Risk Measures

•Banks  use  a  variety  of  risk  measures  for  economic  capital  purposes  with  the  choice  of  risk  measure being dependent on a number of factors including –

1. The properties of the risk measure

2. The risk or product-type being measured

3. The availability of data

4. The tradeoffs between the complexity and usability of the measure

5. The intended use of the risk measure

•An ideal risk measure should be intuitive, stable, easy to compute, easy to understand, coherent  and interpretable in economic terms. Additionally, risk decomposition based on the  risk  measure should be simple and meaningful. These essential characteristics can be defined in the  following way-

a)  Intuitive

The risk measure should meaningfully align with some intuitive notion of risk, such as  unexpected losses. This is essential to ensure that relevant parameters receive bulk of the  focus and the time and energy within the organization is directed in a purposeful and deliberate way.

b) Stable
Small changes in model parameters should not produce large changes in the estimated loss distribution and the risk measure. Similarly, a second run of a simulation model in order to generate a loss distribution, should not produce a dramatic change in the risk measure. Also, it is desirable that the risk measure is not overly sensitive to modest changes in the underlying model assumptions.

c) Easy to compute
The calculation of the risk measure should be as easy as possible. In particular, the selection of more complex risk measures should be supported by evidence that the incremental gain in accuracy outweighs the cost of the additional complexity.

d) Easy to understand
The risk measure should be easily understood by the bank’s senior management. There should be a link to other well-known risk measures that influence the risk management of a bank. If not understood by senior management, the risk measure will most likely not have much impact on daily risk management and business decisions, which would limit its appropriateness.

e) Coherent
The risk measure should be coherent and should satisfy the following conditions –
I. Monotonicity (if a portfolio YYY is always worth at least as much as XXX in all scenarios, then YYY cannot be riskier than XXX)
II. Positive Homogeneity (if all exposures in a portfolio are multiplied by the same factor, the risk measure also multiplies by that factor)
III. Translation Invariance (if a fixed, risk-free asset is added to a portfolio, the risk measure decreases to reflect the reduction in risk)
IV. Subadditivity (the risk measure of two portfolios, if combined, is always smaller or equal to the sum of the risk measures of the two individual portfolios). This property ensures that a risk measure appropriately accounts for diversification.

Challenges in Defining and Calculating Risk Measures

•While there is a general agreement on the desirable properties a risk measure should have, there  is no singularly preferred risk measure for economic capital purposes. All risk measures  observed in use have advantages and disadvantages which need to be understood within the  context of their intended application. This leads to a good deal of subjectivity in the decision  regarding the choice of risk measure.

•In practice, 𝑉𝑎𝑅 and 𝐸𝑆 are the two most widely used risk measures. However, while 𝑉𝑎𝑅 is  more easily explained and understood, it may not always satisfy the subadditivity condition and  this lack of coherence can cause problems in banks’ internal capital allocation and limit setting  for sub-portfolios.

•Expected Shortfall (𝐸𝑆), on the other hand, is coherent, making capital allocation and internal  limit setting consistent with the overall portfolio measure of risk. However, 𝐸𝑆 does not lend  itself to easy interpretation and does not afford a clear link to a bank’s desired target rating.

•A newer class of risk measures, known as spectral and distorted risk measures, allow for  different  weights  to  be  assigned  to  the  quantiles  of  a  loss  distribution,  rather  than  assuming equal weights for all observations, as is the case of 𝐸𝑆.

•Banks typically use several of the aforementioned risk measures, and sometimes different  measures for different purposes. However, 𝑉𝑎𝑅 is the most widely used risk measure. Some  banks use 𝑉𝑎𝑅 for measuring the absolute risk level, but 𝐸𝑆 is increasingly being used (at a  confidence level consistent with overall VaR) for capital allocation within the bank.

•The argument is often made that 𝑉𝑎𝑅 as an absolute risk measure or loss limit is still easier to  communicate to senior management due to its link to a bank’s target rating.

•On the other hand, 𝐸𝑆 is a more stable measure than 𝑉𝑎𝑅 with respect to allocating the overall  portfolio capital to individual facilities.

•𝐸𝑆 is a loss measure estimate given a loss range in the tail of the loss distribution, while 𝑉𝑎𝑅 is  a loss measure that is estimated given a particular point in the tail of the loss distribution.

•Further, it should be noted that while a bank may use different risk measures, the measures are typically  based on the same  estimated loss distribution.

•As visible in this table,  the choice of risk  measure requires careful  weighing of the pros and  cons of the various  available alternatives.  This can be challenging  when the complexity of  the operations increase  dramatically.

	Standard Deviation	VaR	Expected Shortfall	Spectral and Distorted Risk Measures
Intuitive	Sufficiently intuitive	Yes	Sufficiently intuitive	No (involves choice of spectrum or distortion function)
Stable	No, depends on assumptions about loss distribution	No, depends on assumptions about loss distribution	Depends on the loss distribution	Depends on the loss distribution
Easy to compute	Yes	Sufficiently easy (requires estimate of loss distribution)	Sufficiently easy (requires estimate of loss distribution)	Sufficiently easy (weighting of loss distribution by spectrum/distortion function)
Easy to understand	Yes	Yes	Sufficiently	Not immediately understandable
Coherent	Violates monotonicity	Violates subadditivity (for non-elliptical loss distributions)	Yes	Yes
Simple and meaningful risk decomposition	Simple, but not very meaningful	Not simple, might induce distorted choices	Relatively simple and meaningful	Relatively simple and meaningful

Challenges Associated With Risk Aggregation

•One of the more challenging aspects of  developing an economic capital framework relates to  risk aggregation. Practices and techniques in risk aggregation are generally less sophisticated  than the methodologies that are used in measuring individual risk components. They rely  heavily on ad-hoc solutions and judgment without always being theoretically consistent with  the measurement of the components.

