Basel II Advanced IRB Capital Model

From Open Risk Manual


The term Advanced IRB or A-IRB is an abbreviation of advanced internal ratings-based approach and it refers to a set of credit risk measurement techniques proposed under Basel II capital adequacy rules for banking institutions.


Under this approach banks are allowed to develop their own empirical model to quantify required capital for credit risk. Banks can use this approach only subject to approval from their local regulators.

Under A-IRB banks are supposed to use their own quantitative models to estimate PD (probability of default), EAD (exposure at default), LGD (loss given default) and other parameters required for calculating the RWA (risk-weighted asset). The total required capital is calculated as a fixed percentage of the estimated RWA.

There is a wide range of assumptions underpinning the IRB capital model. In this article the focus is specifically on the assumptions that affect the model's ability to capture name concentration.

The nature of idiosyncratic risk

Idiosyncratic risk represents the effects of risks that are particular to individual borrowers and not shared with a broader set of entities. In corporate credit context examples of idiosyncratic risk factors would be the performance of management or of specific projects undertaken by the company.

As a portfolio becomes more fine-grained, in the sense that the largest individual exposures account for a smaller share of total portfolio exposure, idiosyncratic risk is diversified away at the portfolio level. This risk is totally eliminated in the theoretical limit of an infinitely granular portfolio (one with a very large number of exposures). This behavior of name concentration risk links with the wide body of knowledge around diversification and modern portfolio theory.

The trade-offs embedded in the IRB model

The IRB risk-weight functions of Basel II/III were developed with the idea that they would be portfolio invariant, i.e., the capital required for any given loan should only depend on the risk of that loan and must not depend on the portfolio it is added to. This characteristic has been deemed vital in order to make the new IRB framework applicable to a wider range of countries and institutions (as it considerably simplifies the calculation, communication and management of risk based capital measures applicable to each exposure). The penalty for those desirable attributes is that very real risk factors (including but not limited to name and sector concentration) are neglected.

In order to achieve portfolio invariance, at least asymptotically, the ASRF model framework that underpins the IRB approach is based on two key assumptions:

  • bank portfolios are perfectly fine-grained, and
  • there is only one source of systematic risk.

There are important reasons why the Committee opted for the particular additive bottom-up framework. These include the relative simplicity of the bottom-up approach, the fact that the stage of development of more realistic portfolio credit models at the time was judged inadequate for regulatory purposes, and the fact that the validation of inputs is easier than the validation of full models. The desire for portfolio invariance, however, makes recognition of institution-specific diversification effects within the framework difficult: diversification effects depend on how well a new loan fits into an existing portfolio. To maintain internal consistency, the ASRF modelling restrictions were embedded in the methodologies used to calibrate the IRB risk weights. In particular, it assumed a fully granular portfolio in terms of single name exposures, and the asset correlation parameters were chosen to match the economic risk in a credit portfolio that is very well-diversified across sectors (see further discussion on this point below).

The implications of the IRB model weakness

As mentioned earlier, the specific assumptions behind the ASRF model are unlikely to be exactly met by actual portfolios, especially those of institutions that are smaller in size or relatively specialised. Concentration risk can arise from significant single exposures, from concentration in specific business sectors, and from potential loss dependencies because of direct business links between borrowers or indirectly through credit risk mitigation.

The weakness of the IRB model (i.e., Pillar I capital) would show in relation to exposure “lumps” in the portfolio. In other words, when single exposures account for more than a vanishingly small share of the total portfolio.

When the two assumptions are violated, however, there is no guarantee that the bottom-up approach will be accurate. The marginal contribution to overall risk by any single exposure will likely depend on the risk profile of the rest of the portfolio. In particular, adding up the IRB-based capital requirements relating to individual exposures might over- or under-state the risk of the portfolio depending on whether the portfolio is diversified or concentrated relative to the one used as a calibration benchmark.

Mitigating practices and approaches

From a regulatory perspective and practice the mitigation of the above identified weaknesses rests on two control points:

Internal bank practices for managing this risk typically also involve limits (which may be also risk adjusted) and internal models.

Issues and Challenges

Recognized issues before the financial crisis of 2008-2012

As mentioned above a range of issues with the model were recognized before 2008

  • Concentration risk
  • Limited capture of risk in long tenor lending

Recognized issues after the financial crisis of 2008-2012

Some areas within the scope the model that proved inadequate during the crisis (and have since seen adjustments) are

  • Securitisation
  • Exposures to Banking Counterparties

Other issues

In current practice many financial firms practice internal and external (regulatory prescribed) Stress Testing programs. These exercises are essentially overriding the core assumptions of the Basel capital model, yet continue to use it as a metric of require capital in future scenarios.


  1. [1] BIS Website

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