Default probability needs a horizon
A default probability relates to a defined period. Comparing probabilities over different horizons without adjusting the model can be misleading. In the simple one-period example, default either occurs during the stated horizon or it does not.
Loss given default is conditional
Loss given default measures the fraction of exposure lost in the default outcome. It is not the fraction expected to be lost across all possible outcomes. A 45% LGD does not mean there is a 45% probability of default. The two percentages answer different questions.
| Quantity | Question answered |
|---|---|
| PD | How likely is default over the horizon? |
| LGD | What fraction of exposure is lost if default occurs? |
| EAD | How much is exposed at default? |
Combine the outcomes with probability weights
If the default-event loss is 45,000 and default probability is 2%, multiplying gives an expected loss of 900 when the non-default loss is zero. That expectation differs from both possible realised outcomes. It summarizes the model rather than replacing the uncertainty.