Heterogeneous Debt Portfolios

Copyright © 2016 CapitaLogic Limited
This presentation file is prepared in accordance with
Chapter 8 of the text book
“Managing Credit Risk Under The Basel III Framework, 3rd ed”
Website : https://sites.google.com/site/crmbasel
E-mail : crmbasel@gmail.com
Chapter 8
Heterogeneous
Debt Portfolios

Copyright © 2016 CapitaLogic Limited 2
Declaration
Copyright © 2016 CapitaLogic Limited.
All rights reserved. No part of this presentation file may be
reproduced, in any form or by any means, without written
permission from CapitaLogic Limited.
Authored by Dr. LAM Yat-fai (林日辉林日辉林日辉林日辉),
Principal, Structured Products Analytics, CapitaLogic Limited,
Adjunct Professor of Finance, City University of Hong Kong,
Doctor of Business Administration,
CFA, CAIA, CAMS, FRM, PRM.

Heterogeneous debt portfolios
No uniform solution
Relaxation of some assumptions in
homogeneous portfolios
Higher model error
Industry practices dominate academic theories
Monte Carlo simulation as the primarily
feasible approach

Outline
Moody’s binominal expansion technique
Structured heterogeneous portfolio
Total heterogeneous portfolio
Appendices

Moody’s BET portfolio
Portfolio EAD
EAD same for all debts
EAD × NOB
LGD
Same for all debts
PD
Same for all borrowers
RM
Unified to one year
Diversity score
> 10
Default dependency
Exists between two borrowers in the same industry
Does not exist between two borrowers in two different industries

Diversification effect
No. of borrowers
NOB ↑ => Portfolio credit risk ↓
NOB ↓ => Portfolio credit risk ↑
Default dependency
CCC ↑ => Portfolio credit risk ↑
CCC ↓ => Portfolio credit risk ↓

Credit risk equivalent
alternative portfolio
CCC ↓ => Portfolio credit risk ↓
NOB↓ => Portfolio credit risk ↑
CCC → 0
NOB ?

No. of borrowers
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

Diversity score
Diversity score
Column number
= Row number - 1 +
Row number

Diversity score
1 2 3 4 5 6 7 8 9 10
1 1.00
2 1.50 2.00
3 2.33 2.67 3.00
4 3.25 3.50 3.75 4.00
5 4.20 4.40 4.60 4.80 5.00
6 5.17 5.33 5.50 5.67 5.83 6.00
7 6.14 6.29 6.43 6.57 6.71 6.86 7.00
8 7.13 7.25 7.38 7.50 7.63 7.75 7.88 8.00
9 8.11 8.22 8.33 8.44 8.56 8.67 8.78 8.89 9.00
10 9.10 9.20 9.30 9.40 9.50 9.60 9.70 9.80 9.90 10
Example 8.1

Moody’s industry classification (1)
Aerospace and defense
Automotive
Banking
Beverage, food, and tobacco
Capital equipment
Chemicals, plastics and rubber
Construction and building
Consumer goods: durable
Consumer goods: non-durable
Containers, packaging and glass
Energy: electricity
Energy: oil and gas
Environmental industries
FI, retail: finance
FI, retail: insurance
FI, retail: real estate
Forest products and paper
Healthcare and pharmaceuticals
High technology industries
Hotel, gaming and leisure

Moody’s industry classification (2)
Media: advertising,
printing and publishing
Media: broadcasting and
subscription
Media: diversified and
production
Metals and mining
Retail
Services: business
Services: consumer
Government and public
finance
Telecommunications
Transportation: cargo
Transportation: consumer
Utilities: electric
Utilities: oil and gas
Utilities: water
Wholesale

Portfolio diversity score
Each borrower is classified into 1 of 35
industries
For each industry, a diversity score is looked
up according to the NOB
Portfolio diversity score
= Sum of diversity scores of individual
industries
Example 8.2

Outline
Appendices

EAD
Different for individual debts
LGD
PD
Different for individual borrowers
RM
Unified to one year
NOB
> 30
CCC
Following the structure in the Basel III framework
Example 8.3

Worst case loss of
heterogeneous portfolio
Default
depen
-dency
Concen
-tration
PD
LGD
EAD
WCL
(+) (+)
(+) (+)
(+)

Monte Carlo simulation
Generate a systematic standard normal random no. y
For each borrower k (k = 1 to NOB)
Generate a specific standard normal random no. zk
Map to standard uniform random no. uk
If uk < PDk, then
borrower k defaults
default loss of debt k = EADk × LGDk
Portfolio default loss = Sum of all default losses
Repeat the above steps for 10,000 time
( )k k k ku = Normsdist y CCC + z 1 - CCC

Portfolio credit risk measure
Worst case loss
Portfolio default losses,
WCL = Percentile
99.9%
 
 
 

Outline
Appendices

EAD
LGD
PD
Different for individual borrowers
RM
Unified to one year
NOB
> 30
CCC
Unobservable or not quantifiable

Lower bound simulation
Generate a specific standard normal random no. zk
Map to standard uniform random no. uk
If uk < PDk, then
borrower k defaults
( )k ku = Normsdist z
Example 8.4

Upper bound simulation
Generate a systematic standard normal random no. y
Map to standard uniform random no. U
If U < PDk, then
borrower k defaults
( )U = Normsdist y
Example 8.5

Minimum WCL
When CCC = 0
Maximum WCL
When CCC = 1
Actual WCL in between two boundaries

Summary of the WCL calculations (1)
Independent Finite Infinite *
WCL
Simple closed form
solution with
binominal distribution
WCDR with
Closed form solution
with Vasicek default
rate distribution
EAD
Coefficient of variation < 5%
LGD
PD Same credit rating or group of FICO score
RM Reasonably unified to1 year
NOB > 10# > 300
CCC Subject to the same CCC formula
Example 8.6

Summary of the WCL calculations (2)
BET Structured* Total
WCL
Simple closed form
solution with
binominal distribution
and diversity score
Single WCL with
Lower and upper bounds
of the WCL with
EAD Coefficient of variation
< 5%LGD
PD
Same credit rating or
group of FICO score
RM Reasonably unified to1 year
NOB Diversity score > 10# > 30#
CCC
Captured through
diversity score
CCC formulas in the
Basel III framework
Example 8.7

Remarks
* The best industry practices
# The WCL is not an economically meaningful credit
risk measure for a homogeneous debt basket with
less than 10 borrowers or a heterogeneous debt
basket with less than 30 different borrowers
Under such situation, credit risk of debts in the small
debt basket could be well measured by the EL and/or
one-year EL on individual basis

Outline
Appendices

CRA portfolio
For corporate bond portfolio
Individual bonds are assigned
Seniority
Credit rating
Relevant and sufficient long history of LGDs
and DRs (e.g. 30 years)
Example 8.8

Historical simulation (1)
One series of EAD, LGDk and DRk
For each year k = 1 to N
( )
k k k
1 to N
Portfolio default loss = EAD × LGD × DR
WCL = Max Portfolio default loss
Example 8.9

Two series of EADh, LGDh,k and DRh,k
( )
k 1 1,k 1,k
2 2,k 2,k
1 to N
Portfolio default loss = EAD × LGD × DR
+ EAD × LGD × DR
Example 8.10

M series of EADh, LGDh,k and DRh,k
( )
M
k h h,k h,k
h=1
1 to N
Portfolio default loss = EAD LGD DR
× ×∑
Example 8.11

Heterogeneous Debt Portfolios

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