[Federal Register Volume 60, Number 142 (Tuesday, July 25, 1995)]
[Proposed Rules]
[Pages 38082-38142]
From the Federal Register Online via the Government Publishing Office [www.gpo.gov]
[FR Doc No: 95-17542]
[[Page 38081]]
_______________________________________________________________________
Part II
Department of the Treasury
12 CFR Part 3
Federal Reserve System
12 CFR Part 208 et al.
Federal Deposit Insurance Corporation
12 CFR Part 325
_______________________________________________________________________
Market Risk-Based Capital Standards and Capital Requirements for Market
Risk; Proposed Rules
Federal Register / Vol. 60, No. 142 / Tuesday, July 25, 1995 /
Proposed Rules
[[Page 38082]]
DEPARTMENT OF THE TREASURY
Office of the Comptroller of the Currency
12 CFR Part 3
[Docket No. 95-19]
RIN 1557-AB14
FEDERAL RESERVE SYSTEM
12 CFR Parts 208 and 225
[Regulations H and Y; Docket No. R-0884]
FEDERAL DEPOSIT INSURANCE CORPORATION
12 CFR Part 325
RIN 3064-AB64
Risk-Based Capital Standards: Market Risk
AGENCIES: Office of the Comptroller of the Currency (OCC), Department
of the Treasury; Board of Governors of the Federal Reserve System
(Board), and the Federal Deposit Insurance Corporation (FDIC).
ACTION: Joint notice of proposed rulemaking.
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SUMMARY: The Office of the Comptroller of the Currency (OCC), the Board
of Governors of the Federal Reserve System (Board), and the Federal
Deposit Insurance Corporation (FDIC) (the Agencies) are proposing to
amend their risk-based capital requirements to incorporate a measure
for market risk in foreign exchange and commodity activities and in the
trading of debt and equity instruments. Under the proposal, banks and
bank holding companies (institutions) regulated by the OCC, the Board,
and the FDIC with relatively large trading activities would calculate
their capital charges for market risk using either their own internal
value-at-risk model(s) or, alternatively, risk measurement techniques
that were developed by supervisors. The effect of the proposed market
risk measure would be that, in addition to existing capital
requirements for credit risk, certain institutions would be required to
hold capital based on the measure of their market risk exposure.
DATES: Comments must be received on or before September 18, 1995.
ADDRESSES: Comments should be directed to:
OCC: Comments may be submitted to Docket Number 95-19,
Communications Division, Third Floor, Office of the Comptroller of the
Currency, 250 E Street, S.W., Washington, DC 20219. Comments will be
available for inspection and photocopying at that address.
Board: Comments directed to the Board should refer to Docket No.R-
0884 and may be mailed to William W. Wiles, Secretary, Board of
Governors of the Federal Reserve System, 20th Street and Constitution
Avenue, N.W., Washington, D.C. 20551. Comments may also be delivered to
Room B-2222 of the Eccles Building between 8:45 and 5:15 p.m. weekdays,
or to the guard station in the Eccles Building courtyard on 20th
Street, N.W. (between Constitution Avenue and C Street) at any time.
Comments may be inspected in Room MP-500 of the Martin Building between
9 a.m. and 5 p.m. weekdays, except as provided in 12 CFR 261.8 of the
Board's rules regarding availability of information.
FDIC: Written comments should be sent to Jerry L. Langley,
Executive Secretary, Attention: Room F-402, Federal Deposit Insurance
Corporation, 550 17th Street N.W., Washington, D.C. 20429. Comments may
be hand-delivered to Room, F-402, 1776 F Street N.W., Washington, D.C.
20429, on business days between 8:30 a.m. and 5 p.m. (Fax number
(202)898-3838; Internet address: comments@fdic.gov). Comments will be
available for inspection and photocopying in Room 7118, 550 17th
Street, N.W., Washington, D.C. 20429, between 9 a.m. and 4:30 p.m. on
business days.
FOR FURTHER INFORMATION CONTACT:
OCC: Roger Tufts, Senior Economic Advisor (202/874-5070), or
Christina Benson, Capital Markets Specialist, (202/874-5070) Office of
the Chief National Bank Examiner. For legal issues, Ronald Shimabukuro,
Senior Attorney, Legislative and Regulatory Activities Division (202/
874-5090), Office of the Comptroller of the Currency, 250 E Street
S.W., Washington, D.C. 20219.
Board: Roger Cole, Deputy Associate Director (202/452-2618), James
Houpt, Assistant Director (202/452-3358), Barbara Bouchard, Supervisory
Financial Analyst (202/452-3072), Division of Banking Supervision and
Regulation; or Stephanie Martin, Senior Attorney (202/452-3198), Legal
Division. For the hearing impaired only, Telecommunication Device for
the Deaf, Dorothea Thompson (202/452-3544).
FDIC: William A. Stark, Assistant Director, (202/898-6972), Kenton
Fox, Senior Capital Markets Specialist, (202/898-7119), Division of
Supervision; Jamey Basham, Counsel, (202/898-7265), Legal Division,
FDIC, 550 17th Street, N.W., Washington, D.C. 20429.
SUPPLEMENTARY INFORMATION: The Agencies are proposing amendments to
their risk-based capital requirements to incorporate a measure for
market risk. The proposed amendments would generally apply only to
institutions that have (1) total assets exceeding $5 billion and either
on-balance-sheet trading activities representing at least 3.0 percent
of total assets or a volume of off-balance-sheet trading activities
with notional amounts exceeding $5 billion, or (2) total assets of $5
billion or less and a volume of trading activities representing at
least 10.0 percent of total assets.
I. Background
The Agencies' risk-based capital standards are based upon the
principles contained in the agreement on International Convergence of
Capital Measurement and Capital Standards of July, 1988 (the Accord)
that was agreed to by the Basle Committee on Banking Supervision (the
Committee) and endorsed by the central bank governors of the Group of
Ten (G-10) countries.1 That Accord sets forth a framework for
measuring capital adequacy under which weighted risk assets are
calculated by weighting an institution's assets and off-balance-sheet
items on the basis of their perceived credit risk using a relatively
small number of risk categories.
\1\ The Basle Supervisors' Committee is comprised of
representatives of the central banks and supervisory authorities
from the G-10 countries (Belgium, Canada, France, Germany, Italy,
Japan, The Netherlands, Sweden, Switzerland, the United Kingdom, and
the United States) plus Luxembourg.
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By focusing on credit risk, the risk that a loss will be incurred
due to an obligor or counterparty default on a transaction, the Accord
generally excludes coverage of risks arising from adverse movements in
market interest rates, foreign exchange rates, or commodity or equity
prices. The potential for loss from such movements is referred to as
market risk. In April 1993, the Committee, recognizing the need to
incorporate market risk into the risk-based capital standard, requested
comments on an initial measurement framework. The Agencies' current
proposal reflects substantial revisions to that 1993 paper and is based
upon revisions to the Accord that were proposed by the Committee on
April 12, 1995.2
\2\ The Committee's document is entitled ``Proposal to Issue a
Supplement to the Basle Capital Accord to Cover Market Risks'' and
is available through the Board's and the OCC's Freedom of
Information Office and the FDIC's Reading Room.
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The 1993 paper proposed standardized measurement procedures for
assessing risks in traded debt, equity,
[[Page 38083]]
and foreign exchange activities and provided only a limited role for a
bank's internal model(s) in measuring market risk exposure for
regulatory capital purposes. These procedures were strongly criticized
by commenters to the consultative document, especially by institutions
in the United States. These institutions generally believed that the
measurement framework was unduly cumbersome and potentially inaccurate,
especially for institutions with significant and diversified trading
activities.
In lieu of the standardized framework, these institutions urged the
Committee to allow greater use of an institution's internal market risk
models. They noted that large trading banks have materially expanded
the sophistication and coverage of their market risk trading models.
These models are typically described as ``value-at-risk'' (VAR) models,
which estimate the maximum amount by which an institution's portfolio
could decline in market value, given a certain level of statistical
confidence and an assumed holding period. The commenters believed that
these models would provide a more accurate risk measure and would be
better able to incorporate new products and activities than would the
standardized framework. They also believed that imposing a rigid
supervisory measurement system on institutions would result in
unnecessary costs and could encourage improper risk management
practices if institutions sought to minimize the capital requirements
resulting from the proposed risk measure. Many large European banks
also urged the use of internal models for measuring market risks for
regulatory capital purposes, but were generally less critical, in part
because the European Union had adopted into European law a regime
similar to the one outlined in the 1993 paper.3
\3\ The European Union's Second Directive sets forth a capital
regime for market risk that applies to banking and securities firms
that operate in EU member countries. These capital requirements
become effective at the beginning of 1996.
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In response to these and other comments and concerns, the Committee
issued a new proposal on April 12, 1995. In addition to expanding the
earlier proposal by providing measures for risks in commodities and
options, this latest proposal would allow institutions to use their
internal market risk models to measure the level of their market risk
exposure against which they would be required to hold capital. This
approach is referred to as the ``internal models approach.'' An
institution's use of this approach would be subject to the approval of
its appropriate supervisor and would be contingent upon conformance
with certain qualitative and quantitative standards regarding the
measurement and management of market risks. An institution whose
internal model failed to meet those standards or otherwise failed to
gain regulatory approval would be required to use standardized risk
measurement techniques as set forth in the Committee's April 1995
proposal. This latter approach is referred to as the ``standardized
risk measure'' approach, as it applies standardized assumptions and
risk factors to an institution's activities.
The Agencies are now proposing amendments to their risk-based
capital standards that are similar to the proposal recently issued by
the Committee.4 The Agencies would encourage institutions that are
affected by this proposal, and especially those with large trading
accounts, to comply with the proposed requirements by using the
proprietary internal models that they use to manage market risk.
4 As set forth in the regulatory text, the Agencies
propose to adopt the market risk requirements as new appendices to
their capital adequacy standards. The OCC may be required to make
additional conforming amendments to its risk-based capital
guidelines.
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The Agencies believe that such models should provide a more
accurate measure of market risk than the standardized risk measure and
would impose fewer costs and burdens on institutions. By using internal
models not only for operating purposes, but also as a basis for
determining capital requirements, institutions should be further
encouraged to continue their efforts to refine the accuracy of their
proprietary models, especially with regard to options risk. Given their
preference for the use of internal models for measuring market risk,
the Agencies request comments regarding whether institutions should be
permitted a choice between the two measurement procedures, or only be
permitted to use internal models.
II. Scope: Activities and Institutions Covered by the Proposal
This proposal would establish new capital requirements for general
market risk and specific risk as they pertain to the trading activities
of a banking organization and to the organization's other foreign
exchange and commodities activities. As such, the proposed standard, by
creating a risk-based capital ratio adjusted for market risk through
the addition of a market risk-equivalent assets measure, is an
integrated supplement to existing standards that address credit risk
through the current weighted-risk assets measure.
For purposes of this proposal, general market risk refers to
changes in the market value of the covered transactions that arise from
broad market movements, such as changing levels of market interest
rates, broad equity indices, or currency exchange rates. Specific risk
includes the credit risk of an issuer of a traded security, as well as
other factors that affect the market value of specific instruments, but
that do not materially alter broad market conditions. Consequently,
instruments other than over-the-counter (OTC) derivatives that are
covered by this proposal would, in effect, be removed from and no
longer subject to the credit risk standard previously established. OTC
derivatives would remain subject to the counterparty credit risk
requirements set forth in the existing risk-based capital standard.
This proposal defines trading activities as the sum of all trading
assets and liabilities as reported in the quarterly Consolidated
Reports of Condition and Income (call report) and would apply on a
fully consolidated basis to all national banks, state member banks, and
bank holding companies that meet the following criteria:
(1) The institution has total assets exceeding $5 billion, and (a)
the gross sum of trading assets and liabilities on a daily average
basis for the quarter account for 3.0 percent or more of total assets,
or (b) the sum of the notional amount of interest rate, foreign
exchange, equity and commodity off-balance-sheet derivative contracts
relating to trading activities exceeds $5 billion, or
(2) The institution has total assets of $5 billion or less and
trading assets and liabilities exceed 10 percent of total assets.
The Agencies may also apply the standard to other institutions for
safety and soundness purposes in limited circumstances and on a case-
by-case basis.
III. Definition of Capital and the Capital Requirement
The Agencies are also proposing to expand the definition and types
of qualifying capital that an institution could use to meet its market
risk capital requirements. This modification and others require that
the procedures for calculating an institution's overall risk-based
capital ratio be changed.
Definition of capital. The Accord permits institutions to meet
regulatory capital requirements with a combination of ``core'' (Tier 1)
and ``supplementary''
[[Page 38084]]
(Tier 2) capital. Tier 1 includes equity, noncumulative perpetual
preferred stock, and minority interest in consolidated subsidiaries,
less goodwill, while Tier 2 includes the allowance for loan and lease
losses, other preferred stock, and subordinated debt that has an
original weighted average maturity of at least five years.5
\5\ Bank holding companies may include cumulative perpetual
preferred stock in Tier 1 capital, subject to the conditions that
are specified in the Board's capital guidelines.
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This proposal would permit institutions to use a third tier of
capital (Tier 3), consisting of short-term subordinated debt. However,
this capital could be used only to meet capital requirements pertaining
to market risk and only if that debt meets certain qualifying
conditions: It must have an original maturity of at least two years, be
unsecured and fully paid up, and subject to a lock-in provision that
prevents the issuer from repaying the debt even at maturity if the
issuer's capital ratios are, or with repayment would become, less than
the minimum 8.0 percent risk-based capital requirement.
The agencies are proposing to allow the use of Tier 3 capital in
recognition that such short-term subordinated debt can help to protect
depositors and the Bank Insurance Fund against loss. Indeed, because
the underwriting activities of securities firms often create volatile
capital requirements, securities regulators in many countries permit
their institutions to treat such debt as capital, with similar
qualifications. The Agencies, however, believe that Tier 1 instruments
should remain a substantial proportion of an institution's total
capital and, therefore, propose the following constraints:
(1) Tier 3 capital may not exceed 250 percent of the amount of Tier
1 capital allocated for market risk, and
(2) Tier 1 capital must represent at least 50 percent of an
institution's total eligible capital--the sum of Tier 1, qualifying
Tier 2, and Tier 3 to the extent it is permitted in item (1), above.
Note that any element of Tier 2 capital must continue to conform
with the requirements of the original Accord; that is, Tier 2 may not
exceed total Tier 1 capital, and long-term subordinated debt may not
exceed 50 percent of Tier 1.
Calculation of the capital ratio. An institution subject to this
proposal would remain subject to the Agencies' risk-based capital
standards based on credit risk, but would also be required to
supplement its risk-based capital ratio to adjust it for market risk.
Under the proposal, an institution would accomplish this by multiplying
its capital requirement for market risk (as calculated by the internal
model or standardized approach) by 12.5 (the reciprocal of the minimum
capital ratio of 8.0 percent) and adding the resulting market risk
equivalent figure to its weighted risk assets, as calculated by the
credit risk standard. The institution's Tier 1 and total risk-based
capital ratios would be calculated as the sum of the eligible capital
as a percent of the sum of market risk-equivalent assets and weighted
risk assets. This approach avoids the distortions that could result
from allocating the necessary capital to either market or credit risk
and then calculating an institution's capital ratio on the basis of the
remaining capital. It also incorporates the risk-based capital ratio
adjusted for market risk into the capital category definitions under
the Agencies' prompt corrective action regulations.
Due to the 250 percent constraint on Tier 3 capital, an institution
that wishes to use Tier 3 capital must first calculate its minimum
credit risk requirement to determine the amount of Tier 1 capital that
is available to support market risk. This amount sets an upper limit on
the amount of Tier 3 capital that the institution may have. In
calculating its aggregate capital ratio, however, only that portion of
Tier 3 that is actually needed to meet its market risk requirement may
be included as eligible capital. Tier 3 capital in excess of this
amount will not be considered as eligible capital as it is not
permitted to meet credit risk. Eligible capital would be the sum of the
whole of the institution's Tier 1 capital, plus all of its Tier 2
capital under the limits imposed in the credit risk Accord, and Tier 3
capital subject to the above restrictions. The quoted ratio will thus
represent capital that is available to meet both credit risk and market
risk.6
\6\ For example, if an institution had $120 of Tier 1 capital,
of which $100 was needed to meet its minimum 8.0 percent risk-based
capital standard for credit risk, only $20 would be available for
market risk. That $20, in turn, would ``support'' as much as $50 of
Tier 3 capital ($20 X 250%) for purposes of meeting the capital
requirement for market risk. If the market risk capital requirement
were $50, the institution could count only $30 of Tier 3 capital as
eligible capital in calculating its regulatory capital requirements.
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IV. Partial Models
With supervisory approval, institutions whose internal models do
not cover all elements of their trading activities may use components
of the alternative standardized approach to measure market risks for
risk-based capital purposes. Such combinations, however, should be
limited to situations in which the institution is in the process of
developing and implementing the internal models approach for all of its
trading activities and would be permitted only on a temporary basis. In
addition, the combination of approaches used should be consistent with
the method the institution uses in managing its risks. For example, if
an institution has a comprehensive value-at-risk model for its interest
rate exposures in its trading portfolio but not for its equities
exposures, the agencies would expect the institution to use the
standardized measure for equities and the internal model for interest
rate exposures. These conditions are designed to prevent institutions
from selecting the lower of alternative risk measures and are also
intended to encourage institutions to develop and improve their risk
measurement and management practices.
When combinations of the two risk measurement techniques are used,
the institution should measure a complete risk category using a single
approach and not mix techniques within a given category of risk. For
this purpose, the risk categories are defined as interest rates,
foreign exchange, equity prices, and commodity prices. Moreover, once
an institution adopts a comprehensive value-at-risk model that is
acceptable, it may not revert to the standardized risk measure, except
in unusual circumstances and only with supervisory consent. The
proposal provides some flexibility for de minimis positions, activities
in remote locations, in minor currencies, or in activities that present
negligible risk to the institution.
V. Internal Models Approach
The Agencies believe that an institution's market risk can be most
accurately measured using detailed information available only to the
institution and processed by its own proprietary risk measurement
model(s). Accordingly, the Agencies would encourage all institutions--
especially those with significant trading activities--to pursue this
approach. To be most reliable, however, the modelling process must be
fully integrated into the institution's broader procedures for managing
risk and must be actively supported by senior management. It must also
conform with other specific qualitative and quantitative standards that
the Agencies believe are necessary in order to achieve an adequate
level of rigor and consistency in a capital standard. Under this
proposal, institutions that plan to use internal models in calculating
their capital requirements for market risk
[[Page 38085]]
would need to contact their appropriate supervisor and make
arrangements for having their models validated for regulatory capital
purposes.
Modelling Market Risk
In order to measure exposures when evaluating trading risks, many
institutions calculate the ``value-at-risk'' (VAR), representing the
maximum amount by which the market value of their trading portfolios
could decline during a specific period of time and with a certain
degree of statistical confidence. For example, at the close of business
on day one a bank might calculate its VAR to be $10 million, indicating
that it has only some small chance of losing more than that amount on
its existing holdings, if they were held through the end of day two.
Most institutions use this measure as a management tool for evaluating
their trading positions, limits, and strategies. By measuring the risk
daily, management can quickly revise its positions, limits and
strategies as market conditions change.
A value-at-risk model requires a variety of inputs: (1) Accurate
and timely information about the institution's trading positions, (2)
information about past movements of relevant market prices and rates,
and (3) several key measurement parameters, such as the length of the
historical period for which market changes are observed (observation
period), management's required level of confidence, and the assumed
holding period for which the value of current trading positions may
change. When evaluating their current positions and estimating future
market volatility, institutions typically use a series of ``market risk
factors'' that they have determined affect the value of their positions
and the risks to which they are exposed. These factors, in turn, can be
grouped into four categories, depending on the nature of the underlying
risk: interest rates, exchange rates, and equity and commodity prices,
with related options volatilities included in each risk factor
category.
Having determined which risk factors to use, an institution
estimates the potential future volatility of the factors. Most often
this calculation is based on the past movements of these factors over
some specified time horizon, with some institutions using long
historical time periods and others focusing on more recent market
behavior. However derived, the estimates of potential market movements
are combined with current position data to calculate an estimate of the
potential loss that may arise from those positions for a specified
holding period. Just as institutions use different historical time
periods when computing possible changes in market risk factors, they
also use different confidence levels to estimate potential losses. Some
institutions use a 90 or 95 percent confidence level (one-tail), while
others use a higher level of statistical confidence.
Institutions also use different modelling procedures in calculating
their market risk exposures. The most common models are based upon
variance/covariance methodologies, historical simulations, or Monte
Carlo simulation techniques. In the case of the variance/covariance
approach, the change in value of the portfolio is calculated by
combining the risk factor sensitivities of the individual positions--
derived from valuation models--with a variance/covariance matrix based
on risk factor volatilities and correlations. An institution would
calculate the volatilities and correlations of the risk factors on the
basis of the holding period and the observation period. Value-at-risk
is determined according to the desired level of statistical confidence.
Using historical simulations, an institution would calculate the
hypothetical change in value of the current portfolio in the light of
actual historical movements in risk factors. This calculation is done
for each of the defined holding periods over a given historical
measurement horizon to arrive at a range of simulated profits and
losses, and the confidence level, again, determines the value-at-risk.
Monte Carlo techniques also consider historical movements, but only
to determine the probability of particular price and rate changes.
Using these probabilities, the institution would then construct a large
number of theoretical movements to evaluate the range of its
portfolio's potential market values and identify the maximum loss
consistent with the necessary confidence level.
Proposed Modelling Constraints
The Agencies recognize that institutions have adopted different
assumptions and measurement techniques in their internal market risk
models and that such differences often reflect distinct business
strategies and approaches to risk management. In developing a framework
for the use of internal models for regulatory capital purposes, the
Agencies believe that some constraints should be placed on model
parameters and assumptions. Such restrictions would help to ensure that
prudential capital levels are maintained and that institutions with
similar risk exposures have similar capital requirements.
Since institutions use VAR to guide them in setting trading limits,
rather than for evaluating capital adequacy, they set their model
parameters to address normal conditions. Indeed, the models are
designed to ensure that actual trading results often exceed the
projected levels so that management is better able to evaluate the
model's predictive accuracy and to respond to events that generate
unexpectedly large gains or losses. During a given year, for example, a
model based on a 90 percent confidence level (one tail) could be
expected to underestimate actual trading losses more than 20 times.
Moreover, knowing that a day's trading results could be expected to
exceed the VAR ten percent, five percent, or even only one percent of
the time, says nothing about the magnitude by which the VAR might be
exceeded. The probabilities of VAR models cannot be extended to
estimate the size of a highly unlikely event because most models assume
that market movements are distributed normally. While that assumption
may be adequate for a model's intended purpose, it permits the model to
greatly understate the likelihood of a large loss. For example,
assuming a normal distribution, the likelihood of experiencing a four
standard deviation event is approximately 3 in 100,000--in trading
terms, about once in 130 years. In practice, however, such unusual
market movements are seen in most major markets on average almost every
year.7
\7\ Daily rate or price movements of a half-dozen major
currencies and U.S. Treasury maturities and of several U.S. equity
indices each moved by at least four standard deviations on average
about once a year during the period 1977-1994. The drop in the value
of the S&P 500 index on October 19, 1987 represented a 20 standard
deviation event in terms of daily price movements.
These conditions require that regulators impose some constraints or
other adjustments to the VAR figure that each institution derives in
order to provide the rigor and consistency that a capital requirement
demands. At the same time, the Agencies want to minimize the costs and
dislocations to an internal modelling system that external constraints
could create and have sought to balance these conflicting objectives
through a combination of qualitative and quantitative constraints.
Qualitative Standards
The qualitative standards are designed to ensure that institutions
using internal models have market risk management systems that are
conceptually sound and implemented
[[Page 38086]]
with integrity.8 The internal risk measurement model should be
closely integrated in the daily risk management process and serve as a
basis for reporting of risk exposures to senior officers. Institutions
should have, for example, highly trained personnel who can evaluate the
adequacy of the risk models and who are organizationally independent of
personnel responsible for executing trades. These individuals should
compare actual daily trading gains and losses with VAR figures
generated by the model as part of their on-going evaluations of the
modelling process. At least annually, internal auditors should assess
the institution's overall process for managing and measuring trading
risks.
\8\ With respect to the qualitative standards, the OCC is
planning to provide additional guidance through supplementary
banking issuances.
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Notwithstanding the use of VAR as a basis for a regulatory capital
charge, institutions should also routinely evaluate their exposures to
highly stressful events, selected to identify the circumstances to
which their particular trading portfolios are most vulnerable. Such a
program of stress testing supplements the capital standard and
illustrates management's commitment to evaluating trading risks fully.
The stress testing process, along with other relevant internal
policies, controls, and procedures, should be well documented and
available for examiners to review. Examiners will need this
information, as well as comparisons of VAR measures with actual daily
trading results, to judge the acceptability of the institution's model
on an initial and periodic basis. Under the proposal, if key management
procedures are missing or weak, or if the integrity of a model is
questionable, the appropriate supervisor may either disallow the model
for regulatory capital purposes or require capital above the minimum
specified in the proposal. The latter may be done by increasing the
size of the multiplier that would be applied to an institution's VAR
(discussed below under ``Capital Requirement''). Typically, the
Agencies would expect to see any management or modelling shortcomings
addressed and the risk measure improved, rather than seek to resolve
the matter by applying a larger multiplier to a marginally satisfactory
or questionable modelling or management approach.
Quantitative Standards
Whereas the qualitative standards focus on the integrity of the
modelling process and incorporate standards of sound practice, the
quantitative standards are designed to develop a prudential capital
requirement by addressing the level of rigor in an institution's models
and the consistency of model parameters among institutions. The
Agencies have sought to minimize the quantitative constraints and to
make those that were deemed necessary as compatible as practicable with
existing procedures of institutions. The Agencies recognize, however,
that some of these standards may require an institution to make certain
modifications to its internal model when using it for computing
regulatory capital requirements. The Agencies propose that an
institution that elects to use the internal model approach be subject
to the following standards for its internal model:
(1) Value-at-risk should be computed each business day and should
be based on a 99 percent (one-tailed) confidence level of estimated
maximum loss.
(2) The assumed holding period used for the VAR measure must be 10
business days, although for positions that display linear price
characteristics (not options, which display nonlinear characteristics)
the institution may use results based on one-day periods, increased to
ten days by multiplying by the square root of time.9
\9\ For example, one can estimate the ten day price volatility
of an instrument by multiplying the volatility calculated on one-day
changes by the square root of ten.
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(3) The model must measure all material risks incurred by the
institution, although no specific type of model is prescribed.
(4) The model may utilize historical correlations within broad
categories of risk factors (interest rates, exchange rates, and equity
and commodity prices), but not among these categories. That is, the
consolidated value-at-risk is the sum of the individual VARs measured
for each broad category.
(5) The non-linear price characteristics of options must be
adequately addressed, both by ensuring that the model incorporates
potential non-linear price behavior and by evaluating actual minimum 10
day holding periods, rather than multiplying the results based on one-
day periods by the square root of time. The volatility of the rates and
prices (vega) underlying the options must also be included among the
risk factors.
(6) The historical observation period used to estimate future price
and rate changes must have a minimum length of one year. The Agencies
request specific comment on whether they should also require
institutions to calculate their exposures using a shorter observation
period (e.g. less than 6 months), with the capital requirement based on
the higher result.
(7) Data must be updated no less frequently than once every three
months and more frequently if market conditions warrant.
(8) Each yield curve in a major currency must be modeled using at
least six risk factors, selected to reflect the characteristics of the
interest rate sensitive instruments that the institution trades. The
model must also take account of spread risk.
Several of these constraints warrant a discussion of their
underlying rationale:
Minimum holding period (and issues regarding options). Typically,
longer holding periods lead to larger expected price changes and,
consequently, to larger measures of risk. When estimating risk in
trading activities for management purposes, most institutions assume
only a one-day holding period, since trading decisions are made
constantly, and some instruments are held for only minutes or hours.
This approach may be fully satisfactory for day-to-day management
purposes but seems less appropriate when designing a prudent capital
standard.
In periods of market turmoil, when an institution's capital is most
needed, many financial instruments could become unexpectedly illiquid,
as market participants become less willing to accept market risk. One
method of increasing the rigor of the risk measure and addressing an
unexpectedly large price change that could result from a decline in
market liquidity would be to assume a longer holding period. The
proposed requirement that institutions use a 10-day holding period does
not imply that the Agencies would expect them to plan for that
eventuality. Indeed, some positions, such as those involving spot
foreign exchange contracts, will mature and settle within that time
frame and could not be held for 10 days, in any event. Therefore, in
this context, the 10-day period should be viewed simply as a way of
producing a more stressful market shock by assuming an instantaneous
price movement of a size that one would normally expect to witness only
over the longer period of time.
However, in order to minimize modelling costs and recognize the
linear nature of price movements of many financial instruments, the
Agencies would permit institutions to estimate a 10-day price or rate
movement--for instruments other than options--using the risk factor
changes calculated on the basis of one-day holding periods. This
adjustment could be accomplished using the ``square root of time''
method
[[Page 38087]]
by multiplying the one-day results by 3.16 (the square root of ten
trading days).
The prices of options, however, do not change proportionately with
the price of the underlying instrument, and their potential price
volatility cannot be so easily estimated. Therefore, institutions would
be required to take steps to identify the non-linear behavior of option
prices with respect to changes in underlying rates or prices. In
addition, institutions would not, for example, be allowed to scale the
price volatility of an option that was based on one-day sensitivities
using the square root of ten. However, since the price or rate
volatility of the instrument on which the option is based is considered
to increase proportionately with the square root of time, institutions
would be permitted to use the square root of time technique to expand
the one-day volatility of the option's underlying instrument when
calculating the price volatility of the option itself. Alternatively,
institutions could estimate the changes in the value of options on the
basis of actual movements in underlying factors measured during a full
10-day period.
Institutions should also evaluate the effect of changes in the
volatility of rate or price movements of instruments underlying their
option positions (vega) on option values. This can be done by modelling
volatilities as additional risk factors and including them in the
overall set of risk factors affecting the value of the institution's
trading positions. Institutions with relatively large or complex
options portfolios should also measure volatilities across different
points along the maturity yield curve.
Aggregating Exposures
When evaluating the potential change in a portfolio's market value,
one must consider the likelihood that prices of certain instruments in
the portfolio may move together (or in opposite directions). However,
observed correlations among the prices of some instruments are
themselves volatile and may be especially likely to change during
periods of market stress. Therefore, which assumptions are prudent and
which ones are not cannot be determined in advance. Moreover, one
correlation assumption is not always more conservative than another,
since the outcome depends on whether an institution's position in a
given instrument is long or short. In practice, most models calculate
the correlations within risk factor categories, but differ in their
recognition of historical correlations across broad categories of risk
factors (interest rates, foreign exchange, etc.).
The Agencies do not want to specify correlations or to set
standards for what levels of correlations could be recognized by a
model. Given the importance--but also the uncertainty--of historical
correlations, the Agencies propose to permit institutions to use
correlations within categories of risk factors, but not among
categories, where the interrelationships of market factors may be more
tenuous, especially during periods of market stress.10 Thus, total
VAR would be the simple sum of the calculated VAR for individual
categories. The Agencies recognize that this approach is conservative
and believe that it is appropriate for a capital charge against market
price moves during periods of stress, when historic correlations have
been observed to breakdown. The Agencies also note that it is
consistent with the risk measurement practices of many large trading
banks.
\10\ Use of correlations is permitted provided the supervisor is
satisfied that the calculation of correlations within a category is
performed with integrity.
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Minimum Observation Period
In managing market risk, institutions draw from a broad range of
historical periods to calculate historical volatilities and
correlations for the purpose of estimating future price and rate
movements. Some institutions use periods as short as 30-60 days, while
others use periods extending as long as several years. Although the
choice of historical periods may have little effect on a trading
portfolio's level of expected VAR over an extended period of time, it
can have a significant effect on the measure of exposure at any
specific time. VARs based on short historical periods will be more
volatile and responsive to changing market conditions than measures
based on longer periods, producing relatively large VARs during periods
of high market volatility and low VARs when the markets are calm.
Conversely, VARs based on longer periods will exhibit more stability,
reflecting a wider range of market conditions and the smaller effect of
recent observations.
Since VARs based on short periods may, at times, produce small
estimates of risk and could also produce a wide range of risk measures
among institutions having similar portfolios, the Agencies are
proposing a minimum historical observation period of one year. That
constraint should reduce the dispersion and help ensure that
institutions have adequate capital requirements at all times. While the
Agencies believe such a one-year constraint may be sufficient, they are
also requesting comment on whether institutions should be required to
calculate their exposures using two observation periods--one as
constrained above and the other representing a shorter period, such as
six months or less. Under this dual observation approach, the capital
requirement would be based on the period that indicated the greater
risk.
Minimum Number of Risk Factors
The risk factors contained in an institution's market risk
measurement system should be sufficiently comprehensive to capture all
of the material risks inherent in the portfolio of its on- and off-
balance sheet trading positions, including interest and exchange rates,
equity and commodity prices, and the volatilities related to option
positions. Although institutions will have substantial flexibility in
specifying the risk factors that are most relevant to their portfolios,
the Agencies expect the number and composition of factors to be
commensurate with the nature and scope of each institution's risks.
In order to adequately measure exposures to interest rates and to
bring about greater conformity of results among institutions, the
Agencies are proposing a minimum of six maturity bands (each
representing a separate risk factor) to be used for material positions
in the major currencies and markets. All institutions would be expected
to measure spread risk (e.g., the difference between rates on corporate
and U.S. government instruments) adequately, with the required level of
sophistication being a function of the nature and scope of the
institution's activities and exposures.
Capital Requirement
Experience has shown that financial markets can have brief periods
of high volatility preceded or followed by extended periods of calm.
Under some modelling procedures, the large number of small daily market
changes can substantially offset the infrequent periods of high
volatility. Even when constrained and calculated as proposed, there are
several reasons why an institution's need for capital might sometimes
exceed this figure:
(1) The past is not always a good guide to the future;
(2) The assumptions about statistical ``normality'' built into some
models may not be justified because of the relatively high frequency of
large market movements;
[[Page 38088]]
(3) The correlations assumed in the model may prove to be
incorrect;
(4) Market liquidity may become inadequate to close out positions;
and
(5) The institution may face multiple stressful events over short
periods of time.
Consequently, the Agencies believe that in order for an
institution's VAR figure to serve as an adequate basis for a capital
requirement, it should be multiplied by an appropriate prudential
factor. The Agencies are proposing a minimum multiple of three, which
could be increased if the results of ``back-testing'' are not
sufficiently satisfactory.11
\11\ Back-testing refers to the process of comparing calculated
daily VARs with actual daily trading results to determine how
effectively the risk measure identified the boundaries of gains or
losses consistent with the predetermined level of statistical
confidence.
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The Agencies also recognize that institutions may change their
trading positions rapidly and may substantially increase their
exposures for brief periods in order to respond to perceived
opportunities or market conditions. At such times, an institution's
exposure to market risk may be larger than its average VAR times three.
In order to address such circumstances, the Agencies are proposing that
institutions maintain capital on a daily basis to support the larger of
either (1) the average VAR figure for the last 60 business days,
calculated under the proposed criteria and increased by the assigned
multiple, or (2) the previous day's VAR, similarly calculated but
without the multiple. By considering not only an average VAR but also a
single day's measure, the Agencies expect institutions to hold capital
sufficient to cover peak levels of market volatility and to manage
their activities accordingly.
Many VAR models focus principally on measuring general market risks
and incorporate only partial elements of specific risk. Therefore,
institutions would remain subject to separate capital requirements to
cover specific risk on equities and traded debt, to the extent it is
not addressed by their VAR models. This separate charge would be added
after the VAR figure is increased by the multiplier and would, in no
case, be less than one-half the specific risk charge calculated using
the standardized approach. The Agencies specifically request comments
on which features to consider when reviewing models in order to
evaluate their coverage of specific risk.
VI. Standardized Risk Measure
The standardized risk measure calculates separate capital
requirements for specific and general market risks and uses different
techniques to measure an institution's risk exposure, depending upon
its source: debt instruments, equities, foreign currencies, and
commodities, including their respective options.12
\12\ Several techniques are offered for measuring the price risk
in options (see ``Options'', discussed below or in the proposed
regulatory language for each agency). Under one approach, called the
``delta-plus'' approach, an institution would include the delta-
equivalent value of the underlying instrument when evaluating the
market risk of each category of instruments (debt, equity, etc.).
Under the two other approaches, the underlying instrument of an
option may be ``carved-out'', not subject to the prescribed risk
measure for the underlying, and evaluated together with its option
according to the procedures described for options.
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Debt instruments held in trading portfolios
The market risk capital requirement for debt instruments in a
trading account consists of separate charges for general market and
specific risks.
a. General market risk. The general market risk capital requirement
for debt instruments (including off-balance-sheet derivatives) that are
part of trading activities is designed to capture the potential loss
that may arise from movements in market interest rates. An institution
may determine this component of its capital requirement either by using
standardized risk weights that approximate the price sensitivity of
various instruments or by calculating, itself, the precise duration of
each instrument, weighted by a specified change in interest rates.
Both methods use a maturity-ladder approach that employs a series
of time bands and zones, designed to take into account differences in
price sensitivities and interest rate volatilities across various
maturities. Under either method, the institution's capital charge for
general market risk would be the sum of a base charge that results from
fully netting various risk-weighted positions (i.e., longs versus
shorts) and a series of additional charges (add-ons) that effectively
disallow part of the previous full netting in order to address basis
and yield curve risk. The capital charges would be separately computed
for each currency in which an institution has significant positions. No
netting of positions or charges would be allowed across different
currencies.
When using the first approach, referred to as the ``maturity''
method, an institution would first distribute its on- and off-balance-
sheet positions in each currency among a range of time-bands based on
the maturity or nearest interest rate reset date of the instrument.
Long positions would be treated as positive amounts and short positions
would be treated as negative amounts. The institution would then
calculate its net long or short position for each time-band and would
multiply that net position by the risk weight provided by the
supervisor for that time-band. The resulting risk-weighted position
represents the amount by which the market value of that debt position
is expected to change for a specified movement in interest rates. The
risk weights and associated interest rate changes are shown in each
Agency's proposed regulatory language (OCC--Table 2, Board--Table I,
and FDIC--Table 1).13 Adding the sum of all risk-weighted
positions (long or short) across all time-bands results in a final net
risk-weighted position. This amount would be the base capital charge
for general market risk.14
\13\ In the case of securities backed by fixed rate mortgages,
an institution would slot the instruments into time bands on the
basis of their current expected weighted average lives (reflecting
the effect of expected prepayments at current market interest
rates), rather than by their contractual maturities.
\14\ Since the price sensitivity of zero coupon and low coupon
instruments can be materially greater than that of instruments with
higher coupons, institutions would be required to assign higher risk
weights to low coupon instruments as shown in the proposed Tables.
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The base charge is calculated differently under the second, or
alternative ``duration'' method. In this case, an institution would
calculate the estimated price movement for a specific instrument by
multiplying the instrument's modified duration by a specified interest
rate shock that is based on the instrument's duration as shown in the
proposed regulatory language.15 That product, representing the
amount of expected price change of the instrument, is then distributed
into the array of time-bands on the basis of the instrument's duration
(see proposed Table 4--OCC, Table III--Board, Table 3--FDIC). For
example, an instrument with a maturity of 4 years and 3 months might
have a modified duration of 3.5 years. Based on its duration, it would
be ``shocked'' by 75 basis points, resulting in an expected price
change of 2.625 percent (3.5 x 0.75 percent). That estimated 2.625
percent change, multiplied by the current value of the instrument,
would be placed into the 3.3 to 4.0 year time-band for
[[Page 38089]]
determining the charge for general market risk.
\15\ The duration of an instrument indicates its approximate
percentage change in price for a small parallel shift in the yield
curve assuming that its cash flow does not change when the yield
curve shifts.
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As in the maturity method, the base capital charge for general
market risk is the sum of the estimated price changes across all time
bands. If that sum is negative, the base charge would be its absolute
value. Different time-bands are used for the two methods because an
instrument's duration can be substantially different from its maturity.
In addition to the base capital charge for general market risk, as
reflected by the institution's net risk-weighted position, an
institution would be subject to a series of capital ``add-ons'' that
are designed to take into account imperfect and uncertain correlations
among instrument types and maturities. These add-ons recognize that
long and short positions might not, in practice, offset each other by
the full amount that their risk-weightings would suggest, and
therefore, some portion of the hedged or offsetting position should be
disallowed.
The first disallowance (referred to as the vertical disallowance)
is intended to address the basis risk that exists between instruments
with the same or similar maturities and also the possibly different
price movements that may be experienced by different instruments within
the same time-band due to the range of maturities (or repricing
periods) that may exist within a time-band. To capture this risk, a
vertical disallowance is applied to the smaller of the offsetting (long
or short) positions within a time-band.16 This disallowance is 10
percent under the maturity method, and 5 percent under the duration
method. For example, under the maturity method, if the sum of weighted
long positions within a time-band equals $100 million and the sum of
weighted short positions equals $90 million, the vertical disallowance
for the time-band would be 10 percent of $90 million, or $9 million.
This amount would be added to the institution's base capital charge.
The use of two different vertical disallowances recognizes that because
the duration method takes into account an instrument's specific
characteristics (maturity and coupon), there is less opportunity for
measurement error.17
\16\ If the offsetting amounts (long and short) are equal, the
disallowance can be applied to either figure.
\17\ In the case of cash positions and transactions conducted on
an exchange (e.g. futures) an institution has the opportunity to
adjust its market risk either by acquiring a new position or selling
an existing one. However, that is not typically the case with
interest rate swaps, for which an institution almost always adjusts
its position by entering into a new or offsetting swap, rather than
by selling or unwinding one that it already holds. This procedure,
required partly because of the lack of standardization in the terms
and credit risk characteristics of swaps, can produce large swap
portfolios and potentially large disallowances under the
standardized approach.
Consequently, the Agencies' proposal would allow institutions
with large swap books to use alternative procedures for calculating
the amounts that would be distributed into the maturity or duration
time bands. One approach would be to convert the payments required
by a swap into their present values using zero coupon yields and
then to place those amounts into their appropriate time bands using
the procedures that apply to zero (or low) coupon bonds. The net
amounts for each time band would then be weighted and subject to the
disallowances of the general market risk framework as if they were
bonds. The Agencies would also consider other procedures.
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The second disallowance (or horizontal disallowance) addresses the
risk that interest rates along the yield curve are not perfectly
correlated and that risk-weighted positions that might have been
expected to offset will not fully offset, in practice. The horizontal
disallowance applies to the smaller of the offsetting positions across
different time-bands. The amount of this disallowance varies in size by
zone (that is, a grouping of contiguous time bands), with greater
netting allowed for positions in different time bands but within the
same zone than is allowed for positions that are in different zones
(Table 3--OCC, Table II--Board, Table 2--FDIC in the proposed
regulatory language). The horizontal disallowances range from 30
percent to 100 percent of the smaller figure in a pair of offsetting
transactions.18
18 Since the disallowance is applied to only one side of an
offsetting transaction, a 100 percent disallowance effectively
treats the hedge as being 50 percent effective.
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In calculating these disallowances, an institution would first
determine its offsetting positions within a zone and the associated
``within zone'' disallowance amounts. Once the institution has netted
its positions within a zone, it would determine the amount of
offsetting and associated disallowances across zones. An institution's
general market risk requirement for debt instruments within a given
currency would be the sum of (1) the value of its net risk-weighted
position (base charge) and (2) all of its vertical and horizontal
disallowances.
b. Specific risk. Under the proposal, generally every traded
security, whether long or short, would be assessed a capital charge for
specific market risk. In the debt portfolio this charge is based on the
identity of the obligor and, in the case of corporate securities, on
the credit rating and maturity of the instrument. Consistent with the
original Accord, debt instruments of national governments of OECD
countries are assigned zero specific risk. Other securities are
assigned risk weights ranging from 0.25 percent to 1.6 percent if they
are issued by qualifying borrowers. Securities of nonqualifying issuers
are charged a specific risk of 8.0 percent. To be considered as
qualifying, the security must be rated as investment grade by at least
two nationally recognized credit rating firms or, if the issuer has
securities listed on a recognized stock exchange, it must be deemed to
be of comparable investment quality by the reporting institution.
This latter condition is provided to accommodate the fact that in
some countries credit ratings and the coverage of credit rating firms
are not as extensive as in the United States. Consequently, the
securities of many large and well-established foreign companies may not
be rated. In such cases, a company's listing on an organized exchange
may be an acceptable substitute for credit ratings if such listings are
limited to financially strong and well-established firms. In these
cases, and in the absence of independent credit ratings, the securities
of a listed company may qualify for a lower capital charge if the
trading institution and its appropriate supervisor believe the
securities are equivalent to investment grade. However, the Agencies
are proposing that, given the presence and wide coverage in the United
States of credit rating firms, institutions would not be allowed to
qualify the securities of a U.S. firm on the basis of a listing on an
organized exchange.
During the examination process, the Agencies would also consider
the extent to which an institution trades non-investment grade
instruments (sometimes called high yield debt) that do not qualify for
risk weights less than 8.0 percent because of the lack of investment
grade ratings. If these holdings are not well diversified or if they
otherwise represent material exposures to the institution, the Agencies
may prevent an institution from netting the exposures arising from
these instruments with otherwise offsetting exposures resulting from
positions in qualifying instruments.
Equities Held in Trading Portfolios
The standardized measure of market risk in traded equities also
consists of separate charges for specific and general market risk.
These charges would apply not only to direct holdings of equity
securities, but also to equity derivatives and off-balance-sheet
positions whose market values are directly affected by equity prices.
a. General market risk. An institution's general market risk
capital charge would be 8.0 percent of its net
[[Page 38090]]
equity position--the difference between the sum of its long and the sum
of its short positions. The net long or short position against which a
general market risk charge would be assessed must be calculated on a
market-by-market basis, i.e., a separate calculation must be computed
for each national market in which the institution holds equities.
Institutions would not, for example, be able to net a long position in
U.S. companies traded on the New York Stock Exchange against a short
position in Japanese companies traded on the Tokyo Stock Exchange.
b. Specific risk. The capital charge for specific risk is based on
the reporting institution's gross equity positions (i.e., the absolute
sum of all long equity positions and of all short equity positions,
with netting allowed only when the institution has long and short
positions in exactly the same instrument). This charge would also be
8.0 percent, unless the portfolio is both liquid and well-diversified
or the position relates to an index comprising a diversified portfolio
of equities.
Examiners will verify that any portfolio designated as ``liquid and
well-diversified'' by an institution is characterized by a limited
sensitivity to price changes of any single equity issue or closely
related group of equity issues held in the portfolio. In particular,
the volatility of the value of the portfolio should not be dominated by
the volatility of any individual equity issue or by equity issues from
any single industry or economic sector. In general, such portfolios
should be characterized by a large number of individual equity
positions, with no single position representing a large portion of the
portfolio's total market value. In addition, it would generally be the
case that a sizeable proportion of the portfolio would be comprised of
issues traded on organized exchanges.
For such liquid and well-diversified portfolios, the specific risk
charge would be 4.0 percent. A specific risk charge of 2.0 percent
would apply to the net long or short position in a broad-based,
diversified equity index and is viewed as necessary to provide for the
risk that the performance of the index will differ from those of other
market measures and also for potential difficulties that could arise in
executing transactions at expected prices.
Foreign Exchange
This capital requirement covers the risk of holding or taking
positions in foreign currencies, including gold, and is based on an
institution's net positions in individual currencies, whether or not
those positions are booked in the trading account. Net positions, in
turn, include an institution's net spot and forward positions; any
guarantees that are certain to be called and likely to be
irrecoverable; net future income and expenses that are not yet accrued,
but that are already fully hedged; and any other items representing a
profit or loss in foreign currencies. Forward and future positions
would be converted into the reporting currency at spot market rates.
