# Capital attributed to market, credit, & operational risk

Discussion in 'P2.T7. Basel II & Regulatory' started by ckyeh, Oct 14, 2010.

1. ### ckyehNew Member

Dear David:

On your webinar 「2010-7-a-Operational」 page 11:
Explain how capital is attributed to market, credit, & operational risk.
Capital for Market Risk
–In RAROC, market risk capital is attributed as a function of the risk expressed in the VAR calculation.
Charge MR= (F1*VaR)+(F2*Unused portion of limit)+(F3*excess)

I tried to compare it with BASEL Market Risk Charge (Internal Model Approach, 2010-7--Ops-(L2), page 68 )
Charge MR=MAX ( VaRt-1, F*1/60 ∑_(t-1)^60▒〖VaRt-i〗) + Specific Risk
Obviously, there are some differences between these two ways to calculate market risk capital charge. Any comment? Or it is simply one for RAROC Market Risk Charge, the other for Basel Market Risk Charge?

Besides, RAROC credit risk charge seems similar with Basel credit risk charge.
As you mentioned in 「2010-7-a-Operational」 page 11:
RAROC credit risk charge is a function of exposure, probability of default (usually a function of risk rating (RR) or via algorithm), and recovery rates. The capital factors (i.e., applied as a percentage of face value) vary based on RR and tenor.
in 「2010-7-a-Operational」 page 16:
Capital factor=1.89%

For Basel credit risk charge
In 「2010-7-d-Operational」 page 17:
K= LGD*f(PD)*f(M,b)

The K is the same as Capital factor (=1.89%)?

Finally, operational risk measurement is a "work in progress" for RAROC. Why?
Why not use the methods for Basel Operational Risk Charge, like LDA (Loss Distribution Approach), ScoreCard Approach?

Many Thanks!

2. ### David Harper CFA FRMDavid Harper CFA FRM (test)Staff Member

Hi ckyeh,

I maybe should frame the RAROC better. The RAROC (assigned from Crouhy) is the assigned example of an economic capital calculation. Contrast with Basel as the regulatory capital requirement. So, your "mapping" is basically valid but this is two different approaches: external (Basel/regulatory) versus internal (economic). I would add, while there is really just one set of high-level Basel rules (that find variation in their national implementation, of course, as Basel has no global authority), there is nothing magic or necessary about the RAROC economic capital that GARP has assigned; by definition, it's internal, so these are just the approaches Crouhy happens to recommend.

In regard to Market Risk, there is nothing to stop a bank from using the Basel IMA for its economic capital. (you can see this necessarily implies that a bank has at least two types of "books:" regulatory capital and economic capital. Actually, add two more: accounting (does not equal either of those) and tax (also different). So, that's at least four capital "books" simultaneously kept. Though it may be that regulatory and economic are adjusted accounting books.)

In regard to credit risk, yes, you are correct to map the (K) as the Basel capital requirement to the capital factor in Crouhy's EC example. Again, while the Basel IRB formula cannot be changed, the bank is free to use that for its EC calculation. As you imply, they are conceptually similar (they both start from the same premise to quantify the unexpected loss (i.e., credit EC = credit UL) but the Basel IRB actually uses the distribution, which is arguably false precision, while the Crouhy EC is rougher and based on rating clusters).

RAROC for EC OpRisk is a work in progress for same reason that Basel advanced OpRisk (AMA) has very little concrete methodological guidance: unlike credit & market, the market simply hasn't coalesced around any standards. Those methods (LDA) were only named in the Accord briefly and subsequently removed.

Hope that helps, great questions! David

3. ### ckyehNew Member

Dear David:

But I couldn't get this paragraph:

As you imply, they are conceptually similar (they both start from the same premise to quantify the unexpected loss--i.e., credit EC = UL--but the Basel IRB actually uses the distribution, which is arguably false precision, while the Crouch EC is based on rating clusters).

Why you say Basel IRB actually uses the distribution?
I recall Basel IRB as following:

K= LGD*f(PD)*f(M,b)

I couldn't get any idea about distribution.
And why it is arguably false precision?

Actually, In 「International Convergence of Capital Measurement and Capital Standards」page 63,
I found the IRB approach for Credit Risk Charge:

Risk-weighted assets for corporate, sovereign, and bank exposures
(i) Formula for derivation of risk-weighted assets
Correlation (R) = 0.12 × (1 – EXP(-50 × PD)) / (1 – EXP(-50)) +
0.24 × [1 – (1 – EXP(-50 × PD)) / (1 – EXP(-50))]
Maturity adjustment (b) = (0.11852 – 0.05478 × ln(PD))^2
Capital requirement72 (K) = [LGD × N[(1 – R)^-0.5 × G(PD) + (R / (1 – R))^0.5 × G(0.999)]
– PD x LGD] x (1 – 1.5 x b)^-1 × (1 + (M – 2.5) × b)
Risk-weighted assets (RWA) = K x 12.5 x EAD

These equations look very different from 「2010-7-d-Operational」 page 12.

Unless exposures subject to the double default framework
(ii)Calculation of risk-weighted assets for exposures subject to the double default framework

K= LGD*f(PD)*f(M,b)

The equation is the same as 「2010-7-d-Operational」 page 12.

Could clarify my puzzles?

Many Thanks!!!

4. ### David Harper CFA FRMDavid Harper CFA FRM (test)Staff Member

Hi ckyeh,

The (Crouhy's) credit charge for economic capital is a direct linear function; i.e., product of capital factor and other terms.

But the Basel IRB is stylized (abstracted) in my 7d page 12 (it is actually in the assigned de Servigny chapter). What that means is, the f(PD) and F(maturity) embed functions within, making the outer function non-linear and more complex that the linear EC product (in fact, the IRB credit VaR is a copula)

So your citations from the Accord, of course, are correct; e.g., the Correlation (R) param is buried inside the f(PD). Those functions are just breaking out the detail of the IRB function.

Here is a thread with more explain on the IRB:

And here is a great, brief BIS doc (it used to be assigned, I regret they dropped it, it is the best brief explain on IRB that I know of). A study of this will show this IRB tries to estimate the UL of the credit risk distribution (that is what I mean by uses the distribution. Unlike the EC which is a mere product, this IRB is trying to capture the dispersion of the distribution to get UL; the graphic on page 3 may help.):
http://db.tt/ljREV0x

…. So just back to these two functions: