Risk and position size

R: measuring outcomes in units of risk instead of currency

A result in currency tells you about the size of your account. A result in R tells you about the trade. They are different questions, and almost everybody answers the first one while believing they answered the second.

About 9 minutes to read. Free, no account.

The definition, which is deliberately boring

One R is the amount you had at stake when the trade began - the risk amount from the previous lesson. Every outcome of that trade is then reported as a multiple of it.

1R          =  the risk amount set before entry
result in R =  profit or loss  /  1R

stop hit as planned   =  -1.0R
closed at breakeven   =   0.0R
twice the risk made   =  +2.0R

The whole point of the denominator is that it is fixed before you know anything. R is not recomputed when the trade goes well, and it is not the amount you ended up losing - it is what you agreed to lose at the start. That is what makes it a unit.

Why it makes two unlike trades comparable

Take trade A and trade C from the position-size lesson. Same account, same risk amount, completely different coins, completely different stop distances. Suppose both reach a target.

trade A   entry 1.2500   800 units      notional 1,000
          exit  1.3400
          gain  0.0900 x 800            =  72
          as a percent of notional      =  7.20%
          in R   72 / 40                =  +1.80R

trade C   entry 0.0340   20,000 units   notional 680
          exit  0.0375
          gain  0.0035 x 20,000         =  70
          as a percent of notional      =  10.29%
          in R   70 / 40                =  +1.75R

Read the two middle lines against the two bottom ones. By percentage of notional, trade C was clearly the better trade: 10.29% against 7.20%. In R, trade A was the better trade: 1.80 against 1.75. Both statements are arithmetically correct, and they disagree because percentage of notional is mostly a statement about how far away the stop was, which is a property of the chart rather than of your decision.

R strips that out. It asks one question - how much did this trade return relative to what it was allowed to lose - and that question has the same meaning on a coin at 60,000 and a coin at 0.0004, on a 15-minute scalp and on a position held three weeks.

A loss is not automatically minus one R

It is worth recording the actual multiple rather than assuming. The slipped fill from the stop lesson gives a loss larger than 1R on a stop that worked exactly as designed.

planned     1.2500 - 1.2000  =  0.0500 x 800  =  40   =  -1.00R
realised    1.2500 - 1.1940  =  0.0560 x 800  =  44.8 =  -1.12R

the gap exit at 1.1300:
            1.2500 - 1.1300  =  0.1200 x 800  =  96   =  -2.40R

Those extra fractions of an R are where the difference between a plan and its execution lives, and they are invisible if you record "stop hit" instead of a number. A record of exits in R is the cheapest possible measurement of how much your real trading differs from the version of it on paper.

The break-even arithmetic R makes visible

Once results are in R, the question "is this set of rules worth following" becomes a weighted average with no currency in it at all. Suppose a share p of occasions end at plus 2R and the rest at minus 1R.

average  =  p x (+2)  +  (1 - p) x (-1)
         =  2p - 1 + p
         =  3p - 1

zero when 3p = 1, that is p = 1/3 = 33.3%

p = 0.30   ->  3(0.30) - 1  =  -0.10R per occasion
p = 0.40   ->  3(0.40) - 1  =  +0.20R per occasion

The general form is as simple: with a target of T times R and a loss of one R, the break-even share is 1 / (1 + T). A target of 1R needs 50.0%; a target of 3R needs 25.0%; a target of 0.5R needs 66.7%. Check the last one: 1 / 1.5 = 0.667.

Two honest warnings about that arithmetic, because it is the formula most often used to make a bad plan look arithmetically inevitable.

• The share and the target are not independent. Asking for a larger multiple of R makes reaching it less frequent. You cannot improve the average by writing a bigger number in the target column; you can only find out what the bigger number costs you in frequency.
• p is not knowable from a small record. With twenty occasions the share you measure is dominated by noise, and the honest statement is that you do not yet know. The arithmetic above is a definition of break-even, not evidence about any particular set of rules - yours, ours, or anybody’s.

The next lesson adds the term this one leaves out: the average per occasion is not the whole story, because the order the occasions arrive in decides whether you are still there to collect it.

How to keep a record in R

Four columns are enough, and they have to be filled in the right order: the first three before the trade, the last one after it.

• The risk amount in currency. This is 1R for this trade, written down before entry and never edited afterwards.
• Entry and stop, as prices. Not "support", not "the low" - the numbers.
• The target or the exit rule, in R. If you cannot say what the exit rule is, the result you eventually record is a number about your nerve rather than about the rule.
• The realised result in R, computed from the fill you actually got, including slippage and fees.

Thirty rows of that is worth more than any amount of reading, because it is the only document in trading that is about you rather than about the market. It is also the only way to notice the two habits that wreck otherwise sound plans: exits well short of the stated target, and losses consistently worse than 1R.

The terms, defined

R

The risk amount fixed before a trade begins. One unit of what you agreed to lose.

R multiple

An outcome divided by R. Minus one R is the stop working as planned; plus two R is twice the risk returned.

Break-even share

For a target of T times R against a one R loss, 1 / (1 + T). The share of occasions at which the average result is zero.

Average result per occasion

The weighted mean of outcomes in R. A property of a set of rules plus a share, not a forecast of the next trade.

Realised R

The outcome computed from the fill you actually received, fees and slippage included. Often worse than the planned multiple, and that gap is the thing worth measuring.

What this means in practice

• Fix 1R before entry, in currency, and never edit it afterwards.
• Report every outcome as a multiple of R, including the ones that ended near zero.
• Record losses as the multiple they actually were. A string of exits at minus 1.2R is a fact about your execution, not about the market.
• Use the break-even formula to understand what a target demands of you, not to argue that a plan must work.
• Distrust any share measured on a handful of occasions, including your own.
• Compare trades, coins and timeframes in R. Compare account balances in currency. Do not mix the two.

Nothing in this lesson is financial advice or an instruction to trade. See the risk disclaimer. We never recommend a leverage setting - that decision is yours.