Charta is on Google Play: practise on the go. Get the app
Charta

Account for the Basel treatment of regulatory capital and economic capital requirements and show how the two differ.

FRM® Part II · Operational Risk and Resilience · Integrated Risk Management · FRM2.ORR.7.b

The idea

Regulatory capital is the minimum set by supervisors using prescribed rules. Economic capital is the bank's own estimate of the capital needed to absorb unexpected losses at a confidence level matching its target credit rating. Under Basel III, minimum capital is a percentage of risk-weighted assets (RWA). Baseline minima are CET1 4.5 percent, Tier 1 6 percent and total capital 8 percent. A 2.5 percent CET1 conservation buffer sits on top, plus any countercyclical or systemic surcharges, and the requirement applied varies by jurisdiction. Operational risk capital, under any framework, is converted to RWA by multiplying by 12.5. The IRB credit formula uses a 99.9 percent one-year worst-case default rate, WCDR, and charges capital for the unexpected part only. With LGD the loss given default and PD the expected default probability, the capital charge per unit of exposure, written K, is K = LGD × (WCDR − PD). Economic capital, written EC, is the loss quantile VaR minus expected loss, so EC = VaR − EL. Economic capital models can recognise diversification across risk types, whereas Basel simply adds the charges. Do not mix up expected and unexpected loss.

Formulas

IRB capital per unit of exposure

K = LGD × (WCDR − PD)

LGD
loss given default
WCDR
the 99.9% worst-case default rate
PD
the probability of default

Before the maturity adjustment and scaling. PD is deducted because capital covers unexpected loss only; LGD × WCDR alone also charges for expected loss.

Economic capital

EC = VaR − EL

VaR
the loss quantile at the confidence level matching the target rating
EL
the expected loss, covered by provisions and pricing

Capital is held for the unexpected part only. Reporting the full quantile, or adding EL to it, are the slips.

Minimum CET1 including the conservation buffer

CET1 required = (4.5% + 2.5%) × (credit RWA + market RWA + 12.5 × operational charge)

credit RWA
risk-weighted assets for credit risk
market RWA
risk-weighted assets for market risk
operational charge
the operational risk capital charge

Operational risk is given as capital, so convert it to RWA by multiplying by 12.5 before adding. Ignores countercyclical and systemic surcharges, which vary by jurisdiction.

A practice question

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

Under Basel III, the minimum Common Equity Tier 1 (CET1) requirement, before any buffers, is:

  1. 8.0 percent of risk-weighted assets.Why not: This is the minimum total capital ratio, not the CET1 minimum.
  2. 6.0 percent of risk-weighted assets.Why not: This is the minimum Tier 1 ratio, which includes additional Tier 1 instruments as well as CET1.
  3. 4.5 percent of risk-weighted assets. - correct
  4. 2.5 percent of risk-weighted assets.Why not: This is the capital conservation buffer, which sits on top of the 4.5 percent minimum.

The Basel III minimums are CET1 4.5%, Tier 1 6% and total capital 8% of RWA, with the 2.5% conservation buffer in CET1 on top.

A harder one

A bank's credit portfolio loss distribution has a 99.9th percentile loss of USD 500 million and an expected loss of USD 120 million. Economic capital, defined as unexpected loss at that confidence level, is closest to:

  1. USD 620 millionWhy not: Adds expected loss to the quantile instead of subtracting it.
  2. USD 380 million - correct
  3. USD 500 millionWhy not: Uses the full loss quantile and fails to deduct the expected loss already covered by provisions and pricing.
  4. USD 120 millionWhy not: Reports the expected loss itself, which is not what capital is held for.

Economic capital = loss quantile - expected loss = 500 - 120 = 380 million. Expected loss is covered by pricing and provisions; capital covers the unexpected part.

The hardest tier

Under the Basel internal ratings-based approach, a corporate exposure has EAD of USD 100 million, PD of 1 percent and LGD of 45 percent. The model gives a worst-case default rate at 99.9 percent of 11.0 percent. Ignoring the maturity adjustment and scaling factors, the capital requirement for unexpected loss is closest to:

  1. USD 4.95 millionWhy not: Multiplies LGD by the worst-case default rate without subtracting PD, so expected loss is not removed.
  2. USD 0.45 millionWhy not: Computes LGD x PD x EAD, which is the expected loss rather than the capital.
  3. USD 4.5 million - correct
  4. USD 56.3 millionWhy not: Converts the capital figure into risk-weighted assets by multiplying by 12.5 instead of reporting capital.

K = LGD x (WCDR - PD) = 0.45 x (0.110 - 0.010) = 4.5%, so capital = 4.5% x 100 = 4.5 million. Capital covers unexpected loss only, so PD is subtracted.

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

Start free →

More in Integrated Risk Management