1 IFRS 9 (Book: Tiziano Bellini)

Resumo do livro ‘IFRS 9 and CECL Credit Risk Modelling and Validation_ A Practical Guide with Examples Worked in R and SAS’.¹

\(IFRS 9\): International Financial Reporting Standard number 9.
- Compute one-year or lifetime expected credit losses.
\(CECL\): Current Expected Credit Loss.
- Follows a lifetime perspective as a general rule.
\(IASB\): International Accounting Standard Board (IFRS9/2014)
\(FASB\): Financial Accounting Standard Board (CECL/2016)
\(EAD_{i,s,t}\): Exposure at default for account \(i\) in sub-portfolio \(s\) at time \(t\).
- The total value a bank is exposed to when a loan defaults.
- Credit exposure.
\(ECL\): Expected credit loss
\(LGD_{i,s,t}\): Loss given default for account \(i\) in sub-portfolio \(s\) at time \(t\).
\(PD_{i,s,t}\): Probability of default for account \(i\) in sub-portfolio \(s\) at time \(t\).

The key innovation introduced by new accounting standards subsumes a shift from a backward-incurred-losses perspective towards a forward-looking ECL representation.

IFRS 9. Despite the non-prescriptive nature of the accounting principle, common practice suggests relying on the so-called probability of default (PD), loss given default (LGD) and exposure at default (EAD) framework.
- ECL = PD x LGD x EAD (present value).
- Accounting perspective
- Its most important innovation refers to credit losses estimation.

1.1 Staging allocation

one-year ECL (Stage 1):
- includes financial instruments that have not had a significant increase in credit risk since initial recognition or that have low credit risk at the reporting date.
- is the expected loss that results from default events that are possible within one year after the reporting date.
- interest revenue is calculated on the gross carrying amount of the asset (that is, without deduction for credit allowance) (?)
life-time ECL (Stage 2):
- Financial instruments that experienced a significant increase in credit risk since initial recognition, but that do not have objective evidence of impairment.
- Lifetime ECL refers to all possible default events over the expected life of the financial instrument.
- Interest revenue is still calculated on the gross carrying amount of the asset. (?)
impaired credits (Stage 3):
- Assets that have objective evidence of impairment at reporting date.
- Lifetime ECL is recognised.(?)
- Interest revenue is calculated on the net carrying amount (that is, net of credit allowance).

1.2 Definition of significant increase in credit risk

The definition of significant increase in credit risk plays a key role throughout the entire IFRS 9 process.

Indeed, this is the trigger causing ECL to be computed over a one-year instead of lifetime horizon.
Reasonable and supportable information—available without undue cost or effort—including past and forward-looking information, are at the very root of the decision.
A bank compares the risk of a default occurring over the expected life of the financial instrument, at the reporting date and at the date of initial recognition.
Factors to consider in determining the occurrence of a significant increase in credit risk include, but are not limited to, the following:
- Quantitative indicators: A residual lifetime PD should be used. It implies that the same remaining period is considered for both PD at origination and reporting date. As a practical expedient, a one-year PD can be used if changes in one-year PD are a reasonable approximation to changes in the lifetime PD.
- Qualitative indicators:
  - credit spread
  - credit default swap price
  - market information related to the borrower
  - significant change in the credit rating
  - internal credit rating downgrade and
  - significant change in the value of the collateral.
  Qualitative factors should be considered separately, when they have not already been included in the quantitative assessment.
Judgement is applied in determining what threshold would be considered a significant increase in credit risk.
What is a significant change varies, based on a series of circumstances. The same absolute change in the risk of default will be more significant for an instrument with a lower initial credit risk, compared to an instrument with a higher initial risk of default.
It is evident that a key issue in measuring expected losses is to specify when a default occurs. IFRS 9 does not provide a specific definition.
There is a rebuttable presumption that a default does not occur later than 90 days past due.

1.3 ECL Ingredients

ECL must reflect an unbiased evaluation of a range of possible outcomes and their probabilities of occurrence.

Estimates also need to reflect the time value of money by means of relevant discounting.

Default definition plays a crucial role.

Probability of default (PD):
- Default events can be interpreted as realisations of a random variable. PD represents the expectation of these occurrences over a given time frame. When applied to a financial instrument,
- PD provides the likelihood that a borrower will be unable to meet debt obligations within a certain period.
Loss given default (LGD):
- LGD represents the portion of a non-recovered credit in case of default.
- One needs to consider all recoveries occurred after default without imposing time restrictions.
- In this connection, LGD may be regarded as a lifetime metric.
- Accurately investigating whether and how macroeconomic conditions affect LGDs is necessary.
Exposure at default:
- A key distinction arises between loan-type products (for example, mortgages) and uncommitted facilities (such as overdrafts=cheque especial).
- Full prepayments and overpayments (partial prepayments) require adequate modelling.

