This chapter provides guidance on various aspects of the credit risk standard, including illustrative examples.
The guidance set out in this chapter relates to the chapters of the credit risk standard (CRE). This chapter includes the following:
Table 1 provides illustrative risk weights calculated for four exposure types under the IRB approach to credit risk. Each set of risk weights for unexpected loss (UL) was produced using the appropriate riskweight function of the riskweight functions set out in CRE31. The inputs used to calculate the illustrative risk weights include measures of the probability of default (PD), lossgivendefault (LGD), and an assumed effective maturity (M) of 2.5 years, where applicable.
A firmsize adjustment applies to exposures made to small or mediumsized entity 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). Accordingly, the firm size adjustment was made in determining the second set of risk weights provided in column two for corporate exposures given that the turnover of the firm receiving the exposure is assumed to be €5 million.
Illustrative IRB risk weights for UL 
Table 1 

Asset class 
Corporate Exposures 
Residential Mortgages 
Other Retail Exposures 
Qualifying Revolving Retail Exposures 

LGD: 
45% 
45% 
45% 
25% 
45% 
85% 
45% 
85% 

Turnover (millions of €): 
50 
5 

Maturity: 
2.5 years 
2.5 Years 

PD: 

0.03% 
14.44% 
11.30% 
4.15% 
2.30% 
4.45% 
8.41% 
0.98% 
1.85% 

0.05% 
19.65% 
15.39% 
6.23% 
3.46% 
6.63% 
12.52% 
1.51% 
2.86% 

0.10% 
29.65% 
23.30% 
10.69% 
5.94% 
11.16% 
21.08% 
2.71% 
5.12% 

0.25% 
49.47% 
39.01% 
21.30% 
11.83% 
21.15% 
39.96% 
5.76% 
10.88% 

0.40% 
62.72% 
49.49% 
29.94% 
16.64% 
28.42% 
53.69% 
8.41% 
15.88% 

0.50% 
69.61% 
54.91% 
35.08% 
19.49% 
32.36% 
61.13% 
10.04% 
18.97% 

0.75% 
82.78% 
65.14% 
46.46% 
25.81% 
40.10% 
75.74% 
13.80% 
26.06% 

1.00% 
92.32% 
72.40% 
56.40% 
31.33% 
45.77% 
86.46% 
17.22% 
32.53% 

1.30% 
100.95% 
78.77% 
67.00% 
37.22% 
50.80% 
95.95% 
21.02% 
39.70% 

1.50% 
105.59% 
82.11% 
73.45% 
40.80% 
53.37% 
100.81% 
23.40% 
44.19% 

2.00% 
114.86% 
88.55% 
87.94% 
48.85% 
57.99% 
109.53% 
28.92% 
54.63% 

2.50% 
122.16% 
93.43% 
100.64% 
55.91% 
60.90% 
115.03% 
33.98% 
64.18% 

3.00% 
128.44% 
97.58% 
111.99% 
62.22% 
62.79% 
118.61% 
38.66% 
73.03% 

4.00% 
139.58% 
105.04% 
131.63% 
73.13% 
65.01% 
122.80% 
47.16% 
89.08% 

5.00% 
149.86% 
112.27% 
148.22% 
82.35% 
66.42% 
125.45% 
54.75% 
103.41% 

6.00% 
159.61% 
119.48% 
162.52% 
90.29% 
67.73% 
127.94% 
61.61% 
116.37% 

10.00% 
193.09% 
146.51% 
204.41% 
113.56% 
75.54% 
142.69% 
83.89% 
158.47% 

15.00% 
221.54% 
171.91% 
235.72% 
130.96% 
88.60% 
167.36% 
103.89% 
196.23% 

20.00% 
238.23% 
188.42% 
253.12% 
140.62% 
100.28% 
189.41% 
117.99% 
222.86% 

Illustrative examples for recognition of dilution risk when applying SECIRBA to securitisation exposures
The following examples are provided to illustrate the recognition of dilution risk according to CRE44.12 and CRE44.13. The first example in CRE99.5 to CRE99.8 assumes a common waterfall for default and dilution losses. The second example in CRE99.9 to CRE99.19 assumes a noncommon waterfall for default and dilution losses.
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 lossallocation process does not distinguish between different sources of losses within the pool.
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.
Pool of €1,000,000 of corporate receivables
N = 100
M = 2.5 years1
PD_{Dilution} = 0.55%
LGD_{Dilution} =100%
PD_{D}_{efault} = 0.95%
LGD_{D}_{efault} = 45%
The capital structure is characterised as follows:
Tranche A is a senior note of €700,000
Tranche B is a secondloss guarantee of €250,000
Tranche C is a purchase discount of €50,000
Final legal maturity of transaction / all tranches = 2.875 years, ie M_{T} = 2.5 years2
RWA calculation:
Step 1: calculate K_{IRB,Dilution} and K_{IRB,Default} for the underlying portfolio:
K_{IRB,Dilution} = €1,000,000 x (161.44% x 8% x 1.06 + 0.55% x 100%) / €1,000,000 = 14.24%
K_{IRB,Default} = (€1,000,000 – €136,900)3 x (90.62% x 8% x 1.06 + 0.95% x 45%) / €1,000,000 = 7%
Step 2: calculate K_{IRB,}_{Pool }= K_{IRB,Dilution} + K_{IRB,Default} = 14.24% + 7% = 21.24%
Step 3: apply the SECIRBA to the three tranches
Pool parameters:
N = 100
LGD_{Pool} = (LGD_{Default} x K_{IRB,Default} + LGD_{Dilution} x K_{IRB,Dilution}) / K_{IRB,Pool} = (45% x 7% + 100% x 14.24%) / 21.24% = 81.87%
Tranche parameters:
M_{T} = 2.5 years
Attachment and detachment points shown in Table 2
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% 

