QIS 3 FAQ: R. Examples

QIS 3 FAQ: R. Examples

Credit Risk Mitigation Examples

We have received a range of questions relating to the credit risk mitigation proposals and how guarantees, credit derivatives and eligible collateral should be treated for QIS purposes. The following examples have been constructed to help clarify how credit protected exposures should be entered into the QIS spreadsheets under the standardised and IRB approaches.

Please note that in order to facilitate analysis an important tenet of the QIS is that banks should avoid reporting the same exposure in different portfolios on the different worksheets. This is to ensure comparability of the results calculated under the different approaches. Thus:

· for guaranteed and similar exposures, pre- and post-protection amounts should generally be reported in the portfolio of the guarantor (as in example 1) in all approaches (i.e. current, standardised and IRB). The exception is in the AIRB (and/or IRB retail) approach where a bank may choose to reflect the effect of a guarantee by adjusting its LGD rather than PD estimate. In this case, pre- and post-protection amounts should be reported in the portfolio of the underlying obligor in all approaches (also shown in example 1);

· similarly, where the Technical Guidance calls for an exposure to be included in different portfolios under the various calculation approaches, banks should use a consistent portfolio throughout the QIS spreadsheets - generally this should be the portfolio that would be applicable under the most sophisticated approach reported by each bank.⁸ For example, the definition of a retail exposure differs between the standardised and IRB approaches. Banks completing the IRB approach should use the IRB definition for the current, standardised and IRB approaches while banks completing only the standardised approach should follow the standardised definition. Likewise, where banks that reflect the effect of a guarantee by adjusting their LGD rather than PD estimates under the AIRB (and/or IRB retail) approach, the protected exposure (both pre- and post-protection) should be reported in the portfolio of the underlying borrower for all calculation approaches. All other respondent banks should report the exposure in the portfolio of the guarantor (again refer example 1).

Please also note that where default probabilities have been associated with external ratings in these examples this has been done for exposition purposes only and has no significance of a more general nature (refer FAQ I.8 for more information).

(i) Credit protection (guarantees, credit derivatives etc)

Example 1: € 100 million loan to unrated corporate (PD=1%) fully guaranteed by AA-rated bank (PD=0.05%)

Answer: As shown below, under all calculation approaches (with the exception of where the bank chooses the option under AIRB (and/or IRB retail) approach to reflect the effect of the guarantee by adjusting its LGD rather than PD estimate), both the pre-protection and post-protection amounts should be entered under the portfolio of the guarantor rather than the underlying obligor. Refer also to example 5, which shows how to enter partially guaranteed exposures.

Standardised approach

Post-protection, substitute the risk weight of the guarantor for that of the underlying obligor.

Risk weight category	All exposures	Exposures w/o CRM	Exposures with credit protection
Risk weight category	All exposures	Exposures w/o CRM	Pre-protection	Post-protection
Corporates
20%
100%, unrated
Banks
20%				100
100%, not including unrated	100		100

FIRB approach

Post-protection, substitute the PD of the guarantor for that of the underlying obligor.

Corporates		Effects of credit protection		Banks		Effects of credit protection
		Exposures before credit protection	Exposures after credit protection			Exposures before credit protection	Exposures after credit protection

	PD				PD
	0.05%				0.05%		100
	1.00%				1.00%	100

As the guarantor bank has not posted any collateral in this example, in the LGD grid within the Banks spreadsheet, also enter 100 in the PD=0.05% row and LGD=45% column.

AIRB approach

Under the AIRB approach, banks may reflect guarantees either by adjusting borrower grades or LGDs, but not both. Under both options, the risk weight must not be less than that of a comparable direct exposure to the protection provider (refer paragraph 267 of the Technical Guidance).

(i) the bank reflects the guarantee by adjusting PD

In this case, enter the exposure as in the FIRB example. The only difference is that when completing the LGD grid the bank's own LGD estimate for an unsecured corporate exposure should be used instead of the FIRB 45% LGD assumption.

(ii) the bank reflects the guarantee by adjusting LGD

In this case, further assume that the bank's LGD estimate for an unsecured direct exposure to the corporate obligor is 50% and to the bank guarantor it is 30%. The bank's loss history also suggests a 5% LGD for its bank-guaranteed corporate exposures.

