Thursday, 1 July 2010

The fallacy inherent in the "Black Swan" Theory

The "Black Swan" theory so elegantly proposed by Taleb [1] asserts that risk is an unpredictable function which collapses under tong-tail events. This is based on a certain formulation of induction and the inductive process itself. The problem here is not induction per se, but a misapplication of the same. The following quote which is used as a foundation to the theory demonstrates the flaw as it can not be validly induced:

  • Every swan I’ve ever seen has been white, therefore all swans are white

To be logically correct and inductive in nature, this quote should rightly read in a similar manner to the one below:

  • Every swan I’ve ever seen in the limited location I have visited has been white, therefore it is highly probable that all swans in the given locations are white and I can state this with 95% certainty”.

As I noted already, the former statement is logically unsound. It is not inductive (nor is it deductive). For the statement to be deductive, the viewer would have seen all swans that have existed, do currently exist and will exist at any time in the future. This is of course the reason why little if any valid deductive thought can survive outside of philosophy and except under the extremes of unsupported assumptions.

Science has a strong reliance on induction for this reason. It assumes that a hypothesis is valid within a set uncertainty range. The later statement still allows for risk and we also have to have a set of processes based on statistically sound methods.We can also insure against the losses that are due to uncertainty and distribute these across market segments.

A poor comprehension of inductive processes and meaning does not make these errors logically valid. If we use the more correct inductive process we have a means of formulating risk. To truly make this exercise scientifically valid, we have to go further than the simplified inductive statement given as a more correct formulation. We need to report our data (and methodology, but I will leave this for another time).

For instance, if our hypothetical observer was truly a scientist and not simply a philosopher with little (if any) grounding in logic, we would need to report the swan case in a manner as follows (here I am assuming that a valid methodology for the collection of the data was used and am ignoring error rates in this process for the sake of brevity - which also have to be incorporated for this to be accurate):
  • I have noted 209 swans from 20 similar pools. These pools all have similar temperature and ecological structures and hold similar environmental conditions (as described in the appendix).  Each of the pools held 10 adult swans [at a 95% confidence interval we are 95% confident that similar ponds would hold a range of (9,11) swans]. The ponds where all sampled in the first week of Spring. All ponds where within a 250 radius of a defined central point. Every swan noted in this experiment has been white. Therefore it is highly probable that all swans in the given locations (latitude and longitude) and which experience similar environments are white (at least in the time periods being observed as no tests to whether swans change color at other times in the year have been conducted)  and I can state this with 95% certainty”.
The issue with risk is not the uncertainty of a calculation nor the long tail of many distributions. Rather, it is a combination of the lack of scientific vigor and a willingness to overlook the uncertainty and account for this.

If this principle had been applied to financial markets (and they had to insure - either self insure or via market methods), the error rates of the Copula and other algorithmic methods would have required a 1-2% risk assignment to account for error (this was simply ignored). Had this occurred, an amount of around 16 trillion would have been available to account for the losses and no government intervention would have been needed.

Too big to fail and the uncertainty as to who receives this treatment lead to perverse incentives for banks to ignore risk. This does not mean it is not able to be assessed.

[1] N.N. Taleb, The Black Swan, Penguin, 2007

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