The math behind optimal position sizing. Learn when to use full Kelly, why fractional Kelly is safer, and how to implement it in your strategy.
Kelly Criterion calculates the optimal percentage of capital to risk per trade to maximize compound growth over time.
Kelly % = (p × b) - q / b
Where p = win probability, q = loss probability (1 - p), b = odds (avg win / avg loss)
Simplified: Kelly % = (Win Rate × R:R) - (1 - Win Rate) / R:R
Result is the percentage of your account to risk per trade
Given:
Kelly = (0.55 × 2.0) - (0.45 / 2.0)
Kelly = 1.10 - 0.225 = 0.875 = 8.75%
Interpretation: Risk 8.75% of account per trade for optimal growth
Given:
Kelly = (0.50 × 2.0) - (0.50 / 2.0)
Kelly = 1.0 - 0.25 = 0.75 = 7.5%
Given:
Kelly = (0.45 × 1.0) - (0.55 / 1.0)
Kelly = 0.45 - 0.55 = -0.10 = -10%
Don't trade this! Negative Kelly means you're losing money long-term.
Only use if you're extremely confident in your edge and can tolerate large swings
Use 25-50% Kelly for most real trading
| Kelly Level | Annual Return | Max Drawdown | Realistic Use |
|---|---|---|---|
| 100% Kelly (8.75%) | 45% | -42% | Very rare |
| 50% Kelly (4.375%) | 30% | -22% | Good balance |
| 25% Kelly (2.2%) | 20% | -12% | Safest, recommended |
Kelly assumes your win rate and R:R are accurate. If your backtest overestimates edge, Kelly goes too high and you risk ruin.
Solution: Use conservatively low estimates. If backtest shows 60% win rate, assume 55%. If 2:1 R:R, use 1.8:1.
Your edge changes. Market regimes shift, your system becomes crowded, or conditions change. Kelly locks in past parameters.
Solution: Recompute Kelly quarterly. If live trading shows different statistics, adjust downward.
Kelly assumes independent trades. But if you're long tech and SPY simultaneously, a crash hits both. Kelly underestimates true risk.
Solution: Apply Kelly to uncorrelated strategies separately. Never use Kelly for individual trades if you hold multiple positions.
Backtest result: 56% win, 2.0 R:R
Conservative: 52% win, 1.8 R:R
Kelly = (0.52 × 1.8) - (0.48 / 1.8) = 0.936 - 0.267 = 0.669 = 6.69%
50% Kelly = 3.34% risk per trade
25% Kelly = 1.67% risk per trade (safest)
→ Use 1.67-3.34% per trade
Yes, but use very conservative estimates. Crypto volatility is extreme, so reduce your win rate estimate by 10%, not just 2-5%. Consider 10-25% Kelly maximum for crypto.
Cap it at 25%. Very rarely do strategies have edges that large. High Kelly suggests either overfitting, survivorship bias, or unrealistic cost assumptions. Recheck your backtest.
Kelly adapts to your edge, so theoretically it's better. But fixed 1-2% risk is simpler, easier to follow, and less prone to errors. Both work; Kelly is for experienced traders comfortable with math.