Resulting riskweighted exposure amounts shown in Table 3
Riskweighted exposure amounts for each tranche 
Table 3 


SECIRBA risk weight 
RWA 

Tranche A 
28.78% 
€201,460 

Tranche B 
1056.94% 
€2,642,350 

Tranche C 
1250% 
€625,000 

Noncommon 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.
As the SECIRBA 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.
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 CRE44.13).
The capital structure is characterised as follows:
Tranche A is a senior note of €950,000
Tranche C is a purchase discount of €50,000
Tranches A and C will cover both default and dilution losses
In addition, the structure also contains a secondloss guarantee of €250,000 (Tranche B)4 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:
Default waterfall
Tranche A is a senior note of €950,000
Tranche C is a purchase discount of €50,0005
Dilution waterfall
Tranche A is a senior note of €700,000
Tranche B is a secondloss guarantee of €250,000
Tranche C is a purchase discount of €50,0006
M_{T} of all tranches is 2.5 years.
Tranche B (secondloss guarantee) is exposed only to dilution risk, but not to default risk. Therefore, K_{IRB}, for the purpose of calculating a capital requirement for Tranche B, can be limited to K_{IRB,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 K_{IRB} for Tranche B, the bank can assume that K_{IRB} is not affected by the reduced portfolio size.
RWA calculation for tranche B:
Step 1: calculate K_{IRB,}_{Pool}.
K_{IRB,Pool }= K_{IRB,Dilution} = 14.24%
Step 2: apply the SECIRBA.
Pool parameters:
N = 100
LGD_{Pool} = LGD_{Dilution} = 100%
Tranche parameters:
M_{T} = 2.5 years
Attachment point = 0%
Detachment point = €250,000 / €950,000 = 26.32%
Resulting riskweighted exposure amounts for tranche B:
SECIRBA risk weight = 925.47%
RWA = €2,313,675
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 secondloss guarantee. A possible treatment for Tranche A would be to add K_{IRB,Default} and K_{IRB,Dilution} (as in CRE99.7 to CRE99.10), but not to recognise the secondloss guarantee as credit enhancement at all because it is covering only dilution risk.
Although this is a simple approach, it is also fairly conservative. Therefore the following alternative for the senior tranche could be considered:
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.
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 recognise 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 recognised for the calculation of the capital requirement for default or dilution risk but not for both.7
RWA calculation for tranche A:
Step 1: calculate RWA for CRE99.18(1).
Pool parameters:
K_{IRB,}_{Pool }= K_{IRB,D}_{efault} = 7%
LGD_{Pool} = LGD_{D}_{efault} = 45%
Tranche parameters:
M_{T} = 2.5 years
Attachment point = €50,000 / €1,000,000 = 5%
Detachment point = €1,000,000 / €1,000,000 = 100%
Resulting riskweighted exposure amounts:
SECIRBA risk weight = 56.58%
RWA = €537,510.
Step 2: calculate RWA for CRE99.18(2).
Pool parameters:
K_{IRB,}_{Pool }= K_{IRB,D}_{ilution} = 14.24%
LGD_{Pool} = LGD_{D}_{ilution} = 100%
Tranche parameters:
M_{T} = 2.5 years
Attachment and detachment points shown in Table 4
Attachment and detachment points for each tranche 
Table 4 


Attachment point 
Detachment point 

Tranche A* 
30% 
100% 

Tranche C 
0% 
5% 

Resulting riskweighted exposure amounts shown in Table 5
Riskweighted exposure amounts for each tranche 
Table 5 


SECIRBA risk weight 
RWA 

Tranche A* 
13.65% 
€95,550 

Tranche C 
1250% 
€625,000 

This section (CRE99.20 to CRE99.97) sets out the calculation of exposure at default (EAD) for five sample portfolios using SACCR. The calculations for the sample portfolios assume that intermediate values are not rounded (ie the actual results are carried through in sequential order). However, for ease of presentation, these intermediate values as well as the final EAD are rounded.
The EAD for all netting sets in SACCR is given by the following formula, where alpha is assigned a value of 1.4:
Netting set 1 consists of three interest rates derivatives: two fixed versus floating interest rate swaps and one purchased physicallysettled European swaption. The table below summarises the relevant contractual terms of the three derivatives. All notional amounts and market values in the table are given in USD thousands.
Trade 
Nature 
Residual 
Base 
Notional 
Pay Leg 
Receive Leg 
Market 
1 
Interest rate swap 
10 years 
USD 
10,000 
Fixed 
Floating 
30 
2 
Interest rate swap 
4 years 
USD 
10,000 
Floating 
Fixed 
20 
3 
European swaption 
1 into 10 years 
EUR 
5,000 
Floating 
Fixed 
50 
(*) For the swaption, the legs are those of the underlying swap 

