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# Credit Risk Mitigation or LGD mitigation?

#### jyothi1965

##### New Member
David

Credit risk is defined as PD* LGD (in % terms) or PD*LGD*EAD in dollar terms.

Now when we hedge credit risk (CRM in Basel II lingo) which part of the equation are we actually mitigating? PD? LGD?

For example say that we have a exchange traded contract which requires daily MTM and margining. Now is this margining a hedge for PD or the LGD (assuming zero recovery)? My view is that the the margining is actually offsetting the LGD.

Similarly when you have a cash collateral (assume that the loan is collateralised 100%) then the collateral is strictly a hedge for the LGD. This is because you can't control PD (it is external) and hence you want to control LGD in order that the product (LGD*PD) is under control.

Let us take a example. Suppose we have PD= 3% and RR = 0% so that LGD = 100%. Now the credit risk for a $100 exposure is 3$. So should we be taking 3$worth of collateral? No way!! In practice we take collateral to cover the entire value of the exposure. So we take 100$ in cash, in which case it becomes LGD mitigation and not credit risk mitigation.

Is there some gap here in my thinking?

Jyothi

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi Jyothi, I hope you are doing well!

Yes, agreed, under IRB: conditional EL% = PD * LGD [* EAD, if dollars].

Agree with everything else you write, too. I suppose "mitigants" is a broad bucket in Basel; e.g., in Operational Risk, insurance is called a 'risk mitigant'

But whereas standardized handles collateral (mitigant) in either the risk weight (if simple) or the exposure (if comprehensive)--the only two choices in standardized, it must be either in RWA or exposure!--under IRB, you are correct, mitigants reduce the LGD.

The details are under the RISK COMPONENT (LGD) for each of the exposure types. But, for example, the "rules for corporate, sovereign, and bank" show the idea:

A collateralized exposure has an EFFECTIVE LGD* = LGD x (E*/E)

where E is exposure and E* is exposure net of collateral, per the haircut method [Net exposure = (Exposure + haircut) - (collateral - haircut - FX).

So, you are absolutely right, if the collateral is $100 against$100 exposure, this will look something like LGD* = (<100 / 100). The multiplier will be far less than one but it won't be zero, the "volatility adjusting" which is a way to handle BASIS RISK makes the E* < E even if they both are 100.

David