•Most banks rely on the summation of individual risk components either equally-weighted (i.e.,  assuming no diversification or a fixed percentage of diversification gains across all  components) or weighted by an estimated variance-covariance matrix that represents the co-  movement between risks. Few banks attempt technically more sophisticated aggregation  methods such as copulas or even bottom-up approaches that build overall economic estimates  from the common relationship of individual risk components to underlying factors.

•Validation is a general problem with aggregation techniques. Diversification benefits embedded  in inter-risk aggregation processes (including in the estimation of entries in the variance-  covariance matrix) are often based on, internal or external, “expert judgment” or average  industry benchmarks. However, these are not (and cannot be) compared to the actual historical or expected future experience of a bank, due to lack of  relevant data. Since  individual risk components are typically estimated without much regard to the interactions  between risks (e.g., between market and credit risk), the aggregation methodologies used may  underestimate overall risk even if “no diversification” assumptions are used.

•Moreover, harmonization of the measurement horizon is a difficult issue. For example,  extending the shorter horizon applied to market risk to match the typically used annual horizon  of economic capital assessments for other types of risks (which is often performed by using a  square root of time rule on the economic capital measure). This simplification can distort the  calculation. Similar issues arise when risk measured at one confidence level is then scaled to  become (nominally) comparable with other risk components measured at a different  confidence level.

•Different aggregation methodologies have different advantages and disadvantages and thus,  there is a degree of subjective judgement on the part of the senior management and the risk  management team in deciding the right methodology that would suit their organization and  objective.

1.Simple summation

This simple approach involves adding the individual risk components. Typically, this is  perceived as a conservative approach since it ignores potential diversification benefits and  produces an upper bound to the true economic capital figure. Technically, it is equivalent to  assuming that all inter-risk correlations are equal to one and that each risk component receives  equal weight in the summation.

2.Applying a fixed diversification percentage

This approach is essentially the same as the simple summation approach with the only  difference being that it assumes the sum delivers a fixed level of diversification benefits, set at  some pre-specified level of overall risk.

3.Aggregation on the basis of a risk variance-covariance matrix

The approach allows for a richer pattern of interactions across risk types. However, these  interactions are still assumed to be linear and fixed over time. The overall diversification  benefit depends on the size of the pairwise correlations between risks.

4.Copulas

This is a much more flexible approach to combine individual risks as compared to the use of  a covariance matrix. The copula is a function that combines marginal probability distributions  into a joint probability distribution. The choice of the functional form for the copula has a  material effect on the shape of the joint distribution and can allow for rich interactions  between risks.

5.Full modelling of common risk drivers across all portfolios

This represents a theoretically pure approach. Common underlying drivers of  risk are  identified, and their interactions modelled. Simulation of the common drivers (or scenario  analysis) provides the basis for calculating the distribution of outcomes and economic capital  risk measure. Applied literally, this method would produce an overall risk measure in a single  step since it would account for all risk interdependencies and effects for the entire bank. A  less comprehensive approach would use estimated sensitivities of risk types to a large set of  underlying fundamental risk factors and construct the joint distribution of outcomes by  tracking the effect of simulating these factors across all portfolios and business units.

Comparing Different Methodologies for Risk Aggregation

 

Aggregation Methodology	Advantages	Disadvantages
Summation: Adds together individual capital components	Simplicity, typically considered to be conservative	It does not discriminate across risk types; imposes equal weighting assumption. Does not capture nonlinearities
Constant diversification: Similar to summation but subtracts fixed percentage from overall figure	Simplicity and recognition of diversification effects	The fixed diversification effect is not sensitive to underlying interactions between components. Does not capture nonlinearities
Variance-Covariance: Weighted sum of components on the basis of bilateral correlation between risks	Better approximation of analytical method. Relatively simple and intuitive	Estimates of inter-risk correlations difficult to obtain. Does not capture nonlinearities
Copulas: Combine marginal distributions through copula function	More flexible than covariance matrix. Allows for nonlinearities and higher order dependencies	Parameterization very difficult to validate. Building a joint distribution very difficult
Full modelling/Simulation: Simulate the impact of common risk drivers on all risk components and construct the joint distribution of losses	Theoretically the most appealing method. Potentially the most accurate method. Intuitive	Practically the most demanding in terms of inputs. Very high demands on IT. Time consuming. Can provide false sense of accuracy

 

Challenges Associated With Validation of Models

•Economic capital models can be complex, embodying many component parts and it may not  be immediately obvious that a complex model works satisfactorily.

•Moreover, a model may embody assumptions about relationships between variables or about  their behavior that may not hold in all circumstances (e.g., under periods of stress).

•Validation can provide a degree of confidence that the assumptions are appropriate, increasing  the confidence of users (internal and external to the bank) in the outputs of the model.

•Additionally, validation can be also useful in identifying the limitations of economic capital  models (where embedded assumptions do not fit reality). The validation of economic capital  models is at a very preliminary stage. There exists a wide range of  validation techniques, each  of which provides evidence for (or against) only some of the desirable properties of a model.

•Moreover, validation techniques are powerful in some areas such as risk sensitivity but not in  other areas such as overall absolute accuracy or accuracy in the tail of the loss distribution.  Used in combination with good controls and governance, a range of validation techniques can provide more substantial evidence for or against the performance of the model.

•There appears to be scope for the industry to improve the validation practices that shed light  on the overall calibration of models, particularly in cases where assessment of  overall capital is  an important application of the model.

Types of Qualitative Processes Used for Validation of Models

1.Use test

1. The philosophy of the use test has been fully incorporated into the Basel II Framework  and its relevance as a tool of validation is straightforward.

2. If  a  bank  is  actually  using  its  risk  measurement  systems  for  internal  purposes,  then  supervisors can place more reliance on the systems’ outputs for regulatory capital.