The netting set is not subject to a margin agreement and there is no exchange of collateral (independent amount/initial margin) at inception. For unmargined netting sets, the replacement cost is calculated using the following formula, where:
V is a simple algebraic sum of the derivatives’ market values at the reference date
C is the haircut value of the initial margin, which is zero in this example
Since VC is positive (ie USD 60,000), the value of the multiplier is 1, as explained in CRE52.22.
The remaining term to be calculated in the calculation EAD is the aggregate addon (AddOnaggregate). All the transactions in the netting set belong to the interest rate asset class. The AddOnaggregate for the interest rate asset class can be calculated using the seven steps set out in CRE52.57.
Step 1: Calculate the effective notional for each trade in the netting set. This is calculated as the product of the following three terms: (i) the adjusted notional of the trade (d); (ii) the supervisory delta adjustment of the trade (δ); and (iii) the maturity factor (MF). That is, for each trade i, the effective notional D_{i} is calculated as D_{i} = d_{i} * MF_{i} * δ_{i}.
For interest rate derivatives, the tradelevel adjusted notional (d_{i}) is the product of the trade notional amount and the supervisory duration (SD_{i}), ie d_{i} = notional * SD_{i}. The supervisory duration is calculated using the following formula, where:
S_{i} and E_{i} are the start and end dates, respectively, of the time period referenced by the interest rate derivative (or, where such a derivative references the value of another interest rate instrument, the time period determined on the basis of the underlying instrument). If the start date has occurred (eg an ongoing interest rate swap), S_{i} must be set to zero.
The calculated value of SD_{i} is floored at 10 business days (which expressed in years, using an assumed market convention of 250 business days a year is 10/250 years.
Using the formula for supervisory duration above, the tradelevel adjusted notional amounts for each of the trades in Example 1 are as follows:
Trade 
Notional 
S_{i} 
E_{i} 
SD_{i} 
Adjusted 
1 
10,000 
0 
10 
7.87 
78,694 
2 
10,000 
0 
4 
3.63 
36,254 
3 
5,000 
1 
11 
7.49 
37,428 
CRE52.48 sets out the calculation of the maturity factor (MF_{i}) for unmargined trades. For trades that have a remaining maturity in excess of one year, which is the case for all trades in this example, the formula gives a maturity factor of 1.
As set out in CRE52.38 to CRE52.41, a supervisory delta is assigned to each trade. In particular:
Trade 1 is long in the primary risk factor (the reference floating rate) and is not an option so the supervisory delta is equal to 1.
Trade 2 is short in the primary risk factor and is not an option; thus, the supervisory delta is equal to 1.
Trade 3 is an option to enter into an interest rate swap that is short in the primary risk factor and therefore is treated as a bought put option. As such, the supervisory delta is determined by applying the relevant formula in CRE52.40, using 50% as the supervisory option volatility and 1 (year) as the option exercise date. In particular, assuming that the underlying price (the appropriate forward swap rate) is 6% and the strike price (the swaption’s fixed rate) is 5%, the supervisory delta is:
The effective notional for each trade in the netting set (D_{i}) is calculated using the formula D_{i} = d_{i} * MF_{i} * δ_{i} and values for each term noted above. The results of applying the formula are as follows:
Trade 
Notional 
Adjusted 
Maturity Factor, MF_{i} 
Delta, δ_{i} 
Effective notional, D_{i} (USD, thousands) 
1 
10,000 
78,694 
1 
1 
78,694 
2 
10,000 
36,254 
1 
1 
36,254 
3 
5,000 
37,428 
1 
0.2694 
10,083 
Step 2: Allocate the trades to hedging sets. In the interest rate asset class the hedging sets consist of all the derivatives that reference the same currency. In this example, the netting set is comprised of two hedging sets, since the trades refer to interest rates denominated in two different currencies (USD and EUR).
Step 3: Within each hedging set allocate each of the trades to the following three maturity buckets: less than one year (bucket 1), between one and five years (bucket 2) and more than five years (bucket 3). For this example, within the hedging set “USD”, trade 1 falls into the third maturity bucket (more than 5 years) and trade 2 falls into the second maturity bucket (between one and five years). Trade 3 falls into the third maturity bucket (more than 5 years) of the hedging set “EUR”. The results of steps 1 to 3 are summarised in the table below:
Trade 
Effective notional, D_{i} (USD, thousands) 
Hedging 
Maturity bucket 
1 
78,694 
USD 
3 
2 
36,254 
USD 
2 
3 
10,083 
EUR 
3 
Step 4: Calculate the effective notional of each maturity bucket (DB1, DB2 and DB3) within each hedging set (USD and EUR) by adding together all the trade level effective notionals within each maturity bucket in the hedging set. In this example, there are no maturity buckets within a hedging set with more than one trade, and so this case the effective notional of each maturity bucket is simply equal to the effective notional of the single trade in each bucket. Specifically:
For the USD hedging set: DB1 is zero, DB2 is 36,254 (thousand USD) and DB3 is 78,694 (thousand USD).
For the EUR hedging set: DB1 and DB2 are zero and DB3 is 10,083 (thousand USD).
Step 5: Calculate the effective notional of the hedging set (EN_{HS}) by using either of the two following aggregation formulas (the latter is to be used if the bank chooses not to recognise offsets between long and short positions across maturity buckets):
In this example, the first of the two aggregation formulas is used. Therefore, the effective notionals for the USD hedging set (EN_{USD}) and the EUR hedging (EN_{EUR}) are, respectively (expressed in USD thousands):
Step 6: Calculate the hedging set level addon (AddOn_{hs}) by multiplying the effective notional of the hedging set (EN_{hs}) by the prescribed supervisory factor (SF_{hs}). The prescribed supervisory factor in the interest rate asset class is set at 0.5%. Therefore, the addon for the USD and EUR hedging sets are, respectively (expressed in USD thousands):
