Fat Tails and Tall Heads

One of the bigger CTAs in the business – Transtrend – recently released their 2012 review newsletter, and of particular interest to us was their discussion of the often ignored “Tall Head” aspect of kurtosis. Now, most people aren’t even discussing Kurtosis, much less different aspects of Kurtosis – but you don’t get to $8 billion under management without knowing a thing or two about math.

As a refresher, Kurtosis is a term that refers to the shape of a statistical distribution. The normal shape is a bell curve, and we often hear of kurtosis when talking about “fat tails,” or outlier readings in a statistical distribution which make the edges of the bell curve upwards.  In investing, a fat tail on the left side is a bad thing, as that is an outlier loss greater than expected given a normal distribution.

We illustrated this a while back by comparing the historical daily returns of the S&P 500 to a randomly-generated set of returns that followed a normal distribution. You can see that there are many more ticks (readings) above 3% and below -3% than would be expected in the normal curve. Kurtosis is the statistic which measures that phenomenon.

Disclaimer: past performance is not necessarily indicative of future results.

But what we didn’t touch on in our look at this graph was the tall head associated with the large kurtosis distribution. You can clearly see in the chart above that the middle of the distribution is a lot taller than the normal curve. Indeed, that is the defining characteristic of the graph, versus the barely noticeable fat tails.

Transtrend does a wonderful job of explaining that the “fat tails” everyone worries about (and invests in managed futures to protect against) are a result of supposedly volatility-reducing “tall heads.” When adding in small or zero returns to a distribution (say, by government intervention), the curve gets pinched in the middle, pushing the head up and tails out. Voila, fat tails.

In Transtrend’s words:

[after adding in 0% returns]… we now have a return series with a smaller standard deviation, but with the same risk. Where does the ‘missing’ risk hide? Precisely: in a higher kurtosis. All these 0% return days form a high peak…this peak pulls the distribution ‘inward’ (i.e., like we have seen above, the standard deviation downwards), causing the returns on the outsides to now overshoot the Normal curve. There we have our ‘fat tails.’

What we see here is the exchange of standard deviation for kurtosis. The risk stays the same, but through the lower standard deviation it is more treacherous. It is now hidden in the higher kurtosis. Remember we did not increase the kurtosis by a direct addition of tail-risk, but by adding an (in itself not dangerous) high peak. To those who are not alert to this phenomenon, such a high peak may give a false sense of security.

They continue on to point out that outside intrusion in the markets (such as central bank interventions) tend to generate those higher peaks – with the government artificially absorbing part of the risk, which contributes to a higher-than-normal share of “small move” days. Managed futures, in turn, tends to struggle during these “small move” periods, and shine when larger moves, further out on the tails, take place. They explain this is especially true when looking at longer time series – say, monthly returns rather than daily. (Transtrend left out that their size precludes them from participating in a meaningful way in some markets (grains) which did see big moves, but that’s a discussion for another day).

Finally – they make a nice comparison explaining tall heads and fat tails to building architecture:

The interaction between deviation and kurtosis is well known in building engineering. In the Netherlands the top floors of high-rise office buildings sway a couple of meters when it storms. It is really not that hard to construct buildings that are less flexible. But they would not be safer. Better bend than break. In physics terms: a choice between stiffness and strength. During earthquakes the least flexible buildings are the first to collapse. Every now and then a ‘resident’ may complain about this scary swaying, but no architect will take this complaint seriously.

Are global markets currently stiff or flexible? That is the big question.  Transtrend would have us believe that the current “tall head” environment means we’re living in a stiff building, ready to break at the first sign of tremors.  We heartily agree.