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# RWA under IRB

#### afterworkguinness

##### Active Member
Hi @David Harper CFA FRM CIPM ,
Little confused with terminology in the Hull reading on RWA.

First Hull says

The capital required is derived as the excess of 99.9% worst-case loss over the expected loss i.e ∑EADi∗LGDi∗(WCDRi−PDi)

Then he gives us a means to calculate RWA for bank, sovereign and corporate exposures.

My questions:

#1
Is the first method above simply a way of calculating RWA? Hull says that capital is still 8% of total RWA and now includes operational risk RWA too.
#2
Assuming above is actually an RWA, is it a general case / a case to use for exposure types where no specific one is prescribed (such as how a specific one is described for banks, corporates and sovereigns) ?

I looked at the Basel II accord but couldn't reconcile with Hull for some things.

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#### afterworkguinness

##### Active Member
Coming back to this, I can see now that ∑EADi∗LGDi∗(WCDRi−PDi) is indeed the capital which = 8% of the RWA. A case of not being able to see the forest for the trees I'm afraid.

#### NNath

##### Active Member
Hi @David Harper CFA FRM , I have a question about in the IRB approach.

1. In your excel sheet. T7.c_2012_XLS_basel_v1010.xls, sheet 7c.3 Basel2_IRB you seem to be adding Expected Loss and Unexpected Loss. As per the formula
∑ EADi∗LGDi∗(WCDRi−PDi) in Hull, when the WCDR is subtracted from PD wouldn't it mean that the Unexpected loss - EL.

2. Also, the Maturity Adjustment formula needs to be corrected in the yellow box. It should be

(1 + (M – 2.5) × b)/(1 – 1.5 × b). The calculation seem to be correct.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @NNath
1. I don't see any inconsistency. Yes, you are correct that Hull correctly represents the Basel IRB capital requirement as an unexpected loss; i.e., WCDR is a 99.9% quantile such that (WCDR-EL) is UL(@99.9%), but so does my spreadsheet UL (at cell C17) which matches the yellow formula "K = " (please notice the formula subtracts LGD*PD). The only difference is, yes, I do add expected loss (EL) for total capital requirement but that is deliberate as EL requires evidence of (may be convered by) provisioning, or if there is not adequate provisioning for EL, then capital is required to cover it. EL is part of the IRB requirement. The bank is still required to cover the entire UL+EL. I realize the label "total capital requirement" may be slightly confusing, but the formula (K), except for the maturity image typo, matches Basel and Hull. Selected Basel paragraphs below
2. Yes, agreed, that is a typo in the graphic, but the formula looks good

Treatment of EL and provisions
384. As specified in paragraph 43, banks using the IRB approach must compare the total amount of total eligible provisions (as defined in paragraph 380) with the total EL amount as calculated within the IRB approach (as defined in paragraph 375). In addition, paragraph 42 outlines the treatment for that portion of a bank that is subject to the standardised approach to credit risk when the bank uses both the standardised and IRB approaches.
385. Where the calculated EL amount is lower than the provisions of the bank, its supervisors must consider whether the EL fully reflects the conditions in the market in which it operates before allowing the difference to be included in Tier 2 capital. If specific provisions exceed the EL amount on defaulted assets this assessment also needs to be made before using the difference to offset the EL amount on non-defaulted assets.
386. The EL amount for equity exposures under the PD/LGD approach is deducted 50% from Tier 1 and 50% from Tier 2. Provisions or write-offs for equity exposures under the PD/LGD approach will not be used in the EL-provision calculation. The treatment of EL and provisions related to securitisation exposures is outlined in paragraph 563.

#### NNath

##### Active Member
Thanks, @David Harper CFA FRM , Unfortunately I am still not getting results in the C17 (189,044)., there seems to be something wrong. Exposure = 1M, LGD = 45%, PD = 4%, MA = 1.4, asset rho=0.2 WCDR = N(((N^-1(PD) + N^-1(0.999)*sqrt(rho))/sqrt(1-rho)) = N(((-1.75 + 3.09*sqrt(0.2))/sqrt(1-0.2)) =0.6591 so UL = 1M * 0.45 * (0.6591 - 0.04) * 1.4 =~ 390,000.

And, actually the the formula in the graphic is as per the BASEL not Hull so that need not change. BASEL reading shows b as a function of PD like b(PD).

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#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @NNath Love the deep dive! But I get:

[N^-1(PD) + N^-1(0.999)*sqrt(rho)] /sqrt(1-rho) =
[N^-1(0.04) + N^-1(0.999)*sqrt(0.20)] /sqrt(1-0.20) =
[-1.7507 + 3.09*0.4472] /0.8944 = -0.4122, such that
N(-0.4122) = 0.340, and
UL = 1M * 0.45 * (0.340 - 0.04) * 1.4 =~ 189,000. Let me know what you think?

#### NNath

##### Active Member
Was wrong in step 4 of 5. Thank you David.