Credit Risk
Nicolas Beudin
& Maxime Riche
Agenda
1.
•Overview
2.
•Valuation
3.
•Dealing with credit risk
4.
•Conclusion
5.
•Appendix
2
Overview
4
Definition
Borrower
Credit
Risk
Lender
Players
Households
Financial Institutions
• Insurance companies, asset management firms, investments
banks, depository institutions…
Governments
Corporates
Non-profit organizations
5
Corporate bonds
Public utilities
• Electricity, gas, water…
Transportations
• Roads, trucks, airlines…
Financial Institutions
• Banks, insurances, brokerages…
Industrials
6
7
Corporate bonds
Bond indentures
Maturity
Security
Provisions
for
retirement
Valuation
9
Valuation
Historical
Stats
Ratings
• Moody’s
• S&P
• Fitch
Models
• Merton
(Black &
Scholes)
Value
• Probability
of default
• Recovery
rate
10
Bonds Safety
Coverage ratios:
EBIT/Interest
Cash flow to debt:
Free cash
flow/Total debt
Financial key ratios
Profitability ratio:
Return on Capital
Leverage ratio:
Total Debt/Capital
11
Rating Classes
Rating
Category
Coverage
Ratio
Cash Flow Return on LT Debt to
to Debt % Capital % Capital %
AAA
17.5
55.4
28.2
15.2
AA
10.8
24.6
22.9
26.4
A
6.8
15.6
19.9
32.5
BBB
3.9
6.6
14.0
41.0
BB
2.3
1.9
11.7
55.8
B
1.0
(4.6)
7.2
70.7
Source: Bodies, Kane, Marcus 2002 Table 14.3
12
Credit Spreads
Spread = Cost of borrowing – Risk-free rate
Reuters Corporate Spreads for Industrial
January 2004
http://bondchannel.bridge.com/publicspreads.cgi?Industrial
600
B
500
400
Spread
B
300
B
B
B
B
B
BB
BB
BB
200
BB
BB
BB
BB
100
BBB
BBB
BBB
BBB
A
AA
AAA
A
AA
AAA
A
AA
AAA
0
BBB
BBB
A
A A
AA AA
AA AAA AAA
AAA
0
5
10
BBB
A
AA
AAA
15
Maturity
20
25
30
Dealing with credit risk
14
Dealing with CR?
Try to mitigate it
(at the source)
Collateralisation
with assets
Guarantees
Covenants
Price it
Various models
Hedge it / Share
it
Securitization
Insurance
15
Dealing with CR?
Types of Credit
Derivatives
Structured
Credit
Credit Default
Swaps (CDS)
Collateralized
Debt Obligations
(CDOs)
Credit Spread
Options &
Forwards, TRS...
ABS, MBS, CLOs,
CMOs...
16
CDS Structure
Spread = xx bps per
year
Default
Protection
Buyer, A
Default
Protection
Seller, B
Payoff if there is
default by reference
entity
Source : Fundamentals of Options and Futures, J. Hull
17
CDO
Tranche 1
1st 5% of loss
Yield = 35%
Bond 1
Bond 2
Bond 3

Bond n
Average Yield
8.5%
Trust
Tranche 2
2nd 10% of loss
Yield = 15%
Tranche 3
3rd 10% of loss
Yield = 7.5%
Tranche 4
Residual loss
Yield = 6%
Source : Fundamentals of Options and Futures, J. Hull
Conclusion
Conclusion
Credit risk has become a key
concern
Financial engineering
Reduce the risk or spread it ?
19
Thank you !
20
Appendix
22
Merton model
• Idea to use OPM to price credit risk
D Market value of debt
E Market value of equity
F
Loss given
default
Bankruptcy
F
Face value
of debt
V
Market
value of
company
F
Face value
of debt
V
Market
value of
company
Toward Black Scholes formulas
Value
Increase the
number to time
steps for a fixed
maturity
The probability distribution of
the firm value at maturity is
lognormal
Bankruptcy
Today
Maturity
Time
23
24
Valuation
Value of a risky debt :
Credit spread :


h
D0risky  F  Pdef
LGD h e   rf  crp T
cs  y  rf
1  D0risky 
y   ln 

T  F 
Using Black & Scholes :
De
 rT 
Discount
factor
1  N (d1 ) 
]
F  [1  N (d 2 )]  [ F  Ve
1  N (d 2 ) 

rT
Face
Value
Probability
of default
Loss if no
recovery
Expected Amount of
recovery given default
Expected loss given default
25
Example
Data
Market value unlevered company
€ 100,000
Debt = 2-year zero coupon Face value € 60,000
Risk-free interest rate
Volatility unlevered company
5%
30%
Using Black-Scholes formula
Market value unlevered company € 100,000
Market value of equity
€ 46,626
Market value of debt
€ 53,374
Discount factor
N(d1)
N(d2)
0.9070
0.9501
0.8891
Using Black-Scholes formula
Value of risk-free debt € 60,000 x
0.9070 = 54,422
Probability of default
N(-d2) = 1-N(d2) = 0.1109
Expected recovery given default
V erT N(-d1)/N(-d2)
= (100,000 / 0.9070) (0.05/0.11)
= 49,585
Expected recovery rate | default
= 49,585 / 60,000 = 82.64%
References
Fabozzi, F. J., & Modigliani, F. (2009). Capital Markets Institutions and Instruments.
Pearson International Edition.
Hull, J. C. (2008). Fundamentals of Futures and Options Markets. Pearson
International Edition.
Pirotte, H. (2010). Course of Advanced Finance. Risky Debt . Brussels: Solvay
Brussels School of Economics and Management.
Bodies, Kane, Marcus 2002 Table 14.3
http://www.bondchannel.bridge.com
http://www.paulfellcartoons.com
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