Kelly Criterion Calculator
Strategy assumptions
Kelly summary
Kelly fractions are theoretical outputs from the entered binary assumptions. They are not recommended risk limits, and they are not position notionals. Full Kelly can imply aggressive risk when the estimated edge is large.
Full, half, and quarter Kelly
Each row treats the Kelly fraction as the share of current account equity lost in the modeled losing outcome. A modeled win earns that risk amount multiplied by the entered average win / average loss ratio.
| Sizing level | Risk % of equity | Risk dollars | Modeled win profit | Modeled loss | Expected arithmetic P/L | Expected log growth / trial |
|---|---|---|---|---|---|---|
| Full Kelly | 20% | $20,000 | $20,000 | -$20,000 | +$4,000 | +2.01% |
| Half Kelly | 10% | $10,000 | $10,000 | -$10,000 | +$2,000 | +1.5% |
| Quarter Kelly | 5% | $5,000 | $5,000 | -$5,000 | +$1,000 | +0.88% |
What the Kelly formula means here
This calculator uses the binary fixed-fraction form of the Kelly criterion. Let p be the probability of a win, q = 1 − p the probability of a loss, and R the average win divided by the average loss. The full-Kelly fraction is:
Break-even win rate = 1 / (1 + R)
The formula assumes the losing outcome loses one full unit of the amount put at risk and the winning outcome earns R units. Under that specific setup, full Kelly maximizes expected logarithmic wealth growth across repeated opportunities when the probabilities and payoffs are known and stable.
Why show fractional Kelly too?
Full Kelly can generate substantial drawdowns even when the model assumptions are correct. Fractional Kelly simply scales the theoretical full-Kelly fraction down. Research from Stanford notes that fractional Kelly reduces drawdown exposure at the cost of lower theoretical growth. Half and quarter Kelly are shown here as mechanical comparisons, not recommendations.
Estimation error is often the bigger problem. A backtest win rate or average payoff can be unstable, regime-dependent, overfit, or distorted by costs. The Backtest Win Rate Confidence tool can help quantify sampling uncertainty, while the Trading Losing Streak Calculator shows how clustered losses affect fixed-fraction equity.
Turn a risk fraction into an actual position separately
Kelly answers a risk-budget question in this simplified model; it does not know your entry price, stop, option maximum loss, or futures point value. If you choose to use one of the displayed risk fractions as an assumption, convert it into an instrument size separately with the Stock Position Sizing, Futures Position Sizing, or Options Position Sizing Calculator.
Model boundaries
The calculator assumes independent repeated opportunities with one constant win probability, one average winning payoff, one average losing payoff, and fixed-fraction risk applied to then-current equity. It does not model variable outcomes, fat tails, gaps beyond the planned loss, correlated trades, simultaneous positions, leverage constraints, taxes, commissions, slippage, changing market regimes, or estimation uncertainty.
Expected arithmetic P/L and expected log growth are model outputs, not forecasts. Kelly sizing is especially sensitive to overstated win rates and understated losses, so historical estimates should not be treated as known probabilities.
Method sources
- CFA Institute: The Kelly Criterion — You Don't Know the Half of It, discussing the binary win-rate/payoff-ratio Kelly formula and the importance of defining the payoff model correctly.
- Stanford: Risk-Constrained Kelly Gambling, discussing Kelly growth optimization, drawdown risk, and fractional Kelly as a lower-risk scaling approach.