2. Foundation and advanced approaches

244. For each of the asset classes covered under the IRB framework, there are three key elements:

• Risk components ─ estimates of risk parameters provided by banks some of which are supervisory estimates.

• Risk-weight functions ─ the means by which risk components are transformed into risk-weighted assets and therefore capital requirements.

• Minimum requirements ─ the minimum standards that must be met in order for a bank to use the IRB approach for a given asset class.

245. For many of the asset classes, the Committee has made available two broad approaches: a foundation and an advanced. Under the foundation approach, as a general rule, banks provide their own estimates of PD and rely on supervisory estimates for other risk components.

Under the advanced approach, banks provide more of their own estimates of PD, LGD and EAD, and their own calculation of M, subject to meeting minimum standards.

For both the foundation and advanced approaches, banks must always use the risk-weight functions provided in this Framework for the purpose of deriving capital requirements.

The full suite of approaches is described below.

(i) Corporate, sovereign, and bank exposures

246. Under the foundation approach, banks must provide their own estimates of PD associated with each of their borrower grades, but must use supervisory estimates for the other relevant risk components.

The other risk components are LGD, EAD and M. *

* As noted in paragraph 318, some supervisors may require banks using the foundation approach to calculate M using the definition provided in paragraphs 320 to 324.

247. Under the advanced approach, banks must calculate the effective maturity (M) * and provide their own estimates of PD, LGD and EAD.

* At the discretion of the national supervisor, certain domestic exposures may be exempt from the calculation of
M (see paragraph 319).

248. There is an exception to this general rule for the five sub-classes of assets identified as SL.

The SL categories: PF, OF, CF, IPRE, and HVCRE

249. Banks that do not meet the requirements for the estimation of PD under the corporate foundation approach for their SL assets are required to map their internal risk grades to five supervisory categories, each of which is associated with a specific risk weight.

This version is termed the ‘supervisory slotting criteria approach’.

250. Banks that meet the requirements for the estimation of PD are able to use the foundation approach to corporate exposures to derive risk weights for all classes of SL exposures except HVCRE.

At national discretion, banks meeting the requirements for HVCRE exposure are able to use a foundation approach that is similar in all respects to the corporate approach, with the exception of a separate risk-weight function as described in paragraph 283.

251. Banks that meet the requirements for the estimation of PD, LGD and EAD are able to use the advanced approach to corporate exposures to derive risk weights for all classes of SL exposures except HVCRE.

At national discretion, banks meeting these requirements for HVCRE exposure are able to use an advanced approach that is similar in all respects to the corporate approach, with the exception of a separate risk-weight function as described in paragraph 283.

(ii) Retail exposures

252. For retail exposures, banks must provide their own estimates of PD, LGD and EAD.

There is no distinction between a foundation and advanced approach for this asset class.

(iii) Equity exposures

253. There are two broad approaches to calculate risk-weighted assets for equity exposures not held in the trading book: a market-based approach and a PD/LGD approach.

These are set out in full in paragraphs 340 to 361.

254. The PD/LGD approach to equity exposures remains available for banks that adopt the advanced approach for other exposure types.

(iv) Eligible purchased receivables

255. The treatment potentially straddles two asset classes.

For eligible corporate receivables, both a foundation and advanced approach are available subject to certain operational requirements being met. For eligible retail receivables, as with the retail asset class, there is no distinction between a foundation and advanced approach.

3. Adoption of the IRB approach across asset classes

256. Once a bank adopts an IRB approach for part of its holdings, it is expected to extend it across the entire banking group. The Committee recognises however, that, for many banks, it may not be practicable for various reasons to implement the IRB approach across all material asset classes and business units at the same time.

Furthermore, once on IRB, data limitations may mean that banks can meet the standards for the use of own estimates of LGD and EAD for some but not all of their asset classes/business units at the same time.

257. As such, supervisors may allow banks to adopt a phased rollout of the IRB approach across the banking group.

The phased rollout includes

(i) adoption of IRB across asset classes within the same business unit (or in the case of retail exposures across individual sub-classes);

(ii) adoption of IRB across business units in the same banking group; and

(iii) move from the foundation approach to the advanced approach for certain risk components.

However, when a bank adopts an IRB approach for an asset class within a particular business unit (or in the case of retail exposures for an individual sub-class), it must apply the IRB approach to all exposures within that asset class (or sub-class) in that unit.

