Not Normal

'Never forget the six-foot man who drowned crossing the river that was five feet deep on average' (Howard Marks)

The average actually tells us very little about something. The average family in the UK has 1.7 children. In other words, there is no average family. Enter the mathematicians and statisticians and you get various curves and distributions to describe things in more detail. Something like a map of the river that would have been useful for the six-foot man.

The most basic of all of these river maps is the normal distribution, otherwise known as the Bell Curve for obvious reasons. It is amazing how many things are distributed in roughly this shape. So much so that with a few other points (called moments), statisticians can give pretty good maps. You can make very good predictions about what is going to happen if you know how tall and how wide the bell is, and whether it is leaning to one side or the other.

Harriete Estel Berman Bell Sculpture

Unless you get 'Fat Tails'. In the sculpture above, the tails are the white one on the left and the black one on the right. These tails are outliers. Normally, there aren't very many of them and they don't tell us very much. Normally they aren't fat. Roger Federer is an outlier. He doesn't tell us very much about the normal experience of playing tennis. What we are normally far more interested in is what is going to happen to most people. You can't plan your life around being Roger Federer.

A Fat Tail is when the Federer's matter because there are lots of them. Then there are game changing events where the distribution doesn't actually matter. Nassim Taleb calls these single events which change everything 'Black Swans'. It doesn't matter how many white swans you see, you can't claim that all swans are white. The absence of evidence of a black swan isn't evidence of absence of black swans. One Black Swan changes your whole view.

Normally we build up our view of the world from what we see. We watch, we learn, and then when we think we understand, we act. This works very well when the underlying map of the river is reliable. This normally works very well. When there are Black Swans however, all the information that matters isn't how high the curve is, whether it is bending to the side, or how thick it is. What matters is the Black Swan.

Insurance works on normal things. When they happen often and predictably. Then you can spread the risk amongst lots of people so what you do matters more than luck. Insurance doesn't work for 'Acts of God'. Things like Earthquakes, Hurricanes and huge disasters crashes. They change everything.

There is a big fight going on between Steven Pinker and Nassim Taleb over whether the world is indeed getting better. Pinker has written a wonderful book called 'The Better Angels of our Nature' which talks about the bumpy progress of mankind in creating a more peaceful world. Max Roser has created many visual graphs on OurWorldinData.org showing how much better life is today in many, many ways. Taleb thinks both of them basically don't understand statistics. He believes Peace is a 'Fat Tailed Distribution' and that we are basically getting much better at wiping ourselves out in some tragic disaster.

'As technology increases, misunderstanding of ruin by a small segment of the population is sufficient to guarantee ruin' Taleb

Knowing you can't insure for something doesn't mean you can't do anything about it. It just means you can't avoid it hurting. You can't insure against the emotional side of a break-up, a divorce, a death, being fired etc. You can plan around the things that normally happen, and you can build resilience around the Black Swans. You can wrap your head and heart around worst case scenarios and try think of ways to not let them destroy you. To get back up.

I think Pinker and Roser are right. I do think the world is getting better and we should celebrate that. I also think that Taleb is right. We should always think about risk more deeply than the surface things we observe. A full picture of risk can't be reduced to a number or a map. The truth is always more complicated than that. 

We can plan and do. But things can happen that change everything. We should be careful and we should invest in our ability to get back up. Being insured and investing in resilience are different things. 

Correction:

Hugh Du Toit correctly points out that Black Swans don't make tails Fat. They make the whole distribution irrelevant. There can be fat tail and long tails. With a bunch of outliers still being part of the distribution, but very important. A Black Swan makes the observations largely irrelevant. I changed 'Nassim Taleb calls these Fat Tails 'Black Swans' to 'Then there are game changing events where the distribution doesn't actually matter. Nassim Taleb calls these single events that change everything 'Black Swans''. Thanks Hugh.