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?

Because it is only the second moment. Standard Deviation measures dispersion but says nothing about which side the outliers favor or how heavy the tails run. Identical volatility can hide very different downside risk.

Why did a reading jump with no obvious news?

The third and fourth moments raise each deviation to the 3rd and 4th power, handing a single extreme bar outsized influence. A reading can lurch when an old outlier drops out of the 252-bar sample — an artifact of the window, not fresh information.

Should I use raw or excess kurtosis?

They differ by exactly 3, nothing more: Raw benchmarks the normal distribution at 3, Excess at 0. Pick whichever convention your other sources use — the alerts evaluate raw kurtosis either way.