258. A bank must produce an implementation plan, specifying to what extent and when it intends to roll out IRB approaches across significant asset classes (or sub-classes in the case of retail) and business units over time.

The plan should be exacting, yet realistic, and must be agreed with the supervisor.

It should be driven by the practicality and feasibility of moving to the more advanced approaches, and not motivated by a desire to adopt a Pillar 1 approach that minimises its capital charge.

During the roll-out period, supervisors will ensure that no capital relief is granted for intra-group transactions which are designed to reduce a banking group’s aggregate capital charge by transferring credit risk among entities on the
standardised approach, foundation and advanced IRB approaches.

This includes, but is not limited to, asset sales or cross guarantees.

259. Some exposures in non-significant business units as well as asset classes (or subclasses in the case of retail) that are immaterial in terms of size and perceived risk profile may be exempt from the requirements in the previous two paragraphs, subject to supervisory approval.

Capital requirements for such operations will be determined according to the standardised approach, with the national supervisor determining whether a bank should hold more capital under Pillar 2 for such positions.

260. Notwithstanding the above, once a bank has adopted the IRB approach for all or part of any of the corporate, bank, sovereign, or retail asset classes, it will be required to adopt the IRB approach for its equity exposures at the same time, subject to materiality.

Supervisors may require a bank to employ one of the IRB equity approaches if its equity exposures are a significant part of the bank’s business, even though the bank may not employ an IRB approach in other business lines.

Further, once a bank has adopted the general IRB approach for corporate exposures, it will be required to adopt the IRB approach for the SL sub-classes within the corporate exposure class.

261. Banks adopting an IRB approach are expected to continue to employ an IRB approach.

A voluntary return to the standardised or foundation approach is permitted only in extraordinary circumstances, such as divestiture of a large fraction of the bank’s creditrelated business, and must be approved by the supervisor.

262. Given the data limitations associated with SL exposures, a bank may remain on the supervisory slotting criteria approach for one or more of the PF, OF, CF, IPRE or HVCRE sub-classes, and move to the foundation or advanced approach for other sub-classes within the corporate asset class.

However, a bank should not move to the advanced approach for the HVCRE sub-class without also doing so for material IPRE exposures at the same time.

4. Transition arrangements

(i) Parallel calculation

263. Banks adopting the foundation or advanced approaches are required to calculate their capital requirement using these approaches, as well as the 1988 Accord for the time period specified in paragraphs 45 to 49.

Parallel calculation for banks adopting the foundation IRB approach to credit risk will start in the year beginning year-end 2005.

Banks moving directly from the 1988 Accord to the advanced approaches to credit and/or operational risk will be subject to parallel calculations or impact studies for the year beginning year-end 2005 and to parallel calculations for the year beginning year-end 2006.

(ii) Corporate, sovereign, bank, and retail exposures

264. The transition period starts on the date of implementation of this Framework and will last for 3 years from that date. During the transition period, the following minimum requirements can be relaxed, subject to discretion of the national supervisor:

• For corporate, sovereign, and bank exposures under the foundation approach, paragraph 463, the requirement that, regardless of the data source, banks must use at least five years of data to estimate the PD; and

• For retail exposures, paragraph 466, the requirement that regardless of the data source banks must use at least five years of data to estimate loss characteristics (EAD, and either expected loss (EL) or PD and LGD).

• For corporate, sovereign, bank, and retail exposures, paragraph 445, the requirement that a bank must demonstrate it has been using a rating system that was broadly in line with the minimum requirements articulated in this document for at least three years prior to qualification.

• The applicable aforementioned transitional arrangements also apply to the PD/LGD approach to equity. There are no transitional arrangements for the market-based approach to equity.

265. Under these transitional arrangements banks are required to have a minimum of two years of data at the implementation of this Framework. This requirement will increase by one year for each of three years of transition.

266. Owing to the potential for very long-run cycles in house prices which short-term data may not adequately capture, during this transition period, LGDs for retail exposures secured by residential properties cannot be set below 10% for any sub-segment of exposures to which the formula in paragraph 328 is applied. *

During the transition period the Committee will review the potential need for continuation of this floor.

* The 10% LGD floor shall not apply, however, to sub-segments that are subject to/benefit from sovereign guarantees. Further, the existence of the floor does not imply any waiver of the requirements of LGD estimation as laid out in the minimum requirements starting with paragraph 468.

