Hey! Who are you saying has a ‘fat tail’?
May 10th, 2007 | Filed under: Performance, Analytics & MetricsAside from being a wonderful source of sophomoric humour about bizarre medical conditions, “kurtosis” is also a useful way of mathematically describing what many people say will be the downfall of hedge funds - their performance during “extreme events”. But unfortunately, kurtosis (a.k.a. “fat tails”) is entering the mainstream as a poorly understood measure.
Kurtosis refers to the extent to which a return distribution has “outliers”. A fund with a low kurtosis would be more pointed than the familiar bell-shaped normal distribution. With more of its returns grouped around the middle, one might be excused for thinking that such a fund is “safer” or more “predictable” than a fund with a high kurtosis (i.e. which tend to experience more severe returns on both the upside and downside).
A recent Morningstar advertisement is exemplary of this common assumption. The half-page ad is titled “The Skinny on Fat Tails” and was published recently in a popular trade magazine. It contains statements about kurtosis that are technically accurate, but misleading such as:
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I think this is a good post, and investors should consider as many moments of the return distribution and they can reasonably develop expectations for! However, your statement that
“…kurtosis only refers to the shape of the return distribution, not the actual “probability of extreme returns†as Morningstar suggests.”
is simply false. I understand you ‘get to the point’ of ceteris paribus conditions later in the post, but that statement is simply misleading.
Jon
Two expansions of what you posted that are relevant: If you break a normal distribution synmmetrically up into thirds, kurtosis is when less observations are in the 1/3 to 2/3 portion than the normal and more in the first 1/3 and last 1/3. Therefore high kurtosis may say nothing about fat tails.
Secondly kurtosis is notoriously unstable-one observation among 60 can alter the number significantly. To stabilize the measure you need to calculate the L-moment which bounds the set between 0 and 1 in quantile space as opposed to the unbounded set in probability space.
Mr. Lett:
Your comments are technically true, in that I can increase the excess kurtosis of a distribution without affecting the shape of the tails - I believe maybe that my statement in the comments section was too strong, and I should have been more careful with my wording. On that note, is there research that you could direct me to that suggests that any observed kurtosis in ‘hedge fund’ returns is due to returns clustering around the mean without any changes in the shape of tails of the distribution (when compared to, say, a normal dist.)? I think that empirically, with financial market returns, positive excess kurtosis does imply fat tails.
Jon
Jon:
I will get back to you on that point. Sorry it took so long to respond, but I could not see a response to the article, including my own.
Tris
No problem - I’ll check in later.
Jon
Jon:
As it turns out the point we are discussing has been of interest to some academics, but to date no one has come up with a proof that what I said is true, though clearly it is not a new thought. So I graciously concede the point to you…
Tris
I’ve enjoyed the discussion - it’s been quite educational for me.
Technical matters aside, I agree with your sentiment that kurtosis is not just a hedge fund issue. It is unlikely that any financial asset has a return distribution that is truly normal, and so using kurtosis as a means of warning about hedge fund investing is sort of a weak argument.
Regards,
Jon
Did I miss something? The article suggests that a -50% return on stocks or multi strat funds is a 1 in 139 or 1 in 592 year event. -100% losses happen all the time. LTCM and Amaranth occured a bit closer than 592 years apart.
Stop using normal distributions to consider the finer details of probabilities.
I think normal distributions have some value as they can help describe most general asset returns, but the fat tail needs to be considered and the notion that large unexpected drops can occur needs to be remembered.