Title[ Part 2: The First Pillar - Minimum Capital Requirements
Section[ C. Rules for corporate, sovereign, and bank exposures
270. Section III.C presents the method of calculating the unexpected loss (UL) capital requirements for corporate, sovereign and bank exposures. As discussed in Section C.1, one risk-weight function is provided for determining the capital requirement for all three asset classes with one exception. Supervisory risk weights are provided for each of the specialised lending sub-classes of corporates, and a separate risk-weight function is also provided for HVCRE. Section C.2 discusses the risk components. The method of calculating expected losses, and for determining the difference between that measure and provisions is described in Section III.G.
1. Risk-weighted assets for corporate, sovereign, and bank exposures
(i) Formula for derivation of risk-weighted assets
271. 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 318 to 324 discuss the circumstances in which the maturity adjustment applies.
272. 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: 70, 71
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 requirement72 (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 x 12.5 x 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 468) and the bank’s best estimate of expected loss (described in paragraph 471). 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 Annex 5.
(ii) Firm-size adjustment for small- and medium-sized entities (SME)
273. Under the IRB approach for corporate credits, banks will be permitted to separately distinguish exposures to SME borrowers (defined as corporate exposures where the reported sales for the consolidated group of which the firm is a part is less than €50 million) from those to large firms. A firm-size adjustment (i.e. 0.04 x (1 – (S – 5) / 45)) is made to the corporate risk weight formula for exposures to SME borrowers. S is expressed as total annual sales in millions of euros with values of S falling in the range of equal to or less than €50 million or greater than or equal to €5 million. Reported sales of less than €5 million will be treated as if they were equivalent to €5 million 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–5) / 45)
274. Subject to national discretion, supervisors may allow banks, 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.
(iii) Risk weights for specialised lending
Risk weights for PF, OF, CF, and IPRE
275. 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 Annex 6. 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%
276. Although banks are expected to map their internal ratings to the supervisory categories for specialised lending using the slotting criteria provided in Annex 6, 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
277. At national discretion, supervisors may allow banks to assign preferential risk weights of 50% to “strong” exposures, and 70% to “good” exposures, provided they have a remaining maturity of less than 2.5 years or the supervisor determines that banks’ underwriting and other risk characteristics are substantially stronger than specified in the slotting criteria for the relevant supervisory risk category.
278. 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.
279. Banks that meet the requirements for the estimation of PD and LGD and/or EAD will be able to use the general advanced approach for the corporate asset class to derive risk weights for SL sub-classes.
Risk weights for HVCRE
280. Banks that do not meet the requirements for estimation of PD, or whose supervisor has chosen not to implement the foundation or advanced approaches to HVCRE, 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 Annex 6. 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%
281. As indicated in paragraph 276, each supervisory category broadly corresponds to a range of external credit assessments.
282. At national discretion, supervisors may allow banks to assign preferential risk weights of 70% to “strong” exposures, and 95% to “good” exposures, provided they have a remaining maturity of less than 2.5 years or the supervisor determines that banks’ underwriting and other risk characteristics are substantially stronger than specified in the slotting criteria for the relevant supervisory risk category.
283. Banks that meet the requirements for the estimation of PD and whose supervisor has chosen to implement a foundation or advanced approach to HVCRE exposures 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 x PD)) / (1 – EXP(-50)) +
0.30 x [1 – (1 – EXP(-50 x PD)) / (1 – EXP(-50))]
284. Banks that do not meet the requirements for estimation of LGD and EAD for HVCRE
exposures must use the supervisory parameters for LGD and EAD for corporate exposures.
(iv) Calculation of risk-weighted assets for exposures subject to the double default framework
284 (i). For hedged exposures to be treated within the scope of the double default framework, capital requirements may be calculated according to paragraphs 284 (ii) and
284 (iii).
284 (ii). 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):
w is calculated in the same way as a capital requirement for an unhedged corporate exposure (as defined in paragraphs 272 and 273), but using different parameters for LGD and the maturity adjustment.
PDo and PDg are the probabilities of default of the obligor and guarantor, respectively, both subject to the PD floor set out in paragraph 285. The correlation ?os is calculated according to the formula for correlation (R) in paragraph 272 (or, if applicable, paragraph 273), with PD being equal to PDo, and LGDg is the LGD of a comparable direct exposure to the guarantor
(i.e. consistent with paragraph 301, 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 303 or 279 and 468 to
473, 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 272, 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.
284 (iii). The risk-weighted asset amount is calculated in the same way as for unhedged exposures, i.e.
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