Basel II's IRB approach to credit risk assumes the bank's credit portfolio is diversified (granular or perfectly fine-grained). This assumption is convenient but unrealistic.
1-1. Credit Risk
- Systematic risk: unexpected changes in financial market conditions
- Nonsystematic (idiosyncratic) risk: borrower-specific risks
1-2. Two Approaches for Calculating Capital Requirements
- Standardized Approach
- IRB Approach
1-3. Function for Calulating Credit Risk Capital Requirements
Asymptotic Single-Risk Factor (ASRF) model: IRB risk weight function
- Portfolio invariance
- Capital requirements are based soley on systematic risk -> underestimation of total risk
1-3-1. Assumptions
- Risk weights should be portfolio invariant (independent): only the systematic component of credit risk is a factor for calculation of capital requirements -> difficulites of calibrating the risk weight function for a well-diversified bank
- Expected losses are covered by revenue or provisions
- Unexpected losses will be covered by bank capital
- Unexpected losses will exceed capital at a small pre-determined acceptable probability
1-3.2 Problem
- infinitely granular portfolios do not exist in practice
- low granularity leads to higher capital requirements
**portfolio invariance:
- if we add a loan to a portfolio, the additional capital charge is based on the loan's features, not on the portfolio
- the risk of the loan is a function only of the single systematic risk factor
2. Credit Risk Concentration
2-1. Concentration risk: disproportionately large exposure to a single borrower (name concentration) or a common sector (sector concentration) or economic variable
2-2. Name Concentration
2-2-1. imperfect granularity: portfolio not properly diversified
- ASRF model assumption violation: 'portfolio is composed of numerous relatively small exposures'
- underestating the true level of risk
**granularity: the number of the exposures in the portfolio
2-2-2. Granularity adjustment model: Gordy & Lutkebohmert Model
Development of an upperbound for the granularity adjustment
Problems with adjustment:
- not work well on small portfolios
- based on a different model of credit risk (inconsistent with IRB model) -> basis risk or model mismatch
Alternative models:
- Vasicek model: systematic risk be leveraged to account for the extra idiosyncratic risk
- Emmer & Tasche model: based on Merton model
2-2-3. tradeoff between lowering the cutoff point of exposures and the implied reduction in capital (Gordy & Lutkebohmert): lowering the cutoff results in a relatively small change in the upper bound calculation
2-3. Sector Concentration
Heavy exposure to a specific geographic area or industry
Underestimation of economic capital
**The size of the underestimation is a function of the portfolio weight in a specific sector and the correlation of the sector to systematic risk. As the correlation between sector risk and systematic risk increases, the model moves closer to the single risk factor model
2-3-1. Gap between real EC and ASRF performance
The gap is substantial and dependent on model structure and correlation estimates
The sector model estimates lower EC than the IRB model.
** Duellmann & Masschelein (Multi-Factor Model)
- measured the impact of various degrees of sector concentration on EC.
Estimates of EC: diversified portfolio 7.8%, portfolio similar to regional bank 9.5%, mid-sized bank 10.7%, portfolio concentration in one asset 11.7%
- market model & sectoral model: the market model generates estimates of capital 10~90% higher than a sector model. The difference in capital estimates varies over time depending on the stability of asset correlations and an increase in PD over the period.
**Binomial Expansion Technique (BET) by Moody's
- mapping of an actual portfolio with potential complicated credit risk dependencies across individual exposures onto a hypothetical portfolio of homogeneous uncorrelated exposures
- mapping performed by calibration of two parameters: (common) PD for the exposures & diversity score
- infection model by Duellmann: extension of BET; infection probability between exposures
3. Contagion
Exposures to independent obligors that exhibit default dependencies which exceed what one should expect on the basis of their sector affiliations.
- the probability of an obligor's default conditional on another obligor defaulting is higher than the unconditional probability of default for the same obligor.
- difficult to estimate & currently not properly accounted for in credit risk portfolio model
- lack of info regarding biz interactions between banks & relationships between a bank's custmers and other firms
4. Stress Testing Sector Concetration
4-1. Desirable properties for stress tests
- plausibility
- consistency
- adaptability to the portfolio
- adaptability to internal reporting requirements
4-2. Plausibility
credibility of the stress scenario which is believable and have a certain probability of actual occurring.
e.g.) evaluating data from historical stress events
4-2. Consistency
consistency across the relevant risks within the portfolio
- use a consistent quantitative framework which captures and aggregares the relevant risks and serves as the basis for risk management actions.
e.g.) historical dependencies (correlations) of risk factors & stressing the systematic risk factors
4-3. Adaptability to the portfolio
- The test focuses on exposures which are significant in the portfolio
4-4. Adaptability to the internal reporting
- The results can be easily deciphered so that the firm can take an appropriate action RE: future composition of portfolio
5. Open Technical Issues
5-1. Adequacy of sector schemes
- same sector: similar characteristics? or colse correlation of asset returns?
5-2 Definition of a benchmark for concentration risk correlation
5-3. Data-related issues
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