Institutions may, subject to supervisory approval, exclude from
this calculation any structural positions in foreign currencies. For
this purpose, such structural positions are limited to transactions
designed to hedge an institution's capital ratios against the effect of
adverse exchange rate movements on (1) subordinated debt, equity, or
minority interests in consolidated subsidiaries and dotation capital
assigned to foreign branches that are denominated in foreign
currencies, and (2) any positions related to unconsolidated
subsidiaries and to other items that are deducted from an institution's
capital when calculating its capital base. In any event, such
structural foreign currency positions should reflect long-term policies
of the institution and not relate to trading positions.
The standardized approach assumes the same volatility for all
currencies and requires an institution to hold capital equal to 8.0
percent of the sum of (a) its net position in gold and (b) the sum of
the net short positions or the sum of the net long positions in each
foreign currency, whichever is greater. With supervisory approval, an
institution may be exempt from this capital requirement if the sum of
its gross long and short positions does not exceed 100 percent of its
eligible capital and its overall net foreign exchange position does not
exceed 2.0 percent of this capital, as defined above in Section II.
Commodities
The capital requirement for commodities risk applies to holdings or
positions taken in commodities, including precious metals, but
excluding gold (which is treated as a foreign currency because of its
market liquidity). As with foreign currencies, the coverage extends to
all commodities positions of the institution, not only to those booked
in trading accounts. For this purpose, a commodity is defined as a
physical product which is or can be traded on a secondary market, e.g.,
agricultural products, minerals, and precious metals. The standardized
approach for measuring general market risk in commodities provides only
a rough indication of the risk exposure and is appropriate only for
institutions with relatively small amounts of commodities activity.
Within the standardized approach, two alternative measures are
available, referred to as the ``simple'' and the ``maturity'' methods.
Both measures address directional risk, which is the risk that a
commodity's spot price will increase or decrease, as well as basis
risk, interest rate risk, and forward gap risk, which are also
important risks, especially for institutions that engage in forward or
derivative contracts. These institutions can face significant losses in
their positions as a result of adverse changes in the relationship
between prices of similar commodities, increases in the cost of
financing forward positions, or changes in forward prices produced by
any number of economic or market conditions.
Both the simple and maturity approaches require an institution to
calculate its net position in each commodity on the basis of spot
rates. Long and short positions in the same commodity may be netted,
but positions in different commodities would generally not be allowed
to offset, except where different sub-categories of commodities are
deliverable against each other.
Under the simple approach, an institution's capital charge for
directional risk would equal 15 percent of its net position, long or
short, in each commodity. A supplemental charge of 3.0 percent of the
gross position in each commodity would be added to cover basis,
interest rate and forward gap risk.
The capital charge using the maturity method reflects not only the
net and gross positions in each commodity, but also the maturity of
each commodity contract. For each commodity, positions would first be
distributed among seven time bands. Physical holdings of commodities
would be allocated to the first band. The matched long position plus
the matched short position within each time-band would then be
multiplied by a ``spread rate,'' (proposed at a uniform 1.5 percent
rate) to capture forward gap and interest rate risk. Net positions from
one time-band must be used to offset opposite positions in another
time-band and would incur a ``surcharge'' equal to 0.6 percent of the
net position for every time-band it is carried forward in recognition
that such offsetting may not be perfect. This process ultimately
produces an overall net position for each commodity. A 15 percent
capital charge would be applied to that net position. The total capital
charge for any given commodity would be the sum of (a) the initial 1.5
percent
[[Page 38091]]
charge for the matched positions in each time band, (b) any surcharge,
and (c) the charge on the overall net position.
Options
The Agencies recognize the diversity of activities in options and
the difficulties in measuring an option's price risk. Accordingly, the
proposal provides three alternative risk measures for institutions that
do not adopt the internal models approach. These alternatives are: (a)
a ``simplified'' method, which is available to institutions that only
purchase traded options, (b) a ``scenario analysis'' method that
evaluates option values under a range of market scenarios, and (c) a
``delta-plus'' method that provides specific measures of individual
components of an option's risk. The method used should be commensurate
with and appropriate for the nature and scope of the institution's
options activities. Institutions that have extensive dealings in
options must have appropriately accurate measures of risk.
Several variables determine an option's price:
(1) The current price of the underlying asset;
(2) The strike price of the option, which is the price of the
underlying security at which the option has value;
(3) The volatility of the price of the underlying security;
(4) The time remaining before the option expires; and
(5) The prevailing ``risk free'' interest rate.
The effect of these variables on an option's value are represented
by a series of Greek letters: delta (the price sensitivity of an option
relative to price changes in the underlying security, rate, or index--
the ``underlying''), gamma (the change in delta for a given change in
the underlying), vega (the effect of changes in the volatility of the
underlying), theta (the effect given the passage of time), and rho (how
the option price changes for a given change in risk free interest
rates). Delta is a frequently used indicator of an option's risk, but
others--particularly gamma--should be specifically addressed by
institutions that trade options to any material extent. Such
institutions should not rely merely on linear approximations of price
movements, but should undertake to capture the non-linear relation
between changes in the option's price and changes in the underlying
rate or price.
Simplified Approach
The simplified approach for options may only be used by
institutions whose options activities are confined to a small volume of
purchased options. This approach permits an institution either to
``carve out'' both the option and a corresponding underlying position
from other elements of the standardized approach or to view the option
as ``naked''--that is, without a matching cash position. In order to
avoid potentially penalizing an institution for purchasing an option,
institutions could avoid linking (and subsequently carving-out) a
purchased option and a corresponding cash position if doing so would
create an exposure within the underlying position and produce a capital
requirement that exceeded the value of the purchased option.
Consequently, there are two possibilities:
(1) If a carve-out is made, the capital charge is equal to the
specific and general market risk charge on the underlying position,
less the amount the option is in the money, bounded at zero.
(2) If the purchased option is viewed by itself, the charge for the
option is the smaller of (a) its market value or (b) the sum of the
specific and general market risk charge that would apply to its
underlying instrument. Any existing related (but not linked) cash
position would continue to receive the full specific and general market
risk charge produced by other elements of the standardized approach.
In both cases, the method is relatively conservative, creating an
incentive for institutions to use a more accurate measure of risk.
Institutions that want a more accurate measure of option risk or whose
trading activities include the writing (selling) of options must use
either the scenario or the delta-plus methods offered under the
standardized approach, or the previously described internal models
approach.
Scenario Analysis
Using scenario analysis, institutions would evaluate the market
values of their options and related hedging positions by changing the
underlying rate or price over a specified range and by also assuming
different levels of volatility for that rate or price. Each combination
of assumed volatilities and rate or price changes would represent a
scenario.
The range of rate or price movements would be based on the nature
of the option. For options based on debt instruments or interest rates,
the range would be consistent with the maximum rate movement indicated
in the proposal dealing with traded debt: 100 basis points for
underlying instruments in zone 1, 90 basis points for those in zone 2,
and 75 basis points for those in zone 3. Similarly, the ranges used for
other options would be consistent with the assumed price or rate change
applied to their underlying cash positions: 8 percent for foreign
exchange, 12 percent for individual equities, 8 percent for equity
indices, and 15 percent for commodities. In all cases, the range would
cover both an increase and decrease from current values of the
underlying security (or rate) by these percentages and would be divided
into at least 10 equally spaced intervals centered by the current rate
or price.
Given the near-linear relationship between volatility and option
values for many options, the Agencies believe it would be sufficient in
most cases to evaluate the option portfolio assuming a 25 percent
increase and decrease in the level of volatility from that implied by
current market prices. If warranted, however, the Agencies may require
a different change in volatility and the consideration of intermediate
points.
An institution would determine the market value of each option and
any related hedging position or group of options and related hedging
positions for each scenario.19 Such options and positions based on
debt instruments in the same zone, or on the same equity, equity index,
exchange rate, or commodity may be grouped together and evaluated on a
portfolio basis when evaluating the effect of a given scenario. The
market risk capital charge for a portfolio would be the largest loss
estimated for that portfolio from among the evaluated scenarios. The
charge for all option portfolios would be the sum of the charges on the
individual portfolios. The Agencies recognize that this approach is
conservative, since it assumes that the largest loss will occur within
each segment of the option portfolio simultaneously.
\19\ For this purpose, a single option and any related hedging
position and a group of options and any related hedging positions
are all referred to as an ``options portfolio.''
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The delta-plus method
Institutions that write options would be allowed to include delta-
weighted options positions within the standardized methodology. Such
options should be reported as a position equal to the market value of
the underlying instrument multiplied by the delta. However, since an
option's delta does not sufficiently address other risks associated
with the option's market value, institutions would also be required to
measure the option's gamma and vega in order to calculate the total
capital charge for the option. These sensitivities would be calculated
by an approved exchange model or by the
[[Page 38092]]
institution's proprietary options pricing model, subject to oversight
by the appropriate supervisor.
Delta-weighted positions of options based on debt securities or
interest rates would be slotted into the debt securities time-bands, as
set out above for debt instruments, under the following procedure. A
two-legged approach would be used as for other derivatives, requiring
one entry at the time the underlying contract takes effect and a second
at the time the underlying contract matures. For instance, a bought
call option on a June three-month interest-rate future will in April be
considered, on the basis of its ``delta'' equivalent value, to be a
long position with a maturity of five months and a short position with
a maturity of two months. The written option would be similarly slotted
as a long position with a maturity of two months and a short position
with a maturity of five months. Floating rate instruments with caps or
floors would be treated as a combination of floating rate securities
and a series of European-style options. For example, the holder of a
three-year floating rate bond indexed to six month LIBOR with a cap of
15 percent would treat the instrument as: (1) A debt security that
reprices in six months; and (2) a series of five written call options
on a floating rate asset (FRA) with a basis of 15 percent, each with a
negative sign at the time the underlying FRA takes effect and a
positive sign at the time the underlying FRA matures.
In addition to the above capital charges arising from delta risk,
the proposal requires capital for gamma and vega risks. Institutions
using this method would be required to calculate the gamma and vega for
each option position. The results would be slotted into separate
maturity ladders by currency. For options such as caps and floors whose
underlying instrument is an interest rate, the delta and gamma would be
expressed in terms of a hypothetical underlying security. Subsequently:
(1) For gamma risk, for each time-band, net gammas which are
negative would be multiplied by the risk weights set out in the
proposed regulatory language (OCC--Table 5, Board--Table IV, FDIC--
Table 4) and by the square of the market value of the underlyings (net
gammas which are positive would be disregarded);
(2) For volatility risk, institutions would be required to
calculate the capital charges for vegas in each time-band assuming a
proportional shift in volatility of 25 percent;
(3) The capital charge would be the absolute value of the sum of
the individual capital charges for net negative gammas plus the
absolute value of the sum of the individual capital charges for vega
risk for each time-band.
The capital charge for options on equities would also be based on
the delta weighted positions of the options by incorporating those
weighted positions into the market risk measure for equities described
above. For purposes of this calculation individual equity issues and
indices are to be treated as separate underlyings. In addition to the
capital charge for delta risk, institutions would apply a further
capital charge for gamma and vega risk:
(1) For gamma risk, the net negative gammas for each underlying
instrument would be multiplied by 0.72 percent when that instrument is
an individual equity and by 0.32 percent when it is an index.20
That product would then be multiplied by the square of the market value
of the underlying;
20 Using the Taylor expansion, the risk weights are
calculated as follows: Risk weight for gamma =0.5 x (assumed price
change of underlying)\2\ For an individual equity, 0.5 x 0.12\2\=
0.72%. In the case of an index as the underlying, the assumed price
change of the underlying equals 8.0 percent.
(2) For volatility risk, institutions would be required to
calculate the capital charges for vegas for each underlying instrument
assuming a proportional shift in volatility of plus or minus 25
percent;
(3) The capital charge would be the absolute value of the sum of
the individual capital charges for net negative gammas plus the
absolute value of the sum of the individual capital charges for vega
risk.
The capital charge for options on foreign exchange and gold
positions would be based on the shorthand method set out earlier. For
delta risk, the net delta (or delta-based) equivalent of the total book
of foreign currency and gold options would be incorporated into the
measurement of the exposure in a single currency position. The gamma
and vega risks would be measured as follows:
(1) For gamma risk, for each underlying exchange rate net gammas
which are negative would be multiplied by 0.32 percent and by the
square of the market value of the position; 21
\21\ The assumed price change is 8.0 percent.
---------------------------------------------------------------------------
(2) For volatility risk, institutions would be required to
calculate the capital charges for vegas for each currency pair and gold
assuming a proportional shift in volatility of plus or minus 25
percent;
(3) The capital charge would be the absolute value of the sum of
the individual capital charges for net negative gammas plus the
absolute value of the sum of the individual capital charges for vega
risk.
The capital charge for options on commodities would be based on the
same approach set out above for commodities. The delta weighted
positions would be incorporated into one of the two measures described
in that section. In addition to the capital charge for delta risk,
institutions would incur a further capital charge for gamma and vega
risk:
(1) For gamma risk, net negative gammas for each underlying would
be multiplied by 1.125 percent and by the square of the market value of
the commodity; 22
\22\ The assumed price change is 15 percent.
---------------------------------------------------------------------------
(2) For volatility risk, institutions would be required to
calculate the capital charges for vegas for each commodity as defined
above in the section dealing with commodities, assuming a proportional
shift in volatility of plus or minus 25 percent;
(3) The capital charge would be the absolute value of the sum of
the individual capital charges for net negative gammas plus the
absolute value of the sum of the individual capital charges for vega
risk.
A worked example of the delta-plus method for commodities is set
out in Attachment IV of the Board's and the FDIC's proposed regulatory
language. In the case of options based on debt securities or interest
rates and with the approval of the appropriate supervisor, institutions
that are significant traders in options could be allowed to net
positive and negative gammas and vegas across time-bands to a limited
extent. However, such netting would be permitted only if it is based on
prudent and conservative assumptions and the institution materially
satisfies the qualitative standards outlined under the internal models
approach.
In addition, instead of applying a uniform relative change in
volatility to measure vega risk, institutions may base the calculation
on a volatility ladder in which the implied change in volatility varies
with the maturity of the option. When using such a volatility ladder
the assumed proportional shift in volatility should be at least 25
percent at the short end of the maturity spectrum. The proportional
shift in volatility for longer maturities should be at least as
stringent in statistical terms as the 25 percent shift at the short
end. Use of this alternative would be subject to validation by the
supervisor, and to the qualitative standards listed in the internal
models section that are relevant to this aspect of the institution's
[[Page 38093]]
business. In the long term, institutions using this alternative would
be expected to move to fully articulated value-at-risk models, subject
to the full qualitative and quantitative standards for models.
Besides the options risks mentioned above, the Agencies recognize
that there are other risks associated with options, e.g., rho and
theta. While they are not proposing a measurement system for those
risks at present, institutions undertaking significant options business
would still be expected to monitor such risks closely.
VII. Questions on Which the Agencies Specifically Request Comment
General Topics
1. The Agencies propose to apply these standards to a relatively
small number of institutions that have material trading activities. As
the criteria are proposed, about 25 ``large'' institutions and a few
other smaller institutions with relatively more significant trading
activities would meet the requirements and be subject to the new
capital standards. Is the exemption of smaller institutions
appropriate, given their risk profile and the implied regulatory
burden, or does it provide them with an undue competitive advantage? On
the other hand, would the amendment affect too many institutions, given
the nature of their trading activities and market risk profiles?
2. Consistent with their procedures for existing capital standards,
the Agencies would apply the proposed standard to any national bank,
state member bank and bank holding company that meets the criteria on a
consolidated basis. What are the burden implications of applying the
standard to both banks and bank holding companies?
3. The Board currently evaluates the capital adequacy of bank
holding companies that have Section 20 subsidiaries on a fully
consolidated basis and also without the assets and capital of the
Section 20 subsidiaries. Should it continue this practice regarding
market risk, or should it focus on only the consolidated holding
company?
4. Should the Agencies permit institutions the choice of the
standardized or internal model approaches, or should it permit only the
internal model approach on the basis that the institution's trading
activities are sufficient to warrant the more accurate measure of risk?
5. The Agencies are interested in comments on whether the internal
model quantitative standards, together with the scaling factor, could
result in capital requirements that on average are significantly
different (for example, higher) than those required under the
standardized approach.
6. The Agencies propose to allow institutions to use the
standardized method for measuring some categories of risk (e.g., debt,
equities, etc.), and internal models for other categories. Should
institutions be given this flexibility, or should they be required to
use one approach throughout?
7. The Agencies propose a reduced capital charge for specific risk
in equities if an institution's equities portfolio is ``liquid and
well-diversified,'' a concept that is defined in qualitative terms in
the proposal. Should this concept be described more specifically and,
if so, what criteria should be applied?
Questions on the Standardized Method
1. Under the proposal, institutions would be allowed to net
offsetting positions in different commodities only if the commodities
were deliverable against each other. To what extent, if any, should the
Agencies allow netting on the basis of the historical correlations of
price movements of different commodities within the standardized
approach? If netting is allowed on the basis of past correlations, what
specific criteria should be required?
2. One of the alternative ways of measuring the market risk of
options in the standardized approach is to calculate separate charges
for an option's delta, gamma, and vega risk (see the delta-plus
method). This approach permits an institution to measure the risk of
its options positions while measuring the risk of its other positions
and, thereby, to evaluate them more fully on a portfolio basis. It also
permits an institution to avoid incurring the worst-case charge for the
option under the scenario method. The delta-plus calculations, however,
are complex and potentially inaccurate since they do not permit full
use of a revaluation model. Is the method sufficiently useful to
warrant its complexity, and does it provide a sufficiently conservative
measure of risk for institutions that write options but do not have
options pricing models integrated into their risk measurement systems?
Questions on the Internal Model Method
1. The Agencies are considering whether to require institutions to
calculate their VARs using two observation periods (one long, one
short) and basing the capital requirement on the larger figure. What
are the costs and burden implications of requiring such a dual
calculation?
2. All institutions affected by the proposal would be required to
have capital covering both general market and specific risks.
Institutions using the internal model approach would be required to
apply the specific risk charge (or a portion thereof) calculated using
the standardized approach, if their models do not adequately capture
specific risk. What modelling techniques should the Agencies consider
when evaluating an institution's model and determining the extent to
which the model includes specific risk in its VAR measure?
3. As part of an on-going process of evaluating the accuracy of an
institution's internal model, actual daily trading profits and losses
would be compared with the measured VAR (so-called ``back-testing'').
The Agencies would expect this back-testing normally to rely upon the
VARs actually used by the institution for nonregulatory purposes, which
in most cases would reflect a confidence level less than the 99 percent
level on which the capital requirement would be based. Would this
approach be less burdensome to the institution than requiring a
separate calculation for the 99 percent confidence level, and would it
provide a more statistically reliable basis for evaluating the results?
Please comment on these procedures and any other considerations the
Federal Reserve should take into account in reviewing back-tests.
4. The Agencies recognize that daily VAR is used by institutions
for setting daily trading limits, rather than for evaluating capital
adequacy. The regulatory use of VAR as a basis for a capital
requirement is predicated on the specification of several constraints
on modelling parameters, as well as the use of a multiplication factor.
Do these constraints provide sufficient capital for the underlying
activities?
5. To qualify for the use of the internal models approach, an
institution must have a rigorous stress testing program which would be
subject to supervisory review. What stress tests for market risk should
institutions be expected to perform as part of their internal
management process?
VIII. Regulatory Flexibility Act Analysis
OCC Regulatory Flexibility Act Analysis
Pursuant to section 605(b) of the Regulatory Flexibility Act, the
Comptroller of the Currency certifies that this proposal would not have
a significant impact on a substantial
[[Page 38094]]
number of small business entities in accord with the spirit and
purposes of the Regulatory Flexibility Act (5 U.S.C. 601 et seq.).
Accordingly, a regulatory flexibility analysis is not required. The
impact of this proposed rule on banks regardless of size is expected to
be minimal. Further, this proposed rule generally would apply to larger
banks with significant trading account activities and would cover only
trading activities and foreign exchange and commodity positions
throughout the bank.
Board Regulatory Flexibility Act Analysis
Pursuant to section 605(b) of the Regulatory Flexibility Act, the
Board does not believe this proposal would have a significant impact on
a substantial number of small business entities in accord with the
spirit and purposes of the Regulatory Flexibility Act (5 U.S.C. 601 et
seq.). Accordingly, a regulatory flexibility analysis is not required.
In addition, because the risk-based capital standards generally do not
apply to bank holding companies with consolidated assets of less than
$150 million, this proposal would not affect such companies.
FDIC Regulatory Flexibility Act Analysis
Pursuant to section 605(b) of the Regulatory Flexibility Act (Pub.
L. 96-354, 5 U.S.C. 601 et seq.), it is certified that the proposed
rule would not have a significant impact on a substantial number of
small entities.
IX. Paperwork Reduction Act and Regulatory Burden
OCC Regulatory Burden
Section 302 of the Riegle Community Development and Regulatory
Improvement Act of 1994, Pub. L. 103-325, 108 Stat. 2160 (September 23,
1994), provides that the federal banking agencies must consider the
administrative burdens and benefits of any new regulations that impose
additional requirements on insured depository institutions. As
discussed, this proposed rule would affect only a small number of banks
and generally would cover only trading account activities and foreign
exchange and commodity positions throughout the bank. Additionally, any
burden imposed would be lessened to the extent that a bank may use its
own qualifying internal market risk model. The OCC believes that any
additional burden placed on a bank is outweighed by the advantages of
greater accuracy in risk management and capital allocation, which
contribute to increased safety and soundness in the banking system.
Board Paperwork Reduction Act and Regulatory Burden
The Board has determined that this proposal would not increase the
regulatory paperwork burden of banking organizations pursuant to the
provisions of the Paperwork Reduction Act (44 U.S.C. 3501 et seq.).
Section 302 of the Riegle Community Development and Regulatory
Improvement Act of 1994 (Pub. L. 103-325, 108 Stat 2160) provides that
the federal banking agencies must consider the administrative burdens
and benefits of any new regulations that impose additional requirements
on insured depository institutions. As noted above, the proposed market
risk measure would affect only a small number of institutions. The
Board believes that any additional burden placed on these institutions
is outweighed by the advantages of greater accuracy in risk measurement
and capital allocation, which contribute to increased safety and
soundness in the banking system.
FDIC Paperwork Reduction Act
The FDIC has determined that his proposed rulemaking does not
contain any collections of information as defined by the Paperwork
Reduction Act (44 U.S.C. 3501 et seq.).
X. OCC Executive Order 12866 Determination
The Comptroller of the Currency has determined that this notice of
proposed rulemaking is not a significant regulatory action under
Executive Order 12866.
XI. OCC Unfunded Mandates Reform Act of 1995 Determination
Section 202 of the Unfunded Mandates Reform Act of 1995 (Unfunded
Mandates Act), Pub. L. 104-4, 109 Stat. 48 (March 22, 1995) requires
that an agency prepare a budgetary impact statement before promulgating
a rule that includes a Federal mandate that may result in the
expenditure by state, local, and tribal governments, in the aggregate,
or by the private sector, of $100 million or more in any one year. If a
budgetary impact statement is required, section 205 of the Unfunded
Mandates Act also requires an agency to identify and consider a
reasonable number of regulatory alternatives before promulgating a
rule. Because the OCC has determined that this notice of proposed
rulemaking will not result in expenditures by state, local and tribal
governments, or by the private sector, of more than $100 million in any
one year, the OCC has not prepared a budgetary impact statement or
specifically addressed the regulatory alternatives considered. As
discussed in the preamble, this proposed rule may require additional
capital for market risks. However, the application of this proposed
rule would be generally limited to banks with significant trading
account activities and would cover only foreign exchange and commodity
positions throughout the bank. Currently, the OCC estimates that less
than 25 national banks will be subject to the requirements of this
proposed rule. In addition, any burden imposed on this small group of
national banks would be lessened to the extent that a bank may use its
own qualifying internal market risk model.
List of Subjects
12 CFR Part 3
Administrative practice and procedure, Capital, National banks,
Reporting and recordkeeping requirements, Risk.
12 CFR Part 208
Accounting, Agriculture, Banks, banking, Confidential business
information, Crime, Currency, Federal Reserve System, Mortgages,
Reporting and recordkeeping requirements, Securities.
12 CFR Part 225
Administrative practice and procedure, Banks, banking, Federal
Reserve System, Holding companies, Reporting and recordkeeping
requirements, Securities.
12 CFR Part 325
Administrative practice and procedure, Banks, banking, Capital
adequacy, Reporting and recordkeeping requirements, Savings
associations, State non-member banks.
Authority and Issuance
OFFICE OF THE COMPTROLLER OF THE CURRENCY
12 CFR Chapter I
For the reasons set out in the preamble, part 3 of title 12,
chapter I of the Code of Federal Regulations is proposed to be amended
as set forth below.
PART 3--MINIMUM CAPITAL RATIOS; ISSUANCE OF DIRECTIVES
1. The authority citation for part 3 continues to read as follows:
Authority: 12 U.S.C. 93a, 161, 1818, 1828(n), 1828 note, 1831n
note, 1835, 3907, and 3909.
[[Page 38095]]
2. New appendix B is added to part 3 to read as follows:
Appendix B to Part 3--Market Risk
Section 1. Purpose, Applicability, Effective Date, and Definitions
(a) Purpose. The purpose of this appendix B is to ensure that
banks maintain adequate capital for market risk. Market risk is
generally the risk of loss arising from movements in market prices.
The market risk requirements of this appendix B are limited to the
market risk associated with the trading account of the bank and to
the overall foreign exchange risk and the commodities risk
throughout the bank, including related options and other derivative
contracts. Under this appendix B a bank may measure its market risk
exposure with either its own qualifying internal market risk model
or the alternative standardized market risk model provided. However,
the OCC generally expects that banks with significant trading
activities will calculate their market risk using a qualifying
internal market risk model.
(b) Applicability. The market risk requirement of this appendix
B applies to the following banks:
(1) Any bank with total assets in excess of $5 billion and
either total on-balance sheet trading account activities of 3
percent or more of the total assets of the bank, or total notional
off-balance sheet trading account activities in excess of $5
billion; and
(2) Any bank with total assets of $5 billion or less and total
trading account activities in excess of 10 percent of the total
assets of the bank; and
(3) Any bank with a significant exposure to market risk and the
OCC deems necessary to protect the safety and soundness of the bank.
(c) Effective date. The market risk requirements of this
appendix B are effective December 31, 1997.
(d) Definitions. For the purposes of this appendix B, the
following definitions apply:
(1) Covered market risk assets means all trading account assets
plus all other on- and off-balance sheet assets which have foreign
exchange risk, equity price risk, and commodity risk throughout the
bank including related options and other derivative contracts.
(2) Derivative contract means generally a financial contract
whose value is derived from the values of one or more underlying
asset, reference rate or index of asset values. Derivative contracts
include both standardized contracts that are traded on exchanges and
customized, privately negotiated contracts known as over-the-counter
(OTC) derivative contracts.
(3) Lock-in clause means a provision in a subordinated debt
agreement that precludes payment by the bank of either interest or
principal (even upon maturity) of the subordinated debt if such
payment would cause the issuing bank to fall or remain below the
minimum risk-based capital requirement as provided in appendix A of
this part 3 as adjusted for market risk.
(4) Market risk means the risk of loss resulting from movements
in market prices. Market risks consist of both general and specific
market risks. General market risk is the change in market value of a
particular asset that results from broad market movements such as a
change in market interest rates, foreign exchange rates, equity
prices, and commodity prices. Specific market risks are those risks
that affect the market value of a specific instrument, such as the
credit risk of the issuer of that particular instrument, but do not
materially alter broad market conditions.
(5) Tier 3 capital means capital that may be used by a bank to
satisfy the market risk capital requirements under this appendix B
as determined in accordance with section 3 of this appendix B.
(6) Total assets means the quarter-end total assets figure
required to be computed for and stated in a bank's most recent
quarterly Consolidated Report of Condition and Income (Call Report).
(7) Trading account activities means the sum of trading account
assets and trading account liabilities.
(8) Trading account assets means all positions in financial
instruments acquired with the intent to resell in order to profit
from short-term price movements. Trading account assets include, but
are not limited to:
(i) Assets acquired with the intent to resell to customers;
(ii) Positions in financial instruments arising from matched
principal brokering or market making; or
(iii) Positions in financial instruments taken in order to hedge
positions in other financial instruments of the trading
account.1
\1\ When non-trading account instruments are hedged with trading
account instruments, whether on- or off-balance-sheet, the bank may
include the non-trading account instruments in the measure for
general market risk. However, such non-trading account instruments
remain subject to the credit risk capital charges of appendix A of
this part.
---------------------------------------------------------------------------
(9) Value-at-risk means the statistical estimate representing
the maximum amount by which the market value of covered market risk
assets could decline during a specific period for a stated level of
statistical confidence.
Section 2. Market Risk Capital Requirement
(a) Capital requirement. All banks subject to this appendix B
shall maintain a minimum market risk capital ratio of 8 percent. The
market risk capital ratio is the ratio of eligible market risk
capital to adjusted market risk assets. Eligible market risk capital
consists of Tier 1, Tier 2, and Tier 3 capital as determined in
accordance with section 3 of this appendix B. Adjusted market risk
assets is the sum of the risk weighted assets as determined in
accordance with appendix A of this part 3 (risk-based capital
guidelines) plus the market risk equivalent assets. The market rate
equivalent assets equal 12.5 times the market risk exposure as
determined in accordance with section 4 of this appendix B.
(b) Relationship to risk-based capital requirement. The amount
of capital required for market risk is in addition to the amount of
capital required for counterparty credit risk under the risk-based
capital guidelines as determined in accordance with appendix A of
this part 3.
Section 3. Eligible Market Risk Capital
(a) Types of eligible market risk capital. A bank may use Tier 1
and Tier 2 capital, as determined in accordance with Sec. 3.2 of
this part 3, to satisfy the market risk requirement. A bank also may
use Tier 3 capital to satisfy its market risk requirement as
determined in accordance with section 3(b) and subject to the
limitations of section 3(c) of this appendix B.
(b) Tier 3 capital. For the purposes of this appendix B, Tier 3
capital consists of short-term subordinated debt subject to a lock-
in clause. In addition, the subordinated debt must have an original
maturity of at least two years, be unsecured and subordinated to the
claims of depositors must be fully paid-in, and may not be subject
to any covenants, terms, or restrictions inconsistent with safe and
sound banking practices.
(c) Limitations. Tier 3 capital only may be used to satisfy the
market risk capital requirements under this appendix B and may not
be used to satisfy the capital risk-based capital requirements for
counterparty risk under appendix A of this part 3, including
counterpart credit risk associated with derivative transactions in
either the trading or nontrading accounts. In addition, the use of
Tier 3 capital is subject to the following quantitative limitations:
(1) Tier 3 capital may not exceed 250 percent of a bank's Tier 1
capital allocated for market risk.
(2) The total of Tier 2 capital and Tier 3 capital is limited to
100 percent of Tier 1 capital.
(3) Tier 2 capital may be substituted for Tier 3 capital up
subject to the same 250 percent limitation on Tier 3 capital and all
other limitations on Tier 2 capital under the risk-based capital
guidelines, as determined by appendix A of this part 3.
Section 4. Market Risk Exposure
Market risk exposure represents the total dollar amount at risk
arising from movements in market prices. A bank may determine its
market risk exposure either through a qualifying internal market
risk model as provided in accordance with section 5 of this appendix
B, or through the standardized market risk model as provided in
accordance with section 6 of this appendix B.
(a) Qualifying internal market risk model. For a bank permitted
or required by the OCC to use a qualifying internal market risk
model, the market risk exposure of covered market risk assets is
equal to the greater of:
(1) The aggregate value-at-risk amount for the previous day; or
(2) The average of the daily value-at-risk amounts for each of
the preceding 60 business days times a multiplication factor of
three.
(b) Standardized market risk model. For banks using the
standardized market risk model, the market risk exposure equals the
measured value-at-risk amount for covered market risk assets as
determined in section 6 of this appendix B.
Section 5. Qualifying Internal Market Risk Model
As provided in this section, a bank may use a qualifying
internal market risk model
[[Page 38096]]
to determine its market risk exposure. The qualifying internal market
risk model may use any generally accepted measurement technique
including, but not limited to, variance-covariance models,
historical simulations, or monte carlo simulations; however, the
qualifying internal market risk model must capture all material
market risk.
(a) Value-at-risk measurement. A qualifying internal market risk
model must incorporate a value-at-risk measurement that adequately
evaluates the market risk associated with all covered market risk
assets.
(b) Risk factor categories. The value-at-risk measurement must
include risk factors sufficient to capture the market risk inherent
in all covered market risk assets. In addition, the risk factors
must cover the risk categories of interest rates, exchange rates,
equity prices, commodity prices, and the volatility of related
market factors.
(c) Prior approval. Prior OCC approval is required before a bank
may use an internal market risk model for the purposes of the market
risk requirement of this appendix B. A qualifying internal market
risk model must satisfy the following criteria:
(1) Qualitative factors. (i) The level of sophistication and
accuracy of the internal market risk model must be commensurate with
the nature and volume of bank's trading account activities.
(ii) The market risk management systems must adequately monitor
compliance with internal procedures and controls which generally
would include independent risk management, annual internal audits,
back testing, and stress testing.
(2) Quantitative factors. (i) The value-at-risk measurement must
be calculated with sufficient frequency to allow the bank enough
time to react to changing market conditions.
(ii) The value-at-risk measurement must be based on a 99th
percentile, one-tailed confidence interval 2 with an assumed
holding period of ten trading days.
\2\ A one-tailed confidence interval of 99 percent means that
there is a 1 percent probability based on historical experience that
the combination of positions in a bank's portfolio would result in a
loss higher than the measured value-at-risk.
---------------------------------------------------------------------------
(iii) For positions that display linear price relationships, a
bank may use value-at-risk measurement using shorter holding periods
which are scaled up to ten days by the square root of time.3
\3\ This transformation entails multiplying a bank's value-at-
risk by the square root of the ratio of the required holding period
(ten days) to the holding period embodied in the value-at-risk
exposure. For example, the value-at-risk calculated according to a
one-day holding period would be scaled-up by the ``square root of
time'' by multiplying the value-at-risk by 3.16 (the square root of
the ratio of a ten-day holding period to a one-day holding period).
---------------------------------------------------------------------------
(iv) The value-at-risk measurement must be calculated using an
observation period of at least one year to measure historical
changes in rates and prices.
(v) A bank must update its historical rates and prices at least
once every three months and must reassess them whenever market
conditions change materially.
(vi) A bank may incorporate into its value-at-risk measurement
empirical correlations within each risk category. However, empirical
correlations across risk categories may not be incorporated. The
value-at-risk measurement for each risk category must be added
together on a simple sum basis to determine the aggregate value-at-
risk exposure.
(vii) The value-at-risk measurement must capture the unique
risks associated with options within each of the risk categories
subject to the following criteria:
(A) The value-at-risk measurement must capture the non-linear
price characteristics of option positions using an options pricing
technique.
(B) The bank must apply a minimum ten-day holding period to
option positions or positions that display option-like
characteristics. Options may not be scale-up the daily value-at-risk
exposure by the square root of time.
(C) The value-at-risk measurement must capture the volatilities
of the rates and prices underlying option positions.
(viii) The accuracy of a bank's qualifying internal market risk
model must be validated by auditors.
Section 6. Standardized Market Risk Model
As provided in this section, a bank may use the standardized
market risk model to determine its market risk exposure.
(a) Debt Instruments. (1) Specific Risk. (i) The market risk
requirement for specific risk is based on the identity of the
obligor and, in the case of corporate securities, on the credit
rating and maturity of the instrument. The specific risk is
calculated by weighting the current market value of each individual
position, whether long or short, by the appropriate specific risk
factor and summing the weighted values. In measuring specific risk,
the bank may offset and exclude from its calculations any matched
positions in the identical issue (including positions in derivative
contracts). Even if the issuer is the same, offsetting is not
permitted between different issues. The specific risk factors are
set forth in Table 1--Specific Risk Factors for Debt Instruments, as
follows:
Table 1.--Specific Risk Factors for Debt Instruments
------------------------------------------------------------------------
Remaining contractual Factor (In
Category maturity percent)
------------------------------------------------------------------------
Government................... N/A......................... 0.00
Qualifying................... 6 months or less............ 0.25
Over 6 to 12 months......... 1.00
Over 12 months.............. 1.60
Other........................ N/A......................... 8.00
------------------------------------------------------------------------
(ii) The government category includes all forms of debt
instruments of central governments of the OECD-based group of
countries including bonds, Treasury bills and other short-term
instruments, as well as local currency instruments of non-OECD
central governments to the extent that the bank has liabilities
booked in that currency.
(iii) The qualifying category includes securities of U.S.
government-sponsored agencies, general obligation securities issued
by states and other political subdivisions of the OECD-based group
of countries, multilateral development banks, and debt instruments
issued by U.S. depository institutions or OECD-banks that do not
qualify as capital of the issuing institution. It also includes
other securities, including revenue securities issued by states and
other political subdivisions of the OECD-based group of countries,
that are rated investment-grade by at least two nationally
recognized credit rating services, or rated investment-grade by one
nationally recognized credit rating agency and not less than
investment-grade by any other credit rating agency, or, with the
exception of securities issued by U.S. firms and subject to review
by the OCC, unrated but deemed to be of comparable investment
quality by the reporting bank and the issuer has securities listed
on a recognized stock exchange.
(iv) The other category includes debt securities not qualifying
as government or qualifying securities. This would include non-OECD
central government securities that do not meet the criteria for the
government or qualifying categories. This category also includes
instruments that qualify as capital issued by other banking
organizations.
(v) The OCC will consider the extent of a bank's position in
non-investment grade instruments (sometimes referred to as ``high
yield debt'') that do not have investment-grade ratings. If those
holdings are not well-diversified or otherwise represent a material
position to the institution, the OCC may prohibit a bank from
offsetting positions in these instruments with other positions in
qualifying instruments that may be offset when calculating its
general market risk requirement. In addition, the OCC may impose a
specific risk capital requirement as high as 16.0 percent.
(2) General Market Risk. (i) A bank may measure its exposure to
general market risk using, on a continuous basis, either the
maturity method (which uses standardized risk weights that
approximate the price sensitivity of various instruments) or the
duration method (where the institution calculates the precise
duration of each instrument, weighted by a specified change in
interest rates).
(ii) Both methods use a maturity-ladder that incorporates a
series of ``time bands'' and ``zones'' to group together securities
of similar maturities and that are designed to take into account
differences in price sensitivities and interest rate volatilities
across different maturities. Under either method, the capital
requirement for general market risk is the sum of a base charge that
results from fully netting various risk-weighted positions and a
series of additional charges (add-ons), which effectively
``disallow'' part of the previous full netting to address basis and
yield curve risk.
(iii) For each currency in which a bank has significant
positions, a separate capital requirement must be calculated. No
netting of positions is permitted across different currencies.
Offsetting positions of the same amount in the same issues, whether
actual or
[[Page 38097]]
notional, may be excluded from the calculation, as well as closely
matched swaps, forwards, futures, and forward rate agreements (FRAs)
that meet the conditions set out in section 6(a)(3) of this appendix
B.
(iv) In the maturity method, the bank distributes each long or
short position (at current market value) of a debt instrument into
the time bands of the maturity ladder. Fixed-rate instruments are
allocated according to the remaining term to maturity and floating-
rate instruments according to the next repricing date. A callable
bond trading above par is slotted according to its first call date,
while a callable bond priced below par is slotted according to
remaining maturity. Fixed-rate mortgage-backed securities, including
collateralized mortgage obligations (CMOs) and real estate mortgage
investment conduits (REMICs), are slotted according to their
expected weighted average lives.
(v) Once all long and short positions are slotted into the
appropriate time band, the long positions in each time-band are
summed and the short positions in each time-band are summed. The
summed long and/or short positions are multiplied by the appropriate
risk-weight factor (reflecting the price sensitivity of the
positions to changes in interest rates) to determine the risk-
weighted long and/or short position for each time-band. The risk
weights for each time-band are set out in Table 2--Maturity Method:
Time-Band and Weights, as follows:
Table 2.--Maturity Method: Time-Bands and Weights
------------------------------------------------------------------------
Coupon less than 3% and Risk
Zone Coupon 3% or more zero coupon bonds weights
------------------------------------------------------------------------
1....... Up to 1 month............ Up to 1 month........... 0.00
1 up to 3 months......... 1 up to 3 months........ 0.20
3 up to 6 months......... 3 up to 6 months........ 0.40
6 up to 12 months........ 6 up to 12 months....... 0.70
2....... 1 up to 2 years.......... 1 up to 1.9 years....... 1.25
2 up to 3 years.......... 1.9 up to 2.8 years..... 1.75
3 up to 4 years.......... 2.8 up to 3.6 years..... 2.25
3....... 4 up to 5 years.......... 3.6 up to 4.3 years..... 2.75
5 up to 7 years.......... 4.3 up to 5.7 years..... 3.25
7 up to 10 years......... 5.7 up to 7.3 years..... 3.75
10 up to 15 years........ 7.3 up to 9.3 years..... 4.50
15 up to 20 years........ 9.3 up to 10.6 years.... 5.25
Over 20 years............ 10.6 up to 12 years..... 6.00
12 up to 20 years....... 8.00
Over 20 years........... 12.50
------------------------------------------------------------------------
(vi) Within each time-band for which there are risk-weighted
long and short positions, the risk-weighted long and short positions
are then netted, resulting in a single net risk-weighted long or
short position for each time-band. Because different instruments and
different maturities may be included and netted within each time-
band, a capital requirement, referred to as the vertical
disallowance, is assessed for basis risk. The vertical disallowance
capital requirement is 10.0 percent of the position eliminated by
the intra-time-band netting, that is, 10.0 percent of the smaller of
the net risk-weighted long or net risk-weighted short position, or
if the positions are equal, 10.0 percent of either position.4
The vertical disallowances for each time-band are absolute values,
that is, neither long nor short. The vertical disallowances for all
time-bands in the maturity ladder are summed and included as an
element of the general market risk capital requirement.
\4\ For example, if the sum of the weighted longs in a time-band
is $100 million and the sum of the weighted shorts is $90 million,
the vertical disallowance for the time-band is 10.0 percent of $90
million, or $9 million.
---------------------------------------------------------------------------
(vii) Within each zone for which there are risk-weighted long
and short positions in different time-bands, the weighted long and
short positions in all of the time-bands within the zone are then
netted, resulting in a single net long or short position for each
zone. Because different instruments and different maturities may be
included and netted within each zone, a capital requirement,
referred to as the horizontal disallowance, is assessed to allow for
the imperfect correlation of interest rates along the yield curve.
The horizontal disallowance capital requirement is calculated as a
percentage of the position eliminated by the intra-zone netting,
that is, a percentage of the smaller of the net risk-weighted long
or net risk-weighted short position, or if the positions are equal,
a percentage of either position.5 The percent disallowance
factors for intra-zone netting are set out in Table 3--Horizontal
Disallowances in section 6(a)(2)(H). The horizontal disallowances,
like the vertical disallowances, are absolute values that are summed
and included as an element of the general market risk capital
requirement.
\5\ For example, if the sum of the weighted longs in the 1- to
3-month time-band in Zone 1 is $8 million and the sum of the
weighted shorts in the 3- to 6-month time-band is $10 million, the
horizontal disallowance for the zone is 40 percent of $8 million, or
$3.2 million.
(viii) Risk-weighted long and short positions in different zones
are then netted between the zones. Zone 1 and zone 2 are netted if
possible, reducing or eliminating the net long or short position in
zone 1 or zone 2 as appropriate. Zone 2 and zone 3 are then netted
if possible, reducing or eliminating the net long or short position
in zone 2 or zone 3 as appropriate. Zone 3 and zone 1 are then
netted if possible, reducing or eliminating the long or short
position in zone 3 and zone 1 as appropriate. A horizontal
disallowance capital requirement is then assessed, calculated as a
percentage of the position eliminated by the inter-zone netting. The
horizontal disallowance capital requirements for each zone are then
summed as absolute values and included in the general market risk
capital charge. The percent disallowance factors for inter-zone
netting are set out in Table 3--Horizontal Disallowances, as
follows:
Table 3.--Horizontal Disallowances
------------------------------------------------------------------------
Between
Within the adjacent Between
Zone Time-band zone zones zones 1 and
(percent) (percent) 3 (percent)
------------------------------------------------------------------------
1....... 0 up to 1 month........ 40 40 100
1 up to 3 months.......
3 up to 6 months ......
[[Page 38098]]
6 up to 12 months......
2....... 1 up to 2 years........ 30 40 100
2 up to 3 years
3 up to 4 years
3....... 1 up to 5 years........ 30 40 100
5 up to 7 years
7 up to 10 years
10 up to 15 years
15 up to 20 years
Over 20 years
------------------------------------------------------------------------
(ix) Finally, the net risk-weighted long or net risk-weighted
short positions remaining in the zones are summed to reach a single
net risk-weighted long or net risk-weighted short position for the
bank's portfolio. The sum of the absolute value of this position and
the vertical and horizontal disallowances is the capital requirement
for general market risk.
(x) In the duration method, the bank, after calculating each
instrument's modified duration,6 multiplies that modified
duration by the interest rate shock specified for an instrument of
that duration in Table 4--Duration Method: Time-Band and Assumed
Changes in Yield in section 6(a)(2)(K). The resulting product
(representing the expected percentage change in the price of the
instrument for the given interest rate shock) is then multiplied by
the current market value of the instrument. The resulting amount is
then slotted as a long or short position into a time-band in the
maturity ladder in Table 4--Duration Method: Time-Band and Assumed
Changes in Yield on the basis of the instrument's modified
duration.7
\6\ The duration of an instrument is its approximate percentage
change in price for a 100 basis point parallel shift in the yield
curve assuming that its cash flows do not change when the yield
curve shifts. Modified duration is duration divided by a factor of 1
plus the interest rate.
\7\ Example, an instrument held by a bank with a maturity of 4
years and 3 months and a current market value of $1,000 might have a
modified duration of 3.5 years. Based on its modified duration, it
would be subjected to the 75-basis point interest rate shock,
resulting in an expected price change of 2.625 percent (3.5 x
0.75). The corresponding expected change in price of $26.25,
calculated as 2.625 percent of $1,000, would be slotted as a long
position in the 3.3 to 4.0 year time-band of the maturity ladder.
---------------------------------------------------------------------------
(xi) Once all of the bank's traded debt instruments have been
slotted into the maturity ladder, the bank conducts the same rounds
of netting and disallowances described in sections 6(a)(2)(F)
through (H) of the maturity method in this appendix B, with the
exception that the vertical disallowance requirement for the
duration method is 5.0 percent (horizontal disallowances continue to
be those set out in Table 3--Horizontal Disallowances). As with the
maturity method, the sum of the absolute value of the final net
position and the vertical and horizontal disallowances is the
general market risk capital requirement.
(xii) The duration method maturity ladder is set out in Table
4--Duration Method: Time Bands and Assumed Changes in Yield, as
follows:
Table 4.--Duration Method: Time-Bands and Assumed Changes in Yield
------------------------------------------------------------------------
Assumed
Zone Time-band change in
yield
------------------------------------------------------------------------
1....... Up to 1 month.................................... 1.00
1 up to 3 months................................. 1.00
3 up to 6 months................................. 1.00
6 up to 12 months................................ 1.00
2....... 1.0 up to 1.8 years.............................. 0.90
1.8 up to 2.6 years.............................. 0.80
2.6 up to 3.3 years.............................. 0.75
3....... 3.3 up to 4.0 years.............................. 0.75
4.0 up to 5.2 years.............................. 0.70
5.2 up to 6.8 years.............................. 0.65
6.8 up to 8.6 years.............................. 0.60
8.6 up to 9.9 years.............................. 0.60
9.9 up to 11.3 years............................. 0.60
11.3 up to 16.6 years............................ 0.60
Over 16.6 years.................................. 0.60
------------------------------------------------------------------------
(3) Interest rate derivative contracts. (i) Derivative contracts
and other off-balance sheet positions that are affected by changes
in interest rates are included in the measurement system under
section 6(a) of this appendix B (except for options and the
associated underlyings, which are included in the measurement system
under the treatment discussed in section 6(e) of this appendix B).
