Topics 49-50 Flashcards
Properties of a coherent risk measure
The properties are as follows:
- Monotonicity: A portfolio with greater future returns will likely have less risk.
- Subadditivity: The risk of a portfolio is at most equal to the risk of the assets within the portfolio.
- Positive homogeneity: The size of a portfolio will impact the size of its risk.
- Translation invariance: The risk of a portfolio is dependent on the assets within the portfolio.
Within the economic capital implementation framework describe the challenges that appear in defining and calculating risk measures
Prior to defining specific measures, one should be aware of the general characteristics of ideal risk measures. They should be: intuitive, stable, easy to compute, easy to understand, coherent, and interpretable in economic terms. In addition, the risk decomposition process must be simple and meaningful for a given risk measure.
The following section is a summary of challenges encountered when considering the appropriateness of each risk measure.
Standard deviation
- Not stable because it depends on assumptions about the loss distribution.
- Not coherent because it violates the monotonicity condition.
- Simple, but not very meaningful in the risk decomposition process.
VaR (the most commonly used measure)
- Not stable because it depends on assumptions about the loss distribution.
- Not coherent because it violates the subadditivity condition (could cause problems in internal capital allocation and limit setting for sub-portfolios).
Expected shortfall
- May or may not be stable, depending on the loss distribution.
- Not easy to interpret, and the link to the banks desired target rating is not clear.
Spectral and distorted risk measures
- Not intuitive nor easily understood (and rarely used in practice).
- May or may not be stable, depending on the loss distribution.
Within the economic capital implementation framework describe the challenges that appear in risk aggregation
There are three items to consider: risk metric, confidence level, and time horizon.
- Risk metric: Relies on the metrics used in the quantification of different risk types. Must consider whether the metric satisfies the subadditivity condition.
- Confidence level: Loss distributions for different types of risk are assumed to have different shapes, which implies differences in confidence intervals. The lack of consistency in choosing confidence levels creates additional complexity in the aggregation process.
- Time horizon: Choosing the risk measurement time horizon is one of the most challenging tasks in risk measurement. For example, combining risk measures that have been determined using different time horizons creates problems irrespective of actual measurement methods used. Specifically, there will be inaccurate comparisons between risk types.
Five commonly used aggregation methodologies
There are five commonly used aggregation methodologies. The following is a brief description of them, as well as the challenges associated with using them.
1. Simple summation
- Adding together individual capital components.
- Does not differentiate between risk types and therefore assumes equal weighting. Also, does not take into account the underlying interactions between risk types or for differences in the way the risk types may create diversification benefits. In addition, complications arising from using different confidence levels are ignored.
2. Constant diversification
- Same process as simple summation except that it subtracts a fixed diversification percentage from the overall amount.
- Similar challenges as simple summation.
3. Variance-covariance matrix
- Summarizes the interdependencies across risk types and provides a flexible framework for recognizing diversification benefits.
- Estimates of inter-risk correlations (a bank-specific characteristic) are difficult and costly to obtain, and the matrix does not adequately capture non-linearities and skewed distributions.
4. Copulas
- Combines marginal probability distributions into a joint probability distribution through copula functions.
- More demanding input requirements and parameterization is very difficult to validate. In addition, building a joint distribution is very difficult.
5. Full modeling/simulation
- Simulate the impact of common risk drivers on all risk types and construct the joint distribution of losses.
- The most demanding method in terms of required inputs. Also, there are high information technology demands, the process is time consuming, and it may provide a false sense of security.
The variance-covariance approach is commonly used by banks. Frequently, however, bank-specific data is not available or is of poor quality. As a result, the items in the variance-covariance matrix are completed on the basis of expert judgment. On a related note, banks often use a “conservative” variance-covariance matrix where the correlations are reported to be approximate and biased upward. In order to reduce the need for expert judgment, banks may end up limiting the dimensionality of the matrix and aggregating risk categories so that there are only a few of them, not recognizing that such aggregations embed correlation assumptions. Clearly, a disadvantage of such a practice is that each category becomes less homogenous and therefore, more challenging to quantify.
One potential disadvantage of the more sophisticated methodologies is that they often lead to greater confidence in the accuracy of the output. It is important to consider robustness checks and estimates of specification and measurement error so as to prevent misleading results.
