Introduction
Every edge has variance. Every edge has losing streaks. The traders who survive long enough to profit from edge are the ones whose sizing math survives the streaks. The ones who don’t, don’t get a second chance.
This guide is the math. R-multiples, expectancy, sizing, drawdown, correlation, and the rules that turn abstract probability into concrete per-trade decisions you can actually execute.
R-Multiples: The Unit of Trading
R is your initial risk on a trade - the dollar amount you lose if the stop is hit. Every outcome is measured in multiples of R.
Example
You buy 100 shares at $50 with a stop at $48. Risk per share = $2. Position risk = $200 = 1R. If you exit at $54, you made $4/share × 100 = $400 = +2R. If the stop gets hit, you lose $200 = -1R.
Why R matters more than P&L
- It normalizes across position sizes. A +2R trade on a 50-share lot compares directly to a +2R trade on a 500-share lot.
- It normalizes across markets. +2R on ES futures and +2R on AAPL shares mean the same thing in system terms.
- It’s the unit of expectancy. You can’t compute a real edge without it.
Expectancy: Whether Your System Works
Expectancy is the average R per trade. Positive means you have an edge. Negative means you don’t.
The formula
Expectancy = (Win% × Avg Win R) − (Loss% × Avg Loss R)
Worked example
You win 40% of trades. Your average winner is +2.5R; your average loser is -1R. Expectancy = (0.40 × 2.5) − (0.60 × 1.0) = 1.0 − 0.6 = +0.4R per trade. Over 200 trades, that’s +80R of realized edge.
The counterexample
You win 75% of trades. Your average winner is +0.5R; your average loser is -2R. Expectancy = (0.75 × 0.5) − (0.25 × 2.0) = 0.375 − 0.50 = -0.125R per trade. You have a losing system that feels great because you win most trades.
Position Sizing
Position sizing answers: how many shares / contracts / lots, given my account, my % risk, and my stop distance?
The formula
Position size = (Account × Risk %) / Stop distance per unit
Worked example
$20,000 account. 1% risk = $200. Stop distance = $1.50. Shares = $200 / $1.50 = 133 shares.
Fixed vs Variable Risk
- Fixed fractional (1% per trade)
- Risk the same % of current equity on every trade. Grows with the account; shrinks during drawdowns. Simple, robust, recommended default.
- Fixed dollar risk
- Same $ on every trade regardless of account. Predictable but doesn’t scale with growth.
- Variable / scaled
- Risk varies by setup grade - A+ setup 2%, B setup 1%, C setup 0.5%. Requires very honest trade grading; easy to self-deceive.
- Volatility-scaled
- Risk adjusted to current ATR so dollar risk is same but % risk changes with volatility. Better for pairs with variable volatility (crypto, FX).
Kelly Criterion (and Why Half-Kelly)
The Kelly Criterion computes the optimal bet fraction for long-run growth given your edge.
The formula (simplified for win/loss)
Kelly % = W − (1 − W) / R where W = win rate, R = avg win / avg loss ratio.
Example
60% win rate, 2:1 avg win/avg loss. Kelly = 0.60 − 0.40/2 = 0.40 = 40% per trade. Correct in theory, suicidal in practice.
Drawdown Math
Drawdown is asymmetric. A 50% loss requires a 100% gain to recover. This is the single most important thing new traders don’t intuit.
The recovery table
- -10% drawdown
- Needs +11% to recover
- -20% drawdown
- Needs +25% to recover
- -30% drawdown
- Needs +43% to recover
- -40% drawdown
- Needs +67% to recover
- -50% drawdown
- Needs +100% to recover
- -60% drawdown
- Needs +150% to recover
- -70% drawdown
- Needs +233% to recover
- -80% drawdown
- Needs +400% to recover
Correlation: The Hidden Risk
Your open risk is the sum of your open stops - IF those trades are uncorrelated. Two correlated longs (e.g. ES + NQ) are essentially one bigger position when risk-off hits.
Rules
- Count correlated positions as one combined position for total-open-risk calculations.
- Common correlation traps: long SPY + long QQQ; long EUR/USD + short USD/CHF; long BTC + long ETH.
- Sector correlation: 3 long tech names = 1 tech trade with 3x size.
- In risk-off regimes, everything correlates to 1 temporarily. Sizing for correlation-1 is the safe default.
Risk of Ruin
Risk of ruin is the probability that a negative streak wipes your account. It’s a function of: edge, risk per trade, and account size.
Rough intuition
- At 1% per trade with positive expectancy, risk of ruin is effectively zero over any realistic time horizon.
- At 5% per trade with positive expectancy, you can still have a 10%+ probability of catastrophic drawdown over 500 trades.
- At 10% per trade, you’re essentially guaranteed ruin within a reasonable sample size, regardless of edge.
Daily & Weekly Loss Limits
Variance is a force multiplier for tilt. Hard caps stop bad days from becoming bad weeks.
- Daily loss limit: 2R or 2% of account. Whichever is lower. Hit, platform closed.
- Weekly loss limit: 4R or 4%. Hit, trading paused until Monday with a written breakdown of what’s going wrong.
- Max consecutive losses: after 4–5 in a row, size down to 0.5% until you have 3 winners.
- Max drawdown pause: at 10% account drawdown from peak, reduce size by 50% until fully recovered.
Profit-Taking Frameworks
Profit-taking is a risk-management discipline, not just greed management.
- Fixed-R target (single exit)
- Exit full position at +2R or +3R. Simple; works for mechanical systems.
- Tranched (one-third rule)
- One third out at +1R, one third at +2R, stop to breakeven, let the last third run with trailing stop. Most popular retail framework.
- Scale out at levels
- Exit a tranche at each key resistance. Aligns with chart structure, not pure math.
- Trailing stop
- Mechanical trail (e.g. 1 ATR below recent swing low). Lets winners run; no early exits from FOMO.
- Time-based exit
- If target not hit in X bars, flat the position. Useful for day-trade setups that should move fast if right.
Tail Risk & Black Swans
Markets have fatter tails than normal distributions suggest. 10-sigma events happen more than once per decade because the real distribution isn’t Gaussian.
What to do
- Hard stops always. Mental stops get gap-over-ed.
- Don’t concentrate overnight risk. Overnight gaps skip stops.
- Cash reserves: at least 25% of your account as dry powder. Crashes create setups; you need capital to take them.
- Avoid binary-event holds: earnings, FDA, policy announcements. The tail is asymmetric.
- Geographic/broker diversification: don’t keep everything at one firm or on one exchange.
The Practical Rulebook
The condensed version you can actually execute:
- Risk 1% per trade. 0.5% in your first 90 days. 2% only when you’ve got 200+ logged trades with stable expectancy.
- Always have a stop in the market. OCO bracket at entry.
- Minimum 2:1 R:R. Lower isn’t a trade, it’s a gamble.
- Max 3 open positions. Correlated pairs count as one.
- Daily loss limit: 2R. Hit, platform closed.
- Never add to losers without a pre-written mechanical rule.
- Flatten before news. Or explicitly trade them with smaller size and pre-planned orders.
- Size down after drawdown. 50% for a week after any 10%+ drawdown from peak.
- Withdraw profits. Monthly or quarterly. Realized money cannot be unrealized.
Put It to Work
- Compute R at entry on every trade. Calculator handles the math.
- Log R-multiples in Journal - the system derives expectancy for you.
- Review expectancy monthly in Reports. If it drops two months in a row, something in your setups is decaying - investigate before scaling.
- Track discipline via Progress Tracker. Rule adherence % is the leading indicator of drawdown.