## A Black swan

This is a term commonly used – but I struggle to understand what people mean by it.

Types of probabilistic events?

In Taleb’s book of the same name, “Black Swan” appears to be used in a variety of ways:

1. For a well-defined outcome with a low probability
for example: selling lottery tickets or buying CDOs in 2006/7.
(perhaps the people buying such CDOs did not understand that they were selling lottery tickets but they should have!)
2. For general uncertainty
We all know it is possible to have a currency crisis in the UK in the next 5 years but it is not very sensible to put a single number on it. This is concept of “uncertainty” from Knight and Keynes and many macro issues fit into this category. A frequentist approach to probability works for rolling dice but often not for rare events.
3. For “fat tail” events
Extreme events occur in reality more commonly than a normal distribution would suggest.
4. For when the distribution is just unknown
It is possible that it will be known at a later stage, but currently there is insufficient information.
5. For an unknown, possible outcome
This seems to be the new, popular meaning.

Numbers 1 through 4 are well-known and have perfectly good ways to describe them. I think that only number 5 really makes sense as a potential separate meaning for “Black Swan”.

Does number 5 actually exist?

This is also the meaning I have most problem with as I struggle to find real-world examples of it. There are many examples where people did not consider the possibility of a given outcome, but at the same time you can find many people who did and even had decent reasons to expect it to happen. At the individual level it makes some sense as being imaginative can be hard work! However, if some people are not surprised at the occurrence, then how can it be something which “is not even imagined as a possibility prior to its occurrence” unless as you say it is entirely subjective and individual.

It may have been unimaginable to Cheney that the Iraqi people did not embrace US troops as liberators in 2003. Does that mean it was a Black Swan as it was not conceived possible and was clearly important? Or does it just mean Cheney was wrong?

Common usage

Let’s consider what many see as the great Black Swan of 2008:

This is what I think people mean:

· 2008 was a massive drop in markets

· A great deal of common practice in managing risk was terrible

· They didn’t see it coming because it was unforeseeable

Therefore

· Black Swans are very rare, so we should not expect it to happen again

· We should carry on pretty much as before

Why it annoys me

This version of events is just an excuse for being wrong, for not learning from it or changing behavior. It should be obvious that I find the term annoying in this way of excusing poor decision making and avoiding responsibility.

Alan Greenspan indeed said that the financial crisis was “unforeseeable”.

On Epistemology

Another confusion I had about the theory of the “Black swan” laid out in the book, is the way it sits at odds with the philosophy of science and specifically Popper. Popper, in fact, gets no mention in Taleb’s book, even though Popper’s key concept of falsifiability has long been linked and explained via the original example of black swans.

Quick aside on jargon

• A conjecture – is an unproven proposition which appears correct
• A hypothesis – is a testable statement

To illustrate Popper’s concept:
If your hypothesis is that all swans are white.
It would be disproved if you find a black swan.

Given its falsifiability, this is compatible with scientific enquiry

It is clear in this example, to be testable, you have to have considered what events would falsify it.

If we now put Taleb into similar language:

• Taleb
a Black Swan is an unimagined event for certain people which disproves their conjecture
• Popper
a Black Swan is a defined event which would falsify a hypothesis

Written this way, I think it show the two meanings are incompatible. Popper’s version makes sense and is useful. It is therefore such a shame that Taleb’s popularisation of the term “Black Swan” has taken something important and meaningful and turned it into nonsense.