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Distinguish a credit portfolio's stress loss from its stressed expected loss, and calculate stress loss for both a loan portfolio and a derivative portfolio.

FRM® Part II · Credit Risk Measurement and Management · The Evolution of Stress Testing Counterparty Exposures · FRM2.CR.21.d

The idea

Expected loss for a credit exposure is written EL, and the portfolio figure sums it. EL = EAD × PD × LGD. Stressed expected loss is the same sum recomputed with the scenario values of all the inputs. Stress loss is the increase over the base case, and it is written SL. SL = stressed EL − base EL. The base expected loss is already priced and provisioned, so the increment is what the scenario adds. For a loan portfolio, stress the EAD, PD and LGD of each loan. For derivatives, stressed EAD is the exposure after revaluing the netting set under shocked market factors and deducting collateral, floored at zero. Then apply the stressed PD and LGD. Common mistakes are reporting stressed expected loss as the stress loss, leaving derivative exposure at its current value, shocking only PD, and forgetting netting and collateral. Use the definition given in the question, though the increment over base expected loss is the usual one.

Formulas

Stress loss on a credit portfolio

SL = stressed EL − base EL

stressed EL
Σ EAD × PD × LGD with every input at its scenario value
base EL
the same sum with base-case inputs

Stress loss is the increment, since base EL is already priced and provisioned. Reporting stressed EL itself is the common error.

Exposure at default on a committed facility

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

Stress scenarios raise the CCF, as borrowers draw lines in a downturn. Apply it to the undrawn amount, not to the drawn balance or the full limit.

A practice question

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

Which statement distinguishes a portfolio's stressed expected loss from its stress loss?

  1. Stressed expected loss is the 99.9% percentile of the loss distribution under stress, while stress loss is the mean of that same distributionWhy not: Confuses stressed EL with credit VaR; EL stays an expected value computed with stressed inputs.
  2. Stress loss reflects only the PD shock, while stressed expected loss reflects PD, LGD and EADWhy not: Stress loss uses the same stressed PD, LGD and EAD; it differs by subtracting base EL.
  3. Stress loss is stressed expected loss minus the capital held against the portfolioWhy not: Subtracts capital instead of the base-case expected loss.
  4. Stressed expected loss is EL recomputed with stressed inputs; stress loss is the amount by which it exceeds the base-case expected loss - correct

Both use stressed EAD, PD and LGD. Stressed EL is the full level; stress loss is the increment over the base EL.

A harder one

A loan portfolio has two loans. Loan 1: EAD USD 50 million, PD 2% (stress 8%), LGD 45% (stress 60%). Loan 2: EAD USD 30 million, PD 1% (stress 5%), LGD 40% (stress 55%). EAD is unchanged under stress. Defining stress loss as stressed EL minus base EL, with EL = EAD x PD x LGD, what is the stress loss, closest to?

  1. USD 2.66 million - correct
  2. USD 3.23 million, the stressed expected loss aloneWhy not: Reports stressed EL (3.23) rather than the increase over base EL.
  3. USD 1.83 millionWhy not: Stresses PD only and leaves LGD at base values.
  4. USD 0.19 millionWhy not: Stresses LGD only and leaves PD at base values.

Base EL = 0.45 + 0.12 = 0.57. Stressed EL = 2.40 + 0.825 = 3.225. Stress loss = 3.225 - 0.57 = 2.655, about 2.66. PD and LGD must both be stressed.

The hardest tier

A portfolio has (i) a loan with EAD USD 40 million, PD 3% (stress 9%), LGD 50% (stress 65%), and (ii) a derivative netting set with MTM USD 12 million in the base case and USD 30 million in the stress, with USD 8 million of collateral held in both cases, counterparty PD 2% (stress 10%) and LGD 60% (stress 75%). Exposure for the derivative is MTM less collateral, floored at zero. With stress loss as stressed EL minus base EL, what is the portfolio stress loss, closest to?

  1. USD 3.85 millionWhy not: Ignores collateral on the derivative, using gross MTM as exposure.
  2. USD 1.99 millionWhy not: Leaves the derivative exposure at its base net value of 4 instead of revaluing under stress.
  3. USD 3.34 million - correct
  4. USD 3.99 millionWhy not: Reports the total stressed expected loss rather than the increase over base EL.

Loan: base 0.600, stressed 2.340. Derivative: base exposure 12 - 8 = 4, EL 0.048; stressed exposure 30 - 8 = 22, EL 1.650. Stress loss = (2.340 + 1.650) - (0.600 + 0.048) = 3.342.

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