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2000 - Rules and Regulations
Appendix A to Subpart A
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
that a Risk Category I institution will be downgraded to a composite
CAMELS rating of 3 or worse within one year;
• Minimum and maximum downgrade probability cutoff values, based
on data from June 2006, that will determine which small institutions
will be charged the minimum and maximum assessment rates in Risk
Category I;
• The minimum base assessment rate for Risk Category I, equal to
two basis points, and
• The maximum base assessment rate for Risk Category I, which
is two basispoints higher than the minimum rate.
{{12-31-08 p.2296.02-A}}
II. The Statistical Model
The Statistical Model is defined in equation 1a below.
Equation 1a
Downgrade (0,1)i,t = β0 + β1 (Tier 1
leverage ratioit)
+ β2 (Loans past due 30 to 89
days ratioit)
+ β3 (Nonperforming asset
ratioit)
+ β4 (Net loan charge-off
ratioit)
+ β5 (Net income before taxes
ratioit)
+ β6 (Weighted average of the C, A, M, E
and L component ratingsit)
where Downgrade (0,1)i,t (the dependent variable--the
event being explained) is the incidence of downgrade from a composite
rating of 1 or 2 to a rating of 3 or worse during an on-site
examination for an institution i between 3 and 12 months after time t.
Time t is the end of a year within the multi-year period over which the
model was estimated (as explained below). The dependent variable takes
a value of 1 if a downgrade occurs and 0 if it does not.
The explanatory variables (regressors) in the model are five
financial ratios and a weighted average of the "C," "A,"
"M," "E," and "L" component ratings. The five
financial ratios included in the model are:
• Tier 1 leverage ratio
• Loans past due 30--89 days/Gross assets
• Nonperforming assets/Gross assets
• Net loan charge-offs/Gross assets
• Net income before taxes/Risk-weighted assets
The financial ratios and the weighted average of the "C,"
"A," "M," "E" and "L" component ratings
(collectively, the regressors) are defined in Table A.1. The component
rating for sensitivity to market risk (the "S" rating) is not
available for years prior to 1997. As a result, and as described in
Table A.1, the Statistical Model is estimated using a weighted average
of five component ratings excluding the "S" component. In
addition, delinquency and non-accrual data on government guaranteed
loans are not available before 1993 for Call Report filers and before
the third quarter of 2005 for TFR filers. As a result, and also
described in Table A.1, the Statistical Model is estimated without
deducting delinquent or past-due government guaranteed loans from
either the loans past due 30--89 days to gross assets ratio or the
nonperforming assets to gross assets ratio.
TABLE A.1—DEFINITIONS OF REGRESSORS
| Regressor |
Description
|
|---|
| Tier 1 Leverage Ratio
(%) |
Tier 1 capital for Prompt
Corrective Action (PCA) divided by adjusted average assets based on the
definition for prompt corrective action |
| Loans Past Due 30--89
Days/Gross Assets (%) |
Total loans and lease financing receivables
past due 30 through 89 days and still accruing interest divided by
gross assets (gross assets equal total assets plus allowance for loan
and lease financing receivable losses and allocated transfer
risk) |
| Nonperforming Assets/Gross Assets (%) |
Sum of total loans
and lease financing receivables past due 90 or more days and still
accruing interest, total nonaccrual loans and lease financing
receivables, and other real estate owned divided by gross
assets
{{12-31-08 p.2296.02-B}} |
| Net Loan
Charge-Offs/Gross Assets (%) |
Total charged-off loans and lease
financing receivables debited to the allowance for loan and lease
losses less total recoveries credited to the allowance to loan and
lease losses for the most recent twelve months divided by gross
assets |
| Net Income before Taxes/Risk-Weighted Assets (%) |
Income
before income taxes and extraordinary items and other adjustments for
the most recent twelve months divided by risk-weighted
assets |
| Weighted Average of C, A, M, E and L Component Ratings |
The
weighted sum of the "C," "A," "M," "E" and
"L" CAMELS components, with weights of 28 percent each for the
"C" and "M" components, 22 percent for the "A"
component, and 11 percent each for the "E" and "L"
components. (For the regression, the "S" component is
omitted.)
|
The financial ratio regressors used to estimate the downgrade
probabilities are obtained from quarterly reports of condition (Reports
of Condition and Income and Thrift Financial Reports). The weighted
average of the "C," "A," "M," "E" and "L"
component ratings regressor is based on component ratings obtained from
the most recent bank examination conducted within 24 months before the
date of the report of condition.
The Statistical Model uses ordinary least squares (OLS) regression
to estimate downgrade probabilities. The model is estimated with data
from a multi-year period (as explained below) for all institutions in
Risk Category I, except for institutions established within five years
before the date of the report of condition.
