Risk-to-reward ratios

The ratio

A trade with a stop 25 pips away and a target 50 pips away risks one unit to make two, a risk-to-reward ratio of 1:2. The ratio is set before the trade by where the stop and the target are placed, and it is independent of the position size, which scales both sides equally. It is usually written with the risk first, so 1:2 or 1:3 means the target is two or three times the stop.

Why it only means something with the win rate

A ratio on its own says nothing about whether a trade is a good idea, because a target three times the stop is also three times as far away and less likely to be reached. What matters is the combination of the ratio and how often the target is hit. The break-even win rate for a ratio of 1:R is 1 divided by (1 + R): a trader taking 1:1 trades needs to win more than half; at 1:2, more than a third; at 1:3, more than a quarter. Above that rate the approach makes money over enough trades, below it the approach loses, and the size of the gap decides how fast.

The expectancy per trade, in units of risk, is the win rate times the reward minus the loss rate times the risk. A trader winning 40 percent of 1:2 trades has an expectancy of 0.4 times 2 minus 0.6 times 1, or 0.2 units per trade: a fifth of the risk amount, on average, per trade, before costs.

The costs sit on both sides

The spread and commission are paid whether the trade wins or loses, and they shift the arithmetic. A 25 pip stop and a 50 pip target on a pair with a 1 pip spread is really a 26 pip risk and a 49 pip reward, which is 1:1.9 rather than 1:2, and the shorter the stops the larger the effect. On a five pip stop a one pip spread is a fifth of the risk. This is why scalping strategies with tight stops are so sensitive to the broker's spread, and why the spread comparison is worth reading with the ratio in mind.

How the ratio is misused

The common error is to choose the ratio first and place the target to fit it, regardless of whether the chart offers any reason to expect the price to get there. A target placed at twice the stop because the ratio says so is a wish, not a plan. The stop and the target should each be placed where the market gives a reason, and the ratio is then a fact about the trade that helps decide whether to take it.

The opposite error is to refuse any trade under a favourite ratio. A 1:1 trade with a 65 percent win rate has a better expectancy than a 1:3 trade with a 20 percent win rate. The ratio and the win rate have to be judged together, from a record of actual trades, which is the argument for keeping one.