Fat tails: When the impossible happens often

For centuries, Europeans believed all swans were white. One black swan, in Australia, was enough to overturn it all.

In two thousand seven, Nassim Taleb made it a book: The Black Swan. A rare, huge event, always explained after the fact.

His idea: in finance, it is not the ordinary days that decide. It is the rare extreme days.

Yet many models assume a bell curve. In that world, extremes are almost impossible.

Say a volatility of one per cent a day. A five per cent fall in one session is five standard deviations.

On a bell curve, that only happens about once every fourteen thousand years of trading.

Yet in autumn two thousand eight, the main American index had several sessions like that within a few weeks.

And on the nineteenth of October nineteen eighty-seven, the Dow Jones lost more than twenty-two per cent in a single day.

The same phrase comes back with every crisis: "an event that was only supposed to happen once every ten thousand years".

In the app, this chapter is animated and narrated, card by card. Start free trial.

In two thousand seven, Goldman Sachs's finance director spoke of twenty-five standard deviation moves, several days in a row.

When the impossible happens several times a decade, it is not the world that is wrong. It is the model.

Markets look more like a power law. Large moves are rare there, but not impossible.

Let's compare. On a bell curve, a move twice as big is about seven hundred times rarer.

With a power law, say with an exponent of three, it is only eight times rarer. Extremes stay in play.

To measure how fat these tails are, we use kurtosis. For a bell curve, it equals three.

For daily share returns, it often measures far more. Fat tails: more calm days, and more crazy days.

The trap is that calm days are the most numerous. Risk measures feel safe, until the crazy day.

What to do? First, never believe a number that says "impossible". On the stock market, "rare" is the strongest word there is.

Next, avoid whatever cannot survive a crazy day: too much debt, or money you will need next month.

Finally, ask yourself: if the worst in history happened again tomorrow, and a bit stronger, would I hold on?

You cannot predict a black swan. You organise yourself so it does not sweep you away.