What reward to risk describes

Two distances measured from one price 

A plan that specifies an exit in both directions contains three prices. There is the price at which the position opens. There is the level at which the position is closed against the account, which is where a stop order rests. And there is the level at which the position is closed in its favour, which is where a limit order to exit, conventionally called a take profit, rests. The first of those is a price the market has actually traded at. The other two are levels chosen by the person writing the plan, and neither of them is a statement about the market. They are instructions waiting for the market to reach them.

The ratio is not built from the prices themselves but from the gaps between them. The distance from the opening price down to the stop level is the risk distance. The distance from the opening price up to the planned exit is the reward distance. For a position held the other way round the two levels swap sides, the stop sitting above the opening price and the planned exit below it, and the arithmetic is unchanged: it is the sizes of the two gaps that enter the calculation, never their direction. Dividing the reward distance by the risk distance produces a single dimensionless number, because whatever unit the distances were measured in cancels out.

That cancellation is why the number gets used at all. Distances quoted in pips on a currency pair, in index points on an index contract and in cents on a share cannot be compared with one another. A ratio built from two distances in the same instrument can be, because the quoting convention divides out of it. The same property is what makes the number easy to overstate: it survives the removal of every fact about the instrument, which means it also contains none of them.

The ratio is complete before anything happens 

The number in the block above was finished before the position existed. Nothing about the market was consulted to produce it, and nothing the market subsequently does can change it, because every quantity in it was chosen. This is the single most misread property of reward to risk. A ratio of two to one is often spoken about as though it described a relationship between an amount gained and an amount lost, when it describes a relationship between two distances on a chart, only one of which will ever be reached, and possibly neither.

Four outcomes are open to a position with both levels resting. The stop level trades. The planned exit trades. Neither trades and the position stays open, in which case the ratio describes a plan that is still pending. Or the position is closed by hand, or by a limit reached elsewhere in the account, at a price that is neither of the two levels, in which case the ratio describes a plan that was written and then not followed. Only one of those four outcomes produces the numbers the ratio was built from.

The opening price is not fixed either, and that is the part most often left out. A market order fills at whatever price is available when it reaches the venue, which may differ from the price on screen when it was sent, and a stop order used as an entry fills at whatever price is available after the level is touched rather than at the level itself. Because both distances are measured from the opening price, a fill away from the expected price lengthens one distance and shortens the other at the same time. The ratio a position actually carries is therefore known only after it has opened, and it is not always the ratio that was calculated.

The adverse distance carries a further qualification that the favourable one does not. A resting stop order is an instruction to close a position once a level is reached, not an agreement about the price at which it closes. When a market gaps through the level, at a weekend open or on a scheduled release, the position closes at the first price available beyond it, so the realised loss can be larger than the planned distance implied and can exceed the amount deposited. The planned exit has no equivalent asymmetry working in the other direction as a matter of course, so a ratio computed on planned distances quietly assumes the one side that is least assured.

Costs are subtracted from one distance and added to the other 

The cost of opening and closing a position, the round turn, is charged whichever of the two levels trades. It does not wait to see how the position resolves. That single fact is what separates the ratio a plan states from the ratio the account records, and it works in the same direction every time. Cost reduces the amount credited when the favourable level trades, and it increases the amount debited when the adverse level trades. It lands on the numerator and the denominator in opposite senses, so the ratio after cost is always lower than the ratio before it, for any cost above zero.

How much the ratio moves is a question of proportion rather than of the cost itself. A round turn is a broadly fixed amount for a given instrument and a given size, while the two distances are chosen freely, so the same cost is a small fraction of a wide stop and a large fraction of a narrow one. Two plans with an identical stated ratio and identical costs can therefore record materially different ratios once the account settles, purely because one was drawn with more room in it than the other. The block below is the previous plan with the distances shortened and nothing else changed.

Two consequences follow from reading the blocks together. A stated reward to risk is not comparable between two plans unless the cost is stated beside it. And the shorter the distances a plan works over, the more of the ratio the cost consumes, which is the same arithmetic that makes cost the dominant term for anything traded frequently over small distances. That relationship was established in the costs module. Reward to risk only makes it visible in a second place.

The two things the number does not contain 

The first omission is frequency. The ratio compares two distances and is silent about how often the market reaches either of them. A plan whose planned exit sits further away is a plan whose exit level requires a longer move before it trades, and moving a stop level closer to the opening price raises the ratio while placing the stop inside a smaller band of ordinary movement. Both adjustments improve the arithmetic without touching the market. This page carries no figure for how often either level is reached, for any plan, because no such figure exists here in a form that could be verified, and a ratio computed on distances cannot supply one.

The consequence is that a higher ratio is not, on its own, a better one. It is a larger number produced by a calculation whose inputs are chosen, and the same number can be produced by widening the exit, by narrowing the stop, or by both. Nothing in the arithmetic distinguishes those cases, and nothing in it registers that the second one puts the stop level closer to the range the instrument moves through in an ordinary session. How the two levels relate to the instrument's own behaviour is the subject of the lessons on stop placement later in this module, and it is a separate question from the ratio entirely.

The second omission is the account. A ratio is a shape, not a size. The same two to one plan can be expressed at a contract size that puts a trivial amount at risk or at one that puts a large fraction of an account at risk, and the ratio is identical in both cases because size divides out of it exactly as the quoting convention does. The amount at risk comes from the risk per trade decision and the stop distance, which the earlier lessons in this module derived. Reward to risk sits alongside that decision and does not participate in it, so a plan described only by its ratio has not been described at all.

• It describes two distances chosen in advance, expressed as one dimensionless number.
• It does not describe how often either distance is covered by the market.
• It does not describe how much money is at risk, which comes from size and the stop distance.
• It does not survive contact with cost unchanged, and the direction of that change is always downward.

Where practitioners disagree 

The first argument is whether a stated minimum ratio belongs in a plan as a filter. One convention holds that a floor written down in advance removes a decision from the moment it is hardest to make, and that a rule with one input is a rule that survives contact with a live screen. The criticism is exact and is not answered by that reasoning: a filter on a ratio is a filter on arithmetic rather than on a market, and it is satisfied just as easily by moving the stop level closer as by finding a plan with more room in it. A constraint that can be met by changing the constraint's own inputs constrains very little.

The second argument is whether a single ratio is even well defined once an exit stops being one level. A plan that closes a position in parts, or that moves its stop level as the position runs, produces a range of possible results rather than one, and the reward distance in the calculation becomes a representative figure standing in for something that varies. Practitioners who work that way generally treat the ratio as an approximation stated at entry and nothing more. Practitioners who keep both levels fixed answer that a number which changes after the position opens is not a plan but a commentary, and that the fixed version is the only one that can be checked afterwards.

The third argument is which ratio should be recorded once a position has closed: the one calculated from the levels that were planned, or the one calculated from the prices that actually occurred, including the fill, the cost and any gap through the stop level. The planned figure is comparable across positions and describes an intention. The realised figure describes what happened and is not comparable, because every position carries its own fill and its own cost. The disagreement matters mostly because the two numbers drift apart in the same direction over time, which is a fact about costs rather than about intentions.