Search the learning sections below.
LEARNING SECTION 01
Why does a bank need capital?
Capital is funding capable of absorbing losses. Deposits and borrowings remain contractual obligations when asset values fall; equity absorbs the initial loss.
| Assets | ₹ crore | Funding | ₹ crore |
|---|---|---|---|
| Loans | 700 | Deposits | 850 |
| Securities | 250 | Borrowings | 50 |
| Cash | 50 | Equity | 100 |
| Total | 1000 | Total | 1000 |
Before a ₹30 crore loss
₹100 crore equityAssets ₹1,000 crore; liabilities ₹900 crore.
After the loss
₹70 crore equityAssets ₹970 crore; liabilities still ₹900 crore. Tax effects ignored.
Capital is a loss-absorbing cushion, not necessarily cash held separately. Liquidity meets payments; capital absorbs losses.
LEARNING SECTION 02
What is credit risk, and where does it arise?
| Exposure | Potential credit loss |
|---|---|
| Corporate loan | Borrower defaults on principal or interest |
| Bond | Issuer fails to honour the debt |
| Guarantee | Bank pays after the customer fails |
| Undrawn commitment | Customer draws before default |
| Derivative | Counterparty defaults while owing a positive amount |
The calculation begins by identifying the exposure and its regulatory class. Loans, commitments, guarantees and derivatives do not all use the same exposure calculation.
LEARNING SECTION 03
How do exposures become risk-weighted assets?
CAR / CRAR = eligible regulatory capital ÷ total RWA × 100
Total RWA = credit RWA + market RWA + operational RWA
| Exposure ₹ crore | Assumed RW | Credit RWA | Capital at illustrative 8% |
|---|---|---|---|
| 100 | 0% | 0 | 0 |
| 100 | 20% | 20 | 1.60 |
| 100 | 100% | 100 | 8.00 |
| 100 | 150% | 150 | 12.00 |
A 150% risk weight is not a 150% probability of default. It means ₹100 exposure contributes ₹150 RWA. A 0% credit risk weight does not remove market or liquidity risk.
Calculate exposure equivalents first, RWA second, and capital requirements third. Overall CAR generally uses all three major RWA categories.
LEARNING SECTION 04
How did Basel I, II and III evolve?
The Basel Committee was established in 1974 following international banking disturbances. It sets standards; national regulators implement them. [Source 1]
Common floor
Broad credit-risk buckets and an 8% capital standard.
Risk sensitivity
SA and IRB credit approaches, operational risk and three pillars.
Resilience
Stronger capital, buffers, leverage, liquidity and later RWA reforms.
| Milestone | Development |
|---|---|
| 1988 | Basel Capital Accord; 8% target by end-1992 |
| 1996 | Market Risk Amendment; effective by end-1997 |
| 2004 / 2006 | Basel II framework and comprehensive version |
| 2010–11 | Initial Basel III capital and liquidity reforms |
| 2017 | Final post-crisis reforms: revised SA, constrained IRB and output floor |
These dates describe international standards, not a single worldwide legal implementation date. “Basel IV” is sometimes used informally for the final Basel III reforms; it is not a separate official Basel accord.
LEARNING SECTION 05
How did Basel I measure credit risk?
Basel I used broad categories with limited differentiation within each category. This historical summary assumes qualifying claims; not every sovereign, bank claim or mortgage received the lowest weight. [Source 1]
| Simplified historical asset class | Typical qualifying RW |
|---|---|
| Cash and qualifying sovereign claims | 0% |
| Qualifying bank claims | 20% |
| Qualifying residential mortgages | 50% |
| Ordinary private-sector corporate claims | 100% |
A strong corporate and a weak corporate could both attract 100%. This made the framework easy to apply but less sensitive to differences in credit quality.
LEARNING SECTION 06
Case 1: calculate a Basel I portfolio requirement
| Asset | Exposure | RW | RWA |
|---|---|---|---|
| Cash / qualifying sovereigns | 200 | 0% | 0 |
| Qualifying bank claims | 100 | 20% | 20 |
| Qualifying mortgages | 300 | 50% | 150 |
| Corporate loans | 400 | 100% | 400 |
| Total | 1000 | — | 570 |
With eligible capital of ₹50 crore: CAR = 50 / 570 = 8.77%
Accounting capital / assets = 50 / 1,000 = 5.00%
This is a credit-only historical illustration. The 8.77% risk-weighted ratio and 5% accounting ratio measure different things.
