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11.
Calculation of capital charges for equity
exposures
(i)
The internal models market-based
approach
525.
To be eligible for the internal models
market-based approach a bank
must
demonstrate
to its supervisor that it meets certain
quantitative and qualitative
minimum
requirements
at the outset and on an ongoing basis. A bank
that fails to demonstrate
continued
compliance with the minimum requirements must
develop a plan for rapid return to compliance,
obtain its supervisor’s approval of the plan,
and implement that plan in a timely fashion. In
the interim, banks would be expected to compute
capital charges using a simple risk weight
approach.
526.
The Committee recognises that differences in
markets, measurement
methodologies,
equity investments and management practices
require banks and
supervisors
to customise their operational procedures. It is
not the Committee’s intention
to
dictate
the form or operational detail of banks’ risk
management policies and
measurement
practices
for their banking book equity holdings.
However,
some of the minimum requirements are specific.
Each supervisor will develop detailed
examination procedures to ensure that banks’
risk measurement systems and management controls
are adequate to serve as the basis for the
internal models approach.
(ii)
Capital charge and risk
quantification
527.
The following minimum quantitative standards
apply for the purpose of
calculating
minimum
capital charges under the internal models
approach.
(a)
The capital charge is equivalent to the
potential loss on the institution’s
equity
portfolio arising
from an assumed instantaneous shock equivalent
to the 99th
percentile,
one-tailed confidence interval of the difference
between quarterly returns
and
an appropriate risk-free rate computed over a
long-term sample period.
(b)
The estimated losses should be robust to adverse
market movements relevant to
the
long-term risk profile of the institution’s
specific holdings. The data used
to
represent
return distributions should reflect the longest
sample period for which data
are
available and meaningful in representing the
risk profile of the bank’s
specific
equity
holdings.
The
data used should be sufficient to provide
conservative, statistically reliable and robust
loss estimates that are not based purely on
subjective or judgmental considerations.
Institutions must demonstrate to supervisors
that the shock employed provides a conservative
estimate of potential losses over a relevant
long-term market or business
cycle.
Models
estimated using data not reflecting realistic
ranges of long-run experience, including a
period of reasonably severe declines in equity
market values relevant to a bank’s
holdings,
are
presumed to produce optimistic results unless
there is credible evidence of appropriate
adjustments built into the model. In the absence
of built-in adjustments, the bank must combine
empirical analysis of available data with
adjustments based on a variety of factors in
order to attain model outputs that achieve
appropriate realism and
conservatism.
In
constructing Value at Risk (VaR) models
estimating potential quarterly losses,
institutions may use quarterly data or convert
shorter horizon period data to a quarterly
equivalent using an analytically appropriate
method supported by empirical evidence. Such
adjustments must be applied through a
well-developed and well-documented thought
process and analysis.
In
general, adjustments must be applied
conservatively and consistently over time.
Furthermore, where only limited data are
available, or where technical limitations
are
such
that estimates from any single method will be of
uncertain quality, banks must
add
appropriate margins of conservatism in order to
avoid over-optimism.
(c)
No particular type of VaR model (e.g.
variance-covariance, historical simulation,
or
Monte
Carlo) is prescribed.
However,
the model used must be able to capture
adequately all of the material risks embodied in
equity returns including both the general market
risk and specific risk exposure of the
institution’s equity portfolio. Internal models
must adequately explain historical price
variation, capture both the magnitude and
changes in the composition of potential
concentrations, and be robust to adverse market
environments. The population of risk exposures
represented in the data used for estimation must
be closely matched to or at least comparable
with those of the bank’s equity
exposures.
(d)
Banks may also use modelling techniques such as
historical scenario analysis to
determine
minimum capital requirements for banking book
equity holdings. The use
of
such models is conditioned upon the institution
demonstrating to its supervisor
that
the methodology and its output can be quantified
in the form of the loss
percentile
specified under (a).
(e)
Institutions must use an internal model that is
appropriate for the risk profile
and
complexity
of their equity portfolio. Institutions with
material holdings with values
that
are
highly non-linear in nature (e.g. equity
derivatives, convertibles) must employ
an
internal
model designed to capture appropriately the
risks associated with such
instruments.
(f)
Subject to supervisory review, equity portfolio
correlations can be integrated into
a
bank’s
internal risk measures. The use of explicit
correlations (e.g. utilisation of
a
variance/covariance
VaR model) must be fully documented and
supported using
empirical
analysis. The appropriateness of implicit
correlation assumptions will be
evaluated
by supervisors in their review of model
documentation and estimation
techniques.
