Basel
ii in the United States of America
From the
Basel ii
Compliance Professionals Association (BCPA),
the largest association of Basel ii Professionals in the
world
Final Rule, USA: Risk-Based Capital Standards:
Advanced Capital Adequacy Framework — Basel II
Supervisory
Formula Approach (SFA)
General requirements
Under the proposed rule, a bank using the
SFA would determine the risk weighted asset amount for a securitization exposure
by multiplying the SFA risk-based capital requirement for the exposure (as
determined by the supervisory formula set forth below)
by 12.5.
If the SFA risk weight for
a securitization exposure was 1,250 percent or greater, however, the bank would deduct
the exposure from total capital rather than risk weight
the exposure.
The
agencies noted that deduction is consistent with the
treatment of other high-risk securitization
exposures, such as CEIOs.
The SFA capital requirement for a
securitization exposure depends on the following seven inputs:
(i) The amount of the underlying exposures
(UE);
(ii) The securitization exposure’s
proportion of the tranche that contains the securitization exposure (TP);
(iii) The sum of the risk-based capital
requirement and ECL for the underlying exposures (as determined under the final
rule as if the underlying exposures were held directly on the bank’s balance sheet)
divided by the amount of the underlying exposures (KIRB);
(iv) The tranche’s credit enhancement
level (L);
(v) The tranche’s thickness (T);
(vi) The securitization’s effective number
of underlying exposures (N); and
(vii) The securitization’s exposure-weighted average loss given default (EWALGD).
A bank may only use the SFA to determine
its risk-based capital requirement for a securitization exposure if the bank can
calculate each of these seven inputs on an ongoing basis.
In particular, if a bank cannot
compute KIRB
because the bank
cannot compute the risk-based capital requirement for all
underlying exposures, the bank may not use the SFA to compute its risk-based capital
requirement for the securitization exposure.
In those cases, the bank must deduct the
exposure from regulatory capital.
The SFA capital requirement for a
securitization exposure is UE multiplied by TP
multiplied by the greater of
(i) 0.0056 * T; or
(ii) S[L+T] – S[L], where:
In these expressions,
β
[Y; a, b] refers to the
cumulative beta distribution with parameters a and b evaluated at Y.
In the
case where N = 1 and EWALGD =100 percent, S[Y] in formula (1) must be
calculated with K[Y] set equal to the product of KIRB and Y, and d set
equal to 1- KIRB.
The major inputs to the SFA formula (UE, TP, KIRB,
L, T, EWALGD, and N) are defined below and in section 45
of the final rule.
The agencies are modifying the SFA
treatment of certain high risk securitization exposures in the final rule. Under the
proposed treatment described above, a bank would have to deduct from total capital any
securitization exposure with a SFA risk weight equal to
1,250 percent.
Under
certain circumstances, however, a slight increase in the thickness of the tranche that contains the
securitization exposure (T), holding other SFA risk parameters fixed, could cause the
exposure’s SFA risk-weight to fall below 1,250 percent.
As a
result, the bank would not deduct any part of the exposure
from capital and would, instead, reflect the entire amount
of the SFA risk-based capital requirement in its risk-weighted assets.
Consistent with the
New Accord,97
the agencies have
removed this anomaly from the final rule. Under the
final rule a bank must deduct from total capital any part of a securitization exposure that
incurs a 1,250 percent risk weight under the SFA (that is, any part of a securitization
exposure covering loss rates on the underlying assets between zero and KIRB).
Any part of a securitization exposure that incurs less
than a 1,250 percent risk weight must be risk
weighted rather than deducted.
To illustrate, suppose that an exposure’s
SFA capital requirement equaled $15, and UE, TP, KIRB,
and L equaled $1000, 1.0, 0.10, and 0.095, respectively.
The bank must deduct from total capital $5 (UE x TP
x (KIRB
-L)), and the
exposure’s risk weighted
asset amount would be $125 (($15-$5) x
12.5).
