Basel II and VaR

[hsuwang]

Hello David,

I'm a bit confused about the requirements under Basel II that requires a 99.9% confidence and 1 year horizon for both Op and Credit Risk capital requirements. I understand how the requirement (99%, 10-day) fits market capital requirements since you actually calculate it based on the VaR measure, but for credit and operational risks, the capital requirements calculated based on IRB, BIA, standard, AMA aren't really based on VaR (they are based on gross income, PD,LGD,EAD..etc) so how does the VaR requirement (99.9%, 1 year) fit into the calculation for Op and Credit capital requirements?

for example, under BIA, we use average gross incomes times 15% to get the required capital, so how does this relate to the 99.9%, 1 year VaR?

Thanks!

 

[David Harper CFA FRM]

Hi Jack,

The 99.9% 1-year horizon refers to the advanced approaches (i.e., IRB for credit & AMA for OpRisk) ... if i wrote/said that universally (did I?), I should have been more specific to the advanced approaches.
...you are right about the basic approaches: while it's conceivable the 99.9% quantiles informed a calibration (i really don't know, I speculate), neither standardized credit (i.e., risk weight * exposure) nor BIA/SA OpRisk (% of GOI) are VaR-based quantiles

but both advanced approaches are indeed aspirationally calibrated @ 99.9%, 1-year:

For IRB: in the capital charge equation (e.g., http://forum.bionicturtle.com/viewreply/3722/)
... the confidence is captured in the NORMSINV(99.9%) which is hard-wired

For AMA OpRisk, as the bank has methodological latitude, it informs a quantitative standard.
From Basel 667. Given the continuing evolution of analytical approaches for operational risk, the Committee is not specifying the approach or distributional assumptions used to generate the operational risk measure for regulatory capital purposes. However, a bank must be able to demonstrate that its approach captures potentially severe ‘tail’ loss events. Whatever approach is used, a bank must demonstrate that its operational risk measure meets a soundness standard comparable to that of the internal ratings-based approach for credit risk (i.e. comparable to a one year holding period and a 99.9th percentile confidence interval)."

David

 

[hsuwang]

Hello David,

If that is the case, I am not sure if this test question is valid..

Which one of the following measurement tools will NOT be used under the new Basel Accord to determine the capital set aside for operational risk?
ANSWER: Operational risk VaR

Thanks!

 

[David Harper CFA FRM]

Hi Jack,

That sure looks wrong to me....although note your original point about the "basic" OpRisk approaches, BIA/SA, where for example the BIA is just 15% of Gross Operating Income: if the question said, "which is not a tool of Basic Indicator Approach (BIA) under new Basel?" ... then VaR is (I suppose) a valid answer if restricted to basic approachese
...but if it doesn't specify, that's wrong..
...more likely, it's a lazy question based on a list-based review of Basel that has in mind part of the AMA criteria which includes these (4):
"internal data, relevant external data, scenario analysis and factors reflecting the business environment and internal control systems"
(the FRM seems to like qo quiz on these)
...so VaR isn't one of these *necessary standards* to qualify for AMA, but these are just one of many criteria...David

 

[hsuwang]

Hello David,

Does the 99.9% VaR requirement applies to both standard and advanced IRB? I'm not sure if the capital requirement formula (the more complex one) applies to just the advanced IRB or does it apply to both standard and advance? If it applies to both, then how does the "12.5 x K x EAD" formula fit into the IRB? (It would make more sense to me if standard IRB uses the simple formula (which doesn't include the 99.9% requirement), and the advance IRB use the complex requirement formula).

Can you please clarify for me on this.

Thank you!

 

[David Harper CFA FRM]

Hi Jack,

There are three credit approaches: standardized (sometimes informally "basic") , foundation IRB and advanced IRB ("internal"); so please note that "standardized IRB" is probably not a useful term.

Re: "Does the 99.9% VaR requirement applies to both standard and advanced IRB?"
Yes, the complex function applies to both standard/advanced IRB; the key difference is "where do the input paramaters come from?"
Foundation IRB: bank only supplies PD (e.g., Maturity = 2.5, LGD = 45%/75%, EAD = 100%)
Advanced IRB: bank can supply all four params
...but it is a classic test question about the function/formula that asks "can the bank use its own formula in advanced IRB?" Answer: NO, the bank supplies param inputs but the formula is never negotiable

Re: "If it applies to both, then how does the “12.5 x K x EAD” formula fit into the IRB?"
K(%) is given the function (i.e., the complex function that includes the hardwired confidence of 99.9%) that applies to both foundation/advanced IRB.
Standardized charge = 8% of risk weighted assets (RWA) where RWA = exposure * risk weight (20, 50, 100, 150%)
foundation/advanced IRB charge = K(%) or, in dollars, K(%) * EAD; 12.5 * K * EAD converts the IRB to a risk-weight equivalent
...because 8% of RWA = 8% * (12.5 * K * EAD), and by design 8%*12.5 = 1, so 8% of RWA = K*EAD
...so 12.5 * K * EAD only refers to IRB

David

 

[hsuwang]

Thank you for the explanation! I think I wasn't thinking clearly and actually thought they are two distinct formulas. The complex capital requirement formula is the K in the RWA=12.5 x K x EAD function. I get it now. Thanks!

 

[rahul.goyl]

Hi David,
Thanks David for sharing such deep understanding with us.
Just to add what you said about four parameter, there is another one called Correlation, which would always be given by Basel ( which fits into your Complex Function of ASRF).

Regards,
Rahul