01.2 credit risk factors and measures

Copyright © 2018 CapitaLogic Limited
Chapter 1
Credit Risk
Factors and Measures
This presentation file is prepared in accordance with
Chapter 1 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

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.

 Introduction
 Credit risk factors
 Credit risk measures
 A simple loan
 Appendices
Outline

Banking activities
Deposits
< 1%
Shareholders’
equity
Dividend +
equity price
appreciation
3% - 20%
Term loans,
credit cards,
mortgages,
corporate bonds
Bank

Funding source
 Loan
 Private lending placement
 Bond
 A loan transferable among lenders
 Equity
 Media focus in developed countries and China
DEBT

Credit
 Credit
 The idea that a borrower uses other people’s monies in
pursuit of his financial needs
 Spend today but pay tomorrow
 Interest
 To compensate a lender for supplying temporary funds to
a borrower
 Time value of money
 Default of borrower
 Service charge

Time value of money
Bank
My money today
USD 10,000
My money in one year
USD 10,000 + USD 1,200
Principal
+ interest

Default
 A borrower fails to pay to the lender the
interest and/or principal in full on schedule
 Debt collection efforts will then be initiated
by the lender to recover the whole or part of
the principal plus interest

Credit risk
 In this book, credit risk means
 The risk of loss to a lender caused by the default
of a debt intended to be held
 until maturity; or
 for a longer period of time (> 1 year)
 A lender must charge a nominal yield higher
than the risk-free rate to compensate the credit
risk

Credit risk management
Credit risk
management
Credit risk
identification
Credit risk
measurement
Credit risk
monitoring
Credit risk
mitigation

Credit risk factors and measures
Single debt Debt portfolio
EL/
1-year
EL
EAD
LGD
PD
RM XCL
EAD
LGD
PD
Concen
-tration
Default
depend
-ency

Basel Accord
 A hybrid approach consolidates theories and
practices of
 Finance – economic reasoning
 Accounting – rule based
 Statistics – scientific quantification
 Banking operations – industry practices
 Regulatory considerations – views from bank regulators
 Currently the most comprehensive credit risk
management framework with international
recognition
 Scale down version may be applied to other industries

 Introduction
 A simple loan
 Appendices
Outline

Credit risk factors
Credit risk
Default loss
Exposure at default
Default chance
Probability of default
Loss given default Residual maturity

Exposure at default (EAD)
 The amount
 that a borrower owes a lender
 when the borrower defaults
 For many debts
 Term loans, mortgages and corporate bonds
 EAD = Principal + Interest
Example 1.1

Exposure at default
 Revolving loan
 Subject to a credit limit
 Credit card, credit line
 Outstanding debt amount varys over time
 EAD
 <= credit limit
 In general approaching credit limit

Loss given default (LGD)
 Default loss
 The net amount suffered by a lender when a
borrower defaults
 LGD
 The net default loss expressed as a percentage of
the EAD
 Polarized due to collateral arrangement
 With excessive collaterals: 0% to 20%, typical
10%
 Without collaterals: 80% to 100%, typical 90%
Example 1.2

Probability of default (PD)
 The chance that a borrower will default in the
following ONE year
 Credit quality of a borrower
 Forward looking
 Ranging
 from 0% (will surely survive)
 to 100% (will definitely default)
Example 1.3

Residual maturity (RM)
 The remaining time horizon over which a debt
will generate cash flows to a lender
Example 1.4

 Introduction
 A simple loan
 Appendices
Outline

Default loss
 By definition
Default loss
LGD =
EAD
Default loss = EAD × LGD

Default chance
 The chance that a borrower will default during
the remaining lending period RM years
 
 
RM
RM
1 - Default chance = 1 - PD
Default chance = 1 - 1 - PD

Bernoulli distribution
0%
20%
40%
60%
80%
100%
To survive To default

Risk map
Larger loss at
lower chance
Preferred debts
Smaller loss at
higher chance
Default chance →
Copyright © 2018 Dr. LAM Yat-fai
Defaultloss→
24

Expected loss
 The default loss weighted by the default
chance
 For a debt with short to medium RM where
the EAD, LGD and PD can be estimated with
sufficient accuracy
 