Within the economic capital implementation framework describe the challenges that appear in qualitative validation of models
The validation of economic capital models differs from the validation of an IRB (internal ratings based) model because the output of economic capital models is a distribution rather than a single predicted forecast against which actual outcomes may be compared. Also, economic capital models are quite similar to VaR models despite the longer time horizons, higher confidence levels, and greater lack of data.
There are six qualitative validation processes to consider. The following is a brief description of them, as well as the challenges associated with using them (where applicable).
1. Use test
- If a bank uses its measurement systems for internal purposes, then regulators could place more reliance on the outputs for regulatory capital.
- The challenge is for regulators to obtain a detailed understanding of which models properties are being used and which are not.
2. Qualitative review
- Must examine documentation and development work, have discussions with the models developers, test and derive algorithms, and compare with other practices and known information.
- The challenge is to ensure that the model works in theory and takes into account the correct risk drivers. Also, confirmation of the accuracy of the mathematics behind the model is necessary.
3. Systems implementation
- For example, user acceptance testing and checking of code should be done prior to implementation to ensure implementation of the model is done properly.
4. Management oversight
- It is necessary to have involvement of senior management in examining the output data from the model and knowing how to use the data to make business decisions.
- The challenge is ensuring that senior management is aware of how the model is used and how the model outputs are interpreted.
5. Data quality checks
- Processes to ensure completeness, accuracy, and relevance of data used in the model. Examples include: qualitative review, identifying errors, and verification of transaction data.
6. Examination of assumptions—sensitivity testing
- Assumptions include: correlations, recovery rates, and shape of tail distributions. The process involves reviewing the assumptions and examining the impact on model outputs.
Within the economic capital implementation framework describe the challenges that appear in quantitative validation of models
There are also six quantitative validation processes to consider. The following is a brief description of them, as well as the challenges associated with using them (where applicable).
1. Validation of inputs and parameters
- Validating input parameters for economic capital models requires validation of those parameters not included in the IRB approach, such as correlations.
- The challenge is that checking model inputs is not likely to be fully effective because every model is based on underlying assumptions. Therefore, the more complex the model, the more likely there will be model error. Simply examining input parameters will not prevent the problem.
2. Model replication
- Attempts to replicate the model results obtained by the bank.
- The challenge is that the process is rarely enough to validate models and in practice, there is little evidence of it being used by banks. Specifically, replication simply by re-running a set of algorithms to produce the same set of results is not considered enough model validation.
3. Benchmarking and hypothetical portfolio testing
- The process is commonly used and involves determining whether the model produces results comparable to a standard model or comparing models on a set of reference portfolios.
- The challenge is that the process can only compare one model against another and may provide little comfort that the model reflects “reality.” All that the process is able to do is provide broad comparisons confirming that input parameters or model outputs are broadly comparable.
4. Backtesting
- Considers how well the model forecasts the distribution of outcomes—comparison of outcomes to forecasts.
- The challenge is that the process can really only be used for models whose outputs can be characterized by a quantifiable metric with which to compare an outcome. Obviously, there will be risk measurement systems whose outputs cannot be interpreted this way. Also, backtesting is not yet a major part of banks’ validation practices for economic purposes.
5. Profit and loss attribution
- Involves regular analysis of profit and loss—comparison between causes of actual profit and loss versus the model’s risk drivers.
- The challenge is that the process is not widely used except for market risk pricing models.
6. Stress testing
- Involves stressing the model and comparing model outputs to stress losses.
Within the economic capital implementation framework describe the challenges that appear in dependency modeling in credit risk
In general, dependencies can be modeled using: credit risk portfolio models, models using copulas, and models based on the asymptotic single-risk factor (ASRF) model. With the ASRF approach, banks may use their own estimates of correlations or may use multiple systematic risk factors to address concentrations. Such an approach would result in questioning the method used to calibrate the correlations and the ways in which the bank addressed the infinite granularity and single-factor structure of the ASRF model. ASRF can be used to compute the capital requirement for credit risk under the IRB framework.
In the past, the validity of the following assumptions have been questioned:
- the ASRF Gaussian copula approach,
- the normal distribution for the variables driving default,
- the stability of correlations over time, and
- the joint assumptions of correctly specified default probabilities and doubly-stochastic processes, which suggest that default correlation is sufficiently captured by common risk factors.
