Appendix A to Subpart A of Part 327—Method to Derive Pricing Multipliers and Uniform Amount

Appendix A - Appendix A to Subpart A of Part 327—Method to Derive Pricing Multipliers and Uniform Amount

I. Introduction

The uniform amount and pricing multipliers are derived from:

• A model (the Statistical Model) that estimates the probability of failure of an institution over a three-year horizon;

• The minimum initial base assessment rate;

• The maximum initial base assessment rate;

• Thresholds marking the points at which the maximum and minimum assessment rates become effective.

II. The Statistical Model

The Statistical Model estimates the probability of an insured depository institution failing within three years using a logistic regression and pooled time-series cross-sectional data; 1 that is, the dependent variable in the estimation is whether an insured depository institution failed during the following three-year period. Actual model parameters for the Statistical Model are an average of each of three regression estimates for each parameter. Each of the three regressions uses end-of-year data from insured depository institutions' quarterly reports of condition and income (Call Reports and Thrift Financial Reports or TFRs 2 ) for every third year to estimate probability of failure within the ensuing three years. One regression (Regression 1) uses insured depository institutions' Call Report and TFR data for the end of 1985 and failures from 1986 through 1988; Call Report and TFR data for the end of 1988 and failures from 1989 through 1991; and so on, ending with Call Report data for the end of 2009 and failures from 2010 through 2012. The second regression (Regression 2) uses insured depository institutions' Call Report and TFR data for the end of 1986 and failures from 1987 through 1989, and so on, ending with Call Report data for the end of 2010 and failures from 2011 through 2013. The third regression (Regression 3) uses insured depository institutions' Call Report and TFR data for the end of 1987 and failures from 1988 through 1990, and so on, ending with Call Report data for the end of 2011 and failures from 2012 through 2014. The regressions include only Call Report data and failures for established small institutions.

1 Tests for the statistical significance of parameters use adjustments discussed by Tyler Shumway (2001) “Forecasting Bankruptcy More Accurately: A Simple Hazard Model,” Journal of Business 74:1, 101-124.

2 Beginning in 2012, all insured depository institutions began filing quarterly Call Reports and the TFR was no longer filed.

Table A.1 lists and defines the explanatory variables (regressors) in the Statistical Model.

Table A.1—Definitions of Measures Used in the Financial Ratios Method

Variables	Description	Leverage Ratio (%)	Tier 1 capital divided by adjusted average assets. (Numerator and denominator are both based on the definition for prompt corrective action.)	Net Income before Taxes/Total Assets (%)	Income (before applicable income taxes and discontinued operations) for the most recent twelve months divided by total assets. 1	Nonperforming Loans and Leases/Gross Assets (%)	Sum of total loans and lease financing receivables past due 90 or more days and still accruing interest and total nonaccrual loans and lease financing receivables (excluding, in both cases, the maximum amount recoverable from the U.S. Government, its agencies or government-sponsored enterprises, under guarantee or insurance provisions) divided by gross assets. 2 3	Other Real Estate Owned/Gross Assets (%)	Other real estate owned divided by gross assets. 2	Brokered Deposit Ratio	The ratio of the difference between brokered deposits and 10 percent of total assets to total assets. For institutions that are well capitalized and have a CAMELS composite rating of 1 or 2, reciprocal deposits are deducted from brokered deposits. If the ratio is less than zero, the value is set to zero.	Weighted Average of C, A, M, E, L, and S Component Ratings	The weighted sum of the “C,” “A,” “M,” “E”, “L”, and “S” CAMELS components, with weights of 25 percent each for the “C” and “M” components, 20 percent for the “A” component, and 10 percent each for the “E”, “L”, and “S” components. In instances where the “S” component is missing, the remaining components are scaled by a factor of 10/9. 4	Loan Mix Index	A measure of credit risk described below.	One-Year Asset Growth (%)	Growth in assets (adjusted for mergers 5) over the previous year in excess of 10 percent. 6 If growth is less than 10 percent, the value is set to zero.

1 For purposes of calculating actual assessment rates (as opposed to model estimation), the ratio of Net Income before Taxes to Total Assets is bounded below by (and cannot be less than) -25 percent and is bounded above by (and cannot exceed) 3 percent. For purposes of model estimation only, the ratio of Net Income before Taxes to Total Assets is defined as income (before income taxes and extraordinary items and other adjustments) for the most recent twelve months divided by total assets.

