Risk Management — Position Sizing & Kelly

📐 Position Sizing (Fixed Fractional)

Position Size = (Capital × Risk%) ÷ (Entry − Stop)

The most important formula in trading. Not to maximise profit, but to stay in the game.

Example: Capital $10,000 · Risk 1% · Entry $180 · Stop $175 → Risk/share $5 · Position size = 20 shares ($3,600 deployed)

⚖️ Risk/Reward Ratio

R/R = (Target − Entry) ÷ (Entry − Stop)

How much do you risk for how much potential gain? Minimum 1:2, ideally 1:3.

Example: Entry $180 · Stop $170 · Target $210 → Risk $10 · Gain $30 → R/R = 1:3.0

🎯 Break-Even Win Rate

Min. Win Rate = 1 ÷ (1 + R/R)

The minimum win rate to be profitable long-term — independent of luck.

R/R 1:1 → 50% needed · 1:2 → 33.3% · 1:3 → 25% · 1:5 → 16.7%

🧮 Kelly Criterion

Kelly% = Win Rate − ((1 − Win Rate) ÷ R/R)

Mathematically optimal position size. In practice: use Half-Kelly (Kelly ÷ 2) — psychologically more bearable with nearly identical growth.

Example: Win rate 45% · R/R 1:3 → Kelly 26.7% → Half-Kelly = 13.3% per trade (upper limit!)

📉 Drawdown Recovery Maths — what −20% really means

Drawdown	Required gain	Formula: 1 ÷ (1 − DD%) − 1	Assessment
−5 %	+5,3 %	1 ÷ 0,95 − 1	✅ Normal
−10 %	+11,1 %	1 ÷ 0,90 − 1	✅ Manageable
−20 %	+25,0 %	1 ÷ 0,80 − 1	✅ Still OK
−30 %	+42,9 %	1 ÷ 0,70 − 1	⚠ Critical
−40 %	+66,7 %	1 ÷ 0,60 − 1	⚠ Very critical
−50 %	+100,0 %	1 ÷ 0,50 − 1	❌ Dangerous
−75 %	+300,0 %	1 ÷ 0,25 − 1	❌ Almost irreparable
−90 %	+900,0 %	1 ÷ 0,10 − 1	❌ Game Over

Per Trade

1–2 %

Max. loss per trade. With $10,000 capital: max. $100–$200 risk.

Per Trading Day

−4 %

Daily stop. After −4% account loss: no more trading today. Fresh start tomorrow.

Max. Drawdown

−15 %

Hard stop. At −15% account loss: pause, review strategy.

🧠 The 4 Most Dangerous Psychological Traps

❌ Loss Aversion Holding losses, taking profits too early. Pain of loss weighs 2× as much as joy of gain (Kahneman/Tversky).

Fix: Set stop-loss before entry, never move it. Trailing stops for winners.

❌ Overconfidence Increasing risk after a winning streak. Luck gets mistaken for skill. The next loss wipes it all out.

Fix: Fixed risk rules, no adjustments before < 50 trades. No "reward" through bigger risk.

❌ Revenge Trading Doubling down immediately after a loss to "get it back". Fight-or-flight mode instead of system.

Fix: 24-hour rule after a losing day. Strictly respect daily loss limit.

❌ FOMO Entering running moves "because the price is moving". Usually at the worst point (top).

Fix: Only trade with a defined setup. Wait for pullbacks, don't chase the market.

✅ Pre-Trade Checklist — before EVERY entry

Stop-loss defined? Level noted in writing before entry.

Risk calculated? 1–2% of account max.

R/R ≥ 1:2? Only trade asymmetric setups.

Setup conditions met? Not "gut feeling".

Strongest counter-argument considered? Pre-mortem analysis.

Emotionally neutral? No frustration, no euphoria.

Daily loss limit still open? Not after 2 losses.

Exit plan in place? When profit, when loss?

The Kelly formula assumes stationary probabilities — real markets are not. Half-Kelly as a safety margin. Not investment advice; only deploy capital you can afford to lose.