Annex 6
to the Regulations No. 60
of the Financial and Capital Market Commission
of 2 May 2007
Calculation of Capital Requirement for Credit Risk under the Internal Ratings Based Approach
Section 1. Risk–weighted Exposure Amount and Expected Loss Amount
1. Calculation of Risk–weighted Exposure Amount
1. Unless noted otherwise, the input parameters of the probability of default (PD), loss given default (LGD) and maturity value (M) shall be determined as set out in Section 2 and the exposure value shall be determined as set out in Section 3.
2. The risk–weighted exposure amount for each exposure shall be calculated in accordance with the formulae set out in Paragraphs 3–27.
1.1. Risk–weighted Exposure Amount for Exposures to Corporates, Institutions, Central Governments and Central Banks
3. Subject to Paragraphs 5–9, the risk–weighted exposure amount for exposures to corporates, institutions, central governments and central banks shall be calculated according to the following formulae:
Correlation (R) = 0,12*(1─EXP(─50* PD))/(1─EXP(─50))+0,24*
[1─(1─EXP(─50*PD))/(1─EXP(─50))]
Maturity factor (b) = (0,11852─0,05478*ln(PD))2
Risk weighting (RW) = PD*(N[(1─R)–0,5*G(PD)+(R/(1─R))0,5*G(0,999)]─
PD*LGD)*(1─1,5*b)–1*(1+(T–2,5)*b)*12,5*1,06,
where:
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 1 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 X such that N(X)=Z)
Where PD = 0, RW shall be also 0%.
Where PD = 1, then:
— for defaulted exposures where an institution applies LGD in accordance with Paragraph 44 of Section 2, RW shall be 0%;
— for defaulted exposures where an institution uses its own estimates of LGD, RW shall be Max{0, 12,5 *(LGD–ELBE) where ELBE is the best estimate of expected loss for defaulted exposures, in accordance with Paragraph 157 of Section 4 of this Annex.
Risk—weighted exposure amount = RW * exposure value.
4. The risk–weighted exposure amount for each exposure whose collateral meets the requirements set out in Paragraph 14 of Section 1 of Annex 3 and Paragraph 40 of Section 2 of Annex 3 may be adjusted according to the following formula:
Risk—weighted exposure amount = RW * exposure value * ((0,15 + 160*PDPP)]
where PDPP is the PD of the protection provider.
In this case, RW shall be calculated using the formula set out in Paragraph 3 by entering the following parameters:
–PD is the PD of the obligor;
–LGD is the LGD determined for direct exposures to protection provider;
–maturity factor (b) is calculated using the lower of PD of the protection provider and the PD of the obligor.
5. For calculating risk weights for exposures to corporates in the consolidation group where the total annual turnover is less than EUR 50 million, an institution shall be entitled to use the following correlation formula:
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),
where S is the total annual turnover, expressed in millions of euros, of the consolidation group and S is larger than 5 million euros but smaller than 50 million euros. Where the turnover is less than 5 million euros, it shall be treated as if it were equivalent to 5million euros. For the purchased receivables the total annual turnover shall be determined in proportion to the weighted average value for individual exposures in the portfolio.
An institution shall substitute the total annual turnover with the assets of the consolidated group where the total annual turnover is not a meaningful indicator of a corporate's size but total assets are a more meaningful indicator than the total annual turnover.
6. For specialised lending exposures in respect of which PD is determined not in compliance with the minimum requirements set out in Section 4 of this Annex, risk weights shall be assigned according to Table 1.
Table 1.Risk weights of specialised lending exposures
Residual maturity / Class 1* / Class 2 / Class 3 / Class 4 / Class 5Less than 2,5 years / 50% / 70% / 115% / 250% / 0%
Equal to or more than 2,5 years / 70% / 90% / 115% / 250% / 0%
*Basel II document sets out the probable distribution of specialised lending exposures across classes
When assigning risk weights to specialised lending exposures, an institution shall take into account the following factors: financial strength of a corporate, political and legal environment, characteristics of a transaction or of an asset, strength of the sponsor and the developer, including any public private partnership income flow, and security package.
