We can take a look at the credibility of the current AA+ rating on General Electric by looking at what the KRIS default probability service says about GE at this point in time.

In addition to default probabilities, the KRIS default probability service contains the "implied credit ratings" for each of the 22,000 companies in KRIS. These implied ratings rely on the joint assumptions that (a) a credit rating was actually granted to the company and that (b) the rating is consistent with the average behavior of the rating agencies over the period for which the implied ratings relationship was derived. In the case of KRIS version 4.1, this period is 1995-2004. A complete description of the calculation of implied ratings is contained in Appendix E to the KRIS Version 4.1 Technical Guide (February 2006) that is available to KRIS subscribers only. Appendix E was authored by Professor Robert A. Jarrow, Li Li, Mark Mesler and Dr. Donald R. van Deventer

Background on Deriving Implied Ratings

Many financial institutions and corporations are extremely interested not only in default probabilities for various maturities but also

(a) estimated rating agency ratings for those institutions that do not have ratings and
(b) statistical estimates of the probability of various ratings even for those firms that have ratings, in order to assess the probability of a downgrade or an upgrade in the current rating. In our case, we're interested in whether or not the AA+ rating of GE today is consistent with average rating agency behavior or not--is it an outlier and therefore very likely to be incorrect?

The uncertainty in rating agency behavior is attributable to the long periods of stability in ratings, like the long period when GE had an AAA rating, during times of great changes in default probabilities, financial ratios, stock price inputs, and macro economic factors. Until its recent financial difficulties, for example, Citigroup was rated AA- for more than ten years by Standard & Poor’s during a period that spanned the tech crash in 2001-2002 and a number of difficult periods in the 1990s. As noted in a March 15, 2006 press release from Kamakura Corporation, the Kamakura version 4.1 default probabilities have a 99.00% accuracy in predicting default of rated public companies, compared to an accuracy of only 96.44% for agency ratings. The ROC accuracy ratio for KRIS is well above the predictive capability of public debt ratings at every monthly time horizon measured through 60 months forward. This relative lack of accuracy also contributes to the uncertainty in rating agency behavior.

KRIS Implied Ratings

The ratings data used for the implied rating modeling was the ratings of Standard & Poor’s as reported by S&P affiliate Compustat. The Compustat data was supplemented with a separate file from S&P that contains the exact date of the ratings change for all companies rated by Standard & Poor’s. The probability of being “not rated” or “rated” is based on 2.2 million monthly observations of rated and non-rated companies in the KRIS default data base from January 1990 to October 2004. The predicted rating, conditional on being rated, is based on 282,000 monthly observations of public debt ratings of C or above over the same time period.

There are three primary methods for mapping from default probabilities to ratings.

1. Create a one to one mapping from a specific default probability range to a specific rating

2. Create a probability of a given rating from the observed default probabilities, a variation on Alternative 1 that allows for the uncertainty in knowing the rating from default probabilities alone

3. Estimate the probability of each rating from default probabilities and other inputs, assigning the “mapped rating” to the median rating grade of the full probability distribution of potential ratings conditional on having a rating. This method also predicts the probability of an upgrade and a downgrade. This technique does not use the existing rating as an input, so it is the equivalent of the predicted rating given that the company had had no prior rating or rating history

4. Estimate the probability of each rating from both the existing rating and other inputs like default probabilities. This is the equivalent of predicting the speed at which S&P will move its rating as the default probabilities and other inputs drift from the “normal” range for companies with that debt rating.

When one looks at the distribution of companies by rating and default probability for the default models on KRIS, it's easy to confirm that alternative 1 is not realistic, because there is definitely not a clear one to one mapping from default probability to rating and vice versa. For example, for a two year period ending about 2 years ago, not a single European public company had defaulted for two years. A perfect default probability model for Europe during this period would have assigned a short term default probability of zero to every public company, and the correlation of this zero PD across all companies with their ratings would have also been zero. This is just one example to illustrate that mapping from default probabilities to average rating agency behavior is not a simple exercise.

Given a default probability, it is much more realistic and practical to say that there is a probability that the company may have a number of ratings, assign a probability to each one, and “map” to the median rating grade. This is a step forward from a one to one mapping of PD to rating, but it is possible to do much better. For example, it has often been observed that ratings agencies have a bias in favor of large companies that is much greater than the impact of size on actual rates of default. The ratings for large companies are said to be biased “high” or “good” relative to their actual default experience. GE, in fact, has been a big beneficiary of this phenomenon. In modeling implied ratings, we can use size as a potential explanatory variable and confirm whether or not this is true.

The other thing we know is that actual default rates and estimated default probabilities for all maturities and all ratings grades rise and fall over the business cycle, but ratings generally vary relative little over the course of the business cycle. This means that we need to explicitly incorporate where we are in the business cycle as part of the implied ratings modeling. Potential explanatory variables include the full KRIS 4.1 reduced form default probability term structure, all of the KRIS 4.1 input variables individually, company size, macro economic factors, and market capitalization and liabilities level variables.

For these reasons Kamakura has derived implied ratings using the third method above. We describe the modeling in the following section. Kamakura is also very interested in forecasting the future ratings of a company using its existing ratings as an input, instead of method 3 where the prediction is done as if the company had no prior ratings history. For this prediction using the existing rating as an input to have meaning, one would make the prediction time dependent, with a different probability distribution for various points in the future. So far, client demand for the latter type of implied rating has been modest, but Kamakura would be pleased to add this second method to KRIS when demand warrants.

