TO BE NOTED: From DefaultRisk.Com:FRBNY ECONOMIC POLICY REVIEW / OCTOBER 1998 53
Industry Practices in Credit Risk Modeling
and Internal Capital Allocations:
Implications for a Models-Based
Regulatory Capital Standard
Summary of Presentation
David Jones and John Mingo
I. WHY SHOULD REGULATORS BE
INTERESTED IN CREDIT RISK MODELS?
Bank supervisors have long recognized two types of shortcomings
in the Basle Accord’s risk-based capital (RBC)
framework. First, the regulatory measures of “capital” may
not represent a bank’s true capacity to absorb unexpected
losses. Deficiencies in reported loan loss reserves, for
example, could mask deteriorations in banks’ economic net
worth. Second, the denominator of the RBC ratios, total
risk-weighted assets, may not be an accurate measure of
total risk. The regulatory risk weights do not reflect
certain risks, such as interest rate and operating risks.
More importantly, they ignore critical differences in credit
risk among financial instruments (for example, all commercial
credits incur a 100 percent risk weight), as well as
differences across banks in hedging, portfolio diversification,
and the quality of risk management systems.
These anomalies have created opportunities for
“regulatory capital arbitrage” that are rendering the formal
RBC ratios increasingly less meaningful for the largest,
most sophisticated banks. Through securitization and
other financial innovations, many large banks have lowered
their RBC requirements substantially without reducing
materially their overall credit risk exposures. More
recently, the September 1997 Market Risk Amendment to
the Basle Accord has created additional arbitrage opportunities
by affording certain credit risk positions much lower
RBC requirements when held in the trading account rather
than in the banking book.
Given the prevalence of regulatory capital arbitrage
and the unstinting pace of financial innovation, the current
Basle Accord may soon become overwhelmed. At least for
the largest, most sophisticated banks, it seems clear that
regulators need to begin developing the next generation of
capital standards now—before the current framework is
completely outmoded. “Internal models” approaches to
prudential regulation are presently the only long-term
solution on the horizon.
The basic problem is that securitization and other
forms of capital arbitrage allow banks to achieve effective
capital requirements well below the nominal 8 percent
Basle standard. This may not be a concern—indeed, it may
be desirable from a resource allocation perspective—when,
David Jones is an assistant director and John Mingo a senior adviser in the
Division of Research and Statistics of the Board of Governors of the Federal
Reserve System.
54 FRBNY ECONOMIC POLICY REVIEW / OCTOBER 1998
The Relationship between PDF and Allocated
Economic Capital Losses
Note: The shaded area under the PDF to the right of X (the target insolvency rate)
equals the cumulative probability that unexpected losses will exceed the allocated
economic capital.
Probability density
function of losses
(PDF)
Allocated economic capital
Expected
losses
X
Losses
in specific instances, the Basle standard is way too high in
relation to a bank’s true risks. But it is a concern when
capital arbitrage lowers overall prudential standards.
Unfortunately, with the present tools available to supervisors,
it is often difficult to distinguish these cases,
especially given the lack of transparency in many offbalance-
sheet credit positions.
Ultimately, capital arbitrage stems from the
disparities between true economic risks and the “one-sizefits-
all” notion of risk embodied in the Accord. By contrast,
over the past decade many of the largest banks have
developed sophisticated methods for quantifying credit
risks and internally allocating capital against those risks.
At these institutions, credit risk models and internal
capital allocations are used in a variety of management
applications, such as risk-based pricing, the measurement
of risk-adjusted profitability, and the setting of portfolio
concentration limits.
II. THE RELATIONSHIP BETWEEN PDF
AND ALLOCATED ECONOMIC CAPITAL
Before discussing various credit risk models per se, it may
be helpful to describe how these models are used within
banks’ capital allocation systems. Internal capital allocations
against credit risk are based on a bank’s estimate of
the probability density function (PDF) for credit losses.
Credit risk models are used to estimate these PDFs (see
chart). A risky portfolio is one whose PDF has a relatively
long, fat tail—that is, where there is a significant likelihood
that actual losses will be substantially higher than
expected losses, shown as the left dotted line in the chart.
