Kurtosis – why empirical models are buggered
by Benjamin on February 11, 2009
Nassim Taleb and Daniel Kahneman were on stage in Munich a few weeks back discussing the global financial crisis, and in the process Taleb made the statement that not a single empirical piece of work in economics replicates out of sample. This, he argues, is because there are single instances in almost all financial and economic time-series which are hugely different than the rest of the sample, and as such skews the distribution beyond ‘normality’. These extreme single events (which are unknowable in advance) are so large that the normal distribution goes out the window, and with it most of our empirical work.
The Black Swan: Worth a read... or two
Here’s the jist of the argument: Some things fit well in the gaussian framework (in “Mediocristan”) such as weight; if you take a thousand Americans and get their average weight (177.5 lb), then adding the fattest person you can think of won’t add much to the average (Even adding Carol Jager who topped at an astounding 1,600 pounds, will only add 1.4 pounds to the average) so using the normal distribution to model weight is ok. This is not the case in ‘Extremistan’ where single observations skew the distribution. For example in the matter of income. Take 1,000 Americans, get their average income ($46,800) and the add Bill Gates. Noiw Bill is a decent enough person, really, but he made $6,300,000,000 last year and will throw the distribution completely off the scale! With Bill in the sample, the average person now makes $6.34 million ! This is ‘Extremistan’ and Taleb argues that the world of finance and economics are characterised by these distributions. (On a side-note Bill adds just over $20 to the per capita GDP of the whole United States single-handedly)
If Finance and economics are characterised by single large outliers, and the models cannot predict them, we have some cause for concern, and Taleb shows in a working paper that this is indeed the case for a sample going back 40 years on:
almost ALL transacted macro data representing >98% of worldwide volume. I used interest rates, commodities (oil, agricultural), all available equity indices (US, UK, Continental Europe, Russia, Indonesia, Brazil), main traded currencies. I selected tradability because of its “cleanliness” compared to merely computed data. I also added some micro data: although indices encompass single equities, I processed >18 million pieces of single stock daily data, and select industry datasuch as drug sales, movie returns, etc. (what “clean” data I could find). While we have a plethora of data with business variables, we don’t have enough in epidemics, terrorism, wars, etc.
The results seem to indicate that for the large majority of our economic variables, we live in Extremistan.
Departure from the Gaussian Normal as measured by fourth moment of one observation
For Silver, one single observation in 40 years (out of 10,000 data points) represents 90% of the variation away from the normal! The numbers are pretty stagering. You want 20 standard deviations distance from the mean, no problem. A good 500 examples are found in stock returns, with 5 actually passing the 100 standard deviations distance. Normal is not that normal at all.
The original video found via Stephen Kinsella‘s blog
Get Taleb’s paper from Edge, and the appendix here
Tags: Black Swan, extremistan, kurtosis, mediocristan, Nassim Taleb, normal distribution
