Position size and risk/reward, explained with worked examples

01 What the formula actually solves

Every trade needs two decisions made before it is placed: how much of the account is acceptable to lose if the trade is wrong (a risk percentage), and where the market proves the trade wrong (a stop-loss price). Position sizing is the arithmetic that turns those two decisions into one number — how many units of the asset to buy or sell.

Skip that step and one of the two numbers becomes a guess. Deciding "buy 0.2 BTC" without first fixing a risk percentage means the amount actually at risk isn't known until the stop is already set — and by then the position can't be sized correctly, only checked after the fact.

02 Worked example 1 — a long trade

BTC/USDT, a $10,000 account, 1% risked on the trade.

1. Risk amount = $10,000 × 1% = $100. That is the most this trade is allowed to lose.
2. Entry price = $60,000. Stop-loss = $58,800, placed below the last swing low.
3. Stop distance = $60,000 − $58,800 = $1,200.
4. Position size = $100 ÷ $1,200 = 0.0833 BTC.
5. Position value = 0.0833 × $60,000 = $5,000 — half the account, well within what a $10,000 balance can actually hold.
6. Take-profit = $63,600, so reward distance = $63,600 − $60,000 = $3,600.
7. Risk/reward = $3,600 ÷ $1,200 = 3:1. For every $1 risked, the target pays $3.

If the trade is stopped out, the loss is exactly the $100 fixed in step 1 — not a cent more, because the position size was derived from the stop, not the other way around.

03 Worked example 2 — a short trade

ETH/USDT, the same account, 1.5% risked. Shorting changes only where the stop sits: above entry instead of below it.

1. Risk amount = $10,000 × 1.5% = $150.
2. Entry price (short) = $3,000. Stop-loss = $3,090, above the recent high.
3. Stop distance = $3,090 − $3,000 = $90.
4. Position size = $150 ÷ $90 = 1.667 ETH.
5. Position value = 1.667 × $3,000 = $5,000.
6. Take-profit = $2,820, so reward distance = $3,000 − $2,820 = $180.
7. Risk/reward = $180 ÷ $90 = 2:1.

Same formula, same order of operations — only the direction of the stop and target flips.

04 Worked example 3 — the R:R that looks perfect and isn't

SOL/USDT, the same $10,000 account, 1% risked. This time the stop is placed as close as possible, to make the ratio look as good as possible.

1. Risk amount = $10,000 × 1% = $100.
2. Entry price = $150.00. Stop-loss = $149.85 — ten cents away.
3. Stop distance = $150.00 − $149.85 = $0.15.
4. Position size = $100 ÷ $0.15 = 666.67 SOL.
5. Position value = 666.67 × $150 = $100,000 — ten times the entire account, for a $100 risk.
6. Take-profit = $154.50, so reward distance = $154.50 − $150.00 = $4.50.
7. Risk/reward = $4.50 ÷ $0.15 = 30:1.

The ratio is real arithmetic, and on paper it is spectacular. The position size is what exposes the problem: sizing a $100 risk against a ten-cent stop asks for a position worth ten times the account, which a $10,000 balance cannot actually hold without extreme leverage. A ten-cent stop on a $150 asset also sits inside the range a single candle's wick crosses routinely — it gets hit by ordinary price noise, not by the market disagreeing with the trade thesis. Every one of those stop-outs happens for a reason that has nothing to do with whether the original idea was right.

The fix is not to accept the leverage. It's to widen the stop to a level the market actually respects and accept the lower, more realistic ratio that comes with it — or to skip the setup. A risk/reward ratio only means something once the stop is where it belongs, not wherever makes the number biggest.

05 Breakeven win rate

Every risk/reward ratio implies a minimum win rate before a strategy is merely breakeven, ignoring fees:

where R is the reward-to-risk ratio from the sizing above.

The last row is example 3's ratio, and it's exactly why that setup is tempting — a breakeven bar of 3.2% looks almost impossible to miss. But the formula assumes every stop-out means the trade idea was wrong. A stop placed inside normal price noise breaks that assumption: it can be hit far more often than the market actually invalidates the trade, and no formula corrects for a stop that was never a real level to begin with.

06 Putting it into practice

All three examples use the same four inputs — account balance, risk %, entry, stop — and produce the same two outputs: position size and risk/reward. Decide the first four before looking at a chart, not after. A risk percentage chosen after seeing how big a position "feels right" isn't risk management; it's a story told backward from a size someone already wanted.

A reasonable starting point is a fixed risk of 0.5%–2% per trade, with the stop placed at the price level that actually invalidates the setup — a swing high or low, not a distance picked to make the ratio look good. From there, position size stops being a judgment call: it's the arithmetic above, and it's worth running against real historical candles before it's run against real money.

FreeBacktest is an educational tool. Nothing here is investment advice. Past results — real or simulated — do not predict future results.