Annex 12
The ways of the calculation of risk-weighted exposure amounts under the IRB Approach
1. Input parameters
a) In calculating the risk-weighted exposure amount for credit risk the input parameters
represented by PD and LGD values, maturity (M) and exposure value (E) are set
subject to Annex 13 of the Decree, unless this Annex stipulates otherwise.
b) In calculating the risk-weighted exposure amount for dilution risk the input parameters
represented by PD and LGD values and exposure value (E) are set subject to Annex
13 of the Decree and the input parameter, represented by maturity (M), shall be one
year.
c) The method for calculating the risk-weighted exposure amount for credit risk depends
on whether the exposure is assigned to the class of
1.
exposures to central governments and central banks, exposures to institutions
or corporate exposure,
retail exposures,
equity exposures, or
other exposures.
2.
3.
4.
2. Class of exposures to central governments and central banks, institutions or
corporates
a) For exposures in this class the risk-weighted exposure amount for credit risk is
calculated according to the formulae
Correlation(R ) = 0.12 ⋅
1 − exp(− 50 ⋅ PD )
1 − exp(− 50 )

+ 0.24 ⋅ 1 −

1 − exp(− 50 ⋅ PD )
1 − exp(− 50 )


Maturity factor (b) = (0.11852 – 0.05478 · ln(PD))2,
Risk Weight (r ) =
 1



R
=  LGD ⋅ N 
⋅ G (PD ) +
⋅ G (0.999 ) − PD ⋅ LGD  ⋅
1− R
 1 − R



⋅
1
1 − 1.5 ⋅ b
where: N(x)
G(z)
⋅ (1 + (M − 2.5) ⋅ b ) ⋅ 12.5 ⋅ 1.06
denotes the cumulative distribution function for a standard normal random variable,
i.e. the probability that a random variable which has a standard normal distribution
is less then or equal to x,
denotes the inverse cumulative distribution function for a standard normal variable,
i.e. the value x such that N(x) = z.
Risk-weighted exposure = E · r,
where:
E
r
denotes the exposure value,
denotes the risk weight.
If PD = 0 %, then r = 0.
If PD = 100 %, then:
a) for defaulted exposures, for which the liable entity is not authorised to use own LGD value estimates,
r = 0,
b) for defaulted exposures, for which the liable entity is authorised to use own LGD value estimates r =
max{0;12.5 · (LGD-ELBE )}
where ELBE is the best estimate of the expected loss for defaulted exposures performed by the liable
entity in accordance with Annex 10 to the Decree.
b) For all exposures subject to the provisions on credit risk mitigation techniques in the
case of double default, pursuant to Articles 102 to 107 and Annex 15 to the Decree,
the risk-weighted exposure amount may be adjusted according to the formula:
Risk-weighted exposure amount = E · r · (0.15 + 160 · PDpp)
where: PDpp
r
denotes the probability of default of the protection provider,
is calculated using the relevant risk weight formula stated in point a) for the exposure,
the obligor’s PD value and the LGD value of a comparable direct exposure to the
provider. The maturity factor (b) is calculated using the lower of the PD value of the
protection provider and the obligor’s PD value.
c) For corporate exposures to persons whose total annual turnover for the consolidated
group, of which the relevant person is a part, is less than EUR 50 000 000, the liable
entity may calculate risk weights using the formula for the correlation.
( )
Correlation R = 0.12 ⋅
(
1 − exp − 50 ⋅ PD
(
1 − exp − 50
)
)
(