Step 7: Calculate the asset class level addon (AddOn^{IR}) by adding together all of the hedging set level addons calculated in step 6. Therefore, the addon for the interest rate asset class is (expressed in USD thousands):
For this netting set the interest rate addon is also the aggregate addon because there are no derivatives belonging to other asset classes. The EAD for the netting set can now be calculated using the formula set out in CRE99.21 (expressed in USD thousands):
Netting set 2 consists of three credit derivatives: one long singlename credit default swap (CDS) written on Firm A (rated AA), one short singlename CDS written on Firm B (rated BBB), and one long CDS index (investment grade). The table below summarises the relevant contractual terms of the three derivatives. All notional amounts and market values in the table are in USD thousands.
Trade 
Nature 
Reference entity / 
Rating reference entity 
Residual maturity 
Base 
Notional 
Position 
Market 
1 
Singlename CDS 
Firm A 
AA 
3 years 
USD 
10,000 
Protection 
20 
2 
Singlename CDS 
Firm B 
BBB 
6 years 
EUR 
10,000 
Protection 
40 
3 
CDS index 
CDX.IG 5y 
Investment 
5 years 
USD 
10,000 
Protection 
0 
As in the previous example, the netting set is not subject to a margin agreement and there is no exchange of collateral (independent amount/initial margin) at inception. For unmargined netting sets, the replacement cost is calculated using the following formula, where:
V is a simple algebraic sum of the derivatives’ market values at the reference date
C is the haircut value of the initial margin, which is zero in this example
Since in this example VC is negative (equal to V, ie 20,000), the multiplier will be activated (ie it will be less than 1). Before calculating its value, the aggregate addon (AddOnaggretate) needs to be determined.
All the transactions in the netting set belong to the credit derivatives asset class. The AddOnaggretate for the credit derivatives asset class can be calculated using the four steps set out in CRE52.61.
Step 1: Calculate the effective notional for each trade in the netting set. This is calculated as the product of the following three terms: (i) the adjusted notional of the trade (d); (ii) the supervisory delta adjustment of the trade (δ); and (iii) the maturity factor (MF). That is, for each trade i, the effective notional D_{i} is calculated as D_{i} = d_{i} * MF_{i} * δ_{i}.
For credit derivatives, like interest rate derivatives, the tradelevel adjusted notional (d_{i}) is the product of the trade notional amount and the supervisory duration (SD_{i}), ie d_{i} = notional * SD_{i}. The tradelevel adjusted notional amounts for each of the trades in Example 2 are as follows:
Trade 
Notional 
S_{i} 
E_{i} 
SD_{i} 
Adjusted 
1 
10,000 
0 
3 
2.79 
27,858 
2 
10,000 
0 
6 
5.18 
51,836 
3 
10,000 
0 
5 
4.42 
44,240 
CRE52.48 sets out the calculation of the maturity factor (MF_{i}) for unmargined trades. For trades that have a remaining maturity in excess of one year, which is the case for all trades in this example, the formula gives a maturity factor of 1.
As set out in CRE52.38 to CRE52.41, a supervisory delta is assigned to each trade. In particular:
Trade 1 and Trade 3 are long in the primary risk factors (CDS spread) and are not options so the supervisory delta is equal to 1 for each trade.
Trade 2 is short in the primary risk factor and is not an option; thus, the supervisory delta is equal to 1.
The effective notional for each trade in the netting set (D_{i}) is calculated using the formula D_{i} = d_{i} * MF_{i} * δ_{i} and values for each term noted above. The results of applying the formula are as follows:
Trade 
Notional 
Adjusted 
Maturity Factor, MF_{i} 
Delta, δ_{i} 
Effective notional, D_{i} (USD, thousands) 
1 
10,000 
27,858 
1 
1 
27,858 
2 
10,000 
51,836 
1 
1 
51,836 
3 
10,000 
44,240 
1 
1 
44,240 
Step 2: Calculate the combined effective notional for all derivatives that reference the same entity. The combined effective notional of the entity (EN_{entity}) is calculated by adding together the trade level effective notionals calculated in step 1 that reference that entity. However, since all the derivatives refer to different entities (single names/indices), the effective notional of the entity is simply equal to the trade level effective notional (D_{i}) for each trade.
Step 3: Calculate the addon for each entity (AddOn_{entity}) by multiplying the entity level effective notional in step 2 by the supervisory factor that is specified for that entity (SF_{entity}). The supervisory factors are set out in table 2 in CRE52.72. A supervisory factor is assigned to each singlename entity based on the rating of the reference entity (0.38% for AArated firms and 0.54% for BBBrated firms). For CDS indices, the SF is assigned according to whether the index is investment or speculative grade; in this example, its value is 0.38% since the index is investment grade. Thus, the entity level addons are the following (USD thousands):
Reference Entity 
Effective notional, D_{i} (USD, thousands) 
Supervisory factor, SF_{entity} 
Entitylevel addon, AddOn_{entity}(=D_{i}*SF_{entity}) 
Firm A 
27,858 
0.38% 
106 
Firm B 
51,836 
0.54% 
280 
CDX.IG 
44,240 
0.38% 
168 
Step 4: Calculate the asset class level addon (AddOnCredit) by using the formula that follows, where:
The summations are across all entities referenced by the derivatives.
AddOn_{entity} is the addon amount calculated in step 3 for each entity referenced by the derivatives.
ρ_{entity} is the supervisory prescribed correlation factor corresponding to the entity. As set out in table 2 in CRE52.72, the correlation factor is 50% for single entities (Firm A and Firm B) and 80% for indexes (CDX.IG).
The following table shows a simple way to calculate of the systematic and idiosyncratic components in the formula:
Reference Entity 
ρ_{entity} 
AddOn_{entity} 
ρ_{entity} * AddOn_{entity} 
1(ρ_{entity})2 
(AddOn_{entity})2 
(1(ρ_{entity})2)* (AddOn_{entity})2 

