Methods for calculating capital requirements on securitisation positions under EU banking law

The Capital Requirements Regulation (CRR) prescribes three methods for calculating the risk-weighted exposure amount (RWEA) of a securitisation position held by a bank in the European Union: the Securitisation Internal Ratings Based Approach (SEC-IRBA, Article 259), the Securitisation Standardised Approach (SEC-SA, Article 261) and the Securitisation External Ratings Based Approach (SEC-ERBA, Article 263). The Risk-Weighted Exposure amount (RWEA) of each tranche is calculated from a risk weight which is then multiplied by the tranche exposure value as determined under Article 248:

RWEA = EV ⋅ RW.

The framework was introduced into the CRR by Regulation (EU) 2017/2401, transposing the revised Basel securitisation standard, and replaced the earlier ratings-based and supervisory formula methods. It applies from 1 January 2019.

The first two approaches share a single closed-form expression, the simplified supervisory formula approach (SSFA), and differ only in the capital charge fed into it and in one supervisory parameter. The third is a table look-up driven by external credit ratings, adjusted for tranche maturity and thickness.

History And Background

The current Basel 3 calculations for securitizations supersede the previous calculations that relied of cumulative beta distribution calculations and are built on a consultation paper from the Bank for International Settlements published in 2013. That paper derived the risk weights for tranches using marked-to-market calculations of value distributions that simulated the rating migrations of calibrated underlying pools.

Hierarchy of methods

Article 254 sets a strict order of preference. An institution must use SEC-IRBA where it satisfies the conditions in Article 258 — broadly, where it can calculate K_IRB for the underlying pool and has not been precluded from doing so by its supervisor. Failing that it must use SEC-SA, and failing that SEC-ERBA for positions that are rated or can be assigned an inferred rating.

The ordering is then partially reversed. For rated positions, SEC-ERBA must be used in place of SEC-SA in three situations:

• where SEC-SA would produce a risk weight above 25% for an STS position;
• where SEC-SA would produce a risk weight above 25%, or SEC-ERBA above 75%, for a non-STS position;
• for transactions backed by pools of auto loans, auto leases and equipment leases.

Outside those cases an institution may elect to apply SEC-ERBA to all of its rated positions, on notification to its competent authority, and must then apply that choice consistently for the whole year. Supervisors may also prohibit the use of SEC-SA case by case where the result is not commensurate with the risk.

Attachment and detachment points

Under Article 256 the attachment point A is the share of the underlying pool that must be lost before the position loses anything, and the detachment point D is the share at which the position is wiped out. Both are expressed as decimals between zero and one. The difference T = D − A is the tranche thickness.

Where two positions in the same transaction have different maturities but share losses pro rata, they are treated as one tranche with common attachment and detachment points. For synthetic securitisations, an originator treats synthetic excess spread as a tranche and adjusts the other retained tranches accordingly; other institutions do not make that adjustment.

Tranche maturity

Article 257 permits two measures of tranche maturity M_T: the weighted-average maturity of the contractual payments, or a formula based on final legal maturity:

$M_T=\frac{\sum_t t\cdot CF_t}{\sum_t CF_t}\qquad\text{or}\qquad M_T=1+(M_L-1)\cdot 80\%.$

In both cases the result is floored at one year and capped at five. The cap matters more than it might appear: it means a thirty-year tranche and a five-year tranche attract identical treatment, and it is the reason the SEC-ERBA tables need only two maturity columns.

The SSFA kernel

Articles 259(1) and 261(1) contain the same expression, differing only in whether the pool capital charge is K_IRB or K_A. Writing K for either:

$K_{SSFA(K)}=\frac{e^{a\,u}-e^{a\,l}}{a\,(u-l)},$

where

$a=-\frac{1}{p\cdot K},\qquad u=D-K,\qquad l=\max(A-K,\,0).$

The risk weight is then assigned in three branches, subject in all cases to a floor of 15%:

$RW=\begin{cases}1250\%, & D\leq K\\[6pt] 12.5\cdot K_{SSFA(K)}, & A\geq K\\[6pt] \dfrac{K-A}{D-A}\cdot 12.5+\dfrac{D-K}{D-A}\cdot 12.5\cdot K_{SSFA(K)}, & A<K<D\end{cases}$

The logic is straightforward once the branches are read as positions relative to the pool's own capital charge. A tranche that sits entirely below K is expected to be consumed by losses the pool is already known to carry, and receives a 1250% risk weight — equivalent to full deduction from capital at an 8% ratio, since 12.5 is the reciprocal of 8%. A tranche entirely above K is charged according to the SSFA, whose value falls exponentially as the attachment point rises. A tranche straddling K is charged as a weighted blend of the two, the weights being the shares of the tranche lying below and above.

