International Finance and Accounting Handbook

The term denotes the cumulative distribution function for a standard normal
random variable (i.e., the probability that a normal random variable with mean zero
and variance of one is less than or equal to ) and the term denotes the inverse
cumulative distribution function for a standard normal random variable (i.e., the
value such that ). The BRW formula is calibrated so that a three-year cor-
porate loan with a PD equal to 0.7% and a LGD equal to 50% will have a capital re-
quirement of 8%, calibrated to an assumed loss coverage target of 99.5% (i.e., losses
to exceed the capital allocation occur only 0.5% of the time, or five years in 1,000).^41
Appendix B shows the calibration of equation (2) for retail loans, demonstrating that
the BRW for retail loans is set lower than the BRW for corporate loans for all levels
of PD. Exhibit 3.6 shows the continuous relationship between the BRW and the PD.
Note that this continuous function allows the bank to choose the number of risk cat-
egories in the internal risk rating system, as long as there is a minimum of six to nine
grades for performing borrowers and two grades for nonperforming borrowers.^42
Consultation between the Basel Committee on Banking Supervision and the pub-
lic fueled concerns about the calibration of the Foundation Approach as presented in
equations (1) and (2). This concern was galvanized by the results of a Quantitative
Impact Study (QIS2) that examined the impact of the BIS II proposals on the capital
requirements of 138 large and small banks from 25 countries. Banks that would have
adopted the IRB Foundation Approach would have seen an unintended 14% increase
in their capital requirements. Potential modifications were released on November 5,

y N 1 y 2 
z

y G 1 z 2

N 1 y 2

3 • 12 BIS BASEL INTERNATIONAL BANK CAPITAL ACCORDS

Source: BIS (2001), “The Internal Ratings–Based Approach.”

Exhibit 3.6. Proposed IRB Risk Weights for Hypothetical Corporate Exposure Having LGD
Equal to 50 Percent.

700

600

500

400

300

200

100

0

0 5 10 15 20

PD (Percent)

Risk Weight (Percent)

(^41) Historical insolvency for AA (A) rated bonds corresponds to a 99.97% (99.5%) target loss per-
centile, Jackson et al. (2001) use CreditMetrics to show that BIS I provides a 99.9% solvency rate (equiv-
alent to a BBB rating) for a high-quality bank portfolio and 99% (BB rating) for a lower-quality bank
portfolio.
(^42) Treacy and Carey (2000) document that bank internal ratings systems generally have more than 10
rating classifications.