Trends/Statistics and risk

Kurtosis

How often very large daily moves occur compared with a bell curve.

Statistics and riskBest on 3Y, 5YAlso called fat tails

Illustration of the kurtosis shape. It is a sketch, not real price data.

What it shows

Kurtosis measures the weight in the tails of the return distribution. A bell curve has an excess kurtosis of 0. Stocks usually have positive excess kurtosis, which means extreme days are more common than a bell curve predicts.

Mandelbrot argued that markets have 'fat tails'. We calculate it from the last 252 daily returns.

How we find it

The same code that draws it on your chart follows these steps, with the same result every time.

Daily returns for 252 days.
Standardize them.
Raise to the fourth power and average.
Subtract 3 for excess kurtosis.

Starting values: Window 252 bars. These are proposed and will be tuned on real price data before launch.

How to read it

The panel shows excess kurtosis.
Zero: bell curve.
Higher: more extreme days.

Status labels you may see

Label	What it means
Fat tails	Above 3.
Moderate	1 to 3.
Near normal	Below 1.

What cancels it

Nothing cancels it.

What traders check next

The biggest days.
Volatility.
Skewness.

Limits

Sensitive to single days.
Needs a long window.
Unstable.

Try it in forecastviz

Open any ticker and choose Statistics and risk → Kurtosis in the left menu.
Switch between 3Y, 5Y to see how the picture changes.
Compare with Skewness and Historical volatility on the same chart.

Open on a ticker

Questions

What are fat tails?

Large moves that happen more often than a bell curve says.

Why does it matter?

Models that assume a bell curve understate extreme risk.