In contrast, when banks use a regulatory-type approach, the assumptions of such an approach create other challenges for both banks and regulators:
- Correlation estimates need to be estimated, but there may be limited historical data on which to base the correlation estimates. Also, the assumptions used to generate the correlations may not be consistent with the underlying assumptions of the Basel II credit risk model.
- A banks use of the Basel II risk weight model requires concentration risk to be accounted for by other measures and/or management methods. It will also require regulators to evaluate such measures/methods.
A key challenge to overcome is the use of misspecified or incorrectly calibrated correlations and the use of a normal distribution (which does not replicate the details of the distribution of asset returns). This may lead to large errors in measuring portfolio credit risk and economic capital.
Within the economic capital implementation framework describe the challenges that appear in evaluating counterparty credit risk
(Market-risk-related challenges to counterparty exposure at default (EAD) estimation)
Such a task is a significant challenge because it requires: obtaining data from multiple systems, measuring exposures from an enormous number of transactions (including many that exhibit optionality) spanning a wide range of time periods, monitoring collateral and netting arrangements, and categorizing exposures across many counterparties. As a result, banks need to have well-developed processes and trained staff to deal with these challenges.
Market-risk-related challenges to counterparty exposure at default (EAD) estimation.
- Counterparty credit exposure requires simulation of market risk factors and the revaluation of counterparty positions under simulated risk factor shocks, similar to VaR models. Consider the following two challenges that occur when attempting to use VaR model technology to measure counterparty credit exposure.
- Market risk VaR models combine all positions in a portfolio into a single simulation. Therefore, gains from one position may fully offset the losses in another position in the same simulation run. However, counterparty credit risk exposure measurement does not allow netting across counterparties. As a result, it is necessary to compute amounts at the netting set level (on each set of transactions that form the basis of a legally enforceable netting agreement), which increases computational complexity.
- Market risk VaR calculations are usually performed for a single short-term holding period. However, counterparty credit exposure measurement must be performed for multiple holding periods into the future. Therefore, market risk factors need to be simulated over much longer time periods than in VaR calculations, and the revaluation of the potential exposure in the future must be done for the entire portfolio at certain points in the future.
Within the economic capital implementation framework describe the challenges that appear in evaluating counterparty credit risk
(Credit-risk-related challenges to PD and LGD estimation)
- Some material transactions are performed with counterparties with which the bank does not have any other exposures. Therefore, the bank must calculate a probability of default (PD) and loss given default (LGD) for the counterparty and transaction.
- For hedge funds, the measurement challenge occurs when there is little information provided on underlying fund volatility, leverage, or types of investment strategies employed.
- Even for counterparties with which the bank has other credit exposures, the bank still needs to calculate a specific LGD for the transaction.
Within the economic capital implementation framework describe the challenges that appear in evaluating counterparty credit risk
(Interaction between market risk and credit risk—wrong-way risk)
- Identifying and accounting for wrong-way risk (exposures that are negatively correlated with the counterparty’s credit quality) is a significant challenge because it requires an understanding of the market risk factors to which the counterparty is exposed. That would be difficult to do in the case of a hedge fund, for example, which would be less transparent.
- It also requires a comparison of those factor sensitivities to the factor sensitivities of the bank’s own exposures to the counterparty.
- The magnitude of wrong-way risk is difficult to quantify in an economic capital model since it requires a long time horizon at a high confidence level.
Within the economic capital implementation framework describe the challenges that appear in evaluating counterparty credit risk
(Operational-risk-related challenges in managing counterparty credit risk)
- The challenge is that managing such risk requires specialized computer systems and people. Complicated transactions, such as daily limit monitoring, marking-to-market, collateral management, and intraday liquidity and credit extensions, increase the risk of measurement errors.
- The quantification of operational risks is a significant challenge, especially when it pertains to new or rapidly growing businesses, new products or processes, intraday extensions of credit, and infrequently occurring but severe events.
Within the economic capital implementation framework describe the challenges that appear in evaluating counterparty credit risk
(Differences in risk profiles between margined and non-margined counterparties)
- The modeling difference between the two types of counterparties is primarily concerned with the future forecasting period. For margined counterparties, the forecasting period is short, and for non-margined counterparties, it is usually much longer.
