| 27.1. | The following two examples are provided to illustrate the recognition of dilution risk according to Paragraph 22.12 of Minimum Capital Requirements for Credit Risk and Paragraph 22.13 of Minimum Capital Requirements for Credit Risk . The first example in 27.2 to 27.5 assumes a common waterfall for default and dilution losses. The second example in 27.6 to 27.16 assumes a non-common waterfall for default and dilution losses.
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| 27.2. | Common waterfall for default and dilution losses: in the first example, it is assumed that losses resulting from either defaults or dilution within the securitised pool will be subject to a common waterfall, ie the loss allocation process does not distinguish between different sources of losses within the pool.
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| 27.3. | The pool is characterised as follows. For the sake of simplicity, it is assumed that all exposures have the same size, same PD, same LGD and same maturity.
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| | (1) | Pool of €1,000,000 of corporate receivables
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| | (2) | N = 100
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| | (3) | M = 2.5 years126
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| | (4) | PDDilution = 0.55%
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| | (5) | LGDDilution =100%
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| | (6) | PDDefault = 0.95%
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| | (7) | LGDDefault = 45%
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| 27.4. | The capital structure is characterised as follows:
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| | (1) | Tranche A is a senior note of €700,000
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| | (2) | Tranche B is a second-loss guarantee of €250,000
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| | (3) | Tranche C is a purchase discount of €50,000
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| | (4) | Final legal maturity of transaction / all tranches = 2.875 years, ie MT = 2.5 years127
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| 27.5. | RWA calculation:
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| | (1) | Step 1: calculate KIRB, Dilution and KIRB, Default for the underlying portfolio:
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| | | (a) | KIRB, Dilution = €1,000,000 x (161.44% x 8% + 0.55% x 100%) / €1,000,000 = 13.47%
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| | | (b) | KIRB, Default = (€1,000,000 – €129,200)128 x (90.62% x 8% + 0.95% x 45%) / €1,000,000 = 6.69%
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| | (2) | Step 2: calculate KIRB, Pool = KIRB, Dilution + KIRB, Default = 13.47% + 6.69% = 20.16%
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| | (3) | Step 3: apply the SEC-IRBA to the three tranches
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| | | (a) | Pool parameters:
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| | | | (i) | N = 100
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| | | | (ii) | LGDPool = (LGDDefault x KIRB, Default + LGDDilution x KIRB, Dilution) / KIRB, Pool = (45% x 6.69% + 100% x 13.47%) / 20.16% = 81.75%
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| | | (b) | Tranche parameters:
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| | | | (i) | MT = 2.5 years
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| | | | (ii) | Attachment and detachment points shown in Table 2
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| Attachment and detachment points for each tranche | Table 2 | | | Attachment point | Detachment point | | Tranche A | 30% | 100% | | Tranche B | 5% | 30% | | Tranche C | 0% | 5% |
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| | (4) | Resulting risk-weighted exposure amounts shown in Table 3
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| Risk-weighted exposure amounts for each tranche | Table 3 | | | SEC-IRBA risk weight | RWA | | Tranche A | 21.22% | €148,540 | | Tranche B | 1013.85% | €2,534,625 | | Tranche C | 1250% | €625,000 |
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| 27.6. | Non-common waterfall for default and dilution losses: in the second example, it is assumed that the securitisation transaction does not have one common waterfall for losses due to defaults and dilutions, ie for the determination of the risk of a specific tranche it is not only relevant what losses might be realised within the pool but also if those losses are resulting from default or a dilution event.
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| 27.7. | As the SEC-IRBA assumes that there is one common waterfall, it cannot be applied without adjustments. The following example illustrates one possible scenario and a possible adjustment specific to this scenario.
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| 27.8. | While this example is meant as a guideline, a bank should nevertheless consult with its national supervisor as to how the capital calculation should be performed (see paragraph 22.13 of Minimum Capital Requirements for Credit Risk).
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| 27.9. | The pool is characterized as in 27.3.
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| 27.10. | The capital structure is characterized as follows:
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| | (1) | Tranche A is a senior note of €950,000
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| | (2) | Tranche C is a purchase discount of €50,000
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| | (3) | Tranches A and C will cover both default and dilution losses
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| | (4) | In addition, the structure also contains a second-loss guarantee of €250,000 (Tranche B)129 that covers only dilution losses exceeding a threshold of €50,000 up to maximum aggregated amount of €300,000, which leads to the following two waterfalls:
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| | | (a) | Default waterfall
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| | | | (i) | Tranche A is a senior note of €950,000
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| | | | (ii) | Tranche C is a purchase discount of €50,000130
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| | | (b) | Dilution waterfall
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| | | | (i) | Tranche A is a senior note of €700,000
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| | | | (ii) | Tranche B is a second-loss guarantee of €250,000
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| | | | (iii) | Tranche C is a purchase discount of €50,000131
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| | (5) | MT of all tranches is 2.5 years.
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| 27.11. | Tranche C is treated as described in 27.4 to 27.7.