RM
Expected loss = Default loss × Default chance
EL = EAD × LGD × 1 - 1 - PD 
 

Convenient approximation to the EL
 For small PD and short RM
 e.g. PD < 3% and RM < 5 years
 A practical situation of most short to medium
term debts in a real bank lending operation
 The EL is approximated conveniently as
 EL ≈ EAD × LGD × PD × RM
 Increase in any credit risk factors will
increase the EL

Expected loss of a single debt
(+)
(+)
EL = EAD × LGD × [1 - (1 - PD)RM]
≈ EAD × LGD × PD × RM
when PD (< 3%) and RM (< 5 years)
are relatively small in real bank lending
(+)
EL/
1-year
EL
EAD
LGD
PD
RM(+)

A debt with longer term RM
 Longer term debt
 Remote maturity day
 Difficult to estimate a set of reliable EAD, LGD, and PD
throughout the remaining life of the debt
 The lender will review and control the credit risk
at the end of the following ONE year
 The economic risk horizon is one year
 The RM is set artificially to one year

One-year expected loss
 For a debt with the RM < 1
 No credit risk review and control during its life
 1-year EL = EL
 The EL in one year
   
 
 
1 RM
RM
1-year EL
= EAD × LGD × Min 1 - 1 - PD , 1 - 1 - PD
= EAD × LGD × Min PD , 1 - 1 - PD
EAD × LGD × PD × Min 1, RM
 
 
 
 

Example 1.5

A debt with no fixed RM
 Revolving loan
 On-going drawdown transactions
 On-going re-payment transactions
 No fixed maturity day
 The lender will review and control the credit risk
at the end of the following ONE year
 The economic risk horizon is one year
 The RM is set artificially to one year

One-year expected loss
 The EL in one year

 Three credit risk factors only
 EAD, LGD and PD
   
 
1
1-year EL
= EAD × LGD × Min 1 - 1 - PD , 1 - 1 - PD
= EAD × LGD × Min PD , 1 - 1 - PD
= EAD × LGD × PD


 
 
 
 

Which credit risk measure
should be used?
Residual maturity Credit risk measure
Short to medium term only EL
Longer term only 1-year EL
No fixed maturity only 1-year EL
Short term, medium term
longer term and
no fixed maturity
1-year EL = EL
for short term debts
1-year EL = EL in one year
for debts with the RM > 1 year

 Introduction
 A simple loan
 Appendices
Outline

A simple loan
 EAD USD 10,000
 LGD 90%
 PD 3%
 RM 3 years
 Default loss 8,000
 Default chance 8.7327%
 EL USD 786
 1-year EL USD 270
Example 1.6

A simple loan
 Functional purpose
 Borrower
 Needs immediate cash
 Lender
 With spare cash for three
years
 To seek an excess return
over the risk-free rate
 Cash flows
 Out
 Principal at origination
 In
 Principal at maturity
 Interest at maturity
 Default
 Principal and/or interest not
paid in full on schedule
 Debt collection
100
?
Loan

 Introduction
 A simple loan
 Appendices
Outline

Standard normal distribution
 Distribution
 Thick middle
 Thin tails
 Symmetric
 Mean 0
 Standard deviation 1
 Density
 Value of the curve
 Cumulate
 Area to the left of x
x
 x
 Φ x

Standard normal distribution functions
 Cumulative standard normal distribution function
 Inverse cumulative standard normal distribution function
 
   
 
     
-1
2
x
-
2
x
-1
-
Φ
1 τ
Φ x = exp - dτ
22π
= Normsdist x 0,1
1 τ
x = exp - dτ
22π
= NormsΦ inv x - ,+x


 
 
 
 
 
 
 


Example 1.7

Probit
   
   
2
Probit
-
1 τ
PD = exp - dτ
22π
PD = Normsdist Probit 0,1
Probit = Normsinv PD - ,+

 
 
 
 


PD vs Probit
0%
20%
40%
60%
80%
100%
-5 -4 -3 -2 -1 0 1 2 3 4 5
Probit = Normsinv(PD)
PD=Normsdist(Probit)

Credit risk measurements of debts vs
market risk measurements of equities
Credit risk of debts
 1-year EL rate = LGD × PD
 EAD
 Bernoulli distribution
 PD
 Copula correlation coefficient
 1-year 99.9% XCL
Market risk of equities
 Expected return
 Equity value
 Normal distribution
 Standard deviation
 Beta
 10-day 99% VaR

01.2 credit risk factors and measures

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