LEARNING SECTION 07
Why did Basel II introduce three pillars?
Basel II retained the 8% total minimum but strengthened risk measurement and supervision. [Source 2]
| Pillar | Purpose | Example |
|---|---|---|
| 1 · Minimum capital | Credit, market and operational risk requirements | Calculate credit RWA |
| 2 · Supervisory review | Internal assessment and risks beyond Pillar 1 | Stress losses and concentration |
| 3 · Market discipline | Risk and capital disclosures | Publish RWA and capital composition |
A bank can satisfy a mechanical Pillar 1 ratio while remaining exposed to concentrated borrowers or severe stress. Pillar 2 links capital assessment to the institution’s broader risk profile.
LEARNING SECTION 08
What are SA, F-IRB and A-IRB?
| Parameter / feature | Standardised | Foundation IRB | Advanced IRB |
|---|---|---|---|
| Credit assessment | Regulatory categories and eligible external ratings | Bank-estimated PD | More bank-estimated parameters |
| PD | Not directly inserted into a corporate IRB formula | Bank estimates | Bank estimates |
| LGD | Reflected through prescribed treatments | Supervisory treatment | Internal estimates where permitted |
| EAD / CCF | Prescribed rules | Generally supervisory treatment | Internal estimates where permitted |
| Maturity | Exposure-specific rules | Prescribed or measured as required | Measured under relevant rules |
| Approval / controls | Eligibility and due diligence | Supervisory approval and validation | Supervisory approval and validation |
This comparison refers mainly to eligible corporate-type exposures. Retail IRB has a different structure. Internal credit ratings used for lending decisions do not by themselves establish regulatory IRB adoption.
IRB does not allow banks to choose capital freely. Models, parameters, data and validation face regulatory constraints.
LEARNING SECTION 09
How do historical and revised corporate risk weights differ?
| Corporate rating | Historical Basel II SA | Revised Basel III SA |
|---|---|---|
| AAA to AA− | 20% | 20% |
| A+ to A− | 50% | 50% |
| BBB+ to BBB− | 100% | 75% |
| BB+ to BB− | 100% | 100% |
| Below BB− | 150% | 150% |
| Unrated ordinary corporate | Generally 100% | Generally 100%; exceptions apply |
These are Basel corporate tables for jurisdictions using external ratings. They are not RBI domestic rating mappings. Exposure class, due diligence and national rules determine the applicable treatment. [Source 3]
₹100 crore BBB corporate exposure
Historical table: RWA ₹100 crore and capital ₹8 crore at 8%. Revised table: RWA ₹75 crore and capital ₹6 crore at the same 8%. This isolates the risk-weight change; it does not compare every feature of the two regimes.
LEARNING SECTION 10
Step 1 · What are PD, LGD and EAD?
| Input | Meaning | Illustration |
|---|---|---|
| PD | One-year probability of default | 1% |
| LGD | Economic loss proportion conditional on default | 40% |
| EAD | Exposure when default occurs | ₹100 crore |
| M | Effective maturity used later | 2.5 years |
EAD can exceed current utilisation if facilities are drawn before default. LGD reflects recovery amounts, timing and costs under the relevant methodology. These case amounts are hypothetical.
This example uses the revised Foundation IRB supervisory LGD of 40% for a senior unsecured claim on a non-financial corporate. Under Foundation IRB, senior unsecured claims on sovereigns, banks and other specified financial institutions use 45%; approved A-IRB LGDs follow separate estimation and floor requirements. BCBS CRE32.6.
LEARNING SECTION 11
Step 2 · What is expected credit loss?
₹100 crore × 40% × 1% = ₹0.4000 crore
This is the model’s average default loss, not its tail loss or capital requirement. Pricing and provisioning address expected credit costs. Accounting ECL and regulatory IRB expected loss are not interchangeable.