3. Applying  the  use  test  successfully  will  entail  gaining  a  careful  understanding  of  which  model properties are being used and which are not.

2.Qualitative review

1. Banks tend to subject their models to some form of qualitative assessment process. This  process could entail review of documentation, review of development work, dialogue with  model developers, review and derivation of  any formulae, comparison with what other  firms are known to do, and comparison with publicly available information.

2. Qualitative review is best able to answer questions regarding whether the model works in at  least theory and whether it incorporates the right risk drivers. The questions pertaining to  the validity of  the theories on which the model is based on and the assumptions that we  take as a given are important factors in determining whether a certain model should be deployed.

3.Systems implementation

1. Production-level risk measurement systems should go through extensive testing prior to  implementation, such as user acceptance testing, checking of model code, etc.

2. These processes could be viewed as part of the overall validation effort, since they would  assist in evaluating whether the model is implemented with integrity.

4.Management oversight

1. Management oversight refers to the involvement of senior management in the validation  process, in reviewing output from the model, and using the results in business decisions.

2. Senior management needs to be clear regarding how the model is to be used and how the  model outputs are interpreted, while taking into account the specific implementation  framework that their firm has adopted and the assumptions underlying the model and its  parameterization.

5.Data quality checks

1. Data quality checks was not traditionally viewed by the industry as a form of validation but  is increasingly forming a major part of regulatory thinking.

2. Data quality check refers to the processes designed to provide assurance of the  completeness, accuracy and appropriateness of  data used to develop, validate and operate  the model.

3. These processes could include –

i.Qualitative review (e.g., of data collection and storage)

ii.Data cleaning processes (such as identifying errors)

iii.Reviews of the extent of proxy data

iv.Review of any processes that need to be followed to convert raw data into suitable  model inputs (e.g., scaling processes)

v.Verification of transaction data (such as exposure levels)

4. Such a list is often a helpful indication of the level of understanding of the model.

6.Examination of assumptions – sensitivity testing

1. Models rest on assumptions of various kinds, some of  which are obvious, but some are  less so. As such, certain aspects of models are “built-in” and cannot be altered without changing the model

2. These assumptions could be –

i.Assumptions about fixed model parameters such as correlations or recovery rates

ii.Assumptions about the shape of tail distributions

iii.Assumptions about the behavior of senior management or of customers.

3. Some banks go through a deliberate process of  detailing the assumptions underpinning  their models. This should include examination of the impact on model outputs, and the  limitations that the assumptions place on model usage and applicability

Types of Quantitative Processes Used for Validation of Models

1.Validation of inputs and parameters

1. Some model parameters may be estimated. Examples include the main IRB parameters and  correlation parameters.

2. A complete model validation would involve validation of the inputs themselves. Validation of  input  parameters  to  economic  capital  models  would  entail  validation  of  parameters not included in IRB, such as correlations.

3. Techniques could include –

i.Checking model parameters against historical data

ii.Comparison of parameters against outcomes over time

iii.Comparison of model parameters to market-implied parameters such as implied  volatility or implied correlation

iv.Assessing materiality of model output to input and parameters through sensitivity  testing.

4. Testing of input parameters would be a complement to the examination of assumptions  and sensitivity testing described in the preceding paragraph. It is worth noting that  checking of model inputs is unlikely to be fully satisfactory since every model is based on  underlying assumptions.

5. The richer or more sophisticated the model, the more susceptible it may be to model  error. Checking of input parameters will not shed light on this area.

2.Model replication

1. A useful quantitative technique is to try to replicate the model results obtained by the bank.

2. A truly independent replication would use independently developed algorithms and an  alternative source of  data but in practice replication might be done by leveraging some of  the bank’s processes.

3. For example, it could be done by running the bank’s algorithms on a different data set or  using the bank’s own databases with independently derived algorithms, once the banks’  processes have been validated and are reliable.

4. This technique (and the questions that often arise in attempting to replicate results) can  help to identify whether or not the definitions and the algorithms that the bank says it is  using are correctly understood by staff in the bank who develop, maintain, operate and  validate the model and that they are used in practice by the bank.

5. The technique also facilitates code checking and may be helpful in determining whether the  databases analyzed in the validation process are those used by the bank to obtain its results.

6. This technique is rarely sufficient to validate models and in practice there is little evidence  of it being used by banks for either validation or to explore the degree of accuracy of their  models.

7. It is important to note that replication simply by re-running a set of algorithms to produce  an identical set of results would not be sufficient model validation due diligence.

3.Benchmarking and hypothetical portfolio testing

1. Benchmarking and hypothetical portfolio testing refers to the examination of whether the  model produces results comparable to a standard reference model or comparing models on  a set of reference portfolios.

2. Examples of benchmarking could include comparison of risk ranking provided by internal  rating systems and agency ratings, or comparison of an in-house portfolio credit model to  other well-known models after standardization of parameters.

3. In the regulatory field, this permits comparison of several banks’ models against the same  reference model. It would allow identification of models that produce outliers.

4. Hypothetical portfolio testing refers to the comparison of models against the  same  reference portfolio. It is capable of addressing similar questions to benchmarking by different means.

5. The technique is a powerful one and can be adapted to analyze many of  the preferred  model properties such as rank-ordering and relative risk quantification.

6. However, there are also limitations. In particular, benchmarking can only compare one  model against another and may provide little assurance that the model accurately reflects  reality or about the absolute levels of model output.

7. In a benchmarking exercise, there may be good reasons as to why models produce outliers.  They may, for example, be designed to perform well under differing circumstances, or may  be conservatively parameterized, or may differ in their economic foundations, all of which  complicate interpretation of the results.

8. Benchmarking is a commonly used form of quantitative validation. Comparisons are made  with industry survey results, against alternative models such as a rating agency model,  industry-wide models, consultancy firms, academic papers and regulatory capital models.

