Quantifying Regulatory Capital Charges Using SFA and SSFA for RMBS Tranches
As highlighted in this article, the SFA framework could result in significant regulatory capital relief when compared to the SSFA framework. While banks are in the process of analyzing which approach to use, this study shows that there are many pool and bondlevel characteristics that can assist with the process.
As banks operate in challenging regulatory and business environments, it is essential that they make sound regulatory choices in their risk management plans. In the structured finance domain, most banks choose the Supervisory Formula Approach (SFA) and the Simplified Supervisory Formula Approach (SSFA) for the regulatory capital charges, and compare the expected cost with the benefits of moving to SFA in the search for regulatory capital relief. The methodology for SFA and SSFA regulatory capital calculations are based on the most recent rules as listed in the Federal Register, Vol. 78, No. 198, (October 11, 2013). Please refer to Appendix 1 and 2 for the detailed mechanics and formula of both approaches. Also, an illustrative example of a single bond’s regulatory capital charge using both approaches is illustrated in Appendix 3.
For this analysis, a large RMBS portfolio was considered, along with loanlevel credit analytics to estimate pool losses of underlying residential mortgages. The analysis used Mortgage Portfolio Analyzer (MPA) as the loanlevel credit model in the calculation of expected loss (EL) and loss given default (LGD) to assess the credit risk of pools backing the RMBS bonds.
MPA was used to analyze mortgage pools in three steps:
 For each loan in the portfolio, the model calculates quarterly default and prepayment probabilities as a function of loanspecific and macroeconomic factors.
 Given these probabilities, the model then simulates default events, prepayment events, and loss given default, and aggregates the simulated losses across all loans in the portfolio for each trajectory.
 Finally, these simulated losses are themselves aggregated across all trajectories to produce an estimate of the distribution of poollevel losses.
Furthermore, both approaches require normalization of the waterfall to attachment and detachment points. This analysis uses the same values for both approaches.
We randomly selected more than 600 securities across 120 deals with a vintage range of 2002 2013, across various types of deals and broad initial credit ratings.^{1} The portfolio of tranches was based on the following criteria:
 Tranche balance greater than $1 million
 Tranche thickness greater than 2%
 Underlying exposure balance greater than $50 million
The motivation behind these criteria was to focus the analysis on a broad representation of outstanding bonds.
The primary metric used in this analysis is the Capital Relief between SFA and SSFA:
Capital Relief = Regulatory Capital_{SSFA}  Regulatory Capital_{SFA}
A positive number indicates Capital Relief by using SFA over SSFA; whereas a negative number implies the reverse.
SFA should result in Capital Relief for improved quality pools as the framework is more sensitive to underlying loan characteristics and considers the LGD, EL, and granularity of the assets. The waterfall structure in both frameworks – SFA and SSFA – is normalized for attachment and detachment parameters; thereby, not affecting risk sensitivity for this analysis. It is commonly assumed that the tradeoff for the added complexity of calculating the SFA is regulatory Capital Relief. However, this may not always be the case. In the analysis, observed securities floored at the regulatory capital floor for both approaches. Furthermore, it is conceivable that for some securities backed by poor quality and concentrated pools, a higher capital charge is present under the SFA as compared to the SSFA. Nonetheless, in most cases the SFA method was found to provide fairly significant Capital Relief relative to the more prescriptive SSFA method.
Example of a Prime 2004 CUSIP (See Appendix 3)
The current attachment point is 8% and the tranche detaches at 100%, and as it is a wellseasoned deal, the granularity is low. The prescriptive expected loss under the SSFA method is approximately 7% (set at 50% of parameter w) compared to the loanlevel simulation based expected loss of approximately 2% allowed under the more granular SFA method. As a result, Capital Relief is expected under SFA. The results under the two approaches are listed below:
Regulatory Capital_{SSFA} = 13.8%
Regulatory Capital_{SFA} = 3.7%
Capital Relief = 10.1%
Table 1. Analysis results
Source: Moody's Analytics
Figure 1. Median and interquartile range Capital Relief based on EWALGD
Source: Moody's Analytics
Results
The results of our analysis show that the average capital requirements are 14.2% and 21.4% under the SFA and SSFA approaches, respectively, with an average Capital Relief of 7.2% under the SFA method. In the portfolio analyzed, 96% exhibited Capital Relief under the SFA method for an average capital charge of 14.8% and a Capital Relief relative to the SSFA method of 7.5%. The other 4% within the tranches exhibited an average SSFA capital charge at the floor of 1.6%, with no Capital Relief relative to the SFA method. The results are summarized in Table 1.
