(Posted by Aly)

One of the most interesting and awkward features of financial time series from a perspective of risk management is the well known phenomenon of "fat tails" in the distributions of such series. Basically this means that the likelihood of what one might call "extreme events" is much higher than what would have been predicted from a standard Normal or Gaussian distribution.

Graphically we can illustrate this concept very easily as follows:

Graphically we can illustrate this concept very easily as follows:

It is immediately obvious that the real data is clustered differently and that there is a good deal more risk of large falls in the market than we might expect from a Normal distribution. Of course we all found this out over the last couple of years when the woeful inadequacy of Gaussian copula models became apparent. It's not just market risk that suffers (although that is important) as assumptions about underlying distributions form the basis of derivative pricing in credit markets for example (pdf).

Related to this are the observations that financial time series have a multi-fractal nature, obey power law distributions (pdf), struggle with volatility clustering and all sorts of other nasty (from a modelling point of view, anyway) features.

The question is why?

There is a recent paper out that seems to explain this in a nice intuitive manner. Leverage + some simple assumptions naturally leads to fat tails... essentially borrowing money to invest causes investor's behaviour to change as they have to repay the debts and interest on money borrowed to invest with. This means that investors need to sell into falling markets, thereby accelerating the down moves, rather than being able to take contrarian views which would serve to counter the down moves and make the distributions more "Normal".

Remove the leveraged buying and the fat tails disappear.

This is one of the best explanations of "why" that I have seen.

Related to this are the observations that financial time series have a multi-fractal nature, obey power law distributions (pdf), struggle with volatility clustering and all sorts of other nasty (from a modelling point of view, anyway) features.

The question is why?

There is a recent paper out that seems to explain this in a nice intuitive manner. Leverage + some simple assumptions naturally leads to fat tails... essentially borrowing money to invest causes investor's behaviour to change as they have to repay the debts and interest on money borrowed to invest with. This means that investors need to sell into falling markets, thereby accelerating the down moves, rather than being able to take contrarian views which would serve to counter the down moves and make the distributions more "Normal".

Remove the leveraged buying and the fat tails disappear.

This is one of the best explanations of "why" that I have seen.