Find the loss in the default outcome
Exposure is 100,000 and the assumed loss fraction if default happens is 45%. The default-event loss is therefore 45,000. That conditional loss is separate from the probability that the event occurs.
Weight both outcomes
Multiply each possible loss by its probability and add the weighted amounts. The probability weights sum to one, so the table is a complete two-outcome distribution for this simplified example.
| Outcome | Probability | Loss | Contribution to expected loss |
|---|---|---|---|
| No default | 98% | 0 | 0 |
| Default | 2% | 45,000 | 900 |
| Total | 100% | 900 |
Interpret the expectation
The expected value is not one of the two realised outcomes. It is the model’s probability-weighted average. Changing probability changes how often the loss is weighted; changing LGD changes the severity of the default outcome. More detailed models can add states, timing and discounting.