3. USD 210 million.Why not: Adds the expected loss to the quantile instead of subtracting it.
  4. USD 30 million.Why not: Uses the expected loss, which is provisioned for, rather than the unexpected loss.

Economic capital = loss at the confidence level - expected loss = 180 - 30 = 150 million. Expected loss is covered by pricing and provisions.

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