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

Calculate a financial institution's capital adequacy ratio after estimating its risk-weighted assets.

FRM® Part II · Credit Risk Measurement and Management · Introduction to Credit Risk Modeling and Assessment · FRM2.CR.5.c

The idea

The capital adequacy ratio compares regulatory capital with risk-weighted assets, and supervisors set a minimum, for example 8 percent for total capital under the Basel framework, plus buffers. RWA is built by multiplying each exposure by a risk weight reflecting its credit risk. For illustration, the weights are 0 percent for cash and sovereign claims, 20 percent for interbank exposures, 35 percent for residential mortgages and 100 percent for corporate loans. Off-balance-sheet items such as guarantees are first converted to an on-balance-sheet equivalent with a credit conversion factor and then risk-weighted. Market and operational risk capital charges are converted into RWA by multiplying by 12.5, the reciprocal of 8 percent, and added in. The ratio divides capital by the sum of these amounts, not by total assets. CAR = capital ÷ RWA. Dividing by total assets gives a leverage-type ratio instead. A write-off cuts capital and, if the asset leaves the book, RWA too.

Formulas

Capital adequacy ratio

CAR = capital ÷ RWA

capital
regulatory capital
RWA
risk-weighted assets for credit, market and operational risk

Divide by risk-weighted assets, not total assets, which would give a leverage-type ratio.

Risk-weighted assets

RWA = Σ(exposure × risk weight) + 12.5 × (market charge + operational charge)

exposure
each on-balance-sheet amount, or off-balance-sheet notional times its credit conversion factor
risk weight
the weight for its credit risk
market charge
the market risk capital charge
operational charge
the operational risk capital charge

Convert off-balance-sheet items with the CCF before weighting. 12.5 is the reciprocal of 8 percent.

A practice question

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

The capital adequacy ratio of a bank is defined as:

  1. Regulatory capital divided by total assetsWhy not: This is a leverage-type ratio; the capital adequacy ratio weights assets by their credit risk.
  2. Regulatory capital divided by risk-weighted assets - correct
  3. Risk-weighted assets divided by regulatory capitalWhy not: Inverts the ratio, giving a multiple of capital rather than a capital ratio.
  4. Equity capital divided by gross loansWhy not: Uses only loans in the denominator and ignores risk weights and other asset classes.

CAR = capital / risk-weighted assets. Risk weights make a ratio sensitive to the riskiness of the asset mix, unlike a simple capital-to-assets ratio.

A harder one

A bank has cash and government bonds of USD 250 million (0 percent risk weight), interbank deposits of USD 100 million (20 percent), residential mortgages of USD 300 million (35 percent) and corporate loans of USD 400 million (100 percent). It also has guarantees with a notional of USD 100 million, a credit conversion factor of 50 percent and a 100 percent risk weight. Total capital is USD 62 million. The capital adequacy ratio is closest to:

  1. 11.81%Why not: Leaves the off-balance-sheet guarantees out of RWA.
  2. 10.78% - correct
  3. 5.90%Why not: Divides by total on-balance-sheet assets (1,050) instead of risk-weighted assets.
  4. 8.05%Why not: Applies a 100 percent risk weight to the mortgages instead of 35 percent.

RWA = 0 + 20 + 105 + 400 + 50 = 575 (guarantees: 100 x 50% x 100%). CAR = 62 / 575 = 10.78%.

The hardest tier

A bank has total capital of USD 90 million and risk-weighted assets of USD 1,200 million. It wants a ratio of 10 percent without raising capital, by selling corporate loans (100 percent risk weight) and holding the proceeds in cash (0 percent risk weight). The loans it must sell are closest to:

  1. USD 30 millionWhy not: This is the capital that would be needed to reach 10 percent if the balance sheet were unchanged, not the RWA reduction.
  2. USD 300 million - correct
  3. USD 75 millionWhy not: Uses the 8 percent minimum (RWA of 1,125) as the target instead of the 10 percent target.
  4. USD 900 millionWhy not: This is the maximum RWA consistent with 10 percent, 90 / 0.10, not the amount to be sold.

Target RWA = 90 / 0.10 = 900. Required reduction = 1,200 - 900 = 300. Each USD 1 of loans swapped into cash removes USD 1 of RWA, so USD 300 million of loans must be sold.

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

Start free →

More in Introduction to Credit Risk Modeling and Assessment