9. However, as a validation technique, benchmarking has limitations, providing comparison of  one model against another or one calibration to others, but not testing against “reality”. It  is therefore difficult to assess the degree of comfort provided by such benchmarking  methods, as they may only be capable of providing broad comparisons confirming that input parameters or model outputs are broadly comparable.

4.Backtesting

1. Backtesting addresses the question of how well the model forecasts the distribution of  outcomes based on past data. All backtesting approaches entail some degree of  comparison of outcomes to forecasts, and there is a wide literature on the subject.

2. For portfolio credit models, the weak power of backtesting is noted in BCBS (1999).  However, as has been suggested by some authors, there are variations to the basic  backtesting approach which can increase the power of the tests. Examples include-

i.Performing backtesting more frequently over shorter holding periods (e.g., using a  one-day market risk backtesting standard versus the 10 -day regulatory capital  standard)

ii.Using cross-sectional data by backtesting on a range of reference portfolios

iii.Using information in forecasts of the full distribution

iv.Testing expected losses only; and comparing outcomes against the expected values of  distributions as opposed to high quantiles.

3. Backtesting is useful principally for models whose outputs can be characterized by a quantifiable metric with which to compare an outcome. There may be risk measurement  systems in use whose outputs cannot be interpreted in this way. Examples could include  rating systems sensitivity tests and aggregated stress losses. Such risk measurement  approaches might nevertheless be valuable tools for banks.

4. The role of backtesting for such models, if they were to be used, would need elaboration.  In practice, backtesting is not yet a key component of banks’ validation practices for  economic capital purposes.

5.Profit and loss attribution

Analysis of  profit and loss on a regular basis (e.g., annually) and comparison between causes  of actual profit and loss and the risk drivers in the model can be instrumental in developing a  perspective regarding the performance of the company. Attribution is not widely used except  for market risk pricing models.

6.Stress testing

1. This covers both stressing of the model and comparison of model outputs to stress losses.

2. The outputs of the model might be examined under conditions of stress, where model inputs and model assumptions might be stressed.

3. This process can reveal model limitations or highlight capital constraints that might only  become apparent under stress.

4. Stress testing of regulatory capital models, particularly IRB models, is undertaken by banks  but there is more limited evidence of stress testing of economic capital models.

Challenges in Dependency Modelling in Credit Risk

•Portfolio credit risk models form a significant component of most economic capital  frameworks. A particularly important and difficult aspect of  portfolio credit risk modelling is  the modelling of the dependency structure, including both linear relationships and non-linear  relationships, between obligors.

•Dependency modelling is an important link between the Basel II risk weight function (with  supervisory imposed correlations) and portfolio credit risk models which rely on internal bank  modelling of dependencies.

•Understanding the way dependencies are modelled is important for supervisors when they  examine a bank’s internal capital adequacy assessment process (ICAAP) under Pillar 2, since  these dependency structures are not captured in regulatory capital measures.

•The underlying methodologies applied by banks in the area of dependency modelling in credit  risk portfolios have not changed much over the past ten years. Rather, improvements have  been made in the infrastructure supporting the methodologies (e.g., improved databases) and  better integration with internal risk measurement and risk management.

•The main concern in this area of economic capital continues to focus on the accuracy and  stability of correlation estimates, particularly during times of stress. The correlation estimates  provided by current models still depend heavily on explicit or implicit model assumptions.

Challenges Regarding Counterparty Credit Risk

•The measurement and management of counterparty credit risk creates unique challenges for  banks. Measurement of counterparty credit risk represents a complex exercise, as it involves  gathering data from multiple systems, measuring exposures from potentially millions of  transactions (including an increasingly significant percentage that exhibit optionality) spanning  variable time horizons ranging from overnight to thirty or more years, tracking collateral and  netting arrangements and categorizing exposures across thousands of counterparties.

•This complexity creates unique market-risk-related challenges (requiring calculations at the  counterparty level and over multiple and extended holding periods) and credit risk-related  challenges (estimation of credit risk parameters for which the institution may not have any  other exposures). In addition, wrong-way risk, operational risk-related challenges, differences in  treatment between margined and non-margined counterparties, and a range of aggregation  challenges need to be overcome before a firm can have a bank-wide view of  counterparty  credit risk for economic capital purposes.

•Banks usually employ one of two general modelling approaches to quantify counterparty credit  risk exposures – a value-at-risk (𝑉𝑎𝑅)-type model or a Monte Carlo Simulation approach. The decision of which approach to use involves a variety of trade-offs.

•The 𝑉𝑎𝑅-type model cannot produce a profile of exposures over time, which is necessary for  counterparties that are not subject to daily margining agreements, whereas the simulation  approach uses a simplified risk factor representation and may therefore be less accurate. While  these models may be supplemented with complementary measurement processes such as stress  testing, such diagnostics are frequently not fully comprehensive of all counterparty credit risk  exposures.

Challenges Regarding Interest Rate Risk in the Banking Books

•The main challenges associated with the calculation of economic capital, for interest rate risk in  the banking book, relate to the long holding period for balance sheet assets and liabilities and  the need to model indeterminate cash flows on both the asset and liability side due to  embedded optionality in many banking book items.

•If not adequately measured and managed, the asymmetrical payoff characteristics of  instruments with embedded option features can present risks that are significantly greater than  the risk measures suggest.

•The two main techniques for assessing interest rate risk in the banking book are repricing  schedules (gap and duration analyses) and simulation approaches.

•Although commonly used, the simple structure and restrictive assumptions make repricing  schedules less suitable for the calculation of economic capital. Most banks use simulation  approaches for determining their economic capital, based on losses that would occur given a  set of worst-case scenarios. The magnitude of such losses and their probability of occurrence  determine the amount of economic capital.

