Distribution Moments

Distribution Moments turns a rolling window of returns into the numbers that describe its shape (mean, variance and standard deviation, skewness, and kurtosis), plotting one of them in the pane while a dashboard reports them all. Built as the reference implementation of distribution moments for charts, it computes log returns of the close over 252 bars by default, plots skewness against a dotted reference level, and fires alerts when asymmetry or tail weight crosses your thresholds.

How to Trade the Distribution Moments?

• Skewness at or below -0.5: the dashboard flags Left Tail (recent surprises lean downside); readings at or above +0.5 flag Right Tail.
• Kurtosis above 3: heavier tails than the normal benchmark, an argument for wider stops and smaller size.
• Std Dev row: per-bar return dispersion, the scale the shape numbers are standardized by.
• Regime drift: watch the plotted moment's trend rather than single prints. Return shape tells you how far to trust the other statistical tools.

Distribution Moments Settings

• Source (default close): series the return sample is built from.
• Return Type (default Log): log returns are standard; Simple for comparison.
• Window Length (default 252): returns in the rolling sample. Higher moments want hundreds of observations.
• Plotted Moment (default Skewness): which of the five series the pane displays.
• Kurtosis Convention (default Raw (Normal = 3)): Raw benchmarks normal at 3; Excess subtracts that 3.
• Skewness Alert Threshold (default 0.5): absolute level for the tail alerts and dashboard read.
• Kurtosis Alert Threshold (default 3.0): raw kurtosis level marking fat tails.
• Show Dashboard (default enabled) and Gradient Fill (default enabled) round out the pane.

Frequently Asked Questions

Why not just watch standard deviation?

Why did a reading jump with no obvious news?

Should I use raw or excess kurtosis?