Lesson 8 Risk Reward and Expectancy

Express results in R, calculate basic expectancy, and explain why win rate alone is incomplete.

Compare reward with planned risk

If a hypothetical trade risks 10 USD and targets 20 USD, its planned reward to risk ratio is 2 to 1. A target is an intended exit, not an amount the market owes you. Define 1R as the trade’s initial planned cash loss including the costs and execution assumptions used in sizing. Realised R equals actual net result divided by that fixed initial amount. If the initial planned risk is 8 USD and the realised net loss is 10 USD, the outcome is −1.25R. Keep the original denominator; do not rewrite it after the result. For simple classroom calculations below, assume fixed 10 USD risk, no costs, and exact exits. Live and detailed demo records should use net results and state their cost treatment.

Calculate expectancy

Expectancy is the average outcome per trade in a defined sample or probability model: Expectancy = win probability × average win − loss probability × average loss. In a hypothetical model with a 40% win probability, a 2R average win, and a 1R average loss: 0.40 × 2 − 0.60 × 1 = +0.20R per trade before costs. If average cost is 0.10R per trade, the model becomes +0.10R. This arithmetic does not establish the true probability of winning. A small historical sample is an estimate with uncertainty, not proof that the same average will continue. When computing expectancy directly from net outcomes, do not subtract costs a second time. With wins of 2R and losses of 1R, the theoretical break even win rate before costs is 1 ÷ (2 + 1) = 33.33%. Costs raise the required rate. A 90% win rate can still lose money if the rare losses are very large.

Understand drawdown

Drawdown is a decline from an equity peak to a subsequent lower value. A fall from 2,000 USD to 1,800 USD is a 10% drawdown. Returning from 1,800 to 2,000 requires an 11.11% gain. Smaller losses reduce the recovery required, but no chosen risk fraction makes a strategy profitable by itself. If you lose 0.5% of the remaining equity ten times in a row, equity is multiplied by 0.995 ten times. The decline is about 4.89%, before extra charges or losses beyond planned stops. Losing streaks remain possible even in a model with positive expectancy.

Practice

For ten hypothetical trades with four wins of +2R and six losses of −1R, calculate total R, average R, win rate, and USD result if 1R is fixed at 10 USD. Then deduct a total sample cost of 1R and recalculate average net R.

Check your understanding

After the four lessons in this module, complete Module 2 knowledge check from the course overview. It contains the three questions from each lesson with feedback after submission. Keep written calculations in your workbook.

Glossary

Drawdown: Decline from an equity peak to a subsequent lower value
Equity: Account value including open profit or loss and applicable adjustments
Expectancy: Average trade outcome in a defined sample or probability model
R: A result measured relative to the initial planned cash risk