After completing this reading you should be able to:

- Describe external rating scales, the rating process, and the link between ratings and default.
- Describe the impact of time horizon, economic cycle, industry, and geography on external ratings.
- Define and use the hazard rate to calculate unconditional default probability of a credit asset.
- Define recovery rate and calculate the expected loss from a loan.
- Explain and compare the through-the-cycle and at-the-point internal ratings approaches.
- Describe alternative methods to credit ratings produced by rating agencies.
- Compare external and internal ratings approaches.
- Describe a ratings transition matrix and explain its uses.
- Explain the potential impact of ratings changes on bond and stock prices.
- Explain historical failures and potential challenges to the use of credit ratings in making investment decisions.

## A Description of External Rating Scales and the Rating Process

An external rating scale is a scale used as an ordinal measure of risk. The highest grade on the scale represents the least risky investments, but as we move down the scale, the amount of risk gradually increases (safety decreases).

An **issue-specific credit rating** conveys information about a specific instrument, such as a zero-coupon bond issued by a corporate entity. An **issuer-specific credit rating,** on the other hand, conveys information about the entity behind an issue. The latter usually incorporates a lot more information about the issuer.

Here are S&P’s and Moody’s credit rating scores for long-term obligations:

successive move down the scale represents an increase in risk. In case of Moody’s ratings **Baa and above** are said to be **investment-grade** while those below this level are said to be **non-investment-grade.**

In the case of S&P’s, ratings **BBB and above** are investment-grade. All the others are non-investment-grade.

### The Rating Process

The process leading up to the issuance of a credit rating follows certain steps. These are:

- A qualitative analysis of the company, including assessments of the quality of management and competitive aspects
- A quantitative analysis of financials such as ratio analysis
- A meeting with the firm’s management
- A meeting of the rating agency committee assigned to rating the firm
- A notification is sent to the rated firm detailing the assigned rating
- A fee is paid to the rating agency.
- The rated firm has a window to appeal the assigned rating or offer new information
- The assigned rating is published

#### Outlooks and watchlists

Apart from the ratings themselves, the rating agencies also provide outlooks which shows the changes likely to be experienced over the medium term.

- A positive outlook indicates that a rating is likely to be raised.
- A negative outlook indicates that a rating is likely to be lowered.
- A stable outlook shows that the rating is stationary.
- A developing outlook is an evolving one in which we can’t tell the direction of the change.

When a rating is placed on a watchlist, it shows that a very small short-term change is expected.

### Rating stability

Rating stability is necessary since ratings are majorly used by bond traders. If the ratings were to change, then the bond traders are required to trade more frequently and, in this case, they are likely to incur a lot of transaction costs.

Rating stability is important because ratings are also used in financial contracts, and if the ratings vary for different bonds, it would be difficult to administer the underlying contracts.

### The Impact of Time Horizon, Economic Cycle, Industry, and Geography on External Ratings

#### Time Horizon:

The probability of default given any rating at the beginning of a cycle increases with the time horizon. Non-investment bonds are the worst hit. Their default probabilities can dramatically increase within a short time.

#### Economic Cycle:

Since ratings are generally produced with an eye on a long-term period, they must take into account any economic/industrial cycle on the horizon. Rating agencies make efforts to incorporate the effects associated with an economic cycle in their ratings. Although this practice is generally valid, it can lead to underestimation or overestimation of default if the predicted economic cycle doesn’t play out exactly as expected. Put precisely, the probability of default can be underestimated if an economic recession occurs, or overestimated if an economic boom occurs. In addition, the default rate of lower-grade bonds is correlated with the economic cycle, while the default rate of high-grade bonds is fairly stable.

#### Industry:

Two firms in different industries – say, banking and manufacturing – could have the same rating, but the probability of default may be higher for one of the firms than for the other. What does that mean? The implication here is that for a given rating category, default rates can vary from industry to industry. However, there’s little evidence to support the notion that geographic location has a similar effect.

### Hazard rates

Consider a firm defaulting in a very short time, that is, \({\delta }{\text t}\).

The task is to answer the question, “What is the conditional probability of a firm defaulting between time t and time t+\({\delta }\)t given that there is no default before time t?” We can denote this by h\({\delta }\)t, where h is the rate at which defaults are happening at time t.

Unconditional default probabilities can be calculated using the hazard rates.

Suppose that h is the average hazard rate between time 0 and time t.

