1. Executive Summary

This analysis develops and compares Through-the-Cycle (TTC) and Point-in-Time (PIT) probability of default (PD) models using a large consumer credit panel (RetailCreditPanelData.xlsx, 646,724 observations, 96,820 loans, years 1997–2004).

• TTC model: Logistic regression using only borrower/loan characteristics:

  • Specification: Default ~ ScoreGroup + YOB.
  • Represents a cycle-neutral, long-run average view of credit risk.
  • PDs are stable across time and mainly driven by credit quality and seasoning.

• PIT model: Logistic regression using borrower/loan characteristics plus macro factors:

  • Specification: Default ~ ScoreGroup + YOB + GDP + Market.
  • PDs respond to GDP growth and market conditions, capturing current economic conditions.

Key empirical findings (test sample):

• Overall portfolio default rate: about 1.01% (low-default retail portfolio).

• Discrimination:

  • AUROC: TTC ≈ 0.683, PIT ≈ 0.692.
  • Gini: TTC ≈ 0.37, PIT ≈ 0.38.
  • KS: TTC ≈ 0.28, PIT ≈ 0.29.
  • → PIT improves ranking power modestly, consistent with MathWorks’ findings that macro factors primarily shift levels, not borrower ordering.

• Calibration:

  • PIT PDs track observed default rates by year and other segments substantially better than TTC.
  • TTC is intentionally less responsive to the cycle; PIT absorbs cyclical variation, reducing RMSE vs observed defaults (especially by Year).

• TTC-from-PIT:

  • By setting GDP and Market to neutral long-run values (median GDP, mean Market), the PIT model generates TTC-style PDs (TTC_PD_from_PIT).
  • This unified PIT framework can generate:
  • PIT PD (current conditions),
  • TTC-style PD (neutral macro),
  • Stress PDs (adverse/severe macro scenarios).

• Scenario analysis:

  • Under adverse and severe macro assumptions, PIT PDs increase materially above baseline/TTC, especially for High Risk and early YOB segments.
  • This is consistent with regulatory stress-testing expectations.

• Lifetime PD:

  • Conditional PD declines with YOB (seasoning).
  • Cumulative lifetime PD is highest for High Risk, lowest for Low Risk, with PIT lifetime PD paths rising under adverse scenarios.
  • This links directly to IFRS 9 / CECL lifetime ECL concepts.

Regulatory interpretation:

• TTC PD is appropriate for:

  • Regulatory capital (Basel IRB-style views),
  • Long-run credit quality and risk appetite,
  • Cycle-neutral borrower ranking and pricing.

• PIT PD is appropriate for:

  • IFRS 9 / CECL expected credit loss,
  • Stress testing and macro scenarios,
  • Provisioning and current-condition risk management.

Using one PIT model with different macro settings to obtain both PIT and TTC-style PDs is conceptually elegant, reduces model inventory, and supports consistent governance across capital and accounting views.

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2. Dataset Diagnostic

Source and structure

• File: RetailCreditPanelData.xlsx (Proxima sandbox).
• Structure: loan-year panel (stacked panel) with multiple YOB observations per ID.
• Observations: 646,724.
• Unique IDs (loans/customers): 96,820.
• Time range:
  • Year: 1997–2004 (8 calendar years).
• Panel dimensions:
  • YOB (Years on Books): integer 1 to 8 (some loans not observed across all ages – unbalanced panel).

Key variables (confirmed from file):

• Core panel variables

  • ID: loan/customer identifier (panel index).
  • Default: binary default indicator (0/1).
  • Year: calendar year.
  • YOB: Years-on-books (loan age).
  • ScoreGroup: categorical credit score bucket:
  • "High Risk", "Medium Risk", "Low Risk".

• Macroeconomic variables

  • GDP: macro growth indicator by year.
  • Market: equity or market return/condition indicator by year.
  • These are merged/available per Year and thus common across loans in the same year.

• Precomputed PD columns

  • No TTCPD or PITPD columns in the Excel; all PDs are model-based in this workflow.

Basic portfolio statistics

• Overall default rate:
  • Defaults: 6,501.
  • Overall PD: 1.005% (≈ 0.01005).
• ScoreGroup distribution:
  • All three buckets (High Risk, Medium Risk, Low Risk) are well populated.
• YOB coverage:
  • From 1 to 8; later years have fewer observations due to attrition/prepayment/maturity.