In this chart, the probability of credit losses exceeding the
level X is equal to the shaded area under the PDF to the
right of X.
The estimated capital needed to support a bank’s
credit risk exposure is generally referred to as its “economic
capital” for credit risk. The process for determining this
amount is analogous to VaR methods used in allocating
economic capital against market risks. Specifically, the economic
capital for credit risk is determined in such a way
that the estimated probability of unexpected credit losses
exhausting economic capital is less than the bank’s “target
insolvency rate.” Capital allocation systems generally
assume that it is the role of reserving policies to cover
expected credit losses, while it is the role of equity capital to
cover credit risk, or the uncertainty of credit losses. Thus,
required economic capital is the amount of equity over and
above expected losses necessary to achieve the target insolvency
rate. In the chart, for a target insolvency rate equal
to the shaded area, the required economic capital equals
the distance between the two dotted lines.
In practice, the target insolvency rate is usually
chosen to be consistent with the bank’s desired credit rating.
For example, if the desired credit rating is AA, the target
insolvency rate might equal the historical one-year default
rate for AA-rated corporate bonds (about 3 basis points).
To recap, economic capital allocations for credit
risk are based on two critical inputs: the bank’s target
insolvency rate and its estimated PDF for credit losses. Two
banks with identical portfolios, therefore, could have very
different economic capital allocations for credit risk, owing
to differences in their attitudes toward risk taking, as
reflected in their target insolvency rates, or owing to differences
in their methods for estimating PDFs, as reflected in
FRBNY ECONOMIC POLICY REVIEW / OCTOBER 1998 55
Overview of Risk Measurement Systems
Aggregative Models
(Top-down techniques, generally applied
to broad lines of business)
Structural Models
Top-Down Methods
(Common within consumer and
small business units)
Bottom-Up Methods
(Standard within large corporate business units)
Building blocks
· Peer analysis
· Historical cash flow volatility
· Historical charge-off volatility
Credit Risks Market Risks Operating Risks
1. Internal credit ratings
2. Definition of credit loss
· Default mode (DM)
· Mark-to-market (MTM)
3. Valuations of loans
4. Treatment of credit-related optionality
5. Parameter specification/estimation
6. PDF computation engine
· Monte Carlo simulation
· Mean/variance approximation
7. Capital allocation rule
their credit risk models. Obviously, for competitive equity
and other reasons, regulators prefer to apply the same
minimum soundness standard to all banks. Thus, any
internal models approach to regulatory capital would likely
be based on a bank’s estimated PDF, not on the bank’s own
internal economic capital allocations. That is, the regulator
would likely (a) decide whether the bank’s PDF estimation
process was acceptable and (b) at least implicitly, set a
regulatory maximum insolvency probability (rather than
accept the bank’s target insolvency rate if such a rate was
deemed “too high” by regulatory standards).
III. TYPES OF CREDIT RISK MODELS
When estimating the PDF for credit losses, banks generally
employ what we term either “top-down” or “bottom-up”
methods (see exhibit). Top-down models are often used for
estimating credit risk in consumer or small business portfolios.
Typically, within a broad subportfolio, such as credit
cards, all loans would be treated as more or less homogeneous.
The bank would then base its estimated PDF on the
historical credit loss rates for that subportfolio taken as a
whole. For example, the variance in subportfolio loss rates
over time could be taken as an estimate of the variance of
loss rates associated with the current subportfolio. A limitation
of top-down models, however, is that they may not
be sensitive to changes in the subportfolio’s composition.
That is, if the quality of the bank’s card customers were to
change over time, PDF estimates based on that portfolio’s
historical loss rates could be highly misleading.
Where changes in portfolio composition are a
significant concern, banks appear to be evolving toward
bottom-up models. This is already the predominant
method for measuring the credit risks of large and middlemarket
customers. A bottom-up model attempts to
quantify credit risk at the level of each individual loan,
based on an explicit credit evaluation of the underlying
customer. This evaluation is usually summarized in terms
of the loan’s internal credit rating, which is treated as a
proxy for the loan’s probability of default. The bank
would also estimate the loan’s loss rate in the event of
default, based on collateral and other factors. To measure
credit risk for the portfolio as a whole, the risks of
individual loans are aggregated, taking into account
correlation effects. Unlike top-down methods, therefore,
bottom-up models explicitly consider variations in credit
quality and other compositional effects.
