Including Defaults on New Loans in Capital Requirements for Credit Risk

Abstract

The usual application of the Basel formula for calculating risk-weighted assets (RWA) for credit risk involves estimating losses over the following year on loans in a bank's portfolio at the beginning of the year (the 'back-book'). In practice, the bank will also suffer some losses from new loans that entered during the year (the 'front book') so, if the formula gives an unbiased estimate of expected losses from the back book, it will under-estimate losses from the whole portfolio. To take account of losses from the front book, it is necessary to adjust the calculation, taking account of the inflow rate of new loans. This can be done by either of two broadly equivalent techniques: (1) multiply the RWA for loans in each internal rating grade pool by (one plus half the expected inflow rate of new loans to the pool); or (2) rearrange the Basel RWA formula so that it has three distinct places where PD is used, and replace the value that is used in the dominant one of those places (the `primary PD slot') by an estimate of the unconditional expected portfolio default rate, rather than of individual loan default probability. Making these adjustments will give an unbiased estimate of total defaults in a downturn year, provided the original calculation gives an unbiased estimate of defaults from the back-book. A simpler technique of estimating front-book-inclusive default rates is to remove half the exits from the denominator in calculating observed default rates. This approximation can be reasonably accurate provided that both inflow and exit rates, excluding grade migrations, are low for each grade to which it is applied. That may make it unsuitable for the riskiest grades, but in general it is fairly accurate.