Capital Allocation for Portfolio Credit Risk
34 Pages Posted: 5 Apr 2005
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Capital Allocation for Portfolio Credit Risk
Date Written: December 2006
Abstract
This paper derives unbiased capital allocation rules for portfolios in which credit risk is driven by a single common factor and idiosyncratic risk is fully diversified. The methodology for setting unbiased capital allocations is developed in the context of the Black-Scholes-Merton (BSM) equilibrium model. The methodology is extended to develop an unbiased capital allocation rule for the Gaussian ASRF structural model of credit risk. Unbiased capital allocations are shown to depend on yield to maturity as well as probability of default, loss given default, and asset correlations. Unbiased capital allocations are compared to capital allocations that are set equal to unexpected loss in a Gaussian credit loss model - an approach that is widely applied in the banking industry and used to set minimum bank regulatory capital standards under the Basel II Internal Ratings Based (IRB) approach. The analysis demonstrates that the Gaussian unexpected loss approach substantially undercapitalizes portfolio credit risk relative to an unbiased capital allocation rule. The results include a suggested correction for the IRB capital assignment function. The corrected capital rule calls for a substantial increase in minimum capital requirements over the existing Basel II IRB regulatory capital function.
Keywords: Economic capital, credit risk internal models, Basel II, Internal Ratings Approach
JEL Classification: G12, G20, G21, G28
Suggested Citation: Suggested Citation
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