Compare the risk weight obtained using PD=1% and LGD=5% (i.e. 11%) with the risk weight for a direct exposure to the guarantor bank, PD=0.05% and LGD=30% (i.e. 13%). As the risk weight of the guaranteed exposure cannot be less than the risk weight of a direct exposure to the guarantor bank, a risk weight of 13% would apply in this example. To enter this information into the QIS spreadsheet it is first necessary to calculate the LGD that when combined with a PD=1% results in a risk weight of 13%. As LGD impacts on risk weights linearly, the adjustment is as follows: LGD = 13% / 11% * 5% = 6%. The exposure can now be entered into the corporate spreadsheet as shown below.

Corporates		Effects of credit protection		LGD	6%
		Exposures before credit protection	Exposures after credit protection
	PD
	0.05%
	1.00%	100	100		100

Remember, for QIS purposes the bank should avoid shifting exposures from one portfolio to another between approaches. Thus, in this case the exposure should be reported within the corporate portfolio (i.e. the portfolio of the underlying obligor) for all calculation approaches, not just for the AIRB approach.

Example 2: € 10 million short-term self-liquidating trade finance exposure to unrated corporate (PD=1%) fully guaranteed by AA-rated sovereign (PD=0.05%)

Answer:

Standardised approach

Apply standardised approach trade finance credit conversion factor of 20%

Risk weight category	All exposures	Exposures w/o CRM	Exposures with credit protection
Risk weight category	All exposures	Exposures w/o CRM	Pre-protection	Post-protection
Corporates

100%, unrated
Sovereign
0%				2
Unrated 100%	2		2

FIRB/AIRB approaches

Under FIRB, a trade finance credit conversion factor of 50% should be applied as shown below.

Corporates		Effects of credit protection		Sovereigns		Effects of credit protection
		Exposures before credit protection	Exposures after credit protection			Exposures before credit protection	Exposures after credit protection

	PD				PD
	0.05%				0.05%		5
	1.00%				1.00%	5

Under AIRB, the bank should apply its own credit conversion factor (or EAD) but otherwise should complete the QIS spreadsheets following the general procedure outlined in example 1.

Example 3: € 100 million undrawn commitment with original maturity < 1 year to unrated corporate (PD=1%) fully guaranteed by A-rated parent (PD=0.2%)

Answer:

Standardised approach

Apply the standardised approach credit conversion factor for undrawn commitments with original maturity of under 1 year of 20%

Risk weight category	All exposures	Exposures w/o CRM	Exposures with credit protection
Risk weight category	All exposures	Exposures w/o CRM	Pre-protection	Post-protection
Corporates
50%				20
100%, unrated	20		20

FIRB approach

Apply the FIRB 75% EAD for undrawn commitments

Corporates		Effects of credit protection
		Exposures before credit protection	Exposures after credit protection

	PD
	0.20%		75
	1.00%	75

AIRB approach

In the AIRB spreadsheets undrawn commitments should be entered before credit conversion. The bank should also complete the EAD grid appearing to the far right of the spreadsheet using its own EAD bands.

The table below shows the entries for banks that under AIRB reflect guarantees by adjusting their PD estimates. Refer also example 1 for more information for banks that reflect guarantees by adjusting their LGD estimates.

Corporates		Effects of credit protection
		Exposures before credit protection	Exposures after credit protection

	PD
	0.20%		100
	1.00%	100

Example 4: As in Example 3 but assume BBB-rated parent (PD=0.7%)

Answer:

Standardised approach

Risk weight category	All exposures	Exposures w/o CRM	Exposures with credit protection
Risk weight category	All exposures	Exposures w/o CRM	Pre-protection	Post-protection
Corporates
100%, not including unrated
100%, unrated	20	20

ie the parent guarantee is not recognised in this case as a corporate guarantor must be externally rated A- or better under the standardised approach credit risk mitigation proposals (refer paragraph 159 in the QIS Technical Guidance). In any case, in this example, non-recognition of the guarantee makes no practical difference as both unrated and BBB-rated entities receive a 100% risk weight.

FIRB approach

Corporates		Effects of credit protection
		Exposures before credit protection	Exposures after credit protection

	PD
	0.70%
	1.00%	75	75

Again, the parent guarantee is not recognised as the corporate guarantor must be rated the equivalent of A- or better under the FIRB credit risk mitigation proposals.

AIRB approach

Corporates		Effects of credit protection
		Exposures before credit protection	Exposures after credit protection

	PD
	0.70%		100
	1.00%	100

Under AIRB there is no restriction on the rating of the guarantor. However, again note that in the AIRB spreadsheets undrawn commitments should be entered before credit conversion as described in example 3. Also note that the table above shows the entries for banks that under AIRB reflect guarantees by adjusting their PD estimates. For banks that reflect guarantees by adjusting their LGD estimates refer also example 1.