56 FRBNY ECONOMIC POLICY REVIEW / OCTOBER 1998
IV. MODELING ISSUES
The remainder of this summary focuses on four aspects
of credit risk modeling: the conceptual framework,
credit-related optionality, model calibrations, and model
validation. The intent is to highlight some of the modeling
issues that we believe are significant from a regulator’s
perspective; the full version of our paper provides significantly
greater detail.
A. CONCEPTUAL FRAMEWORK
Credit risk modeling procedures are driven importantly by
a bank’s underlying definition of “credit losses” and the
“planning horizon” over which such losses are measured.
Banks generally employ a one-year planning horizon and
what we refer to as either a default-mode (DM) paradigm or a
mark-to-market (MTM) paradigm for defining credit losses.
1. Default-Mode Paradigm
At present, the default-mode paradigm is by far the most
common approach to defining credit losses. It can be
thought of as a representation of the traditional “buyand-
hold” lending business of commercial banks. It is
sometimes called a “two-state” model because only two
outcomes are relevant: nondefault and default. If a loan
does not default within the planning horizon, no credit
loss is incurred; if the loan defaults, the credit loss equals
the difference between the loan’s book value and the
present value of its net recoveries.
2. Mark-to-Market Paradigm
The mark-to-market paradigm generalizes this approach
by recognizing that the economic value of a loan may
decline even if the loan does not formally default. This
paradigm is “multi-state” in that “default” is only one of
several possible credit ratings to which a loan could
migrate. In effect, the credit portfolio is assumed to be
marked to market or, more accurately, “marked to model.”
The value of a term loan, for example, typically would
employ a discounted cash flow methodology, where the
credit spreads used in valuing the loan would depend on
the instrument’s credit rating.
To illustrate the differences between these two
paradigms, consider a loan having an internal credit rating
equivalent to BBB. Under both paradigms, the loan
would incur a credit loss if it were to default during the
planning horizon. Under the mark-to-market paradigm,
however, credit losses could also arise if the loan were to
suffer a downgrade short of default (such as migrating from
BBB to BB) or if prevailing credit spreads were to widen.
Conversely, the value of the loan could increase if its credit
rating improved or if credit spreads narrowed.
Clearly, the planning horizon and loss paradigm are
critical decision variables in the credit risk modeling process.
As noted, the planning horizon is generally taken to be one
year. It is often suggested that one year represents a reasonable
interval over which a bank—in the normal course of
business—could mitigate its credit exposures. Regulators,
however, tend to frame the issue differently—in the context
of a bank under stress attempting to unload the credit risk of
a significant portfolio of deteriorating assets. Based on
experience in the United States and elsewhere, more than one
year is often needed to resolve asset-quality problems at
troubled banks. Thus, for the banking book, regulators may
be uncomfortable with the assumption that capital is needed
to cover only one year of unexpected losses.
Since default-mode models ignore credit deteriorations
short of default, their estimates of credit risk may be
particularly sensitive to the choice of a one-year horizon.
With respect to a three-year term loan, for example, the
one-year horizon could mean that more than two-thirds of
the credit risk is potentially ignored. Many banks attempt
to reduce this bias by making a loan’s estimated probability
of default an increasing function of its maturity. In
practice, however, these adjustments are often made in an
ad hoc fashion, so it is difficult to assess their effectiveness.
B. CREDIT-RELATED OPTIONALITY
In contrast to simple loans, for many instruments a bank’s
credit exposure is not fixed in advance, but rather depends
on future (random) events. One example of such “creditrelated
optionality” is a line of credit, where optionality
reflects the fact that drawdown rates tend to increase as a
FRBNY ECONOMIC POLICY REVIEW / OCTOBER 1998 57
customer’s credit quality deteriorates. As observed in
connection with the recent turmoil in foreign exchange
markets, credit-related optionality also arises in derivatives
transactions, where counterparty exposure changes randomly
over the life of the contract, reflecting changes in the
amount by which the bank is “in the money.”
