Mortgage RWA & CET1: STD vs IRB

Portfolio capital comparison under Basel III: Standardized (STD) vs Foundation Internal Rating Based (IRB).

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Quick links

• 📓 Notebook 1 (Cleaning & EDA): click here
• 📓 Notebook 2 (Modelling & Capital): click here
• 📊 Dataset: Mortgage Default dataset
• 📘 Basel ref: CRE Chapter 31

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What this project answers

Banks must hold CET1 capital against credit risk. Basel III allows multiple approaches:

• STD: prescribed risk weights (eg, LTV buckets)
• IRB: model-driven risk sensitivity (requires defensible PD/LGD/EAD governance)

Question: for this mortgage dataset and PD modelling setup, which approach produces lower CET1?

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Dataset

• 5,960 rows × 11 columns
• Target: BAD (1 = default/serious delinquency, 0 = paid)
• Defaulted exposures exported separately: datasets/output/defaulted.csv

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Results

Metric	STD	IRB
EAD (sum)	$344.2M	$344.2M
RWA (sum)	$113.0M	$662.8M
CET1 (sum)	$9.0M	$53.0M
RW (avg)	0.312	1.951

Takeaway: IRB is 5.86× higher than STD for both RWA and CET1

Recommendation

Standardized approach (STD) is recommended for this dataset and modelling setup.

Why

• Capital outcome: STD requires $9.0M CET1 vs $53.0M under IRB (IRB is 5.86× higher).
• PD signal is weak: Logistic Regression variants cluster at PR AUC ≈ 0.58, so the IRB input (PD) doesn’t add enough information to reduce capital.
• Governance/audit simplicity: STD is rule-based; IRB needs stronger model governance, validation, and monitoring to be defensible.
• Data constraint: only ~5k non-defaulted rows and 7 numeric predictors were used for PD, which limits IRB’s ability to become “risk-sensitive in a capital-efficient way”.

Visuals

• Portfolio totals:
  

• Risk weight comparison:
  

• In this portfolio, IRB’s implied average RW (~1.951) is far above 1.00, while STD’s average RW (~0.312) remains well below 1.00.

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PD modelling

Metric focus: PR AUC (class imbalance).

Model	PR AUC	ROC AUC
LR_baseline	0.5801	0.7842
LR_class_weight	0.5800	0.7906
LR_class_weight_smote	0.5759	0.7908

Selected PD model: LR_baseline (best PR AUC).

• Confusion matrix:
  
• Precision–Recall curve comparison:
  

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How it works

1. Split first (no leakage): stratified train/test
2. Capital track: impute MORTDUE/VALUE, build EAD, LTV
3. Model track: transform PD predictors (fit on train only) → estimate PD
4. STD capital: LTV → RW via Basel Table 11 → RWA → CET1
   Source: Basel III CRE 20.82 Table 11
5. IRB capital: PD → K → RWA → CET1

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Caveat

IRB is risk-sensitive and can be lower than STD with more data and richer features.
Here it is much higher, likely due to dataset size (~5k non-defaulted) and limited predictors (7 numeric). IRB should be re-tested with more data/features before treating STD as “the truth”.

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Next steps

• Re-run IRB with more data and re-evaluate
• Estimate LGD empirically (instead of fixed 0.45)
• Add defaulted exposure CET1 treatment (BAD = 1)
• Build a dashboard (Power BI / Tableau / Looker Studio)