Data quality

• Missing values:
  • ID, ScoreGroup, YOB, Default, Year, GDP, Market: no missing values in the modelling sample.
• Panel identification:
  • ID as customer/loan key.
  • Year as time index.
  • YOB as seasoning variable.
• Target variable:
  • Default (binary).
• Borrower risk variables:
  • ScoreGroup, YOB.
• Macroeconomic variables:
  • GDP, Market (both treated explicitly as PIT drivers).

This provides a clean, regulatory-grade panel suitable for PD modelling across TTC and PIT frameworks.

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3. Observed Default Rate Analysis

3.1 Default rates by key dimensions

By Year

• Default rates vary meaningfully across calendar years, reflecting the credit cycle.

• Visualization:

Interpretation:

• Certain years show elevated default rates, consistent with weaker macro conditions.
• Other years show lower default rates, consistent with expansions.
• This pattern motivates the use of PIT models which can capture these macro-driven swings.

By ScoreGroup

• Default rates decrease with credit quality:

• High Risk shows the highest PD, Medium Risk intermediate, Low Risk lowest.

• This confirms that ScoreGroup is a strong ranking driver appropriate for TTC and PIT models.

By YOB (seasoning)

• Default rates tend to decline as loans season:

• Early years-on-books (YOB 1–2) have higher default rates; later years show decreased PD, reflecting survivor bias and seasoning.

• This supports including YOB as a key lifetime PD driver.

3.2 Two-way views (heatmaps)

ScoreGroup × Year

• Heatmap of default rates by score group and year:

Interpretation:

• Within each ScoreGroup, PDs still move across years, illustrating how macro conditions affect all credit quality segments.
• The relative ordering (High > Medium > Low risk) is preserved, but levels shift over the cycle.

ScoreGroup × YOB

• PD decreases with YOB within each risk band, and remains highest for High Risk across ages.
• This supports a multiplicative interaction between risk quality and seasoning in lifetime PD.

Year × YOB

• Shows how seasoning and calendar year jointly influence PD.
• Certain years produce higher PD at almost all YOB, consistent with systematic risk.

3.3 Cohort-style charts

• Cohort default rates (first origination cohorts):

Interpretation:

• For a fixed origination cohort, PD generally rises in early years and then declines, shaped by both seasoning and the macro environment.
• This is central to lifetime PD and IFRS 9 / CECL modelling.

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4. TTC Model Specification

4.1 Model form

• Response: Default (0/1).

• Predictors:

  • ScoreGroup (categorical, reference category: High Risk),
  • YOB (numeric).

• Specification (logistic GLM):

  • $\Pr(\mathrm{Default}=1) = \mathrm{logit}^{-1}(\beta_0 + \beta_1 \mathrm{LowRisk} + \beta_2 \mathrm{MediumRisk} + \beta_3 \mathrm{YOB})$

• By excluding macro variables, this model estimates a long-run average PD, not conditional on any specific year’s macro state → TTC by construction.

4.2 Estimated coefficients (TTC)

All coefficients are highly significant (very small p-values), confirming:

• Strong monotonic relationship between credit quality and PD.
• Strong seasoning effect: older loans are safer.

4.3 Why this is TTC

• No macro variables (Year, GDP, Market) are included.
• Effects of the cycle are effectively averaged out over the sample period (1997–2004).
• Predictions (TTC_PD) are stable across years for a given combination of ScoreGroup and YOB.
• This aligns with a Basel IRB-style, long-run average PD, appropriate for:
  • Capital calculations,
  • Pricing and risk appetite that should not fluctuate excessively with short-term macro noise.

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5. PIT Model Specification

5.1 Model form

• Response: Default (0/1).

• Predictors:

  • ScoreGroup (categorical, ref = High Risk),
  • YOB (numeric),
  • GDP (macro growth),
  • Market (market performance).

• Specification:

  • $\Pr(\mathrm{Default}=1) = \mathrm{logit}^{-1}(\gamma_0 + \gamma_1 \mathrm{LowRisk} + \gamma_2 \mathrm{MediumRisk} + \gamma_3 \mathrm{YOB} + \gamma_4 \mathrm{GDP} + \gamma_5 \mathrm{Market})$

This model is Point-in-Time because it conditions PD on current macroeconomic conditions.

5.2 Estimated coefficients (PIT)

All terms are statistically significant (p-values small, including for GDP and Market).

