# 12 CFR § 217.143 - Supervisory formula approach (SFA).

§ 217.143 Supervisory formula approach (SFA).

(a) Eligibility requirements. A Board-regulated institution must use the SFA to determine its risk-weighted asset amount for a securitization exposure if the Board-regulated institution can calculate on an ongoing basis each of the SFA parameters in paragraph (e) of this section.

(b) Mechanics. The risk-weighted asset amount for a securitization exposure equals its SFA risk-based capital requirement as calculated under paragraph (c) and (d) of this section, multiplied by 12.5.

(c) The SFA risk-based capital requirement.

(1) If KIRB is greater than or equal to L + T, an exposure's SFA risk-based capital requirement equals the exposure amount.

(2) If KIRB is less than or equal to L, an exposure's SFA risk-based capital requirement is UE multiplied by TP multiplied by the greater of:

(i) F · T (where F is 0.016 for all securitization exposures); or

(ii) S[L + T]−S[L].

(3) If KIRB is greater than L and less than L + T, the Board-regulated institution must apply a 1,250 percent risk weight to an amount equal to UE · TP (KIRB−L), and the exposure's SFA risk-based capital requirement is UE multiplied by TP multiplied by the greater of:

(i) F · (T−(KIRB−L)) (where F is 0.016 for all other securitization exposures); or

(ii) S[L + T]−S[KIRB].

(d) The supervisory formula:

$\begin{array}{c}\text{(1)}\phantom{\rule{0ex}{0ex}}\text{S [Y] = {}\begin{array}{c}Y\phantom{\rule{0ex}{0ex}}\text{when Y ≤}{K}_{\mathrm{IRB}}\\ {K}_{\mathrm{IRB}}+K\left[Y\right]-K\left[{K}_{\mathrm{IRB}}\right]+\frac{d·{K}_{\mathrm{IRB}}}{20}\left(l-{e}^{\frac{20·\left({K}_{\mathrm{IRB}}-Y\right)}{{K}_{\mathrm{IRB}}}}\right)\phantom{\rule{0ex}{0ex}}\text{when Y}>{K}_{\mathrm{IRB}}\end{array}\text{}}\\ \text{(2)}\phantom{\rule{0ex}{0ex}}\text{}K\left[Y\right]=\left(1-h\right)·\left[\left(1-\beta \left[Y;a,b\right]\right)·Y+\beta \left[Y;a+1,b\right]·c\right]\\ \text{(3)}\phantom{\rule{0ex}{0ex}}\text{}h={\left(1-\frac{{K}_{\mathrm{IRB}}}{\mathrm{EWALGD}}\right)}^{N}\\ \text{(4)}\phantom{\rule{0ex}{0ex}}a=g·c\\ \text{(5)}\phantom{\rule{0ex}{0ex}}\text{}b=g·\left(1-c\right)\\ \text{(6)}\phantom{\rule{0ex}{0ex}}\text{}c=\frac{{K}_{\mathrm{IRB}}}{1-h}\\ \text{(7)}\phantom{\rule{0ex}{0ex}}\text{}g=\frac{\left(1-c\right)·c}{f}-1\\ \text{(8)}\phantom{\rule{0ex}{0ex}}f=\frac{v+{{K}_{\mathrm{IRB}}}^{2}}{1-h}-{c}^{2}+\frac{\left(1-{K}_{\mathrm{IRB}}\right)·{K}_{\mathrm{IRB}}-v}{\left(1-h\right)·1000}\\ \text{(9)}\phantom{\rule{0ex}{0ex}}\text{}v={K}_{\mathrm{IRB}}·\frac{\left(\mathrm{EWALGD}-{K}_{\mathrm{IRB}}\right)+.25·\left(1-\mathrm{EWALGD}\right)}{N}\\ \text{(10)}\phantom{\rule{0ex}{0ex}}\text{}d=1-\left(1-h\right)·\left(1-\beta \left[{K}_{\mathrm{IRB}};a,b\right]\right).\\ \text{(11)}\phantom{\rule{0ex}{0ex}}\text{In these expressions,}\phantom{\rule{0ex}{0ex}}\beta \phantom{\rule{0ex}{0ex}}\text{[Y; a, b] refers to the cumulative beta distribution with}\\ \text{parameters a and b evaluated at Y. In the case where}\phantom{\rule{0ex}{0ex}}N=1\phantom{\rule{0ex}{0ex}}\text{and}\phantom{\rule{0ex}{0ex}}\mathrm{EWALGD}=100\phantom{\rule{0ex}{0ex}}\text{percent, S[Y]}\\ \text{in formula (1) must be calculated with K [Y] set equal to the product of}{K}_{\mathrm{IRB}}\text{and Y, and d set}\\ \text{equal to}\phantom{\rule{0ex}{0ex}}1-{K}_{\mathrm{IRB}}.\end{array}$

(e) SFA parameters. For purposes of the calculations in paragraphs (c) and (d) of this section:

(1) Amount of the underlying exposures (UE). UE is the EAD of any underlying exposures that are wholesale and retail exposures (including the amount of any funded spread accounts, cash collateral accounts, and other similar funded credit enhancements) plus the amount of any underlying exposures that are securitization exposures (as defined in § 217.142(e)) plus the adjusted carrying value of any underlying exposures that are equity exposures (as defined in § 217.151(b)).

