Volatility adjusted position sizing

A fixed distance is not a constant 

A distance stated as a fixed number of pips or points looks like a constant because it is written as one. It is not. Price units are a local convention: a currency pair quoted to four decimal places, an index quoted in whole points, a share quoted in the cents of its listing currency. Converting them all into money removes the first layer of the problem and leaves the second untouched, because what makes a distance tight or wide is not the money it represents but its size relative to how far that instrument routinely travels.

That runs in both directions, and both are worth stating rather than only the one usually mentioned. A distance far inside an instrument's ordinary travel sits within the movement a quiet day produces, so it is reached by the instrument doing nothing in particular. A distance far outside it gives a much smaller position for the same risk amount, held open across a longer stretch of price. Neither case is an error in the arithmetic. The arithmetic did what it was asked, using a number with no relationship to the chart it was applied to.

The same argument applies to one instrument across time, which is the half more easily missed. The height of its bars expands and contracts in stretches: around scheduled releases and policy meetings, at session boundaries, through thin holiday weeks and through the days after a surprise. A distance chosen while bars were short becomes a different proposition once they lengthen, and nothing on the screen announces the change. The distance was never adjusted. The instrument moved out from under it.

Measuring the distance in units of range 

The repair is to state the distance as a multiple of something measured on the instrument itself. Average true range is the measure conventionally used, and the two properties that make it usable were set out in the charts module: it is expressed in the instrument's own price units, and it carries no direction, so it serves as a yardstick rather than as an opinion. Multiplying it by a chosen multiple returns a distance in those same price units, which the sizing calculation can take directly.

One multiple applied to two instruments then produces two different point distances without anyone deciding on either, and applied to one instrument in two regimes it does the same. A distance stated in units of an instrument's own range means the same thing on every chart, which is exactly what a fixed number of points does not.

The multiple is where the judgement sits, and its status is worth stating bluntly: it is not derived from anything. Trading literature cites a narrow band of small multiples, most often between one and three, inherited from the practitioners who published them rather than from results anyone can inspect. A smaller multiple gives a distance close to the ordinary travel of a single bar; a larger one gives a distance the instrument reaches less often, and a smaller position for the same risk amount. Testing multiples against a chart until the distances look convincing is fitting the setting to the evidence it will then be judged on, which is a known failure of the method rather than a use of it.

Size from the measured distance 

Nothing in the sizing calculation changes. The previous lesson set out the chain in full: a risk amount, expressed as a fixed fraction of equity, divided by the distance in price units multiplied by the value of one price unit per contract, gives the number of contracts. The volatility adjustment substitutes one input, the distance, and leaves every other term where it was.

The two sizes differ by a factor of four because the two distances do, while the risk amount is identical in both columns. That is the entire mechanism: the risk amount is held fixed, the measured distance varies with the instrument, and size is whatever is left over. Size is not chosen. It is the residual of a division decided before any instrument was looked at.

What happens when volatility expands 

Because the distance sits in the denominator, size is inversely proportional to the measured range. A reading that doubles halves the size, a reading that halves doubles it, and the amount at stake if the distance is reached is unchanged in every case. That property operates on one instrument over time exactly as it operates across two instruments at one moment.

Two consequences follow, and practitioners argue about the second rather than the first. A violent market produces a smaller size with no decision taken, because the reading feeding the denominator has already grown. The mirror image is that a quiet market produces a larger size by the same arithmetic, and the reading is at its smallest immediately before range expands, since an average of periods that have closed cannot describe a period that has not. The largest sizes the method returns therefore sit on the chart at the moment the measure is least likely to still describe it, and no lookback removes that ordering, because it is a property of measuring backwards rather than a setting.

What does not divide cleanly 

The division returns a number with decimals in it, and instruments are dealt in stated increments, so the size is rounded. Rounding moves the amount at stake away from the amount the calculation was built to hold constant: down leaves less at stake than intended, up leaves more, and the discrepancy depends on how coarse the increment is relative to the position. On a small position in a coarse increment it is not a rounding detail at all.

Two further constraints sit outside the calculation and can override its answer. The first is the margin requirement, the percentage of the full contract value a counterparty holds for as long as a position is open. The size a risk calculation returns and the size a margin requirement permits are computed from different quantities, and the smaller of the two binds. Neither is a version of the other, and a size that satisfies one says nothing about the other.

The second is that a size correct in isolation is not automatically correct alongside anything already open. Every calculation on this page treats one position as though it were the only one, and positions in related instruments can move together, so the amounts at stake can arrive at once rather than independently. That aggregate is a separate calculation on a separate quantity, and it is the subject of the next lesson.

Where practitioners disagree 

The first disagreement is over deriving distances from a measure at all. Traditions that place distances at features of the chart argue that a multiple of a range measure lands wherever the arithmetic puts it, at a price nothing on the chart distinguishes from any other, and is arbitrary in a way that is merely less visible. The volatility traditions answer that a level read off a chart is not free of arbitrariness either, since which feature counts is a judgement made after the fact, and that a measured distance is at least stated in advance. Both criticisms are accurate about the other method, which is why the argument persists.

The second is about which measure. Average true range is the common choice, but the standard deviation of recent returns and a plain percentage of the current price are used for the same job, and the three are not interchangeable. They weight recent movement differently, respond to a single unusual period differently, and the two averaging methods described in the charts module already produce two lines from identical prices. The same instrument on the same day therefore yields several different distances depending only on which measure and which smoothing were selected, and the differences are not marginal. None of them is the correct measure. They answer slightly different questions about the same bars.

The third concerns positions already open when the reading changes. One account holds that a size computed under a reading that no longer applies is inconsistent with the method that produced it. The other holds that the size decision was made once, at a known price and on a known reading, and that revising it on a moving measure is a second decision taken with less information than the first, while a position is running, and at a cost per adjustment. One rule cannot satisfy both accounts, and the literature does not resolve them.

What is not in dispute is narrower than the argument around it. Stating a distance as a multiple of a measured range makes that distance mean the same thing across instruments and regimes, which a fixed number of points does not. That is a claim about comparability and units, and nothing more. It is not a claim that the distance will be reached less often, that the size is the correct one, or that a measure built from periods that have closed describes the period that has not.