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Trading and Capital-Markets Activities Manual

Trading Activities: Capital Adequacy (Continue)
Source: Federal Reserve System 
(The complete Activities Manual (pdf format) can be downloaded from the Federal Reserve's web site)

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Qualitative Requirements 

The qualitative requirements reiterate several basic components of sound risk management discussed in earlier sections of this manual. For example, an institution must have a risk-control unit that reports directly to senior management and is independent from business-trading functions. The risk-control unit is expected to conduct regular back-tests to evaluate the model's accuracy and conduct stress tests to identify the impact of adverse market events on the institution's portfolio. An in-depth understanding of the risk-control unit's role and responsibilities is completed through discussions with the institution's market-risk and senior management teams and through the review of documented policies and procedures. In addition, examiners should review the institution's organizational structure and risk-management committees and minutes. The review of committee minutes provides insights into the level of discussion of market-risk issues by senior management and, in some cases, by outside directors of the institution. 

An institution must have an internal model that is fully integrated into its daily management, must have policies and procedures for conducting appropriate stress tests and back-tests and for responding to the results of those tests, and must conduct independent reviews of its risk-management and -measurement systems at least annually. An institution should develop and use those stress tests appropriate to its particular situation. Thus, the market-risk rules do not include specific stress-test methodologies. 

An institution's stress tests should be rigorous and comprehensive enough to cover a range of factors that could create extraordinary losses in a trading portfolio, or that could make the control of risk in a portfolio difficult. The review of stress testing is important, given that VAR-based models are designed to measure market risk in relatively stable markets (for example, at a 99 percent confidence interval, as prescribed in the market-risk amendment to the capital rules). However, sound risk-management practices require analyses of wider market conditions. Examiners should review the institution's policies and procedures for conducting stress tests and assess the timeliness and frequency of stress tests, the comprehensive capture of traded positions and parameters (for example, changes in risk factors), and the dissemination and use of testing results. Examiners should pay particular attention to whether stress tests result in an effective management tool for controlling exposure and their ''plausibility'' in relation to the institution's risk profile. Stress testing continues to be more of an art than a science, and the role of the examiner is to ensure that institutions have the appropriate capabilities, processes, and management oversight to conduct meaningful stress testing. 

Stress tests should be both qualitative and quantitative, incorporate both market risk and liquidity aspects of market disturbances, and reflect the impact of an event on positions with either linear or nonlinear price characteristics. Examiners should assess whether banks are in a position to conduct three types of broad stress tests-those incorporating (1) historical events, using market data from the respective time periods; (2) hypothetical events, using ''market data'' constructed by the institution to model  extreme market events that would pose a significant financial risk to the institution; and (3) institution-specific analysis, based on the institution's portfolios, that identifies key vulnerabilities. When stress tests reveal a particular vulnerability, the institution should take effective steps to appropriately manage those risks. 

An institution's independent review of its risk-management process should include the activities of business-trading units and the risk-control unit. Examiners should verify that an institution's review includes assessing whether its risk-management system is fully integrated into the daily management process and whether the system is adequately documented. Examiner assessments of the integration of risk models into the daily market-risk-management process is a fundamental component of the review for compliance with the market-risk capital rule. As a starting point, examiners should review the risk reports that are generated by the institution's internal model to assess the ''stratification,'' or level of detail of information provided to different levels of management, from head traders to senior managers and directors. The review should evaluate the organizational structure of the risk-control unit and analyze the approval process for risk-pricing models and valuation systems. The institution's review should consider the scope of market risks captured by the risk-measurement model; accuracy and completeness of position data; verification of the consistency, timeliness, and reliability of data sources used to run the internal model; accuracy and appropriateness of volatility and correlation assumptions; and validity of valuation and risk-transformation calculations. Examiners should assess the degree to which the institution's methodology serves as the basis for trading limits allocated to the various trading-business units. Examiners should review this limit structure to assess its coverage of risk sensitivities within the trading portfolio. In addition, examiners should assess the limit-development and -monitoring mechanisms to ensure that positions versus limits and excessions are appropriately documented and approved. 

In addition to formal reviews, examiners and specialist teams may hold regular discussions with institutions regarding their market-risk exposures and the methodologies they employ to measure and control these risks. These discussions enable supervisors to remain abreast of the institution's changes in methodology (for example, its treatment of nonlinear risks or its approach to stress testing) and its ongoing compliance with the market-risk capital rule. These discussions are particularly important during turbulent markets where exposures and capital may be affected by dramatic swings in market volatility. 

