Credit risk

The borrower(issuer of debt) failing to make full and timely payments of interest and/or principal.
Credit migrations(信用迁移) which bond issuer’s creditworthiness deteriorates.

Credit risk components

Probability of default (PD，违约概率): is the probability that a counterparty default over a given period of time.
Exposure at default (EAD，敞口): is the expected amount of the bank’s credit exposure at the time of default.
Loss rate/Loss given default(LR/LGD，损失比率):is the portion of the loan’s value which will lose at the time of default.
Loss rate/Loss given default=1−recovery rate(回收率)\text{Loss rate}/\text{Loss given default} = 1 - \text{recovery rate(回收率)}Loss rate/Loss given default=1−recovery rate(回收率)

1. External Ratings

1.1 Rating Agencies

Credit ratings answer the question: "How likely is an entity to default on its obligations? "

Rating agencies are organizations provide independent opinions on credit risk, based on specified criteria.

Issue-specific credit ratings: specific obligations or instruments.
Issuer credit ratings: an issuer’s general creditworthiness.

1.2 Rating Scales

Long-term ratings: The ratings for bonds are termed long-term ratings.

Short-term ratings: The ratings for money-market instruments(货币市场工具) are termed short-term ratings.

1.3 Rating Process

First rated when instrument is issued →\to→ The rating is reviewed periodically.

The rating is based on a mixture of analysis and judgement.

Quantitative factors: financial ratios, etc.
Qualitative factors: governance framework, business fundamentals, etc.

The fee arrangement: the rating agency is paid by the issuer even though the product it provides is used by the purchaser.

Outlooks(评级展望): indicates the most likely direction of the rating over the medium term.

Positive outlook: a rating may be raised.
Negative outlook: a rating may be lowered.
Stable outlook: a rating is not likely to change.
Developing (or evolving) outlook: while the rating may change in the medium term, the agency cannot (as of yet) determine.

Watchlists(观察名单): indicates a relatively short-term change is anticipated (usually within three months).

Positive: a review for a possible upgrade
Negative: a review for a possible downgrade

1.4 Ratings Transition Matrix

Ratings Transition Matrix shows the probability of a bond issuer migrating from one rating category to another during a one-year period.

DDD denotes default
NRNRNR denotes that the issuer was not rated at the end of the year.

One-year rating transitions compiled by S&P:

A AAAAAAAAA rated firm has an 87.5%87.5\%87.5% chance of staying AAAAAAAAA.
A BBBBBB rated firm only has a 76.98%76.98\%76.98% chance of staying BBBBBB.

表格从左向右看，纵坐标是初始评级

	AAA	AA	A	BBB	BB	B	CCC/C	D	NR
AAA	87.5	9.03	0.53	0.05	0.08	0.03	0.05	0	3.17
AA	0.52	86.82	8	0.51	0.05	0.07	0.02	0.02	3.99
A	0.03	1.77	87.79	5.33	0.32	0.13	0.02	0.06	4.55
BBB	0.01	0.1	3.51	85.56	3.79	0.51	0.12	0.18	6.23
BB	0.01	0.03	0.12	4.97	76.98	6.92	0.61	0.72	9.63
B	0	0.03	0.09	0.19	5.15	74.26	4.46	3.76	12.06
CCC/C	0	0	0.13	0.19	0.63	12.91	43.97	26.78	15.39

Example: based on the rating transition matrix, please calculate the two period cumulative probability that an A-rated firm would default.

	A	B	C	D
A	94%	4%	2%	0%
B	4%	88%	6%	2%
C	1%	5%	80%	14%
D	0%	0%	0%	100%

A→D=0%A \to D=0\%A→D=0%
A→A→D=0%A \to A \to D=0\%A→A→D=0%
A→B→D=4%×2%A \to B \to D = 4\%\times 2\%A→B→D=4%×2%
A→C→D=2%×14%A \to C \to D = 2\%\times14\%A→C→D=2%×14%

Two-period cumulative probability is 0%+0%+0.08%+0.28%=0.36%0\%+0\%+0.08\%+0.28\%=0.36\%0%+0%+0.08%+0.28%=0.36%

Ratings momentum phenomenon(评级动量现象):

If we assume rating changes in successive years are independent, we can calculate a transition matrix for n years using the transition matrix for one year.
Actual multi-year: Ratings momentum phenomenon
- If a firm has been downgraded in one year, it is more likely to be downgraded the next year.
- If a firm has been upgraded one year, however, it is more likely to be upgraded the next year.