(g)
Mapping of individual positions to proxies,
market indices, and risk factors should
be
plausible,
intuitive, and conceptually sound. Mapping
techniques and processes
should
be fully documented, and demonstrated with both
theoretical and empirical
evidence
to be appropriate for the specific holdings.
Where professional judgement
is
combined with quantitative techniques in
estimating a holding’s return
volatility,
the
judgement must take into account the relevant
and material information not
considered
by the other techniques
utilised.
(h)
Where factor models are used, either single or
multi-factor models are
acceptable
depending
upon the nature of an institution’s holdings.
Banks are expected to
ensure
that the factors are sufficient to capture the
risks inherent in the equity
portfolio.
Risk factors should correspond to the
appropriate equity market
characteristics
(for example, public, private, market
capitalisation industry sectors
and
sub-sectors, operational characteristics) in
which the bank holds
significant
positions.
While banks will have discretion in choosing the
factors, they must
demonstrate
through empirical analyses the appropriateness
of those factors,
including
their ability to cover both general and specific
risk.
(i)
Estimates of the return volatility of equity
investments must incorporate relevant
and
material
available data, information, and methods. A bank
may utilise independently
reviewed
internal data or data from external sources
(including pooled data). The
number
of risk exposures in the sample, and the data
period used for quantification
must
be sufficient to provide the bank with
confidence in the accuracy and
robustness
of its estimates. Institutions should take
appropriate measures to limit
the
potential of both sampling bias and survivorship
bias in estimating return
volatilities.
(j)
A rigorous and comprehensive stress-testing
programme must be in place.
Banks
are
expected to subject their internal model and
estimation procedures,
including
volatility
computations, to either hypothetical or
historical scenarios that
reflect
worst-case
losses given underlying positions in both public
and private equities. At a
minimum,
stress tests should be employed to provide
information about the effect of
tail
events beyond the level of confidence assumed in
the internal models approach.
(iii)
Risk management process and
controls
528.
Banks’ overall risk management practices used to
manage their banking book
equity
investments
are expected to be consistent with the evolving
sound practice guidelines
issued
by
the Committee and national supervisors. With
regard to the development and use
of
internal
models for capital purposes, institutions must
have established policies,
procedures,
and
controls to ensure the integrity of the model
and modelling process used to
derive
regulatory
capital standards. These policies, procedures,
and controls should include the
following:
(a)
Full integration of the internal model into the
overall management information
systems
of the institution and in the management of the
banking book equity
portfolio.
Internal models should be fully integrated into
the institution’s risk
management
infrastructure including use in: (i)
establishing investment hurdle
rates
and
evaluating alternative investments; (ii)
measuring and assessing equity
portfolio
performance
(including the risk-adjusted performance); and
(iii) allocating economic
capital
to equity holdings and evaluating overall
capital adequacy as required
under
Pillar
2. The institution should be able to
demonstrate, through for
example,
investment
committee minutes, that internal model output
plays an essential role in
the
investment management process.
(b)
Established management systems, procedures, and
control functions for ensuring
the
periodic and independent review of all elements
of the internal modelling
process,
including approval of model revisions, vetting
of model inputs, and review
of
model results, such as direct verification of
risk computations. Proxy and
mapping
techniques
and other critical model components should
receive special attention.
These
reviews should assess the accuracy,
completeness, and appropriateness
of
model
inputs and results and focus on both finding and
limiting potential errors
associated
with known weaknesses and identifying unknown
model weaknesses.
Such
reviews may be conducted as part of internal or
external audit programmes, by
an
independent risk control unit, or by an external
third party.
(c)
Adequate systems and procedures for monitoring
investment limits and the risk
exposures
of equity investments.
(d)
The units responsible for the design and
application of the model must
be
functionally
independent from the units responsible for
managing individual
investments.
(e)
Parties responsible for any aspect of the
modelling process must be
adequately
qualified.
Management must allocate sufficient skilled and
competent resources to
the
modelling function.
(iv)
Validation and
documentation
529.
Institutions employing internal models for
regulatory capital purposes are
expected
to
have in place a robust system to validate the
accuracy and consistency of the model
and
its
inputs. They must also fully document all
material elements of their internal models
and
modelling
process. The modelling process itself as well as
the systems used to validate
internal
models including all supporting documentation,
validation results, and the findings of internal
and external reviews are subject to oversight
and review by the bank’s
supervisor.
Validation
530.
Banks must have a robust system in place to
validate the accuracy and
consistency
of
their internal models and modelling processes. A
bank must demonstrate to its
supervisor
that
the internal validation process enables it to
assess the performance of its internal
model
and
processes consistently and
meaningfully.
531.