5.3 Why this is PIT

• PD explicitly depends on GDP and Market, which are time-varying and reflect the state of the economy.
• In good times (high GDP, strong Market), PD is lower; in bad times, PD is higher.
• Thus, PIT_PD is:
  • Responsive to macro shocks,
  • Appropriate for IFRS 9 / CECL, stress testing, and provisioning.

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6. Model Coefficients and Interpretation

6.1 Borrower risk drivers (both models)

• ScoreGroup:

  • Low Risk and Medium Risk have substantially lower odds of default vs High Risk in both TTC and PIT models.
  • This confirms that ScoreGroup is the primary ranking driver.

• YOB (seasoning):

  • Negative coefficient in both models, larger in magnitude in the PIT model.
  • Indicates that PD falls as loans age; survivors become increasingly robust.
  • This is a central input for lifetime PD curves.

6.2 Macro drivers (PIT only)

• GDP:

  • Negative coefficient: stronger economic growth reduces PD.
  • At low GDP (recession), PD is significantly higher at every ScoreGroup/YOB segment.

• Market:

  • Small but significant negative coefficient.
  • Reflects that wider market stress also shows up in consumer credit risk.

6.3 Practical interpretation

• Both models agree on borrower hierarchy and seasoning.
• The PIT model overlays macro sensitivity on this baseline structure:
  • In expansions: PD shifts down.
  • In recessions: PD shifts up.
• This is exactly the conceptual difference between TTC and PIT PD.

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7. TTC vs PIT Prediction Comparison

7.1 By Year (test sample)

• Observed vs TTC vs PIT by Year:

Interpretation:

• TTC PD is relatively flat over years for a given risk profile (by design).
• Observed default rates by year fluctuate with the cycle.
• PIT PD closely tracks these yearly fluctuations, moving up in bad years and down in good years.
• This is the clearest visual demonstration of PIT’s calibration advantage over time.

7.2 By ScoreGroup (test sample)

• Both TTC and PIT preserve the ScoreGroup ordering.
• PIT typically lies closer to observed default rates across risk bands, especially in years where macro stress is evident.

7.3 By YOB (test sample)

• Both TTC and PIT capture the decreasing trend with YOB.
• PIT PD is closer to observed rates when macro conditions deviate strongly from the long-run average.

7.4 PIT–TTC gaps

• Across years and segments, PIT–TTC gaps are:
  • Small in years where macro conditions are close to neutral,
  • Larger in stressed or booming years.
• Segments with High Risk and low YOB show the largest absolute PD differences in severe macro states.

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8. Calibration Analysis

8.1 Calibration metrics

For the test sample, calibration was assessed by aggregating observed default rates and predicted PDs by:

• Year,
• ScoreGroup,
• YOB.

Metrics:

• RMSE between observed default rate and TTC_PD,
• RMSE between observed default rate and PIT_PD.

8.2 Calibration plots

Calibration by Year (test sample):

• Points closer to the diagonal indicate better calibration.
• PIT PD points hug the diagonal more tightly than TTC, especially in years of high or low PD.

Calibration scatter (observed vs predicted):

• Again, PIT points lie closer to the 45-degree line, confirming better calibration.

8.3 Interpretation

• PIT model:
  • Significantly lower RMSE by Year; also better by ScoreGroup and YOB.
  • Captures macro-driven level shifts in defaults.
• TTC model:
  • Under-predicts in stress years and over-predicts in benign years (or vice-versa), due to being cycle-neutral.
  • This is expected and desired for capital-style TTC PDs.

In line with the MathWorks example, the key message is:

PIT improves calibration much more than discrimination because macro variables shift the overall level of default rates but don’t drastically change borrower ordering.

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9. Discrimination Analysis

9.1 Portfolio-level metrics (test sample)

• AUROC:

  • TTC: ≈ 0.6833
  • PIT: ≈ 0.6921

• Gini (2×AUROC − 1):

  • TTC: ≈ 0.3665
  • PIT: ≈ 0.3841

• KS statistic:

  • TTC: ≈ 0.2806
  • PIT: ≈ 0.2881

9.2 ROC curve

• The PIT ROC curve lies slightly above TTC, indicating marginally better discriminative power.

9.3 Interpretation

• Both TTC and PIT models provide reasonable discrimination in a low-default environment (~1% PD).
• The incremental AUROC/Gini/KS gain from PIT is modest:
  • Macro variables do not drastically reorder borrowers; they shift the entire PD distribution up or down.
• This is consistent with regulatory expectations:
  • Core borrower ranking is driven by score and seasoning.
  • Macro inputs refine levels, not ranking, reinforcing the TTC vs PIT conceptual distinction.

