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

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

October 22, 2002 | Michael B. Gordy
This paper discusses the challenges of calibrating ratings-based capital charges within a portfolio model. It shows that ratings-based capital rules can be reconciled with credit value-at-risk (VaR) models, but only under specific conditions. The key findings are that portfolio-invariant capital charges are possible only if there is a single systematic risk factor driving correlations across obligors and no exposure in a portfolio accounts for more than an arbitrarily small share of total exposure. The paper also proposes a simple and accurate portfolio-level add-on charge for undiversified idiosyncratic risk. However, there is no similarly simple way to address violations of the single factor assumption. The paper also discusses the implications of using value-at-risk (VaR) and expected shortfall (ES) as risk measures for economic capital. It shows that ES can deliver portfolio-invariant capital charges for an asymptotic portfolio in a single-factor setting, while EEL cannot. The paper concludes that while a ratings-based scheme may be a necessary "second-best" solution under current conditions, it is desirable that the capital charges be calibrated within a portfolio model to ensure consistency and accuracy. The paper also highlights the importance of a single systematic risk factor, which is empirically untenable but an unavoidable precondition for portfolio-invariant capital charges.This paper discusses the challenges of calibrating ratings-based capital charges within a portfolio model. It shows that ratings-based capital rules can be reconciled with credit value-at-risk (VaR) models, but only under specific conditions. The key findings are that portfolio-invariant capital charges are possible only if there is a single systematic risk factor driving correlations across obligors and no exposure in a portfolio accounts for more than an arbitrarily small share of total exposure. The paper also proposes a simple and accurate portfolio-level add-on charge for undiversified idiosyncratic risk. However, there is no similarly simple way to address violations of the single factor assumption. The paper also discusses the implications of using value-at-risk (VaR) and expected shortfall (ES) as risk measures for economic capital. It shows that ES can deliver portfolio-invariant capital charges for an asymptotic portfolio in a single-factor setting, while EEL cannot. The paper concludes that while a ratings-based scheme may be a necessary "second-best" solution under current conditions, it is desirable that the capital charges be calibrated within a portfolio model to ensure consistency and accuracy. The paper also highlights the importance of a single systematic risk factor, which is empirically untenable but an unavoidable precondition for portfolio-invariant capital charges.
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