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

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

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

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