Then, the unconditional probability between time 0 and t is:

$$ 1-\text{exp}\left( -\text{ht} \right) $$

and the survival probability to time t is therefore given by

$$ \text{exp}\left( -\text{ht} \right) $$

and the unconditional probability between time \({\text{t}_1}\) and \({\text{t}_2}\) is given by the expression;

$$ \text{exp}\left( -\text{ht}_1 \right)-\text{exp}\left( -\text{ht}_2 \right) $$

#### Example: Calculating default probabilities given hazard rates

Suppose you have been given a constant hazard of 0.05,

Calculate:

- The probability of default by the end of 2 years.
- The unconditional probability during the 3rd year.

**Solution**

- The probability of default at the end of the \({2}^{\text{nd}}\) year is given by:
$$ \begin{align*} &1-\text{exp}\left( -\text{ht} \right) \\ =&1-\text{exp}\left(-0.05 \times 2\right) = 0.09516 \end{align*} $$

- The unconditional probability during the \({3}^{\text{rd}}\) year.
$$ \text{exp}\left(-0.05 \times 2 \right)-\text{exp}\left(-0.05 \times 3 \right)=0.04413 $$

### Recovery Rates

In the event that a firm runs bankruptcy or defaults, it may pay part of the amount of the total loan to the lender. This amount that is repaid, expressed as a percentage, is known as the recovery rate.

Since the loan is not fully repaid, then we can calculate the expected loss from the loan over a given period of time as;

$$ \begin{align*} \text{Expected loss}&= \text{Probability of defaulty} \times \text{Loss given default} \\ \text{EL} &= \text{PD} \times \text{LGD} \end{align*} $$

But since \(\text{Loss given default}=1-\text{Recovery rate}\)

Then, the expected loss from a loan is also calculated as

$$ \text{Expected loss}= \text{Probability of defaulty} \times \left(1-\text{Recovery Rate} \right) $$

For example, if the recovery rate is 70%, then

$$ \text{Loss given default}=100\%-70\%=30\%. $$

Suppose the debt instrument has a notional value of $100 million, then the expected loss when the loan defaults is $30 million.

### Credit Spreads and Risk Premiums

The interest rate on a given risky bond and the yield on an equivalent risk-free security will always. This extra interest charged over the risk-free rate is known as a credit spread. This extra interest acts as compensation to investors for bearing the risk of default.

From the following image, we can see the spread between the high yield index (risky bonds) and the treasury notes (risk-free rate) over time.

Since the default rates keep fluctuating, giving rise to a non-diversifiable risk, bond investors, in addition to the credit spread, will require a risk premium. Difficulties are also likely to be experienced in selling off the bonds. Since risky bonds sometimes have low liquidity, the investors will demand additional compensation in the form of a liquidity premium.

### The Impact of Ratings Changes on Bond and Stock Prices

#### Bonds:

There’s overwhelming evidence that a rating downgrade triggers a decrease in bond prices. In fact, bond prices sometimes decrease just because there’s a strong possibility of a downgrade. Anxious investors tend to sell bonds whose credit quality is declining.

A rating upgrade triggers an increase in bond prices, although there’s relatively less market evidence to support this conclusion.

Therefore, the underperformance of bonds whose credit quality has been downgraded is more statistically significant compared to the over-performance of bonds recently upgraded.

#### Stocks:

There’s moderate evidence to support the view that a rating downgrade will lead to a stock price decrease. A ratings upgrade, on the other hand, is somewhat likely to trigger an increase in bond prices.

In practice, the relationship between changes in rating and stock prices can be quite complex and will usually be heavily impacted by the reason behind the changes. Furthermore, downgrades tend to have more impact on the stock price compared to upgrades.

### Comparing External and Internal Ratings Approaches

External ratings are produced by independent rating agencies and aim at revealing the financial stability of both lenders and borrowers. For example, Moody’s periodically releases ratings for big banks around the globe. Such ratings are important because banks usually rely on customer deposits and money raised through the issuance of various assets such as bonds to sustain lending. The funds raised this way create a pool of money that is then loaned to borrowers in smaller chunks. Thus, depositors and bond owners use such ratings to assess the riskiness of giving their money to the bank.

Sometimes, however, banks also need their own ratings so as to undertake an independent assessment of the creditworthiness of a specific borrower – either an individual or a corporate. That’s where **internal credit ratings** come in.

In modern times, internal credit ratings are usually developed based on the techniques used to develop external credit ratings. The same indicators are used, albeit with a few adjustments depending on whether the borrower is an individual or a corporate.

