Advanced Math14 min read

Kelly Criterion for Trading

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.

Key Takeaways

  • • Kelly formula optimizes for long-term compounding but assumes perfect edge estimation.
  • • Full Kelly creates 30-50% drawdowns; fractional Kelly (25-50% of Kelly) balances growth and stability.
  • • Kelly <= 0? Don't trade; your win rate is too low for the risk/reward ratio.
  • • Use Kelly for asset allocation, not individual trade sizing; always cap max Kelly at 25% for safety.

The Kelly Formula

Kelly Criterion calculates the optimal percentage of capital to risk per trade to maximize compound growth over time.

The Formula

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

What Kelly Tells You

  • > 0%: You have an edge; the % tells you how much to risk for optimal growth
  • = 0%: Breakeven; no mathematical edge
  • < 0%: You don't have an edge; don't trade this setup

Worked Examples

Example 1: 55% Win Rate, 1:2 R:R

Given:

  • • Win rate: 55% (p = 0.55)
  • • Loss rate: 45% (q = 0.45)
  • • Avg Win: $200, Avg Loss: $100
  • • R:R ratio (b): 200/100 = 2.0

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

Example 2: 50% Win Rate, 2:1 R:R

Given:

  • • Win rate: 50%
  • • Loss rate: 50%
  • • R:R: 2.0

Kelly = (0.50 × 2.0) - (0.50 / 2.0)

Kelly = 1.0 - 0.25 = 0.75 = 7.5%

Example 3: 45% Win Rate, 1:1 R:R (No Edge)

Given:

  • • Win rate: 45%
  • • Loss rate: 55%
  • • R:R: 1.0

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.

Full Kelly vs Fractional Kelly

Full Kelly

  • ✓ Maximizes growth rate
  • ✗ Creates 30-50% drawdowns
  • ✗ High psychological pressure
  • ✗ Sensitive to parameter errors
  • ✗ Most traders can't handle variance

Only use if you're extremely confident in your edge and can tolerate large swings

Fractional Kelly (25-50%)

  • ✓ Retains 90%+ of growth benefit
  • ✓ Cuts drawdowns to 15-25%
  • ✓ Much easier to follow
  • ✓ Safer against estimation errors
  • ✓ Preferred by professionals

Use 25-50% Kelly for most real trading

Comparison: Growth vs Volatility

Kelly LevelAnnual ReturnMax DrawdownRealistic 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

Risks & Pitfalls

Estimating Parameters

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.

Edge Degradation

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.

Correlated Trades

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.

Implementation Guide

Step-by-Step

  1. 1. Backtest your strategy: Get 200+ sample trades, record win%, avg win, avg loss.
  2. 2. Conservative adjustment: Reduce win% by 2-5%, reduce R:R by 10% to account for overfitting.
  3. 3. Compute Kelly: Use formula to get full Kelly %.
  4. 4. Apply fractional Kelly: Use 25-50% of full Kelly for live trading.
  5. 5. Cap position size: Never risk more than 25% of account in one trade or correlated group.
  6. 6. Recompute quarterly: Update as live data accumulates; adjust down if results differ from backtest.

Example Implementation

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

Frequently Asked Questions

Does Kelly work for crypto?

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.

What if Kelly exceeds 25%?

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.

Is Kelly better than fixed percentage risk?

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.

Related Guides

Test Kelly Sizing on Your Strategies

Backtest with conservative Kelly estimates and fractional Kelly. See how your edge translates to safe, sustainable growth.