7. In order that the treatment applied to exposures to corporate be applied to the purchased receivables of corporates, they shall comply with the minimum requirements set out in Paragraphs 182–186 of Section 4. Where the purchased receivables of corporates meet also the conditions set out in Paragraph 14 of this Section and where it would be unduly burdensome for an institution to apply the risk quantification standards for exposures to corporates as set out in Section 4, an institution shall be entitled to use the risk quantification standards for portfolio of retail exposures as set out in Section 4.
8. For the purchased receivables of corporates, refundable purchase discounts, collateral or partial guarantees that provide first–loss protection for default losses, dilution losses, or both, may be treated as first–loss positions under the IRB securitisation framework.
9. Where an institution provides credit protection for a number of exposures under terms that the nth default among the exposures shall be the threshold at which payments for the credit protection under the contract shall be made and that this credit event shall terminate the contract for the protection, the risk weight for such protection credit derivative instrument shall be determined as follows:
9.1. where the protection instrument has an ECAI rating, the risk weight established in accordance with the requirements of Section 5 of Title II of the Regulations shall apply to exposures subject to protection;
9.2. where the protection instrument does not have an ECAI rating, the risk weight for the basket of protected exposures shall be determined as the sum of proportional risk weights of exposures included in the basket, excluding n–1 exposures. The risk–weighted value of the basket of exposures shall be calculated by multiplying the sum of proportionate risk weights with the sum of the exposure values in the basket, excluding n–1 exposures. Where the sum of the risk–weighted exposure amount of the basket of protected exposures and of the expected loss, multiplied with 12,5, is larger than the protection payment ensured by the credit derivative instrument, multiplied with 12,5, the risk–weighted exposure amount of the basket of protected exposures shall be the result of the last result (protection payment multiplied with 12,5). When establishing n–1 exposures to be excluded from the aggregation, the basis shall be that for each exposure the risk–weighted value is lower than the risk–weighted value for any exposure included in the aggregation.
1.2. Risk–weighted Exposure Amount of a Portfolio of Retail Exposures
10. Subject to the requirements set out in Paragraphs 12 and 13, the risk–weighted exposure amount for a portfolio of retail exposures shall be calculated according to the following formulae:
Correlation (R) = 0,03*(1─EXP(─35*PD))/(1─EXP(─35))+0,16*
[1─(1─EXP(─35*PD))/(1─EXP(─35))]
Risk weight (RW) =
(LGD*N[(1─R)–0,5*G(PD)+(R/(1─R))0,5*G(0.999)]─PD*LGD)*12,5*1,06,
where:
N(X) denotes the cumulative distribution function for a standard normal random variable (i. e., the probability that a normal random variable with the mean value of 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 X such that N(X)=Z).
Where PD=1 (defaulted exposure), RW shall be Max{0, 12.5*(LGD–ELBE)}, where ELBE is the institution’s own best estimate of EL in respect of defaulted exposures according to the conditions of Paragraph 157 of Section 4 of this Annex.
Risk—weighted exposure amount (RWE) = RW * exposure value.
11. Subject to the criteria set out in Paragraph 123 of Chapter 2 of Title II, the risk– weighted exposure amount for each exposure to small and medium sized entities as included in the portfolio of retail exposures may be adjusted in accordance with Paragraph 4 of this Annex provided that the collateral meets the requirements of Paragraph 14of Section 1 of Annex 3 and of Paragraph 40 of Section 2 of Annex 3.
12. For the portfolio of retail exposures secured by a real estate collateral, a correlation (R) of 0,15 shall replace the figure produced by the correlation formula in Paragraph 10.
