Risk and method
Reward-to-Risk Ratio: Entry, Target and Stop, Worked Out
How the reward-to-risk ratio is computed from entry, target and stop, the win rate each ratio needs to break even, expectancy in R, and position sizing.
Updated · 4 min read
Three numbers and a ratio
A trade with a plan has three prices before it has a result. The entry is where it is taken. The stop is where the idea is wrong and the position is closed at a loss. The target is where the profit is taken. The reward-to-risk ratio compares what the trade aims at with what it puts at risk:
R = (Target − Entry) / (Entry − Stop) for a long position
R = (Entry − Target) / (Stop − Entry) for a short position
An entry at 100 with a target at 112 and a stop at 96 risks 4 to make 12: a reward-to-risk of 3, written 3R or 3:1. The ratio is fixed the moment the three levels are, before anything is known about whether the trade will work. That is its value: it is the one number about a trade that is decided rather than discovered.
The win rate each ratio needs
A trade that risks one unit to make R units breaks even, over many trades, when the wins pay for the losses:
Breakeven win rate = 1 / (1 + R)
| Reward to risk | Win rate to break even | At a 40% win rate, the result per trade |
|---|---|---|
| 0.5 | 67% | −0.40R |
| 1 | 50% | −0.20R |
| 2 | 33% | +0.20R |
| 3 | 25% | +0.60R |
| 5 | 17% | +1.40R |
The table says what every experienced trader eventually learns: a method that is right only 40% of the time is profitable at 2R and lucrative at 3R, and a method that is right 60% of the time loses money at 0.5R. Win rate and reward-to-risk trade off against each other, because the further away the target is placed, the less often it is reached. The combination is what matters, and the measure of the combination is expectancy.
Expectancy
Expectancy is the average result per trade, in units of the risk taken:
Expectancy = p × R − (1 − p) × 1
where p is the win rate. At p = 0.4 and R = 2 it is 0.4 × 2 − 0.6 = +0.2R: each trade earns a fifth of its risk on average. Over a hundred trades risking 1% each, that is roughly 20% before costs, which the arithmetic also shows must be subtracted: a spread and commission that costs 0.1R per trade turns a +0.2R method into a +0.1R one.
Measuring a record in R rather than in money or percentages makes trades comparable: a 3R win on a currency pair and a 3R win on a stock are the same achievement, and a record is read as its average R and its win rate rather than as a list of amounts.
Sizing from the stop
The stop also sets the size of the position. Decide the amount to risk on the trade, usually a fixed share of the account, and divide by the distance to the stop:
Position size = Amount risked / (Entry − Stop)
With a 10,000 account risking 1%, 100, and a stop 4 away from the entry, the position is 25 shares. With a stop 2 away, it is 50 shares, and with a stop 10 away, 10 shares. The size follows from the stop, not from conviction, which means a wider stop is paid for with a smaller position and not with more risk.
Where the levels come from
A stop placed at a round number below the entry is a guess; a stop placed below the level that would prove the idea wrong is a plan. The usual sources are market structure, the swing low or high that the trade is betting will hold; volatility, a multiple of the average true range so that ordinary noise does not stop the trade out; and the levels other traders are watching, such as moving averages and pivot points. Targets come from the same places on the other side: the next level of resistance, a measured move, the opposite band.
A trade whose honest stop and honest target give a reward-to-risk below 1 is not improved by moving the stop closer. It is a trade to leave alone.
Judging a record
A list of closed trades is judged by its average R, its win rate, its largest losing run and its drawdown, in that order. A record with a 35% win rate and an average winner of 3R is better than one with a 65% win rate and an average winner of 0.6R, and a record that quotes only its win rate has left out the number that decides whether it made money. The levels have to be stated before the trade, scored from the entry, and the result recorded whether the stop or the target was hit; a record that moves its stops after the fact is a story.
On the desk
The Stock Picker publishes every trade with its instrument, side, entry, target and stop, computes the reward-to-risk from them, shows the live distance from the current price to each level, and scores each pick from its entry until the desk closes it, with the open picks, the closed record, the hit rate and the average move on the page. Every market report stamps the price at publication and is scored against the tape from then on.
Questions
- How do you calculate the reward-to-risk ratio?
- Divide the distance from the entry to the target by the distance from the entry to the stop. For a long trade, R = (Target − Entry) / (Entry − Stop). An entry at 100, a target at 112 and a stop at 96 gives 12 / 4, a reward-to-risk of 3.
- What is a good risk-reward ratio?
- One that, combined with the method's win rate, has a positive expectancy. A ratio of 2 breaks even at a 33% win rate and a ratio of 3 at 25%, so a method that is right less than half the time can be very profitable at 2R or 3R. A ratio below 1 needs a win rate above 50% just to break even.
- What does 3R mean in trading?
- A result equal to three times the amount risked on the trade. If a trade risked 100 from the entry to the stop and made 300, it was a 3R win. Measuring results in R makes trades of different sizes and in different markets comparable.
- How do I size a position from a stop loss?
- Decide the amount you will risk on the trade, usually a fixed share of the account such as 1%, and divide it by the distance from the entry to the stop. Risking 100 with a stop 4 away gives a position of 25 shares. A wider stop means a smaller position, not more risk.
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