- As a result of the difference in time periods, the aggregation of risk between these two types of counterparties is a challenge because the usual procedure is to use a single time period for all positions.
Within the economic capital implementation framework describe the challenges that appear in evaluating counterparty credit risk
(Aggregation challenges)
- In general, the challenges are increased significantly when moving from measuring credit risk of one counterparty to measuring credit risk of the firm in general for economic capital purposes.
- When counterparties have both derivatives and securities financing activities, the problem is especially challenging because the systems in place may not be able to handle such aggregation.
- Further aggregation challenges exist when high-level credit risk measures are required to be aggregated with high-level market risk and operational risk measures in order to calculate economic capital.
- Breaking down counterparty credit risk into detailed component parts (as is often done with market risk) is another challenge. The sheer computational complexities and enormous amounts of data required would generally be cost prohibitive to perform on a frequent basis. The challenge still remains for many banks due to outdated or ineffective computer systems.
Describe the BIS recommendations that supervisors should consider to make effective use of internal risk measures, such as economic capital, that are not designed for regulatory purposes
There are ten Bank for International Settlements (BIS) recommendations to consider:
- Use of economic capital models in assessing capital adequacy. The bank should show how such models are used in the corporate decision-making process so as to assess the model’s impact on which risks the bank chooses to accept. In addition, the board should have a basic understanding of the difference between gross (stand alone) and net (diversified) enterprise-wide risk in assessing the bank’s net risk tolerance.
- Senior management. The economic capital processes absolutely require a significant commitment from senior management. They should understand its importance in the corporate planning process and should ensure that there is a strong infrastructure in place to support the processes.
- Transparency and integration into decision-making. Economic capital results need to be easy to trace and understand in order to be useful. Careful attention must be given to obtaining reliable estimates on an absolute basis in addition to developing the flexibility to conduct firm-wide stress testing.
- Risk identification. This is the crucial starting point in risk measurement. The risk measurement process must be very thorough to ensure that the proper risk drivers, positions, and exposures are taken into account in measuring economic capital. That will ensure that there is little variance between inherent (actual) and measured risk. For example, risks that are difficult to quantify should be considered through sensitivity analysis, stress testing, or scenario analysis.
- Risk measures. No given risk measure is perfect, and a bank must understand the strengths and weaknesses of its chosen risk measures. No one risk measure for economic capital is universally preferred.
- Risk aggregation. The reliability of the aggregation process is determined by the quality of the measurement risk components, plus the interrelationships between such risks. The aggregation process usually requires consistency in the risk measurement parameters. The aggregation methodologies used should mirror the bank’s business composition and risk profile.
- Validation. The validation process for economic capital models must be thorough and corroborating evidence from various tests must show that the model “works” as intended. In other words, within an agreed upon confidence interval and time period, the capital level determined must be enough to absorb the (unexpected) losses.
- Dependency modeling in credit risk. Banks must consider the appropriateness of the dependency structures used within their credit portfolio. Specifically, credit models need to be assessed for their limitations, and such limitations need to be dealt with via appropriate supplementary risk management approaches, such as sensitivity or scenario analysis.
- Counterparty credit risk. There are trade-offs to be considered in deciding between the available methods of measuring counterparty credit risk. Additional methods, such as stress testing need to be used to help cover all exposures. Measuring such risk is complicated and challenging. Specifically, the aggregation process needs to be vetted prior to a bank having a big picture perspective of counterparty credit risk.
- Interest rate risk in the banking book. Specifically, financial instruments with embedded options need to be examined closely in order to control risk levels. Certainly, there are trade-offs between using earnings-based versus economic value-based models to measuring interest rate risk. For example, the former has aggregation problems because other risks are measured using economic value. Also, using economic valuebased models could be inconsistent with business practices.
Explain benefits and impacts of using an economic capital framework within area of credit portfolio management
Constraints imposed:
- Credit quality of each borrower is determined in a portfolio context, not on a standalone basis.
- A loan’s incremental risk contribution is used to determine the concentration of the loan portfolio.
Opportunities offered:
- The process allows one to determine appropriate hedging strategies to use in reducing portfolio concentration.
- Credit portfolio management becomes a means for protecting against risk deterioration.