(ii) Derivatives are converted into positions in the relevant
underlying instrument and are included in the calculation of
specific and general market risk capital charges as described above.
The amount to be included is the market value of the principal
amount of the underlying or of the notional underlying.
(iii) Futures and forward contracts (including FRAs) are broken
down into a combination of a long position and short position in the
notional security. The maturity of a future or a FRA is the period
until delivery or exercise of the contract, plus the life of the
underlying instrument.8 Where a range of instruments may be
delivered to fulfill the contract, the bank may chose which
deliverable instrument goes into the maturity or duration ladder as
the notional underlying. In the case of a future on a corporate bond
index, positions are included at the market value of the notional
underlying portfolio of securities.
\8\ For example, a long position in a June three-month interest
rate future (taken in April) is reported as a long position in a
government security with a maturity of five months and a short
position in a government security with a maturity of two months.
---------------------------------------------------------------------------
(iv) Swaps are treated as two notional positions in the relevant
instruments with appropriate maturities. The receiving side is
treated as the long position and the paying side is treated as the
short position.9 The separate sides of cross-currency swaps or
forward foreign exchange transactions are slotted in the relevant
maturity ladders for the currencies concerned. For swaps that pay or
receive a fixed or floating interest rate against some other
reference price, for example, an equity index, the interest rate
component is slotted into the appropriate repricing maturity
category, with the long or short position attributable to the equity
component being included in the equity framework set out in section
6(b) of this appendix B.10
\9\ For example, an interest rate swap in which a bank is
receiving floating-rate interest and paying fixed is treated as a
long position in a floating rate instrument with a maturity
equivalent to the period until the next interest rate reset date and
a short position in a fixed-rate instrument with a maturity
equivalent to the remaining life of the swap.
\10\ A bank with a large swap book may, with prior approval of
the OCC, use alternative formulae to calculate the positions to be
included in the maturity or duration ladder. For example, a bank
could first convert the payments required by the swap into present
values. For that purpose, each payment would be discounted using
zero coupon yields, and the payment's present value entered into the
appropriate time-band using procedures that apply to zero (or low)
coupon bonds. The net amounts would then be treated as bonds, and
slotted into the general market risk framework. Such alternative
treatments will, however, only be allowed if: (i) the OCC is
satisfied with the accuracy of the system being used, (ii) the
calculated positions fully reflect the sensitivity of the cash flows
to interest rate changes; and (iii) the positions are denominated in
the same currency.
[[Page 38099]]
---------------------------------------------------------------------------
(v) A bank may offset long and short positions (both actual and
notional) in identical derivative instruments with exactly the same
issuer, coupon, currency, and maturity before slotting these
positions into time-bands. A matched position in a future and its
corresponding underlying may also be fully offset and, thus,
excluded from the calculation, except when the future comprises a
range of deliverable instruments. However, in cases where, among the
range of deliverable instruments, there is a readily identifiable
underlying instrument that is most profitable for the trader with a
short position to deliver, positions in the futures contract and the
instrument may be offset. No offsetting is allowed between positions
in different currencies.
(vi) Offsetting positions in the same category of instruments
can in certain circumstances be regarded as matched and treated by
the bank as a single net position which should be entered into the
appropriate time-band. To qualify for this treatment the positions
must be based on the same underlying instrument, be of the same
nominal value, and be denominated in the same currency. The separate
sides of different swaps may also be ``matched'' subject to the same
conditions. In addition:
(A) For futures, offsetting positions in the notional or
underlying instruments to which the futures contract relates must be
for identical instruments and the instruments must mature within
seven days of each other;
(B) For swaps and FRAs, the reference rate (for floating rate
positions) must be identical and the coupon closely matched; and
(C) For swaps, FRAs and forwards, the next interest reset date,
or for fixed coupon positions or forwards the remaining maturity,
must correspond within the following limits: If the reset (remaining
maturity) dates occur within one month, then the reset (remaining
maturity) dates must be on the same day; if the reset (remaining
maturity) dates occur between one month and one year later, then the
reset (remaining maturity) dates must occur within seven days of
each other, or if the reset (remaining maturity) dates occur over
one year later, then the reset (remaining maturity) dates must occur
within thirty days of each other.
(vii) Interest rate and currency swaps, FRAs, forward foreign
exchange contracts and interest rate futures are not subject to a
specific risk charge. This exemption also applies to futures on a
short-term (e.g., LIBOR) interest rate index. However, in the case
of futures contracts where the underlying is a debt security, or an
index representing a basket of debt securities, a specific risk
charge will apply according to the category of the issuer as set out
in section 6(a)(2) of this appendix B.
(b) Equities. (1) Specific risk. The measure of specific risk is
calculated on the basis of the bank's gross equity positions, that
is, the absolute sum of the current market value of all long equity
positions and of all short equity positions.11 The specific
risk capital requirement is 8.0 percent of that sum, unless the
portfolio is both liquid and well-diversified, in which case the
specific risk capital requirement is 4.0 percent of the gross equity
position. A specific risk charge of 2.0 percent applies to the net
long or short position in a broad, diversified equity index.
\11\ Matched positions in each identical equity in each national
market may be treated as offsetting and excluded from the capital
calculation, with any remaining position included in the
calculations for specific and general market risk. For example, a
future in a given equity may be offset against an opposite cash
position in the same equity.
---------------------------------------------------------------------------
(2) General market risk. The measure of general market risk is
based on the difference between the sum of the long positions and
the sum of the short positions (i.e., the overall net position in an
equity market) at current market value. An overall net position must
be separately calculated for each national market in which the bank
holds equities. The capital requirement for general market risk is
8.0 percent of the net position in each equity market.
(3) Equity derivatives. (i) Equity derivatives and other off-
balance-sheet positions that are affected by changes in equity
prices are included in the measurement system under section 6(b) of
this appendix B (except for equity options, equity index options,
and the associated underlying, which are included in the measurement
system under the treatment discussed in section 6(e) of this
appendix B).12 This includes futures and swaps on both
individual equities and on equity indices. Equity derivatives should
be converted into notional equity positions in the relevant
underlying.
\12\ Where equities are part of a forward contract (both
equities to be received or to be delivered), any interest rate or
foreign currency exposure from the other side of the contract should
be appropriately included in sections 6(a) and (c) of this appendix
B.
---------------------------------------------------------------------------
(ii) Futures and forward contracts relating to individual
equities should be reported as current market prices of the
underlying. Futures relating to equity indices should be reported as
the marked-to-market value of the notional underlying equity
portfolio. Equity swaps are treated as two notional positions, with
the receiving side as the long position and the paying side as the
short position.13 If one of the legs involves receiving/paying
a fixed or floating interest rate, the exposure should be slotted
into the appropriate repricing maturity band for debt securities.
The stock index is covered by the equity treatment.
\13\ For example, an equity swap in which a bank is receiving an
amount based on the change in value of one particular equity or
equity index and paying a different index will be treated as a long
position in the former and a short position in the latter.
---------------------------------------------------------------------------
(iii) In the case of futures-related arbitrage strategies, the
2.0 percent specific risk charge applicable to broad diversified
equity indices may be applied to only one index. The opposite
position is exempt from a specific risk charge. The strategies
qualifying for this treatment are:
(A) When the bank takes an opposite position in exactly the same
index at different dates; and
(B) When the bank has an opposite position in different but
similar indices at the same date, subject to supervisory oversight.
(iv) If a bank engages in a deliberate arbitrage strategy, in
which a futures contract on a broad diversified equity index matches
a basket of securities, it may exclude both positions from the
standardized approach on the condition that the trade has been
deliberately entered into and separately controlled and the
composition of the basket of stocks represents at least 90 percent
of the market value of the index. In such a case, the minimum
capital requirement is 4.0 percent (that is, 2.0 percent of the
gross value of the positions on each side). This applies even if all
of the securities comprising the index are held in identical
proportions. Any excess value of the securities comprising the
basket over the value of the futures contract or excess value of the
futures contract over the value of the basket is treated as an open
long or short position.
(v) If a bank takes a position in depository receipts 14
against an opposite position in the underlying equity, it may offset
the position.
\14\ Depository receipts are instruments issued by a trust
company or other depository institution evidencing the deposit of
foreign securities and facilitating trading in such instruments on
U.S. stock exchanges.
---------------------------------------------------------------------------
(c) Foreign Exchange Risk. (1) The capital requirement for
foreign exchange risk covers the risk of holding or taking positions
in foreign currencies, including gold, and is based on a bank's net
open long positions or net open short positions in each currency,
whether or not those positions are in the trading portfolio, plus
the net open position in gold, regardless of sign.15
\15\ Where a bank has future and forward contracts to deliver
and receive gold, a maturity ladder should be constructed in
accordance with section 6(a) of this appendix B treating gold as a
zero coupon instrument.
(2) A bank's net open position in each currency (and gold) is
calculated by summing:
(i) The net spot position (i.e., all asset items less all
liability items, including accrued interest earned but not yet
received and accrued expenses, denominated in the currency in
question);
(ii) All foreign exchange derivative instruments and other off-
balance-sheet positions that are affected by changes in exchange
rates are included in the measurement system under section 6(c) of
this appendix B (except for options and their associated
underlyings, which are included in the measurement system under the
treatment discussed in section 6(e) of this appendix B). Forward
currency positions should be valued at current spot market exchange
rates. For a bank in which the basis of its normal management
accounting is to use net present values, forward positions may be
discounted to net present values as an acceptable way of measuring
currency positions for regulatory capital purposes;
(iii) Guarantees (and similar instruments) that are certain to
be called and are likely to be irrevocable;
(iv) Net future income/expenses not yet accrued but already
fully hedged (at the discretion of the bank). A bank that includes
future income and expenses must do so on a consistent basis without
selecting expected future flows in order to reduce the bank's
position; and
(v) Any other item representing a profit or loss in foreign
currencies.
[[Page 38100]]
(3) For measuring a bank's open positions, positions in
composite currencies, such as the ECU, may be either treated as a
currency in their own right or split into their component parts on a
consistent basis. Positions in gold are measured in the same manner
as described in section 6(d) of this appendix B.16
\16\ Where gold is part of a forward contract (quantity of gold
to be received or to be delivered), any interest rate or foreign
currency exposure from the other side of the contract should be
reported as set out in section 6(a) and (c) of this appendix B.
---------------------------------------------------------------------------
(4) The capital requirement is determined by converting the
nominal amount (or net present value) of the net open position in
each foreign currency (and gold) at spot rates into the reporting
currency. The capital requirement is 8.0 percent of the sum of:
(i) The greater of the sum of the net short open positions or,
the sum of the net long open positions; and
(ii) The net open position in gold, regardless of sign.17
\17\ For example, a bank has the following net currency
positions: Yen = +50, DM = +100, GB = +150, FFR = -20, US$= -180,
and gold = -35. The bank would sum its long positions (total = +300)
and sum its short positions (total = -200). The bank's capital
requirement for foreign exchange market risk would be: (300 (the
larger of the summed long and short positions) + 35 (gold)) x 8.0%
= $26.80.
---------------------------------------------------------------------------
(5) A bank doing negligible business in foreign currency and
that does not take foreign exchange positions for its own account
may be exempted from the capital requirement for foreign exchange
risk provided that:
(i) Its foreign currency business, defined as the greater of the
sum of its gross long positions and the sum of its gross short
positions in all foreign currencies, does not exceed 100 percent of
eligible capital as defined in section 3 of this appendix B; and
(ii) Its overall net open foreign exchange position as
determined in section 6(c)(2) does not exceed 2.0 percent of its
eligible capital.
(6) Where a bank is assessing its foreign exchange risk on a
consolidated basis, it may be impractical in the case of some
marginal operations to include the currency positions of a foreign
branch or subsidiary of the bank. In such cases, the internal limit
in each currency may be used as a proxy for the positions, provided
there is adequate ex post monitoring of actual positions complying
with such limits. In these circumstances, the limits should be
added, regardless of sign, to the net open position in each
currency.
(d) Commodities risk. (1) Measurement methods. This section
provides a minimum capital requirement to cover the risk of holding
or taking positions in commodities. There are two methods under the
standardized approach for measuring commodity market risk--the
simplified method and the maturity method. These methods are only
appropriate for banks that conduct a limited amount of commodities
business. All other banks must adopt an internal measurement system
conforming to the criteria in section 5 of this appendix B.
(2) Base capital requirement. Under both the simplified and
maturity methods, each long and short commodity position (spot and
forward) is expressed in terms of the standard unit of measurement
(such as barrels, kilos, or grams). The open positions in each
category of commodities are then converted at current spot rates
into U.S. currency, with long and short positions offset to arrive
at the net open position in each commodity. Positions in different
categories of commodities may not, generally, be offset.18
Under either method, the base capital requirement is 15.0 percent of
the net open position, long or short, in each commodity.19
\18\ However, netting is permitted between different sub-
categories of the same commodity in cases where the sub-categories
are deliverable against each other.
\19\ When the funding of a commodity position opens a bank to
interest rate or foreign exchange exposure the relevant positions
should be included in the measures of interest rate and foreign
exchange risk described in sections 6(a) and (c) of this appendix B.
When a commodity is part of a forward contract, any interest or
foreign currency exposure from the other side of the contract should
be appropriately included in sections 6(a) and 6(c) of this appendix
B.
---------------------------------------------------------------------------
(3) Simplified method. To protect a bank against basis risk,
interest rate risk, and forward gap risk, each category of commodity
is also subject to a 3.0 percent capital requirement on the bank's
gross positions, long plus short, in the particular commodity. In
valuing gross positions in commodity derivatives for this purpose, a
bank should use the current spot price. The total capital
requirement for commodities risk is the sum of the 15.0 percent base
charges for each net commodity position and the 3.0 percent
requirements on the gross commodity positions.
(4) Maturity method. (i) Under this method, a bank must slot
each long and short commodity position (converted into U.S. currency
at current spot rates) into a maturity ladder. The time-bands for
the maturity ladder are; from zero to one month, one up to three
months, three up to six months, six up to twelve months, one up to
two years, two up to three years, and over three years. A separate
maturity ladder is used for each category of commodity. Physical
commodities are allocated to the first time-band.
(ii) In order to capture forward gap and interest rate risk
within a time-band (together sometimes referred to as curvature/
spread risk), offsetting long and short positions in each time-band
are subject to an additional capital requirement. Beginning with the
shortest-term time-band and continuing with subsequent time-bands,
the amount of the matched short positions plus the amount of the
matched long position is multiplied by a spread rate of 1.5 percent.
(iii) The unmatched net position from a shorter-term time-band
must be carried forward to offset exposures in longer-term time-
bands. A capital requirement of 0.6 percent of the net position
carried forward is added for each time-band that the net position is
carried forward.20 The total capital requirement for
commodities risk is the sum of the 15.0 percent base capital
requirement for each net commodity position and the additional
requirements for matched positions and for unmatched positions
carried forward.
\20\ For example, if $200 short is carried forward from the 3-6
month time-band to the 1-2 year time-band, the capital charge would
be $200 x .006 x 2 = $2.40.
---------------------------------------------------------------------------
(5) Commodity derivatives and other off-balance-sheet positions
that are affected by changes in commodity prices are included in the
measurement system under section 6(d) of this appendix B (except for
options and the associated underlying, which are included in the
measurement system under the treatment discussed in section 6(e) of
this appendix B). Commodity derivatives are converted into notional
commodity positions. Under the maturity method, the positions are
slotted into maturity time-bands as follows:
(i) Futures and forward contracts relating to individual
commodities are incorporated in the measurement system as notional
amounts (of, for example, barrels or kilos) that are converted to
U.S. dollars at current spot rates and are assigned a maturity
according to expiration date;
(ii) Commodity swaps where one side of the contract is a fixed
price and the other side is the current market price are
incorporated as a series of positions equal to the notional amount
of the contract at current spot rates, with one position
corresponding to each payment on the swap and slotted in the
maturity ladder accordingly. The positions are long positions if the
bank is paying a fixed price and receiving a floating price, and
short positions if the bank is receiving a fixed price and paying a
floating price; 21 and
\21\ If one of the sides of the transaction involves receiving/
paying a fixed or floating interest rate, that exposure should be
slotted into the appropriate repricing maturity band in section 6(a)
of this appendix B.
---------------------------------------------------------------------------
(iii) Commodity swaps where the sides of the transaction are in
different commodities are included in the relevant reporting ladder.
No offsetting is allowed unless the commodities are in the same sub-
category.
(e) Options. (1) Several alternatives are available for a bank
to use in measuring its market risk for options activities. A bank
that only has purchased options may use the simplified method set
forth in section 6(e)(2) of this appendix B. A bank that also writes
options may use the scenario method described in section 6(e)(3) of
this appendix B, or the delta-plus method set forth in section
6(e)(4) of this appendix B.22 These methods may only be used by
banks which, in relative terms, have limited options activities.
Banks with more significant options business are expected to adopt
an internal measurement system conforming to the criteria in section
5 of this appendix B. Regardless of the method used, specific risk
related to the issuer of an instrument still applies to options
positions for equities, equity indices and corporate debt securities
as set forth in sections 6(a) and (b) of this appendix B. There
remains a separate capital
[[Page 38101]]
requirement for counterparty credit risk as set forth in appendix A to
this part 3.
\22\ Unless all their written option positions are hedged by
perfectly matched long positions in exactly the same options, in
which case there is no capital requirement for market risk.
---------------------------------------------------------------------------
(2) Under the simplified and scenario methods, the positions for
the options and the associated underlying, cash or forward, are not
included in the measurement framework for debt securities, equities,
foreign exchange or commodities risk as set forth in sections 6(a)
through (d) of this appendix B. Rather, they are subject to capital
requirements as calculated in this section. The capital requirements
calculated under this section should then be added to the capital
requirements for debt securities, equities, foreign exchange and
commodities risk as appropriate. Under the delta-plus method, the
delta equivalent position 23 for each option is included in the
measurement frameworks set forth in sections 6(a) through (d) of
this appendix B.
23 The delta equivalent of an option is the option's delta
value multiplied by its principal or notional value. The delta value
of an option represents the expected change in the option's price as
a proportion of a small change in the price of the underlying
instrument. For example, an option whose price changes $1 for every
$2 dollar change in the price of the underlying instrument has a
delta of 0.50.
---------------------------------------------------------------------------
(3) A bank that has only a limited amount and range of purchased
options may use the following simplified approach to measure its
market risk exposure: 24
24 For example, if a holder of 100 shares currently valued at
$10 each has an equivalent put option with a strike price of $11,
the capital charge would be: $1,000 x 16.0 percent (e.g., 8.0
percent specific plus 8.0 percent general market risk) = $160, less
the amount the option is in the money ($11-$10) x 100 = $100,
i.e., the capital charge would be $60. A similar methodology applies
for options whose underlying is a foreign currency, a debt security
or a commodity.
---------------------------------------------------------------------------
(i) For a bank with a long cash position and a long put or with
a short cash position and a long call, the capital requirement is
the market value of the underlying instrument multiplied by the sum
of the specific and general market risk requirements for the
underlying (that is, the specific and general market risk
requirements that would have applied to the underlying directly
under sections 6(a) through (d) of this appendix B), less the amount
the option is in the money (if any) bounded at zero.25
\25\ Some options (e.g., where the underlying is an interest
rate, a currency, or a commodity) bear no specific risk but specific
risk will be present in the case of options on corporate debt
securities and for options on equities and equity indices.
---------------------------------------------------------------------------
(ii) For a bank with a long call or a long put, the capital
charge is the lesser of:
(A) The market value of the underlying security multiplied by
the sum of specific and general market risk requirements for the
underlying (that is, the specific and general market risk
requirements that would have applied to the underlying directly
under sections 6(a) through (d) of this appendix B); or
(B) The market value of the option.
(iii) Under this measure, the capital requirement for currency
options is 8.0 percent of the market value of the underlying and for
commodity options is 15.0 percent of the market value of the
underlying.
(4) Under the scenario approach, a bank revalues its options and
related hedging positions by changing the underlying rate or price
over a specified range and by assuming different levels of
volatility for that rate or price.
(i) For each of its option portfolios, a bank constructs a grid
based on a fixed range of changes in the portfolio's risk factors
and calculates changes in the value of the option portfolio at each
point within the grid. For this purpose, an option portfolio
consists of an option and any related hedging positions or multiple
options and related hedging positions that are grouped together
according to their remaining maturity or the type of underlying.
(ii) Options based on interest rates and debt instruments are
grouped into portfolios according to the maturity zones that are set
forth in section 6(a) of this appendix B. (Zone 1 instruments have a
remaining maturity of up to 1 year, zone 2 instruments have a
remaining maturity from 1 year up to 4 years, and zone 3 instruments
have a remaining maturity of 4 years or more.)
(iii) These options and the associated hedging positions should
be evaluated under the assumption that the relevant interest rates
move simultaneously. For options based on equities, separate grids
are constructed for each individual equity issue and index. For
options based on exchange rates, separate grids are constructed for
individual exchange rates. For options based on commodities,
separate grids are constructed for each category of commodity (as
defined in sections 6(a) and (d) of this appendix B).
(iv) For option portfolios with options based on equities,
exchange rates, and commodities, the first dimension of the grid
consists of rate or price changes within a specified range above and
below the current market value of the underlying; for equities, the
range is +/- 12.0 percent (or in the case of an index +/- 8.0
percent), for exchange rates the range is +/- 8.0 percent, and for
commodities the range is +/- 15.0 percent. For option portfolios
with options based on interest rates, the range for the first
dimension of the grid depends on the remaining maturity zone. The
range for zone 1 is +/- 100 basis points, the range for zone 2 is +/
- 90 basis points, and the range for zone 3 is +/- 75 basis points.
For all option portfolios, the range is divided into at least ten
equally spaced intervals. The second dimension of each grid is a
shift in the volatility of the underlying rate or price equal to +/-
25.0 percent of the current volatility.26
26 For example, if the underlying in an equity instrument with
a current market value of $100 and a volatility of 20 percent, the
first dimension of the grid would range from $88 to $112, divided
into ten intervals of $2.40 and the second dimension would assume
volatilities of 15 percent, 20 percent, and 25 percent.
---------------------------------------------------------------------------
(v) For each assumed volatility and rate or price change (a
scenario), the bank revalues each option portfolio. The market risk
capital requirement for the portfolio is the largest loss in value
from among the scenario revaluations. The total market risk capital
requirement for all option portfolios is the sum of the individual
option portfolio capital requirements.
(vi) The OCC will review the application of the scenario
approach, particularly regarding the precise way the analysis is
constructed. A bank using the scenario approach should meet the
appropriate qualitative criteria set forth in section 5 of this
appendix B.
(5) Under the delta-plus method, a bank that writes options may
include delta-weighted options positions within each measurement
framework as set forth in sections 6(a) through 6(d) of this
appendix B.
(i) Options positions should be measured as a position equal to
the market value of the underlying instrument multiplied by the
delta. In addition, a bank must measure the sensitivities of the
option's gamma (the change of the delta for a given change in the
price of the underlying) and vega (the sensitivity of the option
price with respect to a change in volatility) to calculate the total
capital requirement. These sensitivities may be calculated according
to an exchange model approved by the OCC or to the bank's own
options pricing model, subject to oversight by the OCC.
(ii) For options with debt instruments or interest rates as the
underlying instrument, delta-weighted options positions should be
slotted into the debt instrument time-bands in section 6(a) of this
appendix B using a two-legged approach (as is used for other
derivatives), requiring one entry at the time the underlying
contract takes effect and one at the time the underlying contract
matures.27 Floating rate instruments with caps or floors should
be treated as a combination of floating rate securities and a series
of European-style options.28 A bank must also calculate the
gamma and vega for each such option position (including hedge
positions). The results should be slotted into separate maturity
ladders by currency. For options such as caps and floors whose
underlying instrument is an interest rate, the delta and gamma
should be expressed in terms of a hypothetical underlying security.
Subsequently:
\27\ For example, in April a purchased call option on a June
three-month interest-rate future would be considered on the basis of
its delta-equivalent value to be a long position with a maturity of
five months and a short position with a maturity of two months. The
written option would be slotted as a long position with a maturity
of two months and a short position with a maturity of five months.
\28\ For example, the holder of a three-year floating rate bond
indexed to six-month LIBOR with a cap of 15 percent would treat the
bond as a debt security that reprices in six months, and a series of
five written call options on a FRA with a strike rate of 15 percent,
each slotted as a short position at the expiration date of the
option and as a long position at the time the FRA matures.
---------------------------------------------------------------------------
(A) For gamma risk, for each time-band, net gammas that are
negative are multiplied by the risk weights set out in Table 5 and
by the square of the market value of the underlying instrument (net
positive gammas may be disregarded);
(B) For volatility risk, a bank calculates the capital
requirements for vega in each time-band assuming a proportional
shift in volatility of 25.0 percent;
(C) The capital requirement is the absolute value of the sum of
the individual capital requirements for net negative gammas plus the
absolute value of the sum of the
[[Page 38102]]
individual capital requirements for vega risk for each time-band; and
(D) The delta plus method risk weights are:
Table 5.--Delta Plus Method Risk Weights
------------------------------------------------------------------------
Modified
duration Assumed Risk-weight
Time-band (average interest for
assumed for rate change gamma\1\
time-band) (%)
------------------------------------------------------------------------
Under 1 month.................... 0.00 1.00 0.00000
1 up to 3 months................. 0.20 1.00 0.00020
3 up to 6 months................. 0.40 1.00 0.00080
6 up to 12 months................ 0.70 1.00 0.00245
1 up to 2 years.................. 1.40 0.90 0.00794
2 up to 3 years.................. 2.20 0.80 0.01549
3 up to 4 years.................. 3.00 0.75 0.02531
4 up to 5 years.................. 3.65 0.75 0.03747
5 up to 7 years.................. 4.65 0.70 0.05298
7 up to 10 years................. 5.80 0.65 0.07106
10 up to 15 years................ 7.50 0.60 0.10125
15 up to 20 years................ 8.75 0.60 0.13781
Over 20 years.................... 10.00 0.60 0.18000
------------------------------------------------------------------------
\1\ According to the Taylor expansion, the risk weights are calculated
as \1/2\ (modified duration x assumed interest rate change) \2\/100.
(iii) For options with equities as the underlying, delta-
weighted option positions should be incorporated in the measure of
market risk set forth in section 6(b) of this appendix B. Individual
equity issues and indices should be treated as separate underlyings.
In addition to the capital requirement for delta risk, a bank should
apply a further capital charge for gamma and vega risk:
(A) For gamma risk, the net gammas that are negative for each
underlying are multiplied by 0.72 percent (in the case of an
individual equity) or 0.32 percent (in the case of an index as the
underlying) and by the square of the market value of the underlying;
(B) For volatility risk, a bank calculates the capital
requirement for vega for each underlying, assuming a proportional
shift in volatility of 25.0 percent; and
(C) The capital requirement is the absolute value of the sum of
the individual capital requirements for net negative gammas plus the
absolute value of the individual capital requirements for vega risk.
(iv) For options on foreign exchange and gold, the net delta (or
delta-based) equivalent of the total book of foreign currency and
gold options is incorporated into the measurement of the exposure in
a single currency position as set forth in section 6(c) of this
appendix B. The gamma and vega risks should be measured as follows:
(A) For gamma risk, for each underlying exchange rate, net
gammas that are negative are multiplied by 0.32 percent and by the
square of the market value of the positions;
(B) For volatility risk, a bank calculates the capital
requirements for vega for each currency pair and gold assuming a
proportional shift in volatility of 25.0 percent; and
(C) The capital requirement is the absolute value of the sum of
the individual capital requirements for net negative gammas plus the
absolute value of the sum of the individual capital requirements for
vega risk.
(v) For options on commodities, the delta-weighted positions are
incorporated in one of the measures described in section 6(d) of
this appendix B. In addition, a bank must apply a capital
requirement for gamma and vega risk:
(A) For gamma risk, net gammas that are negative for each
underlying are multiplied by 1.125 percent and by the square of the
market value of the commodity;
(B) For volatility risk, a bank calculates the capital
requirements for vega for each commodity assuming a proportional
shift in volatility of 25.0 percent; and
(C) The capital requirement is the absolute value of the sum of
the individual capital requirements for net negative gammas plus the
absolute value of the sum of the individual capital requirements for
vega risk.
(vi) Under certain conditions and to a limited extent, the OCC
may permit banks that are significant traders in options with debt
securities or interest rates as the underlying to net positive and
negative gammas and vegas across time-bands. Such netting must be
based on prudent and conservative assumptions and the bank must
materially meet the qualitative standards set forth in section 5 of
this appendix B.
(vii) A bank may base the calculation of vega risk on a
volatility ladder in which the implied change in volatility varies
with the maturity of the option. The assumed proportional shift in
volatility must be at least 25.0 percent at the short
end of the maturity spectrum. The proportional shift for longer
maturities must be at least as stringent in statistical terms as the
25.0 percent shift at the short end.
(viii) A bank should also monitor the risks of rho (the rate of
change of the value of the option with respect to the interest rate)
and theta (the rate of change of the value of the option with
respect to time).
Section 7. Reservation of authority
(a) Partial models. The OCC reserves the authority to require a
bank subject to the market risk requirements of this appendix B to
develop or use an internal market risk model, the supervisory market
risk model, or any combination thereof, for the purposes of
compliance with the capital requirements of this appendix B.29
\29\ The OCC generally expect banks with significant trading
positions to use internal market risk models for the purposes of
this appendix B.
---------------------------------------------------------------------------
(b) De minimis exposures. The OCC also may permit a bank with
negligible exposures to certain types of market risk (activities in
remote locations and minor currencies) to adopt alternative
measurements for those exposures if the alternative measurements are
able to adequately measure the risk.
(c) Multiplication factor for qualifying internal market risk
model. The OCC may increase or decrease the multiplication factor
applicable to the capital requirement under a qualifying internal
market risk model based on an assessment of the quality and historic
accuracy of the bank's risk management system.
Office of the Comptroller of the Currency.
Dated: July 10, 1995.
Eugene A. Ludwig,
Comptroller of the Currency.
FEDERAL RESERVE BOARD
12 CFR Chapter II
For the reasons set out in the preamble, parts 208 and 225 of title
12 of the Code of Federal Regulations are proposed to be amended as set
forth below.
PART 208--MEMBERSHIP OF STATE BANKING INSTITUTIONS IN THE FEDERAL
RESERVE SYSTEM (REGULATION H)
1. The authority citation for part 208 is revised to read as
follows:
Authority: 12 U.S.C. 36, 248(a), 248(c), 321-338a, 371d, 461,
481-486, 601, 611, 1814, 1823(j), 1828(o), 1831o, 1831p-1, 3105,
3310, 3331-3351, and 3905-3909; 15 U.S.C.
[[Page 38103]]
78b, 78l(b), 78l(g), 78l(i), 78o-4(c)(5), 78q, 78q-1 and 78w; 31 U.S.C.
5318; 42 U.S.C. 4012a, 4104a, 4104b, 4106, and 4128.
2. In Part 208, Sec. 208.13 is revised to read as follows:
Sec. 208.13 Capital adequacy.
The standards and guidelines by which the capital adequacy of state
member banks will be evaluated by the Board are set forth in appendix A
and appendix E to part 208 for risk-based capital purposes, and, with
respect to the ratios relating capital to total assets, in appendix B
to part 208 and in appendix B to the Board's Regulation Y, 12 CFR part
225.
3. In Part 208, Sec. 208.31 is amended by revising paragraphs (e),
(h), and (j) to read as follows:
Sec. 208.31 Definitions.
* * * * *
(e) Risk-weighted assets means total weighted risk assets, as
calculated in accordance with the Board's Capital Adequacy Guidelines
for State Member Banks: Risk-Based Measure (appendix A to this part
208) and adjusted for market risk in accordance with the Board's
Capital Adequacy Guidelines for State Member banks: Market Risk Measure
(appendix E to this part 208).
* * * * *
(h) Tier 1 risk-based capital ratio means the ratio of Tier 1
capital to weighted risk assets, as calculated in accordance with the
Board's Capital Adequacy Guidelines for State Member Banks: Risk-Based
Measure (appendix A to this part 208) and adjusted for market risk in
accordance with the Board's Capital Adequacy Guidelines for State
Member Banks: Market Risk Measure (appendix E to this part 208).
* * * * *
(j) Total risk-based capital ratio means the ratio of qualifying
total capital to weighted risk assets, as calculated in accordance with
the Board's Capital Adequacy Guidelines for State Member Banks: Risk-
Based Measure (appendix A to this part 208) and adjusted for market
risk in accordance with the Board's Capital Adequacy Guidelines for
State Member Banks: Market Risk Measure (appendix E to this part 208).
4. In part 208, Appendix A is amended by revising the first and
second paragraphs of section I. to read as follows:
Appendix A to Part 208--Capital Adequacy Guidelines for State Member
Banks: Risk-Based Measure
I. Overview
The Board of Governors of the Federal Reserve System has adopted
a risk-based capital measure to assist in the assessment of the
capital adequacy of state member banks.1 The principal
objectives of this measure are to (i) make regulatory capital
requirements more sensitive to differences in risk profiles among
banks; (ii) factor off-balance-sheet exposures into the assessment
of capital adequacy; (iii) minimize disincentives to holding liquid,
low-risk assets; and (iv) achieve greater consistency in the
evaluation of the capital adequacy of major banks throughout the
world.
\1\ Some banks are also subject to capital requirements for
market risk as set forth in appendix E of this part. Banks that are
subject to the market risk measure are required to follow the
guidelines set forth in appendix E of this part for determining
qualifying and eligible capital, calculating market risk-equivalent
assets and adding them into weighted-risk assets, and calculating
risk-based capital ratios adjusted for market risk. Supervisory
ratios that relate capital to total assets for state member banks
are outlined in appendix B of this part and in appendix B to part
225 of the Board's Regulation Y, 12 CFR part 225.
---------------------------------------------------------------------------
The risk-based capital guidelines include both a definition of
capital and a framework for calculating weighted risk assets by
assigning assets and off-balance-sheet items to broad risk
categories.2 A bank's risk-based capital ratio is calculated by
dividing its qualifying capital (the numerator of the ratio) by its
weighted risk assets (the denominator).3 The definition of
qualifying capital is outlined below in section II. of this appendix
A, and the procedures for calculating weighted risk assets are
discussed in section III. of this appendix A. Attachment I to this
appendix A illustrates a sample calculation of weighted risk assets
and the risk-based capital ratio.
\2\ The risk-based capital measure is based upon a framework
developed jointly by supervisory authorities from the countries
represented on the Basle Committee on Banking Regulations and
Supervisory Practices (Basle Supervisors' Committee) and endorsed by
the Group of Ten Central Bank Governors. The framework is described
in a paper prepared by the Basle Supervisors' Committee entitled
``International Convergence of Capital Measurement,'' July 1988.
\3\ Banks generally are expected to utilize period-end amounts
in calculating their risk-based capital ratios. When necessary and
appropriate, ratios based on average balances may also be calculated
on a case-by-case basis. Moreover, to the extent banks have data on
average balances that can be used to calculate risk-based ratios,
the Federal Reserve will take such data into account.
---------------------------------------------------------------------------
* * * * *
5. In Part 208, a new Appendix E is added to read as follows:
Appendix E to Part 208--Capital Adequacy Guidelines for State Member
Banks: Market Risk Measure
I. Introduction
A. Overview
1. The Board of Governors of the Federal Reserve System has
adopted a framework for determining capital requirements for the
market risk exposure of state member banks.1 For this purpose,
market risk is defined as the risk of losses in a bank's on- and
off-balance-sheet positions arising from movements in market prices.
The market risks subject to these capital requirements are those
associated with debt and equity instruments held in the bank's
trading account, as well as foreign exchange risk and commodities
risk throughout the bank, including options and other derivative
contracts in each risk category.
\1\ The market risk measure is based on a framework developed
jointly by supervisory authorities from the countries represented on
the Basle Committee on Banking Supervision (Basle Supervisors
Committee) and endorsed by the Group of Ten Central Bank Governors.
The framework is described in a paper prepared by the Basle
Supervisors Committee entitled ``[Proposal to issue a] Supplement to
the Basle Capital Accord to Cover Market Risks.'' [April] 1995.
---------------------------------------------------------------------------
2. Effective December 31, 1997, the market risk measure will be
applied to all state member banks that, on a consolidated basis:
a. Have total assets in excess of $5 billion; and either have a
total volume of trading activities (measured as the sum of the
bank's trading assets and liabilities 2 on a daily average
basis for the quarter) that is 3.0 percent or more of the total
assets of the bank, or have interest rate, foreign exchange, equity,
and commodity off-balance-sheet derivative contracts relating to
trading activities whose total notional amounts exceed $5 billion;
or
\2\ As reflected in the bank's quarterly Consolidated Reports of
Condition and Income (call report).
---------------------------------------------------------------------------
b. Have total assets of $5 billion or less; and have trading
activities exceeding 10.0 percent of the total assets of the bank.
3. Such banks are still subject to the risk-based capital
measure set forth in appendix A of this part, subject to the
exclusion of certain assets specified in this appendix E. However,
these banks must calculate their market risk-equivalent assets and
determine risk-based capital ratios adjusted for market risk in
accordance with this appendix E.3
\3\ The Federal Reserve may apply all or portions of this
Appendix E to other banks when deemed necessary for safety and
soundness purposes.
---------------------------------------------------------------------------
4. The market risk measure provides two ways for a bank to
determine its exposure to market risk. A bank may use its internal
risk measurement model, subject to the conditions and criteria set
forth in section III. of this appendix E (referred to as the
internal models approach), or when appropriate, a bank may use all
or portions of the alternative measurement system described in
section IV. of this appendix E (referred to as the standardized
approach).
a. With prior approval from the Federal Reserve, for regulatory
capital purposes, a bank may use its internal risk measurement model
to measure its value-at-risk 4 for each of the following risk
factor categories; interest rates, exchange rates, equity prices,
and commodity prices. The value-at-risk amount for each risk factor
category should include volatilities of related options. The value-
at-risk amount for each risk factor category is
[[Page 38104]]
summed to determine the aggregate value-at-risk for the bank.
\4\ A bank evaluates its current positions and estimates future
market volatility through a value-at-risk measure, which is an
estimate representing, with a certain degree of statistical
confidence, the maximum amount by which the market value of trading
positions could decline during a specific period of time. The value-
at-risk is generated through an internal model that employs a series
of market risk factors (for example, market rates and prices that
affect the value of trading positions).
---------------------------------------------------------------------------
b. The standardized approach uses a set of standardized
calculations and assumptions to measure market risk exposure
depending on its source; debt instruments, equities, foreign
currencies, and commodities, including volatilities of related
options.
5. The Board generally expects any bank that is subject to the
market risk measure, especially those with large trading accounts,
to comply with the measure by using internal risk-measurement
models. A bank may not change its measurement approach for the
purpose of minimizing capital requirements. In limited instances, on
a case-by-case basis, the Federal Reserve may permit a bank that has
internal models to incorporate risk measures of negligible
exposures, for example, de minimis positions, activities in remote
locations, minor exposures in a currency, or activities that present
negligible risk to the bank, in an alternative manner, so long as it
adequately captures the risk.
6. The risk-based capital ratios adjusted for market risk
determined in accordance with this appendix E are minimum
supervisory ratios. Banks generally are expected to operate with
capital positions well above the minimum ratios. In all cases, banks
should hold capital commensurate with the level and nature of the
risks to which they are exposed.
7. The Federal Reserve will monitor the implementation and
effect of these guidelines in relation to domestic and international
developments in the banking industry. When necessary and
appropriate, the Board will consider the need to modify this
appendix E in light of any significant changes in the economy,
financial markets, banking practices, or other relevant factors.
B. Market Risks Subject to a Capital Requirement
1. General Market Risk and Specific Risk. A bank must hold
capital against exposure to general market risk and specific risk
arising from its trading and other foreign exchange and commodity
activities. For this purpose, general market risk refers to changes
in the market value of covered transactions resulting from market
movements, such as changing levels of market interest rates, broad
equity indices, or currency exchange rates. Specific risk refers to
credit risk, that is, the risk that the issuer of a debt or equity
instrument might default, as well as to other factors that affect
the market value of specific instruments but that do not materially
alter market conditions.5
\5\ This appendix E does not impose specific risk capital
requirements for foreign exchange risk and commodities positions
because they do not have the type of issuer-specific risk associated
with debt and equity instruments in the trading account.
---------------------------------------------------------------------------
2. Trading Activities. a. The general market risk and specific
risk capital requirements for trading activities are based on on-
and off-balance-sheet positions in a bank's trading account. For
this purpose, trading account means positions in financial
instruments acquired with the intent to resell in order to profit
from short-term price movements (or other price or interest-rate
variations), including, but not limited to:
i. Assets acquired with the intent to resell to customers;
ii. Positions in financial instruments arising from matched
principal brokering and market making; or
iii. Positions taken in order to hedge other elements of the
trading account (that is, reduce risk by offsetting other positions
that have exposure to changes in market rates or prices).6
Trading activities may include positions in debt instruments,
equities, foreign currencies, and commodity instruments, or related
derivative 7 or other off-balance-sheet contracts.
\6\ At a bank's option, when non-trading account instruments are
hedged with instruments in the trading account, on- or off-balance-
sheet, the non-trading account instruments may be included in the
measure for general market risk. Such non-trading account
instruments remain subject to the credit risk capital requirements
of appendix A of this part.
\7\ In general terms, a derivative is a financial contract whose
value is derived from the values of one or more underlying assets or
reference rates or indexes of asset values (referred to as ``the
underlying''). Derivatives include standardized contracts that are
traded on exchanges and customized, privately negotiated contracts
known as over-the-counter (OTC) derivatives.
---------------------------------------------------------------------------
b. Debt instruments in the trading account are all fixed-rate
and floating-rate debt securities and instruments that behave like
debt, including non-convertible preferred stock. Convertible bonds,
i.e., preferred stock or debt issues that are convertible, at a
stated price, into common shares of the issuer, should be treated as
debt instruments if they trade like debt instruments and as equities
if they trade like equities. Also included are derivative contracts
of debt instruments and other off-balance-sheet instruments in the
trading account that react to changes in interest rates. A security
that has been sold subject to a repurchase agreement or lent subject
to a securities lending agreement is treated as if it were still
owned by the lender of the security. Such transactions remain
subject to capital requirements for credit risk for the off-balance-
sheet portion of the transaction as set forth in section III.D. of
appendix A of this part.
c. Equities in the trading account are equity instruments that
behave like equities. The instruments covered include common stocks
(whether voting or non-voting), convertible securities that behave
like equities, and commitments to buy or sell equity securities.
Also included are derivative contracts of equity instruments and
other off-balance-sheet instruments in the trading account that are
affected by changes in equity prices. However, non-convertible
preferred stock is included in debt instruments.
3. Foreign Exchange and Commodities Risk. Foreign exchange or
commodities positions, whether or not included in a bank's trading
account, are subject to a capital requirement for the market risk of
those positions.
a. The capital requirement for foreign exchange risk applies to
a bank's total currency and gold positions. This includes spot
positions (that is, asset items and liability items, including
accrued interest and expenses, denominated in each currency);
forward positions (that is, forward foreign exchange transactions,
including currency futures and the principal on currency swaps not
included in the spot position); and certain guarantees. It includes
future income and expenses from foreign currency transactions not
yet accrued but already fully hedged (at the discretion of the
reporting bank), foreign exchange derivative and other off-balance-
sheet positions that are affected by changes in exchange rates, and
any other item representing a profit or loss in foreign currencies.
b. A bank may, subject to approval by the Federal Reserve,
exclude from its foreign exchange positions any structural positions
in foreign currencies. For this purpose, such structural positions
are limited to transactions designed to hedge a bank's capital
ratios against the effect of adverse exchange rate movements on
subordinated debt, equity, or minority interests in consolidated
subsidiaries and dotation capital assigned to foreign branches that
are denominated in foreign currencies. Also included are any
positions related to unconsolidated subsidiaries and to other items
that are deducted from a bank's capital when calculating its capital
base. In any event, such structural foreign currency positions must
reflect long-term policies of the institution and not relate to
trading positions.
c. A bank doing negligible business in foreign currency and that
does not take foreign exchange positions for its own account may be
exempted from the capital requirement for foreign exchange risk
provided that:
i. Its foreign currency business, defined as the greater of the
sum of its gross long positions and the sum of its gross short
positions in all foreign currencies, does not exceed 100 percent of
eligible capital as defined in section II. of this appendix E; and
ii. Its overall net open foreign exchange position as determined
in section IV.C.2. of this appendix E does not exceed 2.0 percent of
its eligible capital.
d. The capital requirement for commodities risk applies to a
bank's total commodities positions, including commodity futures,
commodity swaps, and all other commodity derivatives or other off-
balance-sheet positions that are affected by changes in commodity
prices. A commodity is defined as a physical product that is or can
be traded on a secondary market (such as agricultural products,
minerals (including oil), and precious metals), but excluding gold
(which is treated as foreign exchange).
C. Capital Requirements
1. Capital Requirements. The minimum capital requirement for a
state member bank subject to the market risk measure is the sum of:
a. The capital requirement for credit risk as determined in
accordance with appendix A of this part, excluding debt and equity
instruments in the trading book and positions in commodities, but
including the counterparty credit risk requirements on all over-the-
counter derivative activities whether in the bank's trading account
or not; and
b. The capital requirement for market risk as determined by the
internal models approach, the standardized approach, or a
[[Page 38105]]
combination of the two approaches deemed to be appropriate by the
Federal Reserve.
2. Internal Models. a. For a bank approved to use the internal
models approach, the capital requirement for market risk is the
higher of:
i. The bank's previous day's aggregate value-at-risk amount
calculated subject to certain supervisory requirements set forth in
section III. of this appendix E; or
ii. An average of the daily aggregate value-at-risk amounts,
calculated subject to the same restrictions, measured on each of the
preceding sixty (60) business days, multiplied by a minimum
``multiplication factor'' of three (3).8
\8\ The Federal Reserve may adjust the multiplication factor for
a bank to increase its capital requirement based on an assessment of
the quality and historic accuracy of the bank's risk management
system.
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b. A bank approved to use the internal models approach may also
be subject to a separate capital requirement for specific market
risk of traded debt and equity instruments to the extent that the
specific market risk associated with these instruments is not
captured by the bank's models. However, for all banks using internal
models, the total specific risk charge should in no case be less
than one-half the specific risk charges calculated according to the
standardized approach.
3. Standardized approach. A bank whose model has not been
approved by the Federal Reserve must use the standardized approach
for measuring its market risk. For a bank using this approach, the
capital requirement for market risk is the sum of the market risk
capital requirement for debt and equity instruments in the trading
account, foreign exchange and commodities risk throughout the bank,
and options and other derivative positions in each risk category as
set forth in sections IV.A. to IV.E. of this appendix E.9
\9\ Section IV.E. of this appendix E provides several
alternatives for measuring the market risk of options. Under two of
the alternatives, the simplified and scenario methods, the
underlying position of an option is ``carved-out,'' and is not
included in the prescribed risk measure for the underlying. Instead
it is evaluated together with the related option according to the
procedures described for options to determine the capital
requirement. Under the third alternative, the ``delta-plus''
approach, the delta-equivalent value of each position is included in
the measurement framework for the appropriate risk category (that
is, debt or equity instruments in the trading account, foreign
exchange or commodities risk).
---------------------------------------------------------------------------
4. Partial models. a. With approval from the Federal Reserve, a
bank whose internal model does not cover all risk factor categories
may use the standardized approach to measure market risk exposure
arising from the risk factor categories that are not covered. The
Federal Reserve will approve combining the two approaches only on a
temporary basis in situations where the bank is developing, but has
not fully implemented, a comprehensive value-at-risk measurement
system. When a bank uses both approaches, each risk factor category
(that is, interest rates, exchange rates, equity prices, and
commodity prices) must be measured using one or the other approach.
