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Home / Financial Tools / Basel IRB Risk-Weight Function & Portfolio Economic Capital Engine

Graduate-Level Modeling · Bank Regulatory Capital & Portfolio Credit Risk

Basel IRB Risk-Weight Function & Portfolio Economic Capital Engine

Every bank's IRB capital number comes from one formula, built on one assumption: an infinitely diversified portfolio. Real portfolios aren't infinite, and this tool shows you exactly what that costs.

How To Use This Model

Reading This Tool

Enter PD, LGD, exposure and maturity for one exposure class, and this tool computes the exact Basel Internal Ratings-Based capital formula, the Vasicek Asymptotic Single Risk Factor model that underlies every bank's regulatory capital calculation.

Then it goes further: it simulates a real portfolio of correlated defaults via a single-factor Gaussian copula, builds the actual loss distribution, and shows you exactly where the regulatory formula's built-in assumption, an infinitely diversified portfolio, breaks down for a small book of concentrated exposures.

Exposure Class & Risk Parameters

Portfolio Simulation

All exposures in the simulated portfolio are treated as homogeneous, same PD, LGD and EAD, linked only through a single common systematic factor, exactly the assumption behind the regulatory formula itself.

Regulatory Capital Requirement

Corporate

Asset Correlation R

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Capital Requirement K

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Risk Weight

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Regulatory Capital, Full Portfolio

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The IRB Risk-Weight Curve: Capital Requirement K vs. PD

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Simulated Portfolio Loss Statistics

Expected Loss

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Simulated VaR At Confidence

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Simulated Economic Capital

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Economic Vs. Regulatory Capital

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Simulated Portfolio Loss Distribution

Regulatory Capital vs. Simulated Economic Capital

Simulated Economic Capital (Per Unit EAD) As Portfolio Size Grows

Simulated Economic Capital / EADAsymptotic (Regulatory-Style) Target

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What The Asset Correlation Formula Is Actually Encoding

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Why Riskier Borrowers Get A Lower Correlation Assumption

Higher-PD borrowers tend to default for idiosyncratic, firm-specific reasons more than macroeconomic ones, a struggling small business fails for its own reasons more often than because of the broader cycle. Basel's formula reflects this by shrinking the correlation weight toward the lower end of its range as PD rises, safer borrowers are assumed to be more exposed to systematic, economy-wide risk.

What The Maturity Adjustment Is Actually Charging For

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Why Small Portfolios Need More Capital Than The Formula Says

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Bank Regulatory Capital & Credit Portfolio Risk

The Core Formulas (Corporate/Sovereign/Bank)

R = 0.12·g(PD) + 0.24·(1−g(PD)), g(PD) = (1−e−50PD)/(1−e−50)
b = [0.11852 − 0.05478·ln(PD)]²
Maturity Factor = [1 + (M−2.5)b] / (1−1.5b)
K = LGD · [ N( N−1(PD)/√(1−R) + √(R/(1−R))·N−1(0.999) ) − PD ] · Maturity Factor
RWA = K × 12.5 × EAD, Regulatory Capital = 8% × RWA

Retail exposure classes use a fixed correlation (mortgage: 15%, qualifying revolving retail: 4%) or a similar PD-dependent formula with a 35 exponent (other retail), and apply no maturity adjustment at all.

When To Actually Use This Model

  • Teaching the Vasicek Asymptotic Single Risk Factor model and its role as the mathematical foundation of Basel's IRB capital framework.
  • Understanding, quantitatively, why concentrated portfolios (few large exposures) are riskier than the regulatory minimum capital charge implies.
  • Building intuition for the difference between regulatory capital (Pillar 1, formula-driven) and economic capital (internally modeled, portfolio-specific) that every bank's ICAAP process has to reconcile.

Key Assumptions & Limitations

  • This tool simulates a single homogeneous exposure class, real bank portfolios mix exposure classes, sizes and correlations, requiring a full multi-factor granularity adjustment (Gordy & Lütkebohmert, 2013) rather than a single simulated example.
  • The regulatory formula itself is a Pillar 1 minimum, actual required capital under Basel III adds the conservation buffer and Domestic Stability Buffer covered in this site's separate Basel III Capital Adequacy tool.
  • PD, LGD and EAD are treated as point estimates, real IRB models estimate these through the cycle or point-in-time with their own separate validation requirements.

Foundational References

Vasicek, O. (2002). The Distribution of Loan Portfolio Value. Risk, 15(12), 160-162.

Basel Committee on Banking Supervision. (2005). An Explanatory Note on the Basel II IRB Risk Weight Functions. Bank for International Settlements.

Gordy, M. B. (2003). A Risk-Factor Model Foundation for Ratings-Based Bank Capital Rules. Journal of Financial Intermediation, 12(3), 199-232.

Want the bank-wide capital ratio picture too?

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