2. Factors in Credit Ratings

2.1 Time Horizon and Economic Cycle

A firm’s probability of default changes in tandem with economic conditions.

Through-the-cycle ratings capture the average creditworthiness of a firm over a period of several years.

Should not be unduly affected by ups and downs in overall economic conditions.
Consistent with their desire to produce stable ratings, rating agencies produce through-the-cycle estimates.

Point-in-term rating provide the best current estimate of future default probabilities.

2.2 Geographic and Industry

Rating agencies use the same scales to characterize default risk across different industries and different countries.An important question is whether ratings are consistent.

E. G., does a BBB+rating for a firm in a certain industry in California mean the same as a BBB+rating for a firm in different industry in Germany?
It is sometimes difficult to determine whether ratings for non-U. S. Firms are consistent with those of U. S. Firms.

Geographic
Five-year cumulative probabilities for United States, European, and emerging market in 2016 by S&P.

Initial Rating	U.S. Firms	European Firms	Firms in Emerging Markets
AAA	0.42	0	N.A.
AA	0.45	0.21	0
A	0.73	0.29	0.05
BBB	2.05	0.65	2.59
BB	8.38	4.2	6.26
B	19.57	13.86	12.59
CCC/C	51.31	48.01	25.88
Investment Grade	1.17	0.38	1.69
Speculative Grade	17	10.84	10.19
All Rated	7.57	2.54	6.53

European firm: has historically been better than the same rating for a U.S.firm (particularly investment grade ratings).
Emerging markets:
- Firms rated AA and A had a very low five-year default probability.
- Firms rated BBB fared slightly worse than U. S. Firms and much worse compared to European firms.

Industry:

Banks with a given rating show higher default rates than non-financial corporations with the same rating.
There has been less agreement among different rating agencies for banks than for other firms.

2.3 The Impact of Rating Changes on Stock and Bond Price

Whether ratings have information content? Mixed results

Asymmetric reactions(不对称反映):

Downgrades: the stock and bond markets’ reactions to downgrades are significant (particularly from investment grade to non-investment grade).
Upgrades: the market’s reaction to upgrades is much less pronounced.

2.4 Rating Failures of Structured Products in 2007-2008 Crisis

Rating difference of structured products: depends almost entirely on a model.

The rating agencies were quite open about the models they used.
The inputs to their models (particularly the correlations between the defaults on different mortgages) proved to be too optimistic.
Rating agencies were not as independent as they should have been - the reputation suffered as a result.

3. Internal Ratings

3.1 Internal Ratings

Internal Ratings: Banks and other financial institutions develop their own internal rating systems based on their assessment of potential borrowers.

Base internal ratings on several factors: e.g., financial ratios, cash flow projections, and an assessment of the firm’s management.
Banks must back-test(回测) their procedures for calculating

Through-the-cycle ratings are more relevant for relatively long-term lending commitments.

Point-in-time ratings are procyclical (accentuate economic cycles 放大整体经济周期, 亲/顺周期性).

During bad economic conditions:
- Point-in-time PD↑ →\to→ Banks become less inclined to lend →\to→ Economic conditions worsen further
During good economic conditions: vice verse

3.2 Machine Learning Approach

Some banks are currently trying to automate their lending decisions using machine learning.

An algorithm is given a great deal of data on firms and whether they have defaulted.
Come up with a rule for distinguishing between those firms that default from those that do not.

Altman Z-score: discriminant analysis (区分分析)

For publicly traded manufacturing firms, the Z-score was:
Z=1.2X1+1.4X2+3.3X3+0.6X4+0.999X5Z=1.2X_1+1.4X_2+3.3X_3+0.6X_4+0.999X_5Z=1.2X1+1.4X2+3.3X3+0.6X4+0.999X5

X1X_1X1:Woking capital to total assets
X2X_2X2: Retained earning to total assets
X3X_3X3: Earnings before interest and taxes to total assets
X4X_4X4: Market value of equity to book value of total liabilities
X5X_5X5: Sales to total assets
Z−scoreabove3Z-score\; above\;3Z−scoreabove3: the firm was unlikely to default
Z−scorebelow1.8Z-score\; below \;1.8Z−scorebelow1.8: a firm had a very high probability of defaulting

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4.4.1 External and Internal Ratings