Kelly Criterion Calculator

Understanding the Kelly Criterion

The Kelly Criterion is a mathematical formula developed by John L. Kelly Jr. in 1956 that tells you the optimal size for a series of bets to maximize long-term growth of your wealth. In trading, it helps determine what percentage of your account you should risk on each trade.

The Kelly Formula

Where:

• W = Win rate (probability of winning)
• R = Win/Loss ratio (Average Win ÷ Average Loss)

Alternative Formula

Where:

• p = Probability of winning
• q = Probability of losing (1 - p)
• b = Win/Loss ratio (Average Win ÷ Average Loss)

Real World Example

Let's say you have:

• Win Rate: 55%
• Average Win: $200
• Average Loss: $100
• Account Size: $10,000

Calculation:

• W = 0.55
• R = $200 / $100 = 2.0
• Kelly % = 0.55 - [(1 - 0.55) / 2] = 0.55 - 0.225 = 0.325 = 32.5%
• Amount to risk = $10,000 × 0.325 = $3,250

Why Use Half Kelly or Quarter Kelly?

While Full Kelly maximizes growth mathematically, it comes with significant volatility. Most professional traders use fractional Kelly because:

• Reduces volatility - Smoother equity curve with smaller drawdowns
• Accounts for estimation errors - Your win rate and avg win/loss are estimates, not certainties
• Provides safety margin - Protects against black swan events
• Psychological comfort - Easier to stick to the strategy during losing streaks
• Nearly optimal growth - Half Kelly gives 75% of Full Kelly growth with 50% of the volatility

Kelly Criterion Variants Comparison

• Full Kelly: Maximum growth, maximum volatility. For disciplined traders with accurate statistics.
• Half Kelly: 75% of Full Kelly growth, 50% of volatility. Recommended for most traders.
• Quarter Kelly: 50% of Full Kelly growth, 25% of volatility. For very conservative traders.

When Kelly Criterion Works Best

• You have at least 50-100 trades of historical data
• Your trading conditions remain relatively stable
• You have positive expected value (positive edge)
• You can emotionally handle the recommended position sizes
• You're trading liquid markets with consistent execution

Important Warnings

• Never use Full Kelly blindly - It assumes your statistics are perfect, which they never are
• High Kelly % = High Risk - If Kelly suggests >20%, you likely overestimated your edge
• Negative Kelly = No Edge - If Kelly is negative or zero, you don't have an edge and shouldn't trade
• Market conditions change - Recalculate Kelly regularly as markets evolve
• Not for every trade - Kelly assumes similar trades. Adjust for trade-specific factors

How to Use This Calculator

• Input your actual historical win rate from at least 30-50 trades
• Enter your true average win amount (not your best wins)
• Enter your true average loss amount (not your worst losses)
• Input your current account size
• Review the Full Kelly percentage
• Consider using Half Kelly or Quarter Kelly for safer implementation
• Recalculate monthly or after every 20-30 trades

Common Mistakes to Avoid

• Using too few trades - Need at least 30 trades for statistical relevance
• Cherry-picking data - Include all trades, not just your best period
• Ignoring costs - Factor in commissions and slippage in your average win/loss
• Not adjusting for risk - Kelly assumes reinvestment; adjust if you're withdrawing profits
• Over-confidence - Start with Quarter or Half Kelly until you're confident in your statistics

The Bottom Line

The Kelly Criterion is a powerful tool for position sizing, but it's not magic. It requires:

• Honest, accurate statistics from your actual trading
• A strategy with genuine positive expected value
• The discipline to follow the system even during drawdowns
• Regular recalculation as your performance evolves
• Conservative implementation (Half or Quarter Kelly) to account for real-world uncertainty

Remember: Kelly Criterion maximizes long-term growth, not short-term profits. It will recommend larger positions when you have an edge and smaller positions (or no position) when you don't. Trust the math, but use it conservatively.