The methods may not be combined within a risk factor category. Once
a bank adopts an acceptable value-at-risk model for a particular
risk factor category, it may not revert to the standardized approach
except in unusual circumstances and with prior approval of the
Federal Reserve.
b. For a bank using a combination of approaches, the capital
requirement for market risk is the sum of (i) the appropriate value-
at-risk amount (as determined under section I.C.2.a. of this
appendix E), and (ii) the capital requirement for each risk category
that is calculated using the standardized approach.
5. Application. The capital requirements for market risk apply
to state member banks on a worldwide consolidated basis. The Federal
Reserve may, however, evaluate market risk on an unconsolidated
basis when necessary. For example, when there are obstacles to the
repatriation of profits from a foreign subsidiary or where
management structure does not allow timely management of risk on a
consolidated basis.
6. Other considerations. All transactions, including forward
sales and purchases, should be included in the calculation of market
risk capital requirements from the date on which they were entered
into. The Federal Reserve expects a bank to meet its capital
requirements for market risk on a continuous basis (that is, at a
minimum, at the close of each business day).
II. Qualifying Capital and the Market Risk-Adjusted Capital Ratio
A. Qualifying and Eligible Capital
1. The principal forms of qualifying capital for market risk are
Tier 1 capital and Tier 2 capital as defined in section II. of
appendix A of this part and subject to the conditions and
limitations of appendix A of this part. A bank may use Tier 3
capital for the sole purpose of meeting a portion of the capital
requirements for market risk.10
\10\ A bank may not use Tier 3 capital to satisfy any capital
requirements for counterparty credit risk under appendix A of this
part, including counterparty credit risk associated with derivative
transactions in either trading or non-trading accounts.
---------------------------------------------------------------------------
2. Tier 3 capital consists of short-term subordinated debt that
is subject to a lock-in clause providing that neither interest nor
principal payment is due (even at maturity) if such payment would
cause the issuing bank to fall or remain below the minimum 8.0
percent risk-based capital requirement as set forth in appendix A
and adjusted for market risk.
3. In order to qualify as Tier 3 capital, the short-term debt
must be unsecured, subordinated, and fully paid up; it must have an
original maturity of at least two years; and it may not be redeemed
before maturity without prior approval by the Federal Reserve. In
addition, it may not contain or be covered by any covenants, terms,
or restrictions that are inconsistent with safe and sound banking
practices.
4. Eligible Tier 3 capital may not exceed 250 percent of a
bank's Tier 1 capital allocated for market risk and the maximum
eligible amount of Tier 2 and Tier 3 capital together is limited to
100 percent of Tier 1 capital. (Examples of how to calculate these
limits are set forth in Attachment I to this appendix E.) Tier 2
elements may be substituted for Tier 3 up to the same limit of 250
percent, so long as the overall limits for Tier 2 capital set forth
in appendix A of this part are not exceeded, that is, Tier 2 capital
may not exceed total Tier 1 capital, and long-term subordinated debt
may not exceed 50 percent of Tier 1 capital.
B. Calculation of Eligible Capital and the Capital Ratio
1. In order to calculate eligible capital, a bank must first
calculate its minimum capital requirement for credit risk in
accordance with appendix A of this part and then its capital
requirement for market risk. Eligible capital is the sum of the
bank's qualifying Tier 1 capital, its qualifying Tier 2 capital
subject to the limits stated above, and its eligible Tier 3 capital
subject to the conditions set out under section II. of this appendix
E.
2. A bank that is subject to the market risk measure must
calculate its risk-based capital ratios as follows:
a. Determine total weighted-risk assets using the procedures and
criteria set forth in appendix A of this part, excluding debt and
equity instruments in the trading book and positions in commodities,
but including all over-the-counter derivative activities whether in
the bank's trading account or not.
b. Calculate the measure for market risk using the internal
models approach, the standardized approach, or an approved
combination of these two approaches.
c. Multiply the measure for market risk by 12.5 (i.e., the
reciprocal of the 8.0 percent minimum risk-based capital ratio). The
resulting product is referred to as ``market risk-equivalent
assets.''
d. Add market risk-equivalent assets to the weighted-risk assets
compiled for credit risk purposes (section II.B.2.a. of this
appendix E). The sum of these two amounts is the denominator of
risk-based capital ratios adjusted for market risk. The numerator of
the total risk-based capital ratio is eligible capital and the
numerator of the Tier 1 risk-based capital ratio is Tier 1 capital.
III. The Internal Models Approach
A. Use of Models
1. With prior approval of the Federal Reserve, a bank may use
its internal risk measurement model(s) for purposes of measuring
value-at-risk and determining the associated regulatory capital
requirements for market risk exposure.
a. Requests for approval under section III.A.1. of this appendix
E should include, at a minimum, a complete description of the bank's
internal modeling and risk management systems and how these systems
conform to the criteria set forth in this section III., an
explanation of the policies and procedures established by the bank
to ensure continued compliance with such criteria, a discussion of
internal and external validation procedures, and a description of
other relevant policies and procedures consistent with sound
practices.
b. The Federal Reserve will approve an internal model for
regulatory capital
[[Page 38106]]
purposes only after determining that the bank's internal model and risk
management systems meet the criteria in section III. of this
appendix E. Such a determination may require on-site examinations of
the systems. The Federal Reserve may require modification to an
internal model as deemed necessary to ensure compliance, on a
continuing basis, with the provisions of this appendix E. A bank's
internal model will be subject to continuing review, both on- and
off-site, by the Federal Reserve.11
\11\ Banks that need to modify their existing modeling
procedures to accommodate the requirements of this appendix E
should, nonetheless, continue to use the internal models they
consider most appropriate in evaluating risks for other purposes.
---------------------------------------------------------------------------
2. A bank should ensure that the level of sophistication of its
internal model is commensurate with the nature and volume of the
bank's trading activity in the risk factor categories covered by
this appendix E and measures market risk as accurately as possible.
In addition, the model should be adjusted to reflect changing
portfolio composition and changing market conditions.
B. Qualitative Criteria
1. A bank using the internal models approach should have market
risk management systems that are conceptually sound and implemented
with integrity. Internal risk measurement models must be closely
integrated into the day-to-day risk management process of the bank.
For example, the risk measurement model must be used in conjunction
with internal trading and exposure limits.
2. A bank must meet the following minimum qualitative criteria
before using its internal model to measure its exposure to market
risk.12
\12\ If the Federal Reserve is not satisfied with the extent to
which a bank meets these criteria, the Federal Reserve may adjust
the multiplication factor used to calculate market risk capital
requirements or otherwise increase capital requirements.
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a. A bank must have a risk control unit that is independent from
business trading units and reports directly to senior management of
the bank. The unit must be responsible for designing and
implementing the bank's risk management system and analyzing daily
reports on the output of the bank's risk measurement model in the
context of trading limits. The unit must conduct regular back-
testing.13
\13\ Back-testing includes ex post comparisons of the risk
measures generated by the model against the actual daily changes in
portfolio value.
---------------------------------------------------------------------------
b. Senior management must be actively involved in the risk
control process. The daily reports produced by the risk management
unit must be reviewed by a level of management with sufficient
authority to enforce both reductions in positions taken by
individual traders, as well as in the bank's overall risk exposure.
c. The bank must have a routine and rigorous program of stress-
testing 14 to identify the effect of low-probability events on
the bank's trading portfolio. Senior management must routinely
review the results of stress-testing in the context of the potential
effect of the events on bank capital and the appropriate procedures
the bank should take to minimize losses. The policies of the bank
set by management and the board of directors should identify
appropriate stress-tests and the procedures to follow in response to
the test results.
14 Bank stress-testing should cover a range of factors
that can create extraordinary losses or gains in trading portfolios
or make the control of risk in those portfolios difficult. These
factors include low-probability events of all types, including the
various components of market, credit, and operational risks.
---------------------------------------------------------------------------
d. The bank must have established procedures for ensuring
compliance with a documented set of internal policies and controls,
as well as for monitoring the overall operation of the risk
measurement system.
e. Not less than once a year, the bank must conduct, as part of
its regular internal audit process, an independent review of the
risk measurement system. This review must include both the
activities of the business trading units and of the independent risk
control unit of the bank.
f. Not less than once a year, the bank must conduct a review of
its overall risk management process. The review must consider:
i. The adequacy of the documentation of the risk management
system and process and the organization of the risk control unit;
ii. The integration of market risk measures into daily risk
management and the integrity of the management information system;
iii. The process the bank employs for approving risk pricing
models and valuation systems that are used by front- and back-office
personnel;
iv. The scope of market risks captured by the risk measurement
model and the validation of any significant changes in the risk
measurement process;
v. The accuracy and completeness of position data, the accuracy
and appropriateness of volatility and correlation assumptions, and
the accuracy of valuation and risk sensitivity calculations;
vi. The verification process the bank employs to evaluate the
consistency, timeliness, and reliability of data sources used to run
internal models, including the independence of such data sources;
and
vii. The verification process the bank uses to evaluate back-
testing that is conducted to assess the model's accuracy.
C. Market Risk Factors
1. Overview. For regulatory capital purposes, a bank's internal
risk measurement system(s) must use sufficient risk factors to
capture the risks inherent in the bank's portfolio of on- and off-
balance-sheet trading positions and must, subject to the following
guidelines, cover interest rates, equity prices, exchange rates,
commodity prices, and volatilities related to options positions in
each risk factor category. The level of sophistication of the bank's
risk factors must be commensurate with the nature and scope of the
risks taken by the bank.
2. Interest Rates. a. A bank must use a set of market risk
factors corresponding to interest rates in each currency in which it
has material interest rate-sensitive on- or off-balance- sheet
positions. The risk measurement system must model the yield curve
15 using one of a number of generally accepted approaches, for
example, by estimating forward rates of zero coupon yields. The
yield curve must be divided into various maturity segments in order
to capture variation in the volatility of rates along the yield
curve; there will typically be one risk factor corresponding to each
maturity segment.
15 Generally, a yield curve is a graph showing the term
structure of interest rates by plotting the yields of all
instruments of the same quality by maturities ranging from the
shortest to the longest available. The resulting curve shows whether
short-term interest rates are higher or lower than long-term
interest rates.
---------------------------------------------------------------------------
b. For material exposures to interest rate movements in the
major currencies and markets, a bank must model the yield curve
using a minimum of six risk factors. However, the number of risk
factors used should ultimately be driven by the nature of the bank's
trading strategies.16 The risk measurement system must
incorporate separate risk factors to capture spread risk.17
16 For example, a bank that has a portfolio of various types of
securities across many points of the yield curve and that engages in
complex arbitrage strategies would require a greater number of risk
factors to capture interest rate risk accurately.
17 Spread risk refers to the potential changes in value of
an instrument or portfolio arising from differences in the behavior
of baseline yield curves, such as those for U.S. Treasury
securities, and yield curves reflecting sector, quality, or
instrument specific factors. A variety of approaches may be used to
capture the spread risk arising from less than perfectly correlated
movements between government and other interest rates, such as
specifying a completely separate yield curve for non-government
instruments (for example, swaps or municipal securities) or
estimating the spread over government rates at various points along
the yield curve.
---------------------------------------------------------------------------
3. Exchange rates. A bank must use market risk factors
corresponding to the exchange rate between the domestic currency and
each foreign currency in which the bank has a significant exposure.
The risk measurement system must incorporate market risk factors
corresponding to the individual foreign currencies in which the
bank's positions are denominated.
4. Equity prices. A bank must use market risk factors
corresponding to each of the equity markets in which it holds
significant positions. The sophistication and nature of the modeling
technique for a given market must correspond to the bank's exposure
to the overall market as well as to the bank's concentration in
individual equity issues in that market. At a minimum, there must be
a risk factor designed to capture market-wide movements in equity
prices (such as a market index), but additional risk factors could
track various sectors or individual issues.
5. Commodity prices. A bank must use market risk factors
corresponding to each of the commodity markets in which it holds
significant positions. The internal model must encompass directional
risk, forward gap and interest rate risk, and basis risk.18 The
[[Page 38107]]
model should also take into account the market characteristics, for
example, delivery dates and the scope provided to traders to close
out positions.
18 Directional risk is the risk that a spot price will
increase or decrease. Forward gap risk refers to the effects of
owning a physical commodity versus owning a forward position in a
commodity. Interest rate risk is the risk of a change in the cost of
carrying forward positions and options. Basis risk is the risk that
the relationship between the prices of similar commodities changes
over time.
---------------------------------------------------------------------------
D. Quantitative Standards
1. A bank may use one of a number of generally accepted
measurement techniques including, for example, an internal model
based on variance-covariance matrices, historical simulations, or
Monte Carlo simulations so long as the model employed captures all
the material market risks.19 The following minimum standards
apply for purposes of using an internal model for calculating market
risk capital requirements:
19 In a variance/covariance approach, the change in value
of the portfolio is calculated by combining the risk factor
sensitivities of the individual positions--derived from valuation
models--with a variance/covariance matrix based on risk factor
volatilities and correlations. A bank using this approach would
calculate the volatilities and correlations of the risk factors on
the basis of the holding period and the observation period. A bank
using a historical simulation would calculate the hypothetical
change in value of the current portfolio in the light of historical
movements in risk factors. This calculation would be done for each
of the defined holding periods over a given historical measurement
horizon to arrive at a range of simulated profits and losses. A bank
using a Monte Carlo technique would consider historical movements to
determine the probability of particular price and rate changes.
---------------------------------------------------------------------------
a. Value-at-risk must be calculated on a daily basis using a
99th percentile, one- tailed confidence interval 20 and the
holding period must be ten trading days. For positions that display
linear price characteristics, a bank may use value-at-risk numbers
calculated according to shorter holding periods scaled up to ten
days by the square root of time.21
20 A one-tailed confidence interval of 99 percent means that
there is a 1 percent probability based on historical experience that
the combination of positions in a bank's portfolio would result in a
loss higher than the measured value-at-risk.
21 This transformation entails multiplying a bank's value-
at-risk by the square root of the ratio of the required holding
period (ten days) to the holding period embodied in the value-at-
risk figure. For example, the value-at-risk calculated according to
a one-day holding period would be scaled-up by the ``square root of
time'' by multiplying the value-at-risk by 3.16 (the square root of
the ratio of a ten-day holding period to a one-day holding period).
---------------------------------------------------------------------------
b. Value-at-risk must be calculated using an observation period
of at least one year to measure historical changes in rates and
prices.
c. A bank must update its historical rates and prices at least
once every three months and must reassess them whenever market
conditions change materially.
2. A bank may use discretion in recognizing empirical
correlations within each market risk factor category.22
However, empirical correlations among risk categories are not
recognized. The value-at-risk measure for each risk category must be
added together on a simple sum basis to determine the aggregate
value-at-risk amount.
22 While a bank has flexibility to use correlations, the
Federal Reserve must be satisfied that there is integrity in the
bank's process for calculating correlations.
---------------------------------------------------------------------------
3. A bank's models must accurately capture the unique risks
associated with options within each of the market risk factor
categories. The following minimum criteria apply to the measurement
of options risk:
a. A bank's internal model must capture the non-linear price
characteristics of option positions using an options pricing
technique. The bank must apply a minimum ten-day holding period to
option positions or positions that display option-like
characteristics. Banks may not scale-up the daily value-at-risk
numbers by the square root of time.
b. A bank's internal model must capture the volatilities of the
rates and prices (that is, the vega) underlying option positions and
a bank should measure the volatilities of the underlying instruments
broken down by different option maturities.
4. The accuracy of a bank's internal model will be reviewed
periodically by the Federal Reserve. Such review, during which, when
appropriate, the Federal Reserve may take into consideration reports
and opinions generated by external auditors or qualified
consultants, will include, at a minimum:
a. Verification that the internal validation processes described
in section III.B.2. of this Appendix E are operating in a
satisfactory manner;
b. Affirmation that the formulae used in the calculation process
and for the pricing of options and other complex instruments, are
validated by a qualified unit of the bank, which in all cases must
be independent from the trading areas;
c. Confirmation that the structure of the internal model is
adequate with respect to the bank's activities and geographical
coverage;
d. Confirmation that the results of the bank's back-testing of
its internal measurement system (that is, comparing value-at-risk
estimates with actual profits and losses) are being used effectively
to monitor reliability of the model's estimates over time; and
e. Affirmation that, for regulatory capital purposes, the model
processes all relevant data and that the modeling procedures conform
with the parameters and specifications set forth in this appendix E.
IV. The Standardized Approach
A. Debt Instruments
1. Specific Risk. a. The capital requirement for specific risk
is based on the identity of the obligor and, in the case of
corporate securities, on the credit rating and maturity of the
instrument. The specific risk capital requirement is calculated by
weighting the current market value of each individual position,
whether long or short, by the appropriate category factor as set
forth below and summing the weighted values. In measuring specific
risk, the bank may offset and exclude from its calculations any
matched positions in the identical issue (including positions in
derivatives). Even if the issuer is the same, no offsetting is
permitted between different issues since differences in coupon
rates, liquidity, call features, etc., mean that prices may diverge
in the short run. The categories and factors are:
------------------------------------------------------------------------
Factor
Category Remaining maturity (In
(contractual) percent)
------------------------------------------------------------------------
Government.............................. N/A................. 0.00
Qualifying.............................. 6 months or less.... 0.25
6 to 12 months...... 1.00
Over 12 months...... 1.60
Other................................... N/A................. 8.00
------------------------------------------------------------------------
b. The government category includes all forms of debt
instruments of central governments of the OECD-based group of
countries 23 including bonds, Treasury bills and other short-
term instruments, as well as local currency instruments of non-OECD
central governments to the extent that the bank has liabilities
booked in that currency.
\23\ The OECD-based group of countries is defined in section
III.B.1. of appendix A of this part.
---------------------------------------------------------------------------
c. The qualifying category includes securities of U.S.
government-sponsored agencies, general obligation securities issued
by states and other political subdivisions of the OECD-based group
of countries, multilateral development banks, and debt instruments
issued by U.S. depository institutions or OECD-banks that do not
qualify as capital of the issuing institution.24 It also
includes other securities, including revenue securities issued by
states and other political subdivisions of the OECD-based group of
countries, that are rated investment- grade by at least two
nationally recognized credit rating services, or rated investment-
grade by one nationally recognized credit rating agency and not less
than investment-grade by any other credit rating agency, or, with
the exception of securities issued by U.S. firms and subject to
review by the Federal Reserve, unrated but deemed to be of
comparable investment quality by the reporting bank and the issuer
has securities listed on a recognized stock exchange.
\24\ U.S. government-sponsored agencies, multilateral
development banks, and OECD banks are defined in section III.C.2. of
appendix A of this part.
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d. The other category includes debt securities not qualifying as
government or qualifying securities. This would include non-OECD
central government securities that do not meet the criteria for the
government or qualifying categories. This category also includes
instruments that qualify as capital issued by other banking
organizations.
e. The Federal Reserve will consider the extent of a bank's
position in non-investment grade instruments (sometimes referred to
as high yield debt). If those holdings are not well-diversified or
otherwise represent a material position to the institution, the
Federal Reserve may prevent a bank from offsetting positions in
these instruments with other positions in qualifying instruments
that may be offset when calculating its general market risk
requirement. In addition, the Board may impose a specific risk
capital requirement as high as 16.0 percent.
2. General Market Risk. a. A bank may measure its exposure to
general market risk using, on a continuous basis, either the
[[Page 38108]]
maturity method (which uses standardized risk weights that approximate
the price sensitivity of various instruments) or the duration method
(where the institution calculates the precise duration of each
instrument, weighted by a specified change in interest rates).
b. Both methods use a maturity-ladder that incorporates a series
of ``time-bands'' and ``zones'' to group together securities of
similar maturities and that are designed to take into account
differences in price sensitivities and interest rate volatilities
across different maturities. Under either method, the capital
requirement for general market risk is the sum of a base charge that
results from fully netting various risk-weighted positions and a
series of additional charges (add-ons), which effectively
``disallow'' part of the previous full netting to address basis and
yield curve risk.
c. For each currency in which a bank has significant positions,
a separate capital requirement must be calculated. No netting of
positions is permitted across different currencies. Offsetting
positions of the same amount in the same issues, whether actual or
notional, may be excluded from the calculation, as well as closely
matched swaps, forwards, futures, and forward rate agreements (FRAs)
that meet the conditions set out in section IV.A.3. of this Appendix
E.
d. In the maturity method, the bank distributes each long or
short position (at current market value) of a debt instrument into
the time-bands of the maturity ladder. Fixed-rate instruments are
allocated according to the remaining term to maturity and floating-
rate instruments according to the next repricing date. A callable
bond trading above par is slotted according to its first call date,
while a callable bond priced below par is slotted according to
remaining maturity. Fixed-rate mortgage-backed securities, including
collateralized mortgage obligations (CMOs) and real estate mortgage
investment conduits (REMICs), are slotted according to their
expected weighted average lives.
e. Once all long and short positions are slotted into the
appropriate time-band, the long positions in each time-band are
summed and the short positions in each time-band are summed. The
summed long and/or short positions are multiplied by the appropriate
risk-weight factor (reflecting the price sensitivity of the
positions to changes in interest rates) to determine the risk-
weighted long and/or short position for each time-band. The risk
weights for each time-band are set out in Table I below:
Table I.--Maturity Method: Time-Bands and Weights
------------------------------------------------------------------------
Risk
Zone Coupon 3% or more Coupon less than 3% and weights
zero coupon bonds [percent]
------------------------------------------------------------------------
1....... up to 1 month........... up to 1 month.......... 0.00
1 up to 3 months........ 1 up to 3 months....... 0.20
3 up to 6 months........ 3 up to 6 months....... 0.40
6 up to 12 months....... 6 up to 12 months...... 0.70
2....... 1 up to 2 years......... 1 up to 1.9 years...... 1.25
2 up to 3 years......... 1.9 up to 2.8 yrs...... 1.75
3 up to 4 years......... 2.8 up to 3.6 yrs...... 2.25
3....... 4 up to 5 years......... 3.6 up to 4.3 yrs...... 2.75
5 up to 7 years......... 4.3 up to 5.7 yrs...... 3.25
7 up to 10 years........ 5.7 up to 7.3 yrs...... 3.75
10 up to 15 years....... 7.3 up to 9.3 yrs...... 4.50
15 up to 20 years....... 9.3 up to 10.6 yrs..... 5.25
Over 20 years........... 10.6 up to 12 yrs...... 6.00
12 up to 20 yrs........ 8.00
Over 20 years.......... 12.50
------------------------------------------------------------------------
f. Within each time-band for which there are risk-weighted long
and short positions, the risk-weighted long and short positions are
then netted, resulting in a single net risk-weighted long or short
position for each time-band. Since different instruments and
different maturities may be included and netted within each time-
band, a capital requirement, referred to as the vertical
disallowance, is assessed to allow for basis risk. The vertical
disallowance capital requirement is 10.0 percent of the position
eliminated by the intra-time-band netting, that is, 10.0 percent of
the smaller of the net risk-weighted long or net risk-weighted short
position, or if the positions are equal, 10.0 percent of either
position.25 The vertical disallowances for each time-band are
absolute values, that is, neither long nor short. The vertical
disallowances for all time- bands in the maturity ladder are summed
and included as an element of the general market risk capital
requirement.
25 For example, if the sum of the weighted longs in a
time-band is $100 million and the sum of the weighted shorts is $90
million, the vertical disallowance for the time-band is 10.0 percent
of $90 million, or $9 million.
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g. Within each zone for which there are risk-weighted long and
short positions in different time-bands, the weighted long and short
positions in all of the time-bands within the zone are then netted,
resulting in a single net long or short position for each zone.
Since different instruments and different maturities may be included
and netted within each zone, a capital requirement, referred to as
the horizontal disallowance, is assessed to allow for the imperfect
correlation of interest rates along the yield curve. The horizontal
disallowance capital requirement is calculated as a percentage of
the position eliminated by the intra-zone netting, that is, a
percentage of the smaller of the net risk-weighted long or net risk-
weighted short position, or if the positions are equal, a percentage
of either position.26 The percent disallowance factors for
intra-zone netting are set out in Table II in section IV.A.2.h. of
this Appendix E. The horizontal disallowances, like the vertical
disallowances, are absolute values that are summed and included as
an element of the general market risk capital requirement.
\26\ For example, if the sum of the weighted longs in the 1-3
month time-band in Zone 1 is $8 million and the sum of the weighted
shorts in the 3-6 month time-band is $10 million, the horizontal
disallowance for the zone if forty percent of $8 million, or $3.2
million.
---------------------------------------------------------------------------
h. Risk-weighted long and short positions in different zones are
then netted between the zones. Zone 1 and zone 2 are netted if
possible, reducing or eliminating the net long or short position in
zone 1 or zone 2 as appropriate. Zone 2 and zone 3 are then netted
if possible, reducing or eliminating the net long or short position
in zone 2 or zone 3 as appropriate. Zone 3 and zone 1 are then
netted if possible, reducing or eliminating the long or short
position in zone 3 and zone 1 as appropriate. A horizontal
disallowance capital requirement is then assessed, calculated as a
percentage of the position eliminated by the inter-zone netting. The
horizontal disallowance capital requirements for each zone are then
summed as absolute values and included in the general market risk
capital charge. The percent disallowance factors for inter-zone
netting are set out in Table II below:
[[Page 38109]]
Table II.--Horizontal Disallowances
------------------------------------------------------------------------
Between
Within the adjacent Between
Zone Time-band zone zones zones 1-3
(percent) (percent) (percent)
------------------------------------------------------------------------
1....... 0-1 month.............. 40 40 100
1-3 months
3-6 months
6-12 months
2....... 1-2 years.............. 30 40 100
2-3 years
3-4 years
3....... 1-5 years.............. 30 40 100
5-7 years
7-10 years
0-15 years
5-20 years
over 20 years
------------------------------------------------------------------------
i. Finally, the net risk-weighted long or net risk-weighted
short positions remaining in the zones are summed to reach a single
net risk-weighted long or net risk-weighted short position for the
bank's portfolio. The sum of the absolute value of this position and
the vertical and horizontal disallowances is the capital requirement
for general market risk. An example of the calculation of general
market risk under the maturity method is in Attachment II to this
appendix E.
j. In the duration method, the bank, after calculating each
instrument's modified duration 27 using a formula that is
subject to supervisory review, multiplies that modified duration by
the interest rate shock specified for an instrument of that duration
in Table III in section IV.A.2.k. of this appendix E. The resulting
product (representing the expected percentage change in the price of
the instrument for the given interest rate shock) is then multiplied
by the current market value of the instrument. The resulting amount
is then slotted as a long or short position into a time-band in the
maturity ladder in Table III on the basis of the instrument's
modified duration.28
\27\ The duration of an instrument is its approximate percentage
change in price for a 100 basis point parallel shift in the yield
curve assuming that its cash flow does not change the yield curve
shifts. Modified duration is duration divided by a factor of 1 plus
the interest rate.
\28\ For example, an instrument held by a bank with a maturity
of 4 years and 3 months and a current market value of $1,000 might
have a modified duration of 3.5 years. Based on its modified
duration, it would be subjected to the 75-basis point interest rate
shock, resulting in an expected price change of 2.625 percent (3.5
x 0.75). The corresponding expected change in price of $26.25,
calculated as 2.625 percent of $1,000, would be slotted as a long
position in the 3.3 to 4.0 year time-band of the maturity ladder.
---------------------------------------------------------------------------
k. Once all of the bank's traded debt instruments have been
slotted into the maturity ladder, the bank conducts the same rounds
of netting and disallowances described in sections IV.A.2.f. through
IV.A.2.h. of this appendix E for the maturity method, with the
exception that the vertical disallowance requirement for the
duration method is 5.0 percent (horizontal disallowances continue to
be those set out in Table II).29 As with the maturity method,
the sum of the absolute value of the final net position and the
vertical and horizontal disallowances is the general market risk
capital requirement:
\29\ Two different vertical disallowances are used since the
duration method takes into account an instrument's specific
characteristics (maturity and coupon) and there is less opportunity
for measurement error.
Table III.--Duration Method: Time-Bands and Assumed Changes in Yield
------------------------------------------------------------------------
Assumed
Zone Time-band change in
yield
------------------------------------------------------------------------
1....... Up to 1 month.................................... 1.00
1 up to 3 months................................. 1.00
3 up to 6 months................................. 1.00
6 up to 12 months................................ 1.00
2....... 1.0 up to 1.8 years.............................. 0.90
1.8 up to 2.6 years.............................. 0.80
2.6 up to 3.3 years.............................. 0.75
3....... 3.3 up to 4.0 years.............................. 0.75
4.0 up to 5.2 years.............................. 0.70
5.2 up to 6.8 years.............................. 0.65
6.8 up to 8.6 years.............................. 0.60
8.6 up to 9.9 years.............................. 0.60
9.9 up to 11.3 years............................. 0.60
11.3 up to 16.6 years............................ 0.60
Over 16.6 years.................................. 0.60
------------------------------------------------------------------------
3. Interest rate derivatives. a. Debt derivatives and other off-
balance-sheet positions that are affected by changes in interest
rates are included in the measurement system under section IV.A. of
this Appendix E (except for options and the associated underlyings,
which are included in the measurement system under the treatment
discussed in section IV.E. of this Appendix E). A summary of the
treatment for debt derivatives is set out in Attachment III to this
Appendix E.
b. Derivatives are converted into positions in the relevant
underlying instrument and are included in the calculation of
specific and general market risk capital charges as described above.
The amount to be included is the market value of the principal
amount of the underlying or of the notional underlying. For
instruments where the apparent notional amount differs from the
effective notional amount, a bank must use the effective notional
amount.
c. Futures and forward contracts (including FRAs) are broken
down into a combination of a long position and short position in the
notional security. The maturity of a future or a FRA is the period
until delivery or exercise of the contract, plus the life of the
underlying instrument.30 Where a range of instruments may be
delivered to fulfill the contract, the bank may chose which
deliverable instrument goes into the maturity or duration ladder as
the notional underlying. In the case of a future on a corporate bond
index, positions are included at the market value of the notional
underlying portfolio of securities.
\30\ For example, a long position in a June three-month interest
rate future (taken in April) is reported as a long position in a
government security with a maturity of five months an a short
position in a government security with a maturity to two months.
---------------------------------------------------------------------------
d. Swaps are treated as two notional positions in the relevant
instruments with appropriate maturities. The receiving side is
treated as the long position and the paying side is treated as the
short position.31 The separate sides of cross-currency swaps or
forward foreign exchange transactions are slotted in the relevant
maturity ladders for the currencies concerned. For swaps that pay or
receive a fixed or floating interest rate against some other
reference price, for example, an equity index, the interest rate
component is slotted into the appropriate repricing maturity
category, with the long or short position attributable to the equity
component being included in the equity framework set out in section
IV.B. of this Appendix E.32
\31\ For example, an interest rate swap under which a bank is
receiving floating-rate interest and paying fixed is treated as a
long position in a floating rate instrument with a maturity
equivalent to the period until the next interest reset date and a
short position in a fixed-rate instrument with a maturity equivalent
to the remaining life of the swap.
\32\ A bank with a large swap book may, with prior approval of
the Federal Reserve, use alternative formulae to calculate the
positions to be included in the maturity or duration ladder. For
example, a bank could first convert the payments required by the
swap into present values. For that purpose, each payment would be
discounted using zero coupon yields, and the payment's present value
entered into the apprioriate time-band using procedures that apply
to zero (or low) coupon bonds. The net amounts would then be treated
as bonds, and slotted into the general market risk framework. Such
alternative treatments will, however, only be allowed if: (i) the
Federal Reserve is fully satisified with the accuracy of the system
being used, (ii) the positions calculated fully reflect the
sensitivity of the cash flows to interest rate changes; and (iii)
the positions are denominated in the same currency.
[[Page 38110]]
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e. A bank may offset long and short positions (both actual and
notional) in identical derivative instruments with exactly the same
issuer, coupon, currency, and maturity before slotting these
positions into time-bands. A matched position in a future and its
corresponding underlying may also be fully offset and, thus,
excluded from the calculation, except when the future comprises a
range of deliverable instruments. However, in cases where, among the
range of deliverable instruments, there is a readily identifiable
underlying instrument that is most profitable for the trader with a
short position to deliver, positions in the futures contract and the
instrument may be offset. No offsetting is allowed between positions
in different currencies.
f. Offsetting positions in the same category of instruments can
in certain circumstances be regarded as matched and treated by the
bank as a single net position which should be entered into the
appropriate time-band. To qualify for this treatment the positions
must be based on the same underlying instrument, be of the same
nominal value, and be denominated in the same currency. The separate
sides of different swaps may also be ``matched'' subject to the same
conditions. In addition:
i. For futures, offsetting positions in the notional or
underlying instruments to which the futures contract relates must be
for identical instruments and the instruments must mature within
seven days of each other;
ii. For swaps and FRAs, the reference rate (for floating rate
positions) must be identical and the coupon closely matched (i.e.,
within 15 basis points); and
iii. For swaps, FRAs and forwards, the next interest reset date,
or for fixed coupon positions or forwards the remaining maturity,
must correspond within the following limits: If the reset (remaining
maturity) dates occur within one month, then the reset dates must be
on the same day; if the reset dates occur between one month and one
year later, then the reset dates must occur within seven days of
each other, or if the reset dates occur over one year later, then
the reset dates must occur within thirty days of each other.
g. Interest rate and currency swaps, FRAs, forward foreign
exchange contracts and interest rate futures are not subject to a
specific risk charge. This exemption also applies to futures on a
short-term (e.g., LIBOR) interest rate index. However, in the case
of futures contracts where the underlying is a debt security, or an
index representing a basket of debt securities, a specific risk
charge will apply according to the category of the issuer as set out
in section IV.A.1. of this Appendix E.
B. Equities
1. Specific risk. The measure of specific risk is calculated on
the basis of the bank's gross equity positions, that is, the
absolute sum of all long equity positions and of all short equity
positions at current market value.33 The specific risk capital
requirement is 8.0 percent of that sum, unless the portfolio is both
liquid and well-diversified, in which case the specific risk capital
requirement is 4.0 percent of the gross equity position. A specific
risk charge of 2.0 percent applies to the net long or short position
in a broad, diversified equity index and is viewed as necessary to
provide for risks associated with contract execution.34
\33\ Matched positions in each additional equity in each
national market may be treated as offsetting and excluded from the
capital calculation, with any remaining position included in the
calculations for specific and general market risk. For example, a
future in a given equity may be offset against an opposite cash
position in the same equity.
\34\ A portfolio that is liquid and well-diversified is
characterized by a limited sensitivity to price changes of any
single equity issue or closely related group of equity issues held
in the portfolio. The volatility of the portfolio's value should not
be dominated by the volatility of any individual equity issue or by
equity issues from any single industry or economic sector. In
general, such portfolios should be characterized by a large number
of individual equity positions, with no single position representing
a large portion of the portfolio's total market value. In addition,
it would generally be the case that a sizeable proportion of the
portfolio would be comprised of issues traded on organized exchanges
or in well-established over-the-counter markets.
---------------------------------------------------------------------------
2. General Market risk. The measure of general market risk is
based on the difference between the sum of the long positions and
the sum of the short positions (i.e., the overall net position in an
equity market) at current market value. An overall net position must
be separately calculated for each national market in which the bank
holds equities. The capital requirement for general market risk is
8.0 percent of the net position in each equity market.
3. Equity derivatives. a. Equity derivatives and other off-
balance-sheet positions that are affected by changes in equity
prices are included in the measurement system under section IV.B. of
this Appendix E (except for equity options, equity index options,
and the associated underlying, which are included in the measurement
system under the treatment discussed in section IV.E. of this
Appendix E).35 This includes futures and swaps on both
individual equities and on equity indices. Equity derivatives should
be converted into notional equity positions in the relevant
underlying. A summary of the rules for equity derivatives is set out
in Attachment III to this Appendix E.
\35\ Where equities are part of a forward contract (both
equities to be received or to be delivered), any interest rate or
foreign currency exposure from the other side of the contract should
be appropriately included in the measurement systems in sections
IV.A. and IV.C. of this Appendix E.
---------------------------------------------------------------------------
b. Futures and forward contracts relating to individual equities
should be reported at current market prices of the underlying.
Futures relating to equity indices should be reported as the marked-
to-market value of the notional underlying equity portfolio. Equity
swaps are treated as two notional positions, with the receiving side
as the long position and the paying side as the short
position.36 If one of the legs involves receiving/paying a
fixed or floating interest rate, the exposure should be slotted into
the appropriate repricing maturity band for debt securities. The
stock index is covered by the equity treatment.
\36\ For example, an equity swap in which a bank is receiving an
amount based on the change in value of one particular equity or
equity index and paying a different index will be trated as a long
position in the former and a short position in the latter.
---------------------------------------------------------------------------
c. In the case of futures-related arbitrage strategies, the 2.0
percent specific risk charge applicable to broad diversified equity
indices may be applied to only one index. The opposite position is
exempt from a specific risk charge. The strategies qualifying for
this treatment are:
i. When the bank takes an opposite position in exactly the same
index at different dates; and
ii. When the bank has an opposite position in different but
similar indices at the same date, subject to supervisory oversight.
d. If a bank engages in a deliberate arbitrage strategy, in
which a futures contract on a broad diversified equity index matches
a basket of securities, it may exclude both positions from the
standardized approach on condition that the trade has been
deliberately entered into and separately controlled and the
composition of the basket of stocks represents at least 90 percent
of the market value of the index. In such a case, the minimum
capital requirement is 4.0 percent (that is, 2.0 percent of the
gross value of the positions on each side) to reflect risk
associated with executing the transaction. This applies even if all
of the securities comprising the index are held in identical
proportions. Any excess value of the securities comprising the
basket over the value of the futures contract or excess value of the
futures contract over the value of the basket is treated as an open
long or short position.
e. If a bank takes a position in depository receipts \37\
against an opposite position in the underlying equity, it may offset
the position.
\37\ Depository receipts are instruments issued by a trust
company or other depository institution evidencing the deposit of
foreign securities and facilitating trading in such instruments on
U.S. stock exchanges.
---------------------------------------------------------------------------
C. Foreign Exchange Risk
1. The capital requirement for foreign exchange risk covers the
risk of holding or taking positions in foreign currencies, including
gold, and is based on a bank's net open long positions or net open
short positions in each currency, whether or not those positions are
in the trading portfolio, plus the net open position in gold,
regardless of sign.\38\
\38\ Gold is treated as a foreign exchange position rather than
a commodity because its volatility is more in line with foreign
currencies and banks manage it in a manner similar to foreign
currencies.
[[Page 38111]]
---------------------------------------------------------------------------
2. A bank's net open position in each currency (and gold) is
calculated by summing:
a. The net spot position (i.e., all asset items less all
liability items, including accrued interest earned but not yet
received and accrued expenses, denominated in the currency in
question);
b. All foreign exchange derivative instruments and other off-
balance-sheet positions that are affected by changes in exchange
rates are included in the measurement system under section IV.C. of
this Appendix E (except for options and their associated
underlyings, which are included in the measurement system under the
treatment discussed in section IV.E. of this Appendix E). Forward
currency positions should be valued at current spot market exchange
rates. For a bank in which the basis of its normal management
accounting is to use net present values, forward positions may be
discounted to net present values as an acceptable way of measuring
currency positions for regulatory capital purposes;
c. Guarantees (and similar instruments) that are certain to be
called and are likely to be irrevocable;
d. Net future income/expenses not yet accrued but already fully
hedged (at the discretion of the bank). A bank that includes future
income and expenses must do so on a consistent basis without
selecting expected future flows in order to reduce the bank's
position; and
e. Any other item representing a profit or loss in foreign
currencies.
3. For measuring a bank's open positions, positions in composite
currencies, such as the ECU, may be either treated as a currency in
their own right or split into their component parts on a consistent
basis. Positions in gold are measured in the same manner as
described in section IV.D. of this Appendix E.\39\
\39\ Where gold is part of a forward contract (quantity of gold
to be received or to be delivered), any interest rate or foreign
currency exposure from the other side of the contract should be
included in measurement system in section IV.A. (as a zero coupon
instrument) and IV.C. of this Appendix E.
---------------------------------------------------------------------------
4. The capital requirement is determined by converting the
nominal amount (or net present value) of the net open position in
each foreign currency (and gold) at spot rates into the reporting
currency. The capital requirement is 8.0 percent of the sum of:
a. The greater of the sum of the net short open positions or the
sum of the net long open positions (absolute values); and
b. The net open position in gold, regardless of sign.\40\
\40\ For example, a bank has the following net currency
positions: Yen=+50, DM=+100, GB=+150, FFR=-20, US$=-180, and
gold=-35. The bank would sum its long positions (total=+300) and sum
its short positions (total=-200). The bank's capital requirement for
foreign exchange market risk would be: (300 (the larger of the
summed long and short positions) +35 (gold)) x 8.0%=$26.80.
---------------------------------------------------------------------------
5. Where a bank is assessing its foreign exchange risk on a
consolidated basis, it may be technically impractical in the case of
some marginal operations to include the currency positions of a
foreign branch or subsidiary of the bank. In such cases, the
internal limit in each currency may be used as a proxy for the
positions, provided there is adequate ex post monitoring of actual
positions complying with such limits. In these circumstances, the
limits should be added, regardless of sign, to the net open position
in each currency.
D. Commodities Risk
1. Measurement methods. This section provides a minimum capital
requirement to cover the risk of holding or taking positions in
commodities. There are two methods under the standardized approach
for measuring commodity market risk--the simplified method and the
maturity method. These methods are only appropriate for banks that
conduct a limited amount of commodities business. All other banks
must adopt an internal measurement system conforming to the criteria
in section III. of this Appendix E.
2. Base capital requirement. Under both the simplified and
maturity methods, each long and short commodity position (spot and
forward) is expressed in terms of the standard unit of measurement
(such as barrels, kilos, or grams). The open positions in each
category of commodities are then converted at current spot rates
into U.S. currency, with long and short positions offset to arrive
at the net open position in each commodity. Positions in different
categories of commodities may not, generally, be offset.\41\ Under
either method, the base capital requirement is 15.0 percent of the
net open position, long or short, in each commodity.\42\
\41\ However, offsetting is permitted between different sub-
categories of the same commodity in cases where the sub-categories
are deliverable against each other.
\42\ When the funding of a commodity position opens a bank to
interest rate or foreign exchange exposure the relevant positions
should be included in the measures of interest rate and foreign
exchange risk described in sections IV.A. and IV.C. of this Appendix
E. When a commodity is part of a forward contract, any interest or
foreign currency exposure from the other side of the contract should
be appropriately included in the measurement systems in sections
IV.A. and IV.C. of this Appendix E.
---------------------------------------------------------------------------
3. Simplified method. To protect a bank against basis risk,
interest rate risk, and forward gap risk, each category of commodity
is also subject to a 3.0 percent capital requirement on the bank's
gross positions, long plus short, in the particular commodity. In
valuing gross positions in commodity derivatives for this purpose, a
bank should use the current spot price. The total capital
requirement for commodities risk is the sum of the 15.0 percent base
charges for each net commodity position and the 3.0 percent
requirements on the gross commodity positions.
4. Maturity method. a. Under this method, a bank must slot each
long and short commodity position (converted into U.S. currency at
current spot rates) into a maturity ladder. The time-bands for the
maturity ladder are; from zero to one month, one up to three months,
three up to six months, six up to twelve months, one up to two
years, two up to three years, and over three years. A separate
maturity ladder is used for each category of commodity. Physical
commodities are allocated to the first time-band.
b. In order to capture forward gap and interest rate risk within
a time-band (together sometimes referred to as curvature/spread
risk), offsetting long and short positions in each time-band are
subject to an additional capital requirement. Beginning with the
shortest-term time-band and continuing with subsequent time-bands,
the amount of the matched short position plus the amount of the
matched long position is multiplied by a spread rate of 1.5 percent.
c. The unmatched net position from shorter-term time-bands must
be carried forward to offset exposures in longer-term time-bands. A
capital requirement of 0.6 percent of the net position carried
forward is added for each time-band that the net position is carried
forward.\43\ The total capital requirement for commodities risk is
the sum of the 15.0 percent base capital requirement for each net
commodity position and the additional requirements for matched
positions and for unmatched positions carried forward. An example of
this calculation is in Attachment IV to this Appendix E.
\43\ For example, if $200 short is carried forward from the 3-6
month time-band to the 1-2 year time-band, the capital charge would
be $200 x .006 x 2=$2.40.
---------------------------------------------------------------------------
5. Commodity derivatives. Commodity derivatives and other off-
balance-sheet positions that are affected by changes in commodity
prices are included in the measurement system under section IV.D. of
this Appendix E (except for options and the associated underlying,
which are included in the measurement system under the treatment
discussed in section IV.E. of this Appendix E). Commodity
derivatives are converted into notional commodity positions. Under
the maturity method, the positions are slotted into maturity time-
bands as follows:
a. Futures and forward contracts relating to individual
commodities are incorporated in the measurement system as notional
amounts (of, for example, barrels or kilos) that are converted to
U.S. dollars at current spot rates and are assigned a maturity
according to expiration date;
b. Commodity swaps where one side of the contract is a fixed
price and the other side is the current market price are
incorporated as a series of positions equal to the notional amount
of the contract at current spot rates, with one position
corresponding to each payment on the swap and slotted in the
maturity ladder accordingly. The positions are long positions if the
bank is paying a fixed price and receiving a floating price, and
short positions if the bank is receiving a fixed price and paying a
floating price; \44\ and
\44\ If one of the sides of the transaction involves receiving/
paying a fixed or floating interest rate, that exposure should be
slotted into the appropriate repricing maturity band in section
IV.A. of this Appendix E.
---------------------------------------------------------------------------
c. Commodity swaps where the sides of the transaction are in
different commodities are included in the relevant reporting ladder.
No offsetting is allowed unless the commodities are in the same sub-
category.
[[Page 38112]]
E. Options
1. Three alternatives are available for a bank to use in
measuring its market risk for options activities. A bank that only
has purchased options may use the simplified method set forth in
section IV.E.2. of this Appendix E. A bank that also writes options
may use the scenario method described in section IV.E.3. of this
Appendix E or the delta-plus method set forth in section IV.E.4. of
this Appendix E.\45\ These methods may only be used by banks which,
in relative terms, have limited options activities. Banks with more
significant options business are expected to adopt an internal
measurement system conforming to the criteria in section III. of
this Appendix E. Regardless of the method used, specific risk
related to the issuer of an instrument still applies to options
positions for equities, equity indices and corporate debt securities
as set forth in sections IV.A. and IV.B. of this Appendix E. There
remains a separate capital requirement for counterparty credit risk
as set forth in appendix A to this part.
\45\ Unless all their written option positions are hedged by
perfectly matched long positions in exactly the same options, in
which case there is no capital requirement for market risk.
---------------------------------------------------------------------------
2. Under the simplified and scenario methods, the positions for
the options and the associated underlying, cash or forward, are not
included in the measurement framework for debt securities, equities,
foreign exchange or commodities risk as set forth in sections IV.A.
through IV.D. of this Appendix E. Rather, they are subject to
capital requirements as calculated in this section IV.E. The capital
requirements calculated under this section IV.E. should then be
added to the capital requirements for debt securities, equities,
foreign exchange, and commodities risk as appropriate. Under the
delta-plus method, the delta equivalent position \46\ for each
option is included in the measurement frameworks set forth in
sections IV.A. through IV.D. of this Appendix E.
\46\ The delta equivalent of an option is the option's delta
value multiplied by its principal or notional value. The delta value
of an option represents the expected change in the option's price as
a proportion of a small change in the price of the underlying
instrument. For example, an option whose price changes $1 for every
$2 dollar change in the price of the underlying instrument has a
delta of 0.50.