India: accounting ECL and bank provisioning
Ind AS 109 provides an expected-credit-loss impairment framework for entities within its accounting scope. Depending on credit deterioration, measurement uses 12-month or lifetime ECL; it is not simply the one-year Basel regulatory EL calculation.
RBI issued its Commercial Banks—Asset Classification, Provisioning and Income Recognition Directions on 27 April 2026, effective 1 April 2027 for covered banks. The ECL provisioning transition should not be described as blanket adoption of all Ind AS requirements. Until commencement, the applicable existing prudential rules continue.
LEARNING SECTION 12
Step 3 · Why do default dependence and asset correlation matter?
Borrowers share economic influences such as interest rates, demand, industry conditions and asset prices. A weak systematic environment can produce defaults together.
Default occurs when Xᵢ < N⁻¹(PD).
Y = common standard-normal factor; εᵢ = independent borrower-specific factor.
ρ is asset correlation, not the pairwise correlation between observed default indicators. In a large, granular portfolio, idiosyncratic variation diversifies while systematic risk remains.
With fixed PD and LGD, expected loss remains unchanged in this illustration. Greater positive asset correlation raises the illustrated severe tail loss.
LEARNING SECTION 13
Step 4 · How does the Vasicek model calculate WCDR?
N = standard normal cumulative probability; N⁻¹ = its inverse.
Confidence α = 99.9%; PD = 1%; ρ = 0.1927836792.
WCDR ≈ 14.0273%
Worst-Case Default Rate means the default-rate percentile at the chosen confidence level, not the maximum conceivable default rate. Under the homogeneous asymptotic one-factor assumptions, this corresponds to the conditional default rate in a severe systematic state.
The case uses the Basel corporate correlation function. At PD = 1%, A = (1 − exp(−50 × PD))/(1 − exp(−50)); ρ = 0.12A + 0.24(1 − A) = 19.2784%. Recalculate this correlation whenever PD changes.
| Asset correlation | WCDR at 99.9% | Loss quantile on ₹100 crore, LGD 40% |
|---|---|---|
| 0% | 1.0000% | ₹0.4000 crore |
| 10% | 7.7497% | ₹3.0999 crore |
| 19.2784% | 14.0273% | ₹5.6109 crore |
| 30% | 22.4379% | ₹8.9752 crore |
These sensitivity results assume a homogeneous, infinitely granular portfolio with deterministic LGD. They are not an assertion about every portfolio or confidence level.
LEARNING SECTION 14
Step 5 · How does WCDR become credit-loss VaR?
100 × 40% × 14.02726785% = ₹5.6109 crore
Here Credit VaR means the total loss quantile at a stated confidence and one-year horizon. WCDR is a rate; VaR is money. A 99.9% quantile is not an absolute loss ceiling: outcomes in the remaining tail may be worse.
Some textbooks use “Credit VaR” for the loss quantile minus expected loss. This article labels that amount separately to avoid ambiguity. More general credit-portfolio models can also capture migration and spread losses; the present Vasicek example captures default losses.
LEARNING SECTION 15
Step 6 · What is unexpected-loss capital?
5.61090714 − 0.40000000 = ₹5.2109 crore
Equivalent: EAD × LGD × (WCDRα − PD)
Expected loss
₹0.4000 croreAverage modelled default loss.
Tail loss above EL
₹5.2109 croreAt 99.9%, before the corporate maturity adjustment.
Here “UL capital” denotes a quantile-minus-mean measure. It is not the standard deviation of losses, another quantity sometimes called unexpected loss.
LEARNING SECTION 16
Step 7 · How does the Basel IRB maturity adjustment enter?
MA = [1 + (M − 2.5)b] / [1 − 1.5b]
At M = 2.5: MA ≈ 1.25980950
K = LGD × (WCDR99.9% − PD) × MA
K ≈ 6.564750%; K × EAD ≈ ₹6.5648 crore
At 2.5 years the numerator of MA is 1, but its denominator is below 1; the adjustment therefore is not 1. The final amount differs from unadjusted UL capital because the regulatory corporate function includes maturity sensitivity.