The Estimated Weighted Average Loss Given Default (EWALGD) impacts the risk sensitivity of the SFAbased regulatory capital amount, and expectedly – as per the assumed 50% defaulted loan LGD in the SSFA formula – the Capital Relief is lower for pools with higher LGDs, as the LGD of the pool approaches the assumed LGD for delinquent or defaulted loans (parameter w) of 50%.^{2}
As displayed in Figure 1, the Capital Relief diminishes for pools with a higher EWALGD, highlighting the risk sensitivity of SFA, especially for better quality collateral. The lowest EWALGD has the greatest variance, and indicates that good quality pools can have high levels of Capital Relief when using the SFA approach.
Figure 2. Median and interquartile range Capital Relief by vintage
Source: Moody's Analytics
Figure 3. Median and interquartile Capital Relief by pool factor
Source: Moody's Analytics
Figure 4. Median and interquartile Capital Relief by product
Source: Moody's Analytics
When reviewing the Capital Relief by vintage, there is generally a significant amount of relief in the years 20042007. While a higher delinquency – which results in higher SSFA capital charges – should translate to higher ELs, the regulatory Capital Relief does not follow that trend due to varying LGDs for the pool. For example, comparing the 2004 vintage to the 2007 one, the higher EWALGD and EL result in lower Capital Relief for the 2007 securities; whereas, the lower EWALGD and EL result in a greater Capital Relief for the 2004 vintage. In 2008, the lower parameter w results in a lower SSFA capital charge, therefore reducing the amount of Capital Relief compared to SFA.^{3}
When analyzing the portfolio by current pool factor, Capital Relief is present across the range except at the tailend due to low delinquencies and defaults at the topend, and very low tranche thickness at the bottomend.
The Capital Relief is spread across all product types within the 610% Capital Relief range. In the case of this portfolio, the product type did not act as a sound indicator of capital relief treatment.
While the SFAbased regulatory Capital Relief spans across the granularity scale, we observe the EL and LGD for the underlying exposure as expected.
Of note is the variability of the Capital Relief for low granularity pools (N<50), which are especially sensitive to the quality of assets. In addition, for very granular pools where N exceeds 800, the variability around the Capital Relief is very low and the amount of Capital Relief appears to converge primarily within the range of 6%8%.
Even though original ratings did not prove to be diverse enough to properly indicate levels of Capital Relief, due to the fact that most trusts within the given vintage range have their mezzanine and junior tranches written off, the current Moody’s rating was a better indicator of Capital Relief levels.
Figure 5. Median and interquartile Capital Relief by N (granularity)
Source: Moody's Analytics
Figure 6. Median and interquartile Capital Relief by Moody’s ratings
Source: Moody's Analytics
Figure 6 helps highlight the Capital Relief levels of the tranches that are currently rated below investment grade (Ba and lower). The analysis only referenced this rating range due to the relatively small number of RMBS securities within the portfolio that are rated investment grade. The higher delinquencypipeline in the lower rated securities that result in high SSFAbased capital charges do not always translate to higher calculated expected losses.
Regulatory capital relief
As highlighted in this article, the SFA framework could result in significant regulatory Capital Relief when compared to the SSFA framework. While banks are in the process of analyzing which approach to use, this study shows that there are many pool and bondlevel characteristics that can aid with the process. While the exact amount of Capital Relief is dependent on the portfolio mix, this analysis allows banks to obtain an estimate of the extent of the Capital Relief based on known pool characteristics.