---------------------------------------------------------------------------
3. A bank that has only a limited amount and range of purchased
options may use the following simplified approach to measure its
market risk exposure.
a. For a bank with a long cash position and a long put or with a
short cash position and a long call, the capital requirement is the
market value of the underlying instrument multiplied by the sum of
the specific and general market risk requirements for the underlying
(that is, the specific and general market risk requirements that
would have applied to the underlying directly under sections IV.A.
through IV.D. of this Appendix E \47\), less the amount the option
is in the money (if any) bounded at zero.\48\
\47\ Some options (e.g., where the underlying is an interest
rate, a currency, or a commodity) bear no specific risk but specific
risk will be present in the case of options on corporate debt
securities and for options on equities and equity indices.
\48\ For example, if a holder of 100 shares currently valued at
$10 each has an equivalent put option with a strike price of $11,
the capital charge would be: $1,000 x 16.0 percent (e.g., 8.0
percent specific plus 8.0 percent general market risk)=$160, less
the amount the option is in the money ($11-$10) x 100=$100, i.e.,
the capital charge would be $60. A similar methodology applies for
options whose underlying is a foreign currency, a debt security or a
commodity.
---------------------------------------------------------------------------
b. For a bank with a long call or a long put, the capital charge
is the lesser of:
i. The market value of the underlying security multiplied by the
sum of specific and general market risk requirements for the
underlying (that is, the specific and general market risk
requirements that would have applied to the underlying directly
under sections IV.A. through IV.D. of this Appendix E \49\); or
\49\ See footnote 47 in section IV.E.3.a. of this appendix E.
---------------------------------------------------------------------------
ii. The market value of the option.
c. Under this measure, the capital requirement for currency
options is 8.0 percent of the market value of the underlying and for
commodity options is 15.0 percent of the market value of the
underlying.
4. Under the scenario approach, a bank revalues its options and
related hedging positions by changing the underlying rate or price
over a specified range and by assuming different levels of
volatility for that rate or price.
a. For each of its option portfolios, a bank constructs a grid
based on a fixed range of changes in the portfolio's risk factors
and calculates changes in the value of the option portfolio at each
point within the grid. For this purpose, an option portfolio
consists of an option and any related hedging positions or multiple
options and related hedging positions that are grouped together
according to their remaining maturity or the type of underlying.
b. Options based on interest rates and debt instruments are
grouped into portfolios according to the maturity zones that are set
forth in section IV.A. of this Appendix E. (Zone 1 instruments have
a remaining maturity of up to 1 year, zone 2 instruments have a
remaining maturity from 1 year up to 4 years, and zone 3 instruments
have a remaining maturity of 4 years or more.) These options and the
associated hedging positions should be evaluated under the
assumption that the relevant interest rates move simultaneously. For
options based on equities, separate grids are constructed for each
individual equity issue and index. For options based on exchange
rates, separate grids are constructed for individual exchange rates.
For options based on commodities, separate grids are constructed for
each category of commodity (as defined in sections I.B.3. and IV.D.
of this Appendix E).
c. For option portfolios with options based on equities,
exchange rates, and commodities, the first dimension of the grid
consists of rate or price changes within a specified range above and
below the current market value of the underlying; for equities, the
range is 12.0 percent (or in the case of an index
8.0 percent), for exchange rates the range is
8.0 percent, and for commodities the range is
15.0 percent. For option portfolios with options based
on interest rates, the range for the first dimension of the grid
depends on the remaining maturity zone. The range for zone 1 is
100 basis points, the range for zone 2 is 90
basis points, and the range for zone 3 is 75 basis
points. For all option portfolios, the range is divided into at
least ten equally spaced intervals. The second dimension of each
grid is a shift in the volatility of the underlying rate or price
equal to 25.0 percent of the current volatility.\50\
\50\ For example, if the underlying of an equity instrument has
a current market value of $100 and a volatility of 20 percent, the
first dimension of the grid would range from $88 to $112, divided
into ten intervals of $2.40 and the second dimension would assume
volatilities of 15 percent, 20 percent, and 25 percent.
---------------------------------------------------------------------------
d. For each assumed volatility and rate or price change (a
scenario), the bank revalues each option portfolio. The market risk
capital requirement for the portfolio is the largest loss in value
from among the scenario revaluations. The total market risk capital
requirement for all option portfolios is the sum of the individual
option portfolio capital requirements.
e. The Federal Reserve will review the application of the
scenario approach, particularly regarding the precise way the
analysis is constructed. A bank using the scenario approach should
meet the appropriate qualitative criteria set forth in section
III.B. of this Appendix E.
5. Under the delta-plus method, a bank that writes options may
include delta-weighted options positions within each measurement
framework as set forth in sections IV.A. through IV.D. of this
Appendix E.
a. Options positions should be measured as a position equal to
the market value of the underlying instrument multiplied by the
delta. In addition, a bank must measure the sensitivities of the
option's gamma (the change of the delta for a given change in the
price of the underlying) and vega (the sensitivity of the option
price with respect to a change in volatility) to calculate the total
capital requirement. These sensitivities may be calculated according
to an exchange model approved by the Federal Reserve or to the
bank's own options pricing model, subject to review by the Federal
Reserve.
b. For options with debt instruments or interest rates as the
underlying instrument, delta-weighted options positions should be
slotted into the debt instrument time-bands in section IV.A. of this
Appendix E using a two-legged approach (as is used for other
derivatives), requiring one entry at the time the underlying
contract takes effect and one at the time the underlying contract
matures.\51\ Floating rate instruments with
[[Page 38113]]
caps or floors should be treated as a combination of floating rate
securities and a series of European-style options.\52\ A bank must
also calculate the gamma and vega for each such option position
(including hedge positions). The results should be slotted into
separate maturity ladders by currency. For options such as caps and
floors whose underlying instrument is an interest rate, the delta
and gamma should be expressed in terms of a hypothetical underlying
security. Subsequently:
\51\ For example, in April, a purchased call option on a June
three-month interest-rate future would be considered on the basis of
its delta-equivalent value to be a long position with a maturity of
five months and a short position with a maturity of two months. The
written option would be slotted as a long position with a maturity
of two months and short position with a maturity of five months.
\52\ For example, the holder of a three-year floating rate bond
indexed to six-month LIBOR with a cap of 15 percent would treat the
bond as a debt security that reprices in six months, and a series of
five written call options a FRA with a strike rate of 15 percent,
each slotted as a short position at the expiration date of the
option and as a long position at the time the FRA matures.
i. For gamma risk, for each time-band, net gammas that are
negative are multiplied by the risk weights set out in Table IV in
section IV.E.5.b.iv. of this Appendix E and by the square of the
market value of the underlying instrument (net positive gammas may
be disregarded);
ii. For volatility risk, a bank calculates the capital
requirements for vega in each time-band assuming a proportional
shift in volatility of 25.0 percent;
iii. The capital requirement is the absolute value of the sum of
the individual capital requirements for net negative gammas plus the
absolute value of the sum of the individual capital requirements for
vega risk for each time-band; and
iv. The delta plus method risk weights are:
Table IV.--Delta Plus Method Risk Weights
----------------------------------------------------------------------------------------------------------------
Modified duration
Time-band (average assumed Assumed interest Risk-weight for
for time band) rate change (%) gamma\1\
----------------------------------------------------------------------------------------------------------------
Under 1 month....................................... 0.00 1.00 0.00000
1 up to 3 months.................................... 0.20 1.00 0.00020
3 up to 6 months.................................... 0.40 1.00 0.00080
6 up to 12 months................................... 0.70 1.00 0.00245
1 up to 2 years..................................... 1.40 0.90 0.00794
2 up to 3 years..................................... 2.20 0.80 0.01549
3 up to 4 years..................................... 3.00 0.75 0.02531
4 up to 5 years..................................... 3.65 0.75 0.03747
5 up to 7 years..................................... 4.65 0.70 0.05298
7 up to 10 years.................................... 5.80 0.65 0.07106
10 up to 15 years................................... 7.50 0.60 0.10125
15 up to 20 years................................... 8.75 0.60 0.13781
Over 20 years....................................... 10.00 0.60 0.18000
----------------------------------------------------------------------------------------------------------------
\1\ According to the Taylor expansion, the risk weights are calculated as \1/2\ (modified duration x assumed
interest rate change) \2\/100.
c. For options with equities as the underlying, delta-weighted
option positions should be incorporated in the measure of market
risk set forth in section IV.B. of this Appendix E. Individual
equity issues and indices should be treated as separate underlyings.
In addition to the capital requirement for delta risk, a bank must
apply a further capital charge for gamma and vega risk:
i. For gamma risk, the net gammas that are negative for each
underlying are multiplied by 0.72 percent (in the case of an
individual equity) or 0.32 percent (in the case of an index as the
underlying) and by the square of the market value of the underlying;
ii. For volatility risk, a bank calculates the capital
requirement for vega for each underlying, assuming a proportional
shift in volatility of 25.0 percent; and
iii. The capital requirement is the absolute value of the sum of
the individual capital requirements for net negative gammas plus the
absolute value of the individual capital requirements for vega risk.
d. For options of foreign exchange and gold positions, the net
delta (or delta-based) equivalent of the total book of foreign
currency and gold options is incorporated into the measurement of
the exposure in a single currency position as set forth in section
IV.C. of this Appendix E. The gamma and vega risks are measured as
follows:
i. For gamma risk, for each underlying exchange rate, net gammas
that are negative are multiplied by 0.32 percent and by the square
of the market value of the positions;
ii. For volatility risk, a bank calculates the capital
requirements for vega for each currency pair and gold assuming a
proportional shift in volatility of 25.0 percent; and
iii. The capital requirement is the absolute value of the sum of
the individual capital requirements for net negative gammas plus the
absolute value of the sum of the individual capital requirements for
vega risk.
e. For options on commodities, the delta-weighted positions are
incorporated in one of the measures described in section IV.D. of
this Appendix E. In addition, a bank must apply a capital
requirement for gamma and vega risk:
i. For gamma risk, net gammas that are negative for each
underlying are multiplied by 1.125 percent and by the square of the
market value of the commodity;
ii. For volatility risk, a bank calculates the capital
requirements for vega for each commodity assuming a proportional
shift in volatility of 25.0 percent; and
iii. The capital requirement is the absolute value of the sum of
the individual capital requirements for net negative gammas plus the
absolute value of the sum of the individual capital requirements for
vega risk.
f. Under certain conditions and to a limited extent, the Federal
Reserve may permit banks that are significant traders in options
with debt securities or interest rates as the underlying to net
positive and negative gammas and vegas across time-bands. Such
netting must be based on prudent and conservative assumptions and
the bank must materially meet the qualitative standards set forth in
section III.B. of this Appendix E.
g. A bank may base the calculation of vega risk on a volatility
ladder in which the implied change in volatility varies with the
maturity of the option. The assumed proportional shift in volatility
must be at least 25.0 percent at the short end of the
maturity spectrum. The proportional shift for longer maturities must
be at least as stringent in statistical terms as the 25.0 percent
shift at the short end.
h. A bank should also monitor the risks of rho (the rate of
change of the value of the option with respect to the interest rate)
and theta (the rate of change of the value of the option with
respect to time).
Attachments to Appendix E
Attachment I--Sample Calculation of Eligible Tier 1, Tier 2, and Tier 3
Capital for the Risk-Based Capital Ratio Adjusted for Market Risk
a. In each example the weighted-risk assets are $8000 and the
market risk-adjusted assets are $625 (capital requirement for market
risk=$50 $50 x 12.5=$625):
Example 1: A bank has the following qualifying capital:
Tier 1=$600 Tier 2=$100 Tier 3=$1000
[[Page 38114]]
(1) The minimum capital requirement for credit risk is $640
($8000 x 8.0%). This requirement could be satisfied with $540 of
Tier 1 capital and $100 of Tier 2 capital.
(2) The remaining capital available for market risk would be:
Tier 1=$60, Tier 2=0, and Tier 3=$1000. The minimum capital
requirement for market risk is $50 ($625 x 8.0%). Eligible Tier 3
capital would be limited to $125 ($50 x 2.5).
(3) The Tier 1 capital required to support market risk could be
satisfied by allocating $14 ($50 x .285), with eligible Tier 3
capital used for market risk being $36 ($50-$14).
(4) Total qualifying and eligible capital would be:
$540 (Tier 1)+$100 (Tier 2)+$60 (Tier 1, comprising $14 allocated
for market risk and $46 unallocated)+$36 (Tier 3)=$736. The bank's
ratio of qualifying and eligible capital to weighted-risk assets
adjusted for market risk would be: $736/$8,625)=8.5%.
Example 2: A bank has the following qualifying capital:
Tier 1=$500 Tier 2=$140 Tier 3=$600
(1) The minimum capital requirement for credit risk is $640
($8000 x 8.0%). This requirement could be satisfied with $500 of
Tier 1 capital and $140 of Tier 2 capital.
(2) The remaining capital available for market risk would be:
Tier 1=0, Tier 2=$0, and Tier 3=$600. Eligible Tier 3 capital would
be limited to $0 ( 0 x 2.5). Because there is no Tier 1 capital
required to support market risk, no eligible Tier 3 capital may be
used for market risk.
(3) Total qualifying and eligible capital would be: $500 (Tier
1)+$140 (Tier 2)=$640. The bank's ratio of qualifying and eligible
capital to weighted-risk assets adjusted for market risk would be:
$640/$8,625)=7.4%.
b. In both of the examples described in paragraph a. of this
attachment the total of Tier 2 and Tier 3 capital for credit and
market risk is not greater than 100 percent of Tier 1 capital for
credit and market risk and the total of Tier 2 capital for credit
risk is not greater than 100 percent of Tier 1 capital for credit
risk.
Attachment II--Sample Calculation of General Market Risk for Debt
Instruments Using the Maturity Method
a. A bank with the following positions would slot them into a
maturity ladder as shown below:
i. Qualifying bond, $13.33mn market value, remaining maturity 8
years, coupon 8%;
ii. Government bond, $75mn market value, remaining maturity 2
months, coupon 7%;
iii. Interest rate swap, $150 mn, bank receives floating rate
interest and pays fixed, next interest reset after 12 months,
remaining life of swap is 8 years (assumes the current interest rate
is identical to the one the swap is based on); and
iv. Long position in interest rate future, $50mn, delivery date
after 6 months, life of underlying government security is 3.5 years
(assumes the current interest rate is identical to the one the swap
is based on).
--------------------------------------------------------------------------------------------------------------------------------------------------------
Risk wght Risk-weighted Net time-band
Zone Time-band and position [%] position positions Net zone positions
--------------------------------------------------------------------------------------------------------------------------------------------------------
1............... 0-1 mth.................................................. 0.00
1-3 mth Long 75 Gov. bond................................ 0.20 Long 0.15........... Long 0.15........... Long 1.00.
3-6 mth.................................................. 0.40 Short 0.20.......... Short 0.20..........
Short 50 Future
6-12 mths................................................ 0.70 Long 1.05........... Long 1.05...........
Long 150 Swap
2............... 1-2 yrs.................................................. 1.25
2-3 yrs.................................................. 1.75
3-4 yrs.................................................. 2.25 Long 1.125.......... Long 1.125.......... Long 1.125
Long 50 Future
3............... 4-5 yrs.................................................. 2.75
5-7 yrs.................................................. 3.25
7-10 yrs................................................. 3.75 Short 5.625......... Short 5.125......... Short 5.125
Short 150 Swap
Long 13.33 Qual Bond Long 0.50
10-15 yrs................................................ 4.50
15-20 yrs................................................ 5.25
Over 2 yrs............................................... 6.00
--------------------------------------------------------------------------------------------------------------------------------------------------------
b. A vertical disallowance would be calculated for time-band 7-
10 years. It would be 10 percent of the matched positions in the
time-band--10.0 x 0.5=0.05 ($50,000).
c. A horizontal disallowance would be calculated for zone 1. It
would be 40 percent of the matched positions in the zone--
40.0 x 0.20=0.80 ($80,000). The remaining net position in Zone 1
would be +1.00.
d. A horizontal disallowance would be calculated for adjacent
zones 2 and 3. It would be 40 percent of the matched positions
between the zones--40.0 x 1.125=0.45 (450,000). The remaining
position in zone 3 would be -4.00.
e. A horizontal disallowance would be calculated between zones 1
and 3. It would be 100 percent of the matched positions between the
zones--100 x 1.00=1.00 (1,000,000).
f. The remaining net open position for the bank would be 3.00
($3,000,000). The total capital requirement for general market risk for
this portfolio would be:
The vertical disallowance.................................. $50,000
Horizontal disallowance in zone 1.......................... 80,000
Horizontal disallowance--zones 2 and 3..................... 450,000
Horizontal disallowance--zones 1 and 3..................... 1,000,000
Overall net open position.................................. 3,000,000
------------
Total requirement for general market risk.............. 4,580,000
Attachment III--Summary of Treatment for Interest Rate and Equity
Derivatives
Summary of Treatment for Interest Rate Derivatives
----------------------------------------------------------------------------------------------------------------
Specific risk
Instrument charge General market risk charge
----------------------------------------------------------------------------------------------------------------
Exchange-Traded Future
Government security.................................. No........... Yes, as two positions.
Corporate debt security.............................. Yes.......... Yes, as two positions.
Index on short-term interest rates (e.g. LIBOR)...... No........... Yes, as two positions.
OTC Forward
Government security.................................. No........... Yes, as two positions.
[[Page 38115]]
Corporate debt security.............................. Yes.......... Yes, as two positions.
Index on short-term interest rates................... No........... Yes, as two positions.
FRAs, Swaps............................................ No........... Yes, as two positions.
Forward foreign exchange............................... No........... Yes, as one position in each currency.
Options: ............. For each type of transaction, either:
Government security.................................. No........... (a) Carve out together with the
associated hedging positions
--simplified method
--scenario analysis
--internal models, or
Corporate debt security.............................. Yes.......... (b) General market risk charge
according to the Delta-plus method
(gamma and vega receive separate
capital charges)
Index on short-term interest rates................... No...........
----------------------------------------------------------------------------------------------------------------
Note: Specific risk charges relate to the issuer of the instrument. There remains a separate capital requirement
for counterparty credit risk.
Summary of Treatment for Equity Derivatives
----------------------------------------------------------------------------------------------------------------
Specific risk
Instrument charge General market risk charge
----------------------------------------------------------------------------------------------------------------
Exchange-Traded or OTC Future:
Individual equity.................................. Yes.......... Yes, as underlying.
Index.............................................. 2.0%......... Yes, as underlying.
Options: ............. For each type of transactions either:
Individual equity.................................. yes.......... (a) Carve out together with the
associated hedging positions
--simplified method
--scenario approach
--internal models, or
Index.............................................. 2.0%......... (b) General market risk requirement
according to the Delta-plus method
(gamma and vega receive separate
capital charges).
----------------------------------------------------------------------------------------------------------------
Note: Specific risk charges relate to the issuer of the instrument. There remains a separate capital requirement
for counterparty credit risk.
Attachment IV--Sample Calculation of Standardized Approach for
Commodities Risk
----------------------------------------------------------------------------------------------------------------
Spread Capital
Time-band Position rate Capital calculation charge
----------------------------------------------------------------------------------------------------------------
0 up to 1 month............ None
1 up to 3 months........... None
3 up to 6 months........... Long 800.................. 1.5% 800 long+800 short (matched) x 24
1.5%=.
Short 1000................ ......... 200 short carried forward to 1- 2.4
2 yrs, capital charge: 200 x 2
x 0.6%=.
6 up to 12 months.......... None
1 up to 2 yrs.............. Long 600.................. ......... 200 long+200 short (matched) x 6
1.5%=.
400 long carried forward to 4.8
over 3 yrs capital charge: 400
x 2 x 0.6%=.
2 up to 3 yrs.............. None
Over 3 years............... Short 600................. ......... 400 long+400 short (matched) x 12
1.5%=.
Net position: 200 capital 30
charge: 200 x 15.0%=.
----------------------------------------------------------------------------------------------------------------
Note: Assume all positions are in the same commodity and converted at current spot rates into U.S. dollars. The
total capital requirement would be $79.2.
[[Page 38116]]
Attachment V--Sample Calculation for Delta-Plus Method for Options
a. Assume a bank has a European short call option on a commodity
with an exercise price of 490 and a market value of the underlying
12 months from the expiration of the option at 500; a risk-free
interest rate at 8% per annum, and the volatility at 20 percent. The
current delta for this position is according to the Black-Scholes
formula -0.721 (that is, the price of the option changes by -0.721
if the price of the underlying moves by 1). The gamma is -0.0034
(that is, the delta changes by -0.0034 from -0.721 to -0.7244 if the
price of the underlying moves by 1). The current value of the option
is 65.48.
b. The first step under the delta-plus method is to multiply the
market value of the commodity by the absolute value of the delta.
500 x 0.721 = 360.5. The delta-weighted position is then
incorporated into the measure described in section IV.D. of this
Appendix E. If the bank uses the maturity approach and no other
positions exist, the delta-weighted position is multiplied by 0.15
to calculate the capital requirement for delta. 360.5 x 0.15 =
54.075.
c. The capital requirement for gamma is calculated according to
the Taylor expansion by multiplying the absolute value of the
assumed gamma of -0.0034 by 1.125% and by the square of the market
value of the underlying. -0.0034 x 0.0125 x 500\2\ = 10.625.
d. The capital requirement for vega is calculated next. The
assumed current (implied) volatility is 20%. Since only an increase
in volatility carries a risk of loss for a short call option, the
volatility has to be increased by a relative shift of 25%. This
means that the vega capital requirement has to be calculated on the
basis of a change in volatility of 5 percentage points from 20% to
25% in this example. According to the Black-Scholes formula used
here, the vega equals 168. Thus, a 1% or 0.01 increase in volatility
increases the value of the option by 1.68. Accordingly, a change in
volatility of 5 percentage points increases the value of 5 x 1.68 =
8.4. This is the capital requirement for vega risk. The total
capital requirement would be $73.10 (54.075 + 10.625 + 8.4).
PART 225--BANK HOLDING COMPANIES AND CHANGE IN BANK CONTROL
(REGULATION Y)
1. The authority citation for part 225 continues to read as
follows:
Authority: 12 U.S.C. 1817(j)(13), 1818, 1828(o), 1831i, 1831p-1,
1843(c)(8), 1844(b), 1972(1), 3106, 3108, 3310, 3331-3351, 3907, and
3909.
2. In part 225, appendix A to part 225 is amended by revising the
first and second paragraphs of section I. to read as follows:
Appendix A to Part 225--Capital Adequacy Guidelines for Bank Holding
Companies: Risk-Based Measure
I. Overview
The Board of Governors of the Federal Reserve System has adopted
a risk-based capital measure to assist in the assessment of the
capital adequacy of bank holding companies (banking
organizations).1 The principal objectives of this measure are
to (i) make regulatory capital requirements more sensitive to
differences in risk profiles among banking organizations; (ii)
factor off-balance-sheet exposures into the assessment of capital
adequacy; (iii) minimize disincentives to holding liquid, low-risk
assets; and (iv) achieve greater consistency in the evaluation of
the capital adequacy of major banking organizations throughout the
world.
\1\ Some banking organizations are also subject to capital
requirements for market risk as set forth in appendix E of this
part. Banking organizations that are subject to the market risk
measure are required to follow the guidelines set forth in appendix
E of this part for determining qualifying and eligible capital,
calculating market risk-equivalent assets and adding them into
weighted-risk assets, and calculating risk-based capital ratios
adjusted for market risk. Supervisory ratios that relate capital to
total assets for bank holding companies are outlined in appendices B
and D of this part.
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The risk-based capital guidelines include both a definition of
capital and a framework for calculating weighted risk assets by
assigning assets and off-balance-sheet items to broad risk
categories.2 An institution's risk-based capital ratio is
calculated by dividing its qualifying capital (the numerator of the
ratio) by its weighted risk assets (the denominator).3 The
definition of qualifying capital is outlined below in section II. of
this appendix A, and the procedures for calculating weighted risk
assets are discussed in section III. of this appendix A. Attachment
I to this appendix A illustrates a sample calculation of weighted
risk assets and the risk-based capital ratio.
\2\ The risk-based capital measure is based upon a framework
developed jointly by supervisory authorities from the countries
represented on the Basle Committee on Banking Regulations and
Supervisory Practices (Basle Supervisors' Committee) and endorsed by
the Group of Ten Central Bank Governors. The framework is described
in a paper prepared by the Basle Supervisors' Committee entitled
``International Convergence of Capital Measurement,'' July 1988.
\3\ Banking organizations generally are expected to utilize
period-end amounts in calculating their risk-based capital ratios.
When necessary and appropriate, ratios based on average balances may
also be calculated on a case-by-case basis. Moreover, to the extent
banking organizations have data on average balances that can be used
to calculate risk-based ratios, the Federal Reserve will take such
data into account.
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* * * * *
3. In Part 225 a new appendix E is added to read as follows:
Appendix E to Part 225--Capital Adequacy Guidelines for Bank Holding
Companies: Market Risk Measure
I. Introduction
A. Overview
1. The Board of Governors of the Federal Reserve System has
adopted a framework for determining capital requirements for the
market risk exposure of bank holding companies (banking
organizations).1 For this purpose, market risk is defined as
the risk of losses in a banking organization's on- and off-balance-
sheet positions arising from movements in market prices. The market
risks subject to these capital requirements are those associated
with debt and equity instruments held in the banking organization's
trading account, as well as foreign exchange risk and commodities
risk throughout the organization, including options and other
derivative contracts in each risk category.
\1\ The market risk measure is based on a framework developed
jointly by supervisory authorities from the countries represented on
the Basle Committee on Banking Supervision (Basle Supervisors
Committee) and endorsed by the Group of Ten Central Bank Governors.
The framework is described in a paper prepared by the Basle
Supervisors Committee entitled ``[Proposal to issue a] Supplement to
the Basle Capital Accord to Cover Market Risks.'' [April] 1995.
---------------------------------------------------------------------------
2. Effective December 31, 1997, the market risk measure will be
applied to all bank holding companies that, on a consolidated basis:
a. Have total assets in excess of $5 billion; and have a total
volume of trading activities (measured as the sum of the banking
organization's trading assets and liabilities 2 on a daily
average basis for the quarter) that is 3.0 percent or more of the
total assets of the banking organization, or have interest rate,
foreign exchange, equity, and commodity off-balance-sheet derivative
contracts relating to trading activities whose total notional
amounts exceed $5 billion; or
\2\ As reflected in the Consolidated Financial Statements for
Bank Holding Companies (FR Y-9C Report).
b. Have total assets of $5 billion or less; and have trading
activities exceeding 10.0 percent of the total assets of the banking
organization.
3. Such banking organizations are still subject to the risk-
based capital measure set forth in appendix A of this part, subject
to the exclusion of certain assets specified in this appendix E.
However, these banking organizations must calculate their market
risk-equivalent assets and determine risk-based capital ratios
adjusted for market risk in accordance with this appendix E.3
\3\ The Federal Reserve may apply all or portions of this
appendix E to other banking organizations when deemed necessary for
safety and soundness purposes.
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4. The market risk measure provides two ways for a banking
organization to determine its exposure to market risk. A banking
organization may use its internal risk measurement model, subject to
the conditions and criteria set forth in section III. of this
appendix E (referred to as the internal models approach), or when
appropriate, a
[[Page 38117]]
banking organization may use all or portions of the alternative
measurement system described in section IV. of this appendix E
(referred to as the standardized approach).
a. With prior approval from the Federal Reserve, for regulatory
capital purposes, a banking organization may use its internal risk
measurement model to measure its value-at-risk 4 for each of
the following risk factor categories; interest rates, exchange
rates, equity prices, and commodity prices. The value-at-risk amount
for each risk factor category should include volatilities of related
options. The value-at-risk amount for each risk factor category is
summed to determine the aggregate value-at-risk for the banking
organization.
\4\ A banking organization evaluates its current positions and
estimates future market volatility through a value-at-risk measure,
which is an estimate representing, with a certain degree of
statistical confidence, the maximum amount by which the market value
of trading positions could decline during a specific period of time.
The value-at-risk is generated through an internal model that
employs a series of market risk factors (for example, market rates
and princes that affect the value of trading positions).
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b. The standardized approach uses a set of standardized
calculations and assumptions to measure market risk exposure
depending on its source; debt instruments, equities, foreign
currencies, and commodities, including volatilities of related
options.
5. The Board generally expects any banking organization that is
subject to the market risk measure, especially those with large
trading accounts, to comply with the measure by using internal risk-
measurement models. A banking organization may not change its
measurement approach for the purpose of minimizing capital
requirements. In limited instances, on a case-by-case basis, the
Federal Reserve may permit a banking organization that has internal
models to incorporate risk measures of negligible exposures, for
example, de minimis positions, activities in remote locations, minor
exposures in a currency, or activities that present negligible risk
to the banking organization, in an alternative manner, so long as it
adequately captures the risk.
6. The risk-based capital ratios adjusted for market risk
determined in accordance with this appendix E are minimum
supervisory ratios. Banking organizations generally are expected to
operate with capital positions well above the minimum ratios. In all
cases, banking organizations should hold capital commensurate with
the level and nature of the risks to which they are exposed.
7. The Federal Reserve will monitor the implementation and
effect of these guidelines in relation to domestic and international
developments in the banking industry. When necessary and
appropriate, the Board will consider the need to modify this
appendix E in light of any significant changes in the economy,
financial markets, banking practices, or other relevant factors.
B. Market Risks Subject to a Capital Requirement.
1. General Market Risk and Specific Risk. A banking organization
must hold capital against exposure to general market risk and
specific risk arising from its trading and other foreign exchange
and commodity activities. For this purpose, general market risk
refers to changes in the market value of covered transactions
resulting from market movements, such as changing levels of market
interest rates, broad equity indices, or currency exchange rates.
Specific risk refers to credit risk, that is, the risk that the
issuer of a debt or equity instrument might default, as well as to
other factors that affect the market value of specific instruments
but that do not materially alter market conditions.5
\5\ This Appendix E does not impose specific risk capital
requirements for foreign exchange risk and commodities positions
because they do not have the type of issuer-specific risk associated
with debt and equity instruments in the trade account.
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2. Trading Activities. a. The general market risk and specific
risk capital requirements for trading activities are based on on-
and off-balance-sheet positions in a banking organization's trading
account. For this purpose, trading account means positions in
financial instruments acquired with the intent to resell in order to
profit from short-term price movements (or other price or interest-
rate variations), including, but not limited to:
i. Assets acquired with the intent to resell to customers;
ii. Positions in financial instruments arising from matched
principal brokering and market making; or
iii. Positions taken in order to hedge other elements of the
trading account (that is, reduce risk by offsetting other positions
that have exposure to changes in market rates or prices).6
Trading activities may include positions in debt instruments,
equities, foreign currencies, and commodity instruments, or related
derivative 7 or other off-balance-sheet contracts.
\6\ At a banking organization's option, when non-trading account
instruments are hedged with instruments in the trading account, on-
or off-balance-sheet, the non-trading account instruments may be
included in the measure for general market risk. Such non-trading
account instruments remain subject to the credit risk capital
charges of appendix A of this part.
\7\ In general terms, a derivative is a financial contract whose
value is derived from the values of one or more underlying assets or
reference rates or indexes of asset values (referred to as ``the
underlying''). Derivatives include standardized contracts that are
traded on exchanges and customized, privately negotiated contracts
known as over-the-counter (OTC) derivatives.
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b. Debt instruments in the trading account are all fixed-rate
and floating-rate debt securities and instruments that behave like
debt, including non-convertible preferred stock. Convertible bonds,
i.e., preferred stock or debt issues that are convertible, at a
stated price, into common shares of the issuer, should be treated as
debt instruments if they trade like debt instruments and as equities
if they trade like equities. Also included are derivative contracts
of debt instruments and other off-balance-sheet instruments in the
trading account that react to changes in interest rates. A security
that has been sold subject to a repurchase agreement or lent subject
to a securities lending agreement is treated as if it were still
owned by the lender of the security. Such transactions remain
subject to the capital requirements for credit risk for the off-
balance-sheet portion of the transaction as set forth in section
III.D. of appendix A of this part.
c. Equities in the trading account are equity instruments that
behave like equities. The instruments covered include common stocks
(whether voting or non-voting), convertible securities that behave
like equities, and commitments to buy or sell equity securities.
Also included are derivative contracts of equity instruments and
other off-balance-sheet instruments in the trading account that are
affected by changes in equity prices. However, non-convertible
preferred stock is included in debt instruments.
3. Foreign Exchange and Commodities Risk. Foreign exchange or
commodities positions, whether or not included in a banking
organization's trading account, are subject to a capital requirement
for the market risk of those positions.
a. The capital requirement for foreign exchange risk applies to
a banking organization's total currency and gold positions. This
includes spot positions (that is, asset items and liability items,
including accrued interest and expenses, denominated in each
currency); forward positions (that is, forward foreign exchange
transactions, including currency futures and the principal on
currency swaps not included in the spot position); and certain
guarantees. It includes future income and expenses from foreign
currency transactions not yet accrued but already fully hedged (at
the discretion of the reporting bank), foreign exchange derivative
and other off-balance-sheet positions that are affected by changes
in exchange rates, and any other item representing a profit or loss
in foreign currencies.
b. A banking organization may, subject to approval by the
Federal Reserve, exclude from its foreign exchange positions any
structural positions in foreign currencies. For this purpose, such
structural positions are limited to transactions designed to hedge a
banking organization's capital ratios against the effect of adverse
exchange rate movements on subordinated debt, equity, or minority
interests in consolidated subsidiaries and dotation capital assigned
to foreign branches that are denominated in foreign currencies. Also
included are any positions related to unconsolidated subsidiaries
and to other items that are deducted from a banking organization's
capital when calculating its capital base. In any event, such
structural foreign currency positions must reflect long-term
policies of the institution and not relate to trading positions.
c. A banking organization doing negligible business in foreign
currency and that does not take foreign exchange positions for its
own account may be exempted from the capital requirement for foreign
exchange risk provided that:
i. Its foreign currency business, defined as the greater of the
sum of its gross long positions and the sum of its gross short
positions in all foreign currencies, does not exceed 100 percent of
eligible capital as defined in section II. of this appendix E; and
ii. Its overall net open foreign exchange position as determined
in section IV.C.2. of this appendix E does not exceed 2.0 percent of
its eligible capital.
[[Page 38118]]
d. The capital requirement for commodities risk applies to a
banking organization's total commodities positions, including
commodity futures, commodity swaps, and all other commodity
derivatives or other off-balance-sheet positions that are affected
by changes in commodity prices. A commodity is defined as a physical
product that is or can be traded on a secondary market (such as
agricultural products, minerals (including oil), and precious
metals), but excluding gold (which is treated as foreign exchange).
C. Capital Requirements
1. Capital Requirements. The minimum capital requirement for a
bank holding company subject to the market risk measure is the sum
of:
a. The capital requirement for credit risk as determined in
accordance with appendix A of this part, excluding debt and equity
instruments in the trading book and positions in commodities, but
including the counterparty credit risk requirements on all over-the-
counter derivative activities whether in the banking organization's
trading account or not; and
b. The capital requirement for market risk as determined by the
internal models approach, the standardized approach, or a
combination of the two approaches deemed to be appropriate by the
Federal Reserve.
2. Internal Models. a. For a banking organization approved to
use the internal models approach, the capital requirement for market
risk is the higher of:
i. The banking organization's previous day's aggregate value-at-
risk amount calculated subject to certain supervisory requirements
set forth in section III. of this appendix E; or
ii. An average of the daily aggregate value-at-risk amounts,
calculated subject to the same restrictions, measured on each of the
preceding sixty (60) business days, multiplied by a minimum
``multiplication factor'' of three (3).8
\8\ The Federal Reserve may adjust the multiplication factor for
a banking organization to increase its capital requirement based on
an assessment of the quality and historic accuracy of the banking
organization's risk management system.
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b. A banking organization approved to use the internal models
approach may also be subject to a separate capital requirement for
specific market risk of traded debt and equity instruments to the
extent that the specific market risk associated with these
instruments is not captured by the banking organization's models.
However, for all banking organizations using internal models, the
total specific risk charge should in no case be less than one-half
the specific risk charges calculated according to the standardized
approach.
3. Standardized approach. A banking organization whose model has
not been approved by the Federal Reserve must use the standardized
approach for measuring its market risk. For a banking organization
using this approach, the capital requirement for market risk is the
sum of the market risk capital requirement for debt and equity
instruments in the trading account, foreign exchange and commodities
risk throughout the banking organization, and options and other
derivative positions in each risk category as set forth in sections
IV.A to IV.E. of this appendix E.9
\9\ Section IV.E. provides several alternatives for measuring
the market risk of options. Under two of the alternatives, the
simplified and scenario methods, the underlying position of an
option is ``carved-out,'' and is not included in the prescribed risk
measure for the underlying. Instead it is evaluated together with
the related option according to the procedures described for options
to determine the capital requirement. Under the third alternative,
the ``delta-plus'' approach, the delta-equivalent value of each
position is included in the measurement framework for the
appropriate risk category (that is, debt or equity instruments in
the trading account, foreign exchange or commodities risk).
---------------------------------------------------------------------------
4. Partial models. a. With approval from the Federal Reserve, a
banking organization whose internal model does not cover all risk
factor categories may use the standardized approach to measure
market risk exposure arising from the risk factor categories that
are not covered. The Federal Reserve will approve combining the two
approaches only on a temporary basis in situations where the banking
organization is developing, but has not fully implemented, a
comprehensive value-at-risk measurement system. When a banking
organization uses both approaches, each risk factor category (that
is, interest rates, exchange rates, equity prices, and commodity
prices) must be measured using one or the other approach. The
methods may not be combined within a risk factor category. Once a
banking organization adopts an acceptable value-at-risk model for a
particular risk factor category, it may not revert to the
standardized approach except in unusual circumstances and with prior
approval of the Federal Reserve.
b. For a banking organization using a combination of approaches,
the capital requirement for market risk is the sum of (i) the
appropriate value-at-risk amount (as determined under section
I.C.2.a. of this appendix E, aggregating the value-at-risk amount
for each risk factor category included in the internal model), and
(ii) the capital requirement for each risk category that is
calculated using the standardized approach.
5. Application. The capital requirements for market risk apply
to bank holding companies on a worldwide consolidated basis. The
Federal Reserve may, however, evaluate market risk on an
unconsolidated basis when necessary. For example, when there are
obstacles to the repatriation of profits from a foreign subsidiary
or where management structure does not allow timely management of
risk on a consolidated basis.
6. Other Considerations. All transactions, including forward
sales and purchases, should be included in the calculation of market
risk capital requirements from the date on which they were entered
into. The Federal Reserve expects banking organizations to meet
their capital requirements for market risk on a continuous basis
(that is, at a minimum, at the close of each business day).
II. Qualifying Capital and the Market Risk-Adjusted Capital Ratio
A. Qualifying and Eligible Capital
1. The principal forms of qualifying capital for market risk are
Tier 1 capital and Tier 2 capital as defined in section II. of
appendix A of this part and subject to the conditions and
limitations of appendix A of this part. A banking organization may
use Tier 3 capital for the sole purpose of meeting a portion of the
capital requirements for market risk.10
\10\ A banking organization may not use Tier 3 capital to
satisfy any capital requirements for counterparty credit risk under
appendix A of this part, including counterparty credit risk
associated with derivative transactions in either the trading or
non-trading accounts.
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2. Tier 3 capital consists of short-term subordinated debt that
is subject to a lock-in clause providing that neither interest nor
principal payment is due (even at maturity) if such payment would
cause the issuing banking organization to fall or remain below the
minimum 8.0 percent risk-based capital requirement as set forth in
appendix A of this part and adjusted for market risk.
3. In order to qualify as Tier 3 capital, the short-term debt
must be unsecured, subordinated, and fully paid up; it must have an
original maturity of at least two years; and it may not be redeemed
before maturity without prior approval by the Federal Reserve. In
addition, it may not contain or be covered by any covenants, terms,
or restrictions that are inconsistent with safe and sound banking
practices.
4. Eligible Tier 3 capital may not exceed 250 percent of a
banking organization's Tier 1 capital allocated for market risk and
the maximum eligible amount of Tier 2 and Tier 3 capital together is
limited to 100 percent of Tier 1 capital. (Examples of how to
calculate these limits are set forth in Attachment I to this
appendix E.) Tier 2 elements may be substituted for Tier 3 up to the
same limit of 250 percent, so long as the overall limits for Tier 2
capital set forth in appendix A of this part are not exceeded, that
is, Tier 2 capital may not exceed total Tier 1 capital, and long-
term subordinated debt may not exceed 50 percent of Tier 1 capital.
B. Calculation of Eligible Capital and the Capital Ratio
1. In order to calculate eligible capital, a banking
organization must first calculate its minimum capital requirement
for credit risk in accordance with appendix A of this part and then
its capital requirement for market risk. Eligible capital is the sum
of the banking organization's qualifying Tier 1 capital, its
qualifying Tier 2 capital subject to the limits stated above, and
its eligible Tier 3 capital subject to the conditions set out under
section II. of this appendix E.
2. A banking organization that is subject to the market risk
measure must calculate its risk-based capital ratios as follows:
a. Determine total weighted-risk assets using the procedures and
criteria set forth in appendix A of this part, excluding debt and
equity instruments in the trading book and positions in commodities,
but including all over-the-counter derivative activities whether in
the banking organization's trading account or not.
[[Page 38119]]
b. Calculate the measure for market risk using the internal
models approach, the standardized approach, or an approved
combination of these two approaches.
c. Multiply the measure for market risk by 12.5 (i.e., the
reciprocal of the 8.0 percent minimum risk-based capital ratio). The
resulting product is referred to as ``market risk-equivalent
assets.''
d. Add market risk-equivalent assets to the weighted-risk assets
compiled for credit risk purposes (section II.B.2.a. of this
appendix E). The sum of these two amounts is the denominator of the
risk-based capital ratios adjusted for market risk. The numerator of
the total risk-based capital ratio is eligible capital and the
numerator of the Tier 1 risk-based capital ratio is Tier 1 capital.
III. The Internal Models Approach
A. Use of Models
1. With prior approval of the Federal Reserve, a banking
organization may use its internal risk measurement model(s) for
purposes of measuring value-at-risk and determining the associated
regulatory capital requirements for market risk exposure.
a. Requests for approval under section III.A.1. of this appendix
E should include, at a minimum, a complete description of the
banking organization's internal modeling and risk management systems
and how these systems conform to the criteria set forth in this
section III., an explanation of the policies and procedures
established by the banking organization to ensure continued
compliance with such criteria, a discussion of internal and external
validation procedures, and a description of other relevant policies
and procedures consistent with sound practices.
b. The Federal Reserve will approve an internal model for
regulatory capital purposes only after determining that the banking
organization's internal model and risk management systems meet the
criteria in section III. of this appendix E. Such a determination
may require on-site examinations of the systems. The Federal Reserve
may require modification to an internal model as deemed necessary to
ensure compliance, on a continuing basis, with the provisions of
this appendix E. A banking organization's internal model will be
subject to continuing review, both on-and off-site, by the Federal
Reserve.11
\11\ Banking organizations that need to modify their existing
modeling procedures to accommodate the requirements of this appendix
E should, nonetheless, continue to use the internal models they
consider most appropriate in evaluating risks for other purposes.
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2. A banking organization should ensure that the level of
sophistication of its internal model is commensurate with the nature
and volume of the banking organization's trading activity in the
risk factor categories covered by this appendix E and measures
market risk as accurately as possible. In addition, the model should
be adjusted to reflect changing portfolio composition and changing
market conditions.
B. Qualitative Criteria
1. A banking organization using the internal models approach
should have market risk management systems that are conceptually
sound and implemented with integrity. Internal risk measurement
models must be closely integrated into the day-to-day risk
management process of the banking organization. For example, the
risk measurement model must be used in conjunction with internal
trading and exposure limits.
2. A banking organization must meet the following minimum
qualitative criteria before using its internal model to measure its
exposure to market risk.\12\
\12\ If the Federal Reserve is not satisfied with the extent to
which a banking organization meets these criteria, the Federal
Reserve may adjust the multiplication factor used to calculate
market risk capital requirements or otherwise increase capital
requirements.
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a. A banking organization must have a risk control unit that is
independent from business trading units and reports directly to
senior management of the banking organization. The unit must be
responsible for designing and implementing the banking
organization's risk management system and analyzing daily reports on
the output of the banking organization's risk measurement model in
the context of trading limits. The unit must conduct regular back-
testing.\13\
\13\ Back-testing includes ex post comparisons of the risk
measures generated by the model against the actual daily changes in
portfolio value.
---------------------------------------------------------------------------
b. Senior management must be actively involved in the risk
control process. The daily reports produced by the risk management
unit must be reviewed by a level of management with sufficient
authority to enforce both reductions in positions taken by
individual traders, as well as in the banking organization's overall
risk exposure.
c. The banking organization must have a routine and rigorous
program of stress-testing\14\ to identify the effect of low-
probability events on the banking organization's trading portfolio.
Senior management must routinely review the results of stress-
testing in the context of the potential effect of the events on bank
capital and the appropriate procedures the banking organization
should take to minimize losses. The policies of the banking
organization set by management and the board of directors should
identify appropriate stress-tests and the procedures to follow in
response to the test results.
\14\ Stress-testing should cover a range of factors that can
create extraordinary losses or gains in trading portfolios or make
the control of risk in those portfolios difficult. These factors
include low-probability events of all types, including the various
components of market, credit, and operational risks.
---------------------------------------------------------------------------
d. The banking organization must have established procedures for
ensuring compliance with a documented set of internal policies and
controls, as well as for monitoring the overall operation of the
risk measurement system.
e. Not less than once a year, the banking organization must
conduct, as part of its regular internal audit process, an
independent review of the risk measurement system. This review must
include both the activities of the business trading units and of the
independent risk control unit of the banking organization.
f. Not less than once a year, the banking organization must
conduct a review of its overall risk management process. The review
must consider:
i. The adequacy of the documentation of the risk management
system and process and the organization of the risk control unit;
ii. The integration of market risk measures into daily risk
management and the integrity of the management information system;
iii. The process the banking organization employs for approving
risk pricing models and valuation systems that are used by front-
and back-office personnel;
iv. The scope of market risks captured by the risk measurement
model and the validation of any significant changes in the risk
measurement process;
v. The accuracy and completeness of position data, the accuracy
and appropriateness of volatility and correlation assumptions, and
the accuracy of valuation and risk sensitivity calculations;
vi. The verification process the banking organization employs to
evaluate the consistency, timeliness, and reliability of data
sources used to run internal models, including the independence of
such data sources; and
vii. The verification process the banking organization uses to
evaluate back-testing that is conducted to assess the model's
accuracy.
C. Market Risk Factors
1. Overview. For regulatory capital purposes, a banking
organization's internal risk measurement system(s) must use
sufficient risk factors to capture the risks inherent in the banking
organization's portfolio of on- and off-balance-sheet trading
positions and must, subject to the following guidelines, cover
interest rates, equity prices, exchange rates, commodity prices, and
volatilities related to options positions in each risk factor
category. The level of sophistication of the banking organization's
risk factors must be commensurate with the nature and scope of the
risks taken by the banking organization.
2. Interest Rates. a. A banking organization must use a set of
market risk factors corresponding to interest rates in each currency
in which it has material interest rate-sensitive on- or off-balance-
sheet positions. The risk measurement system must model the yield
curve \15\ using one of a number of generally accepted approaches,
for example, by estimating forward rates of zero coupon yields. The
yield curve must be divided into various maturity segments in order
to capture variation in the volatility of rates along the yield
curve; there will typically be one risk factor corresponding to each
maturity segment.
\15\ Generally, a yield curve is a graph showing the term
structure of interest rates by plotting the yields of all
instruments of the same quality by maturities ranging from the
shortest to the longest available. The resulting curve shows whether
short-term interest rates are higher or lower than long-term
interest rates.