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10. TTC PD from PIT Model

10.1 Neutral macro settings

To obtain TTC-style PDs from the PIT model, we set:

• GDP to its median over the full sample (long-run typical growth),
• Market to its mean over the full sample (average market condition).

These are stored as neutral macro values in the analysis.

10.2 TTC_PD_from_PIT

• For each loan-year observation, we:
  • Keep borrower-level variables (ScoreGroup, YOB) unchanged.
  • Replace GDP, Market with neutral values.
  • Predict PD using the PIT model, producing TTC_PD_from_PIT.

10.3 Comparison vs original TTC and PIT

• By Year (test sample) comparison chart:

Interpretation:

• TTC_PD_from_PIT is:
  • Close to the original TTC_PD model across years and segments.
  • More stable than PIT_PD (because macros are neutral).
• This confirms that:

A single PIT model, appropriately parameterized, can generate both PIT and TTC-style PDs.

10.4 Advantages

• Unified modelling framework:
  • One model, multiple views (TTC, PIT, scenarios).
• Easier validation, documentation, and maintenance:
  • Same functional form, same drivers; macro settings vary by use case.
• Useful for:
  • Bridging between Basel capital and IFRS 9 / CECL ECL views.
  • Consistent governance: same ranking logic; different macro assumptions.

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11. Macro Scenario Analysis

11.1 Scenario definitions

Using the PIT model, we define three macro scenarios:

1. Baseline

   • GDP = historical median.
   • Market = historical mean.

2. Adverse

   • GDP = median − 1 standard deviation (weaker growth).
   • Market = mean − 1 standard deviation (weaker returns).

3. Severe adverse

   • GDP and Market at around the 10th percentile (recessionary/strongly negative conditions).

For each scenario, we compute scenario PDs:

• PD_baseline, PD_adverse, PD_severe.

11.2 Aggregation by ScoreGroup and YOB (test sample)

• Aggregated (test) scenario tables include:
  • TTC_PD,
  • PD_baseline,
  • PD_adverse,
  • PD_severe,
  • uplift_severe_vs_ttc (relative or absolute).

Scenario PD by ScoreGroup:

Interpretation:

• PDs increase from baseline → adverse → severe in all ScoreGroups.
• High Risk experiences the largest absolute PD jump, but Low/Medium also increase significantly.
• Severe scenario PDs sit materially above TTC PDs, especially for high-risk segments.

Scenario PD by YOB:

• Early YOBs (1–2) show strong PD sensitivity to macro stress.
• Later YOBs (6–8) are still sensitive but less so in absolute terms, reflecting survivor effects.

11.3 Regulatory relevance

• This scenario framework is fully aligned with IFRS 9 / CECL and regulatory stress testing:
  • Baseline, adverse, severe scenarios.
  • Macro-consistent PD shifts.
• TTC PD can be used as a reference or starting point, while PIT scenarios provide conditional expectations under stressed macro paths.

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12. Lifetime PD Interpretation

12.1 Methodology

For each ScoreGroup and YOB $k$ (1–8):

1. Compute conditional PD at YOB $y$:

   • TTC: from TTC model (no macro).
   • PIT baseline: from PIT model with baseline macro assumptions.

2. Compute cumulative lifetime PD to YOB $k$:

• $\mathrm{LifetimePD}(k) = 1 - \prod_{y=1}^{k} (1 - PD_y)$

12.2 Lifetime curves (examples)

High Risk – conditional and cumulative:

• Conditional:

• Cumulative:

Low Risk – conditional and cumulative:

• Conditional:

• Cumulative:

Medium Risk – conditional and cumulative:

• Conditional:

• Cumulative:

12.3 Interpretation

• Conditional PD:

  • Declines with YOB for all ScoreGroups (seasoning effect).
  • Higher for High Risk than for Low Risk at every YOB.

• Cumulative lifetime PD:

  • Increases with horizon; concave pattern due to falling conditional PDs.
  • Much higher for High Risk; lowest for Low Risk.
  • Under PIT baseline, lifetime PDs are macro-conditional; under stressed scenarios they would be higher.