13. For qualifying revolving exposures included in the portfolio of retail exposures as defined in Paragraphs 13.1–13.5, the correlation (R) of 0,04 shall replace the figure produced by the correlation formula in Paragraph 10. The set of qualifying revolving exposures in the portfolio of retail exposures constitute a sub–portfolio of retail exposures. Exposures shall qualify as qualifying revolving exposures in the portfolio of retail exposures where they meet the following conditions:
13.1. the exposures are to natural persons;
13.2. the exposures are revolving, unsecured, and an institution shall be entitled to cancel them immediately and unconditionally to the extent they are not drawn (in this context, revolving exposures are defined as those exposures where customers' outstanding balances are permitted to fluctuate based on their decisions to borrow and repay, within the limit established by an institution.). Undrawn granted credits may be considered as unconditionally cancellable where the terms of the credit permit the institution to cancel them to the full extent allowable under consumer protection and related legislation. An institution shall be entitled to recognise as unsecured those exposures that are secured with a balance in the salary account. In that case the balance of the exposure that is secured with the balance on the salary account shall not be taken into account when estimating LGD;
13.3. the maximum permissible qualifying revolving retail exposure to a single natural person in the sub–portfolio is EUR 100 000 or less;
13.4. an institution can demonstrate that the use of the correlation formula as set out in this Paragraph is limited to sub–portfolios that have exhibited low volatility of loss rates relative to their average level of loss rates, especially within the transactions of low PD bands;
13.5. the Commission concurs with the institution’s assessment and procedures whereby a qualifying revolving retail exposure is included in the respective sub–portfolio.
14. To be eligible for the inclusion in the portfolio of retail exposures, the purchased receivables shall comply with the minimum requirements set out in Paragraphs 182–186 of Section 4 and the following conditions:
14.1. an institution has purchased the receivables from unrelated third parties and its exposure to the obligor as a result of the purchase does not include any exposures that are directly or indirectly originated by the institution itself;
14.2. the purchased receivables were generated on an arm's–length basis in a transaction between the seller and the obligors. As such, inter–company transactions giving rise to accounts receivable as well as the receivables between corporates that engage in trading and make the settlement by means of mutual netting are ineligible;
14.3. an institution that purchased receivables shall be entitled to all proceeds from the purchased receivables or to a part of the proceeds that represents the part of the receivables purchased;
14.4. the portfolio of purchased receivables is sufficiently diversified.
15. For the purchased receivables in the portfolio of retail exposures, refundable purchase discounts, collateral or partial guarantees that provide first–loss protection for default losses, dilution losses, or both, may be treated as first–loss positions under the IRB securitisation framework.
16. In the case of a sub–portfolio of hybrid portfolio of the portfolio of purchased retail receivables where the purchasing institutions cannot separate exposures secured by a real estate collateral and qualifying revolving exposures included in the portfolio of retail exposures from other exposures of the portfolio of retail exposures, the risk weight function applicable to the portfolio of retail exposures that produces the highest capital requirements for the sub–portfolio of hybrid purchased exposures shall apply.
1.3. Risk–weighted Exposure Amounts for Equity Securities
17. An institution shall be entitled to employ the following approaches to calculating the risk–weighted exposure amounts for equity securities:
17.1. the Simple Risk Weight Approach in accordance with Paragraphs 19–21;
17.2. the PD/LGD Approach in accordance with Paragraphs 22–24;
17.3. the Internal Models Approach in accordance with Paragraphs 25 and 26;
17.4. an institution shall be entitled to apply different approaches to different portfolios where the institution itself uses different approaches to manage credit risk internally. Where an institution uses different approaches, it shall demonstrate to the Commission that the choice is made consistently and is not determined by regulatory arbitrage considerations.
18. Notwithstanding the requirements of Paragraph 17 the risk–weighted exposure amounts for equity securities to ancillary services undertakings may be calculated in accordance to the treatment of other assets that do not constitute institution’s claims against obligors (see Paragraph 27).
1.3.1. Simple Risk Weight Approach
19. The risk–weighted exposure amounts for equity securities shall be calculated according to the following formula:
Risk–weighted exposure amounts = RW * exposure value.
where:
RW=190% for private equity securities in sufficiently diversified portfolios, hereinafter PE exposures;
RW=290% for exchange traded equity securities, hereinafter ETE exposures;
RW=370% for all other equity securities.
20. Short cash positions and derivative instruments held in the non–trading book, future short positions in underlying assets and long positions in the same individual securities may be offset provided that these instruments have been explicitly designated as hedges of specific equity securities and that they provide a hedge for at least another year. Other short positions shall be treated as long positions with the relevant risk weight assigned to the absolute value of each position. In the calculation of the risk–weighted exposure amount the absolute values of short positions shall be used. In the case of maturity mismatched positions, the method is that for exposures to corporates.