---------------------------------------------------------------------------
b. For material exposures to interest rate movements in the
major currencies and markets, a banking organization must model the
yield curve using a minimum of six risk factors. However, the number
of risk factors used should ultimately be driven by the
[[Page 38120]]
nature of the banking organization's trading strategies.\16\ The risk
measurement system must incorporate separate risk factors to capture
spread risk.\17\
\16\ For example, a banking organization that has a portfolio of
various types of securities across many points of the yield curve
and that engages in complex arbitrage strategies would require a
greater number of risk factors to accurately capture interest rate
risk.
\17\ Spread risk refers to the potential changes in value of an
instrument or portfolio arising from differences in the behavior of
baseline yield curves, such as those for U.S. Treasury securities,
and yield curves reflecting sector, quality, or instrument specific
factors. A variety of approaches may be used to capture the spread
risk arising from less than perfectly correlated movements between
government and other interest rates, such as specifying a completely
separate yield curve for non-government instruments (for example,
swaps or municipal securities) or estimating the spread over
government rates at various points along the yield curve.
---------------------------------------------------------------------------
3. Exchange rates. A banking organization must use market risk
factors corresponding to the exchange rate between the domestic
currency and each foreign currency in which the banking organization
has a significant exposure. The risk measurement system must
incorporate market risk factors corresponding to the individual
foreign currencies in which the banking organization's positions are
denominated.
4. Equity prices. A banking organization must use risk factors
corresponding to each of the equity markets in which it holds
significant positions. The sophistication and nature of the modeling
technique for a given market must correspond to the banking
organization's exposure to the overall market as well as to the
banking organization's concentration in individual equity issues in
that market. At a minimum, there must be a risk factor designed to
capture market-wide movements in equity prices (such as a market
index), but additional risk factors could track various sectors or
individual issues.
5. Commodity prices. A banking organization must use market risk
factors corresponding to each of the commodity markets in which it
holds significant positions. The internal model must encompass
directional risk, forward gap and interest rate risk, and basis
risk.\18\ The model should also take into account the market
characteristics, for example, delivery dates and the scope provided
to traders to close out positions.
\18\ Directional risk is the risk that a spot price will
increase or decrease. Forward gap risk refers to the effects of
owning a physical commodity versus owning a forward position in a
commodity. Interest rate risk is the risk of a change in the cost of
carrying forward positions and options. Basis risk is the risk that
the relationship between the prices of similar commodities changes
over time.
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D. Quantitative Standards
1. A banking organization may use one of a number of generally
accepted measurement techniques including, for example, an internal
model based on variance-covariance matrices, historical simulations,
or Monte Carlo simulations so long as the model employed captures
all the material market risks.\19\ The following minimum standards
apply for purposes of using an internal model for calculating market
risk capital requirements:
\19\ In a variance/covariance approach, the change in value of
the portfolio is calculated by combining the risk factor
sensitivities of the individual positions--derived from valuation
models--with a variance/covariance matrix based on risk factor
volatilities and correlations. A banking organization using this
approach would calculate the volatilities and correlations of the
risk factors on the basis of the holding period and the observation
period. A banking organization using a historical simulation would
calculate the hypothetical change in value of the current portfolio
in the light of historical movements in risk factors. This
calculation would be done for each of the defined holding periods
over a given historical measurement horizon to arrive at a range of
simulated profits and losses. A banking organization using a Monte
Carlo technique would consider historical movements to determine the
probability of particular price and rate changes.
a. Value-at-risk must be calculated on a daily basis using a
99th percentile, one-tailed confidence interval 20 and the
holding period must be ten trading days. For positions that display
linear price characteristics, a banking organization may use value-
at-risk numbers calculated according to shorter holding periods
scaled up to ten days by the square root of time.21
\20\ A one-tailed confidence interval of 99 percent means that
there is a 1 percent probability based on historical experience that
the combination of positions in a banking organization's portfolio
would result in a loss higher than the measured value-at-risk.
\21\ This transformation entails multiplying a banking
organization's value-at-risk by the square root of the ratio of the
required holding period (ten days) to the holding period embodied in
the value-at-risk figure. For example, the value-at-risk calculated
according to a one-day holding period would be scaled-up by the
``square root of time'' by multiplying the value-at-risk by 3.16
(the square root of the ratio of a ten-day holding period to a one-
day holding period).
---------------------------------------------------------------------------
b. Value-at-risk must be calculated using an observation period
of at least one year to measure historical changes in rates and
prices.
c. A banking organization must update its historical rates and
prices at least once every three months and must reassess them
whenever market conditions change materially.
2. A banking organization may use discretion in recognizing
empirical correlations within each market risk factor
category.22 However, empirical correlations among risk
categories are not recognized. The value-at-risk measure for each
risk category must be added together on a simple sum basis to
determine the aggregate value-at-risk amount.
\22\ While a banking organization has flexibility to use
correlations, the Federal Reserve must be satisfied that there is
integrity in the banking organization's process for calculating
correlations.
---------------------------------------------------------------------------
3. A banking organization's models must accurately capture the
unique risks associated with options within each of the market risk
factor categories. The following minimum criteria apply to the
measurement of options risk:
a. A banking organization's internal model must capture the non-
linear price characteristics of option positions using an options
pricing technique. The banking organization must apply a minimum
ten-day holding period to option positions or positions that display
option-like characteristics. Banking organizations may not scale-up
the daily value-at-risk numbers by the square root of time.
b. A banking organization's internal model must capture the
volatilities of the rates and prices (that is, the vega) underlying
option positions and a banking organization should measure the
volatilities of the underlying instruments broken down by different
option maturities.
4. The accuracy of a banking organization's internal model will
be reviewed periodically by the Federal Reserve. Such review, during
which, when appropriate, the Federal Reserve may take into
consideration reports and opinions generated by external auditors or
qualified consultants, will include, at a minimum:
a. Verification that the internal validation processes described
in section III.B.2. of this appendix E are operating in a
satisfactory manner;
b. Affirmation that the formulae used in the calculation process
and for the pricing of options and other complex instruments, are
validated by a qualified unit of the banking organization, which in
all cases must be independent from the trading areas;
c. Confirmation that the structure of the internal model is
adequate with respect to the banking organization's activities and
geographical coverage;
d. Confirmation that the results of the banking organization's
back-testing of its internal measurement system (that is, comparing
value-at-risk estimates with actual profits and losses) are being
used effectively to monitor reliability of the model's estimates
over time; and
e. Affirmation that, for regulatory capital purposes, the model
processes all relevant data and that the modeling procedures conform
with the parameters and specifications set forth in this appendix E.
IV. The Standardized Approach
A. Debt Instruments
1. Specific Risk. a. The capital requirement for specific risk
is based on the identity of the obligor and, in the case of
corporate securities, on the credit rating and maturity of the
instrument. The specific risk capital requirement is calculated by
weighting the current market value of each individual position,
whether long or short, by the appropriate category factor as set
forth below and summing the weighted values. In measuring specific
risk, the banking organization may offset and exclude from its
calculations any matched positions in the identical issue (including
positions in derivatives). Even if the issuer is the same, no
offsetting is permitted between different issues since differences
in coupon rates, liquidity, call features, etc., mean that prices
may diverge in the short run. The categories and factors are:
------------------------------------------------------------------------
Factor
Category Remaining maturity [In
[contractual] percent]
------------------------------------------------------------------------
Government.................... N/A........................... 0.00
Qualifying.................... 6 months or less.............. 0.25
[[Page 38121]]
6 to 12 months................ 1.00
over 12 months................ 1.60
Other......................... N/A........................... 8.00
------------------------------------------------------------------------
b. The government category includes all forms of debt
instruments of central governments of the OECD-based group of
countries 23 including bonds, Treasury bills and other short-
term instruments, as well as local currency instruments of non-OECD
central governments to the extent that the subsidiary depository
institutions have liabilities booked in that currency.
\23\ The OECD-based group of countries is defined in section
III.B.1 of appendix A of this part.
---------------------------------------------------------------------------
c. The qualifying category includes securities of U.S.
government-sponsored agencies, general obligation securities issued
by states and other political subdivisions of the OECD-based group
of countries, multilateral development banks, and debt instruments
issued by U.S. depository institutions or OECD-banks that do not
qualify as capital of the issuing institution.24 It also
includes other securities, including revenue securities issued by
states and other political subdivisions of the OECD-based group of
countries, that are rated investment-grade by at least two
nationally recognized credit rating services, or rated investment-
grade by one nationally recognized credit rating agency and not less
than investment-grade by any other credit rating agency, or, with
the exception of securities issued by U.S. firms and subject to
review by the Federal Reserve, unrated but deemed to be of
comparable investment quality by the reporting banking organization
and the issuer has securities listed on a recognized stock exchange.
\24\ U.S. government-sponsored agencies, multilateral
development banks, and OECD banks are defined in section III.C.2. of
appendix A of this part.
---------------------------------------------------------------------------
d. The other category includes debt securities not qualifying as
government or qualifying securities. This would include non-OECD
central government securities that do not meet the criteria for the
government or qualifying categories. This category also includes
instruments that qualify as capital issued by other banking
organizations.
e. The Federal Reserve will consider the extent of a banking
organization's position in non-investment grade instruments
(sometimes referred to as high yield debt). If those holdings are
not well-diversified or otherwise represent a material position to
the institution, the Federal Reserve may prevent a banking
organization from offsetting positions in these instruments with
other positions in qualifying instruments that may be offset when
calculating its general market risk requirement. In addition, the
Board may impose a specific risk capital requirement as high as 16.0
percent.
2. General Market Risk. a. A banking organization may measure
its exposure to general market risk using, on a continuous basis,
either the maturity method (which uses standardized risk weights
that approximate the price sensitivity of various instruments) or
the duration method (where the institution calculates the precise
duration of each instrument, weighted by a specified change in
interest rates).
b. Both methods use a maturity-ladder that incorporates a series
of ``time-bands'' and ``zones'' to group together securities of
similar maturities and that are designed to take into account
differences in price sensitivities and interest rate volatilities
across different maturities. Under either method, the capital
requirement for general market risk is the sum of a base charge that
results from fully netting various risk-weighted positions and a
series of additional charges (add-ons), which effectively
``disallow'' part of the previous full netting to address basis and
yield curve risk.
c. For each currency in which a banking organization has
significant positions, a separate capital requirement must be
calculated. No netting of positions is permitted across different
currencies. Offsetting positions of the same amount in the same
issues, whether actual or notional, may be excluded from the
calculation, as well as closely matched swaps, forwards, futures,
and forward rate agreements (FRAs) that meet the conditions set out
in section IV.A.3. of this appendix E.
d. In the maturity method, the banking organization distributes
each long or short position (at current market value) of a debt
instrument into the time bands of the maturity ladder. Fixed-rate
instruments are allocated according to the remaining term to
maturity and floating-rate instruments according to the next
repricing date. A callable bond trading above par is slotted
according to its first call date, while a callable bond priced below
par is slotted according to remaining maturity. Fixed-rate mortgage-
backed securities, including collateralized mortgage obligations
(CMOs) and real estate mortgage investment conduits (REMICs), are
slotted according to their expected weighted average lives.
e. Once all long and short positions are slotted into the
appropriate time band, the long positions in each time-band are
summed and the short positions in each time-band are summed. The
summed long and/or short positions are multiplied by the appropriate
risk-weight factor (reflecting the price sensitivity of the
positions to changes in interest rates) to determine the risk-
weighted long and/or short position for each time-band. The risk
weights for each time-band are set out in Table I below:
Table I.--Maturity Method: Time-Bands and Weights
------------------------------------------------------------------------
Risk
Zone Coupon 3% or more Coupon less than 3% and weights
zero coupon bonds [percent]
------------------------------------------------------------------------
1....... Up to 1 month........... Up to 1 month.......... 0.00
1 up to 3 months........ 1 up to 3 months....... 0.20
3 up to 6 months........ 3 up to 6 months....... 0.40
6 up to 12 months....... 6 up to 12 months...... 0.70
2....... 1 up to 2 years......... 1 up to 1.9 years...... 1.25
2 up to 3 years......... 1.9 up to 2.8 years.... 1.75
3 up to 4 years......... 2.8 up to 3.6 years.... 2.25
3....... 4 up to 5 years......... 3.6 up to 4.3 years.... 2.75
5 up to 7 years......... 4.3 up to 5.7 years.... 3.25
7 up to 10 years........ 5.7 up to 7.3 years.... 3.75
10 up to 15 years....... 7.3 up to 9.3 years.... 4.50
15 up to 20 years....... 9.3 up to 10.6 years... 5.25
Over 20 years........... 10.6 up to 12 years.... 6.00
12 up to 20 years...... 8.00
Over 20 years.......... 12.50
------------------------------------------------------------------------
f. Within each time-band for which there are risk-weighted long
and short positions, the risk-weighted long and short positions are
then netted, resulting in a single net risk-weighted long or short
position for each time-band. Since different instruments and
different maturities may be included and netted within each time, a
capital requirement, referred to as the vertical
[[Page 38122]]
disallowance, is assessed to allow for basis risk. The vertical
disallowance capital requirement is 10.0 percent of the position
eliminated by the intra-time-band netting, that is, 10.0 percent of
the smaller of the net risk-weighted long or net risk-weighted short
position, or if the positions are equal, 10.0 percent of either
position.\25\ The vertical disallowances for each time-band are
absolute values, that is, neither long nor short. The vertical
disallowances for all time-bands in the maturity ladder are summed
and included as an element of the general market risk capital
requirement.
\25\ For example, if the sum of the weighted longs in a time-
band is $100 million and the sum of the weighted shorts is $90
million, the vertical disallowance for the time-band is 10.0 percent
of $90 million, or $9 million.
---------------------------------------------------------------------------
g. Within each zone for which there are risk-weighted long and
short positions in different time-bands, the weighted long and short
positions in all of the time-bands within the zone are then netted,
resulting in a single net long or short position for each zone.
Since different instruments and different maturities may be included
and netted within each zone, a capital requirement, referred to as
the horizontal disallowance, is assessed to allow for the imperfect
correlation of interest rates along the yield curve. The horizontal
disallowance capital requirement is calculated as a percentage of
the position eliminated by the intra-zone netting, that is, a
percentage of the smaller of the net risk-weighted long or net risk-
weighted short position, or if the positions are equal, a percentage
of either position.\26\ The percent disallowance factors for intra-
zone netting are set out in Table II in section IV.A.2.h. of this
appendix E. The horizontal disallowances, like the vertical
disallowances, are absolute values that are summed and included as
an element of the general market risk capital requirement.
\26\ For example, if the sum of the weighted longs in the 1-3
month time-band in Zone 1 is $8 million and the sum of the weighted
shorts in the 3-6 month time-band is $10 million, the horizontal
disallowance for the zone is forty percent of $8 million, or $3.2
million.
---------------------------------------------------------------------------
h. Risk-weighted long and short positions in different zones are
then netted between the zones. Zone 1 and zone 2 are netted if
possible, reducing or eliminating the net long or short position in
zone 1 or zone 2 as appropriate. Zone 2 and zone 3 are then netted
if possible, reducing or eliminating the net long or short position
in zone 2 or zone 3 as appropriate. Zone 3 and zone 1 are then
netted if possible, reducing or eliminating the long or short
position in zone 3 and zone 1 as appropriate. A horizontal
disallowance capital requirement is then assessed, calculated as a
percentage of the position eliminated by the inter-zone netting. The
horizontal disallowance capital requirements for each zone are then
summed as absolute values and included in the general market risk
capital charge. The percent disallowance factors for inter-zone
netting are set out in Table II below:
Table II.--Horizontal Disallowances
----------------------------------------------------------------------------------------------------------------
Between zones 1-
Zone Time-band Within the zone Between adjacent zones 3
----------------------------------------------------------------------------------------------------------------
1.... 0-1 month................... 40 percent.................. 40 percent................. 100 percent.
1-3 months.
3-6 months.
6-12 months.
2.... 1-2 years................... 30 percent.................. 40 percent................. 100 percent
2-3 years.
3-4 years.
3.... 1-5 years. 30 percent.................. 40 percent................. 100 percent
5-7 years.
7-10 years.
10-15 years.
15-20 years.
Over 20 years.
----------------------------------------------------------------------------------------------------------------
i. Finally, the net risk-weighted long or net risk-weighted
short positions remaining in the zones are summed to reach a single
net risk-weighted long or net risk-weighted short position for the
banking organization's portfolio. The sum of the absolute value of
this position and the vertical and horizontal disallowances is the
capital requirement for general market risk. An example of the
calculation of general market risk under the maturity method is in
Attachment II to this appendix E.
j. In the duration method, the banking organization, after
calculating each instrument's modified duration\27\ using a formula
that is subject to supervisory review, multiplies that modified
duration by the interest rate shock specified for an instrument of
that duration in Table III in section IV.A.2.k. of this appendix E.
The resulting product (representing the expected percentage change
in the price of the instrument for the given interest rate shock) is
then multiplied by the current market value of the instrument. The
resulting amount is then slotted as a long or short position into a
time-band in the maturity ladder in Table III on the basis of the
instrument's modified duration.\28\
\27\ The duration of an instrument is its approximate percentage
change in price for a 100 basis point parallel shift in the yield
curve assuming that its cash flow does not change when the yield
curve shifts. Modified duration is duration divided by a factor of 1
plus the interest rate.
\28\ For example, an instrument held by a banking organization
with a maturity of 4 years and 3 months and a current market value
of $1,000 might have a modified duration of 3.5 years. Based on its
modified duration, it would be subjected to the 75-basis point
interest rate shock, resulting in an expected price change of 2.625
percent (3.5 x 0.75). the corresponding expected change in price of
$26.25, calculated as 2.625 percent of $1,000, would be slotted as a
long position in the 3.3 to 4.0 year time-band of the maturity
ladder.
---------------------------------------------------------------------------
k. Once all of the banking organization's traded debt
instruments have been slotted into the maturity ladder, the banking
organization conducts the same rounds of netting and disallowances
described in sections IV.A.2.f. through IV.A.2.h. of this appendix E
for the maturity method, with the exception that the vertical
disallowance requirement for the duration method is 5.0 percent
(horizontal disallowances continue to be those set out in Table
II).\29\ As with the maturity method, the sum of the absolute value
of the final net position and the vertical and horizontal
disallowances is the general market risk capital requirement:
\29\ Two different vertical disallowances are used since the
duration method takes into account an instrument's specific
characteristics (maturity and coupon) and there is less opportunity
for measurement error.
Table III--Duration Method: Time-Bands and Assumed Changes in Yield
------------------------------------------------------------------------
Assumed
Zone Time-band change in
yield
------------------------------------------------------------------------
1....... Up to 1 month.................................... 1.00
1 up to 3 months................................. 1.00
3 up to 6 months................................. 1.00
6 up to 12 months................................ 1.00
2....... 1.0 up to 1.8 years.............................. 0.90
1.8 up to 2.6 years.............................. 0.80
2.6 up to 3.3 years.............................. 0.75
3....... 3.3 up to 4.0 years.............................. 0.75
4.0 up to 5.2 years.............................. 0.70
5.2 up to 6.8 years.............................. 0.65
6.8 up to 8.6 years.............................. 0.60
8.6 up to 9.9 years.............................. 0.60
9.9 up to 11.3 yrs............................... 0.60
[[Page 38123]]
11.3 up to 16.6 yrs.............................. 0.60
Over 16.6 years.................................. 0.60
------------------------------------------------------------------------
3. Interest rate derivatives. a. Debt derivatives and other off-
balance-sheet positions that are affected by changes in interest
rates are included in the measurement system under section IV.A. of
this appendix E (except for options and the associated underlyings,
which are included in the measurement system under the treatment
discussed in section IV.E. of this appendix E). A summary of the
treatment for debt derivatives is set out in Attachment III to this
appendix E.
b. Derivatives are converted into positions in the relevant
underlying instrument and are included in the calculation of
specific and general market risk capital charges as described above.
The amount to be included is the market value of the principal
amount of the underlying or of the notional underlying. For
instruments where the apparent notional amount differs from the
effective notional amount, a banking organization must use the
effective notional amount.
c. Futures and forward contracts (including FRAs) are broken
down into a combination of a long position and short position in the
notional security. The maturity of a future or a FRA is the period
until delivery or exercise of the contract, plus the life of the
underlying instrument.30 Where a range of instruments may be
delivered to fulfill the contract, the banking organization may
chose which deliverable instrument goes into the maturity or
duration ladder as the notional underlying. In the case of a future
on a corporate bond index, positions are included at the market
value of the notional underlying portfolio of securities.
\30\ For example, a long position in a June three-month interest
rate future (taken in April) is reported as a long position in a
government security with a maturity of five months and a short
position in a government security with a maturity of two months.
---------------------------------------------------------------------------
d. Swaps are treated as two notional positions in the relevant
instruments with appropriate maturities. The receiving side is
treated as the long position and the paying side is treated as the
short position.31 The separate sides of cross-currency swaps or
forward foreign exchange transactions are slotted in the relevant
maturity ladders for the currencies concerned. For swaps that pay or
receive a fixed or floating interest rate against some other
reference price, for example, an equity index, the interest rate
component is slotted into the appropriate repricing maturity
category, with the long or short position attributable to the equity
component being included in the equity framework set out in section
IV.B. of this appendix E.32
\31\ For example, an interest rate swap under which a banking
organization is receiving floating-rate interest and paying fixed is
treated as a long position in a floating rate instrument with a
maturity equivalent to the period until the next interest reset date
and a short position in a fixed-rate instrument with a maturity
equivalent to the remaining life of the swap.
\32\ A banking organization with a large swap book may, with
prior approval of the Federal Reserve, use alternative formulae to
calculate the positions to be included in the maturity or duration
ladder. For example, a banking organization could first convert the
payments required by the swap into present values. For that purpose,
each payment would be discounted using zero coupon yields, and the
payment's present value entered into the appropriate time-band using
procedures that apply to zero (or low) coupon bonds. The net amounts
would then be treated as bonds, and slotted into the general market
risk framework. Such alternative treatments will, however, only be
allowed if: (i) the Federal Reserve is fully satisfied with the
accuracy of the system being used, (ii) the positions calculated
fully reflect the sensitivity of the cash flows to interest rate
changes; and (iii) the positions are denominated in the same
currency.
---------------------------------------------------------------------------
e. A banking organization may offset long and short positions
(both actual and notional) in identical derivative instruments with
exactly the same issuer, coupon, currency, and maturity before
slotting these positions into time-bands. A matched position in a
future and its corresponding underlying may also be fully offset
and, thus, excluded from the calculation, except when the future
comprises a range of deliverable instruments. However, in cases
where, among the range of deliverable instruments, there is a
readily identifiable underlying instrument that is most profitable
for the trader with a short position to deliver, positions in the
futures contract and the instrument may be offset. No offsetting is
allowed between positions in different currencies.
f. Offsetting positions in the same category of instruments can
in certain circumstances be regarded as matched and treated by the
banking organization as a single net position which should be
entered into the appropriate time-band. To qualify for this
treatment the positions must be based on the same underlying
instrument, be of the same nominal value, and be denominated in the
same currency. The separate sides of different swaps may also be
``matched'' subject to the same conditions. In addition:
i. For futures, offsetting positions in the notional or
underlying instruments to which the futures contract relates must be
for identical instruments and the instruments must mature within
seven days of each other;
ii. For swaps and FRAs, the reference rate (for floating rate
positions) must be identical and the coupon closely matched (i.e.,
within 15 basis points); and
iii. For swaps, FRAs and forwards, the next interest reset date,
or for fixed coupon positions or forwards the remaining maturity,
must correspond within the following limits: If the reset (remaining
maturity) dates occur within one month, then the reset dates must be
on the same day; if the reset dates occur between one month and one
year later, then the reset dates must occur within seven days of
each other, or if the reset dates occur over one year later, then
the reset dates must occur within thirty days of each other.
g. Interest rate and currency swaps, FRAs, forward foreign
exchange contracts and interest rate futures are not subject to a
specific risk charge. This exemption also applies to futures on a
short-term (e.g., LIBOR) interest rate index. However, in the case
of futures contracts where the underlying is a debt security, or an
index representing a basket of debt securities, a specific risk
charge will apply according to the category of the issuer as set out
in section IV.A.2. of this appendix E.
B. Equities
1. Specific risk. The measure of specific risk is calculated on
the basis of the banking organization's gross equity positions, that
is, the absolute sum of all long equity positions and of all short
equity positions at current market value.33 The specific risk
capital requirement is 8.0 percent of that sum, unless the portfolio
is both liquid and well-diversified, in which case the specific risk
capital requirement is 4.0 percent of the gross equity position. A
specific risk charge of 2.0 percent applies to the net long or short
position in a broad, diversified equity index and is viewed as
necessary to provide for risks associated with contract
execution.34
\33\ Matched positions in each identical equity in each national
market may be treated as offsetting and excluded from the capital
calculation, with any remaining position included in the
calculations for specific and general market risk. For example, a
future in a given equity may be offset against an opposite cash
position in the same equity.
\34\ A portfolio that is liquid and well-diversified is
characterized by a limited sensitivity to price changes of any
single equity issue or closely related group of equity issues held
in the portfolio. The volatility of the portfolio's value should not
be dominated by the volatility of any individual equity issue or by
equity issues from any single industry or economic sector. In
general, such portfolios should be characterized by a large number
of individual equity positions, with no single position representing
a large portion of the portfolio's total market value. In addition,
it would generally be the case that a sizable proportion of the
portfolio would be comprised of issues traded on organized exchanges
or in well-established over-the-counter markets.
2. General Market risk. The measure of general market risk is
based on the difference between the sum of the long positions and
the sum of the short positions (i.e., the overall net position in an
equity market) at current market value. An overall net position must
be separately calculated for each national market in which the
banking organization holds equities. The capital requirement for
general market risk is 8.0 percent of the net position in each
equity market.
3. Equity derivatives. a. Equity derivatives and other off-
balance-sheet positions that are affected by changes in equity
prices are included in the measurement system under section IV.B. of
this appendix E (except for equity options, equity index options,
and the associated underlying, which are included in the measurement
system under the treatment discussed in section IV.E. of this
appendix E).35 This includes futures and swaps on both
[[Page 38124]]
individual equities and on equity indices. Equity derivatives should be
converted into notional equity positions in the relevant underlying.
A summary of the rules for equity derivatives is set out in
Attachment III to this appendix E.
\35\ Where equities are part of a forward contract (both
equities to be received or to be delivered), any interest rate or
foreign currency exposure from the other side of the contract should
be appropriately included in the measurement system in sections
IV.A. and IV.C. of this appendix E.
---------------------------------------------------------------------------
b. Futures and forward contracts relating to individual equities
should be reported at current market prices of the underlying.
Futures relating to equity indices should be reported as the marked-
to-market value of the notional underlying equity portfolio. Equity
swaps are treated as two notional positions, with the receiving side
as the long position and the paying side as the short
position.36 If one of the legs involves receiving/paying a
fixed or floating interest rate, the exposure should be slotted into
the appropriate repricing maturity band for debt securities. The
stock index is covered by the equity treatment.
\36\ For example, an equity swap in which a banking organization
is receiving an amount based on the change in value of one
particular equity or equity index and paying a different index will
be treated as a long position in the former and a short position in
the latter.
---------------------------------------------------------------------------
c. In the case of futures-related arbitrage strategies, the 2.0
percent specific risk charge applicable to broad diversified equity
indices may be applied to only one index. The opposite position is
exempt from a specific risk charge. The strategies qualifying for
this treatment are:
i. When the banking organization takes an opposite position in
exactly the same index at different dates; and
ii. When the banking organization has an opposite position in
different but similar indices at the same date, subject to
supervisory oversight.
d. If a banking organization engages in a deliberate arbitrage
strategy, in which a futures contract on a broad diversified equity
index matches a basket of securities, it may exclude both positions
from the standardized approach on condition that the trade has been
deliberately entered into and separately controlled and the
composition of the basket of stocks represents at least 90 percent
of the market value of the index. In such a case, the minimum
capital requirement is 4.0 percent (that is, 2.0 percent of the
gross value of the positions on each side) to reflect risk
associated with executing the transaction. This applies even if all
of the securities comprising the index are held in identical
proportions. Any excess value of the securities comprising the
basket over the value of the futures contract or excess value of the
futures contract over the value of the basket is treated as an open
long or short position.
e. If a banking organization takes a position in depository
receipts 37 against an opposite position in the underlying
equity, it may offset the position.
\37\ Depository receipts are instruments issued by a trust
company or other depository institution evidencing the deposit of
foreign securities and facilitating trading in such instruments on
U.S. stock exchanges.
---------------------------------------------------------------------------
C. Foreign Exchange Risk
1. The capital requirement for foreign exchange risk covers the
risk of holding or taking positions in foreign currencies, including
gold, and is based on a banking organization's net open long
positions or net open short positions in each currency, whether or
not those positions are in the trading portfolio, plus the net open
position in gold, regardless of sign.38
\38\ Gold is treated as a foreign exchange position rather than
a commodity because its volatility is more in line with foreign
currencies and banking organizations manage it in a manner similar
to foreign currencies.
2. A banking organization's net open position in each currency
(and gold) is calculated by summing:
a. The net spot position (i.e., all asset items less all
liability items, including accrued interest earned but not yet
received and accrued expenses, denominated in the currency in
question);
b. All foreign exchange derivative instruments and other off-
balance-sheet positions that are affected by changes in exchange
rates are included in the measurement system under section IV.C. of
this appendix E (except for options and their associated
underlyings, which are included in the measurement system under the
treatment discussed in section IV.E. of this appendix E). Forward
currency positions should be valued at current spot market exchange
rates. For a banking organization in which the basis of its normal
management accounting is to use net present values, forward
positions may be discounted to net present values as an acceptable
way of measuring currency positions for regulatory capital purposes;
c. Guarantees (and similar instruments) that are certain to be
called and are likely to be irrevocable;
d. Net future income/expenses not yet accrued but already fully
hedged (at the discretion of the banking organization). A banking
organization that includes future income and expenses must do so on
a consistent basis without selecting expected future flows in order
to reduce the banking organization's position; and
e. Any other item representing a profit or loss in foreign
currencies.
3. For measuring a banking organization's open positions,
positions in composite currencies, such as the ECU, may be either
treated as a currency in their own right or split into their
component parts on a consistent basis. Positions in gold are
measured in the same manner as described in section IV.D. of this
appendix E.39
\39\ Where gold is part of a forward contract (quantity of gold
to be received or to be delivered), any interest rate or foreign
currency exposure from the other side of the contract should be
included in the measurement system in section IV.A. (as a zero
coupon instrument) and IV.C. of this appendix E.
---------------------------------------------------------------------------
4. The capital requirement is determined by converting the
nominal amount (or net present value) of the net open position in
each foreign currency (and gold) at spot rates into the reporting
currency. The capital requirement is 8.0 percent of the sum of:
a. The greater of the sum of the net short open positions or,
the sum of the net long open positions; and
b. The net open position in gold, regardless of sign.40
\40\ For examples, a banking organizations has the following net
currency positions: Yen=+50, DM=+100, GB=+150, FFR=-20, US$=-180,
and gold=-35. The banking organization would sum its long positions
(total=+300) and sum its short positions (total=-200). The banking
organization's capital requirement for foreign exchange market risk
would be: (300 (the larger of the summed long and short positions) +
35 (gold)) x 8.0%=26.80.
---------------------------------------------------------------------------
5. Where a banking organization is assessing its foreign
exchange risk on a consolidated basis, it may be technically
impractical in the case of some marginal operations to include the
currency positions of a foreign branch or subsidiary of the banking
organization. In such cases, the internal limit in each currency may
be used as a proxy for the positions, provided there is adequate ex
post monitoring of actual positions complying with such limits. In
these circumstances, the limits should be added, regardless of sign,
to the net open position in each currency.
D. Commodities Risk.
1. Measurement methods. This section provides a minimum capital
requirement to cover the risk of holding or taking positions in
commodities. There are two methods under the standardized approach
for measuring commodity market risk--the simplified method and the
maturity method. These methods are only appropriate for banking
organizations that conduct a limited amount of commodities business.
All other banking organizations must adopt an internal measurement
system conforming to the criteria in section III. of this appendix
E.
2. Base capital requirement. Under both the simplified and
maturity methods, each long and short commodity position (spot and
forward) is expressed in terms of the standard unit of measurement
(such as barrels, kilos, or grams). The open positions in each
category of commodities are then converted at current spot rates
into U.S. currency, with long and short positions offset to arrive
at the net open position in each commodity. Positions in different
categories of commodities may not, generally, be offset.41
Under either method, the base capital requirement is 15.0 percent of
the net open position, long or short, in each commodity.42
\41\ However, offsetting is permitted between different sub-
categories of the same commodity in cases where the sub-categories
are deliverable against each other.
\42\ When the funding of a commodity position opens a banking
organization to interest rate or foreign exchange exposure the
relevant positions should be included in the measures of interest
rate and foreign exchange risk described in section IV.A. and IV.C
of this appendix E. When a commodity is part of a forward contract,
any interest or foreign currency exposure from the other side of the
contract should be appropriately included in the measurement systems
in sections IV.A. and IV.C. of this appendix E.
---------------------------------------------------------------------------
3. Simplified method. To protect a banking organization against
basis risk, interest rate risk, and forward gap risk, each category
of commodity is also subject to a 3.0 percent capital requirement on
the banking organization's gross positions, long plus short, in the
particular commodity. In
[[Page 38125]]
valuing gross positions in commodity derivatives for this purpose, a
banking organization should use the current spot price. The total
capital requirement for commodities risk is the sum of the 15.0
percent base charges for each net commodity position and the 3.0
percent requirements on the gross commodity positions.
4. Maturity method. a. Under this method, a banking organization
must slot each long and short commodity position (converted into
U.S. currency at current spot rates) into a maturity ladder. The
time-bands for the maturity ladder are; from zero to one month, one
up to three months, three up to six months, six up to twelve months,
one up to two years, two up to three years, and over three years. A
separate maturity ladder is used for each category of commodity.
Physical commodities are allocated to the first time-band.
b. In order to capture forward gap and interest rate risk within
a time-band (together sometimes referred to as curvature/spread
risk), offsetting long and short positions in each time-band are
subject to an additional capital requirement. Beginning with the
shortest-term time-band and continuing with subsequent time-bands,
the amount of the matched short positions plus the amount of the
matched long position is multiplied by a spread rate of 1.5 percent.
c. The unmatched net position from shorter-term time-bands must
be carried forward to offset exposures in longer-term time-bands. A
capital requirement of 0.6 percent of the net position carried
forward is added for each time-band that the net position is carried
forward.43 The total capital requirement for commodities risk
is the sum of the 15.0 percent base capital requirement for each net
commodity position and the additional requirements for matched
positions and for unmatched positions carried forward. An example of
this calculation is in Attachment IV to this appendix E.
\43\ For example, if $200 short is carried forward from the 3-6
month time-band to the 1-2 year time-band, the capital charge would
be $200 x .006 x 2 = $2.40.
---------------------------------------------------------------------------
5. Commodity derivatives. Commodity derivatives and other off-
balance-sheet positions that are affected by changes in commodity
prices are included in the measurement system under section IV.D. of
this appendix E (except for options and the associated underlying,
which are included in the measurement system under the treatment
discussed in section IV.E. of this appendix E). Commodity
derivatives are converted into notional commodity positions. Under
the maturity method, the positions are slotted into maturity time-
bands as follows:
a. Futures and forward contracts relating to individual
commodities are incorporated in the measurement system as notional
amounts (of, for example, barrels or kilos) that are converted to
U.S. dollars at current spot rates and are assigned a maturity
according to expiration date;
b. Commodity swaps where one side of the contract is a fixed
price and the other side is the current market price are
incorporated as a series of positions equal to the notional amount
of the contract at current spot rates, with one position
corresponding to each payment on the swap and slotted in the
maturity ladder accordingly. The positions are long positions if the
banking organization is paying a fixed price and receiving a
floating price, and short positions if the banking organization is
receiving a fixed price and paying a floating price; 44 and
\44\ If one of the sides of the transaction involves receiving/
paying a fixed or floating interest rate, that exposure should be
slotted into the appropriate repricing maturity band in section
IV.A. of this appendix E.
---------------------------------------------------------------------------
c. Commodity swaps where the sides of the transaction are in
different commodities are included in the relevant reporting ladder.
No offsetting is allowed unless the commodities are in the same sub-
category.
E. Options
1. Three alternatives are available for a banking organization
to use in measuring its market risk for options activities. A
banking organization that only has purchased options may use the
simplified method set forth in section IV.E.2. of this appendix E. A
banking organization that also writes options may use the scenario
method described in section IV.E.3. of this appendix E or the delta-
plus method set forth in section IV.E.4. of this appendix E.45
These methods may only be used by banking organizations which, in
relative terms, have limited options activities. Banking
organizations with more significant options business are expected to
adopt an internal measurement system conforming to the criteria in
section III. of this appendix E. Regardless of the method used,
specific risk related to the issuer of an instrument still applies
to options positions for equities, equity indices and corporate debt
securities as set forth in sections IV.A. and IV.B. of this appendix
E. There remains a separate capital requirement for counterparty
credit risk as set forth in appendix A to this part.
\45\ Unless all their written option positions are hedged by
perfectly matched long positions in exactly the same options, in
which case there is no capital requirement for market risk.
---------------------------------------------------------------------------
2. Under the simplified and scenario methods, the positions for
the options and the associated underlying, cash or forward, are not
included in the measurement framework for debt securities, equities,
foreign exchange or commodities risk as set forth in sections IV.A.
through IV.D. of this appendix E. Rather, they are subject to
capital requirements as calculated in this section. The capital
requirements calculated under this section IV.E. should then be
added to the capital requirements for debt securities, equities,
foreign exchange and commodities risk as appropriate. Under the
delta-plus method, the delta equivalent position 46 for each
option is included in the measurement frameworks set forth in
sections IV.A. through IV.D. of this appendix E.
\46\ The delta equivalent of an option is the option's delta
value multiplied by its principal or notional value. The delta value
of an option represents the expected change in the option's price as
a proportion of a small change in the price of the underlying
instrument. For example, an option whose price changes $1 for every
$2 dollar change in the price of the underlying instrument has a
delta of 0.50.
---------------------------------------------------------------------------
3. A banking organization that has only a limited amount and
range of purchased options may use the following simplified approach
to measure its market risk exposure.
a. For a banking organization with a long cash position and a
long put or with a short cash position and a long call, the capital
requirement is the market value of the underlying instrument
multiplied by the sum of the specific and general market risk
requirements for the underlying (that is, the specific and general
market risk requirements that would have applied to the underlying
directly under sections IV.A. through IV.D. of this appendix
E.47), less the amount the option is in the money (if any)
bounded at zero.48
\47\ Some options (e.g., where the underlying is an interest
rate, a currency, or a commodity) bear no specific risk but specific
risk will be present in the case of options on corporate debt
securities and for options on equities and equity indices.
\48\ For example, if a holder of 100 shares currently valued at
$10 each has an equivalent put option with a strike price of $11,
the capital charge would be: $1,000 x 16.0 percent (e.g., 8.0
percent specific plus 8.0 percent general market risk) = $160, less
the amount the option is in the money ($11-$10) x 100 = $100, i.e.,
the capital charge would be $60. A similar methodology applies for
options whose underlying is a foreign currency, a debt security or a
commodity.
---------------------------------------------------------------------------
b. For a banking organization with a long call or a long put,
the capital charge is the lesser of:
i. The market value of the underlying security multiplied by the
sum of specific and general market risk requirements for the
underlying (that is, the specific and general market risk
requirements that would have applied to the underlying directly
under sections IV.A. through IV.D. of this appendix E 49); or
\49\ See footnote 47 in section IV.E.3.a of this appendix E.
---------------------------------------------------------------------------
ii. The market value of the option.
c. Under this measure, the capital requirement for currency
options is 8.0 percent of the market value of the underlying and for
commodity options is 15.0 percent of the market value of the
underlying.
4. Under the scenario approach, a banking organization revalues
its options and related hedging positions by changing the underlying
rate or price over a specified range and by assuming different
levels of volatility for that rate or price.
a. For each of its option portfolios, a banking organization
constructs a grid based on a fixed range of changes in the
portfolio's risk factors and calculates changes in the value of the
option portfolio at each point within the grid. For this purpose, an
option portfolio consists of an option and any related hedging
positions or multiple options and related hedging positions that are
grouped together according to their remaining maturity or the type
of underlying.
b. Options based on interest rates and debt instruments are
grouped into portfolios according to the maturity zones that are set
forth in section IV.A. of this appendix E. (Zone 1 instruments have
a remaining maturity of up to 1 year, zone 2 instruments
[[Page 38126]]
have a remaining maturity from 1 year up to 4 years, and zone 3
instruments have a remaining maturity of 4 years or more.) These
options and the associated hedging positions should be evaluated
under the assumption that the relevant interest rates move
simultaneously. For options based on equities, separate grids are
constructed for each individual equity issue and index. For options
based on exchange rates, separate grids are constructed for
individual exchange rates. For options based on commodities,
separate grids are constructed for each category of commodity (as
defined in sections I.B.3. and IV.D. of this appendix E).
c. For option portfolios with options based on equities,
exchange rates, and commodities, the first dimension of the grid
consists of rate or price changes within a specified range above and
below the current market value of the underlying; for equities, the
range is 12.0 percent (or in the case of an index
8.0 percent), for exchange rates the range is
8.0 percent, and for commodities the range is
15.0 percent. For option portfolios with options based
on interest rates, the range for the first dimension of the grid
depends on the remaining maturity zone. The range for zone 1 is
100 basis points, the range for zone 2 is
90 basis points, and the range for zone 3 is 75 basis
points. For all option portfolios, the range is divided into at
least ten equally spaced intervals. The second dimension of each
grid is a shift in the volatility of the underlying rate or price
equal to 25.0 percent of the current volatility.50
\50\ For example, if the underlying in an equity instrument with
a current market value of $100 and a volatility of 20 percent, the
first dimension of the grid would range from $88 to $112, divided
into ten intervals of $2.40 and the second dimension would assume
volatilities of 15 percent, 20 percent, and 25 percent.
---------------------------------------------------------------------------
d. For each assumed volatility and rate or price change (a
scenario), the banking organization revalues each option portfolio.
The market risk capital requirement for the portfolio is the largest
loss in value from among the scenario revaluations. The total market
risk capital requirement for all option portfolios is the sum of the
individual option portfolio capital requirements.
e. The Federal Reserve will review the application of the
scenario approach, particularly regarding the precise way the
analysis is constructed. A banking organization using the scenario
approach should meet the appropriate qualitative criteria set forth
in section III.B. of this appendix E.
5. Under the delta-plus method, a banking organization that
writes options may include delta-weighted options positions within
each measurement framework as set forth in sections IV.A. through
IV.D. of this appendix E.
a. Options positions should be measured as a position equal to
the market value of the underlying instrument multiplied by the
delta. In addition, a banking organization must measure the
sensitivities of the option's gamma (the change of the delta for a
given change in the price of the underlying) and vega (the
sensitivity of the option price with respect to a change in
volatility) to calculate the total capital requirement. These
sensitivities may be calculated according to an exchange model
approved by the Federal Reserve or to the banking organization's own
options pricing model, subject to review by the Federal Reserve.
b. For options with debt instruments or interest rates as the
underlying instrument, delta-weighted options positions should be
slotted into the debt instrument time-bands in section IV.A. of this
appendix E using a two-legged approach (as is used for other
derivatives), requiring one entry at the time the underlying
contract takes effect and one at the time the underlying contract
matures.51 Floating rate instruments with caps or floors should
be treated as a combination of floating rate securities and a series
of European-style options.52 A banking organization must also
calculate the gamma and vega for each such option position
(including hedge positions). The results should be slotted into
separate maturity ladders by currency. For options such as caps and
floors whose underlying instrument is an interest rate, the delta
and gamma should be expressed in terms of a hypothetical underlying
security. Subsequently:
\51\ For example, in April, a purchased call option on a June
three-month interest-rate future would be considered on the basis of
its delta-equivalent value to be a long position with a maturity of
five months and a short position with a maturity of two months. The
written option would be slotted as a long position with a maturity
of two months and a short position with a maturity of five months.
\52\ For example, the holder of a three-year floating rate bond
indexed to six-month LIBOR with a cap of 15 percent would treat the
bond as a debt security that reprices in six months, and a series of
five written call options on a FRA with a strike rate of 15 percent,
each slotted as a short position at the expiration date of the
option and as a long position at the time the FRA matures.
i. For gamma risk, for each time-band, net gammas that are
negative are multiplied by the risk weights set out in Table IV in
section IV.E.5.b.iv. of this appendix E and by the square of the
market value of the underlying instrument (net positive gammas may
be disregarded);
ii. For volatility risk, a banking organization calculates the
capital requirements for vega in each time-band assuming a
proportional shift in volatility of 25.0 percent;
iii. The capital requirement is the absolute value of the sum of
the individual capital requirements for net negative gammas plus the
absolute value of the sum of the individual capital requirements for
vega risk for each time-band; and
iv. The delta plus method risk weights are:
Table IV.--Delta Plus Method Risk Weights
------------------------------------------------------------------------
Modified
duration Assumed Risk-weight
Time-band (average interest for
assumed for rate change gamma\1\
time band) (%)
------------------------------------------------------------------------
Under 1 month.................... 0.00 1.00 0.00000
1 up to 3 months................. 0.20 1.00 0.00020
3 up to 6 months................. 0.40 1.00 0.00080
6 up to 12 months................ 0.70 1.00 0.00245
1 up to 2 years.................. 1.40 0.90 0.00794
2 up to 3 years.................. 2.20 0.80 0.01549
3 up to 4 years.................. 3.00 0.75 0.02531
4 up to 5 years.................. 3.65 0.75 0.03747
5 up to 7 years.................. 4.65 0.70 0.05298
7 up to 10 years................. 5.80 0.65 0.07106
10 up to 15 years................ 7.50 0.60 0.10125
15 up to 20 years................ 8.75 0.60 0.13781
Over 20 years.................... 10.00 0.60 0.18000
------------------------------------------------------------------------
\1\ According to the Taylor expansion, the risk weights are calculated
as \1/2\ (modified duration x assumed interest rate change) \2\ 100.
c. For options with equities as the underlying, delta-weighted
option positions should be incorporated in the measure of market
risk set forth in section IV.B. of this appendix E. Individual
equity issues and indices should be treated as separate underlyings.
In addition to the capital requirement for delta risk, a banking
[[Page 38127]]
organization should apply a further capital charge for gamma and vega
risk:
i. For gamma risk, the net gammas that are negative for each
underlying are multiplied by 0.72 percent (in the case of an
individual equity) or 0.32 percent (in the case of an index as the
underlying) and by the square of the market value of the underlying;
ii. For volatility risk, a banking organization calculates the
capital requirement for vega for each underlying, assuming a
proportional shift in volatility of 25.0 percent; and
iii. The capital requirement is the absolute value of the sum of
the individual capital requirements for net negative gammas plus the
absolute value of the individual capital requirements for vega risk.
d. For options of foreign exchange and gold positions, the net
delta (or delta-based) equivalent of the total book of foreign
currency and gold options is incorporated into the measurement of
the exposure in a single currency position as set forth in section
IV.C. of this appendix E. The gamma and vega risks should be
measured as follows:
i. For gamma risk, for each underlying exchange rate, net gammas
that are negative are multiplied by 0.32 percent and by the square
of the market value of the positions;
ii. For volatility risk, a banking organization calculates the
capital requirements for vega for each currency pair and gold
assuming a proportional shift in volatility of 25.0
percent; and
iii. The capital requirement is the absolute value of the sum of
the individual capital requirements for net negative gammas plus the
absolute value of the sum of the individual capital requirements for
vega risk.
e. For options on commodities, the delta-weighted positions are
incorporated in one of the measures described in section IV.D. of
this appendix E. In addition, a banking organization must apply a
capital requirement for gamma and vega risk:
i. For gamma risk, net gammas that are negative for each
underlying are multiplied by 1.125 percent and by the square of the
market value of the commodity;
ii. For volatility risk, a banking organization calculates the
capital requirements for vega for each commodity assuming a
proportional shift in volatility of +/- 25.0 percent; and
iii. The capital requirement is the absolute value of the sum of
the individual capital requirements for net negative gammas plus the
absolute value of the sum of the individual capital requirements for
vega risk.
f. Under certain conditions and to a limited extent, the Federal
Reserve may permit banking organizations that are significant
traders in options with debt securities or interest rates as the
underlying to net positive and negative gammas and vegas across
time-bands. Such netting must be based on prudent and conservative
assumptions and the banking organization must materially meet the
qualitative standards set forth in section III.B. of this appendix
E.
g. A banking organization may base the calculation of vega risk
on a volatility ladder in which the implied change in volatility
varies with the maturity of the option. The assumed proportional
shift in volatility must be at least +/- 25.0 percent at the short
end of the maturity spectrum. The proportional shift for longer
maturities must be at least as stringent instatistical terms as the
25.0 percent shift at the short end.
h. A banking organization should also monitor the risks of rho
(the rate of change of the value of the option with respect to the
interest rate) and theta (the rate of change of the value of the
option with respect to time).