1 − exp − 50 ⋅ PD

1 − exp − 50
+ 0.24 ⋅ 1 −
(
)
)
 S − 5
 − 0.04 ⋅  1 − 45 

where: S denotes the total annual turnover in EUR, given that an amount equivalent to EUR 5 000 000
≤ S ≤ an amount equivalent to EUR 50 000 000. If the reported turnover is lower than an
amount equivalent to EUR 5 000 000 the same procedure shall be followed as if it were equal
to an amount equivalent to EUR 5 000 000. For purchased receivables the total annual turnover
shall be the weighted average of the individual exposures in the pool. If the total annual
turnover is not a reasonable indicator of the obligor’s size and a more meaningful indicator is
the balance sheet total, the liable entity shall replace total annual turnover with the consolidated
balance sheet total.
d) Specialised lending exposures for which the liable entity is not able to demonstrate
that its PD value estimates meet the requirements for using the IRB Approach stated in
Annex 10 of the Decree, shall be assigned risk weights according to the Table in this
Annex.
Table
Remaining maturity
Less than 2.5 years
Equal to or more than 2.5
years
Grade 1
50 %
Grade 2
70 %
Grade 3
115 %
Grade 4
250 %
Grade 5
0%
70 %
90 %
115 %
250 %
0%
The competent authority may permit the liable entity to assign a risk weight of 50 % to
all exposures assigned to grade 1, and to assign a risk weight of 70 % to all exposures
assigned to grade 2 provided that the procedures employed by the liable entity, in
particular the underwriting procedures, are sufficiently stringent for the relevant grade.
In assigning risk weights to specialised lending exposures the liable entity shall take
into account the
1.
2.
3.
4.
5.
financial situation,
political and legal environment,
characteristics of the transaction or asset,
strength of the sponsor and developer, including any income streams from a
public private partnership,
security package.
e) For purchased corporate receivables the liable entity shall comply with the
requirements for using the IRB Approach set out in Annex 10 to the Decree, which
are relevant for these exposures.
For purchased corporate receivables that comply, in addition, with the conditions
stipulated for purchased retail exposures, and in whose case it would be unduly
burdensome for the liable entity to meet the requirements for risk quantification, the
liable entity may meet the risk quantification requirements stipulated for retail
exposures.
Purchased corporate receivables, refundable purchase discounts, collateral or partial
guarantees which provide first-loss protection for default losses or dilution losses may
be treated in the same way as first-loss positions under the IRB Approach
securitisation framework.
f) If the liable entity provides credit risk protection for several exposures on condition
that the n-th default among these exposures shall result in the protection’s use and that
this credit event shall terminate the contract then, in the event that
1.
2.
the product has an external rating from an eligible rating agency, the risk
weights set for securitised exposures shall be used,
the product does not have an external rating from an eligible rating agency, the
risk weights of exposures included in the basket shall be aggregated with the
exception of n-1 exposures, provided that the sum of the expected credit loss
amount multiplied by 12.5 and the risk-weighted exposure amount does not
exceed the nominal value of protection provided by the credit derivative
multiplied by 12.5. The relevant n-1 exposures that are to be excluded from the
aggregation shall be defined in such a way that they include exposures which
produce lower risk-weighted exposures than the risk-weighted exposure
amount of any of the exposures included in the aggregation. The following
formula shall apply for this case:
A prerequisite is an existence of k instruments in the basket such that the nth
default results in the use of protection and concludes the contract. It shall apply
that: 1 ≤ n ≤ k
where:
E1, …., En, …, Ek
denotes individual exposure values,
r1, …, rn,…, rk
denotes individual exposure risk weights,
EL1, …, ELn, … ELk
denotes expected loss rates relating to
individual exposures,
NAP
denotes the nominal value of the protection
provided by a credit derivative.
While:
r1 . E1, …, r n-1 . E n-1 are the smallest (n-1) risk-weighted exposures within the
total number of risk-weighted exposures.
Then
Risk-weighted exposure amount = min{C;NAP · 12,5}.
3. Retail exposure class
a) For exposures in this class the risk-weighted exposure amount for credit risk is
calculated according to the formulae
Correlation(R ) = 0.03 ⋅
Risk Weight
=

 LGD

1 − exp(− 35 ⋅ PD )
1 − exp(− 35)

+ 0.16 ⋅ 1 −
1 − exp(− 35 ⋅ PD )
1 − exp(− 35)