1.4 One-year PD

\(DTD\) - Distance to default

\(GLM\) - Generalised linear model

\(IV\) - Information value

\(ML\) - Machine learning

\(SC_i\) - Score for account \(i\)

\(V_t\) - Asset company value at time \(t\)

\(χ_i\) - Vector of behavioural variables (BVs) for account \(i\)

\(y_i\) - Response variable (default vs. non-default) for account \(i\)

\(WOE\) - Weight of evidence

Generalised linear models (GLMs) is the most commonly adopted in the banking industry.
Classification and regression trees (CARTs), bagging, random forest, and boosting are studied both to challenge existing models, and explore new PD modelling solutions.
Lack of deep historical data forces banks to develop ad hoc approaches for one-year PD models.
A default is considered to have occurred when:
- the banking institution considers that an obligor is unlikely to repay in full its credit obligations to the banking group, without recourse by the banking institution to actions such as realising security; or
- the obligor has breached its contractual repayment schedule and is past due for more than 90 days on any material credit obligation to the banking group
- Quantitative indicators. 90 days past due (DPD) or 3 months in arrears (MIA) are common default triggers.
- ?Qualitative indicators.
  - Bankruptcy. This event may be triggered with regards to a bank’s specific exposure, or due to exposures towards other institutions.
  - Maturity or term expiry. Default is caused by an outstanding balance due after the maturity date.
  - Others. Other indicators, such as forbearances, play a major role as a default trigger.
  - a default flag is defined as binary variable. It conventionally assumes the value 0 if no default occurs, and 1 in the case of default.
  - Instant cure. In this case, an account returns to the up-to-date status (that is, non-default) immediately after the cause of default is removed.
  - Probationary period. Contrary to the instant cure setting, when a probationary period (for example, 6 months) is adopted, one needs to wait until the end of this period before returning to the up-to-date status. It is worth noting that a probationary period mitigates potential jumps in and out of default status. Therefore it reduces the risk of the account’s multiple defaults.
Data preparation
- The scope of a one-year PD modelling is to assess the probability that a non-defaulted account (at the beginning of the period) will default within a one-year horizon. Therefore the analysis starts from non-defaulted accounts and investigates their evolution through time.
- Time horizon. A distinction arises between scorecard development??? and calibration??. From an accounting perspective???, a PIT??? estimate requires to calibrate the model over the most recent horizon (for example, the latest available year).

1.4.1 Generalised Linear Models (GLMS)

It is worth noting that PIT PDs estimated in this section do not directly feed ECL formula.
Gini index
Performance and Prediction
Evaluate your R model with MLmetrics
The Relationship between Gini Methodology and the ROC curve
The Gini coefficient is a metric that indicates the model’s discriminatory power, namely, the effectiveness of the model in differentiating between “bad” borrowers, who will default in the future, and “good” borrowers, who won’t default in the future. This metric is often used to compare the quality of different models and evaluate their prediction power.
In the context of credit score models, it measures the ordinal relationship between the models’ predictions, in terms of PD (Probability of Default) or score, and the actual outcome — default or not default. If the model is useful, low scores (high PD) should be more associated with defaults than high scores (low PD).
Lending club data
Predicting Credit Risk - Model Pipeline
Credit score classification
Tiziano Bellini datasets and code

1.4.1.1 GLM Scorecard development

Default definition and data preparation
Univariate analysis: WOE (Weight of Evidence) e IV (Information Value) para variáveis categóricas.
Multivariate analysis: Correlation
Feature selection: Stepwise regression, Boruta, etc
Expert judgement

1.4.1.2 GLM Calibration

1.4.1.3 GLM Validation

Data
- Data representativeness
- Variable appropriateness
- Data completeness: the need to cover at least two economic cycles by including a downturn.
Methodology
Statistical testing
- Discriminatory power
- Calibration
- Out-of-sample and out-of-time stability
- Cross-validation
- Reproducibility
Credit card application model algorithm: application score card

Credit Scoring — Scorecard Development Process

1.5 Lifetime PD

Definições modelo de crédito:
- Default: inadimplente acima de 90 dias?
- Entrou em default ou não durante o período de performance,
- Está em situação de default ao final do período de performance.
- Para os 2 casos acima:
  - cura instantânea e
  - período probatório: definir quantos meses ( 6 meses?)
- Analisar os resultados da análise de sobrevivência para nos apoiar nas definições (indivíduos que nunca defaultaram x indivíduos que defaultaram N vezes)

1.5.1 Data preparation

Default flag creation
- The example refers to quarterly data to align with the most common MV statistic data frequency.

1.5.2 Life time GLM framework

time-on-book (TOB) ???
time-to-maturity (TTM) ???
PD shift ???
MVs variables: short term interest rate (IR), unemployment rate (UER), house price index (HPI), gross domestic product (GDP), consumer price index (CPI), and income.

1.5.3 Life time GLM Validation

1.6 Prepayments

1.7 LGD modelling

Footnotes

Bellini, Tiziano (2019). IFRS 9 and CECL Credit Risk Modelling and Validation: A Practical Guide with Examples Worked in R and SAS. Academic Press.↩︎