Firm A 
0.5 
106 
52.9 
0.75 
11,207 
8,405 

Firm B 
0.5 
280 
140 
0.75 
78,353 
58,765 

CDX.IG 
0.8 
168 
134.5 
0.36 
28,261 
10,174 

sum = 
47.5 
77,344 

(sum)2 = 
2,253 

According to the calculations in the table, the systematic component is 2,253, while the idiosyncratic component is 77,344. Thus, the addon for the credit asset class is calculated as follows:
For this netting set the credit addon (AddOnCredit) is also the aggregate addon (AddOnaggregate) because there are no derivatives belonging to other asset classes.
The value of the multiplier can now be calculated as follows, using the formula set out in CRE52.23:
Finally, aggregating the replacement cost and the potential future exposure (PFE) component and multiplying the result by the alpha factor of 1.4, the EAD is as follows (USD thousands):
Netting set 3 consists of three commodity forward contracts. The table below summarises the relevant contractual terms of the three derivatives. All notional amounts and market values in the table are in USD thousands.
Trade 
Notional 
Nature 
Underlying 
Direction 
Residual 
Market value 
1 
10,000 
Forward 
(West Texas Intermediate, or WTI) Crude Oil 
Long 
9 months 
50 
2 
20,000 
Forward 
(Brent) Crude Oil 
Short 
2 years 
30 
3 
10,000 
Forward 
Silver 
Long 
5 years 
100 
As in the previous two examples, the netting set is not subject to a margin agreement and there is no exchange of collateral (independent amount/initial margin) at inception. Thus, the replacement cost is given by:
Since VC is positive (ie USD 20,000), the value of the multiplier is 1, as explained in CRE52.22.
All the transactions in the netting set belong to the commodities derivatives asset class. The AddOnaggretate for the commodities derivatives asset class can be calculated using the six steps set out in CRE52.70.
Step 1: Calculate the effective notional for each trade in the netting set. This is calculated as the product of the following three terms: (i) the adjusted notional of the trade (d); (ii) the supervisory delta adjustment of the trade (δ); and (iii) the maturity factor (MF). That is, for each trade i, the effective notional D_{i} is calculated as D_{i} = d_{i} * MF_{i} * δ_{i}.
For commodity derivatives, the adjusted notional is defined as the product of the current price of one unit of the commodity (eg barrel of oil) and the number of units referenced by the derivative. In this example, for the sake of simplicity, it is assumed that the adjusted notional (d_{i}) is equal to the notional value.
CRE52.48 sets out the calculation of the maturity factor (MF_{i}) for unmargined trades. For trades that have a remaining maturity in excess of one year (trades 2 and 3 in this example), the formula gives a maturity factor of 1. For trade 1 the formula gives the following maturity factor:
As set out in CRE52.38 to CRE52.41, a supervisory delta is assigned to each trade. In particular:
Trade 1 and Trade 3 are long in the primary risk factors (WTI Crude Oil and Silver respectively) and are not options so the supervisory delta is equal to 1 for each trade.
Trade 2 is short in the primary risk factor (Brent Crude Oil) and is not an option; thus, the supervisory delta is equal to 1.
Trade 
Notional 
Adjusted 
Maturity Factor, MF_{i} 
Delta, δ_{i} 
Effective notional, D_{i} (USD, thousands) 
1 
10,000 
10,000 
(9/12)0.5 
1 
8,660 
2 
20,000 
20,000 
1 
1 
20,000 
3 
10,000 
10,000 
1 
1 
10,000 
Step 2: Allocate the trades in commodities asset class to hedging sets. In the commodities asset class there are four hedging sets consisting of derivatives that reference: energy (trades 1 and 2 in this example), metals (trade 3 in this example), agriculture and other commodities.
Hedging set 
Commodity type 
Trades 
Energy 
Crude oil 
1 and 2 
Natural gas 
None 

Coal 
None 

Electricity 
None 

Metals 
Silver 
3 
Gold 
None 

… 
… 

Agriculture 
… 
… 
… 
… 

Other 
… 
… 
Trade 
Effective notional, D_{i} (USD, thousands) 
Hedging set 
Commodity type 
1 
8,660 
Energy 
Crude oil 
2 
20,000 
Energy 
Crude oil 
3 
10,000 
Metals 
Silver 
Step 3: Calculate the combined effective notional for all derivatives with each hedging set that reference the same commodity type. The combined effective notional of the commodity type (EN_{ComType}) is calculated by adding together the trade level effective notionals calculated in step 1 that reference that commodity type. For purposes of this calculation, the bank can ignore the basis difference between the WTI and Brent forward contracts since they belong to the same commodity type, “Crude Oil” (unless the national supervisor requires the bank to use a more refined definition of commodity types). This step gives the following:
EN_{CrudeOil} = 8,660 + (20,000) = 11,340
EN_{Silver} = 10,000
Step 4: Calculate the addon for each commodity type (AddOn_{ComType}) within each hedging set by multiplying the combined effective notional for that commodity calculated in step 3 by the supervisory factor that is specified for that commodity type (SF_{ComType}). The supervisory factors are set out in table 2 in CRE52.72 and are set at 40% for electricity derivatives and 18% for derivatives that reference all other types of commodities. Therefore:
AddOn_{CrudeOil} = 11,340 * 0.18 = 2,041
AddOn_{Silver} = 10,000 * 0.18 = 1,800
Step 5: Calculate the addon for each of the four commodity hedging sets (AddOn_{HS}) by using the formula that follows. In the formula:
The summations are across all commodity types within the hedging set.
AddOn_{ComType} is the addon amount calculated in step 4 for each commodity type.
ρ_{ComType} is the supervisory prescribed correlation factor corresponding to the commodity type. As set out in table 2 in CRE52.72, the correlation factor is set at 40% for all commodity types.
In this example, however, there is only one commodity type within the “Energy” hedging set (ie Crude Oil). All other commodity types within the energy hedging set (eg coal, natural gas etc) have a zero addon. Therefore, the addon for the energy hedging set is calculated as follows:
The calculation above shows that, when there is only one commodity type within a hedging set, the hedgingset addon is equal (in absolute value) to the commoditytype addon.
Similarly, “Silver” is the only commodity type in the “Metals” hedging set, and so the addon for the metals hedging set is:
Step 6: Calculate the asset class level addon (AddOnCommodity) by adding together all of the hedging set level addons calculated in step 5:
For this netting set the commodity addon (AddOnCommodity) is also the aggregate addon (AddOnaggregate) because there are no derivatives belonging to other asset classes.
Finally, aggregating the replacement cost and the PFE component and multiplying the result by the alpha factor of 1.4, the EAD is as follows (USD thousands):
Netting set 4 consists of the combined trades of Examples 1 and 2. There is no margin agreement and no collateral. The replacement cost of the combined netting set is:
The aggregate addon for the combined netting set is the sum of addons for each asset class. In this case, there are two asset classes, interest rates and credit, and the addons for these asset classes have been copied from Examples 1 and 2:
Netting set 5 consists of the combined trades of Examples 1 and 3. However, instead of being unmargined (as assumed in those examples), the trades are subject to a margin agreement with the following specifications:
Margin frequency 
Threshold, TH 
Minimum Transfer Amount, MTA (USD thousands) 
Independent Amount, IA (USD thousands) 
Total net collateral held by bank (USD thousands) 
Weekly 
0 
5 
150 
200 
The above table depicts a situation in which the bank received from the counterparty a net independent amount of 150 (taking into account the net amount of initial margin posted by the counterparty and any unsegregated initial margin posted by the bank). The total net collateral (after the application of haircuts) currently held by the bank is 200, which includes 50 for variation margin received and 150 for the net independent amount.
First, we determine the replacement cost. The net collateral currently held is 200 and the net independent collateral amount (NICA) is equal to the independent amount (that is, 150). The current market value of the trades in the netting set (V) is 80, it is calculated as the sum of the market value of the trades, ie 30 – 20 + 50 – 50 – 30 + 100 = 80. The replacement cost for margined netting sets is calculated using the formula set out in CRE52.18. Using this formula the replacement cost for the netting set in this example is:
Second, it is necessary to recalculate the interest rate and commodity addons, based on the value of the maturity factor for margined transactions, which depends on the margin period of risk. For daily remargining, the margin period of risk (MPOR) would be 10 days. In accordance with CRE52.50, for netting sets that are not subject daily margin agreements the MPOR is the sum of nine business days plus the remargining period (which is five business days in this example). Thus the MPOR is 14 (= 9 + 5) in this example.
The rescaled maturity factor for the trades in the netting set is calculated using the formula set out in CRE52.52. Using the MPOR calculated above, the maturity factor for all trades in the netting set in this example it is calculated as follows (a market convention of 250 business days in the financial year is used):
For the interest rate addon, the effective notional for each trade (Di = di * MFi * δi) calculated in CRE99.32 must be recalculated using the maturity factor for the margined netting set calculated above. That is:
IR Trade 
Notional 
Base 
Maturity bucket 
Adjusted 
Maturity Factor, MF_{i} 
Delta, δ_{i} 
Effective notional, D_{i} (USD, thousands) 
1 
10,000 
USD 
3 
78,694 