In order to monitor compliance with the market-risk amendment and to further their understanding of market-risk exposures, supervisors should make quarterly requests to institutions subject to the market-risk amendment for the following information:

  total trading gain or loss for the quarter (net interest income from trading activities plus realized and unrealized trading gain or loss) 
  average risk-based capital charge for market risk during the quarter 
  market-risk capital charge for specific risk during the quarter 
  market-risk capital charge for general risk during the quarter 
  average one-day VAR for the quarter 
  maximum one-day VAR for the quarter 
  largest one-day loss during the quarter and the VAR for the preceding day 
  the number of times the loss exceeded the one-day VAR during the quarter, and for each occurrence, the amount of the loss and the prior day's VAR 
  the cause of back-testing exceptions, either by portfolio or major risk factor (for example, volatility in the S&P 500) 
  the market-risk multiplier currently in use 

If significant deficiencies are uncovered, examiners may require the institution's audit group to enhance the scope and independence of its market-risk review processes. If the audit or independent review function lacks expertise in this area, examiners may require that the institution outsource this review to a qualified independent consultant. Follow-up discussions are held with the institution once appropriate review scopes are developed and upon the completion of such reviews. 

Quantitative Requirements 

To ensure that an institution with significant market risk holds prudential levels of capital and that regulatory capital charges for market risk are consistent across institutions with similar exposures, an institution's VAR measures must meet the following quantitative requirements:

  The VAR methodology must be commensurate with the nature and size of the institution's trading activities and risk profile. Because the capital rules do not prescribe a particular VAR methodology, the institution can use generally accepted techniques, such as variance-covariance, historical simulation, and Monte Carlo simulations. 
  VAR measures must be computed each business day based on a 99 percent (one-tailed) confidence level of estimated maximum loss. 
  VAR measures must be based on a price shock equivalent to a 10-day movement in rates and prices. The Federal Reserve believes that shorter periods do not adequately reflect the price movements that are likely during periods of market volatility and that they would significantly understate the risks embedded in options positions, which display nonlinear price characteristics. The Board recognizes, however, that it may be overly burdensome for institutions to apply precise 10-day price or rate movements to options positions at this time and, accordingly, will permit institutions to estimate one-day price movements using the ''square root of time'' approach.25 As banks enhance their modeling techniques, examiners should consider whether they are making substantive progress in developing adequate and more robust methods for identifying nonlinear price risks. Such progress is particularly important at institutions with sizable options positions. 
  VAR measures must be based on a minimum historical observation period of one year for estimating future price and rate changes. If historical market movements are not weighted evenly over the observation period, the weighted average for the observation period must be at least six months, which is equivalent to the average for the minimum one-year observation period. 
  An institution must update its model data at least once every three months and more frequently if market conditions warrant. 
  VAR measures may incorporate empirical correlations (calculated from historical data on rates and prices) both within and across broad risk categories, subject to examiner confirmation that the model's system for measuring such correlation is sound. If an institution's model does not incorporate empirical correlations across risk categories, then the institution must calculate the VAR measures by summing the separate VAR measures for the broad risk categories (that is, interest rates, equity prices, foreign-exchange rates, and commodity prices). 

25. For example, under certain statistical assumptions, an institution can estimate the 10-day price volatility of an instrument by multiplying the volatility calculated on one-day changes by the square root of 10 (approximately 3.16). 

During the examination process, examiners should review an institution's risk-management process and internal model to ensure that it processes all relevant data and that modeling and risk-management practices conform to the parameters and requirements of the market-risk rule. When reviewing an internal model for risk-based capital purposes, examiners may consider reports and opinions about the accuracy of an institution's model that have been generated by external auditors or qualified consultants. 

If a banking institution does not fully comply with a particular standard, examiners should review the banking institution's plan for meeting the requirement of the market-risk amendment. These reviews should be tailored to the institution's risk profile (for example, its level of options activity) and methodologies. 

