Credit risk management

1. Managing Credit Risk Under The Basel III Framework 255
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Internal Ratings Based Approach
18
KEY CONCEPTS
• Retail IRB approach
• Advanced IRB approach
• Foundation IRB approach
• Credit risk mitigation
• Industry implementation
18 Internal ratings based approach
18.1 Theory of the IRB approach ★★★★★★★★★★★★
Under the Basel III framework, subject to the approval from its regulator, a bank with
sufficient quantitative expertise may adopt a more sophisticated methodology, referred to
as the internal ratings based (“IRB”) approach, to calculate the credit provision and
capital charge of credit risk for its debt investments.
The IRB approach assumes that a bank holds a well diversified debt portfolio comprising
a large number of debts with smaller EADs from many debt issuers. In general, this
assumption is representative for describing the debt investments of an internationally
active bank. Under this assumption, the bank’s debt investments can be well
approximated by an infinite homogeneous debt portfolio.
When the RMs of the debt investments are unified to one year,
Portfolio XCL = Portfolio EAD × LGD × XCDR
Portfolio 1-year EL = Portfolio EAD × LGD × PD
Portfolio UL = Portfolio XCL - Portfolio 1-year EL
For each debt k, define:
k k k k
k k k k
k k k
XCL = EAD × LGD × XCDR
1-year EL = EAD × LGD × PD
UL = XCL - 1-year EL
Under these definitions, the XCDRk, XCLk and ULk follow a pure mathematical
treatment without any economic meaning.
If there are NOB individual debts, then:
NOB
k
k=1
EAD = Portfolio EAD∑

2. 256 Managing Credit Risk Under The Basel III Framework
Copyright 2018 CapitaLogic Limited
k
k
k
LGD LGD
XCDR XCDR
PD PD
≈
≈
≈
The portfolio UL can be well approximated as:
( )
NOB NOB
k k
k=1 k=1
NOB
k
k=1
Portfolio UL = Portfolio XCL - Portfolio 1-year EL
= Portfolio EAD × LGD × XCDR - Portfolio EAD × LGD × PD
= EAD × LGD × XCDR - EAD × LGD × PD
= EAD × LGD × XCDR - EAD
   
   
   
∑ ∑
∑ ( )
( ) ( )
( )
NOB
k
k=1
NOB NOB
k k k k k k
k=1 k=1
NOB
k k
k=1
NOB
k
k=1
× LGD × PD
EAD × LGD × XCDR - EAD × LGD × PD
= XCL - 1-year EL
= UL
≈
∑
∑ ∑
∑
∑
This relationship suggests that the portfolio UL is approximately equal to the sum of the
ULs of individual debts. When each debt is treated as a hypothetical infinite
homogeneous portfolio, a XCL is calculated and divided into the 1-year EL and UL. In
most situations, the 1-year EL is assigned as the credit provision of the debt. The sum of
all credit provisions for individual debts then becomes the total credit provision of the
bank’s debt investments and is treated as the bank’s unrealized loss. The UL, after taking
into account the characteristics of various debts, including loan type, issuer type, firm
size and the RM, is further scaled up by a safety factor to arrive at a capital charge. The
sum of all capital charges for individual debts then becomes the total capital charge of the
bank’s debt investments and is matched by the bank’s regulatory capital.
In summary,
Single debt Hypothetical infinite homogeneous portfolio
XCL = EAD × LGD × XCDR
1-year EL = EAD × LGD × PD
UL = XCL - 1-year EL
Credit provision = 1-year EL
Capital charge = UL × Safety factor
⇔