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Expected loss is the average credit loss implied by a specified default probability, loss given default and exposure at default over the same horizon. Multiply the three inputs to express that average in currency. A larger possible recovery reduces loss given default, so using the recovery rate directly in the multiplication gives the wrong answer.
What each input contributes
Probability of default, or PD, is the chance that the borrower defaults during the chosen period. Loss given default, or LGD, is the proportion of the exposure lost if default occurs. Exposure at default, or EAD, is the amount exposed when that event occurs; for a facility with undrawn credit, it need not equal today’s drawn balance. GARP’s credit risk measurement explanation sets out the PD–LGD–EAD framework and the distinction between loss as a percentage and as a currency amount.
Keep the horizon aligned: a one-year PD belongs with an exposure and loss estimate for that same one-year question. Both percentages enter the product as decimals. The Basel Committee’s IRB treatment of expected losses describes PD multiplied by LGD as an expected-loss rate for non-defaulted exposures; multiplying that rate by EAD expresses it in currency.
A worked example with invented inputs
Assume an illustrative loan has £1,000 of exposure at default, a one-year PD of 2% and an LGD of 40%. These are invented round numbers, not estimates for a real borrower. Convert the percentages to decimals before calculating.
One way to read the result is that default is uncommon in this assumption, but a default would lose £400 of the £1,000 exposure. Weighting that conditional £400 loss by the 2% chance of default gives £8. It does not mean that exactly £8 will be lost on this individual loan: its realised outcome could be different.
Recovery is the opposite side of severity
Suppose instead that the same invented example is described as having a 60% recovery rate. That means 60% of exposure is assumed to be recovered after default; the loss fraction is the remaining 40%. The expected loss is still £8. The exam trap is to multiply by 0.60, which would produce £12 and confuse the amount recovered with the amount lost.
For a calculation, label each input before multiplying: probability, loss fraction, and exposure. Then check the unit of the answer. PD times LGD is a percentage of exposure; only after multiplying by EAD do you have a currency amount. The FRM programme page gives the broader syllabus context, and how Omni works describes the study format.
Sources
- Credit Risk Measurement: Alternatives for PD-LGD-EAD on the Horizon? · garp.org · Retrieved
- IRB approach: treatment of expected losses and provisions · bis.org · Retrieved
- IRB approach: risk components · bis.org · Retrieved
