Fourth Business Moment Decision

The fourth business moment decision refers to kurtosis - a measure of how peaked a distribution is, and how heavy or light its tails are, compared to a normal distribution.

Mesokurtic (Normal Peak)

A distribution with kurtosis close to that of a normal distribution - moderate peak, moderate tails.

Leptokurtic (High Peak, Heavy Tails)

A distribution with a sharper peak and heavier tails than normal, meaning more extreme values (outliers) than you'd expect. Financial returns data often shows this pattern.

Platykurtic (Flat Peak, Light Tails)

A distribution that is flatter than normal, with fewer extreme values and data spread more evenly across the range.

Calculating Kurtosis in Pandas

import pandas as pd

returns = pd.Series([2, -1, 0, 15, -12, 1, 0, 2])
print(returns.kurt())

Skewness and Kurtosis Together

Together, the four business moment decisions - mean, variance, skewness, and kurtosis - give a complete statistical picture of a distribution's centre, spread, asymmetry, and tail behaviour.

High kurtosis is a practical warning sign in fields like finance - it means extreme, rare events happen more often than a normal distribution would predict, so risk models that assume normality can seriously underestimate real risk.

Coming Up Next

Next, you'll learn about correlation - how to measure the relationship between two different variables.