•The choice of the technique depends on the bank’s preference towards not only the economic  value or earnings, but also on the type of business. Some businesses, such as commercial  lending or residential mortgage lending, are managed on a present value basis, while others  such as credit cards are managed on an earnings basis.

•The use of an earnings-based measure creates aggregation challenges when other risks are  measured on the basis of economic capital. Conversely, the use of an economic value-based  approach may create inconsistencies with business practices.

Recommendations For Effective Use of Internal Risk Measures

•Economic capital models and the overall frameworks for their internal use can provide  supervisors with information that is complementary to other assessments of bank risk and  capital adequacy.

•While there is benefit from engaging with banks on the design and use of the models,  supervisors should guard against placing undue reliance on the overall level of  capital implied  by the models in assessing capital adequacy.

•The recommendations to identify issues that should be considered by supervisors in order to  make effective use of internal measures of  risk (that are not designed for regulatory purposes)  are as follows –

1.Use of economic capital models in assessing capital adequacy

A bank using an economic capital model in its dialogue with supervisors, should be able to  demonstrate how the economic capital model has been integrated into the business  decision-making process in order to assess its potential impact on the incentives affecting  the bank’s strategic decisions about the mix and direction of inherent risks. The bank’s board of directors should also be able to demonstrate conceptual awareness and  understanding of the gap between gross (stand alone) and net enterprise wide (diversified)  risk when they define and communicate measures of  the bank’s risk appetite on a net  basis.

2.Senior Management Involvement

The viability, usefulness, and ongoing refinement of a bank’s economic capital processes  depend critically on the existence of  credible commitment or “buy-in” on the part of  senior management to the process. In order for this to occur, senior management should  recognize the importance of using economic capital measures in conducting the bank’s  business and capital planning and should take measures to ensure the meaningfulness and  integrity of economic capital measures. In addition, adequate resources should be  committed to ensure the existence of a strong, credible infrastructure to support the  economic capital process.

3.Transparency and integration into decision-making

A bank should effectively document and integrate economic capital models in a transparent way into decision-making. Economic capital model results should be  transparent and taken seriously in order to be useful to senior management for making  business decisions and for risk management. A bank should take a careful approach to its  use of economic capital in internal assessments of capital adequacy. For this purpose,  greater emphasis should be placed on achieving robust estimates of  stand-alone risks on  an absolute basis, as well as developing the flexible capacity for enterprise-wide stress  testing.

4.  Risk identification

Risk measurement begins with a robust, comprehensive and rigorous risk identification  process. If relevant risk drivers, positions or exposures are not captured by the  quantification engine for economic capital, there is great room for slippage between  inherent risk and measured risk. Not all risks can be directly quantified. Material risks that  are difficult to quantify in an economic capital framework (e.g., funding liquidity risk or  reputational risk) should be captured in some form of compensating controls (sensitivity analysis, stress testing, scenario analysis or similar risk control processes).

5.Risk measures

All risk measures observed in use have advantages and disadvantages which need to be  understood  within  the  context  of  their  intended  application.  There  is  no  singularly  preferred risk measure for economic capital purposes. A bank should understand the  limitations of the risk measures it uses, and the implications associated with its choice of  risk measures.

6.Risk aggregation

A bank’s aggregation methods should address the implications stemming from the  definition and measurement of individual risk components. The accuracy of  the  aggregation process depends on the quality of the measurement of individual risk  components, as well as on the interactions between risks embedded in the measurement  process. Aggregation of individual risk components often requires the harmonization of  risk measurement parameters such as the confidence level or measurement horizon. Care  must be taken to ensure that the aggregation methodologies used (e.g., variance-covariance  matrices, use of broad market proxies, and simple industry averages of  correlations) are,  to the extent possible, representative of the bank’s business composition and risk profile.

7.Validation

Economic capital model validation should be conducted rigorously and comprehensively.  Validation of  economic capital models should be aimed at demonstrating that the model  is fit for the purpose. Evidence is likely to come from multiple techniques and tests. To  the extent that a bank uses models to determine an overall level of economic capital,  validation tools should demonstrate to a reasonable degree that the capital level generated  by the model is sufficient to absorb losses over the chosen horizon up to the desired  confidence level. The results of such validation work should be communicated to senior  management to enhance economic capital model usage. Without validation, most of risk  management effort can turn out to be fruitless.

8.Dependency modelling in credit risk

Since the dependency structures embedded in portfolio credit risk models have an  important impact on the determination of economic capital needs for credit risk, banks  should carefully assess the extent to which the dependency structures they use are  appropriate for their credit portfolio. Banks should identify and understand the main  limitations of their credit portfolio models and their implementation. They should address those limitations by using adequate supplementary risk management approaches (e.g.,  sensitivity analysis, scenario analysis, timely review of parameters).

9.Counterparty credit risk

A bank should understand the trade-offs involved in choosing between the currently used  methodologies for measuring counterparty credit risk. Complementary measurement  processes such as stress testing should also be used, though it should be recognized that  such approaches may still not fully cover all counterparty credit risk exposures. The  measurement of counterparty credit risk is complex and entails unique market and credit  risk related challenges. A range of aggregation challenges needs to be overcome before a  firm can have a bank-wide view of counterparty credit risk for economic capital purposes.

10.Interest rate risk in the banking book

Close attention should be paid to measuring and managing instruments with embedded  option features, which if not adequately performed can present risks that are significantly  greater than suggested by the risk measure. Trade-offs between using an earnings-based or  economic value-based approach to measuring interest rate risk in the banking book need to be recognized. The use of an earnings-based measure creates aggregation challenges  when other risks are measured on the basis of economic value. Conversely, the use of an  economic value-based approach may create inconsistencies with business practices.

Use of Economic Capital Framework For Business-Level Units

•The effective use of economic capital at the business-unit level depends on how relevant the  economic capital allocated to or absorbed by a business unit is with respect to the decision-  making processes that take place within it.