(iii) Equity exposures

267. For a maximum of ten years, supervisors may exempt from the IRB treatment particular equity investments held at the time of the publication of this Framework.*

The exempted position is measured as the number of shares as of that date and any additional arising directly as a result of owning those holdings, as long as they do not increase the proportional share of ownership in a portfolio company.

* This exemption does not apply to investments in entities where some countries will retain the existing risk weighting treatment, as referred to in Part 1, see footnote 9.

268. If an acquisition increases the proportional share of ownership in a specific holding (e.g. due to a change of ownership initiated by the investing company subsequent to the publication of this Framework) the exceeding part of the holding is not subject to the exemption.

Nor will the exemption apply to holdings that were originally subject to the exemption, but have been sold and then bought back.

269. Equity holdings covered by these transitional provisions will be subject to the capital requirements of the standardised approach.

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:

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.

* Ln denotes the natural logarithm.

** N(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.

(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 AnneAnnex 6.

The risk weights for unexpected losses associated with each supervisory category are:

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.

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 subclasses.

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:

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).

284(iii). The risk-weighted asset amount is calculated in the same way as for unhedged
exposures, i.e.

2. Risk components

(i) Probability of default (PD)

285. For corporate and bank exposures, the PD is the greater of the one-year PD associated with the internal borrower grade to which that exposure is assigned, or 0.03%.

For sovereign exposures, the PD is the one-year PD associated with the internal borrower grade to which that exposure is assigned.

The PD of borrowers assigned to a default grade(s), consistent with the reference definition of default, is 100%.

The minimum requirements for the derivation of the PD estimates associated with each internal borrower
grade are outlined in paragraphs 461 to 463.

(ii) Loss given default (LGD)

286. A bank must provide an estimate of the LGD for each corporate, sovereign and bank exposure. There are two approaches for deriving this estimate: a foundation approach and an advanced approach.

LGD under the foundation approach

Treatment of unsecured claims and non-recognised collateral

287. Under the foundation approach, senior claims on corporates, sovereigns and banks not secured by recognised collateral will be assigned a 45% LGD.

288. All subordinated claims on corporates, sovereigns and banks will be assigned a 75% LGD.

A subordinated loan is a facility that is expressly subordinated to another facility.

At national discretion, supervisors may choose to employ a wider definition of subordination.

This might include economic subordination, such as cases where the facility is unsecured and the bulk of the borrower’s assets are used to secure other exposures.

Collateral under the foundation approach

289. In addition to the eligible financial collateral recognised in the standardised approach, under the foundation IRB approach some other forms of collateral, known as eligible IRB collateral, are also recognised.

These include receivables, specified commercial and residential real estate (CRE/RRE), and other collateral, where they meet the minimum requirements set out in paragraphs 509 to 524. *

For eligible financial collateral, the requirements are identical to the operational standards as set out in Section II.D beginning with paragraph 111.

* The Committee, however, recognises that, in exceptional circumstances for well-developed and long established markets, mortgages on office and/or multi-purpose commercial premises and/or multi-tenanted commercial premises may have the potential to receive alternative recognition as collateral in the corporate portfolio.

Please refer to footnote 29 of paragraph 74 for a discussion of the eligibility criteria that would apply.

The LGD applied to the collateralised portion of such exposures, subject to the limitations set out in paragraphs 119 to 181 (i) of the standardised approach, will be set at 35%. The LGD applied to the remaining portion of this exposure will be set at 45%.

In order to ensure consistency with the capital charges in the standardised approach (while providing a small capital incentive in the IRB approach relative to the standardised approach), supervisors may apply a cap on the capital charge associated with such exposures so as to achieve comparable treatment in both approaches.

Methodology for recognition of eligible financial collateral under the foundation approach

290. The methodology for the recognition of eligible financial collateral closely follows that outlined in the comprehensive approach to collateral in the standardised approach in paragraphs 147 to 181(i).

The simple approach to collateral presented in the standardised approach will not be available to banks applying the IRB approach.

291. Following the comprehensive approach, the effective loss given default (LGD*) applicable to a collateralised transaction can be expressed as follows, where:

• LGD is that of the senior unsecured exposure before recognition of collateral (45%);

• E is the current value of the exposure (i.e. cash lent or securities lent or posted);

• E* is the exposure value after risk mitigation as determined in paragraphs 147 to 150 of the standardised approach. This concept is only used to calculate LGD*.