The specific securitization exposures that
are subject to this deduction treatment under the SFA may change over time in
response to variations in the credit quality of the underlying exposures.
For example, if the
pool’s IRB capital requirement were to increase after the inception of a
securitization, additional portions of unrated securitization exposures may fall below KIRB
and thus become
subject to deduction under the SFA.
Therefore, if at the inception of
a securitization a bank owns an unrated securitization exposure well in excess of
KIRB,
the capital requirement on the exposure could climb rapidly in the event of marked
deterioration in the credit quality of the underlying exposures and the bank may be
required to deduct the exposure.
The SFA formula effectively imposes a 56
basis point minimum risk-based capital requirement (8 percent of the 7
percent risk weight) per dollar of securitization
exposure.
Although
such a floor may impose a capital requirement that is too
high for some securitization exposures, the
agencies continue to believe that some minimum prudential
capital requirement is appropriate in the securitization
context.
This 7
percent risk-weight floor is also consistent with
the lowest capital requirement available under the
RBA and, thus, should reduce incentives
for regulatory capital arbitrage.
The SFA formula is a blend of credit risk
modeling results and supervisory judgment. The function S[Y]
incorporates two distinct features.
The
first is a pure model-based estimate of the pool’s
aggregate systematic or non-diversifiable credit risk
that is
attributable to a first loss position covering losses up
to and including Y.
Because the tranche of interest covers losses over
a specified range (defined in terms of L and T),
the tranche’s systematic risk can be
represented as S[L+T] – S[L].
The
second feature involves a supervisory add-on primarily
intended to avoid behavioral distortions
associated with what would otherwise be a
discontinuity in capital requirements for relatively thin mezzanine tranches lying
just below and just above the KIRB
boundary.
Without this add-on, all tranches at or
below KIRB
would be deducted
from capital, whereas a very thin tranche just above KIRB
would incur a pure
model-based percentage capital requirement that could vary
between zero and one, depending on the number of effective underlying exposures (N).
The
supervisory add-on applies primarily to positions just above KIRB,
and its quantitative effect diminishes rapidly as the
distance from KIRB
widens.
Apart from the risk-weight floor and other
supervisory adjustments described above, the supervisory formula attempts to
be as consistent as possible with the parameters and assumptions of the IRB
approach that would apply to the underlying exposures if held directly by a bank.
The specification of
S[Y] assumes that KIRB
is an accurate measure of the total systematic
credit risk of the pool of underlying exposures and that a securitization merely
redistributes this systematic risk among its various tranches.
In this way, S[Y] embodies
precisely the same asset correlations as are assumed elsewhere within the IRB approach.
In addition, this specification embodies the result that a pool’s systematic risk (KIRB)
tends to be redistributed toward more senior tranches as N declines.
The importance of
pool granularity depends on the pool’s average loss severity rate, EWALGD.
For
small values of N, the framework implies that, as EWALGD increases, systematic risk is
shifted toward senior tranches.
For highly granular pools, such as securitizations of
retail exposures, EWALGD would have no influence on the SFA capital requirement.
Inputs to the SFA formula
Consistent with the proposal, the final
rule defines the seven inputs into the SFA formula as follows:
(i) Amount of the underlying exposures (UE).
This
input (measured in dollars) is the EAD of any underlying wholesale and
retail exposures plus the amount of any underlying exposures that are
securitization exposures (as defined in section 42(e) of
the
proposed rule) plus the adjusted carrying
value of any underlying equity exposures (as defined in section 51(b) of the proposed
rule).
UE also includes any funded spread accounts, cash collateral accounts, and
other similar funded credit enhancements.
(ii) Tranche percentage (TP).
TP is the
ratio of (i) the amount of the bank’s securitization exposure to (ii) the amount
of the securitization tranche that contains the bank’s securitization exposure.
(iii) KIRB.
KIRB
is the ratio of
(i) the
risk-based capital requirement for the underlying exposures plus the ECL of the
underlying exposures (all as determined as if the underlying exposures were directly
held by the bank) to
(ii) UE. The definition of KIRB
includes the ECL of
the underlying exposures in the numerator because if the
bank held the underlying exposures on its
balance sheet, the bank also would hold reserves against the exposures.
