A Risk-Factor Model Foundation for Ratings-Based Bank Capital Rules

By Michael B. Gordy. 2003

975 citations recorded by the source corpus.

When economic capital is calculated using a portfolio model of credit value-at-risk, the marginal capital requirement for an instrument depends, in general, on the properties of the portfolio in which it is held. By contrast, ratings-based capital rules, including both the current Basel Accord and its proposed revision, assign a capital charge to an instrument based only on its own characteristics. I demonstrate that ratings-based capital rules can be reconciled with the general class of credit VaR models. Contributions to VaR are portfolio-invariant only if (a) there is only a single systematic risk factor driving correlations across obligors, and (b) no exposure in a portfolio accounts for more than an arbitrarily small share of total exposure. Analysis of rates of convergence to asymptotic VaR leads to a simple and accurate portfolio-level add-on charge for undiversified idiosyncratic risk. There is no similarly simple way to address violation of the single factor assumption.

Subfields: Economics and Econometrics, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/583deb11e34d46b638ad3df3a4ee337a33df865f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

In Finance

In Management Science and Operations Research

Citations in the corpus

The empirical relationship between average asset correlation, firm probability of default, and asset size (2002, methodology): “1 I. Introduction As discussed by Gordy (2001), the asymptotic single risk factor (ASRF) approach is a general framework for determining regulatory capital requirements for credit risk, and it has become an integral part of the second Basel Accord.1 A key variable in the ASRF approach is the…”
Transnational regulatory capture? An empirical examination of the transnational lobbying of the Basel Committee on Banking Supervision (2012, methodology): “Internal work conducted by staff economists at the Fed Board enabled this decision, as this work utilized the basic logic and mathematics of credit risk models to produce a regulatory model that the BCBS could use as a (more conservative) proxy for drawing on internal bank practices directly (interv”
Multivariate Survival Modelling: A Unified Approach with Copulas (2001, neutral): “(78) with θ1 = λ12/ (λ1 + λ12) and θ2 = λ12/ (λ2 + λ12).”
Risk factor contributions in portfolio credit risk models (2010, background): “For precise statements of this result, see, for example Gordy (2003), or McNeil et al. (2005).”
A Survey of Cyclical Effects in Credit Risk Measurement Models (2002, positive): “Gordy (2001) shows that this additivity assumption is correct only if the portfolio consists of an infinite number of atomistically small assets or if there is only a single systematic risk factor that drives all correlations in the model.”
Risk-based capital requirements for mortgage loans (2004, background): “For a technical discussion justifying the use of conditional expected loss rates to obtain a portfolio loss distribution, see Gordy (2000b). geographic locations within the bank’s portfolio.”
Corporate Credit Risk Modelling and the Macroeconomy (2004, background): “Gordy [21] examines the relation between portfolio models of credit VaR and ratings-based bucket models.”
Loan Pricing Under Basel Capital Requirements (2004, methodology): “Finally, the single risk factor model is good for tractability: in fact, it is the only model with a bottom-up approach to credit risk that yields simple closed-form solutions for the distribution of credit 2This model is credited to Michael Gordy; see Gordy (2000, 2002).”
Does Competition Reduce the Risk of Bank Failure (2010, methodology): “…Cournot competition in the loan market, in which banks that do not fail in one period have the 2 The 99.9% quantile of this distribution is used for the computation of capital requirements in the framework proposed by theBasel Committee on Banking Supervision(2004), known as Basel II (Gordy2003).”
The Procyclical Effects of Basel II (2008, methodology): “…the flat capital requirements of Basel I, the same economies would exhibit slightly countercyclical buffers and essentially no credit 4As shown by Gordy (2003), the single risk factor model also has the feature that the contribution of a given loan to value-at-risk is additive, that is, it…”