In reviewing the model's ability to capture optionality, examiners' reviews should identify the sub-portfolios in which optionality risk is present and review the flow of deal data to the risk model and the capture of higher-order risks (for example, gamma and vega) within VAR. Where options risks are not fully captured, the institutions should identify and quantify these risks and identify corrective-action plans to incorporate the risks. Examiners should review the calculation of volatilities (implied or historical), sources of this data (liquid or illiquid markets), and measurement of implied price volatility along varying strike prices. The understanding of the institution's determination of volatility smiles and skewness is a basic tenet in assessing a VAR model's reasonableness if optionality risk is material. Volatility smiles reflect the phenomenon that out-of-the-market and in-the-market options both have higher volatilities than at-the-market options. Volatility skew refers to the differential patterns of implied volatilities between out-of-the-market calls and out-of-the-market puts. 

The examiners should review the institution's methodology for aggregating VAR estimates across the entire portfolio. The institution should have well-documented policies and procedures governing its aggregation process, including the use of correlation assumptions. The inspection of correlation assumptions is accomplished through a review of the institution's documented testing of correlation assumptions and select-transaction testing when individual portfolios are analyzed to gauge the effects of correlation assumptions. Although the summation of portfolio VARs is permitted under the capital rules, the aggregation of VAR measures generally overstates risk and may represent an ineffective risk-management tool. Examiners should encourage institutions to develop more rigorous and appropriate correlation estimates to arrive at a more meaningful portfolio VAR. 

The aggregation processes utilized by banking institutions may also be subject to certain ''missing risks,'' resulting in an understatement of risk in the daily VAR. Examiners should understand the aggregation process through discussions with risk-management personnel and reviews of models-related documents. 

Examiners should identify key control points, such as timely updating and determination of correlation statistics, that may result in the misstatement of portfolio VAR. Examiners should evaluate the institution's systems infrastructure and its ability to support the effective aggregation of risk across trading portfolios. They should also review the systems architecture to identify products that are captured through automated processes and those that are captured in spreadsheets or maintained in disparate systems. This review is important in order to understand the aggregation processes, including the application of correlations, and its impact on the timeliness and accuracy of risk-management reports. 

Market-Risk Factors 

For risk-based capital purposes, an institution's internal model must use risk factors that address market risk associated with interest rates, equity prices, exchange rates, and commodity prices, including the market risk associated with options in each of these risk categories. An institution may use the market-risk factors it has determined affect the value of its positions and the risks to which it is exposed. However, examiners should confirm that an institution is using sufficient risk factors to cover the risks inherent in its portfolio. For example, examiners should verify that interest-rate-risk factors correspond to interest rates in each currency in which the institution has interest-rate-sensitive positions. The risk-measurement system should model the yield curve using one of a number of generally accepted approaches, such as by estimating forward rates or zero-coupon yields, and should incorporate risk factors to capture spread risk. The yield curve should be divided into various maturity segments to capture variation in the volatility of rates along the yield curve. For material exposure to interest-rate movements in the major currencies and markets, modeling techniques should capture at least six segments of the yield curve. 

The internal model should incorporate risk factors corresponding to individual foreign currencies in which the institution's positions are denominated, each of the equity markets in which the institution has significant positions (at a minimum, a risk factor should capture market-wide movements in equity prices), and each of the commodity markets in which the institution has significant positions. Risk factors should measure the volatilities of rates and prices underlying options positions. An institution with a large or complex options portfolio should measure the volatilities of options positions by different maturities. The sophistication and nature of the modeling techniques should correspond to the level of the institution's exposure. 


One year after beginning to apply the market-risk rules, an institution will be required to back-test VAR measures that have been calculated for its internal risk-management purposes. The results of the back-tests will be used to evaluate the accuracy of the institution's internal model, and may result in an adjustment to the institution's VAR multiplication factor used for calculating regulatory capital requirements. Specifically, the back-tests must compare the institution's daily VAR measures calculated for internal purposes, calibrated to a one-day movement in rates and prices and a 99 percent (one-tailed) confidence level, against the institution's actual daily net trading profit or loss for the past year (that is, the preceding 250 business days). In addition to recording daily gains and losses arising from changes in market valuations of the trading portfolio, net trading profits (or losses) may include items such as fees and commissions and earnings from bid/ask spreads. These back-tests must be performed each quarter. Examiners should review the institution's back-testing results at both the portfolio and sub-portfolio (for example, business-line) levels. Although not required under the capital rules, sub-portfolio back-testing provides management and examiners with deeper insight into the causes of exceptions. It also gives examiners a framework within which to discuss with risk managers the adequacy of the institution's modeling assumptions as well as issues of position valuation and profit attribution at the business-line level. Examiners should review the profit-and-loss basis of the backtesting process, including actual trading profits and losses (that is, realized and unrealized profits or losses on end-of-day portfolio positions) and fee income and commissions associated with trading activities. 