This revised non-defaulted corporate illustration applies the 40% Foundation IRB unsecured LGD and checks the corporate PD floor. It excludes SME and financial-institution correlation adjustments, expected-loss/provision adjustments and portfolio-level constraints. The historical Basel II 1.06 scaling factor is not applied. Other asset classes use different functions. BCBS CRE31.
PD floor: the revised corporate IRB input floor is 0.05% (5 basis points). Use the greater of the estimated PD and the applicable floor; the case’s 1% PD is above it. This floor does not change the displayed result. BCBS CRE32.3.
LEARNING SECTION 17
Step 8 · How is IRB capital converted into credit RWA?
12.5 × 0.0656475032 × 100 = ₹82.0594 crore
At the Basel 8% minimum: 82.0594 × 8% = ₹6.5648 crore
| Measure | Amount | Meaning |
|---|---|---|
| Expected loss | ₹0.4000 crore | Average default loss |
| WCDR | 14.0273% | Tail default rate |
| Credit-loss VaR | ₹5.6109 crore | Total loss quantile |
| VaR minus EL | ₹5.2109 crore | UL capital before maturity adjustment |
| Illustrative IRB amount | ₹6.5648 crore | After corporate maturity adjustment |
| Credit RWA | ₹82.0594 crore | Risk-weighted exposure equivalent |
12.5 is the reciprocal of 8%. Do not replace it with 1/9% simply because an applicable national total-capital minimum is 9%. Subsequent capital ratios and buffers are applied to the relevant total RWA under the domestic framework. This global IRB illustration is not a claim of RBI IRB approval.
LEARNING SECTION 18
How do commitments and guarantees enter RWA?
RWA = exposure equivalent × risk weight
| Step | Calculation | Result |
|---|---|---|
| Undrawn commitment | Nominal amount | ₹200 crore |
| Exposure equivalent | 200 × assumed 40% CCF | ₹80 crore |
| Credit RWA | 80 × 100% RW | ₹80 crore |
| Capital at illustrative 8% | 80 × 8% | ₹6.40 crore |
The CCF and risk weight are separate adjustments. Use the instrument’s actual classification and effective rules rather than applying this case factor to every commitment.
LEARNING SECTION 19
How do collateral and guarantees change capital?
Case 2A · Eligible financial collateral
E = 100; C = 80; Hₑ = 0%; H꜀ = 10%; Hfx = 0%
E* = 100 − 80 × 90% = ₹28 crore
At 100% residual RW and 8% capital: ₹2.24 crore
Case 2B · Eligible guarantee substitution
A ₹100 crore exposure is 60% covered by an eligible guarantor carrying a 20% risk weight; the borrower attracts 100%.
Capital at 8% = 52 × 8% = ₹4.16 crore
Legal enforceability, collateral eligibility, currency and maturity mismatches matter. Neither example implies that all secured loans or all guarantees qualify for relief.
LEARNING SECTION 20
What did Basel III change in capital quality?
Basel III strengthened the numerator through better-quality capital, deductions and buffers. The later reforms also changed RWA measurement. It is therefore more than a higher headline ratio. [Source 5]
Total capital = CET1 + AT1 + Tier 2
CET1, Tier 1 and total capital requirements are nested. They are not three separate percentages to add.
LEARNING SECTION 21
What are Basel and RBI capital requirements?
| Requirement | Basel baseline | RBI covered commercial banks |
|---|---|---|
| CET1 minimum | 4.5% | 5.5% |
| Tier 1 minimum | 6.0% | 7.0% |
| Total capital minimum | 8.0% | 9.0% |
| CET1 conservation buffer | 2.5% | 2.5% |
| CET1 + full CCB | 7.0% | 8.0% |
| Tier 1 + full CCB | 8.5% | 9.5% |
| Total capital + full CCB | 10.5% | 11.5% |
All percentages are of total RWA. The CCB is CET1. Systemic-bank, countercyclical and supervisory requirements may add to these baselines. A buffer shortfall differs from a breach of a hard minimum. [Source 6] [Source 7]
11.5% is a baseline combined RBI total requirement for covered banks, not a universal final requirement for every Indian bank. CET1 used to fill a lower-tier capital shortfall is not available again for the buffer.