1 
27,934 
2 
10,000 
USD 
2 
36,254 

1 
12,869 
3 
5,000 
EUR 
3 
37,428 

0.2694 
3,579 
Next, the effective notional of each of the three maturity buckets within each hedging set must now be calculated. However, as set out in CRE99.35, given that in this example there are no maturity buckets within a hedging set with more than a single trade, the effective maturity of each maturity bucket is simply equal to the effective notional of the single trade in each bucket. Specifically:
For the USD hedging set: DB1 is zero, DB2 is 12,869 (thousand USD) and DB3 is 27,934 (thousand USD).
For the EUR hedging set: DB1 and DB2 are zero and DB3 is 3,579 (thousand USD).
Next, the effective notional of each of the two hedging sets (USD and EUR) must be recalculated using formula set out in CRE99.37 and the updated values of the effective notionals of each maturity bucket. The calculation is as follows:
Next, the hedging set level addons (AddOn_{hs}) must be recalculated by multiplying the recalculated effective notionals of each hedging set (EN_{hs}) by the prescribed supervisory factor of the hedging set (SF_{hs}). As set out in CRE99.35, the prescribed supervisory factor in this case is 0.5%. Therefore, the addon for the USD and EUR hedging sets are, respectively (expressed in USD thousands):
Finally, the interest rate asset class level addon (AddOnIR) can be recalculated by adding together the USD and EUR hedging set level addons as follows (expressed in USD thousands):
The addon for the commodity asset class must also be recalculated using the maturity factor for the margined netting. The effective notional for each trade (Di = di * MFi * δi) is set out in the table below:
Commodity Trade 
Notional 
Hedging set 
Commodity type 
Adjusted 
Maturity Factor, MF_{i} 
Delta, δ_{i} 
Effective notional, D_{i} (USD, thousands) 
1 
10,000 
Energy 
Crude Oil 
10,000 