If the back-test reveals that an institution's daily net trading loss exceeded the corresponding VAR measure five or more times, the institution's multiplication factor should begin to increase-from three to as high as four if 10 or more exceptions are found. However, the decision regarding the specific size of any increase to the institution's multiplier may be tempered by examiner judgment and the circumstances surrounding the exceptions. In particular, special consideration may be granted for exceptions that produce abnormal changes in interest rates or exchange rates as a result of major political events or other highly unusual market events. Examiners may also consider factors such as the magnitude of an exception (that is, the difference between the VAR measure and the actual trading loss), and the institution's response to the exception. Examiners may determine that an institution does not need to increase its multiplication factor if it has taken adequate steps to address any modeling deficiencies or other actions that are sufficient to improve its risk-management process. The Federal Reserve will monitor industry progress in developing back-testing methodologies and may adjust the back-testing requirements in the future. Where the back-test reveals exceptions, examiners should review the institution's documentation of the size and cause of the exception and any corrective action taken to improve the assumptions or risk factor inputs underlying the VAR model. 

Specific Risk 

An institution may use its internal model to calculate specific risk if it can demonstrate that the model sufficiently captures the changes in market values for covered debt and equity instruments and related derivatives (for example, credit derivatives) due to factors other than broad market movements. These factors include idiosyncratic price variation and event/default risk. The capital rules also stipulate that the model should explain the historical price variation in the portfolio and capture potential concentrations, including magnitude and changes in composition. Finally, the model should be sufficiently robust to capture greater volatility due to adverse market conditions. If the bank's internal model cannot meet these requirements, the bank must use the standardized approach to measuring specific risk under the capital rules. The capital charge for specific risk may be determined either by applying standardized measurement techniques (the standardized approach) or using an institution's internal model. 

Standardized Approach 

Under the standardized approach, trading-account debt instruments are categorized as ''government,'' ''qualifying,'' or ''other,'' based on the type of obligor and, in the case of instruments such as corporate debt, on the credit rating and remaining maturity of the instrument. Each category has a specific-risk weighting factor. The specific-risk capital charge for debt positions is calculated by multiplying the current market value of each net long or short position in a category by the appropriate risk-weight factor. An institution must risk weight derivatives (for example, swaps, futures, forwards, or options on certain debt instruments) according to the relevant underlying instrument. For example, in a forward contract, an institution must risk weight the market value of the effective notional amount of the underlying instrument (or index portfolio). Swaps must be included as the notional position in the underlying debt instrument or index portfolio, with a receiving side treated as a long position and a paying side treated as a short position. Options, whether long or short, are included by risk weighting the market value of the effective notional amount of the underlying instrument or index multiplied by the option's delta. An institution may net long and short positions in identical debt instruments with the same issuer, coupon, currency, and maturity. An institution may also net a matched position in a derivative instrument and the derivative's corresponding underlying instrument. 

The government category includes general obligation debt instruments of central governments of OECD countries, as well as local currency obligations of non-OECD central governments to the extent the institution has liabilities booked in that currency. The risk-weight factor for the government category is zero percent. The qualifying category includes debt instruments of U.S. government-sponsored agencies, general obligation debt instruments issued by states and other political subdivisions of OECD 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. Qualifying instruments also may be corporate debt and revenue instruments issued by states and political subdivisions of OECD countries that are (1) rated as investment grade by at least two nationally recognized credit-rating firms; (2) rated as investment grade by one nationally recognized credit-rating firm and not less than investment grade by any other credit-rating agency; or (3) if unrated and the issuer has securities listed on a recognized stock exchange, deemed to be of comparable investment quality by the reporting institution, subject to review by the Federal Reserve. The risk-weighting factors for qualifying instruments vary according to the remaining maturity of the instrument as set in table 3. Other debt instruments not included in the government or qualifying categories receive a risk weight of 8.0 percent.

The specific-risk charge for equity positions is based on an institution's gross equity position for each national market. Gross equity position is defined as the sum of all long and short equity positions, including positions arising from derivatives such as equity swaps, forwards, futures, and options. The current market value of each gross equity position is weighted by a designated factor, with the relevant underlying instrument used to determine risk weights of equity derivatives. For example, swaps are included as the notional position in the underlying equity instrument or index portfolio, with a receiving side treated as a long position and a paying side treated as a short position. Options, whether long or short, are included by risk weighting the market value of the effective notional amount of the underlying equity instrument or index multiplied by the option's delta. Long and short positions in identical equity issues or indexes may be netted. An institution may also net a matched position in a derivative instrument and its corresponding underlying instrument. 