As with the treatment of optionality in VaR models,
credit-related optionality is a complex topic, and methods
for dealing with it are still evolving. At present, there is
great diversity in practice, which frequently leads to very
large differences across banks in credit risk estimates for
similar instruments. With regard to virtually identical
lines of credit, estimates of stand-alone credit risk can differ
as much as a tenfold. In some cases, these differences reflect
modeling assumptions that, quite frankly, seem difficult to
justify—for example, with respect to committed lines of
credit, some banks implicitly assume that future drawdown
rates are independent of future changes in a customer’s
credit quality. Going forward, in our view the treatment of
credit-related optionality needs to be a priority item, both
for bank risk modelers and their supervisors.
C. MODEL CALIBRATION
Perhaps the most difficult aspect of credit risk modeling is
the calibration of model parameters. To illustrate this
process, note that in a default-mode model, the credit loss
for an individual loan reflects the combined influence of
two types of risk factors—those determining whether or not
the loan defaults and, in the event of default, risk factors
determining the loan’s loss rate. Thus, implicitly or explicitly,
the model builder must specify (a) the expected
probability of default for each loan, (b) the probability
distribution for each loan’s loss-rate-given-default, and
(c) among all loans in the portfolio, all possible pair-wise
correlations among defaults and loss-rates-given-default.
Under the mark-to-market paradigm, the estimation problem
is even more complex, since the model builder needs
to consider possible credit rating migrations short of
default as well as potential changes in future credit spreads.
This is a daunting task. Reflecting the longer term
nature of credit cycles, even in the best of circumstances—
assuming parameter stability—many years of data, spanning
multiple credit cycles, would be needed to estimate default
probabilities, correlations, and other key parameters with
good precision. At most banks, however, data on historical
loan performance have been warehoused only since the
implementation of their capital allocation systems, often
within the last few years. Owing to such data limitations,
the model specification process tends to involve many crucial
simplifying assumptions as well as considerable judgment.
In our full paper, we discuss assumptions that are
often invoked to make model calibration manageable.
Examples include assumptions of parameter stability and
various forms of independence within and among the various
types of risk factors. Some specifications also impose
normality or other parametric assumptions on the underlying
probability distributions.
It is important to note that estimation of the
extreme tail of the PDF is likely to be highly sensitive to
these assumptions and to estimates of key parameters.
Surprisingly, in practice there is generally little analysis
supporting critical modeling assumptions. Nor is it
standard practice to conduct sensitivity testing of a
model’s vulnerability to key parameters. Indeed, practitioners
generally presume that all parameters are known
with certainty, thus ignoring credit risk issues arising
from parameter uncertainty or model instability. In the
context of an internal models approach to regulatory capital
for credit risk, sensitivity testing and the treatment of
parameter uncertainty would likely be areas of keen
supervisory interest.
D. MODEL VALIDATION
Given the difficulties associated with calibrating credit risk
models, one’s attention quickly focuses on the need for
effective model validation procedures. However, the same
data problems that make it difficult to calibrate these models
also make it difficult to validate the models. Owing to insufficient
data for out-of-sample testing, banks generally do not
conduct statistical back testing on their estimated PDFs.
Instead, credit risk models tend to be validated
indirectly, through various market-based “reality” checks.
58 FRBNY ECONOMIC POLICY REVIEW / OCTOBER 1998
Peer-group analysis is used extensively to gauge the reasonableness
of a bank’s overall capital allocation process.
Another market-based technique involves comparing
actual credit spreads on corporate bonds or syndicated
loans with the break-even spreads implied by the bank’s
internal pricing models. Clearly, an implicit assumption of
these techniques is that prevailing market perceptions and
prevailing credit spreads are always “about right.”
In principle, stress testing could at least partially
compensate for shortcomings in available back-testing
methods. In the context of VaR models, for example, stress
tests designed to simulate hypothetical shocks provide
useful checks on the reasonableness of the required capital
levels generated by these models. Presumably, stress-testing
protocols also could be developed for credit risk models,
although we are not yet aware of banks actively pursuing
this approach.