Banks must regularly compare actual return
performance (computed using
realised
and
unrealised gains and losses) with modelled
estimates and be able to demonstrate
that
such
returns are within the expected range for the
portfolio and individual holdings.
Such
comparisons
must make use of historical data that are over
as long a period as possible.
The
methods
and data used in such comparisons must be
clearly documented by the bank.
This
analysis
and documentation should be updated at least
annually.
532.
Banks should make use of other quantitative
validation tools and comparisons
with
external
data sources. The analysis must be based on data
that are appropriate to the
portfolio,
are updated regularly, and cover a relevant
observation period. Banks’
internal
assessments
of the performance of their own model must be
based on long data histories,
covering
a range of economic conditions, and ideally one
or more complete business
cycles.
533.
Banks must demonstrate that quantitative
validation methods and data are
consistent
through time. Changes in estimation methods and
data (both data sources and
periods
covered) must be clearly and thoroughly
documented.
534.
Since the evaluation of actual performance to
expected performance over time
provides
a basis for banks to refine and adjust internal
models on an ongoing basis, it
is
expected
that banks using internal models will have
established well-articulated
model
review
standards. These standards are especially
important for situations where
actual
results
significantly deviate from expectations and
where the validity of the internal model
is
called
into question. These standards must take account
of business cycles and similar
systematic
variability in equity returns. All adjustments
made to internal models in
response
to
model reviews must be well documented and
consistent with the bank’s model
review
standards.
535.
To facilitate model validation through
backtesting on an ongoing basis,
institutions
using
the internal model approach must construct and
maintain appropriate databases on the actual
quarterly performance of their equity
investments as well on the estimates
derived
using
their internal models. Institutions should also
backtest the volatility estimates
used
within
their internal models and the appropriateness of
the proxies used in the model.
Supervisors
may ask banks to scale their quarterly forecasts
to a different, in particular
shorter,
time horizon, store performance data for this
time horizon and perform backtests
on
this
basis.
Documentation
536.
The burden is on the bank to satisfy its
supervisor that a model has good
predictive
power
and that regulatory capital requirements will
not be distorted as a result of its
use.
Accordingly,
all critical elements of an internal model and
the modelling process should be
fully
and adequately documented. Banks must document
in writing their internal
model’s
design
and operational details.
The
documentation should demonstrate banks’
compliance with the minimum quantitative and
qualitative standards, and should address topics
such as the application of the model to
different segments of the portfolio, estimation
methodologies, responsibilities of parties
involved in the modelling, and the model
approval and model review processes. In
particular, the documentation should address the
following points:
(a)
A bank must document the rationale for its
choice of internal modelling
methodology
and
must be able to provide analyses demonstrating
that the model and modelling
procedures
are likely to result in estimates that
meaningfully identify the risk of
the
bank’s
equity holdings. Internal models and procedures
must be periodically
reviewed
to determine whether they remain fully
applicable to the current
portfolio
and
to external conditions. In addition, a bank must
document a history of major
changes
in the model over time and changes made to the
modelling process
subsequent
to the last supervisory review. If changes have
been made in response
to
the bank’s internal review standards, the bank
must document that these
changes
are
consistent with its internal model review
standards.
(b)
In documenting their internal models banks
should:
•
provide a detailed
outline of the theory, assumptions and/or
mathematical and
empirical
basis of the parameters, variables, and data
source(s) used to estimate
the
model;
•
establish a rigorous
statistical process (including out-of-time and
out-of-sample
performance
tests) for validating the selection of
explanatory variables;
and
•
indicate
circumstances under which the model does not
work effectively.
(c)
Where proxies and mapping are employed,
institutions must have performed
and
documented
rigorous analysis demonstrating that all chosen
proxies and mappings
are
sufficiently representative of the risk of the
equity holdings to which they
correspond.
The documentation should show, for instance, the
relevant and material
factors
(e.g. business lines, balance sheet
characteristics, geographic
location,
company
age, industry sector and subsector, operating
characteristics) used in
mapping
individual investments into proxies. In summary,
institutions must
demonstrate
that the proxies and mappings
employed:
•
are
adequately comparable to the underlying holding
or portfolio;
•
are
derived using historical economic and market
conditions that are relevant
and
material
to the underlying holdings or, where not, that
an appropriate adjustment has
been
made; and,
•
are
robust estimates of the potential risk of the
underlying holding.
12.
Disclosure
requirements
537.
In order to be eligible for the IRB approach,
banks must meet the disclosure
requirements
set out in Pillar 3. These are minimum
requirements for use of IRB: failure
to
meet
these will render banks ineligible to use the
relevant IRB approach.
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