City University of Hong Kong

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• City University of Hong Kong
• Professional Seminar
• 17 March 2006
• Part II Introduction to IRB Approaches and
  Internal Rating Systems under Basel II
• Dr Michael Taylor
• Hong Kong Monetary Authority

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Outline

• Background Quantitative Concepts of IRB
• What are internal ratings systems?
• What is validation?
• HKMA Approach to Validation

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Quantitative Concepts of IRBSome Background

• Rating systems have been used by the industry for
  almost 50 years in making credit decisions and
  managing credit risk
• In the past two decades, the industry has put a
  lot of effort into enhancing the application of
  rating systems, in particular by linking the
  outputs of rating systems (i.e. rating grades or
  credit scores) to banks profits and losses and
  to the optimal use of capital
• e.g. to maximise the profit given an acceptable
  level of risk
• This involves the application of theories in
  statistics, economics and finance
• IRB reflects the essence of the evolution in the
  past 20 years in measuring credit risk

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Quantitative Concepts of IRBExpected Loss
Unexpected Loss

• Expected loss, as its name suggests, is
  expected. Under IRB, an AI should cover this by
  provisioning
• Unexpected loss is the loss from unexpected
  unfavourable situations. Under IRB, an AI should
  cover this by capital

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Quantitative Concepts of IRBExpected Loss
Unexpected Loss

• In IRB , the confidence level is set at 99.9,
  meaning that there is a 0.1 chance (once in 1000
  years) that an AIs capital would fail to absorb
  the unexpected loss and becomes insolvent

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Quantitative Concepts of IRBRisk Components

• Under IRB Approach, expected loss and the covered
  portion of unexpected loss are calculated by
  using estimates of risk components as inputs to
  risk-weight functions
• The risk components are
• Probability of default (PD)
• How likely will a borrower default in the coming
  12 months?
• Loss given default (LGD)
• How much will the AI lose, as a percentage of
  EAD, if the borrower defaults?
• Exposure at default (EAD)
• How much will the borrower owe the AI when he
  defaults?
• Effective maturity (M)
• The weighted-average timing of the AI in
  receiving cash flows from a facility

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What is a Rating System?

• A rating system is one by which
  borrowers/facilities are systematically assigned
  to (grouped into) rating grades according to the
  credit risk characteristics (rating criteria or
  risk factors) of the borrowers/facilities

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What is a Rating System?

• Homogeneity
• Borrowers/Facilities assigned to the same rating
  grade should share similar risk characteristics
• Risk differentiation
• Borrowers/Facilities assigned to different rating
  grades should have different risk characteristics
• Risk quantification
• Risk component(s) is/are estimated for each
  rating grade

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Types of Rating SystemExpert Judgement-based
System

• Ratings are assigned subjectively by experienced
  credit officers, usually following some
  guidelines - this is the most classic form of
  expert judgement-based system
• The major problem of an expert judgement-based
  system is that it is not transparent the rating
  assignment process is inside the mind of credit
  officers and may result in inconsistency amongst
  credit officers and over time for the same
  officer
• Usually expert judgement-systems are used for
  portfolios with scarce default events (e.g.
  sovereign)

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Types of Rating SystemExpert Judgement-based
System
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Types of Rating SystemModel-based System

• Rating assignment is based on objective risk
  factors (e.g. income, financial ratios), with
  these factors and their relative importance being
  determined by statistical analysis, and/or
  economic and finance theory - the pure form of
  model-based system
• The rating assignment process is mechanical and
  has little room for manipulations by judgements
• Transparent, but rigid and subject to model risk
• Model-based system can be applied to various
  types of exposures
• Generally, model-based systems are more
  applicable to exposures with abundant default
  data. But there are also some models designed for
  exposures with few default events, especially
  those based on economic and finance theory
  (usually referred to as structural models)
• Risk components can be directly estimated from
  certain types of model-based systems

