# Probability of Default versus Default Rate

## Probability of Default versus Default Rate

These two concepts are sometimes confused as they refer to the same Credit Risk phenomenon, but are substantially different

• The Default Rate is an observed realisation of credit events. It refers to something that has already occurred. It is also denoted as ex-post estimate (NB: There might be residual uncertainties in the measurement of the event rate)
• The Probability of Default is an expectation measure about future credit events. It is also denoted as an ex-ante estimate.

The two concepts are easier to confuse for credit portfolios that are treated as pools (Retail credit) that may exhibit continuous default events.

### Mathematical Distinction

The default rate for a pool of credits is defined as

${\displaystyle {\mbox{DR}}={\frac {N^{D}}{N}}}$

the ratio of defaulted assets ${\displaystyle N^{D}}$ over total assets N. In comparison the probability of default is the expectation of the default rate

${\displaystyle {\mbox{PD}}=\mathbb {E} ({\frac {N^{D}}{N}})}$