LEARNING SECTION 22
Case 3: test all three capital ratios
| Risk component | RWA |
|---|---|
| Credit | 800 |
| Market | 100 |
| Operational | 100 |
| Total | 1000 |
| Capital component | Amount |
|---|---|
| CET1 | 80 |
| AT1 | 15 |
| Tier 2 | 20 |
| Total | 115 |
Tier 1 ratio = 95 / 1,000 = 9.50%
Total CAR = 115 / 1,000 = 11.50%
This hypothetical covered Indian bank exactly meets the baseline including the full CCB, before additional requirements. It has no headroom above those combined thresholds.
A strong total ratio can conceal weak CET1
With CET1 50, AT1 30 and Tier 2 50 against RWA 1,000, total CAR is 13%. But CET1 is only 5%, below the 5.5% RBI baseline minimum. More AT1 or Tier 2 cannot fill the CET1 minimum.
LEARNING SECTION 23
What is the output floor?
At full Basel calibration, the floor rate is 72.5%. Suppose nominated-approach RWA is 600 and the standardised floor base is 1,000.
Final RWA = max(600, 725) = 725
Capital at 8% = 58, versus 48 without the floor
The floor works on the aggregate base specified by the framework, not as a 72.5% risk weight for each loan. Basel’s transition schedule and domestic adoption must be checked separately; the fully phased rate is not a claim about every jurisdiction’s current rule. [Source 8]
The final reforms retain IRB but restrict A-IRB for specified exposures and constrain parameters. More model freedom does not automatically mean more reliable capital measurement.
LEARNING SECTION 24
How do deterioration and new lending affect ratios?
Credit deterioration
CET1 falls from 100 to 85 while RWA rises from 1,000 to 1,100.
10.00% → 7.73%Growth without new capital
Case 3 adds a ₹100 crore loan at 100% RW.
Total CAR: 11.50% → 10.45%After growth, RWA is ₹1,100 crore. The combined baseline targets are CET1 ₹88 crore, Tier 1 ₹104.50 crore and total capital ₹126.50 crore. One mix meeting all three is:
| Capital component | Before | Additional | After |
|---|---|---|---|
| CET1 | 80 | 8.00 | 88.00 |
| AT1 | 15 | 1.50 | 16.50 |
| Tier 2 | 20 | 2.00 | 22.00 |
| Total | 115 | 11.50 | 126.50 |
The resulting ratios are 8.00% CET1, 9.50% Tier 1 and 11.50% total capital. Higher-quality capital may substitute: the ₹1.50 crore AT1 increment can be CET1 instead. With CET1 alone, ₹11.50 crore additional capital meets all displayed targets. Adding only ₹8 crore CET1 leaves Tier 1 at ₹103 crore, or 9.36%, below 9.50%. This is an eligible capital mix illustration, not a claim about which instruments are cheapest to issue.
Provisioning can reduce capital while downgrades or higher PD increase RWA. Actual defaulted-exposure treatment also depends on provisions, collateral and the chosen approach; RWA need not rise after every default.
LEARNING SECTION 25
How does capital affect loan pricing?
| Annual item on ₹100 crore exposure | ₹ crore |
|---|---|
| Interest income at 10% | 10 |
| Funding cost at 6% | −6 |
| Operating cost | −1 |
| Basic expected loss | −0.45 |
| Income before tax / capital return assessment | 2.55 |
Simplified return on allocated capital = 2.55 / 12 = 21.25%
This is not a complete RAROC model. Tax, liquidity costs, fees, economic-capital methods and diversification affect real pricing decisions.
LEARNING SECTION 26
Which credit-risk approach applies in India?
Start with RBI’s Standardised Approach when teaching ordinary Indian commercial-bank regulatory credit RWA. Internal ratings used for sanctioning and pricing are not proof of regulatory IRB adoption.
Issued in 2026; effective 1 April 2027
RBI’s revised Commercial Banks Capital Charge for Credit Risk—Standardised Approach Directions were issued on 27 April 2026 and take effect on 1 April 2027. The directions define their bank and banking-book scope. Keep the rules currently effective before that date separate from the forthcoming framework. [Source 9]
Do not import the Basel international ratings table directly into an RBI calculation. Domestic ratings, exposure categories, special treatments and effective dates must be checked.