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Types of Rating SystemModel-based System
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Types of Rating SystemHybrid Rating System

• Rating systems that uses both expert judgements
  and statistical modelling techniques - the most
  commonly-used rating systems in industry

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Types of Rating SystemAn Example
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Types of Rating SystemAn Example

• The range of scores would lie between 0 (i.e.
  weak management, low entry barrier, gearing gt50
  and earnings growth lt10) to 100 (i.e. strong
  management, high entry barrier, gearing lt50 and
  earnings growth gt10)
• Assume the AI maps score ranges to rating grades

• e.g. if a borrower has a strong management, the
  industry has low entry barrier, the gearing is
  80, and earnings growth is 30, then it would
  have credit score 100?32 0?25 0?34.5
  100?8.5 40.5 and the borrower would be
  assigned to rating grade E

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Quantification of a Rating System

• FIRB Approach for corporate, bank sovereign
  exposures
• an AI estimates PD for each borrower rating
• LGD, EAD and M are prescribed by the HKMA
  (supervisory estimates)
• AIRB Approach for corporate, bank sovereign
  exposures
• an AI estimates PD for each borrower rating
• it also estimates LGD for each facility rating
• it also estimates EAD for each facility type
• it also calculates M according to rules
  prescribed by the HKMA
• For retail exposures
• an AI estimates PD, LGD and EAD for each pool

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Quantification of a Rating SystemPD of
Corporate, Bank Sovereign Exposures

• For FIRB or AIRB Approach for corporate, bank
  sovereign exposures, 3 methods can be used to
  estimate the PD of a borrower rating
• 1. Internal default experience
• 2. Mapping to external data
• 3. Statistical default models

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Quantification of a Rating System PD of
Corporate, Bank Sovereign Exposures
1. Internal default experience e.g. in the past
5 years, annual default rates of borrowers
assigned to rating grade D were 10, 12, 9, 8
and 11 respectively. PD of rating grade D for
this year can be estimated as the simple average
of these default rates, i.e. (10 12 9
8 11) ? 5 10
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Quantification of a Rating System PD of
Corporate, Bank Sovereign Exposures
2. Mapping to external data e.g. By comparing
the rating criteria of its internal rating system
with those of the Moodys, an AI concludes that
50 of the borrowers assigned to its rating grade
B would have Moodys ratings Baa1, 25 A3 and
25 Ba1. In the past 5 years, average annual
default rates of these Moodys ratings were 3,
2 and 4 respectively. The AIs rating grade B
can be estimated as 50 ? 3 25 ? 2 25
? 4 3 There are many types of mapping
methodologies
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Quantification of a Rating System PD of
Corporate, Bank Sovereign Exposures
3. Statistical default models e.g. an AI uses a
model-based rating system, under which PD is
estimated for each borrower. There are 3
borrowers assigned to rating grade C, with PD
estimated to be 4.5, 5 and 5.5 respectively by
the model. PD of rating grade C can be estimated
as the simple average of the individual PDs of
these borrowers, i.e. (4.5 5 5.5) ? 3
5 5 will be used for all the 3 borrowers for
CAR purpose, regardless of the individual PDs
generated from the model
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What is Validation?

• Basel definition encompasses a range of
  processes and activities that contribute to an
  assessment of whether ratings adequately
  differentiate risk, and whether estimates of risk
  components appropriately characterise the
  relevant aspects of risk
• AIs responsibility to demonstrate its rating
  system meets minimum requirements
• Review of an AIs validation process a major part
  of the IRB recognition process

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Six Principles of the Validation Subgroup

• Six Principles of the Validation Subgroup of the
  Basel Accord Implementation Group
• (i) Validation is fundamentally about assessing
  the predictive ability of
• a banks risk estimates and the use of ratings
  in credit processes
• (ii) The bank has primary responsibility for
  validation
• (iii) Validation is an iterative process
• (iv) There is no single validation method
• (v) Validation should encompass both
  quantitative and qualitative elements
• (vi) Validation processes and outcomes should be
  subject to independent review