Example 5: € 100 million loan to unrated corporate (PD=1%) protected by € 50 million credit default swap with the same remaining maturity from AA-rated bank (PD=0.05%)

Answer: Split the exposure into a covered and uncovered amount. For all calculation approaches (with the exception of the AIRB approach where the bank chooses the option to reflect the effect of the guarantee by adjusting its LGD rather than PD estimate), enter the uncovered amount into the corporate portfolio and the covered amount into the portfolio of the guarantor (which in this case is a bank). More generally, when calculating the covered amount the bank would also need to take into account any maturity and/or currency mismatches between the guarantee and the underlying exposure.

Standardised approach

Risk weight category	All exposures	Exposures w/o CRM	Exposures with credit protection
Risk weight category	All exposures	Exposures w/o CRM	Pre-protection	Post-protection
Corporates
20%
100%, unrated	50	50
Banks
20%				50
100%, not including unrated	50		50

FIRB/AIRB approaches

Corporates		Effects of credit protection		Banks		Effects of credit protection
		Exposures before credit protection	Exposures after credit protection			Exposures before credit protection	Exposures after credit protection

	PD				PD
	0.05%				0.05%		50
	1.00%	50	50		1.00%	50

(ii) Collateralised exposures

Example 6: € 10 million loan to an unrated corporate (PD=1%) secured by commercial real estate valued at € 12 million

Answer:

Standardised approach

Generally speaking, the credit risk mitigation effect of commercial real estate collateral is not recognised under the standardised approach. The exception is that in some countries certain loans that meet the strict criteria set out in footnote 18 of the QIS Technical Guidance may receive a preferential risk weight. Assuming that the preferential risk weight does not apply, the loan in the example should be reported in the risk weight category labelled 'Corporate lending collateralised with commercial real estate, 100%' as shown in the table below. (Please note that no figures should be entered in the columns headed 'Collateralised exposures' as these columns should only be used for exposures secured against eligible financial collateral.)

Risk weight category	All exposures	Exposures w/o CRM	Collateralised exposures
Risk weight category	All exposures	Exposures w/o CRM	Pre-collateral	Post-collateral
Corporates
Corporate lending collateralised with residential real estate, 40%
Corporate lending collateralised with CRE, 50%
Corporate lending collateralised with CRE, 100%	10	10

As noted above, subject to national discretion, in some countries, certain loans secured against commercial real estate may qualify for a 50% risk weight for that part of the loan that does not exceed the lower of 50% of the market value or 60% of the mortgage lending value of the property securing the loan. The qualifying portion of such loans should be reported in the risk weight category labelled 'Corporate lending collateralised with commercial real estate, 50%' with any excess reported in the risk weight category labelled 'Corporate lending collateralised with commercial real estate, 100%'.

FIRB approach

As the collateral to loan ratio is 120% the loan in the example does not meet the FIRB overcollateralisation requirement of 140% for loans secured against commercial property. Therefore split the loan into a covered and uncovered amount:

· Covered amount = (% covered by security / overcollateralisation requirement) * exposure

= 120 / 140 * €10 m

= € 8.6 million · LGD = 35%

· Uncovered amount = €10 m - €8.6 m = € 1.4 million · LGD = 45%

Corporates	Collateral type	Unsecured subordinated	Unsecured senior	Commercial real estate
PD	LGD	75%	45%	35%

1.00%			1.4	8.6

Note that if the value of the security had been < € 3 million then the 30% minimum collateralisation requirement for loans secured against commercial property would not have been met and the covered amount would have been set to zero despite the presence of some security.

AIRB approach

Enter the whole exposure amount into the appropriate bank-specified band of the LGD grid in the AIRB spreadsheet.

Example 7: € 10 million loan to unrated corporate (PD=1%) secured by debt securities of AA-rated bank with remaining maturity of 3 years and a market value of € 9.9 million. For standardised and FIRB approaches. Also assume daily revaluation of the collateral and remargining.

Answer:

Standardised approach

Assume that the lending bank is using the comprehensive rather than simple approach for recognising eligible financial collateral (together with supervisory rather than internal haircut estimates).

Split the loan into a covered amount and an uncovered amount (E*) by applying the relevant standard supervisory haircut (H_c) of 4% to the collateral value (C):

· Covered amount = C * (1-H_c)

= €9.9 m * (1 - 0.04)

= € 9.5 million

· Uncovered amount (E*) = €10 m - €9.5 m = € 0.5million

Enter the gross exposure (E) into the pre-collateral column and the uncovered amount (E*) into the post-collateral column.

Risk weight category	All exposures	Exposures w/o CRM	Collateralised exposures
Risk weight category	All exposures	Exposures w/o CRM	Pre-collateral	Post-collateral
Corporates
100%, unrated*	10		10	0.5

FIRB approach

The simple approach to recognising collateral is not available under the FIRB approach. As in the standardised approach example, split the loan into a covered and uncovered amount:

· Covered amount = C * (1-H_c)

= €9.9 m * (1 - 0.04)

= € 9.5 million · LGD = 0%

· Uncovered amount = €10 m - €9.5 m = € 0.5million · LGD = 45%

Enter the covered and uncovered amounts into the appropriate LGD columns in the LGD grid.

Corporates	Collateral type	Unsecured subordinated	Unsecured senior	Financial collateral
PD	LGD	75%	45%	0%

1.00%			0.5	9.5

AIRB approach

Enter the whole exposure amount into the appropriate bank-specified band of the LGD grid in the AIRB spreadsheet.

(iii) Specific risk capital charges for positions hedged by credit derivatives

The following examples should be read in conjunction with paragraphs 642-652 of the QIS Technical Guidance.

Example 8: € 10 million BB-rated corporate bonds with remaining maturity of 3 years, hedged by a 3-year, € 10 million total return swap referenced against the same bonds, provided by a AA-rated bank (PD=0.05%)

Answer: The exposure meets the requirements set out in paragraph 646 of the QIS Technical Guidance for full recognition of the hedge, i.e. a 0% specific risk charge will apply for both legs of the hedged position.

Specific risk charge	Exposures
0%	20
0.25%
1.00%
1.60%
4.00%
8.00%

The add-on factor for counterpary risk for the credit derivative = €10m * 10% = € 1 million (refer paragraph 652 of the QIS Technical Guidance). The counterparty risk exposure (replacement cost + new add-on using the current approach method) should be reported in the panel for "Trading book counterparty exposures: OTC derivatives" in the "Standardised", "FIRB Trading Book", and "AIRB Trading Book" worksheets. Also in the "Current" and "Data" worksheets using existing rules.

Example 9: € 10 million A-rated government bonds with remaining maturity of 3 years, hedged by a credit default swap with the same reference obligation and the same remaining maturity provided by a AA-rated bank (PD=0.05%)

Answer: The exposure meets the requirements set out in paragraph 647 of the QIS Technical Guidance for partial recognition of the hedge, i.e. an 80% offset will apply for one leg and a 0% charge for the other leg of the hedged position. Note that the proposed specific risk charge for A-rated government paper with residual maturity > 24 months is 1.6% (refer paragraph 643 of the QIS Technical Guidance).

Specific risk charge	Exposures
0%	18
0.25%
1.00%
1.60%	2
4.00%
8.00%

The add-on factor for counterpary risk for the credit derivative = €10m * 10% = € 1 million (refer paragraph 652 of the QIS Technical Guidance). The counterparty risk exposure (replacement cost + new add-on using the current approach method) should be reported in the panel for "Trading book counterparty exposures: OTC derivatives" in the "Standardised", "FIRB Trading Book", and "AIRB Trading Book" worksheets. Also in the "Current" and "Data" worksheets using existing rules.

Example 10: € 10 million BBB-rated corporate bonds with remaining maturity of 3 years, hedged by a 1.5-year credit default swap with the same reference obligation, provided by a AA-rated bank (PD=0.05%)

Answer: The exposure meets the requirements in paragraph 648(b) of the QIS Technical Guidance for partial recognition of the hedge (though recognition is lower than in the previous example because of the mismatch between the maturity of the credit swap and the maturity of the underlying bond exposure). In this case, only the higher of the two legs' capital charges will apply. Note that disregarding the hedge the specific risk charges would be 1.6% for the bonds and 1.0% for the credit swap (unchanged from the existing specific risk charges set out in the current Accord). Thus, according to paragraph 648(b):

Specific risk charge	Exposures
0%	10
0.25%
1.00%
1.60%	10
4.00%
8.00%

The add-on factor for counterpary risk for the credit derivative = €10m * 10% = € 1 million (refer paragraph 652 of the QIS Technical Guidance). The counterparty risk exposure (replacement cost + new add-on using the current approach method) should be reported in the panel for "Trading book counterparty exposures: OTC derivatives" in the "Standardised", "FIRB Trading Book", and "AIRB Trading Book" worksheets. Also in the "Current" and "Data" worksheets using existing rules.