Attachments to Appendix E
Attachment I--Sample Calculation of Eligible Tier 1, Tier 2, and Tier 3
Capital for the Risk-Based Capital Ratio Adjusted for Market Risk
a. In each example the weighted-risk assets are $8000 and the
market risk-adjusted assets are $625 (capital requirement for market
risk = $50, $50 x 12.5 = $625):
Example 1: A banking organization has the following qualifying
capital: Tier 1 = $600, Tier 2 = $100, Tier 3 = $1000.
(1) The minimum capital requirement for credit risk is $640
($8000 x 8.0%). This requirement could be satisfied with $540 of
Tier 1 capital and $100 of Tier 2 capital.
(2) The remaining capital available for market risk would be:
Tier 1 = $60, Tier 2 = 0, and Tier 3 = $1000. The minimum capital
requirement for market risk is $50 ($625 x 8.0%). Eligible Tier 3
capital would be limited to $125 ($50 x 2.5).
(3) The Tier 1 capital required to support market risk could be
satisfied by allocating $14 ($50 x .285), with eligible Tier 3
capital used for market risk being $36 ($50 - $14).
(4) Total qualifying and eligible capital would be: $540 (Tier
1) + $100 (Tier 2) + $60 (Tier 1, comprising $14 allocated for
market risk and $46 unallocated) + $36 (Tier 3) = $736. The banking
organization's ratio of qualifying and eligible capital to weighted-
risk assets adjusted for market risk would be: $736/$8,625) = 8.5%.
Example 2: A banking organization has the following qualifying
capital: Tier 1 = $500, Tier 2 = $140, Tier 3 = $600.
(1) The minimum capital requirement for credit risk is $640
($8000 x 8.0%). This requirement could be satisfied with $500 of
Tier 1 capital and $140 of Tier 2 capital.
(2) The remaining capital available for market risk would be:
Tier 1 = 0, Tier 2 = $0, and Tier 3 = $600. Eligible Tier 3 capital
would be limited to $0 (0 x 2.5). Because there is no Tier 1 capital
required to support market risk, no eligible Tier 3 capital may be
used for market risk.
(3) Total qualifying and eligible capital would be: $500 (Tier
1) + $140 (Tier 2) = $640. The banking organization's ratio of
qualifying and eligible capital to weighted-risk assets adjusted for
market risk would be: $640/$8,625) = 7.4%.
b. In both of the examples described in paragraph a. of this
attachment the total of Tier 2 and Tier 3 capital for credit and
market risk is not greater than 100 percent of Tier 1 capital for
credit and market risk and the total of Tier 2 capital for credit
risk is not greater than 100 percent of Tier 1 capital for credit
risk.
Attachment II--Sample Calculation of General Market Risk for Debt
Instruments Using the Maturity Method
a. A banking organization with the following positions would
slot them into a maturity ladder as shown below:
i. Qualifying bond, $13.33mn market value, remaining maturity 8
years, coupon 8%;
ii. Government bond, $75mn market value, remaining maturity 2
months, coupon 7%;
iii. Interest rate swap, $150mn, banking organization receives
floating rate interest and pays fixed, next interest reset after 12
months, remaining life of swap is 8 years (assumes the current
interest rate is identical to the one the swap is based on); and
iv. Long position in interest rate future, $50mn, delivery date
after 6 months, life of underlying government security is 3.5 years
(assumes the current interest rate is identical to the one the swap
is based on).
--------------------------------------------------------------------------------------------------------------------------------------------------------
Risk wght Risk-weighted Net time-band
Zone Time-band and position (%) position positions Net zone positions
--------------------------------------------------------------------------------------------------------------------------------------------------------
1............... 10-1 mth................................................. 0.00
1-3 mth Long 75 Gov.bond................................. 0.20 Long 0.15........... Long 0.15........... Long 1.00
3-6 mt Short 50 Future................................... 0.40 Short 0.20.......... Short 0.20..........
6-12 mths Long 150 Swap.................................. 0.70 Long 1.05........... Long 1.05...........
2............... 1-2 yrs.................................................. 1.25
2-3 yrs.................................................. 1.75
3-4 yrs Long 50.......................................... 2.25 Long 1.125.......... Long 1.125.......... Long 1.125
Future
3............... 4-5 yrs.................................................. 2.75
5-7 yrs.................................................. 3.25
7-10 yrs Short 150 Swap Long 13.13 Qual Bond............. 3.75 Short 5.625......... Short 5.125......... Short 5.125
Long 0.50...........
10-15 yrs................................................ 4.50
[[Page 38128]]
15-20 yrs................................................ 5.25
over 20 yrs.............................................. 6.00
--------------------------------------------------------------------------------------------------------------------------------------------------------
b. A vertical disallowance would be calculated for time-band 7-
10 years. It would be 10 percent of the matched positions in the
time-band--10.0x0.5=0.05 ($50,000).
c. A horizontal disallowance would be calculated for zone 1. It
would be 40 percent of the matched positions in the zone--
40.0x0.20=0.80 ($80,000). The remaining net position in Zone 1 would
be +1.00 .
d. A horizontal disallowance would be calculated for adjacent
zones 2 and 3. It would be 40 percent of the matched positions
between the zones--40.0x1.125=0.45 (450,000). The remaining position
in zone 3 would be -4.00.
e. A horizontal disallowance would be calculated between zones 1
and 3. It would be 100 percent of the matched positions between the
zones--100x1.00=1.00 (1,000,000).
f. The remaining net open position for the banking organization
would be 3.00 ($3,000,000).
The total capital requirement for general market risk for this
portfolio would be:
The vertical disallowance.................................. $50,000
Horizontal disallowance in zone 1.......................... 80,000
Horizontal disallowance between zones 2 and 3.............. 450,000
Horizontal disallowance between zones 1 and 3.............. 1,000,000
The overall net open position.............................. 3,000,000
Total requirement for general market risk.............. 4,580,000
Attachment III--Summary of Treatment for Interest Rate and Equity
Derivatives
Summary of Treatment for Interest Rate Derivatives
------------------------------------------------------------------------
Specific risk
Instrument charge General market risk charge
------------------------------------------------------------------------
Exchange-Traded Future:
Government security..... No........... Yes, as two positions.
Corporate debt security. Yes.......... Yes, as two positions.
Index on short-term No........... Yes, as two positions.
interest rates (e.g.
LIBOR).
OTC Forward:
Government security..... No........... Yes, as two positions.
Corporate debt security. Yes.......... Yes, as two positions.
Index on short-term No........... Yes, as two positions.
interest rates.
FRAs, Swaps............. No........... Yes, as two positions.
Forward foreign exchange No........... Yes, as one position in
each currency.
Options:
Government security..... No........... For each type of
transaction, either:
Corporate debt security. Yes.......... (a) Carve out together with
the associated hedging
positions
Index on short-term No........... --simplified method--
interest rates. scenario analysis--
internal models, or
(b) General market risk
charge according to the
Delta-plus method (gamma
and vega receive separate
capital charges)
------------------------------------------------------------------------
Note: Specific risk charges relate to the issuer of the instrument.
There remains a separate capital requirement for counterparty credit
risk.
Summary of Treatment for Equity Derivatives
------------------------------------------------------------------------
Specific risk
Instrument charge General market risk charge
------------------------------------------------------------------------
Exchange-Traded or OTC
Future:
Individual equity....... Yes.......... Yes, as underlying.
Index................... 2.0%......... Yes, as underlying.
Options:
Individual equity....... yes.......... For each type of
transactions either:
Index................... 2.0%......... (a) Carve out together with
the associated hedging
positions
--simplified method--
scenario approach--
internal models, or
(b) General market risk
requirement according to
the Delta-plus method
(gamma and vega receive
separate capital charges).
------------------------------------------------------------------------
Note: Specific risk charges relate to the issuer of the instrument.
There remains a separate capital requirement for counterparty credit
risk.
Attachment IV--Sample Calculation of Standardized Approach for
Commodities Risk
----------------------------------------------------------------------------------------------------------------
Spread Capital
Time band Position rate Capital calculation charge
----------------------------------------------------------------------------------------------------------------
0 up to 1 month............ None
1 up to 3 months........... None
3 up to 6 months........... Long 800................... 1.5% 800 long+800 short (matched) x 24
1.5%=.
Short 1000................. 200 Short carried forward to 1-2 24
yrs, capital charge: 200 x 2 x
0.6%=.
6 up to 12 months.......... None.......................
1 up to 2 yrs.............. Long 600................... 200 long+200 short (matched) x 6
1.5%=.
[[Page 38129]]
400 long carried forward to over 4.8
3 yrs capital charge: 400 x 2 x
0.6%=.
2 up to 3 yrs.............. None
over 3 years............... Short 600.................. 400 long+400 short 12
(matched)+1.5%=.
Net position: 200 capital 30
charge: 200 x 15.0%=.
----------------------------------------------------------------------------------------------------------------
Note: Assume all positions are in the same commodity and converted at current spot rates into U.S. dollars. The
total capital requirement would be $79.2.
Attachment V--Sample Calculation for Delta-Plus Method for Options
a. Assume a banking organization has a European short call
option on a commodity with an exercise price of 490 and a market
value of the underlying 12 months from the expiration of the option
at 500; a risk-free interest rate at 8% per annum, and the
volatility at 20 percent. The current delta for this position is
according to the Black-Scholes formula -0.721 (that is, the price of
the option changes by -0.721 if the price of the underlying moves by
1). The gamma is -0.0034 (that is, the delta changes by -0.0034 from
-0.721 to -0.7244 if the price of the underlying moves by 1). The
current value of the option is 65.48.
b. The first step under the delta-plus method is to multiply the
market value of the commodity by the absolute value of the delta.
500 x 0.721=360.5. The delta-weighted position is then incorporated
into the measure described in section IV.D. of this Appendix E. If
the banking organization uses the maturity approach and no other
positions exist, the delta-weighted position is multiplied by 0.15
to calculate the capital requirement for delta. 360.5 x 0.15=54.075.
c. The capital requirement for gamma is calculated according to
the Taylor expansion by multiplying the absolute value of the
assumed gamma of -0.0034 by 1.125% and by the square of the market
value of the underlying. 0.0034 x 0.0125 x 500\2\=10.625
d. The capital requirement for vega is calculated next. The
assumed current (implied) volatility is 20%. Since only an increase
in volatility carries a risk of loss for a short call option, the
volatility has to be increased by a relative shift of 25%. This
means that the vega capital requirement has to be calculated on the
basis of a change in volatility of 5 percentage points from 20% to
25% in this example. According to the Black-Scholes formula used
here, the vega equals 168. Thus, a 1% or 0.01 increase in volatility
increases the value of the option by 1.68. Accordingly, a change in
volatility of 5 percentage points increases the value of
5 x 1.68=8.4. This is the capital requirement for vega risk. The
total capital requirement would be $73.10 (54.075+10.625+8.4).
By Order of the Board of Governors of the Federal Reserve
System, July 12, 1995.
William W. Wiles,
Secretary of the Board.
FEDERAL DEPOSIT INSURANCE CORPORATION
12 CFR Chapter III
For the reasons indicated in the preamble, the FDIC Board of
Directors hereby proposes to amend part 325 of chapter III of Title 12
of the Code of Federal Regulations as follows:
PART 325--CAPITAL MAINTENANCE
1. The authority citation for part 325 continues to read as
follows:
Authority: 12 U.S.C. 1815(a), 1815(b), 1816, 1818(a), 1818(b),
1818(c), 1818(t), 1819(Tenth), 1828(c), 1828(d), 1828(i), 1828(n),
1828(o), 1831o, 3907, 3909, 4808; Pub. L. 102-233, 105 Stat. 1761,
1789, 1790 (12 U.S.C. 1831n note); Pub. L. 102-242, 105 Stat. 2236,
2355, 2386 (12 U.S.C. 1828 note).
2. Appendix A to part 325 is amended in the introductory text, by
adding a new paragraph after the third undesignated paragraph to read
as follows:
Appendix A to Part 325--Statement of Policy on Risk-Based Capital
* * * * *
In addition, when certain banks that engage in trading
activities calculate their risk-based capital ratio under this
appendix A, they must also refer to appendix C of this part, which
incorporates capital charges for certain market risks into the risk-
based capital ratio. When calculating their risk-based capital ratio
under this appendix A, such banks are required to refer to appendix
C of this part for supplemental rules to determine qualifying and
eligible capital, calculate risk-weighted assets, calculate market-
risk equivalent assets and add them to risk- weighted assets, and
calculate risk-based capital ratios adjusted for market risk.
* * * * *
3. A new appendix C is added to part 325 to read as follows:
Appendix C to Part 325--Risk-Based Capital for State Non-Member Banks:
Market Risk
(i) The Federal Deposit Insurance Corporation (FDIC) has adopted
a framework to supplement the risk-based capital requirements set
out in appendix A of this part with capital requirements for the
market risk exposure of state non-member banks.1 For this
purpose, market risk refers to the risk of losses in a bank's on-
and off-balance-sheet positions arising from movements in market
prices. The market risks subject to these capital requirements are
those associated with debt and equity instruments held in the bank's
trading account, as well as foreign exchange risk and commodities
risk throughout the bank, including options and other derivative
contracts in each risk category. As is further detailed in section
II of this appendix C, debt and equity instruments and commodities
positions subject to the measure for market risk under this appendix
C are generally excluded from the calculation of risk-weighted
assets under appendix A of this part.
\1\ The market risk measure is based on a framework developed
jointly by supervisory authorities from the countries represented on
the Basle Committee on Banking Supervision (Basle Supervisors
Committee) and endorsed by the Group of Ten Central Bank Governors.
The framework is described in a paper prepared by the Basle
Supervisors Committee entitled ``Proposal to issue a Supplement to
the Basle Capital Accord to Cover Market Risks''. April 1995.
---------------------------------------------------------------------------
(ii) This appendix C provides two ways for a bank to determine
its exposure to market risk. A bank may use its internal risk
measurement model, subject to the conditions and criteria set forth
in section III of this appendix C (referred to as the internal
models approach), or when appropriate, a bank may use all or
portions of the alternative measurement system described in section
IV of this appendix C (referred to as the standardized approach).
(iii) With prior approval from the FDIC, for regulatory capital
purposes, a bank may use its internal risk measurement model to
measure its value-at-risk 2 for each of the following risk
factor categories: interest rates, exchange rates, equity prices,
and commodity prices. The value-at-risk amount for each risk factor
category should include volatilities of related options. The value-
at-risk amount for each risk factor category is summed to determine
the aggregate value-at- risk for the bank.
\2\ A bank evaluates its current positions and estimates future
market volatility through a value-at-risk measure, which is an
estimate representing, with a certain degree of statistical
confidence, the maximum amount by which the market value of trading
positions could decline during a specific period of time. The value-
at-risk is generated through an internal model that employs a series
of market risk factors (for example, market rates and prices that
affect the value of trading positions).
(iv) The standardized approach uses a set of standardized
calculations and assumptions to measure market risk exposure
depending on its source: debt instruments, equities, foreign
currencies, and commodities, including volatilities of related
options.3
\3\ There are three alternatives for measuring the market risk
of options under the standardized approach. Under two of the
alternatives, the simplified and scenario methods, the underlying
position of an option is ``carved-out,'' and is not included in the
prescribed risk measure for the underlying debt, equity, foreign
exchange or commodity. Instead it is evaluated together with the
related option according to the procedures described for options to
determine the capital requirement. Under the third alternative, the
``delta-plus'' approach, the delta-equivalent value of each position
is included in the measurement framework for the prescribed risk
measure for the underlying.
[[Page 38130]]
---------------------------------------------------------------------------
(v) The FDIC generally expects any bank that is subject to this
appendix C, especially those with large trading accounts, to compute
the measure for market risk by using internal risk-measurement
models. A bank may not change its measurement approach for the
purpose of minimizing capital requirements. In limited instances, on
a case-by-case basis, the FDIC may permit a bank that has internal
models to incorporate alternative measures for market risk of
negligible exposures (for example, de minimis positions, activities
in remote locations, minor exposures in a currency, or activities
that present negligible risk to the bank), so long as it adequately
captures the risk.
(vi) The FDIC will monitor the implementation and effect of
these guidelines in relation to domestic and international
developments in the banking industry. When necessary and
appropriate, the FDIC will consider the need to modify this appendix
C in light of any significant changes in the economy, financial
markets, banking practices, or other relevant factors.
I. Scope of the Market Risk Capital Requirement
A. Banks Subject to This Appendix C
1. Effective December 31, 1997, this appendix C will be applied
to any FDIC-insured state-chartered bank that is not a member of the
Federal Reserve System (excluding insured branches of foreign banks)
and that, on a consolidated basis, either:
a. Has total assets in excess of $5 billion, and:
i. Has a total volume of trading activities (measured as the sum
of the bank's trading assets and liabilities 4 on a daily
average basis for the quarter) that is 3.0 percent or more of the
total assets of the bank; or
\4\ As reflected in the bank's quarterly Consolidated Reports of
Condition and Income (call report.)
---------------------------------------------------------------------------
ii. Has interest rate, foreign exchange, equity, and commodity
off-balance-sheet derivative contracts relating to trading
activities whose total notional amounts exceed $5 billion; or
b. Has total assets of $5 billion or less and has a total volume
of trading activities exceeding 10.0 percent of the total assets of
the bank.
2. Such banks identified in paragraph 1 (hereinafter referred to
as ``banks''), when calculating their risk-based capital ratio under
appendix A of this part, are required to refer to this appendix C
for supplemental rules to determine their qualifying and eligible
capital, calculate risk-weighted assets, calculate market-risk
equivalent assets and add them to risk-weighted assets, and
calculate risk-based capital ratios adjusted for market risk.5
\5\ The FDIC may apply all or portions of this appendix C to
other state non-members banks when deemed necessary for safety and
soundness purposes.
---------------------------------------------------------------------------
B. Market Risks Subject to a Capital Requirement
1. General Market Risk and Specific Risk. A bank must hold
capital against exposure to general market risk and specific risk
arising from its trading and other foreign exchange and commodity
activities. For this purpose, general market risk refers to changes
in the market value of covered transactions resulting from market
movements, such as changing levels of market interest rates, broad
equity indices, or currency exchange rates. Specific risk refers to
credit risk, that is, the risk that the issuer of a debt or equity
instrument might default, as well as to other factors that affect
the market value of specific instruments but that do not materially
alter market conditions.6
\6\ This appendix C does not impose specific risk capital
requirements for foreign exchange risk and commodities positions
because they do no have the type of issuer-specific risk associated
with debt and equity instruments in the trading account.
---------------------------------------------------------------------------
2. Trading Activities. a. The measure for market risk in trading
activities is based on on- and off-balance-sheet positions in a
bank's trading account. For this purpose, the trading account
consists of positions in financial instruments acquired with the
intent to resell in order to profit from short-term price movements
(or other price or interest-rate variations), including, but not
limited to:
i. Assets acquired with the intent to resell to customers;
ii. Positions in financial instruments arising from matched
principal brokering and market making; or
iii. Positions taken in order to hedge other elements of the
trading account (that is, reduce risk by offsetting other positions
that have exposure to changes in market rates or prices).7
\7\ Subject to FDIC review, when on- or off-balance-sheet non-
trading account instruments are deliberately used to hedge trading
account instruments, the non-trading account instruments may be
included in the measure for general market risk, but if so included,
are not included in the measure for specific risk and instead remain
an element of risk-weighted assets under section II of appendix A of
this part. Instruments such as swaps used to hedge non-trading
account activities should be excluded from the measure for market
risk if they are not part of the trading account.
---------------------------------------------------------------------------
b. Trading account activities may include positions in debt
instruments, equities, foreign currencies, and commodity
instruments, or related derivative 8 or other off-balance-sheet
contracts.
\8\ In general terms, a derivative is a financial contract whose
value is derived from the values of one or more underlying assets or
reference rates or indexes of asset values (referred to as ``the
underlying''). Derivatives include standardized contracts that are
traded on exchanges and customized, privately negotiated contracts
known as over-the-counter (OTC) derivatives.
---------------------------------------------------------------------------
c. The debt instruments in the trading account category consists
of all fixed-rate and floating-rate debt securities and instruments
that behave like debt, including non-convertible preferred stock.
Convertible bonds, i.e., preferred stock or debt issues that are
convertible, at a stated price, into common shares of the issuer,
should be treated as debt instruments if they trade like debt
instruments and as equities if they trade like equities. Also
included are derivative contracts of debt instruments and other off-
balance-sheet instruments in the trading account that react to
changes in interest rates (for example, forward rate agreements
(FRAs), bond futures, interest rate and cross-currency swaps and
forward foreign exchange positions). A security that has been sold
subject to a repurchase agreement or lent subject to a securities
lending agreement is treated as if it were still owned by the lender
of the security, but the off-balance-sheet portion of the
transaction remains an element of risk-weighted assets as set forth
in section II. of appendix A of this part.
d. The equities in the trading account category consist of
equity instruments that behave like equities. The instruments
covered include common stocks (whether voting or non-voting),
convertible securities that behave like equities, and commitments to
buy or sell equity securities. Also included are derivative
contracts of equity instruments and other off-balance-sheet
instruments in the trading account that are affected by changes in
equity prices. However, non- convertible preferred stock is included
in debt instruments.
3. Foreign Exchange and Commodities Risk. Foreign exchange or
commodities positions, whether or not included in a bank's trading
account, are subject to a measure for market risk of those
positions.
a. The measure for market risk of foreign exchange applies to a
bank's total currency and gold positions. This includes spot
positions (that is, asset items and liability items, including
accrued interest and expenses, denominated in each currency);
forward positions (that is, forward foreign exchange transactions,
including currency futures and the principal on currency swaps not
included in the spot position); and certain guarantees. It also
includes future income and expenses from foreign currency
transactions not yet accrued but already fully hedged (at the
discretion of the reporting bank), foreign exchange derivative and
other off-balance-sheet positions that are affected by changes in
exchange rates, and any other item representing a profit or loss in
foreign currencies.
b. A bank doing negligible business in foreign currency and that
does not take foreign exchange positions for its own account may be
exempted from the market risk measure for foreign exchange risk
provided that:
i. Its foreign currency business, defined as the greater of the
sum of its gross long positions and the sum of its gross short
positions in all foreign currencies as determined under section
IV.C.2 of this appendix C, does not exceed 100 percent of eligible
capital as defined in section II. of this appendix C; and
ii. Its overall net open foreign exchange position as determined
under section IV.C.3. of this appendix C does not exceed 2.0 percent
of eligible capital.
[[Page 38131]]
c. A bank may, subject to approval by the FDIC, exclude from its
foreign exchange positions any structural positions in foreign
currencies. For this purpose, such structural positions are limited
to transactions designed to hedge a bank's capital ratios against
the effect of adverse exchange rate movements on subordinated debt,
equity, or minority interests in consolidated subsidiaries and
dotation capital assigned to foreign branches that are denominated
in foreign currencies. Also included are any positions related to
unconsolidated subsidiaries and to other items that are deducted
from a bank's capital when calculating its capital base. In any
event, such structural foreign currency positions must reflect long-
term policies of the institution and not relate to trading
positions.
d. The measure for market risk of commodities applies to a
bank's total commodities positions, including commodity futures,
commodity swaps, and all other commodity derivatives or other off-
balance-sheet positions that are affected by changes in commodity
prices. A commodity is defined as a physical product that is or can
be traded on a secondary market (such as agricultural products,
minerals (including oil), and precious metals), but excluding gold
(which is treated as foreign exchange).
II. Qualifying Capital and the Market Risk-Adjusted Capital Ratio
A. Qualifying and Eligible Capital
1. The principal forms of qualifying capital for market risk are
Tier 1 capital and Tier 2 capital as defined in, and subject to the
conditions and limitations of, section I of appendix A of this part.
A bank may use Tier 3 capital for the sole purpose of meeting a
portion of the capital requirements for market risk. Tier 3 capital
may be allocated only to support market-risk equivalent assets, and
may in no event be allocated to support capital requirements
associated with risk-weighted assets under appendix A of this part.
2. Tier 3 capital consists of short-term subordinated debt that
is subject to a lock-in clause providing that neither interest nor
principal payment is due (even at maturity) if such payment would
cause the issuing bank to fall or remain below the minimum 8.0
percent risk-based capital requirement as set forth in appendix A of
this part and adjusted for market risk.
3. In order to qualify as Tier 3 capital, the short-term debt
must be unsecured, subordinated, and fully paid up; it must have an
original maturity of at least two years; and it may not be redeemed
before maturity without prior approval by the FDIC. In addition, it
may not contain or be covered by any covenants, terms, or
restrictions that are inconsistent with safe and sound banking
practices.
B. Calculation of Eligible Capital and the Capital Ratio
A bank that is subject to the market risk measure must calculate
its risk-based capital ratio and eligible capital as follows:
1. Determine total risk-weighted assets under appendix A of this
part, excluding from risk-weighted assets:
a. All debt and equity instruments in the trading account
required to be included under the measure for market risk, with the
exception of over-the-counter derivatives or non-trading account
instruments used to hedge trading account instruments and included
in the measure for general market risk at the bank's option; and
b. All positions in commodities required to be included under
the measure for market risk.
2. Calculate the total measure for market risk using the
internal models approach, the standardized approach, or an approved
combination of these two approaches:
a. Internal Models. i. For a bank approved to use the internal
models approach under section III of this appendix C, the total
measure for market risk is the higher of:
A. The bank's previous day's aggregate value-at-risk amount; or
B. An average of the daily aggregate value-at-risk amounts
measured on each of the preceding 60 business days multiplied by a
minimum ``multiplication factor'' of 3. The FDIC may adjust the
multiplication factor for a bank to increase its capital requirement
based on an assessment of the quality and historic accuracy of the
bank's risk management system.
ii. Additionally, if a bank's internal model does not capture
the specific risk of debt and equity instruments in the trading
account,\9\ the specific risk measure as calculated under the
standardized approach may be added to the bank's measure for market
risk.
\9\ If a bank uses an internal model that measures specific risk
of debt and equity instruments in the trading account, the measure
should in no case be less than one-half the specific risk measure as
calculated under the standardized approach (taking into account the
effect of the multiplier under paragraph B.2.a.ii. of this section).
---------------------------------------------------------------------------
b. Standardized Approach. A bank that has not obtained the
FDIC's approval to use an internal model must use the standardized
approach for measuring its market risk. For a bank using this
approach, the total measure for market risk is the sum of the market
risk measures for debt and equity instruments in the trading
account, foreign exchange and commodities risk throughout the bank,
and options and other derivative positions in each risk category as
set forth in sections IV.A through IV.E. of this appendix C.
c. Partial Models. With approval from the FDIC, a bank whose
internal model does not cover all risk factor categories may use the
standardized approach for measuring market risk arising from the
risk factor categories that are not covered. The FDIC will approve
combining the two approaches only on a temporary basis in situations
in which the institution is developing but has not fully implemented
a comprehensive internal model. When a bank uses both approaches,
each risk factor category (i.e., interest rates, equity prices,
exchange rates, and commodity prices) must be measured using one or
the other approach. The methods may not be combined within a single
risk factor category. Once a bank adopts an acceptable internal
model for a particular risk factor category, it may not revert to
the standardized approach except in unusual circumstances and with
the prior approval of the FDIC.\10\ For a bank using a combination
of approaches, the total measure for market risk is the sum of:
\10\ Banks that have modeling capabilities are expected to use
their internal models for measuring market risk for regulatory
capital purposes. However, the FDIC may permit a bank to use another
measurement technique for de minimis positions, activities in remote
locations, minor exposures in a currency, or in activities that
present negligible risk to the bank.
---------------------------------------------------------------------------
i. The appropriate value-at-risk measure (as determined in
paragraph B.2.a. of this section, aggregating the value-at-risk
measure for each risk factor category included in the internal
model); and
ii. The measure for market risk for each risk factor category
that is calculated using the standardized approach.
3. Calculate the market-risk equivalent assets by multiplying
the total measure for market risk by 12.5 (i.e., the reciprocal of
the 8.0 percent minimum risk-based capital ratio).
4. Add the market-risk equivalent assets to total risk-weighted
assets (as determined in paragraph B.1. of this section). The sum of
these two amounts is the denominator of the total risk-based capital
ratio, adjusted for market risk.
5.a. In order to calculate eligible capital to be included in
the numerator of the ratio, a bank must first allocate the
qualifying Tier 1 and Tier 2 capital necessary to support total
risk-weighted assets (as determined in paragraph B.1. of this
section) in accordance with the terms and restrictions of section I
of appendix A of this part, achieving at least the minimum
supervisory ratio in section III. of appendix A of this part.
Remaining Tier 1, eligible Tier 2, and eligible Tier 3 capital
should then be allocated to support market-risk equivalent assets
(as determined in paragraph B.3. of this section), achieving at
least a minimum supervisory ratio of 8.0 percent, subject to the
following restrictions:
i. Eligible Tier 3 capital may not exceed 250 percent of a
bank's Tier 1 capital allocated for market risk;
ii. Tier 2 elements may be substituted for Tier 3 up to the same
250 percent limit, so long as the overall limits for Tier 2 capital
set out in section I of appendix A of this part are not exceeded
(i.e., Tier 2 capital may not exceed total Tier 1 capital, and long-
term subordinated debt may not exceed 50 percent of Tier 1 capital);
and
iii. The maximum eligible amount of Tier 2 and Tier 3 capital,
summed together, may not exceed 100 percent of Tier 1 capital.
b. Eligible capital for the total risk-based capital ratio is
then the sum of the bank's qualifying Tier 1 capital, its qualifying
Tier 2 capital subject to the limits stated in this paragraph and
eligible Tier 3 capital subject to the limits stated in this
paragraph B.5.\11\
\11\ Examples of the method used to calculate eligible capital
are set forth in attachment I to this appendix C.
---------------------------------------------------------------------------
C. Consolidation and Reporting
1. The capital requirements for market risk apply to banks on a
worldwide consolidated basis. The FDIC may, however, evaluate market
risk on an unconsolidated basis when necessary (for example, when
there are
[[Page 38132]]
obstacles to the repatriation of profits from a foreign subsidiary or
where management structure does not allow timely management of risk
on a consolidated basis).
2. All transactions, including forward sales and purchases,
should be included in the calculation of market risk capital
requirements from the date on which they were entered into. Although
banks subject to the capital requirements for market risk will
continue to report their capital on a quarterly basis, the FDIC
expects banks to meet their capital requirements for market risk on
a continuous basis (that is, at a minimum, at the close of each
business day).
3. The risk-based capital ratios adjusted for market risk are
minimum supervisory ratios. The FDIC expects banks to operate with
capital positions well above the minimum ratios. In all cases, banks
should hold capital commensurate with the level and nature of the
risks to which they are exposed.
III. The Internal Models Approach
A. Use of Models
1. With prior approval of the FDIC, a bank may use its internal
risk measurement model(s) for measuring value-at-risk to be used as
the measure for market risk.
a. Requests for approval should include, at a minimum, a
complete description of the bank's internal modeling and risk
management systems and how these systems conform to the criteria set
forth in this section III, an explanation of the policies and
procedures established by the bank to ensure continued compliance
with such criteria, a discussion of internal and external validation
procedures, and a description of other relevant policies and
procedures consistent with sound practices.
b. The FDIC will approve an internal model for regulatory
capital purposes only after determining that the bank's internal
model and risk management systems meet the criteria in this section
III. Such a determination may require on-site examinations of the
systems. The FDIC may require modification to an internal model as
deemed necessary to ensure compliance, on a continuing basis, with
the provisions of this appendix C. A bank's internal model will be
subject to continuing review, both on- and off-site, by the
FDIC.\12\
\12\ Banks that need to modify their existing modeling
procedures to accommodate the requirements of this appendix C
should, nonetheless, continue to use the internal models they
consider most appropriate in evaluating risks for other purposes.
---------------------------------------------------------------------------
2. A bank should ensure that the level of sophistication of its
internal model is commensurate with the nature and volume of the
bank's trading activity in the risk factor categories covered by
this appendix C and measures market risk as accurately as possible.
In addition, the model should be adjusted to reflect changing
portfolio composition and changing market conditions.
B. Qualitative Criteria
1. A bank using the internal models approach should have market
risk management systems that are conceptually sound and implemented
with integrity. Internal risk measurement models must be closely
integrated into the day-to-day risk management process of the bank.
For example, the risk measurement model must be used in conjunction
with internal trading and exposure limits.
2. A bank must meet the following minimum qualitative criteria
before using its internal model as the measure for market risk:\13\
\13\ If the FDIC is not satisfied with the extent to which a
bank meets these criteria, the FDIC may adjust the multiplication
factor used in section II.B.2.a.ii. of this appendix C to determine
the total measure for market risk or otherwise increase capital
requirements.
---------------------------------------------------------------------------
a. A bank must have a risk control unit that is independent from
business trading units and reports directly to senior management of
the bank. The unit must be responsible for designing and
implementing the bank's risk management system and analyzing daily
reports on the output of the bank's risk measurement model in the
context of trading limits. The unit must conduct regular back-
testing.\14\
\14\ Back-testing includes ex post comparisions of the risk
measures generated by the model against the actual daily changes in
portfolio value.
---------------------------------------------------------------------------
b. Senior management must be actively involved in the risk
control process. The daily reports produced by the risk management
unit must be reviewed by a level of management with sufficient
authority to enforce both reductions in positions taken by
individual traders, as well as in the bank's overall risk exposure.
c. The bank must have a routine and rigorous program of stress-
testing to identify the effect of low-probability events on the
bank's trading portfolio. Bank stress-testing should cover a range
of factors that can create extraordinary losses or gains in trading
portfolios or make the control of risk in those portfolios
difficult. These factors include low-probability events of all
types, including the various components of market, credit, and
operational risks. Senior management must routinely review the
results of stress-testing in the context of the potential effect of
the events on bank capital and the appropriate procedures the bank
should take to minimize losses. The policies of the bank set by
management and the bank's board of directors should identify
appropriate stress-tests and the procedures to follow in response to
the test results.
d. The bank must have established procedures for ensuring
compliance with a documented set of internal policies and controls,
as well as for monitoring the overall operation of the risk
measurement system.
e. Not less than once a year, the bank must conduct, as part of
its regular internal audit process, an independent review of the
risk measurement system. This review must include both the
activities of the business trading units and of the independent risk
control unit of the bank.
f. Not less than once a year, the bank must conduct a review of
its overall risk management process. The review must consider:
i. The adequacy of the documentation of the risk management
system and process, and the organization of the risk control unit;
ii. The integration of market risk measures into daily risk
management and the integrity of the management information system;
iii. The process the bank employs for approving risk pricing
models and valuation systems that are used by front- and back-office
personnel;
iv. The scope of market risks captured by the risk measurement
model and the validation of any significant changes in the risk
measurement process;
v. The accuracy and completeness of position data, the accuracy
and appropriateness of volatility and correlation assumptions, and
the accuracy of valuation and risk sensitivity calculations;
vi. The verification process the bank employs to evaluate the
consistency, timeliness, and reliability of data sources used to run
internal models, including the independence of such data sources;
and
vii. The verification process the bank uses to evaluate back-
testing that is conducted to assess the model's accuracy.
C. Market Risk Factors
1. Generally. For regulatory capital purposes, a bank's internal
risk measurement system must use sufficient risk factors to capture
the risks inherent in the bank's portfolio of on- and off-balance-
sheet trading positions and must, subject to the following
guidelines, cover interest rates, equity prices, exchange rates,
commodity prices, and volatilities related to options positions in
each risk factor category. The level of sophistication of the bank's
risk factors must be commensurate with the nature and scope of the
risks taken by the bank.
2. Interest Rates. a. A bank must use a set of market risk
factors corresponding to interest rates in each currency in which it
has material interest rate-sensitive on- or off-balance-sheet
positions. The risk measurement system must model the yield curve
\15\ using one of a number of generally accepted approaches, for
example, by estimating forward rates of zero coupon yields. The
yield curve must be divided into various maturity segments in order
to capture variation in the volatility of rates along the yield
curve; there will typically be one risk factor corresponding to each
maturity segment.
\15\ Generally, a yield curve is a graph showing the term
structure of interest rates by plotting the yields of all
instruments of the same quality by maturities ranging from the
shortest to the longest available. The resulting curve shows whether
short-term interest rates are higher or lower than long-term
interest rates.
---------------------------------------------------------------------------
b. For significant exposures to interest rate movements in the
major currencies and markets, a bank must model the yield curve
using a minimum of six risk factors. However, the number of risk
factors used should ultimately be driven by the nature of the bank's
trading strategies.\16\ The risk measurement system must incorporate
separate risk factors to capture spread risk.\17\
\16\ For example, a bank that has a portfolio of various types
of securities across many points of the yield curve and that engages
in complex arbitrage strategies would require a greater number of
risk factors to accurately capture interest rate risk.
\17\ For these purposes, spread risk refers to the potential
changes in value of an instrument or portfolio arising from
differences in the behavior of baseline yield curves, such as those
for U.S. Treasury securities, and yield curves reflecting sector,
quality, or instrument specific factors. A variety of approaches may
be used to capture the spread risk arising from less than perfectly
correlated movements between government and other interest rates,
such as specifying a completely separate yield curve for non-
government instruments (for example, swaps or municipal securities)
or estimating the spread over government rates at various points
along the yield curve.
[[Page 38133]]
---------------------------------------------------------------------------
3. Exchange Rates. A bank must use market risk factors
corresponding to the exchange rate between the domestic currency and
each foreign currency in which the bank has a significant exposure.
The risk measurement system must incorporate market risk factors
corresponding to the individual foreign currencies in which the
bank's positions are denominated.
4. Equity Prices. A bank must use risk factors corresponding to
each of the equity markets in which it holds significant positions.
The sophistication and nature of the modeling technique for a given
market must correspond to the bank's exposure to the overall market
as well as to the bank's concentration in individual equity issues
in that market. At a minimum, there must be a risk factor designed
to capture market-wide movements in equity prices (such as a market
index), but additional risk factors could track various sectors or
individual issues.
5. Commodity Prices. A bank must use market risk factors
corresponding to each of the commodity markets in which it holds
significant positions. The internal model must encompass directional
risk, forward gap and interest rate risk, and basis risk.\18\ The
model should also take into account the market characteristics, for
example, delivery dates and the scope provided to traders to close
out positions.
\18\ For these purposes, directional risk refers to the risk
that a spot price will increase or decrease. Forward gap risk refers
to the effects of owning a physical commodity versus owning a
forward position in a commodity. Interest rate risk refers to the
risk of a change in the cost of carrying forward positions and
options. Basis risk refers to the risk that the relationship between
the prices of similar commodities changes over time.
---------------------------------------------------------------------------
D. Quantitative Standards
1. A bank may use one of a number of generally accepted
measurement techniques including, for example, an internal model
based on variance-covariance matrices, historical simulations, or
Monte Carlo simulations, so long as the model employed captures all
significant market risks.\19\ The following minimum standards apply
for purposes of using an internal model for calculating market risk
capital requirements:
\19\ For these purposes, a variance/covariance approach refers
to an approach in which the change in value of the portfolio is
calculated by combining the risk factor sensitivities of the
individual positions--derived from valuation models--with a
variance/covariance matrix based on risk factor volatilities and
correlations. A bank using this approach would calculate the
volatilities and correlations of the risk factors on the basis of
the holding period and the observation period. The historical
simulation approach refers to an approach in which a bank would
calculate the hypothetical change in value of the current portfolio
in light of historical movements in risk factors. This calculation
would be done for each of the defined holding periods over a given
historical measurement horizon to arrive at a range of simulated
profits and losses. The Monte Carlo approach refers to an approach
in which a bank would consider historical movements to determine the
probability of particular price and rate changes.
---------------------------------------------------------------------------
a. Value-at-risk must be calculated on a daily basis using a
99th percentile, one-tailed confidence interval \20\ and the holding
period must be ten trading days. For positions that display linear
price characteristics, a bank may use value-at-risk numbers
calculated according to shorter holding periods scaled up to ten
days by the square root of time.\21\
\20\ A one-tailed confidence interval of 99 percent means that
there is a 1 percent probability based on historical experience that
the combination of positions in a bank's portfolio would result in a
loss higher than the measured value-at-risk.
\21\ This transformation entails multiplying a bank's value-at-
risk by the square root of the ratio of the required holding period
(ten days) to the holding period embodied in the value-at-risk
figure. For example, the value-at-risk calculated according to a
one-day holding period would be scaled-up by the ``square root of
time'' by multiplying the value-at-risk by 3.16 (the square root of
the ratio of a ten-day holding period to a one-day holding period).
---------------------------------------------------------------------------
b. Value-at-risk must be calculated using an observation period
of at least one year to measure historical changes in rates and
prices.
c. A bank must update its historical rates and prices at least
once every three months and must reassess them whenever there is a
change in market conditions of any significance.
2. A bank may use its discretion in recognizing empirical
correlations within each market risk factor category, provided that
the FDIC is satisfied that there is integrity in the bank's process
for calculating correlations. However, empirical correlations among
risk categories are not recognized. The value-at-risk measure for
each risk category must be added together on a simple sum basis to
determine the aggregate value-at-risk amount.
3. A bank's model must accurately capture the unique risks
associated with options within each of the market risk factor
categories. The following minimum criteria apply to the measurement
of options risk:
a. A bank's internal model must capture the non-linear price
characteristics of option positions using an options pricing
technique. The bank must apply a minimum ten-day holding period to
option positions or positions that display option-like
characteristics. Banks may not scale-up the daily value-at-risk
numbers by the square root of time.
b. A bank's internal model must, for example, capture the
sensitivity of the value of the options positions to changes in the
volatility of the options' underlying rates or prices (that is, the
vega) and must measure the volatilities of options positions broken
down by different maturities.
4. The accuracy of a bank's internal model will be reviewed
periodically by the FDIC. Such review--during which, when
appropriate, the FDIC may take into consideration reports and
opinions generated by external auditors or qualified consultants--
will include at a minimum:
a. Verification that the internal validation processes described
in paragraph B.2. of this section are operating in a satisfactory
manner;
b. Assurance that the formulae used in the calculation process
and for the pricing of options and other complex instruments, are
validated by a qualified unit of the bank, which in all cases must
be independent from the trading areas;
c. Confirmation that the structure of the internal model is
adequate with respect to the bank's activities and geographical
coverage;
d. Confirmation that the results of the bank's back-testing of
its internal measurement system (that is, comparing value-at-risk
estimates with actual profits and losses) are being used effectively
to monitor reliability of the model's estimates over time; and
e. Assurance that, for regulatory capital purposes, the model
processes all relevant data and that the modeling procedures conform
with the parameters and specifications set forth in this appendix C.
IV. The Standardized Approach
A. Debt Instruments
1. Specific Risk. a. The specific risk element of the measure
for market risk is based on the identity of the obligor and, in the
case of corporate securities, on the credit rating and maturity of
the instrument. The specific risk element is calculated by weighting
the current market value of each individual position, whether long
or short, by the appropriate factor as set forth below and summing
the weighted values. In determining specific risk, the bank may
offset and exclude from its calculations any matched positions in
the identical issue (including positions in derivatives). Even if
the issuer is the same, no offsetting is permitted between different
issues since differences in coupon rates, liquidity, call features,
etc., mean that prices may diverge in the short run. The categories
and factors are:
------------------------------------------------------------------------
Remaining maturity Factor (in
Category (contractual) percent)
------------------------------------------------------------------------
Government................... N/A......................... 0.00
Qualifying................... 6 months or less............ 0.25
6 to 12 months.............. 1.00
over 12 months.............. 1.60
Other........................ N/A......................... 8.00
------------------------------------------------------------------------
b. The government category consists of all forms of debt
instruments of central governments of the OECD-based group of
countries \22\ including bonds, Treasury bills and other short-term
instruments, as well as local currency instruments of non-OECD
central governments to the extent that the bank has liabilities
booked in that currency.
\22\ As defined in section III.B. and III.C. of appendix A of
this part.
---------------------------------------------------------------------------
c. The qualifying category consists of securities of U.S.
government-sponsored
[[Page 38134]]
agencies, general obligation securities issued by states and other
political subdivisions of the OECD-based group of countries,
multilateral development banks, and debt instruments issued by U.S.
depository institutions or OECD-banks that do not qualify as capital
of the issuing institution.\23\ It also includes other securities,
including revenue securities issued by states and other political
subdivisions of the OECD-based group of countries, that are:
\23\ U.S. government-sponsored agencies, multilateral
development banks, and OECD banks are defined in section III.C. of
appendix A of this part.
---------------------------------------------------------------------------
i. Rated investment-grade by at least two nationally recognized
credit rating services, or rated investment-grade by one nationally
recognized credit rating agency and not less than investment-grade
by any other credit rating agency; or
ii. With the exception of securities issued by U.S. firms and
subject to review by the FDIC, unrated but deemed to be of
comparable investment quality by the reporting bank and issued by an
entity which has securities listed on a recognized stock exchange.
d. The other category consists of debt securities not meeting
the criteria for government or qualifying securities. This would
include non-OECD central government securities that do not meet the
criteria for the government or qualifying categories. This category
also includes instruments that qualify as capital issued by other
banking organizations.
e. The FDIC will consider the extent of a bank's position in
non-investment grade instruments (sometimes referred to as ``high
yield debt''). If those holdings are not well- diversified or
otherwise represent a significant position to the institution, the
FDIC may prevent a bank from offsetting positions in these
instruments with other positions in qualifying instruments that may
be offset when calculating its general market risk element. In
addition, the FDIC may impose a specific risk factor as high as 16.0
percent.