The parameter p controls how steeply the curve decays, and is the only structural difference between the two formula approaches. It is fixed at 1 under SEC-SA for non-resecuritisation exposures, and computed from pool characteristics under SEC-IRBA.

SEC-IRBA (Article 259)

SEC-IRBA feeds the institution's own K_IRB — the capital charge the underlying pool would attract if it were held directly on the balance sheet, as defined in Article 255 — into the SSFA kernel. It is the most risk-sensitive of the three approaches and, other things equal, generally the least punitive.

The p-parameter

Under SEC-IRBA the parameter is derived from five coefficients and four pool inputs:

$p=\max\left[0.3,\;\;\mathcal{A}+\mathcal{B}\cdot\frac{1}{N}+\mathcal{C}\cdot K_{IRB}+\mathcal{D}\cdot LGD+\mathcal{E}\cdot M_T\right]$

The coefficients depend on whether the pool is retail or non-retail, whether the position is senior, and — for non-retail pools — whether the pool is granular, meaning an effective number of exposures of at least 25:

Several features of the table are worth drawing out. The coefficient on K_IRB is negative in every row, so a riskier pool produces a lower p and hence a steeper decay — the formula does not double-count pool risk, which already enters through K itself. The retail rows carry no 1/N term at all, granularity being assumed. And the floor at 0.3 binds routinely: for a retail senior position with a pool charge above roughly 16%, or for almost any STS position, the computed value falls below the floor and 0.3 applies.

Where a pool mixes retail and non-retail exposures, Article 259(2) requires it to be split into two subpools, a separate parameter estimated for each with its own N, K_IRB and LGD, and a weighted average taken by nominal size.

Effective number of exposures and average LGD

The effective number of exposures is the reciprocal of the pool's Herfindahl index, with multiple exposures to one obligor consolidated:

$N=\frac{\left(\sum_i EAD_i\right)^{2}}{\sum_i EAD_i^{\,2}}$

and the loss-given-default input is exposure-weighted:

$LGD=\frac{\sum_i LGD_i\cdot EAD_i}{\sum_i EAD_i}.$

Article 259(6) offers a simplification where the largest exposure is no more than 3% of the pool. The institution may then set LGD to 0.50 and compute

$N=\left[C_1\cdot C_m+\frac{C_m-C_1}{m-1}\cdot\max\left(1-m\cdot C_1,\,0\right)\right]^{-1},$

where C_m is the combined share of the largest m exposures and m is chosen by the institution. If only the largest share is known and it is no more than 3%, LGD may be set to 0.50 and N to its reciprocal.

Where credit and dilution risk on purchased receivables are managed together, the LGD input blends the credit-risk LGD with a 100% LGD for dilution risk, weighted by the respective stand-alone IRB capital requirements.

Mixed pools

Where a position is backed by a pool for which the institution can calculate K_IRB on at least 95% of the underlying exposure amounts, Article 259(7) allows a blended charge:

K = d ⋅ K_IRB + (1−d) ⋅ K_SA,

with d the share of exposures covered by the IRB calculation. For the separate purpose of computing p, however, Article 259(3) requires the standardised portion to be ignored entirely, so the parameter is estimated on the IRB exposures alone.

SEC-SA (Article 261)

SEC-SA uses the identical kernel with p fixed at 1 and the pool charge replaced by K_A, a quantity that combines the standardised capital charge of the pool with an explicit penalty for loans already in trouble.

K_A and the delinquency ratio

K_A = (1−W) ⋅ K_SA + W ⋅ 0.5

Here K_SA is the standardised capital charge of the underlying pool and W is the share of the pool in default by nominal amount. An exposure counts as in default if it is 90 or more days past due, is subject to bankruptcy, insolvency or foreclosure proceedings, or is in default under the securitisation documentation.

The construction is blunt: the performing share attracts its ordinary standardised charge, while the defaulted share is charged at a flat 50% regardless of collateral, seniority or expected recovery. Because K_A enters the kernel directly, a rise in W shifts the entire curve to the right, and the effect on a mezzanine tranche can be dramatic — a tranche comfortably above the deduction threshold at origination can fall below it as arrears build.

Unknown delinquency status

Article 261(2) also addresses incomplete data. Where the institution does not know the delinquency status of 5% or less of the pool, it may still use SEC-SA, computing K_A on the known subpool and applying a 1250% treatment to the exposure-weighted share that is unknown. Where more than 5% of the pool has unknown status, the position is risk-weighted at 1250% outright.

SEC-ERBA (Article 263)

SEC-ERBA abandons the formula and reads a risk weight from a table indexed by credit quality step, adjusted for maturity and, for non-senior tranches, thickness.

Look-up tables

For positions with short-term credit assessments, Article 263(2) gives a compact schedule: 15%, 50% and 100% for credit quality steps 1 to 3, and 1250% for everything else.

