How it unfolds, step by step
The setup
On this chart the capital and the fraction at risk are both held fixed. The only thing that varies is the distance from the current level to the level at which the read would be wrong, running from 2 points up to 40.
What happens next
The quantity falls away steeply as the distance widens. A read that is wrong 4 points away supports ten times the quantity of one that is wrong 40 points away. That is for exactly the same amount of money at risk.
What it means — and does not
The same account, the same risk, and quantities that differ tenfold, decided entirely by where the level sits. That is why the level has to be chosen before the quantity. Doing it the other way round fixes the quantity first, and lets the amount at risk fall wherever it lands. That is the arithmetic running backwards.
- Quantity the arithmetic implies (units)
Fixed capital and fixed risk. Only the distance to the level where the read is wrong changes, and the quantity falls away with it.
Show the underlying data
| Distance to the level (points) | Quantity the arithmetic implies (units) |
|---|---|
| 2 | 2,500 |
| 4 | 1,250 |
| 6 | 833 |
| 8 | 625 |
| 10 | 500 |
| 14 | 357 |
| 18 | 278 |
| 22 | 227 |
| 26 | 192 |
| 30 | 167 |
| 34 | 147 |
| 40 | 125 |
What this does not establish
The whole calculation rests on the loss being capped at that level, and it is not always. A gap through the level, an instrument, or an order that cannot be filled at the intended price all mean the actual loss exceeds the planned one. The quantity was correct arithmetic on a premise that did not hold. That premise, not the division, is the thing to check. It fails most often exactly when it matters.
Things to check
4What fraction of capital is at risk on this one decision?
Where is the level at which the read is wrong, and how far away is it?
Does that distance and that risk imply a quantity you would actually take?
Divide the risk budget by the price distance, then round down to an allowed quantity.
Common mistakes
2Choosing the quantity first and discovering the risk afterwards, which is the same arithmetic run backwards.
Treating a strong view as a reason for a larger quantity. The calculation has no term for conviction.
Two decisions, same capital and same fraction at risk, but one has its wrong-level four points away and the other forty. What follows?
- The first supports about ten times the quantity of the second
- They support the same quantity, because the capital and the fraction at risk are identical
- The second supports more, because it allows more room
Show the answer
A. The first supports about ten times the quantity of the second
Quantity is the amount at risk divided by the price distance, so a tenfold difference in that distance is a tenfold difference in quantity for an identical amount of money at risk. Conviction appears nowhere in the calculation.
Frequently asked
3What is the calculation?
Capital multiplied by the fraction at risk, divided by the price distance to the level at which the read is wrong. Round down to a whole lot, so the amount at risk never exceeds the budget.
Does a stronger view justify a bigger position?
The arithmetic has no term for conviction. Varying quantity by how a decision feels is what makes a run of losses arrive at their largest sizes.
Where can I run my own numbers?
The position size calculator on this site takes the capital, the fraction at risk and the two levels, and returns the quantity with the amount actually at risk after rounding.