The specific-risk charge is 8.0 percent of the gross equity position, unless the institution's portfolio is both liquid and well diversified, in which case the capital charge is 4.0 percent. A portfolio is liquid and well diversified if (1) it is characterized by a limited sensitivity to price changes of any single equity or closely related group of equity issues; (2) the volatility of the portfolio's value is not dominated by the volatility of equity issues from any single industry or economic sector; (3) it contains a large number of equity positions, with no single position representing a substantial portion of the portfolio's total market value;26 and (4) it consists mainly of issues traded on organized exchanges or in well-established over-the-counter markets.

For positions in an index comprising a broad-based, diversified portfolio of equities, the specific-risk charge is 2.0 percent of the net long or short position in the index. In addition, a 2.0 percent specific-risk charge applies to only one side (long or short) in the case of certain futures-related arbitrage strategies (for instance, long and short positions in the same index at different dates or in different market centers, and long and short positions at the same date in different, but similar indexes). Finally, under certain conditions, futures positions on a broad-based index that are matched against positions in the equities composing the index are subject to a specific-risk charge of 2.0 percent against each side of the transaction.

26. For practical purposes, examiners may interpret ''substantial'' as meaning more than 5 percent.

Internal-Models Approach 

Institutions using models will be permitted to base their specific-risk capital charge on modeled estimates if they meet all of the qualitative and quantitative requirements for general risk models as well as the additional criteria set out below. Institutions which are unable to meet these additional criteria will be required to base their specific-risk capital charge on the full amount of the standardized specific-risk charge. Conditional permission for the use of specific-risk models is discouraged. Institutions should use the standardized approach for a particular portfolio until they have fully developed a model to accurately measure the specific risk inherent in that portfolio. 

The criteria for applying modeled estimates of specific risk require that an institution's model- 

  explain the historical price variation in the portfolio;27
  demonstrably capture concentration (magnitude and changes in composition);28  
  be robust to an adverse environment;29 and 
  be validated through back-testing aimed at assessing whether specific risk is being accurately captured. In addition, the institution must be able to demonstrate that it has methodologies in place which allow it to adequately capture event and default risk for its trading positions. In assessing the model's robustness, examiners review the banking institution's testing of the model, including regression analysis testing (that is, ''goodness-of-fit''), stress-test simulations of ''shocked'' market conditions, and changing credit-cycle conditions. Examiners evaluate the scope of testing (for example, what factors are shocked and to what degree, and what the resultant changes in risk exposures are), the number of tests completed, and the results of these tests. If testing is deemed insufficient or the results are unclear, the banking institution is expected to address these concerns before supervisory recognition of the model. As previously noted, the review of these models is conducted after supervisory recognition of the banking institution's general market-risk methodology. The examiner reviews are generally conducted on a sub-portfolio basis (for example, investment-grade corporate debt, credit derivatives, etc.), with a focus on the modeling methodology, validation, and back-testing process. The portfolio-level approach addresses the case in which a banking institution's model adequately captures specific risk within its investment-grade corporate-debt portfolio but not within its high-yield corporate-debt portfolio. In this case, the banking institution would generally be granted internal-models treatment for the investment-grade debt portfolio while continuing to apply the standardized approach for its high-yield debt portfolio.

27. The key ex ante measures of model quality are ''goodness-of-fit'' measures which address the question of how much of the historical variation in price value is explained by the model. One measure of this type which can often be used is an R-squared measure from regression methodology. If this measure is to be used, the institution's model would be expected to be able to explain a high percentage, such as 90 percent, of the historical price variation or to explicitly include estimates of the residual variability not captured in the factors included in this regression. For some types of models, it may not be feasible to calculate a goodness-of-fit measure. In such an instance, a bank is expected to work with its national supervisor to define an acceptable alternative measure which would meet this regulatory objective.
28. The institution would be expected to demonstrate that the model is sensitive to changes in portfolio construction and that higher capital charges are attracted for portfolios that have increasing concentrations. 
29. The institution should be able to demonstrate that the model will signal rising risk in an adverse environment. This could be achieved by incorporating in the historical estimation period of the model at least one full credit cycle and ensuring that the model would not have been inaccurate in the downward portion of the cycle. Another approach for demonstrating this is through simulation of historical or plausible worst-case environments.