•Frequently, the success or failure of  an economic capital framework in a bank can be assessed  by looking at how business line managers perceive the constraints economic capital imposes  and the opportunities it offers in the following areas:

i.Credit portfolio management

ii.Risk-based pricing

iii.Customer profitability analysis, customer segmentation, and portfolio optimization

iv.Management incentives.

Economic Capital Framework For Credit Portfolio Management

•Credit portfolio management refers to activities in which banks assess the risk/return profiles  of credit portfolios and enhance their profitability through credit risk transfer transactions  and/or control of the loan approval process.

•In credit portfolio management, the creditworthiness of each borrower is assessed in a  portfolio setting. A loan with a higher stand-alone risk does not necessarily contribute more  risk to the portfolio.

•A loan’s marginal contribution to the portfolio, as a result, is critical to assessing the  concentration of the portfolio. Economic capital is a measurement of the  level of  concentration. It is one of the factors used to determine which hedging facilities to employ in  reducing concentration.

•The use of credit portfolio management for reducing economic capital often seems to be less  dominant than for “management of concentrations” and for “protection against risk  deterioration”.

Economic Capital Framework For Risk Based Pricing

•The relevance of allocated economic capital for pricing certain products (especially traditional  credit products) is widely recognized. In theory, under the assumption of competitive financial  markets, prices are exogenous to banks, which act as price-takers and assess the expected  return (ex ante) and/or performance (ex post) of deals by means of risk-adjusted performance  measures, such as the risk-adjusted return on capital (𝑅𝐴𝑅𝑂𝐶).

•In practice, however, markets are segmented. For example, the market for loans can be viewed  as composed of a wholesale segment, where banks tend to behave more as price-takers, and a  commercial banking segment, where, due to well-known market imperfections (e.g.,  information asymmetries, monitoring costs, etc.), banks have a greater ability to set prices for  their customers.

•From an operational point of  view, the difference is not so straightforward, as decisions on  deals will be based on ex ante considerations with regard to expected 𝑅𝐴𝑅𝑂𝐶 in a price-taking  environment (leading to rejection of  deals whose 𝑅𝐴𝑅𝑂𝐶  is below a given threshold) and on  the proposal of a certain price (interest rate) to the customer in a price-setting environment.

•In both cases, decisions are driven by a floor (the minimum 𝑅𝐴𝑅𝑂𝐶 or minimum interest rate)  computed according to the amount of economic capital allocated to the deal. Risk-based  pricing typically incorporates the variables of a value-based management approach.

•For example, the pricing of credit risk products will include the cost of funding (such as an  internal transfer rate on funds), the expected loss (in order to cover loan loss allowances), the  allocated economic capital, and extra-return (with respect to the cost of funding) as required by  shareholders.

•Economic capital influences the credit process through the computation of a (minimum)  interest rate considered to be adequate for increasing (or, at least, not decreasing) shareholders’  value.

•Depending on the product and the internal rules governing the credit process, decisions  regarding prices can sometimes be overridden. For example, this situation could occur because  of consideration about the overall profitability of the specific customer relationship, or its  desirability (e.g., due to reputational side-effects stemming from maintenance of the customer relationship, even when it proves to be no longer economically profitable).

•Generally, these exceptions to the rule are strictly monitored and require the decision be  elevated to a higher level of management.

Economic Capital Framework For Customer Profitability Analysis

•Regardless of  the role played by the bank as a price-taker or a price-maker, the process cannot  be considered complete until feedback has been provided to management about the final  outcome of the decisions taken.

•The measurement of performance can be extended down to the customer level, through the  analysis of customer profitability. Such an analysis aims at providing a broad and  comprehensive view of all the costs, revenues and risks (and, consequently, economic capital  absorption) generated by each single customer relationship.

•While implementation of this kind of analysis involves complex issues related to  the  aggregation of risks at the customer level, its use is evident in identifying unprofitable or  marginally profitable customers who attract resources that could be allocated more efficiently  to more profitable relationships.

•This task is generally accomplished by segmenting customers in terms of ranges of (net) return  per unit of risk. Provided that the underlying inputs have been properly measured and  allocated (not a simple task as it concerns risks and, even more, costs), this technique provides a straightforward indication of areas for intervention in assessing customer profitability.

•By providing evidence on the relative risk-adjusted profitability of  customer relationships (as  well as products), economic capital can be used in optimizing the risk-return trade-off in bank  portfolios.

Economic Capital Framework For Management Incentives

•To become deeply engrained in internal decision-making processes, the  use of  economic  capital needs to be extended in a way that directly affects the objective functions of decision  makers at the business unit level.

•This is achieved by influencing the incentive structure for  business-unit management.  Anecdotal evidence suggests that incentives are the most sensitive element for the majority of  bank managers, as well as being the issue that motivates their getting involved in the technical  aspects of the economic capital allocation process.

•However, evidence suggests that compensation schemes rank quite low among the actual uses  of economic capital measures at the business unit level.

Governance For Effective Economic Capital Framework

•The corporate governance and control framework surrounding economic capital processes is  an important indicator of the reliability of economic capital measures used by banking  institutions.

•Important parts of an effective economic capital framework include strong controls for  making changes in risk measurement techniques, thorough documentation regarding risk  measurement and allocation methodologies and assumptions, sound policies to ensure that  economic capital practices adhere to expected procedures, and the meaningful application of  economic capital measures to day-to-day business decision-making.

•Moreover, the viability of a bank’s economic capital processes depends critically on  the  existence of a credible commitment on the part of senior management to the process. In order  for this to occur, however, senior management must recognize the importance of using  economic capital measures in running the bank’s business.

Best Practices For Governance of Economic Capital Framework

1.Senior Management’s active involvement in the Economic Capital Process

1. The most widely cited reasons for adopting an economic capital framework are to improve  strategic planning, define risk appetite, improve capital adequacy, assess risk-adjusted  business unit performance and set risk limits.

