Kelly Criterion Calculator
The Kelly Criterion is a mathematical formula used to determine the optimal size of a series of bets. In quantitative finance, it is used to maximize the long-term growth rate of a portfolio while preventing the risk of ruin.
The historical win rate of your strategy.
Average winner divided by average loser (e.g. risking $100 to make $150 = 1.5).
Optimal Kelly Fraction
Risk this percentage of your portfolio to maximize compound growth. Do not take this trade. The edge is negative or insufficient.
Half-Kelly Recommendation:
Most practitioners use "Half-Kelly" to account for variance and estimation errors in win probability.
The Dangers of Overbetting
The Kelly formula is aggressive. It assumes you know your exact probability of winning (p) and your exact payout (b). In financial markets, these parameters are never known with certainty; they are estimates derived from historical backtesting or Monte Carlo simulations.
If you overestimate your edge and bet more than the Kelly fraction, you enter the zone of overbetting. In this zone, your volatility increases dramatically, but your expected compound growth rate actually decreases. If you bet more than double the Kelly fraction, your expected long-term growth rate becomes negative, and ruin is mathematically guaranteed.
This is why quantitative funds often use "Half-Kelly" or "Fractional Kelly." By cutting the optimal size in half, you sacrifice about 25% of the theoretical maximum growth rate, but you reduce variance (drawdowns) by 50%. You can visualize these drawdowns using our Drawdown Analyzer.
Cross-Asset Applications
Kelly sizing isn't just for single trades. It forms the mathematical basis for optimal portfolio growth. When combined with Asset Correlation analysis, the Continuous Kelly formula allows multi-strategy funds to allocate capital across dozens of uncorrelated algorithmic models, balancing risk-adjusted return (measured by the Sharpe Ratio) against the risk of simultaneous drawdowns.
Common Mistakes
- Assuming normal distributions: Financial returns exhibit fat tails. If your worst-case loss is actually much larger than your historical average loser, Kelly will over-allocate. Always stress-test with Value at Risk (VaR).
- Ignoring simultaneous bets: The basic formula assumes sequential betting. If you hold 10 positions simultaneously, you must use the multi-asset Kelly formula, which accounts for covariance.
- Static probabilities: AI models trained on past regimes often suffer from overfitting, leading to inflated win probabilities in backtesting that fail in live trading.