One way of carrying out internal rating is by use of a statistical technique known as the Altman’s Z-score.The following ratios need to be provided when using this technique:

- \({\text{X}_1}\) ∶Working capital to total assets
- \({\text{X}_2}\) ∶Retained earnings to total assets
- \({\text{X}_3}\) ∶Earnings before interest and taxes to total assets
- \({\text{X}_4}\) ∶Market value of equity to book value of total liabilities
- \({\text{X}_5}\) ∶Sales to total asset

Using the discriminant analysis, the Z-score is given by:

$$ \text{Z}=1.2{\text{X}_1}+1.4{\text{X}_2}+3.3{\text{X}_3}+0.6{\text{X}_4}+0.999{\text{X}_5}. $$

A Z-score above 3 means that the firm is not likely to default and when the Z-score is below 3, then the firm is likely to default.

Nowadays, machine learning algorithms use more than five input variables as compared to Altman’s Z-score. Also, the functions used in machine learning algorithms can be non-linear.

Some of the factors that have contributed to the increased sophistication of modern internal credit ratings are:

- The ever-growing use of external credit rating agency language in financial markets
- Enforcement of capital requirements such as Basel II

### Alternative to Rating

Apart from the commonly known rating agencies, that is, Moody’s, S&P and Fitch, we have some organizations such as KMV and Kamakura which use some models to come up with default probabilities and hence can then use probabilities to provide important information to clients.

Factors considered includes:

- The amount of debt the firm has in its capital structure.
- The market value of the firm’s equity.
- The volatility of the firm’s equity.

In the underlying model, a company defaults if the value of its debt exceeds the value of its assets.

Suppose v is the value of the asset and d is the value of the debt, the firm defaults when \( {\text{v}} < {\text{d}} \).

The value of the equity, at a future point in time, is:

$$ \text{Equity}= \text{max}\left( \text{v-d},0 \right) $$

This implies that equity in a company is a call option on the assets of the firm with a strike price equal to the face value of the debt. The firm defaults if the option is not exercised.

### Comparing the Through-the-cycle and At-the-point Internal Ratings Approaches

#### At-the-point Internal Ratings:

At-the-point internal ratings, also called **point-in-time ratings**, evaluate the **current situation** of a customer by taking into account both cyclical and permanent effects. As such, they are known to react promptly to changes in the customer’s current financial situation.

At-the-point ratings try to assess the customer’s quantitative financial data (e.g. balance sheet information), qualitative factors (e.g. quality of management), and information about the state of the economic cycle. Using statistical procedures such as scoring models, all that information is transformed into rating categories.

At-the-point internal ratings **are only valid for the short-term or medium term**, and that’s largely because they take into account cyclic information. They are usually valid for a period not exceeding one year.

#### Through-the-cycle Internal Ratings:

Through-the-cycle (ttc) internal ratings try to evaluate the permanent component of default risk. Unlike at-the-point ratings, they are said to be nearly independent of cyclical changes in the creditworthiness of the borrower. They are not affected by credit cycles, i.e. they are through-the-cycle. As a result, they are less volatile than at-the-point ratings and are valid for a much longer period (exceeding one year).

Advantages of ttc ratings include:,

- They are much more stable over time compared to at-the-point ratings
- Because of their low volatility, ttc ratings help financial institutions to better manage customers. Too many rating changes necessitate changes in the way a bank handles a customer, including the products the bank is ready to offer.

One of the **disadvantages** of ttc ratings over at-the-point ratings is that they can at times be too conservative if the stress scenarios used to develop the rating are frequently materially different from the firm’s current condition. If the firm’s current condition is worse than the stress scenarios simulated, then the ratings may be too optimistic. In fact, ttc ratings have very low default prediction in the short-term.

#### Ratings Transition Matrices and Their Uses

A rating transition matrix gives the probability of a firm ending up in a certain rating category at some point in the future, given a specific starting point. The matrix, which is basically a table, uses historical data to show exactly how bonds that begin, say, a 5-year period with an Aa rating, change their rating status from one year to the next. Most matrices show one-year transition probabilities.

Transition matrices demonstrate that the higher the credit rating, the lower the probability of default.

The table below presents an example of a rating transition matrix according to S&P’s rating categories:

$$ \textbf{One−year transition matrix } $$

### Exam tips:

- Each row corresponds to an initial rating
- Each column corresponds to a rating at the end of 1 year. For example, a bond initially rated BB has a 8.84% chance of moving to a B rating by the end of the year.
- The sum of the probabilities of all possible destinations, given an initial rating, is equal to 1 (100%)
- You will need to recall the rules of probability from mathematics to come up with n-year transition probabilities, where n>1.
- Credit ratings are their most stable over a one-year horizon. Stability decreases with longer horizons.