2. For those institutions that have adopted or plan to adopt economic capital, the risk  management team, senior management, supervisors and the board of directors were the  most influential parties behind the decision.

3. However, not all banks choose to adopt an economic capital framework, citing difficulties  inherent in collecting and modelling data on infrequent and often unquantifiable risk at  extremely high confidence levels.

4. There are clear signs that acceptance of the role played by economic capital is increasingly  embedded in the business culture of banks, driven both by industry progress and  supervisory pressure. In addition, banks now seem to be broadly comfortable with the accuracy of the economic capital measures.

5. This has resulted in increased use of economic capital in management applications and  business decisions, as well as use in discussions with external stakeholders. The barriers to  the successful implementation of economic capital vary widely. However, according to the  Price Waterhouse Coopers Survey (2005) only 14% of respondents cite lack of  support  from senior management as a barrier to successful implementation of an economic capital  framework.

2.Business  Unit’s  involved  in  the  Economic  Capital  Process  and  High  Level  of  Knowledge  amongst Business Unit Heads

1. There is a wide range of organizational governance structures responsible for  the  economic capital framework at banking institutions. These governance structures range  from involving highly concentrated responsibilities to involving highly decentralized  responsibilities.

2. Some banking institutions house a centralized economic capital unit within corporate  treasury,  with  formal  responsibilities.  However,  components  of  the  overall  economic  capital model or some parameters are outside the direct control of the economic capital  owner.

3. Other banks share responsibility for the economic capital framework between the risk  function and the finance function, while others have a more decentralized structure, with  responsibilities spread among a wider range of units.

4. Once capital has been allocated, each business unit then manages its risk so that it does not  exceed its allocated capital. In defining units to which capital is allocated, banks sometimes  take into account their governance structure.

5. Banks that delegate broader discretion to business unit heads tend to allocate capital to the  business unit, leaving the business unit’s internal capital allocation within the business line’s  control.

6. On the other hand, management is likely to be more involved in the allocation of capital  within business units if the bank’s governance structure is more centralized. There seems  to be divergence in the approach to this process.

7. Some banks prefer rigid operation, where allocation units adhere to the original capital  allocation throughout the budgeting period.

8. On the other hand, other banks prefer a more flexible framework, allowing reallocation of  capital during the budgeting period, sometimes with thresholds that trigger reallocation  before consuming all the allocated capital.

3.Adequate frequency of Economic Capital Measurements and Disclosure

1. Economic capital calculations have a strong manual component and data quality is a  prominent concern. Hence, most banks calculate economic capital on a monthly or  quarterly basis.

2. Implementation of Basel II has fostered public disclosure of quantitative information on  economic capital measures among banks. Although disclosure of quantitative economic  capital measures is not mandatory under Pillar 3 (market discipline) of Basel II, the aim of  Pillar 3 is to encourage market discipline by accurately conveying the actual financial  condition of banks to the market.

3. In addition to quantitative economic capital measures, qualitative information on the  governance surrounding the economic capital framework of banks is becoming more  important, since external market participants take into account the sophistication of the  economic capital framework and bank management in their assessments of banks.

4.Policies,  Procedures,  and  Approvals  Relating  to  Economic  Capital  Model  Development,  Validation, On-Going Maintenance and Ownership

1. Most banks have formalized policies and procedures for economic capital governance and  analytics to ensure the consistent application of economic capital across the enterprise. For  those banks that have adopted enterprise-wide policies and procedures, it is the responsibility of the business units to ensure that those policies and procedures are being  followed.
2. Some institutions that do not have formal policies and procedures have economic capital  processes and analytics (e.g., coverage of off-balance sheet items, confidence level and  holding period) that are inconsistent across organizational units.
3. Change-control processes for economic capital models are generally less formalized than  for pricing or risk management models. They typically leverage off change-control  processes of the underlying models and parameters.
4. Changes to economic capital-specific methodologies (e.g., aggregation methodologies) are  managed by the bank’s economic capital owner and may not be the same as the change  control processes in other areas on the banking institution.
5. Diagnostics procedures are typically run after an economic capital model change. Some  banks require responsible parties to sign-off on any changes to methodology. However, formalized validation processes after changes, or internal escalation procedures in the  event of unexpectedly large differences in the economic capital numbers, are uncommon.
6. Some banks specifically name an owner of the economic capital model. Typically, the  owner provides oversight of the economic capital framework. However, few formal  responsibilities are assigned the owner other than ensuring reports from all model areas are  received in a timely manner and mechanically aggregating the individual components of the  economic capital framework into a report.

Key Concerns Regarding Governance of the Framework

•Senior management needs to ensure that there are robust controls and governance surrounding  the entire economic capital process. Key concerns regarding the use and governance of the  Economic Capital Framework are –

1.Concern regarding the standard for Absolute versus Relative Measures of Risk

The robustness and conservativeness of economic capital as an estimate of risk becomes  more important when a bank extends the use of measures designed initially as a common  metric for relative risk measurement and performance to the determination of  the  adequacy of the absolute level of capital. Critical issues generally created by this are with  respect to –

i.Comprehensive capture of the risks by the model

ii.Diversification assumptions

iii.Assumptions about management actions

i.Concern regarding comprehensive capture of risks

1. The types of risk that are included in economic capital models and the ICAAP vary  across banks in a given country as well as across countries (partly because some risk types are more pronounced in some countries).
2. Risks that the economic capital model cannot easily measure may be considered as  a separate judgmental adjustment in the ICAAP. Whether a risk type is included in  the ICAAP may depend on the risk profile of the individual bank, and whether the  individual bank regards these risks as material.
3. There can be variation between banks in the risks covered by their economic capital  models, since an identically named risk type may be defined differently across banks  and across countries. The term business risk, for example, is sometimes confused  with or lumped together with less quantifiable legal and reputational risk.

ii.Concern regarding diversification assumptions

1. In most cases, intra-risk diversification assumptions are built into the models for  individual risk types. For inter-risk diversification assumptions, current practices  vary among banks and the banking industry does not seem to have agreed on best  practices.

