Last week on July 22 and 23, our blog post focused on the issue of which government rescues should constitute a “failed” firm for default modeling and which should not. The view of most of our clients is that FNMA and FHLMC are clear fails, while the rating agencies and a few clients say they are not. The choice one makes has big implications for the accuracy of default modeling. This post shows why.

One of the most important observations about default modeling in general is that one is not confined to one probability measure for credit risk. Here are a few alternatives from which one could produce one or more “credit risk probabilities”:

- Probability of being 30 days or more past due
- Probability of being 60 days or more past due
- Probability of being 90 days or more past due
- Probability of a D or SD rating from a major rating agency
- Probability of a stock price effectively going to zero
- Probability of an ISDA-defined “credit event”
- Probability of a government rescue with a high probability that government funding is temporary
- Probability of a government rescue with a high probability of a loss by the government
- Probability of a government rescue given that a “default event” has occurred

Without going into specifics of the default definition, the recent credit has shown that there are two large groups of firms:

- In Group 1, the firms get in trouble, fail, and there is no rescue. Examples are Bear Stearns, Lehman Brothers, Washington Mutual and more than 1800 others in the Kamakura Risk Information Services data base
- In Group 2, the firms get in trouble and, a few seconds or hours before failure, there is a rescue by the government. Examples are AIG, FNMA, FHLMC and relatively few others. The government, explicitly or implicitly, takes a loss on the rescue funding.

There is a third group, which we’ll ignore in the interests of brevity, where the government assumes partial ownership in order to keep the risk of failure within a certain limit. The expectation of both sides to the investment is that the investment is to be temporary. The government presumably takes an initial loss on the funding (otherwise public market non-governmental funding would have been used). If the rescue is in fact temporary, however, there is a chance that the government profits on its investment. Since modeling of Group 1 and 2 provide insights relevant to modeling Group 3, we defer the Group 3 discussion to another post.

With respect to Groups 1 and 2, one can argue and subsequently prove that the variables that predict failure are essentially the same between the two groups. The only barrier to doing this is the relatively small number of the rescued firms in Group 2. For a given class of securities A, B, C and D for a failed firm we need to know the following:

- Probability that class A is rescued by the government, conditional on the firm failing
- Probability that class B is rescued by the government, conditional on the firm failing
- Probability that class C is rescued by the government, conditional on the firm failing
- Probability that class D is rescued by the government, conditional on the firm failing

We call each of these probabilities PR(i) for probability of a rescue of class i. There can be many classes that include pension obligations, union contracts, senior debt, subordinated debt, preferred stock and common stock. We could complicate this still further by allowing for the possibility of a partial rescue where the “loss given rescue” is not zero, but we ignore that in today’s post.

**Using the Probability of Failure and the Probability of Rescue**

One uses two different data sets to estimate the probability of failure and the probability of rescue. The first data set would include more than 1.4 million observations with 1,747 public firm failures in the Kamakura Risk Information Services version 4.1 data set. The second probability, the probability of a rescue conditional on failure, includes 1,747 failures x (the number of securities classes at each firm), so it has substantially fewer observations than the first data set. Consider this question: Given the failure of the firm, what is the probability that the senior debt holders are rescued? We build this model based only on 1,747 observations of what happened to the senior debt holders of those failed firms. The variable we are trying to predict is 1 if the firm’s senior debt holders were rescued, like AIG, FNMA, and FHLMC. The variable is zero if the firm’s senior debt holders are not rescued. The variables which predict rescue, conditional on the event of failure, are going to be much different from the variables which predict failure. If the commonly cited “too big to fail” policy is in fact real, then the accounting value of assets will be highly significant. Harvard economics professor Benjamin M. Friedman once observed that “too big to fail” is often thought to mean “a company whose CEO is close friends with at least 2 members of the Federal Reserve Open Market Committee.” Other considerations in the probability of rescue involve politics. If Party 1 and Party 2 would act differently on this issue, then the current political environment would also be relevant.in predicting the probability of rescue.

Given these estimates of the probability of failure and the probability of rescue (given that failure has occurred), what is the probability of loss of interest or principal on a senior bond of ABC Company?

- If the probability of rescue of ABC senior debt, conditional on failure, is zero (like CIT, Lehman, and Bear Stearns), then the probability of loss is the probability of failure without modification
- If the probability of rescue of ABC senior debt PR(senior), conditional on failure, is a positive number, then the probability of loss on senior debt is the product of [probability of failure]x[1-PR(senior)]. That is, it is the probability of failure times the probability of NOT being rescued, given that the failure has occurred.

The main point here is that the probability of failure and the probability of rescue, conditional on failure, MUST be modeled separately. The data sets are completely different, and the variables which explain these events are completely different. Political variables are potentially very significant in explaining the probability of a rescue for the pensioners of General Motors, for example.

**What are the Consequences of Mixing the Events of Failure and Rescue?**

What are the consequences of mixing these two events in building a “probability of loss” model? The adverse consequences are very significant:

**Multiple loss models are necessary**: The probability of loss flag is 1 for the common shareholders of AIG, FNMA, and FHLMC but the probability of loss flag is 0 for the senior debt holders of that firm. So one must have a different loss probability for each class of securities.**Mixing the events of failure and rescue lowers accuracy**. If one estimates the senior debt probability of loss with loss flags of 0 for AIG, FNMA, and FHLMC, it will distort loss probabilities for all other firms which would not be rescued. This comes about because the market capitalization of all three firms went to zero without “loss” for the senior debt holders. The market leverage of all three firms went to 100% without “loss” for the senior debt holders. The net impact of this is that these two powerful explanatory variables will have biased coefficients and less statistical significance for the full sample than they would have had if one made a clear distinction between the economic process of failure and the political economics of potential rescues of class A, class B, class C and class D securities for a given firm.

As always, comments are welcome at info@kamakuraco.com.

Donald R. van Deventer

Kamakura Corporation

Honolulu, July 27, 2009