21. An institution may recognise unfunded credit protection obtained on an equity security in accordance with the methods set out in Section 4 of the Regulations.
1.3.2. PD/LGD Approach
22. The risk–weighted exposure amounts of equity securities shall be calculated according to the formulae in Paragraph 3. Where an institution does not have sufficient information to use the definition of default set out in Paragraphs 120–125 of Section 4 of the Regulations, a scaling factor of 1,5 shall be assigned to the risk weights.
23. At the individual exposure level the sum of the EL amount multiplied with 12,5 and the risk–weighted exposure amount shall not exceed the exposure value multiplied with 12,5.
24. An institution shall be entitled to recognise unfunded credit protection for an equity securities in accordance with the methods set out in Section 4 of the Regulations. For exposures to the protection provider LGD shall be 90 %. For private equity securities LGD of 65 % may be used. For these purposes M shall be 5 years.
1.3.3. Internal Models Approach
25. The risk–weighted exposure amounts of equity securities shall be the potential loss on the equity securities as derived using internal value–at–risk (hereinafter, VaR) models provided that they use the 99th percentile one–tailed confidence interval for the difference between quarterly returns and an appropriate long–term sample returns computed at a risk–free rate on the calculation date, multiplied with 12,5. The risk–weighted exposure amounts at the individual exposure level shall not be less than the sum of minimum risk–weighted exposure amounts as calculated under the PD/LGD Approach and the corresponding expected loss amounts multiplied with 12,5 and calculated on the basis of the PD values set out in Paragraph 60.1 of Section 2 and the corresponding LGD values set out in Paragraphs 61 and 62 of Section 2.
26. An institution may recognise unfunded credit protection for the position in equity securities.
1.4. Risk–weighted Exposure Amounts of Other Exposures in Non Credit–obligation Assets
27. The risk–weighted exposure amounts shall be calculated according to the formula:
Risk–weighted exposure amount = 100% * exposure value,
where exposure value is the book value of the exposure, except leasing exposures whose value is their residual value The risk–weighted value for such exposures shall be calculated under the following formula:
Risk–weighted exposure amount = 1/t*100% * exposure value,
where t is the number of years of the lease contract.
2. Calculation of the Risk–weighted Exposure Amounts for Dilution Risk of Purchased Receivables
28. Risk weights for dilution risk of the purchased receivables of corporates and retail receivables shall be calculated according to the formula in Paragraph 3. The input parameters PD and LGD shall be determined as set out in Section 2, the exposure value shall be determined as set out in Section 3 and maturity shall be 1 year. Where an institution can demonstrate to the Commission that dilution risk is immaterial, it may not be taken into account.
3. Calculation of Expected Loss Amount
29. Unless noted otherwise, the input parameters PD and LGD for the formulae in this Section shall be determined as set out in Section 2 and the exposure value shall be determined as set out in Section 3.
30. The EL amount for exposures to corporates, institutions, central governments and central banks and retail exposures shall be calculated according to the following formulae:
EL = PD * LGD
EL amount = EL * exposure value
Where an institution uses its own LGD, then for defaulted exposures (PD=1), EL is ELBE that is an institution’s own best estimate of EL in respect of defaulted exposures as estimated in accordance with the provisions of Paragraph 157 of Section 4 of this Annex.
For exposures subject to the option provided for in Paragraph 4 of Section 1 of this Annex, EL shall be 0%.
31. For specialised lending exposures where an institution uses the methods set out in Paragraph 6 for assigning risk weights, EL amount shall be established according to Table 2.
Table 2. EL for specialised lending exposures
Residual maturity / Category 1 / Category 2 / Category 3 / Category 4 / Category 5Less than 2,5 years / 0% / 0.4% / 2.8% / 8% / 50%
Equal or longer than 2,5 years / 0.4% / 0.8% / 2.8% / 8% / 50%
32. For equity securities whose risk–weighted exposure amounts is calculated under the Simple Risk Weight Approach referred to in Paragraphs 19–21, EL shall be calculated in accordance with the following formula: