Why Regulatory Credit Capital Can Fall at High Default Probabilities
Summary
The document explains an apparent decline in regulatory credit-risk capital as a loan’s probability of default rises. The calculation described separates expected loss, based on default probability and loss given default, from unexpected loss, then applies a correlation factor and a capital multiplier. The answer connects the pattern to the regulatory risk-weight formula, which accounts for expected loss when determining capital for unexpected loss.
As default probability increases, more of the total risk is reflected in expected loss, so the unexpected-loss contribution can become less material and the risk weight may eventually decline. The response notes that regulatory credit models tend to focus on lower default-probability ranges and that very high-probability exposures can be limited in practice. This is an explanation of the cited regulatory framework, not a general rule that risk or total loss falls as default probability rises; results depend on the framework and its inputs.
Key ideas
- Regulatory capital in the described framework targets unexpected loss beyond expected loss.
- Expected loss depends on default probability and loss given default.
- The regulatory risk weight can first rise and later fall as default probability increases.
- A falling unexpected-loss capital contribution does not mean that total credit risk or expected loss has fallen.
- The response describes a regulatory model whose practical exposure is concentrated at lower default probabilities.
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# Answer by Thomasunny (score 0) # Calculation of Total Credit Risk Capital % but seeing lower capital percentage for higher risk band. Is there any correction required? I am trying to calculate the Total Credit Risk capital % for my learning purpose as given below. Assuming adding 1 single loan with different pds. i have noticed one point in the table and have two queries. Point 1: As PD increasing, the highly risky bands gets lower credit risk capital %. Question1: Is there any rational behind this?, why we need to keep lower capital for risky bands? Question2: The calculated credit risk capital % contains both EL+UL or just UL. I mean credit VAR(EL+UL) or Just Unexpected loss capital?. Is there any correction required? a. I am creating the bands from 1 to 10, band 1 is least risky and band 10 is highly risky. I am computing the odds by considering the odds for band 1 is .10 and doubling the odds for rest of the bands. b. Computing the Logodds and PD for each band. formula for Logodds is ln(odds) and EXP(logodds)/(1+EXP(logodds)) in excel. c. PD Variance and LGD Variance using variance formula ie eg for PD --- PD*(1-PD). d. EL% is PD*LGD. e. Unexpected Loss -Single loan "First square the Loss Given Default and multiply it with the Probability of Default Variance. Next multiply the Probability of Default with the Loss Given Default Variance. Add these two values together and take its square root.This new percentage is the standard deviation. f. Portfolio Correlation Factor is 5.36%. g. Multiply this correlation Factor with the newly calculated Unexpected Loss(single loan) and the result is the Unexpected Loss Contribution. h. To get the credit risk capital % -- Multiplying the Unexpected Loss Contribution with the Unexpected Loss Capital Multiplier( say 6) for 99.97% confidence. ## Answer by Thomasunny (score 0) https://quant.stackexchange.com/a/69229 The answers to both your questions are connected: the article 153 of the CRR defines the computation of the regulatory risk-weight for capital purpose. As you can observe, the formula takes into account the expected loss $LGD\times PD$. In other words, the capital requirements (for Unexpected Loss) focus on what happens beyond the expected losses. For high values of PD, the risk is mostly taken into account in the Expected Loss, the contribution from Unexpected Loss is less material. Thus, the Risk-Weight increases with PD at first, then at some point, a decrease can be observed. This article from Chappuis Halder consulting firm provides description of the different functions used in the Regulatory Credit Risk framework. In particular, in pages 12 and 13, you can find some plots of the RW function with respect to large range of PD values (from 0% to 100%). In practice, the modeling of PD focuses on the lower band below 30%. For instance, you can check the Pillar 3 Regulatory publication of BNP Fortis: the PD above 10% are all merged and are rather insignificant in terms of amount. The bulk of the exposure concentrates on small values for PD.
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