Kelly Criterion Calculator

Category: Risk Management

Optimize your position sizes based on the Kelly Criterion formula to maximize long-term growth while managing risk

Trading Parameters

%
Your historical winning percentage
:1
Average win amount / Average loss amount
$
0.5
Lower values are more conservative (Half-Kelly = 0.5)

Kelly Criterion Results

Optimal Kelly Percentage
13.8%
of your account per trade
0% Conservative Aggressive 100%
Recommended Position Size
$690.00
Based on 0.5 Kelly (Half-Kelly)
Full Kelly Position Size
$1,380.00
Maximum theoretical optimal size
Expected Growth Rate
2.37%
Per trade at recommended size
Probability of Ruin
< 0.1%
Chance of losing all capital
Max Drawdown (95% CI)
12.5%
Expected worst-case scenario
Risk-Adjusted Return
1.85
Higher is better (> 1 is good)

Growth Simulation by Kelly Fraction

Kelly Size by Win Rate/Win-Loss Ratio

Kelly Fraction Comparison

Kelly Fraction Position Size Growth Rate Max Drawdown Risk Level

About the Kelly Criterion

The Kelly Criterion is a mathematical formula used to determine the optimal size of a series of bets or trades to maximize long-term growth. It was developed by John L. Kelly Jr. while working at Bell Labs in 1956 and has since been adopted by traders and investors to optimize position sizing.

The Kelly Formula

Kelly % = W - [(1 - W) / R]
W = Win probability (decimal)
R = Win/loss ratio (average win Ă· average loss)
Kelly % = Percentage of capital to risk on each trade

Benefits of Kelly Criterion

  • Mathematically optimal for maximizing long-term growth
  • Dynamically adjusts position size based on edge
  • Prevents over-betting which can lead to ruin
  • Provides a systematic approach to position sizing

Limitations to Consider

  • Assumes win rate and win/loss ratio are known accurately
  • Can suggest aggressive position sizes (hence the half-Kelly recommendation)
  • Doesn't account for psychological factors in trading
  • May not be suitable for all market conditions

Best Practices for Using Kelly Criterion

  1. Use a Fractional Kelly Approach: Most professional traders use 1/4 to 1/2 of the full Kelly percentage to reduce volatility while maintaining most of the growth benefits.
  2. Base Win Rate on Historical Data: Use your actual trading history rather than theoretical projections to determine your true win rate.
  3. Recalculate Regularly: Market conditions change, and so should your position sizing. Update your Kelly calculations as your trading performance evolves.
  4. Consider Correlation: If trading multiple positions simultaneously, account for correlation between trades to avoid overexposure to similar risks.
  5. Set Maximum Position Limits: Regardless of Kelly's recommendation, consider setting absolute limits on position sizes as an additional safeguard.

Position Sizing with Purpose: What Your Kelly Criterion Results Reveal

After using the Kelly Criterion calculator, you've been given a specific percentage to risk on each trade—your “Optimal Kelly Percentage”—along with recommended position sizes, projected growth rates, and other vital metrics. These aren’t just abstract numbers; they represent a data-driven foundation for smarter risk-taking. Here's how to make sense of what the calculator just told you and how to apply it effectively in your trading decisions.

Key Takeaways from Your Kelly Criterion Output

  • Optimal Kelly Percentage: This is the maximum theoretical fraction of your account to risk per trade to maximize long-term growth. If your result was 13.8%, that’s your full-Kelly figure—before any risk adjustments.
  • Recommended Position Size: Based on a more conservative “half-Kelly” approach, this value suggests how much capital to allocate per trade. For example, a $690 position from a $10,000 account reflects 0.5 of the optimal Kelly.
  • Expected Growth Rate: Expressed as a percentage per trade, this shows your compounded return potential at the recommended sizing level. The higher this number (with low risk), the stronger your edge.
  • Probability of Ruin: Often overlooked, this shows how likely it is to blow up your account over time. If this reads under 0.1%, your risk exposure is under control—mathematically speaking.
  • Max Drawdown: Even if your strategy is sound, drawdowns are inevitable. This figure reflects your likely worst-case scenario based on inputs like volatility and correlation.
  • Sharpe Ratio: A higher Sharpe suggests better risk-adjusted performance. Anything above 1 is generally solid; 1.85, for instance, signals favorable reward for each unit of risk.

Signals to Watch in Your Kelly Output

  • If Your Kelly Percentage Is High (e.g., >20%): You likely have a strong edge—but the market is rarely stable enough to support risking that much consistently. Stick with fractional sizing (e.g., 0.25x or 0.5x Kelly).
  • If Your Kelly Percentage Is Near Zero: This means your trading edge is minimal or nonexistent. It’s a prompt to re-examine your strategy, win rate, or reward-to-risk profile.
  • Unexpectedly High Drawdown: Indicates your inputs—especially volatility or correlation—may be elevating risk. Reducing your Kelly fraction can help smooth the ride.

Risk Considerations Before You Place That Trade

  • Kelly Isn't Infallible: It assumes you have accurate, stable win rates and risk/reward figures. In reality, markets fluctuate and past performance is no guarantee of future results.
  • Volatility Can Skew Everything: A market shock or unexpected event can erase the statistical edge you're relying on. Be wary of high-Kelly allocations during turbulent times.
  • Psychological Stress Is Real: Even if math says you can risk 13% per trade, most traders can’t stomach a string of losses at that level. Emotional fatigue often leads to poor decisions.
  • Correlated Trades Compound Risk: If multiple positions are positively correlated (e.g., all tied to USD strength), the effective risk is higher than it appears. The calculator adjusts for this—but only if you input correlation correctly.

Practical Tips for Using Your Results

  • Start Small: If you're new to position sizing via Kelly, begin with 0.25x or 0.5x Kelly to get a feel for it. Full Kelly is rarely used outside of controlled simulations.
  • Reassess Monthly: Win rate and win/loss ratios evolve. Update your inputs regularly to ensure your sizing adapts to your current performance.
  • Layer in Stop-Loss Controls: Kelly assumes average loss size is contained. In practice, hard stops (or mental thresholds) protect against oversized losses.
  • Cap Position Sizes: Even if the Kelly model suggests risking $3,000 on a trade, set a personal or regulatory ceiling (e.g., never more than $1,000 per position).
  • Track Metrics Over Time: Use a trading journal to compare your actual growth vs. projected Kelly-based growth. The insights can fine-tune your future risk models.

Next Steps with Your Kelly Criterion Analysis

The Kelly Criterion provides a powerful lens through which to view your trading strategy—not just in terms of profitability, but in sustainable growth. If your calculator results point to a strong edge, great—but tread carefully. Use fractional sizing, remain vigilant about your performance metrics, and adjust for volatility and correlation. If the results suggest minimal or zero edge, consider it a helpful signal to step back, reassess, and test new strategies before risking more capital.

Ultimately, the Kelly Criterion doesn’t just tell you how much to trade—it tells you whether your trading system is worth scaling at all.