LEARNING SECTION 27
Interactive laboratories: capital and credit conversion
Use the presets to reproduce the cases. Monetary amounts are ₹ crore. These laboratories isolate arithmetic and do not replace complete regulatory calculations.
Lab 1 · Capital composition and RWA
Lab 2 · Exposure → CCF → RWA → capital
CCF applies only to the undrawn / nominal component. No collateral or netting adjustment is included. The 8% default isolates the Basel minimum total-capital arithmetic, excluding buffers.
LEARNING SECTION 28
How can these calculations be reproduced in Excel?
| Input cell | Meaning |
|---|---|
| B2 / B3 / B4 / B5 | Drawn exposure / undrawn amount / CCF / risk weight |
| B8 / B9 / B10 | Credit / market / operational RWA |
| B12 / B13 / B14 | CET1 / AT1 / Tier 2 |
| B18 / B19 / B20 | PD / LGD / EAD |
| Task | Formula |
|---|---|
| Exposure equivalent | =B2+B3*B4 |
| Credit RWA for exposure | =(B2+B3*B4)*B5 |
| Total RWA | =SUM(B8:B10) |
| CET1 ratio | =B12/SUM(B8:B10) |
| Tier 1 ratio | =SUM(B12:B13)/SUM(B8:B10) |
| Total CAR | =SUM(B12:B14)/SUM(B8:B10) |
| Basic expected loss | =B18*B19*B20 |
Enter percentages as Excel percentages. For IRB calculations use NORM.S.DIST(x,TRUE) and NORM.S.INV(p). Validate positive denominators and consistent units.
Excel: follow the credit-loss sequence
| Cell | Input or formula |
|---|---|
| B25 | Effective PD: 1%; use MAX(estimated_PD,0.05%) for this revised corporate illustration |
| B26 | LGD: 40% (Foundation IRB, senior unsecured non-financial corporate) |
| B27 | EAD: 100 |
| B28 | =0.12*(1-EXP(-50*B25))/(1-EXP(-50))+0.24*(1-(1-EXP(-50*B25))/(1-EXP(-50))) |
| B29 | Confidence: 99.9% |
| B30 | Maturity: 2.5 |
| B32 · EL | =B25*B26*B27 |
| B33 · WCDR | =NORM.S.DIST((NORM.S.INV(B25)+SQRT(B28)*NORM.S.INV(B29))/SQRT(1-B28),TRUE) |
| B34 · loss VaR | =B27*B26*B33 |
| B35 · VaR − EL | =B34-B32 |
| B36 · b | =(0.11852-0.05478*LN(B25))^2 |
| B37 · maturity adjustment | =(1+(B30-2.5)*B36)/(1-1.5*B36) |
| B38 · illustrative capital | =B35*B37 |
| B39 · credit RWA | =12.5*B38 |
For this Basel corporate bridge keep confidence at 99.9%. A different confidence produces an economic scenario, not the prescribed Basel calibration. Retain precision in intermediate calculations. Require 0 < PD < 1, 0 ≤ ρ < 1 and a positive maturity-adjustment denominator.
LEARNING SECTION 29
Revision questions: reveal the answers
Select a question to expand its answer. Answers expand automatically for printing.
Is a 100% RW the same as a 100% chance of default?
No. It converts exposure into RWA; it is not a default probability.
Why not add 5.5%, 7% and 9%?
CET1 is included in Tier 1, which is included in total capital. These are nested requirements.
Can a bank have 13% CAR and fail capital requirements?
Yes. The example with CET1 of 5% fails the RBI baseline CET1 minimum despite a high total ratio.
Is expected loss the capital requirement?
No. The basic example has expected loss of ₹0.40 crore and a separate illustrative IRB capital amount of ₹6.5648 crore.
Does a bank using internal loan ratings necessarily use IRB?
No. Regulatory IRB requires permission and compliance with its conditions.
Why use both CAR and LR?
CAR responds to measured risk; LR constrains overall regulatory exposure relative to Tier 1. One can bind before the other.
Does the 72.5% floor apply to every loan?
No. It applies to the aggregate standardised floor base specified by the framework at full calibration.
Does 11.5% describe every Indian bank’s final requirement?