Example 11: € 10 million BB-rated bonds with remaining maturity of 5 years, hedged by a 3-year total return swap with 3-year bonds from the same issuer as the reference obligation, provided by a AA-rated bank (PD=0.05%)

Answer: The exposure meets the requirements set out in paragraph 648(a) of the QIS Technical Guidance that only the higher of the two legs' capital charges will apply. Note that the charge for the bond holding = 8% and for the credit derivative = 8%. Thus:

Specific risk charge	Exposures
0%	10
0.25%
1.00%
1.60%
4.00%
8.00%	10

The add-on factor for counterpary risk for the credit derivative = €10m * 10% = € 1 million (refer paragraph 652 of the QIS Technical Guidance). The counterparty risk exposure (replacement cost + new add-on using the current approach method) should be reported in the panel for "Trading book counterparty exposures: OTC derivatives" in the "Standardised", "FIRB Trading Book", and "AIRB Trading Book" worksheets. Also in the "Current" and "Data" worksheets using existing rules.

Other Examples

Example 1: Within a certain PD band, a bank has the following exposures. (1) a loan of € 100 that will be fully paid back in 6 months time; (2) a loan on which one € 25 payment will be received in 6 months time and a second, equal, payment will be received in 18 months time, (3) a loan on which one € 25 payment will be received in 2 years time and another, equal payment in 10 years time. What is the maturity that should be used for this PD-band?

Answer: First we have to calculate the maturities for the individual loans. Loan 1 has an economic maturity of 0.5 years. Maturities in IRB, however, are subject to a one year floor. Consequently M1=1. The maturity of loan 2 equals (25*0.5+25*1.5)/50 (floors are not applicable to individual cash flows). Consequently M2=1. The maturity of loan 3 would equal (25*2+25*10)/50=6. In this case the 5-year gap on maturity is binding. Consequently, M3=5, rather than 6. The combined maturity of the three loans equals (100*M1+50*M2+50*M3)/200 = (100*1+50*1+50*5)/200 = 2.

Example 2: Assume we have a € 100 loan to an unrated corporate. Under the standardised approach, using the simple approach, what risk weight would apply in the following scenarios (1) no collateral, (2) € 100 securities issues by a AAA-rated sovereign as collateral, (3) € 125 securities issues by a AAA-rated sovereign as collateral, (4) € 100 cash collateral, (5) € 115 gold as collateral

Answer: The five cases result in the following risk weights:

Example 3: What would the answers to the previous example be for a bank using the comprehensive approach (using the standard supervisory haircuts)?

Answer: The five cases result in the following risk weights:

Example 4: When using multiple types of collateral on a single exposure, banks should use the treatment that results in the largest possible recognition of collateral. Generally this implies that collateral should be recognised in the sequence indicated by the table in paragraph 256 of the Technical Guidance. The following (somewhat unrealistic) example illustrates how one should proceed. We assume a € 100 loan to a corporate obligor with a PD of 1%. A bank (PD = 0.05%) guarantees € 30 of this loan and pledges real estate collateral worth € 14 to support this guarantee. The guarantee satisfies the requirements set out in the Technical Guidance. Apart from the guarantee, the loan is supported by € 20 (after haircuts) financial collateral and € 28 of real estate collateral. All collateral meets all the necessary requirements.

Answer: In this example, we first look at the guarantee. Thanks to the guarantee, € 30 is assigned to the 0.05% PD-band. The collateral pledged to support the guarantee equals more than 30% of the guarantee and is eligible, although we should take into account the overcollateralisation requirement set out in paragraph 256 of the Technical Guidance (i.e. divide the value of the collateral by 140%). Consequently, we assign € 10 (14/140%) to the 35% LGD-band and the remainder (€ 20) to the 45% LGD-band.

Corporates		Effects of credit protection
		Exposures before credit protection	Exposures after credit protection	Collateral type:	Unsecured senior claims	Real estate	Financial collateral
				LGD:	45%	35%	0%
	PD
	0.50%
	1.00%	70	70		30	20	20

Bank		Effects of credit protection
		Exposures before credit protection	Exposures after credit protection	Collateral type:	Unsecured senior claims	Real estate	Financial collateral
				LGD:	45%	35%	0%
	PD
	0.50%		30		20	10
	1.00%	30

8 A minor exception to this general rule applies to exposures to public sector enterprises (refer FAQ A.13).

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