Monday, 8 July 2013

What Is The Relevance of Probability?


Probability is central to many concepts in economics and in science. In economics we run across probabilty when we compute VaR, PoD-type ratings, when we design portfolios, estimate expected returns, etc. But the concept of probability is extremely elusive. As Bertrand Russell said in 1929:

Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.

Probability is a "tool" which is supposed to give us a flavor of the likelyhood of future events. But what does this really mean? If an event A is said to have a probability of ocurrence of 99% does that mean it is imminent? Is it more imminent than an event B that has a chance of ocurring of 95%? Does this guarantee that A will necessarily happen before B? Not at all. Both probabilities are in fact irrelevant. In our recent blog we illustrate how PoD ratings, for example, are flawed from a very basic physical perspective. But let us see why the concept of probability is also flawed:

First of all, when you state, for example, that in the past, out of 100 start-ups 60 fail in the first three years, this is an a-posteriori statement of the obvious which says nothing of the future reserved for YOUR start-up. All start-ups are different and therefore you cannot throw them into one basket and run a statistic. Even though the number 60/100 is mathematically correct, it is irrelevant. You can, in principle, divide any two numbers in the Universe and attribute some value to them. Nobody can stop you.

Second. Imagine someone does indeed provide you with a probability of failure of your-startup and it happens to be, say, 95%. What does it mean? Does it mean that failure is imminent? Does it mean you only have two quarters left, after which you are out of business? What does the probability really mean for YOU? It means nothing. Suppose that you don't know that YOUR start-up will fail on December 31-st 2013. The probability of that event is, evidently, 100%. If the company will fail it will do so regardless of the probability of failure you may attach to it. Any probability which is not 100% is wrong. And that means inifinitely many.

Events can only have a probability of 0 or 1. They happen or they don't. The concept of probability, in its current form, is not relevant and its anectodal character, which applies exclusively to the past, is erroneously used in making forward projections. Setting aside relativistic issues and quantum mechanics, there are no known laws of physics which can predict when a company will default. As a matter of fact quantum mechanics can't predict what a single elementary particle will do. But this IS the problem. You are interested in YOUR company or the one you're investing in, not in populations of different companies.

A better concept than probability is that of resilience. Resilience can be computed based on physical quantities and it expresses something real and material. Just ask an engineer if he knows what the pendulum impact test is.