The calculation of KIRB
must reflect the
effects of any credit risk mitigant applied to the underlying exposures (either to an
individual underlying exposure, a group of underlying exposures, or to the entire
pool of underlying exposures).
In addition, all assets related to the securitization must
be treated as underlying exposures for purposes
of the SFA, including assets in a reserve
account (such as a cash collateral account).
In practice, a bank’s ability to calculate
KIRB
will often determine
whether it can use the SFA or whether it must instead
deduct an unrated securitization exposure from total capital.
As noted above, there is a
need for flexibility when the estimation of KIRB is constrained by data shortcomings, such
as when the bank holding the securitization exposure is not the servicer of the
underlying assets.
The final rule clarifies that the simplified approach for eligible purchased
wholesale exposures (Section 31) may be used for calculating KIRB.
To reduce the operational burden of
estimating KIRB,
several commenters urged the agencies to develop a simple
look-through approach such that when all of the assets held by the SPE are externally rated, KIRB
could be determined
directly from the external ratings of theses assets.
The agencies
believe that a look-through approach for estimating KIRB
would be
inconsistent with the New Accord and would increase the
potential for capital arbitrage.
The agencies note that
several simplified methods for estimating risk weighted assets for the underlying exposures for
the purposes of computing KIRB
are provided in other parts of the framework.
For example, the simplified approach for eligible purchased wholesale exposures in
section 31 may be available when a bank can estimate risk parameters for segments of
underlying wholesale exposures but not for each of the individual exposures.
If the assets
held by the SPE are securitization exposures with external ratings, the RBA would be
used to determine risk-weighted assets for the underlying exposures based on these
ratings.
If the assets held by the SPE represent shares in an investment company (that is,
unleveraged, pro rata ownership interests in a pool of financial assets), the bank may be
eligible to determine risk-weighted assets for the underlying exposures using the
Alternative Modified Look-Through Approach of Section 54 (d) based on investment limits
specified in the program’s prospectus or similar documentation.
(iv) Credit enhancement level (L).
L is
the ratio of
(i) the amount of all securitization exposures subordinated to
the securitization tranche that contains the
bank’s securitization exposure
to
(ii) UE.
Banks must determine L before considering the effects of any tranche-specific credit
enhancements (such as third-party guarantees that benefit only a single tranche).
Any
after-tax gain-on-sale or CEIOs associated with the securitization may not be included in L.
Any reserve account funded by accumulated
cash flows from the underlying exposures that is subordinated to the
tranche that contains the bank’s securitization exposure may be included in the numerator
and denominator of L to the extent cash has accumulated in
the account.
Unfunded
reserve accounts (reserve accounts that are to be funded from future cash flows from the
underlying exposures) may not be included in the calculation of L.
In some cases, the purchase price of
receivables will reflect a discount that provides credit enhancement (for example,
first loss protection) for all or certain tranches.
When this arises, L should be calculated
inclusive of this discount if the discount provides credit enhancement for the
securitization exposure.
(v) Thickness of tranche (T).
T is the
ratio of (i) the size of the tranche that contains the bank’s securitization
exposure to (ii) UE.
(vi)
Effective number of exposures (N).
As a
general matter, the effective number of exposures is calculated as follows:
where EADi represents the EAD
associated with the ith
instrument in the
pool of underlying exposures. For purposes of
computing N, multiple exposures to one obligor must be treated as a single underlying
exposure.
In the case of a re-securitization (a securitization in which some or all of the
underlying exposures are themselves securitization exposures), a bank must
treat each underlying securitization exposure as a
single exposure and must not look through
to the exposures that secure the underlying securitization exposures.
N represents the granularity of a pool of
underlying exposures using an “effective” number of exposures concept
rather than a “gross” number of exposures concept to appropriately assess the
diversification of pools that have individual underlying
exposures of different sizes.