V. POSSIBLE NEAR-TERM APPLICATIONS
OF CREDIT RISK MODELS
While the reliability concerns raised above in connection
with the current generation of credit risk models are substantial,
they do not appear to be insurmountable. Credit
risk models are progressing so rapidly it is conceivable they
could become the foundation for a new approach to setting
formal regulatory capital requirements within a reasonably
near time frame. Regardless of how formal RBC standards
evolve over time, within the short run supervisors need to
improve their existing methods for assessing bank capital
adequacy, which are rapidly becoming outmoded in the
face of technological and financial innovation. Consistent
with the notion of “risk-focused” supervision, such new
efforts should take full advantage of banks’ own internal
risk management systems—which generally reflect the
most accurate information about their credit exposures—
and should focus on encouraging improvements to these
systems over time.
Within the relatively near term, we believe that
there are at least two broad areas in which the inputs or
outputs of bank’s internal credit risk models might usefully
be incorporated into prudential capital policies. These
include (a) the selective use of internal credit risk models in
setting formal RBC requirements against certain credit
positions that are not treated effectively within the current
Basle Accord and (b) the use of internal credit ratings and
other components of credit risk models for purposes of
developing specific and practicable examination guidance
for assessing the capital adequacy of large, complex banking
organizations.
A. SELECTIVE USE IN FORMAL RBC REQUIREMENTS
Under the current RBC standards, certain credit risk
positions are treated ineffectually or, in some cases, ignored
altogether. The selective application of internal risk models
in this area could fill an important void in the current RBC
framework for those instruments that, by virtue of their
being at the forefront of financial innovation, are the most
difficult to address effectively through existing prudential
techniques.
One particular application is suggested by the
November 1997 Notice of Proposed Rulemaking on
Recourse and Direct Credit Substitutes (NPR) put forth by
the U.S. banking agencies. The NPR discusses numerous
anomalies regarding the current RBC treatment of recourse
and other credit enhancements supporting banks’ securitization
activities. In this area, the Basle Accord often produces
dramatically divergent RBC requirements for essentially
equivalent credit risks, depending on the specific contractual
form through which the bank assumes those risks.
To address some of these inconsistencies, the NPR
proposes setting RBC requirements for securitization-related
credit enhancements on the basis of credit ratings for these
positions obtained from one or more accredited rating agencies.
One concern with this proposal is that it may be costly
for banks to obtain formal credit ratings for credit enhancements
that currently are not publicly rated. In addition,
many large banks already produce internal credit ratings for
such instruments, which, given the quality of their internal
control systems, may be at least as accurate as the ratings
that would be produced by accredited rating agencies. A
natural extension of the agencies’ proposal would permit a
bank to use its internal credit ratings (in lieu of having to
FRBNY ECONOMIC POLICY REVIEW / OCTOBER 1998 59
obtain external ratings from accredited rating agencies),
provided they were judged to be “reliable” by supervisors.
A further extension of the agency proposal might
involve the direct use of internal credit risk models in setting
formal RBC requirements for selected classes of
securitization-related credit enhancements. Many current
securitization structures were not contemplated when the
Accord was drafted, and cannot be addressed effectively
within the current RBC framework. Market acceptance of
securitization programs, however, is based heavily on the
ability of issuers to quantify (or place reasonable upper
bounds on) the credit risks of the underlying pools of
securitized assets. The application of internal credit risk
models, if deemed “reliable” by supervisors, could provide
the first practical means of assigning economically reasonable
capital requirements against such instruments. The
development of an internal models approach to RBC
requirements—on a limited scale for selected instruments—
also would provide a useful test bed for enhancing supervisors’
understanding of and confidence in such models,
and for considering possible expanded regulatory capital
applications over time.
B. IMPROVED EXAMINATION GUIDANCE
As noted above, most large U.S. banks today have highly
disciplined systems for grading the credit quality of individual
financial instruments within major portions of their
credit portfolios (such as large business customers). In combination
with other information from banks’ internal risk
models, these internal grades could provide a basis for
developing specific and practical examination guidance to
aid examiners in conducting independent assessments of the
capital adequacy of large, complex banking organizations.
To give one example, in contrast to the one-sizefits-
all Basle standard, a bank’s internal capital allocation
against a fully funded, unsecured commercial loan will
generally vary with the loan’s internal credit rating. Typical
internal capital allocations often range from 1 percent or
less for a grade-1 loan, to 14 percent or more for a grade-6
loan (in a credit rating system with six “pass” grades).
