Singapore has some nice perks.

One of them is the variety of books about Indonesia to browse in the library (I am an Indophile).

While spending an afternoon reading about the minutiae of Sumatran history in the 19th century, I read a curious firsthand account from a Dutchman in North Sumatra.

I came across a crowd of villagers. One man in the middle tied to a post. Still alive, the people would slice a piece of flesh from his body. Then ate it raw.

This practice was extreme but not exceptional. It was punishment for the most serious crimes; ensuring that the criminal's soul would never find its body again.

The Batak tribe is still around today. Is it fair to recall those extremes? Do they help us understand the modern Batak people?

Man Eating Black Swans

Similarly, how do historical extremes impair our portfolio analyses?

If you have a normally distributed population, all you need is the sample variance and mean to describe the population well.

The mean weighs all observations equally and describes the central tendency of a distribution.

However, one extreme event, for example Black Monday in 1987 (when the S&P 500 dropped 25%) can be a thousand times larger than a usual day's movement. Moreover, the jump in implied volatility on that day dwarfed the equity index drop. It jumped by 110%.

Every mean calculated since then is impacted by that one day. Its magnitude reverberates more forcefully than any other in history.

Each median has ignored it, as the median only ever counts up to two events which have the middle rank in your data set.

Never Again

On the one hand a Black Monday sized shock has never recurred, on the other it's important to know your history.

Keep in mind the Holocaust, the Great Chinese Famine and Rwanda.

In the same way, we should not ignore extreme market events, but they do not occur in the universe of frequency statistics. They belong to another world.

We cannot build meaningful statistics (i.e. testable) from such rare events.

At the point where an apocalyptic wave hammers down on our statistical analysis, we use purely mechanical tail hedges to ensure our portfolio is safe in the Good Ship Statistics.

Statistics is a powerful tool but a portfolio requires tail hedging to ensure that our statistics remain meaningful.

If an investment manager ignores their tails, you should ignore their statistics.

[For more see Stress Map]