(r ) =

⋅N
1
 1 − R
⋅ G (PD ) +
R
1− R

⋅ G (0 . 999 ) − PD ⋅ LGD


 ⋅ 12 . 5 ⋅ 1 . 06

where:
N(x)
denotes the cumulative distribution function for a standard normal random variable, i.e. the probability
that a random variable which has a standard normal distribution is less than or equal to x.
G(z)
denotes the inverse cumulative distribution function for a standard normal variable, i.e. the value
x such that N(x) = z
Risk-weighted exposure = E · r,
where: E
denotes the exposure value.
If the PD value = 100 % (a defaulted exposure), then r = max {0; 12.5 * (LGD - ELBE )}
provided that ELBE is the best estimate of the expected loss for the defaulted exposure
performed by the liable entity in accordance with Annex 10 to the Decree.
b) For all exposures to small and medium-size entrepreneurs that meet the conditions for
assignment to retail exposures and the conditions set out in Annex 15 to the Decree,
the risk-weighted exposure amount may be calculated according to the formula for
double default.
c) For retail exposures secured by real estate, the figure produced by the correlation
formula shall be replaced with a correlation (R) of 0.15.
d) For qualifying revolving retail exposures, the figure produced by the correlation
formula shall be replaced with a correlation (R) of 0.04. Exposures may be qualified
as qualifying revolving retail exposures if they meet the following conditions:
1.
2.
3.
4.
5.
they are exposures to individuals,
they are unsecured revolving exposures which, if they are not drawn
immediately and unconditionally, are cancellable by the liable entity. In this
context, revolving exposures are defined as exposures where the client’s
outstanding account balances may fluctuate based on their decision to borrow
or repay up to a certain limit set by the liable entity. Undrawn commitments
may be considered unconditionally cancellable if the liable entity is entitled to
cancel them to the full extent allowable under the protection of consumer rights
and other related legislation;
the maximum exposure to a single individual in this subportfolio is not higher
than an amount equivalent to EUR 100 000,
he liable entity is able to demonstrate that the use of the a correlation of 0.04 is
only limited to portfolios that exhibit relatively low volatility of loss rates
relative to their average level of loss rates, especially within the low PD value
bands. The relative loss rate volatility of individual qualifying revolving retail
pools and the loss rate volatility of the aggregated revolving retail portfolio
shall be the subject of review by the competent authority. Information on the
typical loss rate characteristics for qualifying revolving retail exposures across
jurisdictions may be shared by competent authorities;
he competent authority shall have granted its approval on condition that the
treatment of the relevant exposures as qualifying revolving retail exposures is
consistent with the underlying loss characteristics of the subportfolio.
Competent authorities may waive the requirement that the exposure be unsecured
under point 2 in the case of credit transactions secured by collateral and linked to an
account to which the client’s salary is transferred. In this case, however, any amounts
recovered from the collateral shall not be taken into account in the estimates of the
LGD value.
e) The liable entity may treat purchased receivables as retail exposures if the relevant
requirements are met for using the IRB Approach as set out in Annex 10 to the
Decree, and the following conditions are also met:
1.
2.
3.
4.
the liable entity has purchased the receivables from an unrelated third party and
its exposure to the obligor of the relevant receivable does not include any
exposures that are directly or indirectly originated by the liable entity itself,
the purchased receivables are generated on the basis of an independent relation
between the seller and the obligor. Mutual claims and commitments of persons
that sell and purchase between each other, and claims on related persons, are
excluded;
the purchasing liable entity is entitled to all proceeds from the purchased
receivables or to proportionate interest in the proceeds,
the portfolio of purchased receivables is sufficiently diversified.
f) Refundable purchase discounts, collateral or partial guarantees which provide first loss
protection for default losses or dilution losses may, in the case of purchased corporate
receivables, be treated in the same way as first loss positions under the IRB
securitisation framework.
g) In the case of a hybrid portfolio of purchased retail receivables, where the liable entity
is not able to separate exposures secured by real estate and qualifying revolving retail
exposures from other retail exposures, the risk weight function shall be applied which
produces the highest capital requirement for the relevant exposures.
4. Equity exposure class
a) The following approach shall be adopted when using the simple risk weight approach:
