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Kurtosis

Kurtosis measures a distribution’s shape, specifically the total probability in the distribution’s tails compared to the rest of the distribution.

What is Kurtosis?

Kurtosis measures a distribution’s shape, specifically the total probability in the distribution’s tails compared to the rest of the distribution. The higher the kurtosis, the higher the probability in the distribution’s tails. It measures the chance of observing a significant deviation from the mean. Like skewness, kurtosis is naturally unit-free and can be directly compared across random variables with different means and variances.

Example of Kurtosis:

The fourth central moment of a distribution is:
Kurtosis is the standardised fourth moment.
Kurtosis =E{[X − E(X)]^4} = E[(X − μ)^4]

Why is kurtosis important?

Only when used in conjunction with standard deviation is kurtosis useful. Although an investment’s kurtosis (badness) may be significant, the overall standard deviation is low (good). On the other hand, an investment with a low kurtosis (excellent) may have a significant total standard deviation (bad). Hence, risk professionals should be aware of kurtosis to make better decisions.

Owais Siddiqui
1 min read
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