For long-term assessments, Table 2 of Article 263(3) runs to seventeen credit quality steps across four columns — senior and non-senior, at one and five years.

The shape of the table encodes two judgements. Seniority matters enormously — at credit quality step 8 and five years, a senior tranche takes 90% while a thin non-senior tranche takes 260%. And maturity matters more for weak credits than strong ones, since the gap between the one-year and five-year columns widens as quality deteriorates.

Maturity interpolation and thickness

For maturities between the tabulated points, Article 263(4) requires straight-line interpolation:

$RW(M_T)=RW_{1\,\mathrm{yr}}+\frac{M_T-1}{4}\cdot\left(RW_{5\,\mathrm{yr}}-RW_{1\,\mathrm{yr}}\right).$

Article 263(5) then adjusts non-senior tranches for thickness:

RW = RW_{maturity-adjusted} ⋅ [1−min(T, 50%)],   T = D − A.

The reasoning is that the tabulated non-senior weights are calibrated for a thin tranche, which absorbs losses in an all-or-nothing fashion. A thicker tranche behaves more like a blend of the tranches it spans and so is charged less per unit. The relief is capped at half: beyond 50% thickness, no further reduction is granted.

Two floors close the article. Under Article 263(6) the result may not fall below 15%, and may not fall below the weight that a hypothetical senior tranche of the same securitisation with the same rating and maturity would attract. The second floor is what prevents the thickness adjustment from making a subordinated position look better than the paper above it — visible in the charts as the flattening of the low-credit-quality lines.

Inferred ratings

An unrated position may borrow the rating of a reference position in the same transaction, provided the reference position ranks pari passu or is immediately subordinate, benefits from no credit enhancement unavailable to the unrated position, has a maturity at least as long, and the inferred rating is kept current.

Comparison of the three approaches

The approaches are not calibrated to agree, and the gaps between them are large enough to matter commercially. Two effects drive the divergence between SEC-IRBA and SEC-SA. The first is the input: K_SA is typically higher than K_IRB for the same pool, since the Standardised Approach cannot recognise an institution's own default estimates. The second is p, which is fixed at 1 under SEC-SA but frequently lands between 0.3 and 0.6 under SEC-IRBA. Both push in the same direction.

SEC-ERBA behaves differently again, because it is indifferent to where the tranche sits relative to the pool's capital charge. It responds only to the rating, seniority, maturity and thickness. This is why the hierarchy in Article 254 contains the 25% and 75% override thresholds: without them, the ordering of methods would in some cases require an institution to use the more punitive approach on paper the market regards as strong.

STS treatment

Positions in securitisations qualifying as simple, transparent and standardised receive reduced capital under Articles 260, 262 and 264. The mechanism differs by approach. Under SEC-IRBA the bracket in the p-formula is halved before the 0.3 floor is applied, and the risk-weight floor for senior positions falls from 15% to 10%. Under SEC-SA the parameter is set to 0.5 outright and the same 10% senior floor applies. Under SEC-ERBA the short-term schedule becomes 10%, 30% and 60%, and long-term positions are read from Table 4 instead of Table 2.

Because the p-parameter under SEC-IRBA is already close to the floor for many pools, halving the bracket often produces no benefit at all beyond the reduced floor — the calculation lands below 0.3 either way. The STS benefit is therefore concentrated in the senior floor for high-quality pools, and in the p-parameter for pools where the computed value would otherwise be well above the floor.

Criticism

• Non-neutrality. The capital required across all tranches of a securitisation exceeds the capital that would be required for the pool held directly. This is deliberate — it prices model risk and agency risk — but the size of the surcharge, and its concentration in the mezzanine, has been contested since the framework was proposed.
• Cliff effects. The 1250% branch creates a discontinuity in economic terms: a tranche detaching just below the pool charge is deducted in full, while one detaching just above receives a finite weight. Under SEC-SA the position of that cliff moves with the delinquency ratio, so a tranche can cross it without any change in its own terms.
• Reliance on ratings. SEC-ERBA reintroduces external credit assessments into the capital calculation, the feature of the pre-2008 framework most heavily criticised after the crisis, albeit now bounded by floors and by the maturity and thickness adjustments.
• The maturity cap. Capping M_T at five years understates the risk of very long tranches, while the one-year floor overstates the risk of short ones.
• Fixed 50% for defaulted loans. The W term in SEC-SA ignores recovery prospects entirely, which is punitive for well-secured pools with high arrears and lenient for unsecured ones.

See also

• Vasicek distribution
• Securitisation
• Collateralized debt obligation
• Capital Requirements Regulation
• Basel III
• Simple, transparent and standardised securitisation
• Internal ratings-based approach

External links

• Consolidated text of Regulation (EU) No 575/2013 on EUR-Lex