Appendix 1 – SFA Mechanics^{4}
SFA allows a bank a degree of Capital Relief as a tradeoff for the additional data processing and relatively intensive calculation when compared to SSFA. The SFA calculation requires the following input parameters:
 Amount of the underlying exposures (UE) supporting the structure
 Tranche percentage (TP) owned by the bank
 Capital requirement on underlying exposures (K_{IRB}) based on the prescribed treatment in the Implementing the Supervisory Formula Approach for Securitization Exposures paper^{5}
 Credit Enhancement Level (L), which is defined as the amount of securitization exposures subordinated to the security, considering for overcollateralization and reserve accounts
 Thickness of tranche (T), which is the amount of the tranche that contains the bank’s exposure, considering for prorata structures in the deal
 Effective number of exposures (N). For this analysis, the calculation of N was obtained using the following formula:
Additional methods for N and more details on the parameters are available in the source paper. For this analysis, the approach in this section was deemed to be the most appropriate.
To illustrate the mechanics of the calculation, refer to the calculation and example in Appendix 3.
SFA riskbased capital calculation:
 If K_{IRB} is greater than or equal to L + T, an exposure’s SFA riskbased capital requirement equals the exposure amount.

If K_{IRB} is less than or equal to L, an exposure’s SFA riskbased capital requirement is UE
multiplied by TP multiplied by the greater of:
a. F . T (where F is 0.016 for all securitization exposures); or
b. S[L + T] – S[L] 
If K_{IRB} is greater than L and less than L + T, the bank must apply a 1250% risk weight to an
amount equal to the UE . TP (K_{IRB} – L) and the capital requirement is UE multiplied by TP
multiplied by the greater of:
a. F . (T – (K_{IRB} – L)) (where F is 0.016 for all other securitization exposures); or
b. S[L + T] – S[K_{IRB}]
Appendix 2 – SSFA Mechanics^{6}
SSFA – as implied – requires a simpler calculation and data collection processes. The tradeoff is conservative assumptions on the losses of the underlying exposures, which could result in potentially higher regulatory capital requirements. The SSFA calculation requires the following input parameters:
 KG, which is the weighted average total base capital requirements of the underlying exposures.
 Parameter W, which is the ratio of the sum of underlying exposures that are seriously delinquent or defaulted for regulatory purposes. Further details on the criteria are available in Federal Register, Vol. 78, No. 198.
 Parameter A, which is the attachment point of the security.
 Parameter D, which is the detachment point of the security.
 Supervisory calibration parameter p, which is set to 0.5 for securitization exposures and 1.5 for resecuritization exposures. For this analysis, no resecuritizations were included and p was set to 0.5 for the entire portfolio.
SFA riskbased capital calculation:
The risk weight is calculated by the following equation:
SSFA Calculations:
Appendix 3 – Example
Consider the parameters of a 2004 Prime Jumbo bond from the portfolio analyzed:
 Using the above parameters, the calculated SFA riskbased capital charge is 3.7%
 For SSFA, the only additional parameter required is the defaulted amount (parameter w), and for this pool, it stands at 14% (defaults, foreclosed, bankrupt, REO, or 90+ delinquent)
 Using the parameters for SSFA calculation, the SSFA riskbased capital charge is 13.8%
 The Capital Relief as defined as the difference between the SSFA and SFA riskbased capital charge for this analysis is therefore 10.1%
Sources and Notes
1 The portfolio included 629 tranches across 122 deals. Only tranches from a deal that met the criteria were included for the analysis.
2 Refer to Appendix 1 for more details on the SFA parameters.
3 Refer to Appendix 2 for more details on SSFA parameters.
4 Federal Register, Vol. 78, No. 198, October 11, 2013.
5 Board of Governors of the Federal Reserve System, Implementing the Supervisory Formula Approach for Securitization Exposures, BCC 137, October 28, 2013.
6 Federal Register, Vol. 78, No. 198, October 11, 2013.
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