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Recognise the three main inputs to economic capital for credit risk, namely loss rate, exposure and the chance of default, and describe each.

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

The idea

Economic capital for credit risk is built from three inputs. Exposure, or exposure at default (EAD), is the amount owed when default occurs. For a credit line it is the drawn amount plus the share of the undrawn commitment expected to be drawn first, and where exposure amortises or changes over time a period-by-period calculation is needed. The probability of default (PD) is the chance the obligor defaults over the horizon, normally one year, so multi-year cumulative figures must be converted and EAD, PD and LGD must share that horizon. The loss rate, or loss given default (LGD), is the share of exposure lost after recoveries. It depends on seniority, collateral and workout costs rather than on the obligor's quality. A common error is to use the credit limit as exposure, or the recovery rate where the loss rate is required. Put as a formula, LGD = 1 − recovery rate.

Formulas

Loss rate from the recovery rate

LGD = 1 − recovery rate

recovery rate
the share of the exposure recovered after default, net of costs

The loss rate, not the recovery rate, enters EL and UL. Deduct disposal costs from proceeds before computing recovery.

Annual PD from a cumulative PD

PD = 1 − (1 − CPD)^(1 ÷ T)

CPD
the cumulative probability of default over T years
T
the number of years

Assumes a constant annual PD and independence across years. Dividing CPD by T understates the annual figure, because survival compounds.

Exposure at default on a credit line

EAD = drawn + CCF × undrawn

drawn
the amount already drawn
CCF
the conversion factor, the share of the undrawn amount expected to be drawn by default
undrawn
the undrawn commitment

Using the credit limit as exposure is the common error.

A practice question

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

Which three inputs drive the economic capital a bank holds for the credit risk of a loan?

  1. Exposure at default, probability of default and the loss rate given default. - correct
  2. Exposure at default, probability of default and the risk-free interest rate.Why not: Substitutes a market rate for the loss rate; the discount rate is not a credit-loss input.
  3. Loan maturity, borrower's equity price and the credit spread.Why not: Lists market observables rather than the three loss inputs.
  4. Probability of default, recovery rate and the credit limit.Why not: Uses the credit limit instead of the exposure expected at default, and omits exposure itself.

Credit loss = exposure x probability of default x loss rate, so these are the three inputs; the loss rate is one minus the recovery rate.

A harder one

A client has a revolving credit line with a limit of USD 10 million, of which USD 4 million is drawn. The bank expects that, by the time of default, 50 percent of the undrawn amount would have been drawn. The exposure at default is:

  1. USD 4 million.Why not: Uses the current drawn balance only, ignoring further drawing before default.
  2. USD 10 million.Why not: Uses the full limit, which assumes the whole line is drawn.
  3. USD 7 million. - correct
  4. USD 5 million.Why not: Applies the drawdown percentage to the whole limit instead of the undrawn part.

EAD = drawn + CCF x undrawn = 4 + 0.5 x (10 - 4) = 7 million.

The hardest tier

A defaulted loan has an exposure of USD 20 million. It is secured by collateral that is sold for USD 12 million, but disposal costs of 10 percent of the sale value are deducted from the proceeds. There is no other recovery. The loss rate is closest to:

  1. 46 percent. - correct
  2. 40 percent.Why not: Ignores the disposal costs and takes the full sale value as recovery.
  3. 54 percent.Why not: Reports the recovery rate, net proceeds over exposure, instead of the loss rate.
  4. 50 percent.Why not: Applies the 10 percent costs to the exposure rather than to the collateral proceeds.

Net proceeds = 12 x (1 - 0.1) = 10.8; loss = 20 - 10.8 = 9.2; loss rate = 46%.

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