1 
3,550 
2 
20,000 
Energy 
Crude Oil 
20,000 

1 
7,100 
3 
10,000 
Metals 
Silver 
10,000 

1 
3,550 
The combined effective notional for all derivatives with each hedging set that reference the same commodity type (EN_{ComType}) must be recalculated by adding together the trade level effective notionals above for each commodity type. This gives the following:
EN_{CrudeOil} = 3,550 + (7,100) = 3,550
EN_{Silver} = 3,550
The addon for each commodity type (AddOn_{C}_{rudeOil} and AddOn_{Silver}) within each hedging set calculated in CRE99.69 must now be recalculated by multiplying the recalculated combined effective notional for that commodity by the relevant supervisory factor (ie 18%). Therefore:
AddOn_{CrudeOil} = 3,550 * 0.18 = 639
AddOn_{Silver} = 3550 * 0.18 = 639
Next, recalculate the addon for energy and metals hedging sets using the recalculated addons for each commodity type above. As noted in CRE99.72, given that there is only one commodity type with each hedging set, the hedging set level add on is simply equal to the absolute value of the commodity type addon. That is:
Finally, calculate the commodity asset class level addon (AddOnCommodity) by adding together the hedging set level addons:
The aggregate netting set level addon can now be calculated. As set out in CRE52.25, it is calculated as the sum of the asset class level addons. That is for this example:
Finally, aggregating the replacement cost and the PFE component and multiplying the result by the alpha factor of 1.4, the EAD is as follows (USD thousands):
The bank currently has met all past variation margin (VM) calls so that the value of trades with its counterparty (€80 million) is offset by cumulative VM in the form of cash collateral received. There is a small “Minimum Transfer Amount” (MTA) of €1 million and a €0 ”Threshold” (TH). Furthermore, an “Independent Amount” of €10 million is agreed in favour of the bank and none in favour of its counterparty (ie the NICA is €10 million. This leads to a credit support amount of €90 million, which is assumed to have been fully received as of the reporting date.
In this example, the three terms in the replacement formula are:
V  C = €80 million – €90 million = negative €10 million.
TH + MTA – NICA = €0 + €1 million  €10 million = negative €9 million.
The third term in the replacement cost formula is always zero, which ensures that replacement cost is not negative.
The highest of the three terms (€10 million, €9 million, 0) is zero, so the replacement cost is zero. This is due to the large amount of collateral posted by the bank’s counterparty.
The counterparty has met all VM calls but the bank has some residual exposure due to the MTA of €1 million in its master agreement, and has a €0 TH. The value of the bank’s trades with the counterparty is €80 million and the bank holds €79.5 million in VM in the form of cash collateral. In addition, the bank holds €10 million in independent collateral (here being an initial margin independent of VM, the latter of which is driven by marktomarket (MTM) changes) from the counterparty. The counterparty holds €10 million in independent collateral from the bank, which is held by the counterparty in a nonsegregated manner. The NICA is therefore €0 (= €10 million independent collateral held less €10 million independent collateral posted).
In this example, the three terms in the replacement formula are:
V – C = €80 million – (€79.5 million + €10 million  €10 million)= €0.5 million.
TH + MTA – NICA = €0 + €1 million – €0 = €1 million.
The third term is zero.
The replacement cost is the highest of the three terms (€0.5 million, €1 million, 0) which is €1 million. This represents the largest exposure before collateral must be exchanged.
The case of central clearing can be viewed from a number of perspectives. One example in which the replacement cost formula for margined trades can be applied is when the bank is a clearing member and is calculating replacement cost for its own trades with a central counterparty (CCP). In this case, the MTA and TH are generally zero. VM is usually exchanged at least daily and the independent collateral amount (ICA) in the form of a performance bond or initial margin is held by the CCP.
The bank, in its capacity as clearing member of a CCP, has posted VM to the CCP in an amount equal to the value of the trades it has with the CCP. The bank has posted cash as initial margin and the CCP holds the initial margin in a bankruptcy remote fashion. Assume that the value of trades with the CCP are negative €50 million, the bank has posted €50 million in VM and €10 million in initial margin (IM) to the CCP.
Given that the IM is held by the CCP in a bankruptcyremote fashion, CRE52.17 permits this amount to be excluded in the calculation of NICA. Therefore, the NICA is €0 because the bankruptcy IM posted to the CCP can be exclude and the bank has not received any IM from the CCP. The value of C is calculated as the value of NICA plus any VM received less any VM posted. The value of C is thus negative €50 million (= €0 million + €0 million  €50 million).
In this example, the three terms in the replacement cost formula are:
V – C = (€50 million) – (€50 million) = €0. That is, the negative value of the trades has been fully offset by the VM posted by the bank.
TH + MTA – NICA = €0 + €0  €0 = €0.
The third term is zero.
Example 4 is the same as the Example 3, except that the IM posted to the CCP is not bankruptcyremote. As a consequence, the €10 million of IM must be included in the calculation of NICA. Thus, NICA is negative €10 million (= ICA received of €0 minus unsegregated ICA posted of €10 million). Also, the value of C is negative €60 million (=NICA + VM received  VM posted = €10 million + €0  €50 million).
In this example, the three terms in the replacement formula are:
V – C = (€50 million) – (€60 million) = €10 million. That is, the negative value of the trades is more than fully offset by collateral posted by the bank.
TH + MTA – NICA = €0 + €0 – (€10 million)= €10 million.
The third term is zero.
The replacement cost is therefore €10 million. This represents the IM posted to the CCP which risks being lost upon default and bankruptcy of the CCP.
Some margin agreements specify that a counterparty (in this case, a bank) must maintain a level of collateral that is a fixed percentage of the MTM of the transactions in a netting set. For this type of margining agreement, ICA is the amount of collateral that the counterparty must maintain above the net MTM of the transactions.
For example, suppose the agreement states that a counterparty must maintain a collateral balance of at least 140% of the MTM of its transactions and that the MTM of the derivatives transactions is €50 in the bank’s favour. ICA in this case is €20 (= 140% * €50 – €50). Further, suppose there is no TH, no MTA, the bank has posted no collateral and the counterparty has posted €80 in cash collateral. In this example, the three terms of the replacement cost formula are:
V – C = €50  €80 = €30.
MTA + TH  NICA = €0 + €0  €20 = €20.
The third term is zero.
Consider a fund that replicates an equity index. Moreover, assume the following:
The bank uses the Standardised Approach for credit risk when calculating its capital requirements for credit risk and for determining counterparty credit risk exposures it uses the SACCR.
The bank owns 20% of the shares of the fund.
The fund holds forward contracts on listed equities that are cleared through a qualifying CCP (with a notional amount of USD 100); and
The fund presents the following balance sheet:
Assets 

Cash 
USD 20 
Government bonds (AAArated) 
USD 30 
VM receivable (ie collateral posted by the bank to the CCP in respect of the forward contracts) 
USD 50 
Liabilities 

