Oct 09

Basel II: Concentration risk

by David Harper, CFA, FRM, CIPM

FRM |

basel2_concentrationRiskIntro

Learning Outcomes

  • LO 68.7: Define name and sector concentration and the related violation of the conditions for the IRB risk weight function.
  • LO 68.8: Explain the granularity adjustment in Gordy and Lütkebohmert, discussing recent innovation and continued concerns.
  • LO 68.9: Explain the gap between real economic capital and ASRF performance.
  • LO 68.10: Compare and contrast Pykhtin, binomial expansion technique, Duellmann, Duellmann and Masschelein, and Garcia Cespedes et al. models to estimate capital.

 

IRB approach assumes a diversified credit portfolio, and that a loan's risk is function only of exposure to a single factor

All four LOs above relate to the same idea: Basel II's internal ratings-based (IRB) approach to credit risk assumes the bank's credit portfolio is diversified (i.e., "granular" or the perfectly awkward "perfectly fine-grained"). This diversified credit portfolio assumption is convenient and unrealistic. As one of our forum participants observed, "...the assumption that by taking a ASRF approach in a finely granular portfolio, correlations can be ignored, seems to be a big simplification." Indeed!

This is the important, underlying assumption of the ASRF (Asymptotic Single-Risk Factor) model that underpins IRB: it assumes so-called portfolio invariance. Portfolio invariance implies:

  • If we add a loan to a portfolio, the additional capital charge is based on the loan's features, not on the portfolio
  • The risk of the loan is a function only of the single systematic risk factor

As one of customer observed correctly, this reminds us of the capital asset pricing model (CAPM). Except that CAPM refers to return instead of risk; CAPM says a security's return is a function of (at least) a single risk factor called the equity premium. This is a good analogy to ASRF, where the loan's credit risk is a function of exposure to (correlation with) the systematic risk factor. The systematic risk factor "may be interpreted as reflecting the state of the global economy," but don't look for it in the model! (Here is detail from yesterday's post on BIS's clever sleight-of-hand that achieves implicit 'exposure to the systematic risk factor' without the need for an actual fundamental macroeconomic factor.)

 

The models (multi-factor or closed-form) improve on ASRF by incorporating concentration risk (name and/or sector concentration)

So the IRB risk weight function assumes a diversified credit portfolio. The FRM assigned reading, Studies in Concentration Risk (BIS Working Paper 15), finds the following:

  • Sector concentration (i.e., concentration into a macroeconomic variable or sector) tends to increase economic capital by 20-40% while name concentration (i.e., large positions in individual names, or small portfolios) tends to increase economic capital by only two to eight percent. That's what is meant by the gap between real economic capital and ASRF performance: the ASRF model, because it does not acknowledge concentration risk, would underestimate real economic capital required when there is either sector concentration (by 20% or more) or name concentration (by less than 10%).
  • Typical ways to manage concentration risk include exposure limits (e.g., "we can't hold more than 10% in technology credits"), internal economic capital models, and pricing tools. Limit systems, of course, are the traditional method. They are often crafted in light of strategic goals.
  • The risk models that deal with concentration risk can be divided into multi-factor models (e.g., Pykhtin, Duellmann and Masschelein) or closed-form models (Duellmann, binomial expansion technique, and Garcia Cespedes).
  • Multi-factor models have issues that attach to Monte-Carlo simulations: theoretically correct but computationally difficult. The Pykhtin requires inter-sector correlations as inputs; in this manner, it can extend the ASRF with a "multifactor adjustment"
  • Closed form models tend to be more practical. The binomial expansion technique (BET), for example, is intuitive: if the portfolio consists of, say, 100 correlated exposures, based on slotting the exposures into sectors, it translates the portfolio into, say 60 uncorrelated exposures. Then it simply applies a binomial distribution function to estimate default frequencies (i.e., runs a binomial on the smaller, uncorrelated portfolio as a proxy for the larger, correlated portfolio).

Comments

  1. E. 15 Nov 2007

    Dear Mr. David Harper

    Let me have your atention to the following paper:

    http://www.bis.org/bcbs/irbriskweight.pdf?noframes=1

    “An Explanatory Note on the Basel II IRB Risk Weight Functions” - set forth by BIS July 2005

    Please go to Page 5 Paragraph 4, and I cite:

    “Diversification or concentration aspects of an actual portfolio are not specifically treated within an ASRF model.”

    I don’t want to refer to BIS working paper No.15 from Nov. 1990 that has nothing to do with concentration risk, and discusses about “Financial arrangements, ‘soft’ budget constraints and inflation: lessons from the Yugoslav experience”!
    here is the link:
    http://www.bis.org/publ/work15.htm

    I would be happy to know if I’m wrong in some way.

    My best
    E.Halili

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