An
approach that simply counts the gross number of underlying
exposures in a pool treats all exposures in the pool
equally.
This simplifying assumption could radically
overestimate the granularity of a pool with numerous small
exposures and one very large exposure.
The
effective exposure approach captures the notion that the risk profile
of such an unbalanced pool is more like a pool of several medium-sized exposures than like a
pool of a large number of equally sized small
exposures.
For example, suppose Pool A contains four
loans with EADs of $100 each.
Under the formula set forth above, N for
Pool A would be four, precisely equal to the actual number of exposures. Suppose Pool B
also contains four loans: one loan with an EAD of $100 and three loans with an EAD of
$1. Although both pools contain four loans, Pool B is much less diverse and
granular than Pool A because Pool B is dominated by the
presence of a single $100 loan.
Intuitively, therefore, N for Pool B should be closer to one than to four. Under the
formula in the rule, N for Pool B is calculated as follows:
As noted above, when calculating N for a
re-securitization, a bank must treat each underlying
securitization exposure as an exposure to a single
obligor.
This
conservative treatment addresses the concern that AVCs
among securitization exposures can be much
greater than the AVCs among the underlying
individual assets securing these securitization exposures.
Because
the framework’s simple approach to re-securitizations may result in the differential treatment
of economically similar securitization exposures, the agencies sought comment on alternative
approaches for determining the N of a resecuritization.
While a number of commenters urged that a
bank be permitted to calculate N for re-securitizations of
asset-backed securities by looking through to the underlying pools of assets securing these
securities, none provided theoretical or empirical
evidence to support this recommendation.
Absent
such evidence, the final rule remains consistent with New Accord’s
measurement of N for re-securitizations.
(vii) Exposure-weighted average loss given
default (EWALGD).
The EWALGD is calculated as:
where LGDi represents the
average LGD associated with all exposures to the ith
obligor.
In the case of a re-securitization, an LGD
of 100 percent must be assumed for any underlying exposure that is a
securitization exposure.
Although this treatment of EWALGD is
consistent with the New Accord, several commenters asserted that assigning an LGD
of 100 percent to all securitization exposures in the underlying pool was excessively
conservative, particularly for underlying exposures that
are senior, highly rated asset-backed securities.
The
agencies acknowledge that in many situations
an LGD
significantly lower than 100 percent may be
appropriate.
However, determination of the
appropriate LGD depends on many complex factors, including the characteristics of
the underlying assets and structural features of the
securitization, such as the securitization exposure’s
thickness.
Moreover, for thin securitization exposures or certain
mezzanine positions backed by low-quality assets, the
LGD
may in fact be close to 100 percent.
In this light, the agencies believe that any simple alternative to the New Accord’s
measurement of EWALGD would increase the potential for capital arbitrage, and any
more risk-sensitive alternative would take considerable
time to develop.
Thus,
the agencies have retained the proposed treatment, consistent with the New Accord.
Under certain conditions, a bank may
employ the following simplifications to the SFA.
First,
for securitizations all of whose underlying exposures are
retail exposures, a bank may set h = 0 and v = 0.
In addition,
if the share of a securitization corresponding to the largest underlying exposure (C1)
is no more than 0.03 (or 3 percent of the underlying exposures), then for purposes
of the SFA the bank may set N equal to the following amount:
where Cm
is the ratio of
(i)
the sum of the amounts of the largest ‘m’ underlying exposures of the securitization; to
(ii) UE. A bank may select the level of ‘m’ using its discretion.
For example, if the three
largest underlying exposures of a securitization represent 15 percent of the pool of
underlying exposures, C3
for the
securitization is 0.15.
As an alternative simplification option,
if only C1 is available, and C1
is no more than 0.03, then the bank may set N = 1/C1.
Under both simplification options a bank may set EWALGD = 0.50 unless one or more of the
underlying exposures is a securitization exposure.
If one or more of the underlying
exposures is a securitization exposure, a bank using a simplification option must set
EWALGD = 1.
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