### Building, Calibrating, and Backtesting an Internal Rating System

#### Building:

To build an internal rating system, banks try to replicate the methodology used by rating agency analysts. Such a methodology consists of identifying the most meaningful financial ratios and risk factors. After that, these ratios and factors are assigned weights such that the final rating estimate is close to what a rating agency analyst would come up with. Weights attached to financial ratios or risk factors are either defined qualitatively following consultations with an agency analyst, or extracted using statistical techniques.

#### Calibrating:

Internal ratings have two main uses:

- Assessing the creditworthiness of a customer during the loan application process
- To determine the value of inputs used in the modelling of capital required as per the existing regulations, e.g. Basel II

For these reasons, internal ratings have to be calibrated. This involves establishing a link between the internal rating scale and tables displaying the cumulative probabilities of default. The timeline of such tables must capture all maturities, from, say, 1 year to 30 years. Sometimes, it may be necessary to build different transition matrices that are specific to the asset classes owned by the bank.

#### Backtesting:

Before linking default probabilities to internal ratings, back testing of the current internal rating system is vital. The question is: Just how many years are needed to pull this off?

A historical sample of between 11 and 18 years is considered sufficient to test the validity of ratings.

### Biases that May Affect a Rating System

$$ \begin{array}{l|l} \textbf{Bias} & \textbf{Description} \\ \hline \text{Time horizon bias} & {\text{Using a combination of at-the-point and through-the-cycle} \\ \text{approaches to score a company.}} \\ \hline \text{Information bias} & \text{Assigning rating based on insufficient information} \\ \hline \text{Homogeneity bias} & \text{Inability to maintain consistent rating methods.} \\ \hline \text{Principal-agent bias} & {\text{Rating developers fail to act in the best interest of the} \\ \text{management.}} \\ \hline \text{Backtesting bias} & \text{Incorrectly linking rating systems to default rates.} \\ \hline \text{Distribution bias} & {\text{Modeling the probability of a default using an inappropriate } \\ \text{distribution.}} \\ \hline \text{Scale bias} & {\text{Producing ratings that are not stable with the passage of } \\ \text{time}} \end{array} $$

### Questions

#### Question 1

You have been given the following one-year transition matrix:

$$ \begin{array}{c|cccc} \textbf{Rating From} & \textbf{Rating To} & {} & {} & {} \\ \hline {} & \text{A} &\text{B} & \text{CCC} & \text{Default} \\ \hline \text{A} & {80\%} & {10\%} & {10\%} & {0\%} \\ \hline \text{B} & {5\%} & {85\%} & {5\%} & {5\%} \\ \hline \text{CCC} & {0\%} & {10\%} & {70\%} & {20\%} \end{array} $$

Determine the probability that a B –rated firm will default over a two-year period.

- 5%
- 4.25%
- 1%
- 10.25%

The correct answer is **D.**

Required probability = Sum of probabilities of all possible paths that could lead to a rating of D (default) after two years.

In other words, in how many ways can a B-rated firm default over a two-year period? The following are the possible paths:

$$ \begin{array}{c|c} \textbf{Path} & \textbf{Probability} \\ \hline \textbf{B} \text{→ default} & {0.05} \\ \hline \textbf{B} \text{→ B → default} & \text{0.85 x 0.05= 0.0425} \\ \hline \textbf{B} \text{→ CCC → default} & \text{0.05 x 0.20= 0.01} \\ \hline \textbf{Total} & {0.1025} \end{array} $$

#### Question 2

ABC Co., currently rated BBB, has an outstanding bond trading in the market. Suppose the company is upgraded to A. What will be the most likely effect on the bond’s price?

- Positive and stronger than the negative effect triggered by a bond downgrade
- Negative and stronger than the positive effect triggered by a bond downgrade
- Positive and weaker than the negative effect triggered by a bond downgrade
- Positive and as strong as the negative effect triggered by a bond downgrade

The correct answer is **C.**

Rating downgrades tend to have more impact on the stock price compared to upgrades. This can be explained by the fact that firms tend to release good news a lot more often than bad news, and thus the expectations among investors are generally positive. Negative news is usually unexpected and unanticipated, triggering a stronger downward effect.