Title[ Annex
Section[ Annex 7
Illustrative Examples: Calculating the Effect of
Credit Risk Mitigation under Supervisory Formula
Some examples are provided below for determining how collateral and guarantees are to be recognised under the SF.
Illustrative Example Involving Collateral ? proportional cover
Assume an originating bank purchases a 100 securitisation exposure with a credit enhancement level in excess of KIRB for which an external or inferred rating is not available. Additionally, assume that the SF capital charge on the securitisation exposure is 1.6 (when multiplied by 12.5 results in risk weighted assets of 20). Further assume that the originating bank has received 80 of collateral in the form of cash that is denominated in the same currency as the securitisation exposure. The capital requirement for the position is determined by multiplying the SF capital requirement by the ratio of adjusted exposure amount and the original exposure amount, as illustrated below.
Step 1: Adjusted Exposure Amount (E*) = max {0, [E x (1 + He) C x (1 Hc Hfx)]}
E* = max {0, [100 x (1 + 0) 80 x (1 0 0)]} = 20
where (based on the information provided above):
E* = the exposure value after risk mitigation (20)
E = current value of the exposure (100)
He = haircut appropriate to the exposure (This haircut is not relevant because the originating bank is not lending the securitisation exposure in exchange for collateral).
C = the current value of the collateral received (80)
Hc = haircut appropriate to the collateral (0)
Hfx = haircut appropriate for mismatch between the collateral and exposure (0)
Step 2: Capital requirement = (E* / E) x SF capital requirement
where (based on the information provide above):
Capital requirement = 20 / 100 x 1.6 = 0.32.
Illustrative Example Involving a Guarantee ? proportional cover
All of the assumptions provided in the illustrative example involving collateral apply except for the form of credit risk mitigant. Assume that the bank has received an eligible, unsecured guarantee in the amount of 80 from a bank. Therefore, a haircut for currency mismatch will not apply. The capital requirement is determined as follows.
? The protected portion of the securitisation exposure (80) is to receive the risk weight of the protection provider. The risk weight for the protection provider is equivalent to that for an unsecured loan to the guarantor bank, as determined under the IRB approach. Assume that this risk weight is 10%. Then, the capital charge on the protected portion would be: 80 x 10% x 0.08 = 0.64.
? The capital charge for the unprotected portion (20) is derived by multiplying the capital charge on the securitisation exposure by the share of the unprotected portion to the exposure amount. The share of the unprotected portion is: 20 / 100 = 20%. Thus, the capital requirement will be: 1.6 x 20% = 0.32.
The total capital requirement for the protected and unprotected portions is:
0.64 (protected portion) + 0.32 (unprotected portion) = 0.96 .
Illustrative example ? the case of credit risk mitigants covering the most senior parts
Assume an originating bank that securitises a pool of loans of 1000. The KIRB of this underlying pool is 5% (capital charge of 50). There is a first loss position of 20. The originator retains only the second most junior tranche: an unrated tranche of 45. We can summarise the situation as follows:
1. Capital charge without collateral or guarantees
According to this example, the capital charge for the unrated retained tranche that is straddling the KIRB line is the sum of the capital requirements for tranches (a) and (b) in the graph above:
(a) Assume the SF risk weight for this subtranche is 820%. Thus, risk-weighted assets are 15 x 820% = 123. Capital charge is 123 x 8%= 9.84
(b) The subtranche below KIRB must be deducted. Risk-weighted assets: 30 x 1250% =
375. Capital charge of 375 x 8% = 30
Total capital charge for the unrated straddling tranche = 9.84 + 30 = 39.84
2. Capital charge with collateral
Assume now that the originating bank has received 25 of collateral in the form of cash that is denominated in the same currency as the securitisation exposure. Because the tranche is straddling the KIRB level, we must assume that the collateral is covering the most senior subtranche above KIRB ((a) subtranche covered by 15 of collateral) and, only if there is some collateral left, the coverage must be applied to the subtranche below KIRB beginning with the most senior portion (e.g. tranche (b) covered by 10 of collateral). Thus, we have:
The capital requirement for the position is determined by multiplying the SF capital requirement by the ratio of adjusted exposure amount and the original exposure amount, as illustrated below. We must apply this for the two subtranches.
(a) The first subtranche has an initial exposure of 15 and collateral of 15, so in this case it is completely covered. In other words:
Step 1: Adjusted Exposure Amount
E* = max {0, [E x (1 + He) C x (1 Hc Hfx)]} = max {0, [15 15]} = 0
where:
E* = the exposure value after risk mitigation (0)
E = current value of the exposure (15)
C = the current value of the collateral received (15)
He = haircut appropriate to the exposure (not relevant here, thus 0)
Hc and Hfx = haircut appropriate to the collateral and that for the mismatch between the collateral and exposure (to simplify, 0)
Step 2: Capital requirement = (E* / E) x SF capital requirement
Capital requirement = 0 x 9.84 = 0
(b) The second subtranche has an initial exposure of 30 and collateral of 10, which is the amount left after covering the subtranche above KIRB. Thus, these 10 must be allocated to the most senior portion of the 30 subtranche.
Step1: Adjusted Exposure Amount
E* = max {0, [30 x (1 + 0) 10 x (1 0 0)]} = 20
Step 2: Capital requirement = (E* / E) x SF capital requirement
Capital requirement = 20 / 30 x 30 = 20
Finally, the total capital charge for the unrated straddling tranche = 0 + 20 = 20
3. Guarantee
Assume now that instead of collateral, the bank has received an eligible, unsecured guarantee in the amount of 25 from a bank. Therefore the haircut for currency mismatch will not apply. The situation can be summarised as:
The capital requirement for the two subtranches is determined as follows:
(a) The first subtranche has an initial exposure of 15 and a guarantee of 15, so in this case it is completely covered. The 15 will receive the risk weight of the protection provider. The risk weight for the protection provider is equivalent to that for an unsecured loan to the guarantor bank, as determined under the IRB approach. Assume that this risk weight is 20%.
capital charge on the protected portion is 15 x 20% x 8% = 0.24
(b) The second subtranche has an initial exposure of 30 and guarantee of 10 which must be applied to the most senior portion of this subtranche. Accordingly, the protected part is 10 and the unprotected part is 20.
? Again, the protected portion of the securitisation exposure is to receive the risk weight of the guarantor bank.
capital charge on the protected portion is 10 x 20% x 8% = 0.16
The capital charge for the unprotected portion (for an unrated position below KIRB) is
20 x 1250% x 8% = 20
Total capital charge for the unrated straddling tranche = 0.24 (protected portion, above
KIRB) + 0.16 (protected portion, below KIRB) + 20 (unprotected portion, below KIRB) = 20.4
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