1. Risk-weighted Assets for Corporate, Sovereign, and Bank Exposures
(i) Formula for Derivation of Risk-weighted Assets
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.
Apr 08CA-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.
Apr 08(ii) Firm-size Adjustment for Small- and Medium-sized Entities (SME)
CA-5.3.4
Under the IRB approach for corporate credits, banks will be permitted to separately distinguish exposures to SME borrowers (defined as corporate exposures, being an unlisted or unincorporated enterprise where the reported annual sales for the consolidated group of which the firm is a part is less than BD 2 million) from those to large firms. A firm-size adjustment (i.e. 0.04 x (1 - (S - 0.2)/1.8)) is made to the corporate risk weight formula for exposures to SME borrowers. S is expressed as total annual sales in millions of BD with values of S falling in the range of equal to or less than BD 2 million or greater than or equal to BD 0.2 million. Reported sales of less than 0.2 million BD will be treated as if they were equivalent to 0.2 million BD for the purposes of the firm-size adjustment for SME borrowers.
Correlation (R) = 0.12 × (1 - EXP(-50 × PD)) / (1 - EXP(-50)) + 0.24 × [1 - (1 - EXP(-50 × PD)) / (1 - EXP(-50))] - 0.04 × (1 - (S-0.2) / 1.8)
Apr 08CA-5.3.5
Banks are allowed, as a failsafe, to substitute total assets of the consolidated group for total sales in calculating the SME threshold and the firm-size adjustment. However, total assets should be used only when total sales are not a meaningful indicator of firm size. The criteria for definition of SME will be assessed by CBB on a regular basis. The external auditors are required to assess the reasonableness of identification criteria.
Apr 08(iii) Risk Weights for Specialised Lending
Risk Weights for PF, OF, CF, and IPRE
CA-5.3.6
Banks that do not meet the requirements for the estimation of PD under the corporate IRB approach will be required to map their internal grades to five supervisory categories, each of which is associated with a specific risk weight. The slotting criteria on which this mapping must be based are provided in Appendix CA-7. The risk weights for unexpected losses associated with each supervisory category are:
Supervisory Categories and UL Risk Weights for other SL Exposures
Strong Good Satisfactory Weak Default 70% 90% 115% 250% 0% Amended: April 2011
Apr 08CA-5.3.7
Although banks are expected to map their internal ratings to the supervisory categories for specialised lending using the slotting criteria provided in Appendix CA-7, each supervisory category broadly corresponds to a range of external credit assessments as outlined below.
Strong Good Satisfactory Weak Default BBB- or better BB+ or BB BB- or B+ B to C- Not applicable Apr 08CA-5.3.8
Banks that meet the requirements for the estimation of PD will be able to use the general foundation approach for the corporate asset class to derive risk weights for SL sub- classes.
Apr 08Risk Weights for HVCRE
CA-5.3.9
Banks that do not meet the requirements for estimation of PD, must map their internal grades to five supervisory categories, each of which is associated with a specific risk weight. The slotting criteria on which this mapping must be based are the same as those for IPRE, as provided in Appendix CA-7. The risk weights associated with each category are:
Supervisory Categories and UL Risk Weights for High-volatility Commercial Real Estate
Strong Good Satisfactory Weak Default 95% 120% 140% 250% 0% Amended: April 2011
Apr 08CA-5.3.10
As indicated in paragraph CA-5.3.7, each supervisory category broadly corresponds to a range of external credit assessments.
Apr 08CA-5.3.11
Banks that meet the requirements for the estimation of PD will use the same formula for the derivation of risk weights that is used for other SL exposures, except that they will apply the following asset correlation formula:
Correlation (R) = 0.12 x (1 - EXP(-50 × PD)) / (1 - EXP(-50)) + 0.30 x [1 - (1 - EXP(-50 × PD)) / (1 - EXP(-50))]
Apr 08(iv) Calculation of Risk-weighted Assets for Exposures Subject to the Double Default Framework
CA-5.3.12
For hedged exposures to be treated within the scope of the double default framework, capital requirements may be calculated according to paragraphs CA-5.3.13 to CA-5.3.16.
Apr 08CA-5.3.13
The capital requirement for a hedged exposure subject to the double default treatment (KDD) is calculated by multiplying K0 as defined below by a multiplier depending on the PD of the protection provider (PDg):
KDD = K0 . ( 0.15 + 160 . PDg)
Apr 08CA-5.3.14
K0 is calculated in the same way as a capital requirement for an unhedged corporate exposure (as defined in paragraphs CA-5.3.3 and CA-5.3.4), but using different parameters for LGD and the maturity adjustment.
Apr 08CA-5.3.15
PDo and PDg are the probabilities of default of the obligor and guarantor, respectively, both subject to the PD floor set out in paragraph CA-5.3.17. The correlation Pos is calculated according to the formula for correlation (R) in paragraph CA-5.3.3 (or, if applicable, paragraph CA-5.3.4), with PD being equal to PDo, and LGDg is the LGD of a comparable direct exposure to the guarantor (i.e. consistent with paragraph CA-5.3.29, the LGD associated with an unhedged facility to the guarantor or the unhedged facility to the obligor, depending upon whether in the event both the guarantor and the obligor default during the life of the hedged transaction available evidence and the structure of the guarantee indicate that the amount recovered would depend on the financial condition of the guarantor or obligor, respectively; in estimating either of these LGDs, a bank may recognise collateral posted exclusively against the exposure or credit protection, respectively, in a manner consistent with paragraphs CA-5.3.31 or CA-5.3.8 and CA-5.8.79 to CA-5.8.83, as applicable). There may be no consideration of double recovery in the LGD estimate. The maturity adjustment coefficient b is calculated according to the formula for maturity adjustment (b) in paragraph CA-5.3.3, with PD being the minimum of PDo and PDg M is the effective maturity of the credit protection, which may under no circumstances be below the one-year floor if the double default framework is to be applied.
Apr 08CA-5.3.16
The risk-weighted asset amount is calculated in the same way as for unhedged exposures, i.e
RWADD = KDD × 12.5 × EADg
Apr 08
