Credit risk

1. Managing Credit Risk Under The Basel III Framework 55
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Heterogeneous Debt Portfolios
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KEY CONCEPTS
• Moody’s binominal expansion technique
• Monte Carlo simulation
• Structured heterogeneous portfolio
• Total heterogeneous portfolio
4 Heterogeneous debt portfolios
4.1 Heterogeneous portfolio ★★★★★★★★★★★★
A debt portfolio that is not homogeneous may be modelled as a heterogeneous portfolio
which is characterized by the following properties:
• Debts in the portfolio (i) have various EADs and LGDs; and (ii) are lent to many
borrowers with various PDs;
• Several debts lent to a single borrower are combined into one consolidated debt with
the EAD equal to the sum of all component EADs and the LGD equal to the EAD
weighted average of the component LGDs;
• The lender who invests in debts with maturity longer than one year or without fixed
maturity will review and control the credit risk of the debts at the end of the following
one year;
• The lender who invests in debts with maturity shorter than one year will re-invest the
proceeds at maturity in similar debts up to one year;
• The debts with maturity shorter than one year accounts for the minority of the
portfolio, e.g., below 10 percent;
• The NOB in the portfolio is sufficiently large, e.g., equal to or more than 30;7
and
• The default dependency among borrowers is not unified or unknown.
Due to the heterogeneity of the debt portfolio, there is no uniform solution to calculate
the credit risk of a heterogeneous portfolio. Instead, partial solutions are developed by
relaxing some of the constraints to a homogeneous portfolio. As such, the model error is
relatively large since the theory underlying the heterogeneous portfolio is less developed.
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It is straight forward for a lender to manage his debt investments on an individual debt basis when the
total number of debts in a basket is small, e.g., less than 30.

2. 56 Managing Credit Risk Under The Basel III Framework
Copyright 2018 CapitaLogic Limited
Figure 4.1 The XCL vs five credit risk factors
4.2 Moody’s binominal expansion technique
Moody’s adopted the binominal expansion technique (“BET”) in the middle nineties to
calculate the credit risk of a corporate debt portfolio by relaxing the assumption of total
default independency among borrowers in an independent homogeneous portfolio.
Under the BET, default dependency is assumed to exist only among corporate borrowers
in the same industry. For two corporate borrowers in two different industries, it is
assumed that there is no default dependency. Furthermore, the BET recognizes that
within the same industry, the diversification effect increases with increasing NOB but
decreases with increasing default dependency. Therefore, if the default dependency is
suppressed completely, an alternative debt portfolio with the same diversification effect
can be constructed by reducing the NOB to a smaller number, referred to as the diversity
score.
1 2 3 4 5 6 7 8 9 10
1 1
2 2 3
3 4 5 6
4 7 8 9 10
5 11 12 13 14 15
6 16 17 18 19 20 21
7 22 23 24 25 26 27 28
8 29 30 31 32 33 34 35 36
9 37 38 39 40 41 42 43 44 45
10 46 47 48 49 50 51 52 53 54 55
Table 4.1 Triangular NOB grid