Trading
Risk-Reward and Expectancy: Why No Ratio Guarantees an Edge
Understand planned versus realized reward, break-even win rates, trading costs, and why a 1:2 ratio is not a universal minimum.
A risk-reward ratio compares the loss contemplated by a trade plan with its intended profit. Risking one unit to target two is commonly written as 1:2. It can help describe a proposed trade, but it cannot establish whether the trade or strategy has positive expectancy.
There is no universal rule that 1:2 is the minimum viable ratio. A method with smaller average wins can have positive expectancy if it wins often enough after costs. A method with large targets can lose money if those targets are rarely reached or losses exceed the plan.
Define which ratio you mean
Suppose a hypothetical long entry is 100, the planned stop is 98, and the target is 104. The intended price loss is 2 and the intended gain is 4 per share, before costs. That is risk-to-reward of 1:2, or reward divided by risk of 2. State the convention because both are used.
Those prices are intentions. Partial exits, early exits, slippage, and gaps change realized outcomes. A chart labeled 1:3 does not mean the average winning trade earns three times the average loss. Calculate realized statistics from the actual or realistically simulated trade records.
CME's position-sizing material connects the stop location with the risk budget. It helps establish the planned loss unit, often called R. If a hypothetical trade initially budgets 100 of risk and later earns 150 net, its result is +1.5R. Keep the original denominator so later stop changes do not rewrite the record.
Calculate expectancy from outcomes
For a simplified model with wins and losses, expectancy equals the probability of winning multiplied by the average win, minus the probability of losing multiplied by the average loss. Subtract average costs if the win and loss amounts are recorded before costs. Do not deduct them twice when using net results.
Consider a hypothetical method that wins 40% of trades, averages a gross gain of 2R on winners, and loses 1R on losers. Gross expectancy is 0.40 times 2 minus 0.60 times 1, or +0.20R per trade. If average costs are 0.10R, net expectancy becomes +0.10R under those assumptions.
Now keep the same payoff amounts but reduce the win rate to 30%. Gross expectancy becomes 0.60R minus 0.70R, or -0.10R, before costs. The apparently attractive 1:2 relationship has not prevented a negative expectation.
Understand the break-even calculation
With a constant average win W and average loss L, the gross break-even win rate is L divided by W plus L. At an average win of 2R and loss of 1R, that is one-third, or about 33.3%. At equal average wins and losses, gross break-even is exactly 50%.
If an average cost c is charged per trade separately, the break-even rate becomes L plus c, divided by W plus L. In the 2R and 1R example with costs of 0.10R, the threshold is about 36.7%. These formulas describe the stated model; they do not supply a reliable future win rate.
For another hypothetical example, a 70% win rate with average gross wins of 0.75R and losses of 1R gives +0.225R before costs. This disproves the idea that every viable method requires a target twice its risk. It does not establish that such a method is available or sustainable in practice.
Average results hide difficult paths
Positive estimated expectancy does not mean the next trade should win. Losses can cluster, and an account can suffer a large drawdown before a favorable average appears. A few outsized winners can also make a small sample look stronger than the rest of its outcomes justify.
Review the number of observations, the largest losses, changing market conditions, and whether several trades depend on the same event. Compare separate time periods and examine what happens when costs increase or the win rate weakens. These sensitivity checks reveal how much the conclusion depends on optimistic inputs.
FINRA's day-trading risk disclosure emphasizes substantial trading risk and the effect of commissions. A sensible spreadsheet should therefore include execution friction rather than assuming every intended entry and exit occurs at the displayed price.
Use the ratio as one planning input
A farther target can improve the displayed ratio while reducing how often the target is reached. A tighter stop can create an appealing denominator while increasing premature exits. Evaluate the complete rule instead of optimizing the ratio in isolation.
Record intended risk, intended reward, realized net result, and the reason for any deviation. A journal then lets you compare the trade you planned with the trade you actually executed. The useful objective is evidence about the distribution of outcomes after costs, with uncertainty kept visible. An attractive ratio alone is only a description.