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HKMA Approach to Validation (1)

• Closely aligned with the 6 principles
• AI conducts its own internal validation of the
  rating system, estimates of risk components the
  risk ratings generation processes
• Internal validation clearly documented shared
  with HKMA
• Individuals involved in validation must have
  necessary skills knowledge and independence
• No universal validation tool

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HKMA Approach to Validation (2)

• No industry best practice standard on
  validation
• Quantitative techniques very diverse, portfolio
  specific, and still evolving
• Setting prescriptive quantitative standards
  benchmarks for IRB systems could stifle
  innovation
• Principles-based approaches by other supervisors
• Guidance from Basel participation in AIG V
  Subgroup
• Views of external consultants industry experts
  

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HKMA Approach to Validation (3)

• Qualitative and Quantitative elements.
• Qual. - processes, procedures controls
• Corporate governance oversight, independence,
  transparency, accountability, use of internal
  ratings, internal external audit, use of
  external vendor models
• Quant. - generally accepted techniques
• Data quality, accuracy of PDs, LGDs EADs,
  model logic conceptual soundness, estimation
  validation techniques, issues on LDPs,
  back-testing, benchmarking

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Corporate Governance Oversight

• Board senior management involvement
• Understanding of HKMA requirements
• Understanding approval of key aspects of IRB
  system
• Ensures adequate resources and clearly defines
  responsibilities
• Ensures adequate training
• Integrates IRB systems with policies, procedures,
  systems, controls
• Tracks differences between policies actual
  practice (e.g. exceptions/overrides)
• Quarterly MIS on rating system performance
  regular internal review
• Receives regular reports on internal ratings (e.g
  risk profile of the AI, performance predictive
  ability of internal rating system, changes in
  regulatory economic capital, results of
  independent validation)

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Independent Rating Approval Process

• General rule that approval of ratings
  transactions should be separate from sales
  marketing
• Independent separate functional reporting lines
  for rating assignors rating approvers (e.g.
  credit officers, with well-defined performance
  measures)
• Where ratings are assigned approved within
  sales marketing
• mitigate the inherent conflict of interest with
  compensating controls (e.g. limited credit
  limits, independent post-approval review of
  ratings, more frequent internal audit coverage)
• Where rating assignment or approval process is
  automated, verify accuracy completeness of data
  inputs

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Independent Review of IRB System Risk
Quantification

• Annual Review
• Reviews conducted internally or by external
  experts
• Functional independence
• Should encompass all aspects of the process
  generating the risk estimates usage
• Compliance with established policies procedures
• Quantification process accuracy of risk
  component estimates
• Model development, use validation
• Adequacy of data systems controls
• Adequacy of staff skills experience
• Identify weakness, make recommendations take
  corrective actions
• Significant findings reported to senior
  management the Board

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Transparency Accountability

• Transparency
• Enable third parties to understand the design,
  operations accuracy of a rating system to
  evaluate whether it is performing as intended
• An ongoing requirement update documentation when
  there are changes
• Achieved through documentation
• Expert judgement-based vs. Model-based rating
  system

• Accountability
• Identify individuals or parties responsible for
  rating accuracy rating system performance
• Inventory of models accountability chart of
  roles of parties
• Establish performance standards
• Senior individual to take responsibility for
  overall performance

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Use of Internal Ratings

• The IRS risk estimates should have substantial
  influence on decision-making actions
• Credit approval pricing,, individual
  portfolio limit setting
• Portfolio monitoring determining provisioning
• Analysis reporting of credit risk information
• Modelling management of economic capital
• Assessment of total credit risk capital
  requirements under the AIs CAAP
• Formulating business strategies assessment of
  risk appetite
• Assessment of profitability performance, and
  determining performance-related remuneration
• Other aspects (e.g. AIs infrastructure such as
  IT, skills resources and organisational
  structure)