2 For purposes of calculating actual assessment rates (as opposed to model estimation), “Gross assets” are total assets plus the allowance for loan and lease financing receivable losses (ALLL); for purposes of estimating the Statistical Model, for years before 2001, when allocated transfer risk was not included in ALLL in Call Reports, allocated transfer risk is included in gross assets separately.

3 Delinquency and non-accrual data on government guaranteed loans are not available for the entire estimation period. As a result, the Statistical Model is estimated without deducting delinquent or past-due government guaranteed loans from the nonperforming loans and leases to gross assets ratio.

4 The component rating for sensitivity to market risk (the “S” rating) is not available for years before 1997. As a result, and as described in the table, the Statistical Model is estimated using a weighted average of five component ratings excluding the “S” component where the component is not available.

5 Growth in assets is also adjusted for acquisitions of failed banks.

6 For purposes of calculating actual assessment rates (as opposed to model estimation), the maximum value of the One-Year Asset Growth measure is 230 percent; that is, asset growth (merger adjusted) over the previous year in excess of 240 percent (230 percentage points in excess of the 10 percent threshold) will not further increase a bank's assessment rate.

The financial variable measures used to estimate the failure probabilities are obtained from Call Reports and TFRs. The weighted average of the “C,” “A,” “M,” “E,” “L,”, and “S” component ratings measure is based on component ratings obtained from the most recent bank examination conducted within 24 months before the date of the Call Report or TFR.

The Loan Mix Index assigns loans to the categories of loans described in Table A.2. For each loan category, a charge-off rate is calculated for each year from 2001 through 2014. The charge-off rate for each year is the aggregate charge-off rate on all such loans held by small institutions in that year. A weighted average charge-off rate is then calculated for each loan category, where the weight for each year is based on the number of small-bank failures during that year. 3 A Loan Mix Index for each established small institution is calculated by: (1) multiplying the ratio of the institution's amount of loans in a particular loan category to its total assets by the associated weighted average charge-off rate for that loan category; and (2) summing the products for all loan categories. Table A.2 gives the weighted average charge-off rate for each category of loan, as calculated through the end of 2014. The Loan Mix Index excludes credit card loans.

3 An exception is “Real Estate Loans Residual,” which consists of real estate loans held in foreign offices. Few small insured depository institutions report this item and a statistically reliable estimate of the weighted average charge-off rate could not be obtained. Instead, a weighted average of the weighted average charge-off rates of the other real estate loan categories is used. (The other categories are construction & development, multifamily residential, nonfarm nonresidential, 1-4 family residential, and agricultural real estate.) The weight for each of the other real estate loan categories is based on the aggregate amount of the loans held by small insured depository institutions as of December 31, 2014.

Table A.2—Loan Mix Index Categories

	Weighted charge-off rate percent	Construction & Development	4.4965840	Commercial & Industrial	1.5984506	Leases	1.4974551	Other Consumer	1.4559717	Loans to Foreign Government	1.3384093	Real Estate Loans Residual	1.0169338	Multifamily Residential	0.8847597	Nonfarm Residential	0.7286274	1-4 Family Residential	0.6973778	Loans to Depository Banks	0.5760532	Agricultural Real Estate	0.2376712	Agriculture	0.2432737

For each of the three regression estimates (Regression 1, Regression 2 and Regression 3), the estimated probability of failure (over a three-year horizon) of institution i at time T is

where

where the β variables are parameter estimates. As stated earlier, for actual assessments, the β values that are applied are averages of each of the individual parameters over three separate regressions. Pricing multipliers (discussed in the next section) are based on ZiT. 4

4 The ZiT values have the same rank ordering as the probability measures PiT.

III. Derivation of Uniform Amount and Pricing Multipliers

The uniform amount and pricing multipliers used to compute the annual initial base assessment rate in basis points, RiT, for any such institution i at a given time T will be determined from the Statistical Model as follows:

where α0 and α1 are a constant term and a scale factor used to convert ZiT to an assessment rate, Max is the maximum initial base assessment rate in effect and Min is the minimum initial base assessment rate in effect. (RiT is expressed as an annual rate, but the actual rate applied in any quarter will be RiT/4.)

5 RiT is also subject to the minimum and maximum assessment rates applicable to established small institutions based upon their CAMELS composite ratings.

