June 18, 2012
Attain Capital
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This post is part of an ongoing series on the Attain Capital blog that seeks to help investors understand the various metrics we use to evaluate managers. Stay tuned for future pieces!
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Sometimes reading through risk management analysis can be a bit like trying to decipher a long-winded medical diagnosis. Some terms, like skew or deviation, you can probably get a grip on with unrelated contextualization, but then there are terms like “Kurtosis.” Say what?
Kurtosis tells us whether or not there is evidence of extreme values happening with greater frequency than we would expect from a normal distribution. A normal distribution has a kurtosis of 0 (EDIT: a normal distribution has a kurtosis of 3, and an “excess kurtosis” of 0. With excess kurtosis, data sets are described in terms of how much they differ from a normal distribution, which is often simply referred to as “kurtosis”). A large positive reading of kurtosis tells us there are more occurrences of outlier events than we would expect from a normal distribution, whereas a negative reading would tell us that there are fewer than would be expected. For instance, if we got on an airplane with a basketball team, our graph of heights would show an abnormally large number of readings several standard deviations away from the average.
In the investing world, we often label returns with a positive kurtosis as having “fat tails” – referring to the “tails” or end of the curves on the bell curve graph. “Fat tails” are troublesome for investors, as they are created by outlier events such as the -21% down day in US stocks in October of 1987. But a positive kurtosis reading isn’t necessarily a bad thing, either, as it can be brought on by an abnormally high number of very large positive months.
This is where we come back once more to a common theme on our blog – the importance of not getting tunnel vision. Kurtosis is but one risk metric of many, and it’s important to hold it relative to a variety of other data points as well. For instance, you won’t know whether that positive skew is a potentially good or bad thing unless you know your skew as well (as Quest Partners so eloquently explained last year). Kurtosis alone is probably pretty worthless, but when viewed as part of the bigger picture, it can help paint a vivid scene.
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June 18, 2012
A normal distribution has a kurtosis of 3
June 21, 2012
This is true. However, kurtosis is often expressed as “excess kurtosis,” which is how much a data set differs from a normal distribution. In that case, a normal distribution has an excess kurtosis of 0, which is sometimes (confusingly) referred to simply as kurtosis. Thanks for pointing that out – we made it clearer in the post.
June 21, 2012
No problem – I find the blog very informative and helpful.