CA-5.3.2

The derivation of risk-weighted assets is dependent on estimates of the PD, LGD, EAD and, in some cases, effective maturity (M), for a given exposure. Paragraphs CA-5.3.45 to CA-5.3.50 discuss the circumstances in which the maturity adjustment applies.

CA-5.3.3

Throughout this section, PD and LGD are measured as decimals, and EAD is measured as currency (e.g. euros), except where explicitly noted otherwise. For exposures not in default, the formula for calculating risk-weighted assets is:³⁷, ³⁸

Correlation (R) = 0.12 × (1 - EXP(-50 × PD)) / (1 - EXP(-50)) + 0.24 × [1 - (1 - EXP(-50 × PD)) / (1 - EXP(-50))]

Maturity adjustment (b) = (0.11852 - 0.05478 × ln(PD))^2

Capital requirement³⁹ (K) = [LGD × N[(1 - R)^-0.5 × G(PD) + (R / (1 - R))^0.5 × G(0.999)] - PD x LGD] x (1 - 1.5 x b)^-1 × (1 + (M - 2.5) × b)

Risk-weighted assets (RWA) = K × 12.5 × EAD

The capital requirement (K) for a defaulted exposure is equal to the greater of zero and the difference between its LGD (described in paragraph CA-5.8.79) and the bank's best estimate of expected loss (described in paragraph CA-5.8.82). The risk-weighted asset amount for the defaulted exposure is the product of K, 12.5, and the EAD.

Illustrative risk weights are shown in Appendix CA-6.

³⁷Ln denotes the natural logarithm.

³⁸N(x) 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 x). G(z) denotes the inverse cumulative distribution function for a standard normal random variable (i.e. the value of x such that N(x) = z). The normal cumulative distribution function and the inverse of the normal cumulative distribution function are, for example, available in Excel as the functions NORMSDIST and NORMSINV.

³⁹If this calculation results in a negative capital charge for any individual sovereign exposure, banks must apply a zero capital charge for that exposure.