2. General Market Risk. a. A bank may determine the general
market risk element of the measure for market risk by using, on a
continuous basis, either the maturity method (which uses
standardized risk weights that approximate the price sensitivity of
various instruments) or, subject to the FDIC's review, the duration
method (in which the institution calculates the precise duration of
each instrument, weighted by a specified change in interest rates).
b. Both methods use a maturity-ladder that incorporates a series
of ``time bands'' and ``zones'' to group together securities of
similar maturities and that are designed to take into account
differences in price sensitivities and interest rate volatilities
across different maturities. Under either method, the general market
risk element is the sum of a base charge that results from fully
netting various risk-weighted positions and a series of additional
charges (add-ons), which effectively ``disallow'' part of the
previous full netting to address basis and yield curve risk.
c. For each currency in which a bank has significant positions,
a separate maturity ladder must be constructed. No netting of
positions is permitted across different currencies. Offsetting
positions of the same amount in the same issues, whether actual or
notional, may be excluded from the calculation, as well as closely
matched swaps, forwards, futures, and forward rate agreements (FRAs)
that meet the conditions set out in paragraph A.3. of this section.
d. In the maturity method, the bank distributes each long or
short position (at current market value) of a debt instrument into
the time bands of the maturity ladder. Fixed-rate instruments are
allocated according to the remaining term to maturity and floating-
rate instruments according to the next repricing date. A callable
bond trading above par is allocated according to its first call
date, while a callable bond priced below par is allocated according
to remaining maturity. Fixed-rate mortgage-backed securities,
including collateralized mortgage obligations (CMOs) and real estate
mortgage investment conduits (REMICs), are allocated according to
their expected weighted average lives.
e. Once all long and short positions are allocated into the
appropriate time band, the long positions in each time band are
summed and the short positions in each time band are summed. The
summed long and/or short positions are multiplied by the appropriate
risk-weight factor (reflecting the price sensitivity of the
positions to changes in interest rates) to determine the risk-
weighted long and/or short position for each time band. The risk
weights for each time band are set out in Table 1:
Table 1.--Maturity Method: Time Bands and Weights
------------------------------------------------------------------------
Coupon less than 3 % and Risk
Zone Coupon 3% or more zero-coupon bonds weights
------------------------------------------------------------------------
1....... Up to 1 month............ Up to 1 month........... 0.00
1 up to 3 months......... 1 up to 3 months........ 0.20
3 up to 6 months......... 3 up to 6 months........ 0.40
6 up to 12 months........ 6 up to 12 months....... 0.70
2....... 1 up to 2 years.......... 1 up to 1.9 years....... 1.25
2 up to 3 years.......... 1.9 up to 2.8 years..... 1.75
3 up to 4 years.......... 2.8 up to 3.6 years..... 2.25
3....... 4 up to 5 years.......... 3.6 up to 4.3 years..... 2.75
5 up to 7 years.......... 4.3 up to 5.7 years..... 3.25
7 up to 10 years......... 5.7 up to 7.3 years..... 3.75
10 up to 15 years........ 7.3 up to 9.3 years..... 4.50
15 up to 20 years........ 9.3 up to 10.6 years.... 5.25
Over 20 years............ 10.6 up to 12 years..... 6.00
12 up to 20 years....... 8.00
Over 20 years........... 12.50
------------------------------------------------------------------------
f. Next, within each time band for which there are risk-weighted
long and short positions, the risk-weighted long and short positions
are then netted, resulting in a single net risk-weighted long or
short position for each time band. Since different instruments and
different maturities may be included and netted within each time
band, an addition to the risk measure, referred to as the vertical
disallowance, is assessed to allow for basis risk. The vertical
disallowance is 10.0 percent of the position eliminated by the
intra-time band netting, that is, 10.0 percent of the smaller of the
net risk-weighted long or net risk-weighted short position, or if
the positions are equal, 10.0 percent of either position.24 The
vertical disallowances for each time band are absolute values, that
is, neither long nor short. The vertical disallowances for all time
bands in the maturity ladder are summed and included as an element
of the general market risk element.
\24\ For example, if the sum of the weighted longs in a time
band is $100 million and the sum of the weighted shorts is $90
million, the vertical disallowance for the time band is 10.0 percent
of $90 million, or $9 million.
---------------------------------------------------------------------------
g. Next, within each zone for which there are risk-weighted long
and short positions in different time bands, the weighted long and
short positions in all of the time bands
[[Page 38135]]
within the zone are then netted, resulting in a single net long or
short position for each zone. Since different instruments and
different maturities may be included and netted within each zone, an
addition to the risk measure, referred to as the horizontal
disallowance, is assessed to allow for the imperfect correlation of
interest rates along the yield curve. The horizontal disallowance is
calculated as a percentage of the position eliminated by the intra-
zone netting, that is, a percentage of the smaller of the net risk-
weighted long or net risk-weighted short position, or if the
positions are equal, a percentage of either position.25 The
percent disallowance factors for intra-zone netting are set out in
table 2. The horizontal disallowances, like the vertical
disallowances, are absolute values that are summed and included as
an element of the general market risk element.
\25\ For example, if the sum of the weighted longs in the 1-3
month time band in Zone 1 is $8 million and the sum of the weighted
shorts in the 3-6 month time band is $10 million, the horizontal
disallowance for the zone is forty percent of $8 million, or $3.2
million.
---------------------------------------------------------------------------
h. Next, risk-weighted long and short positions in different
zones are then netted between the zones. Zone 1 and zone 2 are
netted if possible, reducing or eliminating the net long or short
position in zone 1 or zone 2 as appropriate. Zone 2 and zone 3 are
then netted if possible, reducing or eliminating the net long or
short position in zone 2 or zone 3 as appropriate. Zone 3 and zone 1
are then netted if possible, reducing or eliminating the long or
short position in zone 3 and zone 1 as appropriate. A horizontal
disallowance is then assessed, calculated as a percentage of the
position eliminated by the inter-zone netting. The horizontal
disallowances for each zone are then summed as absolute values and
included in the general market risk element. The percent
disallowance factors for inter-zone netting are set out in Table 2:
Table 2.--Horizontal Disallowances
------------------------------------------------------------------------
Between
Within the adjacent Between
Zone Time band zone zones zones 1 & 3
(percent) (percent) (percent)
------------------------------------------------------------------------
1....... 0-1 month.............. 40 40 100
1-3 months.............
3-6 months.............
6-12 months............
2....... 1-2 years.............. 30 40 100
2-3 years..............
3-4 years..............
3....... 1-5 years.............. 30 40 100
5-7 years..............
7-10 years.............
10-15 years............
15-20 years............
over 20 years..........
------------------------------------------------------------------------
i. Finally, the net risk-weighted long or net risk-weighted
short positions remaining in the zones are summed to reach a single
net risk-weighted long or net risk-weighted short position for the
bank's portfolio. The sum of the absolute value of this position and
the vertical and horizontal disallowances is the general market risk
element of the measure of market risk. An example of this
calculation is in attachment II to this appendix.
j. In the duration method, the bank, after calculating each
instrument's modified duration 26 using a formula that is
subject to FDIC review, multiplies that modified duration by the
interest rate shock specified for an instrument of that duration in
table 3. The resulting product (representing the expected percentage
change in the price of the instrument for the given interest rate
shock) is then multiplied by the current market value of the
instrument. The resulting amount is then allocated as a long or
short position into a time band in the maturity ladder in table 3 on
the basis of the instrument's modified duration.27
\26\ The duration of an instrument is its approximate percentage
change in price for a 100 basis point parallel shift in the yield
curve assuming that its cash flow does not change when the yield
curve shifts. Modified duration is duration divided by a factor of 1
plus the interest rate.
\27\ For example, an instrument held by a bank with a maturity
of 4 years and 3 months and a current market value of $1,000 might
have a modified duration of 3.5 years. Based on its modified
duration, it would be subjected to the 75-basis point interest rate
shock, resulting in an expected price change of 2.625 percent
(3.5 x 0.75). The corresponding expected change in price of $26.25,
calculated as 2.625 percent of $1,000, would be slotted as a long
position in the 3.3 to 4.0 year time band of the maturity ladder.
---------------------------------------------------------------------------
k. Once all of the bank's traded debt instruments have been
allocated into the maturity ladder, the bank conducts the same
rounds of netting and disallowances described in paragraphs A.2.f.
through h. of the maturity method in this section, with the
exception that the vertical disallowance requirement for the
duration method is 5.0 percent. Horizontal disallowances continue to
be those set out in table 2. As with the maturity method, the sum of
the absolute value of the final net position and the vertical and
horizontal disallowances is the general market risk element of the
measure for market risk:
Table 3.--Duration Method: Time Bands and Assumed Changes in Yield
------------------------------------------------------------------------
Assumed
Zone Time band change in
yield
------------------------------------------------------------------------
1....... Up to 1 month.................................... 1.00
1 up to 3 months................................. 1.00
3 up to 6 months................................. 1.00
6 up to 12 months................................ 1.00
2....... 1.0 up to 1.8 years.............................. 0.90
1.8 up to 2.6 years.............................. 0.80
2.6 up to 3.3 years.............................. 0.75
3....... 3.3 up to 4.0 years.............................. 0.75
4.0 up to 5.2 years.............................. 0.70
5.2 up to 6.8 years.............................. 0.65
6.8 up to 8.6 years.............................. 0.60
8.6 up to 9.9 years.............................. 0.60
9.9 up to 11.3 years............................. 0.60
11.3 up to 16.6 years............................ 0.60
Over 16.6 years 0.75............................. 0.60
------------------------------------------------------------------------
3. Interest Rate Derivatives. a. Debt derivatives and other off-
balance-sheet positions that are affected by changes in interest
rates are included in the measurement system under this section
IV.A. (except for options and the associated underlyings, which are
included in the measurement system under the treatment discussed in
section IV.E. of this appendix C). A summary of the treatment for
debt derivatives is set out in Attachment III to this appendix C.
b. Derivatives are converted into positions in the relevant
underlying instrument and are included in the calculation of the
specific and general market risk elements. The amount to be included
is the market value of the principal amount of the underlying or of
[[Page 38136]]
the notional underlying. If the apparent notional amount of an
instrument differs from the effective notional amount, a bank must
use the effective notional amount.
c. Futures and forward contracts (including FRAs) are broken
down into a combination of a long position and short position in the
notional security. The maturity of a future or a FRA is the period
until delivery or exercise of the contract, plus the life of the
underlying instrument.28 If a range of instruments may be
delivered to fulfill the contract, the bank may choose which
deliverable instrument goes into the maturity or duration ladder as
the notional underlying. In the case of a future on a corporate bond
index, positions are included at the market value of the notional
underlying portfolio of securities.
\28\ For example, a long position in a June three-month interest
rate future (taken in April) is reported as a long position in a
government security with a maturity of five months and a short
position in a government security with a maturity of two months.
---------------------------------------------------------------------------
d. i. Swaps are treated as two notional positions in the
relevant instruments with appropriate maturities. The receiving side
is treated as the long position and the paying side is treated as
the short position.29 The separate sides of cross-currency
swaps or forward foreign exchange transactions are allocated in the
relevant maturity ladders for the currencies concerned. For swaps
that pay or receive a fixed or floating interest rate against some
other reference price, for example, an equity index, the long or
short position attributable to the interest rate component is
allocated into the appropriate repricing maturity category, with the
long or short position attributable to the equity component being
included in the equity framework set out in section IV.B. of this
appendix C.
\29\ For example, an interest rate swap under which a bank is
receiving floating-rate interest and paying fixed is treated as a
long position in a floating rate instrument with a maturity
equivalent to the period until the next interest reset date and a
short position in a fixed-rate instrument with a maturity equivalent
to the remaining life of the swap.
---------------------------------------------------------------------------
ii. A bank with a large swap book may, with prior approval of
the FDIC, use alternative formulae to calculate the positions to be
included in the maturity or duration ladder. For example, a bank
could first convert the payments required by the swap into present
values. For that purpose, each payment would be discounted using
zero coupon yields, and the payment's present value entered into the
appropriate time band using procedures that apply to zero (or low)
coupon bonds. The net amounts would then be treated as bonds, and
allocated into the general market risk framework. Such alternative
treatments will, however, only be allowed if the FDIC is fully
satisfied with the accuracy of the system being used; the positions
calculated fully reflect the sensitivity of the cash flows to
interest rate changes; and the positions are denominated in the same
currency.
e. A bank may offset long and short positions (both actual and
notional) in identical derivative instruments with exactly the same
issuer, coupon, currency, and maturity before allocating these
positions into time bands. A matched position in a future and its
corresponding underlying may also be fully offset and, thus,
excluded from the calculation, except when the future comprises a
range of deliverable instruments. However, if, among the range of
deliverable instruments, there is a readily identifiable underlying
instrument that is most profitable for the trader with a short
position to deliver, positions in the futures contract and the
instrument may be offset. Positions in different currencies are not
subject to offset.
f. Offsetting positions in the same category of instruments can
in certain circumstances be regarded as matched and treated by the
bank as a single net position which should be entered into the
appropriate time band. To qualify for this treatment the positions
must be based on the same underlying instrument, be of the same
nominal value, and be denominated in the same currency. The separate
sides of different swaps may also be ``matched'' subject to the same
conditions. In addition:
i. For futures, offsetting positions in the notional or
underlying instruments to which the futures contract relates must be
for identical instruments and the instruments must mature within
seven days of each other;
ii. For swaps and FRAs, the reference rate (for floating rate
positions) must be identical and the coupon closely matched (i.e.,
within 15 basis points); and
iii. For swaps, FRAs and forwards, the next interest reset date,
or for fixed coupon positions or forwards the remaining maturity,
must correspond within the following limits: If the reset (remaining
maturity) dates occur within one month, then the reset dates must be
on the same day; if the reset dates occur between one month and one
year later, then the reset dates must occur within seven days of
each other, or if the reset dates occur over one year later, then
the reset dates must occur within thirty days of each other.
g. Interest rate and currency swaps, FRAs, forward foreign
exchange contracts and interest rate futures are not subject to a
specific risk charge. This exemption also applies to futures on a
short-term (e.g., LIBOR) interest rate index. However, in the case
of futures contracts in which the underlying is a debt security, or
an index representing a basket of debt securities, a specific risk
charge will apply according to the category of the issuer as set out
in paragraph A.2. of this section.
B. Equities
1. Specific Risk. The specific risk element of the measure for
market risk is calculated on the basis of the bank's gross equity
positions, that is, the absolute sum of all long equity positions
and of all short equity positions at current market value. The risk
measure is 8.0 percent of that sum, unless the portfolio is both
liquid and well-diversified, in which case the specific risk measure
is 4.0 percent of the gross equity position. A specific risk measure
of 2.0 percent applies to the net long or short position in a broad,
diversified equity index and is viewed as necessary to provide for
risks associated with contract execution. A portfolio that is liquid
and well-diversified is characterized by a limited sensitivity to
price changes of any single equity issue or closely related group of
equity issues held in the portfolio. The volatility of the
portfolio's value should not be dominated by the volatility of any
individual equity issue or by equity issues from any single industry
or economic sector. In general, such portfolios should be
characterized by a large number of individual equity positions, with
no single position representing a large portion of the portfolio's
total market value. In addition, it would generally be the case that
a sizeable proportion of the portfolio would be comprised of issues
traded on organized exchanges or in well-established over-the-
counter markets.
2. General Market Risk. The general market risk element of the
measure for market risk is calculated on the difference between the
sum of the long positions and the sum of the short positions (i.e.,
the overall net position in an equity market) at current market
value. An overall net position must be separately calculated for
each national market in which the bank holds equities. The general
market risk element is 8.0 percent of the net position in each
equity market.
3. Matched Positions. Matched positions in each identical equity
in each national market may be treated as offsetting and excluded
from the capital calculation, with any remaining position included
in the calculations for specific and general market risk. For
example, a future in a given equity may be offset against an
opposite cash position in the same equity.
4. Equity Derivatives. a. Equity derivatives and other off-
balance-sheet positions that are affected by changes in equity
prices are included in the measurement system under this section
IV.B. (except for equity options, equity index options, and the
associated underlying, which are included in the measurement system
under the treatment discussed in section IV.E. of this appendix
C).30 This includes futures and swaps on both individual
equities and on equity indices. Equity derivatives should be
converted into notional equity positions in the relevant underlying.
A summary of the rules for equity derivatives is set out in
attachment III to this appendix C.
\30\ If equities are part of a forward contract (either equities
to be received or to be delivered), any interest rate or foreign
currency exposure from the other side of the contract should be
appropriately included in sections IV.A. and IV.C. of this appendix
C.
---------------------------------------------------------------------------
b. Futures and forward contracts relating to individual equities
should be reported at current market prices of the underlying.
Futures relating to equity indices should be reported as the marked-
to-market value of the notional underlying equity portfolio. Equity
swaps are treated as two notional positions, with the receiving side
as the long position and the paying side as the short
position.31 If one of the legs involves receiving/paying a
fixed or floating interest rate, the exposure should be allocated
into the appropriate repricing maturity band for debt securities.
[[Page 38137]]
The stock index is covered by the equity treatment.
\31\ For example, an equity swap in which a bank is receiving an
amount based on the change in value of one particular equity or
equity index and paying a different index will be treated as a long
position in the former and a short position in the latter.
---------------------------------------------------------------------------
c. In the case of futures-related arbitrage strategies, the 2.0
percent specific risk charge applicable to broad diversified equity
indices may be applied to only one index. The opposite position is
exempt from a specific risk charge. The strategies qualifying for
this treatment are:
i. When the bank takes an opposite position in exactly the same
index at different dates; or
ii. When the bank has an opposite position in different but
similar indices at the same date, subject to FDIC review.
d. If a bank engages in a deliberate arbitrage strategy, in
which a futures contract on a broad diversified equity index matches
a basket of securities, it may exclude both positions from the
standardized approach on condition that the trade has been
deliberately entered into and separately controlled and the
composition of the basket of stocks represents at least 90 percent
of the market value of the index. In such a case, the minimum
measure for market risk is 4.0 percent (that is, 2.0 percent of the
gross value of the positions on each side) to reflect risk
associated with executing the transaction. This applies even if all
of the securities comprising the index are held in identical
proportions. Any excess value of the securities comprising the
basket over the value of the futures contract or excess value of the
futures contract over the value of the basket is treated as an open
long or short position.
e. If a bank takes a position in depository receipts 32
against an opposite position in the underlying equity, it may offset
the position.
\32\ Generally, depository receipts are instruments issued by a
trust company or other depository institution evidencing the deposit
of foreign securities and facilitating trading in such instruments
on U.S. stock exchanges.
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C. Foreign Exchange Risk
1. The measure for market risk in foreign exchange covers the
risk of holding or taking positions in foreign currencies, including
gold, whether or not those positions are in the trading
portfolio.33 The measure is calculated as 8.0 percent of the
sum of the greater of a bank's total net open long positions or net
open short positions in each currency and the net open position in
gold.
\33\ Gold is treated as a foreign exchange position rather than
a commodity because its volatility is more in line with foreign
currencies and banks manage it in a manner similar to foreign
currencies.
---------------------------------------------------------------------------
2. When calculating a bank's net open position in each currency
and gold, positions in composite currencies, such as the ECU, may be
either treated as a currency in their own right or split into their
component parts on a consistent basis. Positions in gold (including
futures and forwards) should be converted to U.S. currency at
current spot rates. The bank's net open position in each currency is
the sum of:
a. The net spot position (i.e., all asset items less all
liability items, including accrued interest earned but not yet
received and accrued expenses, denominated in the currency in
question);
b. The net forward position.34 All foreign exchange
derivative instruments and other off-balance-sheet positions that
are affected by changes in exchange rates are included in the
measurement system under this section IV.C. (except for options and
their associated underlyings, which are included in the measurement
system under the treatment discussed in section IV.E. of this
appendix C). Forward currency positions should be valued at current
spot market exchange rates, but for a bank in which the basis of its
normal management accounting is to use net present values, forward
positions may be discounted to net present values as an acceptable
way of measuring currency positions for regulatory capital purposes;
\34\ Where gold is part of a forward contract (quantity of gold
to be received or to be delivered), any interest rate or foreign
currency exposure from the other side of the contract should be
reported as set out in section IV.A. (treating gold as a zero-coupon
instrument) and this section.
---------------------------------------------------------------------------
c. Guarantees (and similar instruments) that are certain to be
called and are likely to be irrecoverable;
d. At the discretion of the bank, net future income/expenses not
yet accrued but already fully hedged. A bank that includes future
income and expenses must do so on a consistent basis without
selecting expected future flows in order to reduce the bank's
position; and
e. Any other item representing a profit or loss in foreign
currencies.
3. The measure for market risk of foreign exchange is determined
by converting the net open position in each foreign currency at spot
rates into U.S. currency. The risk measure is 8.0 percent of the
overall net open foreign exchange position, which is determined by
summing:
a. The greater of the sum of the net long open positions or, the
sum of the net short open positions; and
b. The absolute value (that is, regardless of whether it is long
or short) of the net open position in gold.35
\35\ For example, a bank has the following net currency
positions: Yen=+50, DM=+100, GB=+150, FFR=+-20, US$=-180, and
gold=-35. The bank would sum its long positions (total=+300) and sum
its short positions (total=-200). The bank's capital requirement for
foreign exchange market risk would be: (300 (the larger of the
summed long and short positions)+35 (gold)) x 8.0%=$26.80.
---------------------------------------------------------------------------
4. If a bank is assessing its foreign exchange risk on a
consolidated basis, it may be technically impractical in the case of
some marginal operations to include the currency positions of a
foreign branch or subsidiary of the bank. In such cases, the branch
or subsidiary's internal limit in each currency may be used as a
proxy for the positions, provided there is adequate ex post
monitoring of actual positions complying with such limits. In these
circumstances, the absolute value of the limits should be added to
the net open position in each currency.
D. Commodities Risk
1. Measurement Methods. The measure for market risk in
commodities is calculated by either the simplified method or the
maturity method. These methods are only appropriate for banks that
conduct a limited amount of commodities business. All other banks
must adopt an internal model measurement system conforming to the
criteria in section III. of this appendix C.
2. Base Measure. Under both the simplified and maturity methods,
each long and short commodity position (spot or forward) is
expressed in terms of the standard unit of measurement (such as
barrels, kilos, or ounces). The positions are then converted at
current spot rates into U.S. currency, with long and short positions
in each category of commodities offset to arrive at the net open
position in each commodity. Positions in different categories of
commodities may not, generally, be offset. However, offsetting is
permitted between different sub-categories of the same commodity if
the sub-categories are deliverable against each other. Under the
simplified or maturity method, the base measure for market risk is
15.0 percent of the absolute value (i.e., neither long nor short) of
the net open position in each commodity.36
\36\ When the funding of a commodity position opens a bank to
interest rate or foreign exchange exposure the relevant positions
should be included in the measures of interest rate and foreign
exchange risk described in sections IV.A. and IV.C. of this appendix
C. When a commodity is part of a forward contract, any interest or
foreign currency exposure from the other side of the contract should
be appropriately included in sections IV.A. and IV.C. of this
appendix C.
---------------------------------------------------------------------------
3. Simplified Method. To protect a bank against basis risk,
interest rate risk, and forward gap risk, the measure of market risk
under the simplified method includes an additional 3.0 percent of
the bank's gross positions, long plus short, in each commodity. In
valuing gross positions in commodity derivatives for this purpose, a
bank should use the current spot price. The total measure for
commodities risk is thus the sum of the 15.0 percent base charges
for each net commodity position and the 3.0 percent requirements on
the gross commodity positions.
4. Maturity Method. a. Under this method, a bank must allocate
each long and short commodity position (converted into U.S. currency
at current spot rates) into a maturity ladder with time bands as set
out in table 4. A separate maturity ladder is used for each category
of commodity. Physical commodities are allocated to the first time
band:
Table 4.--Commodity Time Bands
------------------------------------------------------------------------
Time Bands
-------------------------------------------------------------------------
0-1 month
1-3 months
3-6 months
6-12 months
1-2 years
2-3 years
Over 3 years
------------------------------------------------------------------------
b. In order to capture forward gap and interest rate risk within
a time band (together sometimes referred to as curvature/spread
risk), offsetting long and short positions in each time band are
subject to an additional charge. Beginning with the shortest-term
time band and continuing with subsequent time bands, the amount of
the matched short
[[Page 38138]]
positions plus the amount of the matched long position is multiplied by
a spread rate of 1.5 percent.
c. The unmatched net position from shorter-term time bands must
be carried forward to offset exposures in longer-term time bands. A
charge of 0.6 percent of the net position carried forward is added
for each time band that the net position is carried forward.37
The total measure for commodities risk is the sum of the 15.0
percent base measurement for each net commodity position and the
additional charges for matched positions and for unmatched positions
carried forward. An example of this calculation is in attachment IV
to this appendix C.
\37\ For example, if $200 short is carried forward from the 3-6
month time band to the 1-2 year time band, the capital charge would
be $200 x .006 x 2=$2.40.
---------------------------------------------------------------------------
5. Commodity derivatives and other off-balance-sheet positions
that are affected by changes in commodity prices are included in the
measurement system under this section IV.D. (except for options and
the associated underlying, which are included in the measurement
system under the treatment discussed in section IV.E. of this
appendix C). Commodity derivatives are converted into notional
commodity positions. Under the maturity method, the positions are
allocated in maturity time bands as follows:
a. Futures and forward contracts relating to individual
commodities are incorporated in the measurement system as notional
amounts (of, for example, barrels or kilos) that are converted to
U.S. currency at current spot rates and are assigned a maturity
according to expiration date;
b. Commodity swaps in which one side of the contract is a fixed
price and the other side is the current market price are
incorporated as a series of positions equal to the notional amount
of the contract at current spot rates, with one position
corresponding to each payment on the swap and allocated in the
maturity ladder accordingly. The positions are long positions if the
bank is paying a fixed price and receiving a floating price, and
short positions if the bank is receiving a fixed price and paying a
floating price; 38 and
\38\ If one of the sides of the transaction involves receiving/
paying a fixed or floating interest rate, that exposure should be
allocated into the appropriate repricing maturity band in section
IV.A. of this appendix C.
c. Commodity swaps in which the sides of the transaction are in
different commodities are included in the relevant reporting ladder.
No offsetting is allowed unless the commodities are in the same sub-
category.
E. Options
1. Three alternatives are available for a bank to use in
measuring its market risk for options activities under the
standardized approach. A bank that only has purchased options may
use the simplified method set forth in paragraph E.2 of this
section. A bank that also writes options may use the scenario method
described in section IV.E.3., or the delta-plus method set forth in
paragraph E.4. of this section.39 These methods may only be
used by banks which, in relative terms, have limited options
activities. Banks with more significant options business are
expected to adopt an internal measurement system conforming to the
criteria in section III of this appendix C. Regardless of the method
used, specific risk related to the issuer of an instrument still
applies to options positions for equities, equity indices and
corporate debt securities as set forth in sections IV.A. and IV.B.
of this appendix C. Options remain an element of risk-weighted
assets under section II of appendix A of this part.
\39\ Unless all their written option positions are hedged by
perfectly matched long positions in exactly the same options, in
which case there is no measure for market risk.
---------------------------------------------------------------------------
2. Under the simplified and scenario methods, the positions for
the options and the associated underlying, cash or forward, are not
included in the measurement framework for debt securities, equities,
foreign exchange or commodities risk as set forth in sections IV.A.
through IV.D. of this appendix C. Rather, they are subject to the
measure of market risk as calculated in this section. The risk
measures calculated under this section should then be added to the
risk measures for debt securities, equities, foreign exchange and
commodities risk as appropriate. Under the delta-plus method, the
delta equivalent position 40 for each option is included in the
measurement frameworks set forth in sections IV.A. through IV.D. of
this appendix C.
\40\ The delta equivalent of an option is the option's delta
value multiplied by its principal or notional value. The delta value
of an option represents the expected change in the option's price as
a proportion of a small change in the price of the underlying
instrument. For example, an option whose price changes $1 for every
$2 dollar change in the price of the underlying instrument has a
delta of 0.50.
---------------------------------------------------------------------------
3. A bank that has only a limited amount and range of purchased
options may use the following simplified approach to measure its
market risk exposure.
a. For a bank with a long cash position and a long put or with a
short cash position and a long call, the measure for market risk is
the market value of the underlying instrument multiplied by the sum
of the specific and general market risk requirements for the
underlying (that is, the specific and general market risk
requirements that would have applied to the underlying directly
under sections IV.A. through IV.D. of this appendix C 41), less
the amount the option is in the money (if any) bounded at
zero.42
\41\ Because some underlying instruments are not subject to a
specific risk charge under sections IV.A through IV.D of this
appendix C, such instruments will only be multiplied by the general
market risk charge in making this calculation.
\42\ For example, if a holder of 100 shares currently valued at
$10 each has an equivalent put option with a strike price of $11,
the risk measure would be: $1,000 x 16.0 percent (e.g., 8.0 percent
specific plus 8.0 percent general market risk)=$160, less the amount
the option is in the money ($11-$10) x 100=$100, i.e., the measure
for market risk would be $60. A similar methodology applies for
options for which the underlying is a foreign currency, a debt
security or a commodity.
---------------------------------------------------------------------------
b. For a bank with a long call or a long put, the measure for
market risk is the lesser of:
i. The market value of the underlying security multiplied by the
sum of specific and general market risk requirements for the
underlying (that is, the specific and general market risk
requirements that would have applied to the underlying directly
under sections IV.A. through IV.D. of this appendix C) 43; or
\43\ See footnote 41 in section IV.E.3.a. of this appendix C.
---------------------------------------------------------------------------
ii. The market value of the option.
4. Under the scenario approach, a bank revalues its options and
related hedging positions by changing the underlying rate or price
over a specified range and by assuming different levels of
volatility for that rate or price.
a. For each of its option portfolios, a bank constructs a grid
based on a fixed range of changes in the portfolio's risk factors
and calculates changes in the value of the option portfolio at each
point within the grid. For this purpose, an option portfolio
consists of an option and any related hedging positions or multiple
options and related hedging positions that are grouped together
according to their remaining maturity or the type of underlying.
b. Options based on interest rates and debt instruments are
grouped into portfolios according to the maturity zones that are set
forth in section IV.A. of this appendix C. (Zone 1 instruments have
a remaining maturity of up to 1 year, zone 2 instruments have a
remaining maturity from 1 year up to 4 years, and zone 3 instruments
have a remaining maturity of 4 years or more.) These options and the
associated hedging positions should be evaluated under the
assumption that the relevant interest rates move simultaneously. For
options based on equities, separate grids are constructed for each
individual equity issue and index. For options based on exchange
rates, separate grids are constructed for individual exchange rates.
For options based on commodities, separate grids are constructed for
each category of commodity (as defined in section IV.D. of this
appendix C).
c. For option portfolios with options based on equities,
exchange rates, and commodities, the first dimension of the grid
consists of rate or price changes within a specified range above and
below the current market value of the underlying. For equities, the
range is 12.0 percent (or in the case of an index
8.0 percent); for exchange rates the range is
8.0 percent; and for commodities the range is
15.0 percent. For option portfolios with options based
on interest rates, the range for the first dimension of the grid
depends on the remaining maturity zone. The range for zone 1 is
100 basis points, the range for zone 2 is 90
basis points; and the range for zone 3 is 75 basis
points. For all option portfolios, the range is divided into at
least ten equally spaced intervals. The second dimension of each
grid is a shift in the volatility of the underlying rate or price
equal to 25.0 percent of the current volatility.44
\44\ For example, if the underlying in an equity instrument with
a current market value of $100 and a volatility of 20 percent, the
first dimension of the grid would range from $88 to $112, divided
into ten intervals of $2.40 and the second dimension would assume
volatilities of 15 percent, 20 percent, and 25 percent.
---------------------------------------------------------------------------
d. For each assumed volatility and rate or price change (a
scenario), the bank revalues
[[Page 38139]]
each option portfolio. The measure for market risk for the portfolio is
the largest loss in value from among the scenario revaluations. The
total measure for market risk for all option portfolios is the sum
of the individual option portfolio measures.
e. The FDIC will review the application of the scenario
approach, particularly regarding the precise way the analysis is
constructed. A bank using the scenario approach should meet the
appropriate qualitative criteria set forth in section III.B. of this
appendix C.
5. Under the delta-plus method, a bank that writes options may
include delta-weighted options positions within each measurement
framework as set forth in sections IV.A. through IV.D. of this
appendix C.
a. Options positions should be measured as a position equal to
the market value of the underlying instrument multiplied by the
delta. In addition, a bank must measure the sensitivities of the
option's gamma (the change of the delta for a given change in the
price of the underlying) and vega (the sensitivity of the option
price with respect to a change in volatility) to calculate the
measure for market risk. These sensitivities may be calculated
according to an exchange model approved by the FDIC or to the bank's
own options pricing model, subject to review by the FDIC.
b. For options with debt instruments or interest rates as the
underlying instrument, delta-weighted options positions should be
allocated into the debt instrument time bands in section IV.A. of
this appendix C using a two-legged approach (as is used for other
derivatives), requiring one entry at the time the underlying
contract takes effect and one at the time the underlying contract
matures.45 Floating rate instruments with caps or floors should
be treated as a combination of floating rate securities and a series
of European-style options.46 A bank must also calculate the
gamma and vega for each such option position (including hedge
positions). The results should be allocated into separate maturity
ladders by currency. For interest rate options such as caps and
floors, the delta and gamma should be expressed in terms of a
hypothetical underlying security. Subsequently:
\45\ For example, in April a purchased call option on a June
three-month interest-rate future would be considered on the basis of
its delta-equivalent value to a long position with a maturity of
five months and a short position with a maturity of two months. The
written option would be allocated as a long position with a maturity
of two months and a short position with a maturity of five months.
\46\ For example, the holder of a three-year floating rate bond
indexed to six-month LIBOR with a cap of 15 percent would treat the
bond as a debt security that reprices in six months, and a series of
five written call options on a FRA with a strike rate of 15 percent,
each allocated as a short position at the expiration date of the
option and as a long position at the time the FRA matures.
---------------------------------------------------------------------------
i. For gamma risk, for each time band, net gammas on short
positions are multiplied by the risk weights set out in table 5 and
by the square of the market value of the underlying instrument (net
gammas on long positions may be disregarded);
ii. For volatility risk, a bank calculates the risk measure for
vega in each time band assuming a proportional shift in volatility
of 25.0 percent;
iii. The measure for market risk is the absolute value of the
sum of the individual measures for net gammas on short positions
plus the absolute value of the sum of the individual measures for
vega risk for each time band; and
iv. The delta plus method risk weights are:
Table 5.--Delta Plus Method Risk Weights
------------------------------------------------------------------------
Modified
duration Assumed Risk-weight
Time-band (average interest for
assumed for rate change gamma\1\
time band) (%)
------------------------------------------------------------------------
Under 1 month.................... 0.00 1.00 0.00000
1 up to 3 months................. 0.20 1.00 0.00020
3 up to 6 months................. 0.40 1.00 0.00080
6 up to 12 months................ 0.70 1.00 0.00245
1 up to 2 years.................. 1.40 0.90 0.00794
2 up to 3 years.................. 2.20 0.80 0.01549
3 up to 4 years.................. 3.00 0.75 0.02531
4 up to 5 years.................. 3.65 0.75 0.03747
5 up to 7 years.................. 4.65 0.70 0.05298
7 up to 10 years................. 5.80 0.65 0.07106
10 up to 15 years................ 7.50 0.60 0.10125
15 up to 20 years................ 8.75 0.60 0.13781
Over 20 years.................... 10.00 0.60 0.18000
------------------------------------------------------------------------
\1\ According to the Taylor expansion, the risk weights are calculated
as \1/2\ (modified duration x assumed interest rate change) \2\100.
c. For options with equities as the underlying, delta-weighted
option positions should be incorporated in the measure of market
risk set forth in section IV.B. of this appendix C. Individual
equity issues and indices should be treated as separate underlyings.
In addition to the measure for delta risk, a bank should apply a
further charge for gamma and vega risk:
i. For gamma risk, the net gammas on short positions for each
underlying are multiplied by 0.72 percent (in the case of an
individual equity) or 0.32 percent (in the case of an index as the
underlying) and by the square of the market value of the underlying;
ii. For volatility risk, a bank calculates the risk measure for
vega for each underlying, assuming a proportional shift in
volatility of 25.0 percent; and
iii. The measure for market risk is the absolute value of the
sum of the individual measures for net gammas on short positions
plus the absolute value of the individual measures for vega risk.
d. For options on foreign exchange and gold positions, the net
delta (or delta-based) equivalent of the total book of foreign
currency and gold options is incorporated into the measurement of
the exposure in a net open position in each currency as set forth in
section IV.C. of this appendix C. The gamma and vega risks should be
measured as follows:
i. For gamma risk, for each underlying exchange rate, net gammas
on short positions are multiplied by 0.32 percent and by the square
of the market value of the positions;
ii. For volatility risk, a bank calculates the risk measure for
vega for each currency pair and gold assuming a proportional shift
in volatility of 25.0 percent; and
iii. The measure for market risk is the absolute value of the
sum of the individual measures for net gammas on short positions
plus the absolute value of the sum of the individual measures for
vega risk.
e. For options on commodities, the delta-weighted positions are
incorporated in one of the measures described in section IV.D. of
this appendix C. In addition, a bank must apply a capital
requirement for gamma and vega risk:
i. For gamma risk, net gammas on short positions for each
underlying are multiplied by 1.125 percent and by the square of the
market value of the commodity;
ii. For volatility risk, a bank calculates the risk measures for
vega for each commodity assuming a proportional shift in volatility
of 25.0 percent; and
iii. The measure for market risk is the absolute value of the
sum of the individual
[[Page 38140]]
measures for net gammas on short positions plus the absolute value of
the sum of the individual measures for vega risk.
f. Under certain conditions and to a limited extent, the FDIC
may permit banks that are significant traders in options with debt
securities or interest rates as the underlying to net gammas on long
and short positions and vegas across time bands. Such netting must
be based on prudent and conservative assumptions and the bank must
materially meet the qualitative standards set forth in section
III.B. of this appendix C.
g. A bank may base the calculation of vega risk on a volatility
ladder in which the implied change in volatility varies with the
maturity of the option. The assumed proportional shift in volatility
must be at least 25.0 percent at the short end of the
maturity spectrum. The proportional shift for longer maturities must
be at least as stringent in statistical terms as the 25.0 percent
shift at the short end.
h. A bank should also monitor the risks of rho (the rate of
change of the value of the option with respect to the interest rate)
and theta ( the rate of change of the value of the option with
respect to time).
Attachments to Appendix C
Attachment I--Sample Calculation of Eligible Tier 1, Tier 2, and Tier 3
Capital for the Risk-Based Capital Ratio Adjusted for Market Risk
a. In each example the weighted-risk assets are $8000 and the
market risk-adjusted assets are $625 (capital requirement for market
risk=$50 $50 x 12.5=$625):
Example 1: A bank has the following qualifying capital: Tier
1=$600, Tier 2=$100, Tier 3=$1000.
(1) The minimum capital requirement for credit risk is $640
($8000 x 8.0%). This requirement could be satisfied with $540 of
Tier 1 capital and $100 of Tier 2 capital.
(2) The remaining capital available for market risk would be:
Tier 1=$60, Tier 2=0, and Tier 3=$1000. The minimum capital
requirement for market risk is $50 ($625 x 8.0%). Eligible Tier 3
capital would be limited to $125 ($50 x 2.5).
(3) The Tier 1 capital required to support market risk could be
satisfied by allocating $14 ($50 x .285), with eligible Tier 3
capital used for market risk being $36 ($50 x $14).
(4) Total qualifying and eligible capital would be: $540 (Tier
1)+$100 (Tier 2)+$60 (Tier 1, comprising $14 allocated for market
risk and $46 unallocated)+$36 (Tier 3)=$736. The bank's ratio of
qualifying and eligible capital to weighted-risk assets adjusted for
market risk would be: $736/$8,625)=8.5%.
Example 2: A bank has the following qualifying capital: Tier
1=$500, Tier 2=$140, Tier 3=$600.
(1) The minimum capital requirement for credit risk is $640
($8000 x 8.0%). This requirement could be satisfied with $500 of
Tier 1 capital and $140 of Tier 2 capital.
(2) The remaining capital available for market risk would be:
Tier 1=0, Tier 2=$0, and Tier 3=$600. Eligible Tier 3 capital would
be limited to $0 (0 x 2.5). Because there is no Tier 1 capital
required to support market risk, no eligible Tier 3 capital may be
used for market risk.
(3) Total qualifying and eligible capital would be: $500 (Tier
1)+$140 (Tier 2)=$640. The bank's ratio of qualifying and eligible
capital to weighted-risk assets adjusted for market risk would be:
$640/$8,625)=7.4%
b. In both of the examples described in paragraph a. of this
attachment the total of Tier 2 and Tier 3 capital for credit and
market risk is not greater than 100 percent of Tier 1 capital for
credit and market risk and the total of Tier 2 capital for credit
risk is not greater than 100 percent of Tier 1 capital for credit
risk.
Attachment II--Sample Calculation of General Market Risk for Debt
Instruments Using the Maturity Method
a. A bank with the following positions would allocate them into
a maturity ladder as shown below:
i. Qualifying bond, $13.33mn market value, remaining maturity 8
years, coupon 8%;
ii. Government bond, $75mn market value, remaining maturity 2
months, coupon 7%;
iii. Interest rate swap, $150mn, bank receives floating rate
interest and pays fixed, next interest reset after 12 months,
remaining life of swap is 8 years (assumes the current interest rate
is identical to the one the swap is based on); and
iv. Long position in interest rate future, $50mn, delivery date
after 6 months, life of underlying government security is 3.5 years
(assumes the current interest rate is identical to the one the swap
is based on).
----------------------------------------------------------------------------------------------------------------
Risk
Zone Time band and position weight Risk-weighted Net time-band Net zone positions
[%] position positions
----------------------------------------------------------------------------------------------------------------
1....... 0-1 Month............. 0.00
1-3 Months............ 0.20 Long 0.15............ Long 0.15............ Long 1.00
Long 75 Gov. Bond.....
3-6 Months............ 0.40 Short 0.20........... Short 0.20...........
Short 50 Future.......
6-12 Months........... 0.70 Long 1.05............ Long 1.05............
Long 150 Swap.........
2....... 1-2 yrs............... 1.25
2-3 yrs............... 1.75
3-4 yrs............... 2.25 Long 1.125........... Long 1.125........... Long 1.125
Long 50 Future........
3....... 4-5 yrs............... 2.75
5-7 yrs............... 3.25
7-10 yrs.............. 3.75 Short 5.625.......... Short 5.125.......... Short 5.125
Short 150 Swap........
Long 13.33............ Long 0.50............
Qual. Bond............
10-15 yrs............. 4.50
15-20 yrs............. 5.25
Over 20 yrs........... 6.00
----------------------------------------------------------------------------------------------------------------
b. A vertical disallowance would be calculated for time band 7-
10 years. It would be 10 percent of the positions eliminated by
netting in the time band--10.0 x 0.5 = 0.05 ($50,000).
c. A horizontal disallowance would be calculated for zone 1. It
would be 40 percent of the positions eliminated by netting in the
zone--40.0 x 0.20 = 0.80 ($80,000). The remaining net position in
zone 1 would be long 1.00.
d. A horizontal disallowance would be calculated for adjacent
zones 2 and 3. It would be 40 percent of the positions eliminated by
netting between the zones--40.0 x 1.125 = 0.45 ($450,000). The
remaining position in zone 3 would be short 4.00.
e. A horizontal disallowance would be calculated between zones 1
and 3. It would be 100 percent of the positions eliminated by
netting between the zones--100 x 1.00 = 1.00 ($1,000,000).
f. The remaining net open position for the bank would be 3.00
($3,000,000). The total capital requirement for general market risk
for this portfolio would be:
The vertical disallowance.................................. $50,000
Horizontal disallowance in zone 1.......................... 80,000
[[Page 38141]]
The horizontal disallowance between zones 2 and 3.......... 450,000
The horizontal disallowance between zones 1 and 3.......... 1,000,000
The overall net open position.............................. 3,000,000
------------
Total requirement for general market risk.............. $4,580,000
Attachment III--Summary of Treatment for Interest Rate and Equity
Derivatives
Summary of Treatment for Interest Rate Derivatives
------------------------------------------------------------------------
Specific risk
Instrument charge General market risk charge
------------------------------------------------------------------------
Exchange-Traded Future:
Government security..... No........... Yes, as two positions.
Corporate debt security. Yes.......... Yes, as two positions.
Index on short-term No........... Yes, as two positions.
interest rates (e.g.
LIBOR).
OTC Forward:
Government security..... No........... Yes, as two positions.
Corporate debt security. Yes.......... Yes, as two positions.
Index on short-term No........... Yes, as two positions.
interest rates.
FRAs, Swaps............. No........... Yes, as two positions.
Forward foreign exchange No........... Yes, as one position in
each currency.
Options:
Government security..... No........... For each type of
transaction, either:
Corporate debt security. Yes.......... (a) Carve out together with
the associated hedging
positions
Index on short-term No........... --simplified method
interest rates.
--scenario analysis
--internal models, or
(b) General market risk
charge according to the
Delta-plus method (gamma
and vega receive separate
capital charges).
------------------------------------------------------------------------
Note: Specific risk charges relate to the issuer of the instrument.
There remains a separate capital requirement for counterparty credit
risk.
Summary of Treatment for Equity Derivatives
------------------------------------------------------------------------
Specific risk
Instrument charge General market risk charge
------------------------------------------------------------------------
Exchange-Traded or OTC
Future:
Individual equity....... Yes.......... Yes, as underlying.
Index................... 2.0%......... Yes, as underlying.
Options:
Individual equity....... Yes.......... For each type of
transactions either:
Index................... 2.0%......... (a) Carve out together with
the associated hedging
positions
--simplified method
--scenario approach
--internal models, or
(b) General market risk
requirement according to
the Delta-plus method
(gamma and vega receive
separate capital charges).
------------------------------------------------------------------------
Note: Specific risk charges relate to the issuer of the instrument.
There remains a separate capital requirement for counterparty credit
risk.
Attachment IV--Sample Calculation of Standardized Approach for
Commodities Risk
----------------------------------------------------------------------------------------------------------------
Spread Capital
Time-band Position rate Capital calculation charge
----------------------------------------------------------------------------------------------------------------
0 up to 1 month............ None
1 up to 3 months........... None
3 up to 6 months........... Long 800................... 1.5% 800 long + 800 short (matched) 24
x 1.5%=.
Short 1000................. ......... 200 short carried forward to 1-2 2.4
yrs, capital charge: 200 x 2 x
0.6%=.
6 up to 12 months.......... None
1 up to 2 yrs.............. Long 600................... ......... 200 long + 200 short (matched) 6
x 1.5%=.
400 long carried forward to over 4.8
3 yrs capital charge: 400 x 2 x
0.6%=.
2 up to 3 yrs.............. None
Over 3 years............... Short 600.................. ......... 400 long + 400 short (matched) 12
x 1.5%=.
Net position: 200 capital 30
charge: 200 x 15.0%=.
----------------------------------------------------------------------------------------------------------------
Note: Assume all positions are in the same commodity and converted at current spot rates into U.S. dollars. The
total capital requirement would be $79.2.
Attachment V--Sample Calculation for Delta-Plus Method for Options
a. Assume a bank has a European short call option on a commodity
with an exercise price of 490 and a market value of the underlying
12 months from the expiration of the option at 500; a risk-free
interest rate at 8% per annum, and the volatility at 20 percent. The
current delta for this position is according to the Black-Scholes
formula -0.721 (that is, the price of the option changes by -0.721
if the price of the underlying moves by 1). The gamma is -0.0034
(that is, the delta changes by
[[Page 38142]]
-0.0034 from -0.721 to -0.7244 if the price of the underlying moves by
1). The current value of the option is 65.48.
b. The first step under the delta-plus method is to multiply the
market value of the commodity by the absolute value of the delta.
500 x 0.721=360.5. The delta-weighted position is then incorporated
into the measure described in section IV.D. of this appendix C E. If
the bank uses the maturity approach and no other positions exist,
the delta-weighted position is multiplied by 0.15 to calculate the
capital requirement for delta. 360.5 x 0.15=54.075.
c. The capital requirement for gamma is calculated according to
the Taylor expansion by multiplying the absolute value of the
assumed gamma of -0.0034 by 1.125% and by the square of the market
value of the underlying. 0.0034 x 0.0125 x 5002=10.625.
d. The capital requirement for vega is calculated next. The
assumed current (implied) volatility is 20%. Since only an increase
in volatility carries a risk of loss for a short call option, the
volatility has to be increased by a relative shift of 25%. This
means that the vega capital requirement has to be calculated on the
basis of a change in volatility of 5 percentage points from 20% to
25% in this example. According to the Black-Scholes formula used
here, the vega equals 168. Thus, a 1% or 0.01 increase in volatility
increases the value of the option by 1.68. Accordingly, a change in
volatility of 5 percentage points increases the value of
5 x 1.68=8.4. This is the capital requirement for vega risk. The
total capital requirement would be $73.10 (54.075+10.625+8.4).
By Order of the Board of Directors.
Dated at Washington, DC, this 11th day of July 1995.
Jerry L. Langley,
Executive Secretary.
[FR Doc. 95-17542 Filed 7-24-95; 8:45 am]
BILLING CODES 4810-33-P; 6210-01-P; 6714-01-P