Banks must continue to calculate EAD without taking into account the presence of any collateral, unless otherwise specified.

LGD* = LGD x (E* / E)

292. Banks that qualify for the foundation IRB approach may calculate E* using any of the ways specified under the comprehensive approach for collateralised transactions under the standardised approach.

293. Where repo-style transactions are subject to a master netting agreement, a bank may choose not to recognise the netting effects in calculating capital.

Banks that want to recognise the effect of master netting agreements on such transactions for capital purposes
must satisfy the criteria provided in paragraph 173 and 174 of the standardised approach.

The bank must calculate E* in accordance with paragraphs 176 and 177 or 178 to 181 (i) and equate this to EAD. The impact of collateral on these transactions may not be reflected through an adjustment to LGD.

Carve out from the comprehensive approach

294. As in the standardised approach, for transactions where the conditions in paragraph 170 are met, and in addition, the counterparty is a core market participant as specified in paragraph 171, supervisors may choose not to apply the haircuts specified under the comprehensive approach, but instead to apply a zero H.

Methodology for recognition of eligible IRB collateral

295. The methodology for determining the effective LGD under the foundation approach for cases where banks have taken eligible IRB collateral to secure a corporate exposure is as follows.

• Exposures where the minimum eligibility requirements are met, but the ratio of the current value of the collateral received (C) to the current value of the exposure (E) is below a threshold level of C* (i.e. the required minimum collateralisation level for the exposure) would receive the appropriate LGD for unsecured exposures or those
secured by collateral which is not eligible financial collateral or eligible IRB collateral.

• Exposures where the ratio of C to E exceeds a second, higher threshold level of C** (i.e. the required level of over-collateralisation for full LGD recognition) would be assigned an LGD according to the following table.

The following table displays the applicable LGD and required over-collateralisation levels for the secured parts of senior exposures:

74 Other collateral excludes physical assets acquired by the bank as a result of a loan default.

• Senior exposures are to be divided into fully collateralised and uncollateralised portions.

• The part of the exposure considered to be fully collateralised, C/C**, receives the LGD associated with the type of collateral.

• The remaining part of the exposure is regarded as unsecured and receives an LGD of 45%.

Methodology for the treatment of pools of collateral

296. The methodology for determining the effective LGD of a transaction under the foundation approach where banks have taken both financial collateral and other eligible IRB collateral is aligned to the treatment in the standardised approach and based on the following guidance.

• In the case where a bank has obtained multiple forms of CRM, it will be required to subdivide the adjusted value of the exposure (after the haircut for eligible financial collateral) into portions each covered by only one CRM type.

That is, the bank must divide the exposure into the portion covered by eligible financial collateral, the portion covered by receivables, the portion covered by CRE/RRE collateral, a portion covered by other collateral, and an unsecured portion, where relevant.

• Where the ratio of the sum of the value of CRE/RRE and other collateral to the reduced exposure (after recognising the effect of eligible financial collateral and receivables collateral) is below the associated threshold level (i.e. the minimum degree of collateralisation of the exposure), the exposure would receive the appropriate unsecured LGD value of 45%.

• The risk-weighted assets for each fully secured portion of exposure must be calculated separately.

LGD under the advanced approach

297. Subject to certain additional minimum requirements specified below, supervisors may permit banks to use their own internal estimates of LGD for corporate, sovereign and bank exposures.

LGD must be measured as the loss given default as a percentage of the EAD. Banks eligible for the IRB approach that are unable to meet these additional minimum requirements must utilise the foundation LGD treatment described above.

298. The minimum requirements for the derivation of LGD estimates are outlined in paragraphs 468 to 473.

Treatment of certain repo-style transactions

299. Banks that want to recognise the effects of master netting agreements on repo-style transactions for capital purposes must apply the methodology outlined in paragraph 293 for determining E* for use as the EAD. For banks using the advanced approach, own LGD estimates would be permitted for the unsecured equivalent amount (E*).

Treatment of guarantees and credit derivatives

300. There are two approaches for recognition of CRM in the form of guarantees and credit derivatives in the IRB approach: a foundation approach for banks using supervisory values of LGD, and an advanced approach for those banks using their own internal estimates of LGD.

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