The OLS regression estimates coefficients, βj, for a given
regressor j and a constant amount, β0, as specified in equation
1a. As shown in equation 1b below, these coefficients are multiplied by
values or risk measures at time T, which is the date of the report of
condition corresponding to the end of the quarter for which the
assessment rate is computed. The sum of the products is then added to
the constant amount to produce as estimated probability, di,T, that
an institution will be downgraded to 3 or worse within 3 to 12 months
from time T.
The risk measures are financial ratios as defined in Table A.1,
except that the loans past due 30 to 89 days ratio and the
nonperforming asset ratio are adjusted to exclude the maximum amount
recoverable from the U.S. Government, its agencies or
government-sponsored agencies, under guarantee or insurance provisions.
Also, the weighted sum of six CAMELS component ratings is used, 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.
Equation 1b
diT = β0 + β1 (Tier 1 leverage
ratioiT)
+ β2 (Loans past due 30 to 89 days
ratioiT)
+ β3 (Nonperforming asset
ratioiT)
+ β4 (Net loan charge-off
ratioiT)
+ β5 (Net income before taxes
ratioiT)
+ β6 (Weighted average of CAMELS component
ratingsiT)
III. Minimum and maximum downgrade probability cutoff values
The pricing multipliers are also determined by minimum and maximum
downgrade probability cutoff values, which will be computed as
follows:
{{12-31-08 p.2296.02-C}}
• The minimum downgrade probability cutoff value will be the
maximum downgrade probability among the forty-five percent of all small
insured institutions in Risk Category I (excluding new institutions)
with the lowest estimated downgrade probabilities, computed using
values of the risk measures as of June 30,
2006. 1
The minimum downgrade probability cutoff value is approximately 2
percent.
• The maximum downgrade probability cutoff value will be the
minimum downgrade probability among the five percent of all small
insured institutions in Risk Category I (excluding new institutions)
with the highest estimated downgrade probabilities, computed using
values of the risk measures as of June 30,
2006. 2
The maximum downgrade probability cutoff value if approximately 14
percent.
IV. Derivation of uniform amount and pricing multipliers
The uniform amount and pricing multipliers used to compute the
annual base assessment rate in basis points, PiT, for any such
institution i at a given time T will be determined from the Statistical
Model, the minimum and maximum downgrade probability cutoff values, and
minimum and maximum base assessment rates in Risk Category I as
follows:
Equation 2
PiT = α0 + α1 *diT , subject to 2 ≤ PiT
≤ 4
where α0 and α1 are a constant term and a scale
factor used to convert diT (the estimated downgrade probability for
institution i at a given time T from the Statistical Model) to an
assessment rate, respectively, The numbers 2 and 4 in the restriction
to equation 2 are the minimum base assessment rate and maximum base
assessment rate, respectively, and they
Substituting equations 1b, 3 and 4 into equation 2 produces an
annual base assessment rate for institution i at time T, PiT, in
terms of the uniform amount, the pricing multipliers and the ratios and
weighted average CAMELS component rating referred to in 12 CFR
327.9(d)(2)(i):
Equation 5
PiT = [1.67 + 16.67*β0] + 16.67*
[β1 (Tier 1 Leverage RatioT)] +
16.67*[β2 (Loans
past due 30 to 89 days ratioT)] +
16.67*[β3
(Nonperforming asset ratioT)] +
16.67*[β4 (Net loan
charge-off ratioT)] +
16.67*[β5 (Net income before taxes
ratioT)] +
16.67*[β7 (Weighted average CAMELS
component ratingT)] again subject to 2 PiT 4
where 1.67 + 16.67*β0 equals the uniform amount,
16.67*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.
{{12-31-08 p.2296.02-D}}
V. Updating the Statistical Model, uniform amount, and
pricing multipliers
The initial Statistical Model is estimated using year-end financial
ratios and the weighted average of the "C," "A," "M,"
"E" and "L" component ratings over the 1984 to 2004 period
and downgrade data from the 1985 to 2005 period. The FDIC may, from
time to time, but no more frequently than annually, re-estimate the
Statistical Model with updated data and publish a new formula for
determining assessment rates--equation 5--based on updated uniform
amounts and pricing multipliers. However, the minimum and maximum
downgrade probability cutoff values will not change without additional
notice-and-comment rulemaking. The period covered by the analysis will
be lengthened by one year each year; however, from time to time, the
FDIC may drop some earlier years from its analysis.
[Codified to 12 C.F.R. Part 327, Appendix A]
[Appendix A added at 71 Fed. Reg. 69313, November 30,
2006, effective January 1,
2007]
1 As used in this context, a "new institution" means an
institution that has been chartered as a bank or thrift for less than
five years. Go Back to Text
2 As used in this context, a "new institution" means an
institution that has been chartered as a bank or thrift for less than
five years. Go Back to Text
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