Solving equation 3 for minimum and maximum initial base assessment rates simultaneously,

Min = α0 + α1 * ZN and Max = α0 + α1 * ZX where ZX is the value of ZiT above which the maximum initial assessment rate (Max) applies and ZN is the value of ZiT below which the minimum initial assessment rate (Min) applies, results in values for the constant amount, α0, and the scale factor, α1:

The values for ZX and ZN will be selected to ensure that, for an assessment period shortly before adoption of a final rule, aggregate assessments for all established small institutions would have been approximately the same under the final rule as they would have been under the assessment rate schedule that—under rules in effect before adoption of the final rule—will automatically go into effect when the reserve ratio reaches 1.15 percent. As an example, using aggregate assessments for all established small institutions for the third quarter of 2013 to determine ZX and ZN, and assuming that Min had equaled 3 basis points and Max had equaled 30 basis points, the value of ZX would have been 0.87 and the value of ZN −6.36. Hence based on equations 4 and 5,

α0 = 26.751 and α1 = 3.734.

Therefore from equation 3, it follows that

Substituting equation 2 produces an annual initial base assessment rate for institution i at time T, RiT, in terms of the uniform amount, the pricing multipliers and model variables:

again subject to 3≤ RiT ≤30 6

6 As stated above, RiT is also subject to the minimum and maximum assessment rates applicable to established small institutions based upon their CAMELS composite ratings.

where 26.751 + 3.734 * β0 equals the uniform amount, 3.734 * βj is a pricing multiplier for the associated risk measure j, and T is the date of the report of condition corresponding to the end of the quarter for which the assessment rate is computed. IV. Description of Scorecard Measures

