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State what expected loss (EL) is and compute it.

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

The idea

Expected loss (EL) is the average credit loss the bank anticipates over the horizon, the mean of the loss distribution. LGD is the loss rate, which is one minus the recovery rate. For one exposure, EL = EAD × PD × LGD. For a portfolio, EL is simply the sum of the individual ELs, because expectations add whatever the correlations. EL is treated as a cost of doing business. It is built into the loan spread and covered by provisions or reserves, and so it does not call for economic capital. A frequent mistake is to use the recovery rate in place of the loss rate, or to multiply by the credit limit instead of the exposure expected at default. EL is not the risk. The variability around it is.

Formulas

Expected loss on one exposure

EL = PD × LGD × EAD

PD
the probability of default over the horizon
LGD
loss given default, as a share of the exposure
EAD
the exposure at default

For a portfolio, add the individual ELs whatever the correlations. Use the loss rate, not the recovery rate.

A practice question

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

Which expression gives the expected loss on a single credit exposure?

  1. Exposure at default x probability of default x loss rate. - correct
  2. Exposure at default x probability of default x recovery rate.Why not: Uses the recovery rate instead of the loss rate.
  3. Exposure at default x loss rate x (1 - probability of default).Why not: Weights the loss by the probability of survival rather than of default.
  4. Exposure at default x the square root of probability of default x (1 - probability of default) x loss rate.Why not: Gives the unexpected loss, the standard deviation, not the expected loss.

Expected loss is the mean of the loss: the chance of default times the amount lost given default, EAD x PD x LGD.

A harder one

A bank wants the part of a loan's annual credit spread that just covers expected credit loss. The loan has a one-year PD of 1.5 percent and a loss rate of 45 percent. The expected-loss component of the spread is closest to:

  1. 150 basis points.Why not: Uses the PD alone and ignores that only part of the exposure is lost.
  2. 82.5 basis points.Why not: Uses the recovery rate instead of the loss rate.
  3. 333 basis points.Why not: Divides PD by the loss rate instead of multiplying.
  4. 67.5 basis points. - correct

EL rate = PD x LGD = 0.015 x 0.45 = 0.00675, or 67.5 basis points of exposure.

The hardest tier

A bank has a USD 12 million credit line, USD 5 million drawn. It expects that 60 percent of the undrawn amount will be drawn before default. The one-year PD is 2.5 percent and the expected recovery rate is 45 percent. The expected loss is closest to:

  1. USD 126,500. - correct
  2. USD 68,750.Why not: Uses only the current drawn balance as exposure.
  3. USD 165,000.Why not: Uses the full limit as exposure.
  4. USD 103,500.Why not: Uses the recovery rate in place of the loss rate.

EAD = 5 + 0.6 x 7 = 9.2 million; LGD = 1 - 0.45 = 0.55; EL = 9.2m x 0.025 x 0.55 = 126,500.

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