Lesson 4 of 6 · 8 min

Risk-Reward Ratio and Expected Value

Measuring results in money is confusing, because amounts depend on account size. That is why we use R: one unit of risk, that is, the amount you lose if the stop is triggered. With risk of 100, a loss is −1 R and a profit of 250 is +2.5 R. The risk-reward ratio (R:R) tells you how many R you are aiming for relative to 1 R of risk.

Expected value

Expected value per order = hit rate × average win − miss rate × average loss. It is the average outcome of a single order, viewed across many orders, if the assumptions hold.

The break-even threshold without costs is 1 / (1 + R:R). A ratio of 1 requires a 50% hit rate, a ratio of 2 requires 33.33%, a ratio of 3 requires 25%, and a ratio of 0.5 requires 66.67%. A bigger ratio isn't free: a distant target is reached less often, so in practice the hit rate falls.

Costs in R

The costs of a round trip on the demo, with a market buy and an exit at the stop, come to about 0.25% of the position size: twice 0.10% fee plus 0.05% stop slippage. The spread and walking through the book come on top, so count on roughly 0.3%. Divide that by the stop in percent and you get the cost in R. A 5% stop means 0.06 R, a 3% stop means 0.1 R, a 2% stop means 0.15 R, and a 0.5% stop means 0.6 R per order. That is why very tight stops ruin otherwise sensible systems.

Streaks are normal

A system with a 40% hit rate over 100 independent orders will have at least 5 losses in a row with a probability of about 97.6%, at least 8 with about 49%, and at least 10 with about 20.5%. These are calculations, not historical data. So a streak of eight losses in a profitable system is roughly a coin flip within a period of a hundred orders. Anyone who doesn't plan for this abandons the system at the worst moment or raises their risk.

In the lab, set a hit rate and a ratio and then simulate 100 orders several times. With the same settings the curves will differ. Some will stay below the start for longer, even though the expected value is positive. The simulation does not include costs, so subtract their share in R from the expectation it shows. Also see what happens when you lower the hit rate a little.