Scorecard measures 1	Description	Leverage Ratio	Tier 1 capital for Prompt Corrective Action (PCA) divided by adjusted average assets based on the definition for prompt corrective action.	Concentration Measure for Large Insured depository institutions (excluding Highly Complex Institutions)	The concentration score for large institutions is the higher of the following two scores:	(1) Higher-Risk Assets/Tier 1 Capital and Reserves 2	Sum of construction and land development (C&D) loans (funded and unfunded), higher-risk C&I loans (funded and unfunded), nontraditional mortgages, higher-risk consumer loans, and higher-risk securitizations divided by Tier 1 capital and reserves. See Appendix C for the detailed description of the ratio.	(2) Growth-Adjusted Portfolio Concentrations 2	The measure is calculated in the following steps:		(1) Concentration levels (as a ratio to Tier 1 capital and reserves) are calculated for each broad portfolio category:		• C&D,		• Other commercial real estate loans,		• First lien residential mortgages (including non-agency residential mortgage-backed securities),		• Closed-end junior liens and home equity lines of credit (HELOCs),		• Commercial and industrial loans,		• Credit card loans, and		• Other consumer loans.		(2) Risk weights are assigned to each loan category based on historical loss rates.		(3) Concentration levels are multiplied by risk weights and squared to produce a risk-adjusted concentration ratio for each portfolio.		(4) Three-year merger-adjusted portfolio growth rates are then scaled to a growth factor of 1 to 1.2 where a 3-year cumulative growth rate of 20 percent or less equals a factor of 1 and a growth rate of 80 percent or greater equals a factor of 1.2. If three years of data are not available, a growth factor of 1 will be assigned.		(5) The risk-adjusted concentration ratio for each portfolio is multiplied by the growth factor and resulting values are summed.		See Appendix C for the detailed description of the measure.	Concentration Measure for Highly Complex Institutions	Concentration score for highly complex institutions is the highest of the following three scores:	(1) Higher-Risk Assets/Tier 1 Capital and Reserves 2	Sum of C&D loans (funded and unfunded), higher-risk C&I loans (funded and unfunded), nontraditional mortgages, higher-risk consumer loans, and higher-risk securitizations divided by Tier 1 capital and reserves. See Appendix C for the detailed description of the measure.	(2) Top 20 Counterparty Exposure/Tier 1 Capital and Reserves 2	Sum of the 20 largest total exposure amounts to counterparties divided by Tier 1 capital and reserves. The total exposure amount is equal to the sum of the institution's exposure amounts to one counterparty (or borrower) for derivatives, securities financing transactions (SFTs), and cleared transactions, and its gross lending exposure (including all unfunded commitments) to that counterparty (or borrower). A counterparty includes an entity's own affiliates. Exposures to entities that are affiliates of each other are treated as exposures to one counterparty (or borrower). Counterparty exposure excludes all counterparty exposure to the U.S. Government and departments or agencies of the U.S. Government that is unconditionally guaranteed by the full faith and credit of the United States. The exposure amount for derivatives, including OTC derivatives, cleared transactions that are derivative contracts, and netting sets of derivative contracts, must be calculated using the methodology set forth in 12 CFR 324.34(b), but without any reduction for collateral other than cash collateral that is all or part of variation margin and that satisfies the requirements of 12 CFR 324.10(c)(4)(ii)(C)(1)(ii) and (iii) and 324.10(c)(4)(ii)(C)(3) through (7). The exposure amount associated with SFTs, including cleared transactions that are SFTs, must be calculated using the standardized approach set forth in 12 CFR 324.37(b) or (c). For both derivatives and SFT exposures, the exposure amount to central counterparties must also include the default fund contribution. 3	(3) Largest Counterparty Exposure/Tier 1 Capital and Reserves 2	The largest total exposure amount to one counterparty divided by Tier 1 capital and reserves. The total exposure amount is equal to the sum of the institution's exposure amounts to one counterparty (or borrower) for derivatives, SFTs, and cleared transactions, and its gross lending exposure (including all unfunded commitments) to that counterparty (or borrower). A counterparty includes an entity's own affiliates. Exposures to entities that are affiliates of each other are treated as exposures to one counterparty (or borrower). Counterparty exposure excludes all counterparty exposure to the U.S. Government and departments or agencies of the U.S. Government that is unconditionally guaranteed by the full faith and credit of the United States. The exposure amount for derivatives, including OTC derivatives, cleared transactions that are derivative contracts, and netting sets of derivative contracts, must be calculated using the methodology set forth in 12 CFR 324.34(b), but without any reduction for collateral other than cash collateral that is all or part of variation margin and that satisfies the requirements of 12 CFR 324.10(c)(4)(ii)(C)(1)(ii) and (iii) and 324.10(c)(4)(ii)(C)(3) through (7). The exposure amount associated with SFTs, including cleared transactions that are SFTs, must be calculated using the standardized approach set forth in 12 CFR 324.37(b) or (c). For both derivatives and SFT exposures, the exposure amount to central counterparties must also include the default fund contribution. 3	Core Earnings/Average Quarter-End Total Assets	Core earnings are defined as net income less extraordinary items and tax-adjusted realized gains and losses on available-for-sale (AFS) and held-to-maturity (HTM) securities, adjusted for mergers. The ratio takes a four-quarter sum of merger-adjusted core earnings and divides it by an average of five quarter-end total assets (most recent and four prior quarters). If four quarters of data on core earnings are not available, data for quarters that are available will be added and annualized. If five quarters of data on total assets are not available, data for quarters that are available will be averaged.	Credit Quality Measure	The credit quality score is the higher of the following two scores:	(1) Criticized and Classified Items/Tier 1 Capital and Reserves 2	Sum of criticized and classified items divided by the sum of Tier 1 capital and reserves. Criticized and classified items include items an institution or its primary Federal regulator have graded “Special Mention” or worse and include retail items under Uniform Retail Classification Guidelines, securities, funded and unfunded loans, other real estate owned (ORE), other assets, and marked-to-market counterparty positions, less credit valuation adjustments. 4 Criticized and classified items exclude loans and securities in trading books, and the amount recoverable from the U.S. Government, its agencies, or Government-sponsored enterprises, under guarantee or insurance provisions.	(2) Underperforming Assets/Tier 1 Capital and Reserves 2	Sum of loans that are 30 days or more past due and still accruing interest, nonaccrual loans, restructured loans 5 (including restructured 1-4 family loans), and ORE, excluding the maximum amount recoverable from the U.S. Government, its agencies, or government-sponsored enterprises, under guarantee or insurance provisions, divided by a sum of Tier 1 capital and reserves.	Core Deposits/Total Liabilities	Total domestic deposits excluding brokered deposits and uninsured non-brokered time deposits divided by total liabilities.	Balance Sheet Liquidity Ratio	Sum of cash and balances due from depository institutions, federal funds sold and securities purchased under agreements to resell, and the market value of available for sale and held to maturity agency securities (excludes agency mortgage-backed securities but includes all other agency securities issued by the U.S. Treasury, U.S. government agencies, and U.S. government-sponsored enterprises) divided by the sum of federal funds purchased and repurchase agreements, other borrowings (including FHLB) with a remaining maturity of one year or less, 5 percent of insured domestic deposits, and 10 percent of uninsured domestic and foreign deposits. 6	Potential Losses/Total Domestic Deposits (Loss Severity Measure) 7	Potential losses to the DIF in the event of failure divided by total domestic deposits. Appendix D describes the calculation of the loss severity measure in detail.	Market Risk Measure for Highly Complex Institutions	The market risk score is a weighted average of the following three scores:	(1) Trading Revenue Volatility/Tier 1 Capital	Trailing 4-quarter standard deviation of quarterly trading revenue (merger-adjusted) divided by Tier 1 capital.	(2) Market Risk Capital/Tier 1 Capital	Market risk capital divided by Tier 1 capital. 8	(3) Level 3 Trading Assets/Tier 1 Capital	Level 3 trading assets divided by Tier 1 capital.	Average Short-term Funding/Average Total Assets	Quarterly average of federal funds purchased and repurchase agreements divided by the quarterly average of total assets as reported on Schedule RC-K of the Call Reports.

