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Explain how economic capital is derived and how it differs from regulatory capital.

FRM® Part I · Valuation and Risk Models · Measuring Credit Risk · FRM1.VR.6.a

The idea

Economic capital is the amount of equity a bank itself judges necessary to absorb unexpected losses over a horizon, normally one year, at a confidence level tied to its target credit rating. A bank targeting an AA rating, with a one-year default probability near 0.03 percent, sizes capital at roughly the 99.97 percent level. It is built by modelling loss distributions for credit, market and operational risk. The bank takes the loss at the chosen confidence level and subtracts expected loss, which is covered by pricing and provisions. It then aggregates across risk types with allowance for diversification. Regulatory capital is different. It is the minimum set by supervisors using prescribed formulas and parameters, applied to all banks alike. Economic capital is bank specific and drives pricing, performance measurement such as RAROC, and capital allocation. The exam trap is treating the two as the same number.

Formulas

Economic capital from a loss distribution

economic capital = loss at confidence level − EL

loss at confidence level
the loss at the percentile tied to the target rating, for example 99.97 percent for AA
EL
expected loss, covered by pricing and provisions

The confidence level is one minus the target rating's default probability. Do not treat it as regulatory capital, which uses supervisory formulas.

A practice question

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

Which statement best describes economic capital for credit risk?

  1. The bank's own estimate of the capital needed to absorb unexpected losses, at a confidence level tied to its target rating. - correct
  2. The minimum capital that supervisors require under Basel rules, calculated by prescribed formulas and parameters that apply to all banks alike.Why not: Describes regulatory capital, which is set by supervisors, not by the bank's own model and risk appetite.
  3. The loan-loss provisions set aside to cover the average credit losses the bank expects over the year.Why not: Confuses capital for unexpected loss with provisions for expected loss, which are covered by pricing and reserves.
  4. The book value of shareholders' equity shown on the balance sheet at the reporting date.Why not: Confuses a risk-based capital need with accounting equity, which says nothing about the loss distribution.

Economic capital is the bank's internal answer to how much equity it needs so that the probability of insolvency over the horizon matches its target rating. Regulatory capital is imposed by supervisors; provisions cover expected loss; book equity is an accounting number.

A harder one

A bank wants its probability of becoming insolvent over one year to equal the 0.03% one-year default rate of an AA-rated firm. At which confidence level should it calibrate the one-year loss distribution used for economic capital?

  1. 99.9%Why not: Uses the regulatory internal-ratings confidence level instead of the level implied by the bank's own target rating.
  2. 99.7%Why not: Decimal slip: 0.03% is 0.0003, so the confidence level is 99.97%, not 99.7% (which would be a 0.3% failure probability).
  3. 99.97% - correct
  4. 0.03%Why not: Quotes the failure probability itself rather than the confidence level, which is its complement (1 minus 0.03%).

Confidence level = 1 - target default probability = 1 - 0.0003 = 99.97%. The bank chooses the level that corresponds to its target rating, which is why economic capital is bank specific.

The hardest tier

A bank's internal model puts its economic capital at USD 4.2 billion. Basel-based regulatory capital is USD 3.6 billion, and the bank actually holds USD 3.9 billion of capital. Which interpretation is most appropriate?

  1. The bank must immediately raise USD 0.3 billion by law, to bring its holdings up to economic capital.Why not: No rule requires holding economic capital; the shortfall of USD 0.3 billion versus economic capital is a management decision.
  2. The bank breaches its regulatory requirement, because economic capital is higher than regulatory capital.Why not: Treats economic capital as a legal minimum; the regulatory test compares holdings with regulatory capital of USD 3.6 billion.
  3. The bank is fully capitalised, because the regulators' figure is the only binding measure of adequacy.Why not: Ignores that economic capital measures the bank's own safety target; being compliant does not mean the target rating is supported.
  4. The bank is compliant but holds less than its own model requires, so its failure risk exceeds its target. - correct

Holdings of 3.9 exceed the regulatory 3.6 but fall short of the 4.2 economic capital. The bank is compliant, yet by its own models the probability of failure exceeds its target, so management must decide whether to raise capital or cut risk.

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