Introduction

• Rating agencies are an important external source of credit risk data. The most well-known credit rating agencies are Moody’s, Standard and Poor’s (S&P), and Fitch. There are also many smaller rating agencies throughout the world.
• These agencies provide independent opinions on credit risk, based on specified criteria. Traditionally, their main business was to rate bonds and money market instruments issued by corporations and governments. Rating agencies have been doing this for more than 100 years and their track record has generally been quite good.
• One notable exception is the case of structured products. It is considered that rating agencies contributed to the 2007-2008 crisis by giving excessively high ratings to many structured subprime products that subsequently defaulted.
• The role of rating agencies in the credit crisis has had several consequences in the US –
  • The Dodd-Frank Act now requires rating agencies to make the assumptions and methodologies underlying their ratings more transparent.
  • It has increased the potential legal liability of rating agencies.
  • The Office of Credit Ratings was created at the Securities and Exchange Commission to provide oversight of rating agencies.
• The reputations of rating agencies have suffered since the crisis because of their poor performance in rating structured products. However, their performance in rating bonds and money market instruments has been generally good, and many risk managers still rely on these ratings.
• Today, the Basel Committee uses credit ratings when determining credit risk capital for banks. Since the 2007–2008 crisis, however, the United States has indicated it does not want to do this (presumably because it no longer trusts the ratings). For some capital determinations, two alternative calculations have been specified by the Basel Committee: one for countries that are prepared to use external ratings, and one for countries that are not.

Rating Scales – Long-Term Ratings

• Credit ratings are designed to answer the question: “How likely is an entity to default on its obligations?” A bond rating can depend on various factors (e.g., collateral, the term of the instrument, and so on), but often an agency will give all instruments issued by an entity the same rating. As a result, bond ratings are often assumed to be attributes of the entity.
• The ratings for bonds are termed as long-term ratings. The highest bond rating assigned by Moody’s is 𝐴𝑎𝑎 and 𝐴𝐴𝐴 by S&P. Bonds with this rating are considered to have almost no chance of defaulting. The next highest rating is 𝐴𝑎 by Fitch and 𝐴𝐴 by S&P. After that, the following ratings (in decreasing order) are 𝐴, 𝐵𝑎𝑎, 𝐵𝑎, 𝐵, 𝐶𝑎𝑎, 𝐶𝑎, and 𝐶 by Fitch and 𝐴, 𝐵𝐵𝐵, 𝐵𝐵, 𝐵, 𝐶𝐶𝐶, 𝐶𝐶, and 𝐶 by S&P. The rating of 𝐷 is used for firms already in default.
• Modifiers are used to create finer rating measures. For example, Moody’s divides the 𝐴𝑎 rating category into 𝐴𝑎1, 𝐴𝑎2, and 𝐴𝑎3. Similarly, S&P divides its 𝐴𝐴 rating category into 𝐴𝐴+, 𝐴𝐴, and 𝐴𝐴−. Moody’s 𝐴𝑎𝑎 and S&P’s 𝐴𝐴𝐴 ratings are not subdivided, nor usually are their two lowest rating categories. Fitch’s rating categories are like those of S&P. Instruments with ratings of 𝐵𝐵𝐵 (𝐵𝑎𝑎3) or above are considered investment grade. Those with ratings below 𝐵𝐵𝐵− (𝐵𝑎𝑎3) are termed non-investment grade, speculative grade, or junk bonds.
• The rating agencies have different ways of rating money market instruments. Ratings for money-market instruments are termed short-term ratings. Moody’s uses 𝑃-1, 𝑃-2, and 𝑃-3 as its three prime rating categories.
  • Instruments rated 𝑃-1 have a superior ability to repay short-term obligations,
  • Instruments rated 𝑃-2 have a strong ability to repay short-term obligations, and
  • Instruments rated 𝑃-3 have an acceptable ability to repay short-term obligations.

  These can be thought of as the investment grade ratings. The rating 𝑁𝑃 denotes non-prime and can be thought of as a noninvestment grade rating.

• The S&P rating category corresponding to 𝑃-1 is divided into two: A-1+ and A-1. The categories equivalent 𝑃-2 and 𝑃-3 are A-2 and A -3 (respectively). S&P has three lower rating categories: 𝐵, 𝐶, and 𝐷. Fitch subdivides its ratings in a similar way to S&P, with its ratings being 𝐹1+, 𝐹1, 𝐹2, 𝐹3, 𝐵, 𝐶, and 𝐷.