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| 27.12. | Tranche B (second-loss guarantee) is exposed only to dilution risk, but not to default risk. Therefore, KIRB, for the purpose of calculating a capital requirement for Tranche B, can be limited to KIRB, Dilution. However, as the holder of Tranche B cannot be sure that Tranche C will still be available to cover the first dilution losses when they are realised – because the credit enhancement might already be depleted due to earlier default losses – to ensure a prudent treatment, it cannot recognise the purchase discount as credit enhancement for dilution risk. In the capital calculation, the bank providing Tranche B should assume that €50,000 of the securitised assets have already been defaulted and hence Tranche C is no longer available as credit enhancement and the exposure of the underlying assets has been reduced to €950,000. When calculating KIRB for Tranche B, the bank can assume that KIRB is not affected by the reduced portfolio size.
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| 27.13. | RWA calculation for tranche B:
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| | (1) | Step 1: calculate KIRB,Pool.
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| | | KIRB,Pool = KIRB,Dilution = 13.47%
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| | (2) | Step 2: apply the SEC-IRBA.
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| | | (a) | Pool parameters:
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| | | | (i) | N = 100
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| | | | (ii) | LGDPool = LGDDilution = 100%
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| | | (b) | Tranche parameters:
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| | | | (i) | MT = 2.5 years
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| | | | (ii) | Attachment point = 0%
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| | | | (iii) | Detachment point = €250,000 / €950,000 = 26.32%
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| | (3) | Resulting risk-weighted exposure amounts for Tranche B:
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| | | (a) | SEC-IRBA risk weight = 886.94%
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| | | (b) | RWA = €2,217,350
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| 27.14. | The holder of Tranche A (senior note) will take all default losses not covered by the purchase discount and all dilution losses not covered by the purchase discount or the second-loss guarantee. A possible treatment for Tranche A would be to add KIRB, Default and KIRB, Dilution (as in 27.4 to 27.7), but not to recognize the second-loss guarantee as credit enhancement at all because it is covering only dilution risk.
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| 27.15. | Although this is a simple approach, it is also fairly conservative. Therefore the following alternative for the senior tranche could be considered:
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| | (1) | Calculate the RWA amount for Tranche A under the assumption that it is only exposed to losses resulting from defaults. This assumption implies that Tranche A is benefiting from a credit enhancement of €50,000.
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| | (2) | Calculate the RWA amounts for Tranche C and (hypothetical) Tranche A* under the assumption that they are only exposed to dilution losses. Tranche A* should be assumed to absorb losses above €300,000 up to €1,000,000. With respect to dilution losses, this approach would recognize that the senior tranche investor cannot be sure if the purchase price discount will still be available to cover those losses when needed as it might have already been used for defaults. Consequently, from the perspective of the senior investor, the purchase price discount could only be recognized for the calculation of the capital requirement for default or dilution risk but not for both.132
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| | (3) | Sum up the RWA amounts under 27.15(1) and 27.15(2) and apply the relevant risk weight floor in paragraph 22.26 of Minimum Capital Requirements for Credit Risk or paragraph 22.29 of Minimum Capital Requirements for Credit Risk to determine the final RWA amount for the senior note investor.
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| 27.16. | RWA calculation for Tranche A:
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| | (1) | Step 1: calculate RWA for 27.15 (1).
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| | | (a) | Pool parameters:
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| | | | (i) | KIRB,Pool = KIRB,Default = 6.69%
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| | | | (ii) | LGDPool = LGDDefault = 45%
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| | | (b) | Tranche parameters:
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| | | | (i) | MT = 2.5 years
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| | | | (ii) | Attachment point = €50,000 / €1,000,000 = 5%
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| | | | (iii) | Detachment point = €1,000,000 / €1,000,000 = 100%
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| | | (c) | Resulting risk-weighted exposure amounts:
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| | | | (i) | SEC-IRBA risk weight = 51.67%
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| | | | (ii) | RWA = €490,865
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| | (2) | Step 2: calculate RWA for 27.15(2).
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| | | (a) | Pool parameters:
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| | | | (i) | KIRB,Pool = KIRB,Dilution = 13.47%
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| | | | (ii) | LGDPool = LGDDilution = 100%
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| | | (b) | Tranche parameters:
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| | | | (i) | MT = 2.5 years
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| | | | (ii) | Attachment and detachment points shown in Table 4
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| Attachment and detachment points for each tranche | Table 4 | | | Attachment point | Detachment point | | Tranche A* | 30% | 100% | | Tranche C | 0% | 5% |
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| | | (c) | Resulting risk-weighted exposure amounts shown in Table 5
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| Risk-weighted exposure amounts for each tranche | Table 5 | | | SEC-IRBA risk weight | | | Tranche A* | 11.16% | €78,120 | | Tranche C | 1250% | €625,000 |
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| | (3) | Step 3: Sum up the RWA of 27.16 (1) and 27.16 (2)133
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| | | (a) | Final RWA amount for investor in Tranche A = €490,865 + €78,120 + €625,000 = €1,193,985
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| | | (b) | Implicit risk weight for Tranche A = max (15%, €1,193,985 / €950,000) = 125.68%
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