2. Thus, the methods remain preliminary and require further analysis. In light of the  uncertainty in estimating diversification effects, especially for inter-risk  diversification, due consideration for conservatism may be important.

iii.Concern regarding assumptions about management actions

1. In some banks, potential management actions are taken into account in economic  capital models. However, one of the main reasons that banks do not include  management actions in their economic capital models is that these actions are  difficult to model.

2. Even if management actions are not explicitly included in economic capital models  due to unreliability, banks would nevertheless prepare for them via contingency  plans in stress situations.

3. Potential management actions are grouped into two categories –

a)Those actions that increase capital supply

b)Those actions that reduce capital demand

4. Examples of the actions that increase capital supply include raising new capital,  reducing costs and cutting dividends.

5. Examples of actions that reduce capital demand include reducing new investment  or selling assets with positive risk weights.

6. In addition to explicit actions, actions may be implicitly accounted for in the  economic capital model itself. In measuring market risk, for example, some  assumptions may be made to adjust the short time horizon in the model to the  typically longer time horizon used in an economic capital framework.

7. Finally, banks do not seem to take into account constraints that could impede the  effective implementation of  management actions. Such constraints may relate to  legal issues, reputational effects, and cross-border operations. Further analysis of  the range and plausibility of these built-in assumptions about management action,  particularly in times of stress, may be warranted.

2.Concern regarding the role of stress testing

1. Currently, many banks apply stress tests, including scenario analysis and sensitivity  analysis, to individual risks, although the framework and procedures still need to be  improved.

2. The use of integrated stress tests is gradually becoming more wide-spread in the  industry, probably reflecting the need to assess the impact of stress events on overall  economic capital measures and to provide complementary estimates of capital needs in  the context of ICAAR.

3. At present, there exists wide variation among banks in the  level and extent of  integrated stress tests being utilized. In general, however, practices are still in the  development stage.

4. Stress test results do not necessarily lead to additional capital. Rather, it seems more  common that stress tests are used to confirm the validity of economic capital measures,  to provide complementary estimates of capital needs, to consider contingency planning and management actions, and gradually to formulate capital planning. In some cases,  banks use stress tests to determine the effects of stressed market conditions on  earnings rather than on economic capital measures.

3.Concern regarding the economic capital being the sole determinant of required capital

1. In general, both rating agencies and shareholders influence the level of a bank’s capital,  with the former stressing higher capital for solvency and the latter stressing on lower  capital for profitability.

2. Banks also look to peers in targeting their capital ratios. Nearly all large, internationally  active banks set their economic capital solvency standard at a level they perceive to be  required to maintain a specific external rating (e.g., AA).

3. Banks tend to look to peers in choosing external ratings and associated solvency  standards. There is not a lot of evidence that bank counterparties have an impact on  capital levels, other than indirectly through the need to deal with institutions having an  acceptably high external rating.

4. Many banks claim to target a high external rating because of  their desire to access  capital and derivatives markets. This is obviously because a high external rating would  make the company look less risky to potential investors and counterparties (in  derivative contracts)

4.Concern regarding defining available capital

1. There is no common definition of available capital across banks, either within a  country or across countries. Some of the confusion surrounding the  notion  of  available capital may arise from the fact that economic capital has its origin in assessing  relative profitability for the shareholder on a risk-adjusted basis.

2. To the extent that a bank recognizes its capital needs are not limited by the more  quantifiable risks in its economic capital model, the broader it may choose to define  available capital.

3. At the root of many banks’ definitions of available capital are tangible equity, tier 1 capital or capital definitions used by rating agencies. In order to cover losses at higher  levels of confidence, some banks consider capital instruments that may be loss-  absorbing, more innovative or uncertain forms of capital such as subordinated debt.

4. Among the various items that can be included in the definition of  available capital  (some of them included in the regulatory definition of capital) are –

i. Common  equity,  preferred  shares,  adjusted  common  equity,  perpetual  non-  cumulative preference shares

ii. Retained earning

iii. Intangible assets (e.g., goodwill)

iv. Surplus provisions, reserves, contributed surplus

v.Current net profit, planned earning, unrealized profits

vi. Mortgage servicing rights

5. This range of practices is confirmed by the IFRI and CRO Forum (2007) survey of  enterprise-wide risk management at banks and insurance companies, which found 80%  of participants adjusted their tier 1 capital in arriving at available capital resources against which economic capital was compared.

6. Banks do not limit themselves to a single capital measure. Some banks manage their  capital structure against external demands, such as regulatory capital requirements or  credit rating agency expectations. Often banks’ definition of  capital aligns with the  more tangible capital measures such as those used by rating agencies and are, therefore,  more restrictive than regulatory definitions of capital.

5.Concern regarding senior management commitment to the economic capital process

1. The viability and usefulness of a bank’s economic capital processes depend critically on  the existence of credible commitment or “buy-in” on the part of  senior management  to the process.

2. In order for this to occur, senior management must recognize the importance of using  economic capital measures in conducting the bank’s business and capital planning. In  addition, adequate resources must be committed to ensure the existence of a strong,  credible infrastructure to support the economic capital process.

6.Concern regarding transparency and meaningfulness of economic capital measures

1. Economic capital model results need to be transparent and taken seriously in order to  be useful to senior management for making business decisions and for  risk  management.

2. The level of documentation and integrity of calculations and model version control  increase with the scope and significance of economic capital models in a bank’s  decision-making process.

3. Internal transparency is a necessary condition for internal acceptance and use.