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Credit Risk Analysis
The deviations from the mean11

Measuring credit risk
Credit risk diversification
A portfolio of loans is less risky than single loans
The most important feature of credit risk management is the ability to
diversify across defaults

Measuring credit risk
Question (1)13

Measuring credit risk
Question (2)14

Measuring actuarial default risk15

Credit event
Credit event
A credit event is a discrete state
Either it happens or not
Definition of ISDA
Failure to pay
Obligation/cross default
Obligation/cross acceleration
Currency inconvertibility
Governmental action

Credit event

Default Rates
Credit ratings
The rating is an “evaluation of
creditworthiness” issued by a
rating agency
represent actuarial probabilities
of default
Moody’s definition
an opinion of the future ability,
legal obligation, and willingness
of a bond issuer or other obligor
to make full and timely
payments on principal and
interest due to investors
Credit ratings (1)18

Default Rates
Accounting ratios
Cash flow coverage
Z-score model
Working capital over total assets
Retained earnings over total assets
EBIT over total assets
Market value of equity over total
Net sales over total assets
Credit ratings (2)
0.4 0.9 114 CCC
1.2 1.9 76 B
2.5 3.5 54 BB
4.7 6.5 43 BBB
8.0 10.2 38 A
19.5 24.6 28 AA
23.8 25.5 12 AAA
Cash flow coverage leverage19

Credit ratings
Question (1)20

Credit ratings
Question (2)21

Default Rates
How to understand the historical default rate ?
The proportion of firms that default, which is a statistical estimate of the
true default probability
Historical default rate
Higher ratings are associated with lower default rates
For an initial credit rating, credit risk increases sharply with the horizon
For investment-grade credits, the increase is more than proportional with
the horizon
For speculative-grade credits, the increase is less than proportional with
the horizon
Low sample size
In non-U.S. markets
When the true p is changing over time
Historical default rate

Cumulative and Marginal default rates
Sequential default process
We define
is the number of issuers rated R at the end of year that
default in T= t + N
is the number of issuers rated R at the end of year that
have not defaulted by the beginning of year t + N
Default process (1)
[|()] nt N Rt +
[ | ()] mt N Rt +23

Cumulative and Marginal default rates
Five important rates
Marginal Default Rate during Year T
Survival Rate
Marginal Default Rate from Start to Year T
Cumulative Default Rate
Average Default Rate

Why use the market prices
Infer credit risk from corporate bond prices
Infer credit risk from equity prices

Why use the market prices35

Why use market prices
Credit risk ratings
External ratings focus on forecasting credit losses from historical default
rates and recovery rates
Market prices method
Credit risk can be measured by market price of securities whose value are
affected by default
These securities include corporate bond, equity, and other derivatives
Market price method can provide more up-to-date and accurate measures
of credit risk, because financial markets have access to a large amount of
External rating and market price36

Infer credit risk from bond prices38
Spreads and credit risk
Default bond
Consider a bond which makes only one payment of $100 in one period, its
market price is , we can get the market-determined yield
This bond also can be describe as a simple default process
Using risk neutral pricing, we get
Default bond pricing