Examiner assessments of the adequacy of a banking institution's specific-risk modeling address the following major points: 

  the type, size, and composition of the modeled portfolio and other relevant information (for example, market data) 

  the VAR-based methodology and relevant assumptions applicable to the modeled portfolio and a description of how it captures the key specific-risk areas-idiosyncratic variation and event and default risk 

  the back-testing analysis performed by the banking institution that demonstrates the model's ability to capture specific risk within the identified portfolio (This back-testing is specific to the modeled portfolio, not the entire trading portfolio.) 

  additional testing (for example, stress testing) performed by the banking institution to demonstrate the model's performance under market-stress events 

Institutions which meet the criteria set out above for models but that do not have methodologies in place to adequately capture event and default risk will be required to calculate their specific-risk capital charge based on the internal-model measurements plus an additional prudential surcharge as defined in the following paragraph. The surcharge is designed to treat the modeling of specific risk on the same basis as a general market-risk model that has proven deficient during back-testing. That is, the equivalent of a scaling factor of four would apply to the estimate of specific risk until such time as an institution can demonstrate that the methodologies it uses adequately capture event and default risk. Once an institution is able to demonstrate this, the minimum multiplication factor of three can be applied. However, a higher multiplication factor of four on the modeling of specific risk would remain possible if future back-testing results were to indicate a serious deficiency with the model. 

For institutions applying the surcharge, the total of the market-risk capital requirement will equal a minimum of three times the internal model's general- and specific-risk measure plus a surcharge in the amount of either- 

  the specific-risk portion of the value-at-risk measure which should be isolated according to supervisory guidelines30 or 
  the value-at-risk measures of sub-portfolios of debt and equity positions that contain specific risk.31 

Institutions using the second option are required to identify their sub-portfolio structure ahead of time and should not change it without supervisory consent. 

Institutions which apply modeled estimates of specific risk are required to conduct back-testing aimed at assessing whether specific risk is being accurately captured. The methodology an institution should use for validating its specific-risk estimates is to perform separate backtests on sub-portfolios using daily data on sub-portfolios subject to specific risk. The key subportfolios for this purpose are traded-debt and equity positions. However, if an institution itself decomposes its trading portfolio into finer categories (for example, emerging markets or traded corporate debt), it is appropriate to keep these distinctions for sub-portfolio back-testing purposes. Institutions are required to commit to a sub-portfolio structure and stick to it unless it can be demonstrated to the supervisor that it would make sense to change the structure. 

Institutions are required to have in place a process to analyze exceptions identified through the back-testing of specific risk. This process is intended to serve as the fundamental way in which institutions correct their models of specific risk if they become inaccurate. Models that incorporate specific risk are presumed unacceptable if the results at the sub-portfolio level produce 10 or more exceptions. Institutions with unacceptable specific-risk models are expected to take immediate action to correct the problem in the model and ensure that there is a sufficient capital buffer to absorb the risk that the back-test showed had not been adequately captured. 

Examiners must confirm with the institution that its model incorporates specific risk for both debt and equity positions. For instance, if the model addressed the specific risk of debt positions but not equity positions, then the institution could use the model-based specific-risk charge (subject to the limitation described earlier) for debt positions, but must use the full standard specific-risk charge for equity positions. 

30. Techniques for separating general market risk and specific risk would include the following: Equities 
The market should be identified with a single factor that is representative of the market as a whole, for example, a widely accepted, broadly based stock index for the country concerned. 
Institutions that use factor models may assign one factor of their model, or a single linear combination of factors, as their general-market-risk factor. Bonds 
The market should be identified with a reference curve for the currency concerned. For example, the curve might be a government bond yield curve or a swap curve; in any case, the curve should be based on a well-established and liquid underlying market and should be accepted by the market as a reference curve for the currency concerned. Institutions may select their own technique for identifying the specific-risk component of the value-at-risk measure for purposes of applying the multiplier of four. Techniques would include- 
using the incremental increase in value-at-risk arising from the modeling of specific-risk factors; 
using the difference between the value-at-risk measure and a measure calculated by substituting each individual equity position by a representative index; or
using an analytic separation between general market risk and specific risk implied by a particular model. 
31. This would apply to sub-portfolios containing positions that would be subject to specific risk under the standardized-based approach.

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