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Data Quality

• Accuracy, completeness appropriateness

Management oversight control
IT infrastructure
Data quality assessment programme internal
audit
Data architecture
Staff competency
Storage, retrieval deletion
Data processing
Data collection
IRB data
External pooled data
Reconciliation
Use of statistical techniques
A/C data
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Quantitative Requirements

• Accuracy of PD, LGD, EAD
• Discriminatory power and calibration
• Benchmarking
• Stress testing

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Validation of a Rating SystemBack-testing

• Back-testing is the direct comparison between the
  risk component estimates with the realised
  figures, e.g. PD against default rate of a
  borrower grade (or pool for retail)
• In practice, estimates will never be exactly the
  same as realised figures. The question is
  whether the deviation is acceptable, especially
  when the estimates are smaller than the realised
  figures (i.e. underestimation)
• In general, statistical hypothesis testing can be
  applied
• Null hypothesis (H0)The estimate of the risk
  component is correct
• Alternative hypothesis (H1) The risk component
  is underestimated
• To use the hypothesis testing technique, a
  confidence level needs to be set and a
  probability distribution of the risk component
  needs to be defined.

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Validation of a Rating SystemBenchmarking

• Benchmarking is the comparison of an AIs risk
  component estimates with those of a third party
  such as estimates by rating agencies
• For PD, external benchmarks are generally most
  useful where backtesting is difficult
• For LGD and EAD, as well as PD of small-sized
  borrowers (e.g. individuals and SMEs), external
  benchmarks may not be available
• LGD and EAD depend heavily on individual AIs
  recovery and credit monitoring policies, and
  therefore it is possible for there to be big
  differences of internal estimates from the
  benchmarks, even for the same type of facilities

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Validation of a Rating SystemStability Analysis

• Even if a rating system performs well under
  certain situations or for certain types of
  borrowers/facilities, it may not do so in other
  situations or with other types of
  borrowers/facilities
• Stability analysis examines whether a rating
  system and/or the risk component estimates remain
  valid under different situations or for different
  types of borrowers/facilities. It involves
  asking questions like
• Would the back-testing results remain
  satisfactory during economic boom as well as
  recession?
• How would distribution of borrowers/facilities
  amongst rating grades and estimates of risk
  components change if certain assumptions are
  modified (e.g. discount rates in workout LGD)?
• What would be the risk component estimates if
  only a sub-sample of data are used in
  quantification?

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Validation of a Rating SystemDiscriminatory
Power

• Discriminatory power is about the rank order of
  borrowers. It assesses the ability of a rating
  system to differentiate bad borrowers (i.e.
  those going to default) from good borrowers
  (i.e. those not going to default).
• Many quantitative techniques can be used to
  assess discriminatory power
• Accuracy Ratio
• Receiver Operating Characteristic Measure
• Pietra Index
• Bayesian Error Rate
• Conditional Information Entropy Ratio
• Information Value
• Brier Score
• Divergence

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Validation of a Rating SystemDiscriminatory
Power

• Generally speaking, all these techniques are to
  measure the difference between the distribution
  of the good borrowers and that of the bad
  borrowers in relation to risk characteristics,
  e.g. credit scores, rating grades, income

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Validation of a Rating SystemDiscriminatory
Power

• For a perfect rating system, the distribution of
  bad borrowers would not overlap with that of
  good borrowers
• Discriminatory power analysis can be applied to
  borrower ratings of corporate, bank and sovereign
  exposures
• For retail exposures, discriminatory power can be
  assessed for individual rating criteria that are
  used in segmentation
• As with back-testing, it is difficult to set a
  passing mark for a rating systems
  discriminatory power

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Conclusion

• Basel IIs most important innovation is to rely
  on internal rating systems for regulatory capital
  purposes
• But regulators need some assurance that these
  systems are fit for the purpose
• Validation is key to this assurance