Return Distribution lays out the shape of daily performance across the whole record instead of collapsing it to an average. Which way the extremes lean and how often the extremes turn up at all are separate facts, and both live here.

Both matter for sizing. A position built around what an ordinary session does will be wrong-footed by the sessions that are not ordinary, and this view exists to make those sessions impossible to overlook.

What it actually measures

Which way the surprises lean is the first reading. Extremes clustering on the upside describes many modest losses paying for occasional large gains, which is the shape anyone running a trend system wants to see.

How heavy the extremes are is the second, and it is easily the one that catches people out. Where the outlying sessions carry more weight than a bell curve would allow, they do most of the damage and most of the good.

A typical daily move sits alongside as a reference, and roughly two thirds of sessions fall inside it. It is exactly what makes it the wrong figure to build a position around whenever the extremes are running heavy.

The bell curve is drawn so you can see it fail

A fitted normal curve sits over the histogram, and its job is not to describe the data. Its job is to show precisely where the data refuses to cooperate, which is the whole reason for putting it there.

Everywhere the histogram stands proud of that curve is a class of session that standard risk arithmetic assumes is close to impossible and this market produces routinely. Sizing off the assumption instead of off the record is how people get hurt by events they were told were once in a lifetime.

What it does not tell you

The whole record is treated as one population. Conditions that have not repeated sit in the same pile as conditions that recur constantly, so a shape assembled across many eras describes none of them exactly.

Shape says nothing about sequence. A distribution reports how often extremes turn up without any hint about when, and extremes have a documented habit of arriving in clusters rather than politely spaced.

Which way the extremes lean describes surprises rather than trend. A market going nowhere at all can produce a lopsided distribution, and reading the lean as a forecast confuses the two entirely.

How to read it

Right-skewed. The surprises land on the upside: many modest losses paying for occasional large gains, the shape trend systems prefer.

Symmetric. Upside and downside extremes are evenly matched, with neither doing more of the work.

Left-skewed. Extreme sessions lean negative, which raises the odds of trouble arriving in the tail.

Fat tailed. Outliers dominate the risk. A typical session badly understates real exposure, and sizing on one will be wrong-footed.

Find Return Distribution on the Volatility dashboard, alongside Entropy, Waves and Volatility Comparison.

Common questions

Why do the lean and the tails both matter?

The lean says which way surprises fall. The weight of the tails says how often surprises turn up at all, and a heavy reading warns that extremes arrive far more often than standard arithmetic allows.

What does the typical-move figure mean in practice?

It is the size of an unremarkable session, and roughly two thirds of days land inside it. Building a position around it alone goes wrong once the extremes are running heavy.

When do the tails count as heavy?

Once the outlying sessions carry more weight than a bell curve permits. Beyond there the handful of unusual days account for most of the harm and most of the reward, and ordinary risk arithmetic falls short.

What is the dashed curve for?

It is a bell curve fitted to the same data, and it is there to fail. The gap between it and the real histogram is the entire point of the view.

Does an upside lean mean the market is rising?

No. What it captures is the shape of the surprises, not the direction of travel, and a market drifting sideways can produce one perfectly happily.