In Basel II, EL is useful. It's calculated as

$$EL = PD \cdot EAD \cdot LGD $$

in advance IRB (internal rate-based approach),

Correlation $$R = 0.12 \frac{1 – e^{-50 \cdot PD}}{1 – e^{-50}} + 0.24 \cdot (1- \frac{ 1 – e^{-50 \cdot PD}} {1 – e^{-50}} )$$

Maturity adjustment

$$b = [0.11852 – 0.05478 \ln(PD)]^2$$

Capital requirement $$K = \{ LGD \cdot N(\sqrt{\frac{1}{1 – R}} \cdot G(PD) + \sqrt{\frac{R}{1 – R}} \cdot G(0.999)) – PD \cdot LGD\} \cdot \frac{1 + (M – 2.5) b}{1 – 1.5 b} $$

here Ln denotes the natural logarithm; N(x) denotes the cumulative distribution function for a standard normal random variable; G(z) denotes the inverse cumulative distribution function for a standard normal random variable (i.e. the value of x such that N(x) = z).


Risk-weighted assets $$RWA = K \cdot 12.5 \cdot EAD$$


$$CAR = \frac{Tier 1 capital + Tier 2 capital}{Total Asset}$$

-- Basel II defines limits on CAR.

But, for unexpected loss, did Basel II make any restriction on it?

FRM has a set of formula calculating UL from LGD, EAD etc... Unexpected Loss $$UL = EAD \sqrt{PD\cdot \sigma_{LGD}^2 + LGD^2 \cdot \sigma_{PD}}$$

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    $\begingroup$ You should add a power of 2 to the $\sigma_{PD}$ in the last equation. $\endgroup$ Nov 15, 2013 at 11:16

2 Answers 2


let me try answer my own questions, partially, from below that are exerpted from FRM exam notes. FRM notes p1 FRM notes p2

So actually the K above, is UL, though it derives only from PD and maturity, but the G, N and 0.999, actually are calculating the VaR and UL.

So, CAR is defined based on EAD and K, while K means UL. the essence is, CAR is to cover Unexpected Loss -- captical reserved is not for EL, EL shall be calculated in the cost already.

However, how the K formular using G, and N comes from PD, I don't know... maybe need dig some papers.


For more explanations you can also try out "An explanatory note on the Basel II IRB Risk Weight Functions", or if you read german, "Die IRB Formel".


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