04.2 heterogeneous debt portfolio

Copyright © 2018 CapitaLogic Limited
This presentation file is prepared in accordance with
Chapter 4 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 4
Heterogeneous
Debt Portfolios

Copyright © 2018 CapitaLogic Limited 2
Declaration
 Copyright © 2018 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),
Director, 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
 Shared equally among all borrowers
 LGD
 Same for all debts
 PD
 Same for all borrowers
 Diversity score
 > 30
 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 4.1

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 4.2

Outline
 Appendices

XCL of heterogeneous portfolio
Default
depen
-dency
Concen
-tration
PD
LGD
EAD
XCL
(+) (+)
(+) (+)
(+)

Structured heterogeneous portfolio
 EAD
 Different for individual debts
 LGD
 PD
 Different for individual borrowers
 NOB
 > 30
 CCC
 Following the structure in the Basel III framework
Example 4.3

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 1,000,000 time
 k k k ku = Normsdist y CCC + z 1 - CCC

Portfolio credit risk measure
 Extreme case loss
Portfolio default losses,
XCL = Percentile
99.9%
 
 
 

Outline
 Appendices

Total heterogeneous portfolio
 EAD
 LGD
 PD
 Different for individual borrowers
 NOB
 > 30
 CCC
 Unobservable or unquantifiable

Lower bound simulation
 Generate a specific standard normal random no. zk
 Map to standard uniform random no. uk
 If uk < PDk, then
 k ku = Normsdist z
Example 4.4

Upper bound simulation
 Generate a systematic standard normal random no. y
 Map to standard uniform random no. U
 If U < PDk, then
 U = Normsdist y
Example 4.5

Portfolio credit risk measure
 Minimum XCL
 When CCC = 0
 Maximum XCL
 When CCC = 1
 Actual XCL in between two extremities

Summary of the XCL calculations (1)
Independent Finite Infinite *
XCL
Simple closed form
solution with
binominal distribution
XCDR with
Closed form solution
with Vasicek default
rate distribution
EAD
Coefficient of variation < 10%
LGD
PD Same credit rating or FICO score category
RM Below one year < 10% and unified to one year
NOB > 30# > 300
CCC Subject to the same CCC formula
Example 4.6

Summary of the XCL calculations (2)
BET Structured* Total
XCL
Simple closed form
solution with
binominal distribution
and diversity score
Single XCL with
Lower and upper bounds
of the XCL with
EAD Coefficient of variation
< 10%LGD
PD
Same credit rating or
FICO score category
RM Below one year < 10% and unified to one year
NOB Diversity score > 30 > 30#
CCC
Captured through
diversity score
CCC formulas in the
Basel III framework
Example 4.7

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

Outline
 Appendices

Corporate bond 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 4.8

Historical simulation (1)
 One series of EAD, LGDk and DRk
 For each year k = 1 to N
 Portfolio credit risk measure
 
k k k
1 to N
Portfolio default loss = EAD × LGD × DR
XCL = Max Portfolio default loss
Example 4.9

 Two series of EADh, LGDh,k and DRh,k
 For each year k = 1 to N
 
k 1 1,k 1,k
2 2,k 2,k
1 to N
Portfolio default loss = EAD × LGD × DR
+ EAD × LGD × DR
Example 4.10

 M series of EADh, LGDh,k and DRh,k
 For each year k = 1 to N
 
M
k h h,k h,k
h=1
1 to N
Portfolio default loss = EAD LGD DR
 
Example 4.11

04.2 heterogeneous debt portfolio

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04.2 heterogeneous debt portfolio