(2) Tranche percentage (TP). TP is the ratio of the amount of the Board-regulated institution's securitization exposure to the amount of the tranche that contains the securitization exposure.

(3) Capital requirement on underlying exposures (KIRB).

(i) KIRB is the ratio of:

(A) The sum of the risk-based capital requirements for the underlying exposures plus the expected credit losses of the underlying exposures (as determined under this subpart E as if the underlying exposures were directly held by the Board-regulated institution); to

(B) UE.

(ii) The calculation of KIRB must reflect the effects of any credit risk mitigant applied to the underlying exposures (either to an individual underlying exposure, to a group of underlying exposures, or to all of the underlying exposures).

(iii) All assets related to the securitization are treated as underlying exposures, including assets in a reserve account (such as a cash collateral account).

(4) Credit enhancement level (L).

(i) L is the ratio of:

(A) The amount of all securitization exposures subordinated to the tranche that contains the Board-regulated institution's securitization exposure; to

(B) UE.

(ii) A Board-regulated institution must determine L before considering the effects of any tranche-specific credit enhancements.

(iii) Any gain-on-sale or CEIO associated with the securitization may not be included in L.

(iv) Any reserve account funded by accumulated cash flows from the underlying exposures that is subordinated to the tranche that contains the Board-regulated institution'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 (that is, reserve accounts that are to be funded from future cash flows from the underlying exposures) may not be included in the calculation of L.

(v) 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 of the securitization. When this arises, L should be calculated inclusive of this discount if the discount provides credit enhancement for the securitization exposure.

(5) Thickness of tranche (T). T is the ratio of:

(i) The amount of the tranche that contains the Board-regulated institution's securitization exposure; to

(ii) UE.

(6) Effective number of exposures (N).

(i) Unless the Board-regulated institution elects to use the formula provided in paragraph (f) of this section,

$N=\frac{{\left(\sum _{i}{\mathrm{EAD}}_{i}\right)}^{2}}{\sum _{i}{\mathrm{EAD}}_{i}^{2}}$

where EADi represents the EAD associated with the ith instrument in the underlying exposures.

(ii) Multiple exposures to one obligor /must be treated as a single underlying exposure.

(iii) In the case of a resecuritization, the Board-regulated institution must treat each underlying exposure as a single underlying exposure and must not look through to the originally securitized underlying exposures.

(7) Exposure-weighted average loss given default (EWALGD). EWALGD is calculated as:

$\mathrm{EWALGD}=\frac{\sum _{i}{\mathrm{LGD}}_{i}×{\mathrm{EAD}}_{i}}{\sum _{i}{\mathrm{EAD}}_{i}}$

where LGDi represents the average LGD associated with all exposures to the ith obligor. In the case of a resecuritization, an LGD of 100 percent must be assumed for the underlying exposures that are themselves securitization exposures.

(f) Simplified method for computing N and EWALGD.

(1) If all underlying exposures of a securitization are retail exposures, a Board-regulated institution may apply the SFA using the following simplifications:

(i) h = 0; and

(ii) v = 0.

(2) Under the conditions in §§ 217.143(f)(3) and (f)(4), a Board-regulated institution may employ a simplified method for calculating N and EWALGD.

(3) If C1 is no more than 0.03, a Board-regulated institution may set EWALGD = 0.50 if none of the underlying exposures is a securitization exposure, or may set EWALGD = 1 if one or more of the underlying exposures is a securitization exposure, and may set N equal to the following amount:

$N=\frac{1}{{C}_{1}{C}_{m}+\left(\frac{{C}_{m}-{C}_{1}}{m-1}\right)max\left(1-m{C}_{1},0\right)}$

where:

(i) Cm is the ratio of the sum of the amounts of the `m' largest underlying exposures to UE; and

(ii) The level of m is to be selected by the Board-regulated institution.

(4) Alternatively, if only C1 is available and C1 is no more than 0.03, the Board-regulated institution may set EWALGD = 0.50 if none of the underlying exposures is a securitization exposure, or may set EWALGD = 1 if one or more of the underlying exposures is a securitization exposure and may set N = 1/C1.