As mentioned above it has been a historic week, 2 unthinkable things happened and both involved England. Great Britain voted to leave the European Union and England became the 1st visiting team in 45 years to beat Australia 3 – 0 in a home rugby series.
There is a statistical bias that understates the chances of an improbable event happening. Just because we have never seen a black swan doesn’t mean they don’t exist. For 1500 years the metaphor that something didn’t exist was represented by the Dutch as a black swan. This myth persisted until the 1st black swan was sighted in 1697. In Australia black swans are quite common in certain parts of the country.
Ok here is the point; the reason why statistical models often underestimate the likelihood of an event happening is because as humans we suffer from the psychological stress of living with uncertainty and to overcome uncertainty in a statistical context we build models to give us the appearance that we know with some degree of statistical certainty when an event is likely to happen in the future. The models 99.9% of people use build on a 1733 mathematical discovery called the Central Limits Theorem which imply finite mean and variance and rely on what we all know as a normal distribution assumption.
As we have seen with the 2 English examples the British Pound moving 10% in a day and the English whitewashing the Aussies in a 3-0 home series thrashing is what is commonly known as a fat tail event which highlights the fact that the world doesn’t necessarily operate in a normally distributed manner, and this is certainly the case with financial markets.
The truth of the matter is that models assuming markets are normally distributed work most of the time and provide us with cool information, and that all important psychological comfort of control, the issue I am highlighting is that it is an error to place too much reliance on a model that is built on a false assumption of normal distribution.
Lets meet a famous French mathematician discoverer of the Levy Distribution now commonly referred to as alpha stable distributions. My partner Dr Krouglov is a world authority in alpha stable distributions which allows a model to capture more parameters and effectively fit a model more realistically than the traditional normally distributed models. This is pretty complex stuff so let me show you in a chart what I mean.
The blue line above is a normally distributed line (Gaussian) and the orange line is an alpha stable line which we built fitting much more snuggly to the data than the normal distribution.
I don’t know about you but I would rather work in an environment which is able to capture more accurately the real world than a model operating on an unrealistic assumption.