1.
The risk-weighted equity exposure amount for credit risk shall be calculated
according to the formula
Risk-weighted exposure = E · r,
where: E
r
denotes the exposure value,
denotes the risk weight, which is
a) 190 % for private equity in sufficiently diversified portfolios,
b) 290 % for exchange traded equity exposures,
c) 370 % for other equity exposures.
2.
Long positions of individual equities may be offset
2.1 against commitments from short sales of the same equities if the liable entity
does not create a trading portfolio and assigns these commitments to the
investment portfolio,
2.2 by means of hedging with equity derivatives in the investment portfolio on
condition that their residual maturity is at least one year. The liable entity shall
treat other short positions (commitments from short equity sales and short
positions from derivatives, if the liable entity does not create a trading
3.
portfolio and assigns these instruments to the investment portfolio) in the
same way as long positions with the relevant risk weight applied to the
absolute value of each position. In the case of maturity mismatched positions
the method shall be used for calculating the risk-weighted corporate exposure
amount.
Personal protection obtained on an equity exposure may be recognised on
condition that it is subject to the credit risk mitigation techniques pursuant to
Articles 102 to 107 and Annexes Nos. 15 and 16 to the Decree.
b) The following approach shall be adopted when using the PD/LGD approach.
1.
2.
The amount of risk-weighted equity exposure for credit risk shall be calculated
according to the formulae for calculating the risk-weighted corporate exposure
amount. If the liable entity does not have sufficient information to use the
definition of default pursuant to Heading II, it shall use a factor of 1.5 for
increasing the risk weights.
At the individual exposure level, the sum of the expected credit loss amount
multiplied by 12.5 and the risk-weighted exposure amount shall not exceed the
exposure amount multiplied by 12.5. This requirement can be expressed as
follows:
for an individual exposure i it is determined
min{ELi · Ei · 12.5 + ri · Ei; Ei · 12.5},
where: ELi
3.
denotes the expected loss rate amount,
Ei
denotes the exposure amount,
ri
denotes the risk weight.
In the case of equity exposures, eligible unfunded credit protection may be
considered on condition that it is subject to the credit risk mitigation techniques
pursuant to Articles 102 to 107 and Annexes Nos. 15 and 16 to the Decree. For
an exposure to the protection provider in this case an LGD value of 90 % shall
be applied. For private equities in sufficiently diversified portfolios an LGD
value of 65 % may be used. Maturity (M) for these purposes shall be five years.
c) The following approach shall be adopted when using the internal models approach.
1.
2.
The risk-weighted equity exposure amount for credit risk corresponds to the
potential loss on the liable entity’s equity exposures as derived using internal
VaR models, provided that a one-tailed confidence interval is used with the
confidence level of 99 % for the difference between quarterly returns and an
appropriate risk-free interest rate. The calculation is being made over a long
period and the percentile is multiplied by 12.5.
At the equity portfolio level the risk-weighted equity exposure amount shall not
fall below the sum of the minimum risk-weighted exposure amounts required
under the PD and LGD approach and the corresponding sum of expected credit
losses multiplied by 12.5. The PD and LGD values are calculated for this
purpose pursuant to Annex 13 to this Decree using the PD and LGD approach
for the equity exposure class.
3.
Unfunded credit protection for equity exposure credit risk may be recognised
on condition that it is subject to the credit risk mitigation techniques pursuant
to Articles 102 to 107 and Annexes Nos. 15 and 16 to the Decree.
5. Other exposure class
In the case of cash items or monetary gold held by a liable entity and/or deposited in the safes
of a third party, the risk-weighted exposure amount shall equal zero.
The risk weighted exposure amount of a leased asset shall be calculated according to the
formula:
risk-weighted exposure = 100 % · E,
where: E
denotes the exposure amount.
except for when the exposure is the residual value of a leased item and provided that this
residual value is not considered in the leasing exposure assigned to the relevant exposure
class, in such a case the following formula shall be used:
risk-weighted exposure = 1/t · 100 % · E,
where:
E
t denotes the remaining number of whole years of the lease contract term, but at least
1 year,
denotes the exposure amount.
6. Dilution risk
a) Risk weights and risk-weighted exposures shall be calculated according to the formula
for risk weights in the corporate exposure class.
b) The liable entity does not have to recognise dilution risk if it is able to demonstrate
that this is immaterial.