Internal economic capital allocations against classified, but
not-yet-charged-off, loans may approach 40 percent—not
counting any reserves for expected future charge-offs.
Examiners could usefully compare a particular bank’s
actual capital levels (or its allocated capital levels) with the
capital levels implied by such a grade-by-grade analysis
(using as benchmarks the internal capital allocation ratios,
by grade, of peer institutions). At a minimum, such a comparison
could initiate discussions with the bank on the
reliability of its internal approaches to risk measurement
and capital allocation. Over time, examination guidance
might evolve to encompass additional elements of banks’
internal risk models, including analytical tools based on
stress-test methodologies. Regardless of the specific details,
the development and field testing of examination guidance
on the use of internal credit risk models would provide useful
insights into the longer term feasibility of an internal models
approach to setting formal regulatory capital standards.
More generally, both supervisors and the banking
industry would benefit from the development of sound
practice guidance on the design, implementation, and
application of internal risk models and capital allocation
systems. Although important concerns remain, this field
has progressed rapidly in recent years, reflecting the growing
awareness that effective risk measurement is a critical
ingredient to effective risk management. As with trading
account VaR models at a similar stage of development,
banking supervisors are in a unique position to disseminate
information on best practices in the risk measurement
arena. In additional to permitting individual banks to
compare their practices with those of peers, such efforts
would likely stimulate constructive discussions among
supervisors and bankers on ways to improve current risk
modeling practices, including model validation procedures.
VI. CONCLUDING REMARKS
The above discussion provides examples by which information
from internal credit risk models might be usefully
incorporated into regulatory or supervisory capital policies.
In view of the modeling concerns described in this summary,
incorporating internal credit risk measurement and
capital allocation systems into the supervisory and/or
60 FRBNY ECONOMIC POLICY REVIEW / OCTOBER 1998
regulatory framework will occur neither quickly nor without
significant difficulties. Nevertheless, supervisors should
not be dissuaded from embarking on such an endeavor. The
current one-size-fits-all system of risk-based capital
requirements increasingly is inadequate to the task of
measuring large bank soundness. Moreover, the process of
“patching” regulatory capital “leaks” as they occur appears
to be less and less effective in dealing with the challenges
posed by ongoing financial innovation and regulatory
capital arbitrage. Finally, despite difficulties with an internal
models approach to bank capital, no alternative long-term
solutions have yet emerged.
ENDNOTE
The views expressed in this summary are those of the authors and do not necessarily
reflect those of the Federal Reserve System or other members of its staff. This paper
draws heavily upon information obtained through our participation in an ongoing
Federal Reserve System task force that has been reviewing the internal credit risk
modeling and capital allocation processes of major U.S. banking organizations.
The paper reflects comments from other members of that task force and Federal
Reserve staff, including Thomas Boemio, Raphael Bostic, Roger Cole, Edward
Ettin, Michael Gordy, Diana Hancock, Beverly Hirtle, James Houpt, Myron
Kwast, Mark Levonian, Chris Malloy, James Nelson, Thomas Oravez, Patrick
Parkinson, and Thomas Williams. In addition, we have benefited greatly from
discussions with numerous practitioners in the risk management arena, especially
John Drzik of Oliver, Wyman & Company. We alone, of course, are responsible
for any remaining errors.
Jones, David, and John Mingo. 1998. “Industry Practices in Credit Risk
Modeling and Internal Capital Allocations: Implications for a
Models-Based Regulatory Capital Standard.” Paper presented at the
conference “Financial Services at the Crossroads: Capital Regulation in
the Twenty-First Century,” Federal Reserve Bank of New York,
February 26-27.
NOTES
REFERENCES
The views expressed in this article are those of the authors and do not necessarily reflect the position of the Federal Reserve
Bank of New York or the Federal Reserve System. The Federal Reserve Bank of New York provides no warranty, express or
implied, as to the accuracy, timeliness, completeness, merchantability, or fitness for any particular purpose of any information
contained in documents produced and provided by the Federal Reserve Bank of New York in any form or manner whatsoever.
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