No. Bank category, systemic status, countercyclical and supervisory requirements can change the applicable level.
Is WCDR the same as Credit VaR?
No. WCDR is a tail default rate. Multiplying by EAD and fixed LGD produces the default-loss quantile under the stated model assumptions.
Why is the maturity adjustment not 1 at 2.5 years?
Its numerator becomes 1, but the denominator remains 1 − 1.5b. For the case this gives about 1.2598.
COMPANION EXCEL WORKBOOK
Credit VaR and WCDR: calculations, cases and practice
Use the consolidated workbook to move from expected loss and portfolio diversification to WCDR, corporate IRB capital and simulated credit losses.
Follow the learning sequence
| Workbook section | What to practise |
|---|---|
| 1–2 · Single loan and portfolio | Calculate EL, loss standard deviations and normal-approximation Credit VaR. |
| 3–4 · Correlation and concentration | Change dependence and loan-book granularity while tracing diversification. |
| 5 · Vasicek / IRB | Follow PD → asset correlation → WCDR → maturity adjustment → K → RWA. |
| 6 · Downturn | Explore simultaneous changes in PD, LGD and dependence. |
| 7 · Monte Carlo | Inspect a discrete, skewed credit-loss distribution using 5,000 fixed simulated scenarios. |
| 8–10 · Practice and caselets | Attempt student questions and follow formula, substitution and answer steps. |
Illustration: the four-loan book
On the main portfolio sheet, EAD totals ₹200 crore, expected loss is ₹1.6175 crore and loss standard deviation is ₹7.62165 crore at 0.25 default correlation. The normal approximation gives Credit VaR above EL of ₹23.55267 crore.
The corporate IRB sheet uses its stated borrower LGDs, Basel asset correlations and maturity adjustment. It gives total illustrative capital of ₹17.06717 crore and RWA of ₹213.33963 crore. These are model-specific teaching cases, not a universal Foundation IRB LGD schedule.
Illustration: simulation and a separate caselet
The saved Monte Carlo scenarios give a mean loss of ₹1.5835 crore, an interpolated 99.9% loss quantile of ₹40.014 crore and a worst-five-scenario average of ₹59.60 crore. The simulation uses asset correlation 0.20; it is not a like-for-like comparison with the portfolio sheet’s 0.25 default correlation. Tail estimates from 5,000 scenarios remain sensitive to a small number of observations.
The separate NBFC caselet uses ₹ lakh, rather than ₹ crore. Its portfolio EL is ₹1.7575 lakh, loss standard deviation ₹7.4263 lakh, and normal-approximation Credit VaR above EL ₹22.9473 lakh with the stated rounded z = 3.090.
In the normal-approximation sheets, UL denotes loss standard deviation and Credit VaR denotes z × UL above the mean. In the Vasicek sequence, loss VaR denotes the total loss quantile and capital starts with VaR minus EL. Asset correlation and default correlation are different quantities.
The optional corporate IRB caselet separates the simplified calculation before maturity adjustment from the extension including it. At M = 2.5 years, the full adjustment is 1/(1 − 1.5b), generally above 1. A 99.9% annual confidence level is a model tail percentile, not a fixed calendar recurrence.
LEARNING SECTION 30
Sources and connected learning
- BCBS history: Basel I, II and III milestones
- Basel II comprehensive framework, June 2006
- BCBS CRE20: revised standardised exposure treatments
- BCBS CRE31: IRB risk-weight functions
- Basel III: Finalising post-crisis reforms, December 2017
- BCBS RBC20: minimum risk-based capital requirements
- RBI Commercial Banks: prudential capital adequacy directions
- BCBS RBC20: fully phased output floor
- RBI revised credit-risk SA directions, effective 1 April 2027
Search keywords: Basel I, Basel II, Basel III, credit risk, CAR, CRAR, RWA, CET1, AT1, Tier 2, SA, F-IRB, A-IRB, PD, LGD, EAD, CCF, output floor, capital conservation buffer.
Educational guide. All numerical portfolios are hypothetical. Cases isolate selected rules and do not constitute complete regulatory returns. Historical Basel tables, revised international standards and RBI implementation are labelled separately.