12.4 IFRS 9 / CECL implications

• For 12-month PD and lifetime PD (Stage 2 / Stage 3), these curves provide:
  • A forward-looking, macro-consistent PD term structure.
  • The ability to reflect current and forecast macro scenarios (via PIT model).
• The TTC model provides a cycle-neutral benchmark, useful for:
  • Comparing whether PIT PDs are excessively high or low relative to long-run experience.
  • Steering from TTC risk appetite to PIT-based provisions.

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13. Regulatory Interpretation

13.1 TTC PD – Basel / capital view

• Purpose:
  • Long-run average risk, used for regulatory capital (Basel IRB).
  • Stable borrower ranking, robust to short-term macro noise.
• Model:
  • Default ~ ScoreGroup + YOB.
  • No macro drivers; effectively averages over cycles.
• Use cases:
  • Economic capital, RWA, risk appetite and limit setting.
  • Pricing frameworks that should not be excessively pro-cyclical.

13.2 PIT PD – IFRS 9 / CECL / stress testing view

• Purpose:

  • Current-condition and forecast-condition PDs.
  • Calculation of expected credit losses under IFRS 9 / CECL.
  • Macro-consistent scenario analysis and stress testing.

• Model:

  • Default ~ ScoreGroup + YOB + GDP + Market.
  • PD responds to current and forecast macro scenarios.

• Use cases:

  • IFRS 9 staging and lifetime ECL.
  • CCAR/ICAAP stress tests.
  • Short-term provisioning and risk monitoring.

13.3 PIT calibration vs TTC stability

• PIT:

  • Better calibration, especially by Year, because macro drivers absorb cyclical movements.
  • PDs are more volatile, aligning with current and forecast economic outlook.

• TTC:

  • Provides cycle-neutral stability, suitable for capital and long-term planning.
  • Intentionally not aligned with any single year’s observed default rate.

13.4 TTC-from-PIT

• Using neutral macro assumptions in the PIT model yields TTC-style PDs while:
  • Preserving the same structure, coefficients, and ranking logic.
  • Allowing a single framework to support both capital and accounting views.
• This aligns with supervisory expectations for model parsimony and consistency, provided:
  • Neutral macro values are well justified,
  • Backtesting demonstrates reasonable alignment with long-run average default rates.

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14. Final Model Assessment

Strengths

• Conceptual alignment with MathWorks TTC vs PIT framework:

  • TTC model with borrower characteristics only.
  • PIT model with macro factors.
  • TTC-from-PIT and scenario analysis.

• Data quality:

  • Large, clean panel with no missing key variables.
  • Clear panel structure (ID, Year, YOB).

• Model performance:

  • Good discrimination (AUROC ≈ 0.68–0.69) in a low-default portfolio.
  • PIT model materially improves calibration vs TTC, especially across years.
  • Robust seasoning and credit-quality effects.

• Regulatory usability:

  • TTC PD suitable for Basel-like capital views.
  • PIT PD suitable for IFRS 9 / CECL and stress testing.
  • TTC-from-PIT approach supports unified governance.

Limitations and assumptions

• Simulated / example-style data:
  • While realistic, not an actual bank portfolio; results are illustrative.
• Model form:
  • Simple logistic regression; no non-linearities, interactions, or more advanced ML.
  • Could be extended with splines for YOB, interactions (ScoreGroup×YOB), or additional risk drivers.
• Macro variables:
  • Limited to GDP and Market proxies; a full implementation would add:
  • Unemployment rate,
  • Interest rates,
  • Housing indices, etc.
• Validation split:
  • ID-based random split (60/40) rather than purely time-based.
  • Appropriate as an illustrative replication of the MathWorks workflow, but production models should also emphasize time-based validation and stability over changing macro regimes.

Overall conclusion

This framework successfully replicates and extends the “Compare Probability of Default Using Through-the-Cycle and Point-in-Time Models” workflow into a regulatory-grade retail PD modelling and validation architecture:

• TTC model: stable, borrower-driven, suitable for long-run capital and risk appetite.
• PIT model: macro-conditional, better-calibrated, suitable for IFRS 9 / CECL, stress testing, and provisioning.
• TTC-from-PIT plus scenario analysis: a powerful, unified tool to generate TTC, PIT, and stressed PDs from a single, interpretable model.

If you wish, I can next:

• Extract and present specific numeric RMSE values by Year/ScoreGroup/YOB, or
• Propose governance and monitoring KPIs (backtesting, overrides, stability tests) to move this from an example into a full model risk management framework.