Notes payable 
USD 5 
Equity 

Shares, retained earnings and other reserves 
USD 95 
The funds exposures will be risk weighted as follows:
The RWA for the cash (RWA_{cash}) are calculated as the exposure of USD 20 multiplied by the applicable standardised approach (SA) risk weight of 0%. Thus, RWA_{cash} = USD 0.
The RWA for the government bonds (RWA_{bonds}) are calculated as the exposure of USD 30 multiplied by the applicable SA risk weight of 0%. Thus, RWA_{bonds} = USD 0.
The RWA for the exposures to the listed equities underlying the forward contracts (RWA_{underlying}) are calculated by multiplying the following three amounts: (1) the SA credit conversion factor of 100% that is applicable to forward purchases; (2) the exposure to the notional of USD 100; and (3) the applicable risk weight for listed equities under the SA which is 100%. Thus, RWA_{underlying} = 100% * USD100 * 100% = USD 100.
The forward purchase equities expose the bank to counterparty credit risk in respect of the market value of the forwards and the collateral posted that is not held by the CCP on a bankruptcy remote basis. For the sake of simplicity, this example assumes the application of SACCR results in an exposure value of USD 56. The RWA for counterparty credit risk (RWA_{CCR}) are determined by multiplying the exposure amount by the relevant risk weight for trade exposures to CCPs, which 2% in this case (see CRE54 for the capital requirements for bank exposures to CCPs). Thus, RWA_{CCR} = USD 56 * 2% = USD 1.12. (Note: There is no credit valuation adjustment, or CVA, charge assessed since the forward contracts are cleared through a CCP.)
The leverage of a fund under the LTA is calculated as the ratio of the fund’s total assets to its total equity, which in this examples is 100/95.
Therefore, the RWA for the bank’s equity investment in the fund is calculated as the product of the average risk weight of the fund, the fund’s leverage and the size of the bank’s equity investment. That is:
Consider a fund with assets of USD 100, where it is stated in the mandate that the fund replicates an equity index. In addition to being permitted to invest its assets in either cash or equities, the mandate allows the fund to take long positions in equity index futures up to a maximum nominal amount equivalent to the size of the fund’s balance sheet (USD 100). This means that the total on balance sheet and off balance sheet exposures of the fund can reach USD 200. Consider also that a maximum financial leverage (fund assets/fund equity) of 1.1 applies according to the mandate. The bank holds 20% of the shares of the fund, which represents an investment of USD 18.18.
First, the onbalance sheet exposures of USD 100 will be risk weighted according to the risk weights applied to equity exposures (risk weight =100%), ie RWA_{on}_{BS} = USD 100 * 100% = USD 100.
Second, we assume that the fund has exhausted its limit on derivative positions, ie USD 100 notional amount. The RWA for the maximum notional amount of underlying the derivatives positions calculated by multiplying the following three amounts: (1) the SA credit conversion factor of 100% that is applicable to forward purchases; (2) the maximum exposure to the notional of USD 100; and (3) the applicable risk weight for equities under the SA which is 100%. Thus, RWA_{underlying} = 100% * USD100 * 100% = USD 100.
Third, we would calculate the counterparty credit risk associated with the derivative contract. As set out in CRE60.7(3):
If we do not know the replacement cost related to the futures contract, we would approximate it by the maximum notional amount, ie USD 100.
If we do not know the aggregate addon for potential future exposure, we would approximate this by 15% of the maximum notional amount (ie 15% of USD 100=USD 15).
The counterparty credit risk exposure is calculated by multiplying
the sum of the replacement cost and aggregate addon for potential future exposure; by
1.4, which is the prescribed value of alpha.
The counterparty credit risk exposure in this example, assuming the replacement cost and aggregate addon amounts are unknown, is therefore USD 161 (= 1.4 *(100+15)). Assuming the futures contract is cleared through a qualifying CCP, a risk weight of 2% applies, so that RWA_{CCR} = USD 161 * 2% = USD 3.2. There is no CVA charge assessed since the futures contract is cleared through a CCP.
The RWA of the fund is hence obtained by adding RWA_{on}_{BS}, RWA_{underlying} and RWA_{CCR}, ie USD 203.2 (=100 + 100 + 3.2).
The RWA (USD 203.2) will be divided by the total assets of the fund (USD 100) resulting in an average riskweight of 203.2%. The bank’s total RWA associated with its equity investment is calculated as the product of the average risk weight of the fund, the fund’s maximum leverage and the size of the bank’s equity investment. That is the bank’s total associated RWA are 203.2% * 1.1 * USD 18.18 = USD 40.6.
Consider a fund with assets of USD 100 that invests in corporate debt. Assume that the fund is highly levered with equity of USD 5 and debt of USD 95. Such a fund would have financial leverage of 100/5=20. Consider the two cases below.
In Case 1 the fund specialises in lowrated corporate debt, it has the following balance sheet:
Assets 

Cash 
USD 10 
A+ to A bonds 
USD 20 
BBB+ to BB bonds 
USD 30 
Below BB bonds 
USD 40 
Liabilities 

Debt 
USD 95 
Equity 

Shares, retained earnings and other reserves 
USD 5 
The average risk weight of the fund is (USD10*0% + USD20*50% + USD30*100% + USD40*150%)/USD100 = 100%. The financial leverage of 20 would result in an effective risk weight of 2,000% for banks’ investments in this highly levered fund, however, this is capped at a conservative risk weight of 1,250%.
In Case 2 the fund specialises in highrated corporate debt, it has the following balance sheet:
Assets 

Cash 
USD 5 
AAA to AA bonds 
USD 75 
A+ to A bonds 
USD 20 
Liabilities 

Debt 
USD 95 
Equity 

Shares, retained earnings and other reserves 
USD 5 
The average risk weight of the fund is (USD5*0% + USD75*20% + USD20*50%)/USD100 = 25%. The financial leverage of 20 results in an effective risk weight of 500%.
The above examples illustrate that the rate at which the 1,250% cap is reached depends on the underlying riskiness of the portfolio (as judged by the average risk weight) as captured by standardised approach risk weights or the IRB approach. For example, for a “risky” portfolio (100% average risk weight), the 1,250% limit is reached fairly quickly with a leverage of 12.5x, while for a “low risk” portfolio (25% average risk weight) this limit is reached at a leverage of 50x.