Federal Deposit InsuranceCorporation• Center for Financial Researchh
Sanjiv R. Das
Darrell Duffie
Nikunj Kapadia
Risk-Based Capital Standards,
Deposit Insurance and Procyclicality
Risk-Based Capital Standards,
Deposit Insurance and Procyclicality
FDIC Center for Financial Research
Working Paper
No. 2005-04
Unbiased Capital Allocation in an Asymptotic Single
Risk Factor (ASRF) Model of Credit Risk
Paul Kupiec
February 2005
Sanjiv R. Das
Darrell Duffie
Nikunj Kapadia
Risk-Based Capital Standards,
Deposit Insurance and Procyclicality
Risk-Based Capital Standards,
Deposit Insurance and Procyclicality
FDIC Center for Financial Research
Working Paper
No. 2005-04
Unbiased Capital Allocation in an Asymptotic Single
Risk Factor (ASRF) Model of Credit Risk
Paul Kupiec
February 2005
Unbiased Capital Allocation in an Asymptotic Single Risk Factor
(ASRF) Model of Credit Risk
by
Paul H. Kupiec∗
February 2005
FDIC Center for Financial Research Working Paper No. 2005-04
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.
Key words: economic capital, credit risk internal models, Basel II, Internal Ratings Approach
JEL Classification: G12, G20, G21, G28
CFR research programs: risk measurement, bank regulatory policy
∗ Associate Director, Division of Insurance and Research, Federal Deposit Insurance
Corporation. The views expressed in this paper are those of the author and do not reflect the
views of the FDIC. Email: pkupiec@fdic.gov; phone 202-898-6768.
(ASRF) Model of Credit Risk
by
Paul H. Kupiec∗
February 2005
FDIC Center for Financial Research Working Paper No. 2005-04
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.
Key words: economic capital, credit risk internal models, Basel II, Internal Ratings Approach
JEL Classification: G12, G20, G21, G28
CFR research programs: risk measurement, bank regulatory policy
∗ Associate Director, Division of Insurance and Research, Federal Deposit Insurance
Corporation. The views expressed in this paper are those of the author and do not reflect the
views of the FDIC. Email: pkupiec@fdic.gov; phone 202-898-6768.