Kurtosis is a term used to describe probability distributions, and comes up frequently during discussions of hedge funds. While normal distributions, or bell curves, all have the same general shape, kurtosis helps us describe exactly how these curves differ. Generally speaking, the higher the kurtosis, the heavier the “tails” of the curve are, meaning the likelihood of extreme values is greater. When speaking about something like risk, higher kurtosis means that extreme events are more likely to occur, hence the existence of “fat-tail” funds, which are designed to perform well during such extreme scenarios, unlikely though they may be.
Q. Another geeky term for investors looking at hedge funds, right? It goes along with Sharpe and Sortino ratios?
A. Yes, it’s a way of talking about tail risk: excess kurtosis means fat tail risk. As we’ve discussed, a really critical issue for evaluating hedge fund managers is how much volatility their results have shown, because more volatility means more risk. You can think of this whole question as being a picture of a bell curve, what folks call a “normal distribution” of outcomes.
Q. OK, so where does “Kurtosis” fit in?
A. The exact the shape of that curve tells you what the pattern of outcomes is likely to be. If the ends of the curve are “fat,” we have lots of risk of extreme events. Kurtosis is a good shorthand way to understand this. You can picture it pretty easily if you remember that kurtosis is also called “peakedness”. The more pointy the bell curve is in the middle, the higher the kurtosis.
Q. So what kind of numbers are we looking for here?
A. Normal or low kurtosis is nice: that would be a number of 3 or less. Excess kurtosis means that we’re looking at a bell curve with fat tails– an enhanced possibility of events that are out on the extreme ends of the curve.
Q. And why is that, exactly?
A. Well, imagine a normal smooth bell curve. We’ve just said that it has a kurtosis of 3. And a high kurtosis curve looks be very pointy in the middle, instead of being smooth. Now, at first that sounds good, because it means the outcomes are closely grouped around the middle. But the problem is, that to compensate for that compression of results, the tails of the curve are fatter than normal. And that shows non-normal results are more likely.
So high kurtosis is usually a sign that very extreme events are more likely than is typical. That’s why its also known as “the volatility of volatility”.
Q. So how does this relate to some of the other ratios? Where does it fit in?
A. This one is better for understanding not just average risks, but the possibility of extreme ones. Investors should ask about it, right along with Sharpe, Sortino, and the others.