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Leptokurtic: Definition and Examples

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Leptokurtic is directly related to kurtosis (a guide to how “peaked” your graph is), so you may want to read this article first: What is Kurtosis?

A leptokurtic distribution has excess positive kurtosis, where the kurtosis is greater than 3. “Lepto-” means slender, referring to the tall, slender peak in the distribution. The distribution looks like a normal distribution at first glance. The following illustration1 shows a leptokurtic distribution along with a normal distribution (dotted line).
lepto

As you can probably tell, a leptokurtic distribution has a sharper peak around the mean. In other words, there are more values closer to the mean. The opposite is a platykurtic distribution, which is broad and flat like the uniform distribution.

Uniform distribution. Image courtesy of the University of Houston.

Uniform distribution. Image courtesy of the University of Houston.

The Leptokurtic T-Test

The Student’s t-test is an example of a leptokurtic distribution. The t-distribution has fatter tails than the normal (you can also look at the first image above to see the fatter tails). Therefore, the critical values in a Student’s t-test will be larger than the critical values from a z-test.

leptokurtic

The t-distribution.

Financial Markets

Kurtosis isn’t just a theory confined to mathematical textbooks; it has real life applications, especially in the world of economics. Fund managers usually focus on risks and returns, kurtosis (in particular if an investment is lepto- or platy-kurtic). According to stock trader and analyst Michael Harris, a leptokurtic return means that risks are coming from outlier events. This would be a stock for investors willing to take extreme risks. For example, real estate (with a kurtosis of 8.75) and High Yield US bonds (8.63) are high risk investments while Investment grade US bonds (1.06) and Small cap US stocks (1.08) would be considered safer investments.

Leptokurtic: Definition and Examples was last modified: November 14th, 2016 by Andale

2 thoughts on “Leptokurtic: Definition and Examples

  1. Andale Post author

    Thanks for your comment, Peter. It’s become widespread to think of kurtosis as peakedness. This could possibly be because it’s much easier for the average student to visualize what a tall or flat-peaked distribution looks like (as opposed to a distribution with fat tails or thin tails). I did add a little more info about the fact that fat tails leads to a flatter peak. I hope that clarifies it!

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