1 The FDIC retains the flexibility, as part of the risk-based assessment system, without the necessity of additional notice-and-comment rulemaking, to update the minimum and maximum cutoff values for all measures used in the scorecard. The FDIC may update the minimum and maximum cutoff values for the higher-risk assets to Tier 1 capital and reserves ratio in order to maintain an approximately similar distribution of higher-risk assets to Tier 1 capital and reserves ratio scores as reported prior to April 1, 2013, or to avoid changing the overall amount of assessment revenue collected. 76 FR 10672, 10700 (February 25, 2011). The FDIC will review changes in the distribution of the higher-risk assets to Tier 1 capital and reserves ratio scores and the resulting effect on total assessments and risk differentiation between banks when determining changes to the cutoffs. The FDIC may update the cutoff values for the higher-risk assets to Tier 1 capital and reserves ratio more frequently than annually. The FDIC will provide banks with a minimum one quarter advance notice of changes in the cutoff values for the higher-risk assets to Tier 1 capital and reserves ratio with their quarterly deposit insurance invoice.

2 The applicable portions of the current expected credit loss methodology (CECL) transitional amounts attributable to the allowance for credit losses on loans and leases held for investment and added to retained earnings for regulatory capital purposes pursuant to the regulatory capital regulations, as they may be amended from time to time (12 CFR part 3, 12 CFR part 217, 12 CFR part 324, 85 FR 61577 (Sept. 30, 2020), and 84 FR 4222 (Feb. 14, 2019)), will be removed from the sum of Tier 1 capital and reserves.

3 SFTs include repurchase agreements, reverse repurchase agreements, security lending and borrowing, and margin lending transactions, where the value of the transactions depends on market valuations and the transactions are often subject to margin agreements. The default fund contribution is the funds contributed or commitments made by a clearing member to a central counterparty's mutualized loss sharing arrangement. The other terms used in this description are as defined in 12 CFR part 324, subparts A and D, unless defined otherwise in 12 CFR part 327.

4 A marked-to-market counterparty position is equal to the sum of the net marked-to-market derivative exposures for each counterparty. The net marked-to-market derivative exposure equals the sum of all positive marked-to-market exposures net of legally enforceable netting provisions and net of all collateral held under a legally enforceable CSA plus any exposure where excess collateral has been posted to the counterparty. For purposes of the Criticized and Classified Items/Tier 1 Capital and Reserves definition a marked-to-market counterparty position less any credit valuation adjustment can never be less than zero.

5 Restructured loans include troubled debt restructurings and modifications to borrowers experiencing financial difficulty, as these terms are defined in the glossary to the Call Report, as they may be amended from time to time.

6 Deposit runoff rates for the balance sheet liquidity ratio reflect changes issued by the Basel Committee on Banking Supervision in its December 2010 document, “Basel III: International Framework for liquidity risk measurement, standards, and monitoring,” http://www.bis.org/publ/bcbs188.pdf.

7 The applicable portions of the CECL transitional amounts attributable to the allowance for credit losses on loans and leases held for investment and added to retained earnings for regulatory capital purposes will be removed from the calculation of the loss severity measure.

8 Market risk is defined in 12 CFR 324.202.

[74 FR 9557, Mar. 4, 2009, as amended at 76 FR 10720, Feb. 25, 2011; 76 FR 17521, Mar. 30, 2011; 77 FR 66015, Oct. 31, 2012; 78 FR 55594, Sept. 10, 2013; 79 FR 70437, Nov. 26, 2014; 83 FR 17740, Apr. 24, 2018; 85 FR 4443, Jan. 24, 2020; 85 FR 71228, Nov. 9, 2020; 86 FR 11399, Feb. 25, 2021; 87 FR 64340, 64354, Oct. 24, 2022]