Historical Performance

• One way of testing the performance of certain rating is to look at how firms with a specific rating subsequently performed. This table exhibits a small data set out of the cumulative average default rates produced by S&P for bonds within the period of 1981 to 2016. It shows the probability that an issuer with a certain rating will default within one year, within two years, and so on.
• The probability of a bond defaulting during a future year (unconditional default probability) can be calculated by subtracting successive numbers in this able. For example, the probability of a B-rated bond defaulting during the fifth year is 18.32%−15.87%=2.45%
  Similarly, the probability of default of all bonds defaulting during any year can be calculated. The results of these calculations are shown in the table in the next page. These probabilities in this table are known as unconditional probabilities.

  	1	2	3	4	5	6
  AAA	0.00	0.03	0.13	0.24	0.35	0.46
  AA	0.02	0.06	0.13	0.23	0.33	0.44
  A	0.06	0.15	0.25	0.38	0.53	0.69
  BBB	0.18	0.51	0.88	1.33	1.78	2.24
  BB	0.72	2.24	4.02	5.80	7.45	8.97
  B	3.76	8.56	12.66	15.87	18.32	20.32
  CCC/C	26.78	35.88	40.96	44.06	46.42	47.38

• Another way of expressing the probability of default during a given year is as a conditional default probability. In this case, we are asking the question; “If the firm survives to the end of year n, what is the probability that it will default during year 𝑛+1 ?”
  

  	1	2	3	4	5	6
  AAA	0.00	0.03	0.10	0.11	0.11	0.11
  AA	0.02	0.04	0.07	0.10	0.10	0.11
  A	0.06	0.09	0.10	0.13	0.15	0.16
  BBB	0.18	0.33	0.37	0.45	0.46	0.47
  BB	0.72	1.52	1.78	1.78	1.65	1.52
  B	3.76	4.80	4.10	3.21	2.45	2.00
  CCC/C	26.78	9.10	5.08	3.10	2.36	0.96

• Consider again the probability a bond rated B will default during the fifth year. The probability it will survive to the end of the fourth year is 84.13%(=100%−15.87%) based the probabilities from the table in the previous page. The unconditional probability that the bond will default during the fifth year has already been calculated above as 2.45% (or 0.0245). The probability that it will default during the fifth year, conditional on no earlier default, is therefore 2.91%(=0.0245/0.8413). The following table shows the results of these conditional default probability calculations for all rating categories and all future years.
• For the investment grade bonds, the probability of default per year is an increasing function of time for the first four years. This is because the chance that its financial health will decline increases as time passes. By the fourth year, however, its business environment and financial condition may have changed and can lead to a decrease in default probability.
  

  	1	2	3	4	5	6
  AAA	0.00	0.03	0.10	0.11	0.11	0.11
  AA	0.02	0.04	0.07	0.10	0.10	0.11
  A	0.06	0.09	0.10	0.13	0.15	0.16
  BBB	0.18	0.33	0.37	0.45	0.46	0.47
  BB	0.72	1.53	1.82	1.85	1.75	1.64
  B	3.76	4.99	4.48	3.68	2.91	2.45
  CCC/C	26.78	12.43	7.92	5.25	4.22	1.79

• For the 𝐶𝐶𝐶/𝐶 bonds, the probability of default per year is a decreasing function of time for first few years because if bond survives the first year, there is a good chance its financial condition has improved. Surviving first two years is even better for its future financial condition.

Hazard Rates

• The hazard rate is the rate at which defaults are happening at time 𝑡(or the default intensity) and is commonly used by analysts. It can be a function of time; in some models it is assumed to be stochastic (i.e., varying randomly through time).
• Hazard rates are attractive because they can be used to calculate unconditional default probabilities. Suppose that h is the average hazard rate between time zero and time 𝑡. The unconditional default probability between time zero and time 𝑡 is The probability of survival (or survival rate) to time 𝑡 is
• The unconditional probability of default between times 𝑡₁ and 𝑡₂ is where 1 and 2 are the average hazard rates between today and times 𝑡₁ and 𝑡₂ (respectively).
• As an example, suppose that the hazard rate is constant at 1% per year.
  • The probability of a default by the end of the third year is
  • The unconditional probability of a default occurring during the fourth year is
  • The conditional probability of defaulting in the fourth year, given that it has survived until the end of the third year, can be calculated by dividing the unconditional probability of a default occurring during the fourth year by the probability of surviving to the end of the third year. It is
• If the cumulative default probability over five years for a 𝐵-rated firm is 18.32% (or 0.1832). The average hazard rate over the five years is obtained by solving
  
  This gives: per year.

