# Probability of Default Versus the Principle of Incompatibility

In circumstances characterized by high turbulence and interdependency:

• it is impossible to make predictions – in fact, even the current economic crisis (of planetary proportions) has not been forecast
• only very rough estimates can be attempted
• there is no such thing as precision
• it is impossible to isolate “cause-effect” statements as everything is linked
• optimization is unjustified – one should seek acceptable solutions, not pursue perfection
The well known Principle of Incompatibility states in fact that “high precision is incompatible with high complexity”. However, this fundamental principle, which applies to all facets of human existence, as well as in Nature, goes unnoticed. Neglecting the Principle of Incompatibility clashes with reality and hard facts. One example is that of ratings. While the concept of rating lies at the very heart of our economy, and, from a point of view of principle, it is a necessary concept and tool, something is terribly wrong. A rating, as we know, measures the Probability of Default (PoD). Ratings are stratified according to classes. One example of such classes is shown below:

Class     PoD
1              =<0.05%
2              0.05% – 0.1%
3              0.1% – 0.2%
4              0.2% – 0.4%
5              0.4% – 0.7%
6              0.7% – 1.0%
etc.

A rating affects the way stocks of a given company are traded – this is precisely its function. What is shocking in the above numbers, however, is the precision (resolution). A PoD of 0.11% puts a company in class 3, while a 0.099 in class 2. How can this be so? Isn’t the world  supposed to be a highly complex system? Clearly, if even a crisis of planetary proportions cannot be forecast, it not only points to high complexity but it also says a lot about all the analytics and Business Intelligence technology that is used in economics, finance, or management and decision making. So, where does all this precision in ratings come from? From a parallel virtual universe of equations and numbers in which everything is possible but which, unfortunately, does not map well onto reality. It appears that while hard facts and evidence are interesting they are also irrelevant.

The above example of PoD stratification reflects very little understanding of Nature and of its mechanisms. As Aristotle wrote in his Nikomachean Ethics: an educated mind is distinguished by the fact that it is content with that degree of accuracy which the nature of things permits, and by the fact that it does not seek exactness where only approximation is possible.

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