KRIS Implied Rating Calculations

Two estimates are provided in KRIS from the mapping of default probabilities to ratings:

1. The probability that a company has any rating higher than D or SD. For many small companies, for example, no rating is assigned no matter how strong their financials are because the company is simply too small to be a public debt issuer.

2. The probability of various ratings, given that we are to assume the company has a rating, without using the knowledge of the current rating.

The probability that the company has a rating is done by defining a 0/1 dependent variable. The variable is assigned a value of 1 if the company has a rating that is C or above. Using logistic regression, by estimating this variable, we are estimating the probability of a company having a rating of C or above. If the probability of having a C rating or above is less than 100%, the remaining probability is the probability of being not rated.

The probability of having a specific rating, say BBB, is done using an estimation technique called ordinal logistic regression. This estimation is done by defining a single variable which takes on an ordinal value for each ratings grade. Using the ordinal ranking of ratings, we define the variable by which AAA is defined as 1, AA+ is defined as 2, AA is defined as 3, etc. down to C. In this case there would be one regression for all ratings grades and the output would be a smoothed probability distribution by rating grade. We pick the median rating grade from the distribution as “most likely” rating conditional on having a rating. In addition, we could also derive the probability of an upgrade and a downgrade from the distribution.

More specifically, ordinal logistic regression can be thought of as a special combination of more traditional 0/1 logistic regressions. The first logistic regression can be thought of as the probability of being rated AAA. The second logistic regression can be thought of as producing the probability of being rated AA+ or better. The probability of being rated AA+ is the probability in the second logistic regression minus the probability of the first logistic regression. Ordinal logistic regression is an efficient methodology for accomplishing this objective, and it tends to produce a very smooth probability distribution of implied ratings.

Implied Ratings were calculated using ordinal logistic regression and the following explanatory variables: the KRIS 4.1 reduced form default term structure of default probabilities and their inputs, including all of the individual macro economic factors, market capitalization and various dummy variables. 30 variables, including the constant term, are used to predict the probability of having a rating of C or above. The ROC accuracy ratio is 0.9303, a fairly good level of accuracy. Company size is more important than any other variable in predicting whether a company has a rating. In addition to market capitalization, having liabilities in excess of $90 million is a very important factor in predicting whether or not a company is rated.

The best fitting relationship for predicting the probability of various ratings conditional on having a rating was done on a smaller data set; the data set used consists only of those companies with a rating at that point in time. Using ordinal logistic regression, we find the full term structure of reduced form default probabilities and a number of company attributes (especially size, with a z-score of 225) are all statistically significant in explaining rating agency behavior. The huge statistical significance of company size in explaining ratings, even though the impact of size on default probabilities has already been taken into account, is one of the most important causes of error in agency ratings, as the recent credit crisis has confirmed.

The longer term reduced form default probabilities are more statistically significant than shorter term default probabilities in driving ratings, as one would expect. In all, 31 variables drive rating agency behavior, not just a long term default probability as one might at first expect. One interesting result is that the one year default probability, the primary focus of the Basel II capital guidelines for banks, has less statistical significance in predicting S&P ratings than any other default probability maturity. This shows why it is very difficult to compare default probabilities and ratings---rating agency behavior is driven by many considerations even when the existing rating is not used as an input. Full details of the implied ratings formula and related coefficients are given in Appendix E of the KRIS Version 4.1 Technical Guide, February 2006. This Technical Guide is available only to KRIS subscribers.

Interpreting KRIS Implied Ratings

What is an implied rating? Given the way that predicted ratings have been modeled, we can say this: The implied rating is the rating most likely to be assigned by S&P if (a) the company had not been previously rated and (b) S&P assigned the rating based on company default probabilities and other attributes in the same way that it behaved in rating companies from 1995 to 2004. The case of GE provides a perfect example of this interpretation. In March of 2009, S&P downgraded GE from AAA to AA+. On March 19, 2009, however, the KRIS Implied Rating for GE was BBB. The implied rating of BBB, compared with the newly refreshed rating of AA+, shows that S&P has been much “kinder” to GE, even after the downgrade, than it has been on average to all of the companies it rated at each month end during the period 1995 to 2004. GE default probabilities, observable credit default swap quotes, and bond spreads all point to the same conclusion.

The KRIS implied ratings have many important uses:

• They are an important supplement to Moody’s and S&P ratings, a “third opinion” so to speak. The opinion is that of S&P itself, as it behaved over the 1995-2004 period, as implemented by Kamakura and driven in large part by Kamakura default probabilities

• They point out where current agency ratings are inconsistent with average rating agency actions over the 1995-2004 period

• They provide early warning of future ratings changes

• They provide an estimate of the probability that a currently unrated company can in fact obtain a debt rating.  They provide a rating for companies that have not been rated by either major rating agency

• They provide an explicit linkage between KRIS default probabilities and the ratings concept, which is useful to managers still in the process of moving from the 100 year old ratings concept to modern quantitative default models that are updated daily.

Donald R. van Deventer

Kamakura Corporation
Honolulu, March 20, 2009