Black Swans and Kurtosis, too ... an appendage to Kurtosis


Them way out negative returns, like market crashes, are sometimes called Black Swans ... and the swans don't like it one bit!
Indeed, any unlikely, unexpected event is a Black Swan ... just as black swans were unexpected, until discovered in Australia
One measure of the number and size of fat tails is the KURTOSIS associated with the distribution of returns.
However, one can go from a comfortable, Gaussian (or Normal) distribution
(with SKEW=0 and KURTOSIS=0) to a wildandwooly distribution with huge Kurtosis by including a single, remote Black Swan.
>For example?
>^AORD?
The Australian Index which got hit hard in 1987 'cause of the crash in October and ...
>So what's your point?
Note that, when the Oct/87 return is replaced by a nice, comfortable 0%, the Index becomes almost Gaussian with small Skew and Kurt.
>Ain't that interesting? Black swans first discovered in Australia and ...
... and the Aussie Index has got a nice one.
Here's a spreadsheet that you can play with:
kurtskewdistribution.xls
It looks like this.

There was a Black Swan from Down Under
That tore the Index asunder
When it was kill'd
Gauss was instilled
The new Index inspired awe and wonder 