Recovery Rates

• A bankruptcy leads creditors to file claims against a firm. Sometimes the assets of the firm are liquidated so that the claimants can receive partial payments. Sometimes there is an agree upon reorganization in which the claimants agree to their claims being adjusted in some way.
• Lenders are ultimately interested in estimating the amount of money they could lose when they lend money to a firm. The probability of default (𝑃𝐷) is one important input to estimating this amount. The other is the recovery rate (𝑅𝑅). It is usually defined as the value of the bond shortly after default and it is expressed as a percentage of its face value. The loss given default (𝐿𝐺𝐷), which provides the same information, is the percentage recovery rate subtracted from 100, i.e. 𝐿𝐺𝐷=1−𝑅𝑅
• The expected loss (𝐸𝐿)from a loan over a certain period is
  or
  
• Bonds vary according to their seniority (i.e., the extent to which the bond holder will rank above other claimants in the event of default) and to the extent to which there is security (i.e., collateral has been posted). Statistics produced by Moody’s show the average recovery rate varies from around 25% for junior bonds (i.e., bonds that are subordinate to others) to around 50% for senior secured bonds.
• An important point is that recovery rates are negatively correlated with default rates. During a recessionary period, default rates on bonds are high and recovery rates are low and opposite when the economy is doing well. This is because the value of the defaulting firm’s assets tends to be low (high) during bad (good) economic conditions. This negative correlation creates additional difficulties for bond portfolio managers: High default rates are doubly bad because they are accompanied by low recovery rates.

Credit Spreads And Premiums

• The extra interest earned on an asset over the risk-free rate for assuming risk is known as a credit spread. The credit spreads for bonds is relatively high. Bond holders need a risk premium in addition to the actuarial compensation. The reason they need a risk premium is that bonds do not default independently of each other. During some years, the default rate is high and during other years it is low. This creates systematic risk, in other words, risk bond portfolio managers cannot diversify away.
• Another possible reason for a relatively high credit spread is liquidity. Bonds are relatively illiquid instruments, and bond traders may require compensation for difficulties they will experience when they try to sell bonds.

The Rating Process

• Rating agencies rate publicly traded bonds and money market instruments. An instrument is typically first rated when it is issued; the rating is also reviewed periodically (usually at least every 12 months).
• The rating, based on a mixture of analysis and judgement, is only provided when there is information of sufficient quality for the rating agency to form an opinion. In addition, the analysis is based on qualitative factors, such as the institutional or governance framework. A meeting with management is also commonly undertaken.
• The fee for the rating is paid by the firm being rated. This is generally a few basis points applied to the notional amount of the bond. If a firm chooses not to pay the fee, the rating agency may not issue a rating.

The Rating Process – Outlooks And Watchlists

• Outlooks are indications of the most likely direction of the rating over the medium term. Outlooks are of 4 different types:
  • A positive outlook means that a rating may be raised,
  • A negative outlook means that a rating may be lowered,
  • A stable outlook means a rating is not likely to change.
  • A developing (or evolving) outlook means that while the rating may change in the medium term, the agency can not (as of yet) determine the direction of this change.
• Placing a rating on a watchlist indicates a relatively short-term change is anticipated (usually within three months). Watchlists can be positive (indicating a review for a possible upgrade) or negative (indicating a review for a possible downgrade).

The Rating Process – Rating Stability

• Rating stability is an important objective for rating agencies. Some reasons for this are as follows:
  • Bond traders are major users of ratings. If ratings changed frequently, bond traders might have to trade more frequently (and incur high transaction costs) to maintain the required bond rating distributions in their portfolios.
  • Ratings are used in financial contracts and (in some countries) by financial regulators. Frequent changes in ratings would cause problems. For example, a bond rated 𝐴− might be acceptable as collateral in a contract, whereas one rated 𝐵𝐵𝐵+ is not. If a bond’s rating switched frequently between these two rating categories, it would create difficulties in the administration of the underlying contract.
• As a result of this need for stability, ratings only change when rating agencies believe there has been a long-term change in a firm’s creditworthiness.

The Rating Process – Through-The-Cycle Versus Point-In-Time

• A firm’s probability of default changes along with economic conditions. Rating agencies must therefore decide whether to rate firms “through-the-cycle” or at a “point-in- time.”
  • A through-the-cycle rating captures the average creditworthiness of a firm over a period of several years and is not too much affected by ups and downs in overall economic conditions.
  • A point-in-time rating is designed to provide the best current estimate of future default probabilities.

  In theory, a through-the-cycle estimate will understate the probability of default during the down part of the economic cycle and overstate it during the up part of the cycle.

• Consistent with their desire to produce stable ratings, rating agencies produce through-the-cycle estimates. It is therefore not always the case that ratings worsen when the economy is doing poorly (or improve when the economy is doing well).
• Sometimes, rating users adjust ratings produced by rating agencies to convert them from through-the-cycle to point-in- time. To do this, it is necessary to find a way to index the health of the economy and then apply this measure to the through-the-cycle ratings. The index is applied in such a way that ratings increase when the economy is doing well and decrease when it is doing poorly.

The Rating Process – Industry And Geographic Consistency

• An important question is whether ratings are consistent. For example, 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 ?
• Moody’s, S&P, and Fitch are based in the United States and much of the information they report is based on U.S. data. The rating history for firms outside the United States is shorter than for firms in the United States. As a result, it is sometimes difficult to determine whether ratings for non-US firms are consistent with those of US firms.
• S&P provides statistics on cumulative default probabilities for firms in the United States, Europe, and emerging markets. The US data considers default experience over a 15-year period, the European data considers default experience for a seven-year period, and the emerging markets data considers default experience over just five years. The table given in the next page, compares the five-year default percentages for the three groups.
• As rating agencies are continuously striving for geographic consistency, these performance differences are not necessarily the same in the future as they have been in the past.
• There is less available data on the consistency of ratings across industries. Previously, it was true that banks with a given rating showed higher default rates than non-financial corporations with the same rating. Also, there has been less agreement among different rating agencies for banks than for other firms. Again, it is worth stressing that rating agencies strive for consistency and that extrapolating from past data is dangerous.
  

  Initial Rating	U.S. Firms	European Firms	Firms in Emerging Markets
  AAA	0.42	0.00	N.A.
  AA	0.45	0.21	0.00
  A	0.73	0.29	0.05
  BBB	2.05	0.65	2.59
  BB	8.38	4.20	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	17.00	10.84	10.19
  All Rated	7.57	2.54	6.53

Alternative To Ratings

• Organizations such as KMV (which is now part of Moody’s) and Kamakura use models to estimate default probabilities and provide the output from these models to clients for a fee. The model includes factors such as:
  • The amount of debt in the firm’s capital structure,
  • The market value of the firm’s equity, and
  • The volatility of the firm’s equity.
• In the simplest version of the model, default can occur at just one future time. The default happens if the value of the assets falls below the face value of the debt repayment that is required at that time. If 𝑉 is the value of the assets and 𝐷 is the face value of the debt, the firm defaults when 𝑉 < 𝐷. The value of the equity at the future time is
• This shows that the equity 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. The probability of this can be calculated from standard option pricing theory.
• KMV and Kamakura provide point-in-time estimates and do not have the stability objective of rating agencies. It can be argued the output from these models responds to changing circumstances much more quickly than the ratings provided by agencies. Equity prices, which are a key input to their models, are continually changing to reflect the latest information. Ratings, on the other hand, are only reviewed periodically.

Internal Ratings

• It is important for banks to develop their own internal rating procedures because –
  • First, external ratings are not always available.
  • Second, regulatory credit risk capital depends on probabilities of defaults (PDs).
  • Third, the accounting standard require banks to take default probabilities into account when loans are valued on the balance sheet.
• Banks develop their own internal rating systems based on their assessment of potential borrowers. They typically base their ratings on several factors (e.g., financial ratios, cash flow projections). In general, each factor is scored, and then a weighted average score is calculated to determine the overall final rating.
• Like external ratings, internal ratings can be either through-the-cycle or point-in-time. There is a tendency for them to be point-in-time, but through-the-cycle ratings may be more relevant for relatively long-term lending commitments.
• Like external ratings, internal ratings can be either through-the-cycle or point-in-time. There is a tendency for them to be point-in-time, but through-the-cycle ratings may be more relevant for relatively long-term lending commitments.
  • During bad economic conditions, point-in-time probabilities of default increase and banks become less inclined to lend, and
  • During good economic conditions, the reverse happens an economic conditions are helped by an easing of credit.
• So, it can be argued that regulators should encourage banks to use through-the-cycle ratings (e.g., they may ask banks to use through-the-cycle probabilities for determining regulatory capital). Banks must back-test their procedures for calculating internal ratings. This typically requires at least ten years of data and involves producing table of cumulative default probabilities. If the default statistics show that firms with higher ratings have performed better than those with low ratings, then a bank can have some confidence in its rating methodology.
• Some banks are currently trying to automate their lending decisions using machine learning. With this approach, an algorithm is given a great deal of data on firms and whether they have defaulted. This is used to come up with a rule for distinguishing between those firms that default from those that do not.
• The first attempt to do something like this was proposed by Altman in 1968. He developed a tool known as the Z-score. Using a statistical technique known as discriminant analysis, he looked at the following ratios:
  • Working capital to total assets,
  • Retained earnings to total assets,
  • Earnings before interest and taxes to total assets,
  • Market value of equity to book value of total liabilities
  • Sales to total assets.
• Today’s machine learning algorithms use far more than five input variables and far more data than that used by Altman. Furthermore, the discriminant function does not have to be linear.

Rating Transitions

• Rating agencies produce rating transition matrices showing the probability of a bond issuer migrating from one rating category to another during a one-year period. This table shows the one-year rating transitions produced by S&P in its 2016 study.
  

  	AAA	AA	A	BBB	BB	B	CCC/C	D	NR
  AAA	87.05	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

  According to the table, an issuer that has just been giving an A rating has an 87.79% probability of being 𝐴-rated one year later. It also has a 1.77% chance being upgraded to 𝐴𝐴. It has a 5.33% chance of being downgraded to 𝐵𝐵𝐵.

• The 𝑁𝑅 column in the previous table indicates the probability that a firm is no longer rated at the end of a year. For analysis, it is often necessary to proportionally allocate the 𝑁𝑅 number to the other rating categories.
• If it is assumed that rating changes in successive years are independent, a transition matrix for 𝑛 years can be calculated using the transition matrix for one year. The actual multi-year transition matrices (as reported by the rating agencies) are not quite the same as those calculated using this independence assumption. This is because of the 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.
• Rating transition matrices are calculated for internal as well as external ratings. One test of ratings is whether rating transitions remain roughly the same from one year to the next. Transition matrices also seem to depend on the economic cycle. Specifically, downgrades increase significantly during recessions (this is despite the fact the ratings are designed to be through-the-cycle).

Are Credit Rating Changes Anticipated?

• An interesting question is whether ratings have information content. It is possible that when a rating is moved down, new information is being provided to the market so that both the stock and bond prices decline while credit default swaps spreads increase. It is also possible that the market has anticipated the information, making the rating agency a follower rather than a leader.
• Researchers who have investigated this question have produced mixed results. Most agree that the stock and bond markets’ reactions to downgrades are significant. This is particularly true when the downgrade is from investment grade to non-investment grade.
• However, the market’s reaction to upgrades is much less pronounced. Part of the reason why downgrades impact prices while upgrades do not is that downgrades (particularly those from investment to non-investment grade) affect the willingness of investors to hold bonds. Also, these firms may have entered into contracts involving rating triggers, and a downgrade may have negative implications for them.

The Rating Of Structured Products

• A key difference between rating structured products and the traditional business of the rating agencies is that the rating of a structured product depends almost entirely on a model. During 2007-08 crisis, the rating agencies were quite open about the models they used; S&P and Fitch based their ratings on the probability that the structured product would give a loss, while Moody’s based its ratings on expected loss as a percent of the principal. Unfortunately, the inputs to their models (particularly the correlations between the defaults on different mortgages) proved to be too optimistic, and their ratings of structured products created from other structured products proved to be questionable.
• Once the creators of structured products understood the models used by rating agencies, they found that they could design the structured products in a way that would achieve the ratings they desired. Products that did not receive the desired rating were adjusted until they did.
• Rating agencies found the work on structured products to be very profitable, and they were not as independent as they should have been. Also, many of the structured products created from mortgages defaulted during the 2007–2008 crisis; the reputation of rating agencies suffered as a result. Rating agencies are now subject to more oversight than before.