Question about Bionic Turtle's 2009 FRM Program
07 Jan 2009
Oct
03
Basel II: Approaches to credit risk
by David Harper, CFA, FRM, CIPM
FRM |
- LO 67.5: Describe how the necessary components for calculating capital requirements are determined under the standardized and internal ratings-based approaches.
- LO 68.3: Describe the Basel II Accord’s requirements for calculating risk-weights using both the standardized and the internal ratings-based approaches when accounting for credit risk.
Don't lose sight of the big picture: 8% of RWA
Before getting mired in the credit risk approaches, remember they contribute to the denominator of the Cooke ratio: the bank's equity capital must constitute a buffer of at least 8% of risk-weighted assets. Under these credit risk approaches, we are estimating one term (albeit the most important term) in the denominator:
So, the big picture is, we are talking about risk-weighted assets (RWA) for credit risk--which will be combined with market risk and operational risk--under the First Pillar of Basel II.
Two approaches to credit risk: standardized (external ratings) or internal (models)
Why two approaches? Basel II gives alternatives throughout. The theory is that banks will evolve ("take an evolutionary approach") away from the standardized approach and toward the internal approach, over time, as their risk methods become more sophisticated. The irony is that markets may evolve with too much complexity for Basel II. Still, the quid pro quo is (i) banks are likely to estimate lower risk-weighted assets under internal approaches but (ii) in order to do so, their national supervisor must approve this so internal approaches lean mightily on Basel's Second Pillar (Supervisory Review)
In summary, under Basel's First Pillar, the calculation of risk-weighted credit assets can follow either a standardized or an internal ratings-based (IRB) approach.
Standardized approach is a "lookup table"
The standardized approach solves a major problem of the original Accord: the original Basel barely differentiates risks.
Under the Basel II standardized approach, an exposure is multiplied by a risk weighting to derive a risk-weighted asset (RWA). For example, a AAA rated corporate loan is assigned a risk weight of 20%, but a BB- rating earns a 100% weight. So, on a $100 million exposure, the bank must hold only $1.6 million against the AAA bond (=$100 MM x 20% x 8% capital). But the bank must hold $8 million against a rating of BB- (= $100 MM x 100% 2 8%).
Internal ratings-based approach (IRB) is a function
The IRB approach includes three elements (risk components, risk-weight function, and minimum requirements). The components are estimates of risk parameters:
- PD: probability of default
- EAD: exposure at default
- LGD: loss given default
- M: maturity
The risk-weight function
Instead of using a lookup table based on external ratings, the internal ratings-based approaches (IRB) use a function. The risk-weight assets (RWA) are a function of exposure at default (EAD), loss given default (LGD), probability of default (PD) and maturity (M), where (K) is the capital requirement:
This may seem confusing, but we can break it down. It really amounts to (reduces to) the simple: capital charge = worst-case expected loss (EL).
First, the f(M,b) is an adjustment for the exposure's maturity. A longer maturity will require more capital (an upward adjustment). Further, the small (b) refers to the probability of default; so this maturity adjustments incorporates both maturity and probability of default (PD). Higher quality exposures (lower PDs) translate into a higher maturity adjustment; higher quality exposures are penalized. As de Servigny observes, "some of the relief granted in Basel II to the best credits is offset by the maturity adjustment."
If we temporarily omit the maturity adjustment, the function is simply 12.5 x EAD x expected loss (EL), since LGD x PD = EL:
- RWA = 12.5 x EAD x LGD x PD
- RWA = 12.5 x EAD x EL ----> [EL, expected loss = LGD x PD]
The 12.5 multiplier used simply so that the capital requirement (K) can be plugged into the Cooke ratio formula: (8% x 12.5) x EAD x EL = 1 x EAD x EL.
The three elements
In exploring the risk-weight function, we've already covered two of the three elements:
- Risk components: estimates of risk parameters provided by banks some of which are supervisory estimates.
- Risk-weight functions: the means by which risk components are transformed into RWA and therefore capital requirements.
- Minimum requirements: the minimum standards that must be met in order for a bank to use the IRB approach for a given asset class.
Foundation IRB versus Advanced IRB - who estimates the components?
Within the IRB approach, there are two sub-approaches: foundation IRB and advanced IRB. They share the same risk-weight function. Aside from a more rigorous set of requirements (including supervisor approval), the key difference is the inputs ('components') into the risk-weight function:
- Internal IRB: banks provide their own estimates of PD but rely on supervisors for other inputs. Maturities are assumed to be 2.5 years.
- Advanced IRB: banks rely more on their own internal estimates for PD, LGD, EAD. Banks impact their own calculation of the maturity adjustment (M).
A common FRM test question is: can the bank use its own function or model under advanced IRB? The answer is "No." The function is still supplied; they cannot change it. Rather, under the Advanced IRB, the bank can develop internal estimates as inputs ("components") that plug into the function.
Comments
I am a bit confused most literature that I read defines as EL = EaD x PD x LGD
however the Basel II: Approaches to credit risk tutorial defines EL as PD x LGD
Could you please clarify . Thank You
Ekim,
Either. It’s like VaR can be a percentage VaR or a dollar VaR. With EAD, it’s currency expressed; without, it is a percentage. Basel will sometimes refer to an EL amount, which includes EAD.
You’ll notice the IRB in Basel calculates (K) as function of LGD & PD. So, K is a conditional expected loss expressed as a percentage. Then the (K), consistent with your literature, gets multiplied by EaD to get the RWA (the percentage needs to translate into dollars)
Thanks, David
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