Topic 1. Risk Measures Overview
Topic 2. Common Risk Measures
Topic 3. Practical Challenges
Topic 4. Risk Aggregation Overview
Topic 5. Risk Aggregation Challenges: Standardization and Measurement Issues
Topic 6. Five Common Risk Aggregation Methodologies
Topic 7. Variance-Covariance Approach
Objective: To quantify risk for a given bank.
Ideal Risk Measure Characteristics:
Intuitive and easy to understand
Stable and easy to compute
Coherent (satisfies monotonicity, subadditivity, positive homogeneity, and translation invariance)
Interpretable in economic terms
Key Challenge: No single measure perfectly captures all necessary elements.
Standard Deviation
Challenge 1: Not stable; depends on assumptions about the loss distribution.
Challenge 2: Not coherent; violates the monotonicity condition.
Challenge 3: Simple, but not very meaningful for risk decomposition.
Challenge 1: Not stable; depends on assumptions about the loss distribution.
Challenge 2: Not coherent; violates the subadditivity condition. This can cause problems with internal capital allocation and limit setting.
Expected Shortfall (ES)
Challenge 1: May or may not be stable, depending on the loss distribution.
Challenge 2: Not easy to interpret, and the link to the bank's desired target rating is unclear.
Spectral and Distorted Risk Measures
Challenge 1: Not intuitive or easily understood, and rarely used in practice.
Challenge 2: May or may not be stable, depending on the loss distribution.
VaR is commonly used for measuring absolute risk and is easier to communicate to senior management.
ES is increasingly used for capital allocation due to its stability.
Regulatory Challenge: Regulators do not have a clear preference for one measure. If a bank uses different measures for internal and external purposes, a logical connection must exist. This presents an analytical challenge for regulators to compare a bank's internal and regulatory capital amounts.
Q1. Which of the following risk measures is the least commonly used measure in the practice of risk management?
A. Value at risk.
B. Standard deviation.
C. Expected shortfall.
D. Spectral risk measures.
Explanation: D is correct.
Spectral and distorted risk measures are the least used of the four measures and are mainly of academic interest only.
Challenge: Does not differentiate between risk types, assumes equal weighting, and ignores diversification benefits and interactions between risks.
Challenge: Similar to simple summation, but subtracts a fixed diversification percentage. It still suffers from the same fundamental challenges.
Challenge: Inter-risk correlations are difficult and costly to obtain, and the method does not adequately capture nonlinearities or skewed distributions. Often relies on expert judgment due to poor data quality.
Challenge: Demanding input requirements, very difficult to validate parameterization, and building a joint distribution is complex.
Challenge: The most demanding method in terms of inputs, information technology, and time. Can provide a false sense of security.
Q2. Which of the following aggregation methodologies is characterized by great difficulty in validating parameterization and building a joint distribution?
A. Copulas.
B. Constant diversification.
C. Variance-covariance matrix.
D. Full modeling/simulation.
Explanation: A is correct.
Copulas have two notable disadvantages:
Topic 1. Validation of Models
Topic 2. Six Qualitative Validation Processes
Topic 3. Six Quantitative Validation Processes
Topic 4. Model Validation Limitations and Regulatory Concerns
Topic 5. Dependency Modeling in Credit Risk: Overview
Topic 6. Credit Risk Model Assumptions and Validity Challenges
Topic 7. Equity Price Models and Regulatory Approach Challenges
Topic 8. Evaluating Counterparty Credit Risk
Topic 9. Assessing Interest Rate Risk in the Banking Book
Challenge: Regulators need a detailed understanding of how the model's properties are being used.
Qualitative Review: Examining documentation, discussing with developers, and testing algorithms.
Challenge: Ensuring the model works in theory, considers correct risk drivers, and has accurate mathematics.
Management Oversight: Senior management must be involved in interpreting model outputs for business decisions.
Challenge: Ensuring management understands the model's use and output interpretation.
Data Quality Checks: Processes to ensure data used is complete, accurate, and relevant.
Examination of Assumptions: Reviewing assumptions (e.g., correlations, recovery rates) and performing sensitivity testing.
Challenge: Every model is based on underlying assumptions, so simply checking inputs is not fully effective, especially in complex models.
Model Replication: Attempts to replicate the model results obtained by the bank.
Challenge: Rarely sufficient for validation. Simply re-running algorithms to get the same results is not enough.
Benchmarking & Hypothetical Portfolio Testing: Involves determining whether the model produces results comparable to a standard model or comparing models on a set of reference portfolios.
Challenge: Compares models but provides little assurance the model reflects reality.
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.
Challenge: Not widely used except for market risk pricing models.
Stress Testing: Stressing the model and comparing its outputs to stress losses.
Q3. Which of the following model validation processes is specifically characterized by the limitation that it provides little comfort that the model actually reflects reality?
A. Backtesting.
B. Benchmarking.
C. Stress testing.
D. Qualitative review.
Explanation: B is correct.
With benchmarking and hypothetical portfolio testing, the process has its limitations because it can only compare one model against another and may provide little comfort that the model actually reflects “reality.” All that the process is able to do is provide broad comparisons confirming that input parameters or model outputs are broadly comparable.
Challenges in Evaluating Counterparty Credit Risk
Market Risk-Related Challenges to Counterparty EAD Estimation
Counterparty Credit Exposure Challenges: Requires simulating market risk factors and revaluating counterparty positions under risk factor shocks, similar to VaR models, but faces two key challenges when adapting VaR technology.
Netting: Unlike VaR models, which net positions across a portfolio, counterparty credit risk requires calculation at the netting set level, significantly increasing computational effort.
Holding Periods: VaR is usually for a short-term holding period, but counterparty credit exposure must be measured over much longer time horizons. 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.
Credit Risk-Related Challenges to PD and LGD Estimation
Differences in Risk Profiles Between Margined and Non-Margined Counterparties
Are not based on probabilities and, therefore, are dificult to integrate into
economic capital models based on VaR.
Are not necessarily sensitive to the current rate or economic environment.
Do not take into account changes in the slope or curvature of the yield curve.
Do not allow for an integrated analysis of interest rate and credit risks on banking book items.
Topic 1. BIS Recommendations for Supervisors
Topic 2. Economic Capital Constraints and Opportunities
Topic 3. Governance of Economic Capital - Best Practices
Topic 4. Governance of Economic Capital - Key Concerns
Constraints Imposed: (1) Credit quality of each borrower is determined in a portfolio context, not on a standalone basis; (2) A loan’s incremental risk contribution is used to determine the concentration of the loan portfolio.
Opportunities Offered: (1) The process allows one to determine appropriate hedging strategies to use in reducing portfolio concentration; (2) Credit portfolio management becomes a means for protecting against risk deterioration.
Q4. Which of the following categories of BIS recommendations specifically refers to the need to consider using additional methods, such as stress testing, to help cover all exposures?
A. Risk aggregation.
B. Counterparty credit risk.
C. Dependency modeling in credit risk.
D. Interest rate risk in the banking book.
Explanation: B is correct.
There are tradeoffs to be considered when 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.
Constraints Imposed: (1) The analysis is complicated in that many risks need to be aggregated at the customer level. (2) Customers need to be segmented in terms of ranges of (net) return per unit of risk; the underlying information is difficult to measure and allocate.
Opportunities Offered: (1) Assuming that the measurement obstacles have been overcome, the analysis can be easily used to determine unprofitable or only slightly profitable customers. Such customers could be dropped and economic capital allocated to the more profitable customers. (2) Economic capital is used in maximizing the risk-return tradeoff (through relative risk-adjusted profitability analysis of customers).
Q5. The use of which of the following items is meant more for protecting against risk deterioration?
A. Risk based pricing.
B. Management incentives.
C. Credit portfolio management.
D. Customer profitability analysis.
Explanation: C is correct.
Credit portfolio management is used as a means to protect against risk deterioration. In contrast, risk based pricing is used to maximize the bank’s profitability; customer profitability analysis is used to determine unprofitable or only slightly profitable customers; and management incentives are used to motivate managers to participate in the technical aspects of the economic capital allocation process.