How to use the Kelly criterion calculator
There are two tools, for the two ways a strategy can be described.
Win/loss trades is for trading with a defined risk, where each trade either hits its stop or makes some multiple of the risk:
- Enter the win probability, your win rate from a long record of comparable trades.
- Enter the payoff ratio: the average win divided by the average loss.
- Optionally enter your account balance to see the dollar risk at each fraction.
Continuous returns is for a strategy or portfolio held with leverage, described by its expected excess return and volatility. Enter both as annual figures, and optionally the risk-free rate to see total growth rates.
The Kelly formulas
Growth per bet g(f) = p × ln(1 + b × f) + (1 − p) × ln(1 − f)p is the win probability, b the payoff ratio and f the fraction of the account risked. f* maximizes g, the expected logarithmic growth per bet. If f* is zero or negative, the bet should not be taken.
Growth rate g(L) = r + L × μ − L² × σ² ÷ 2
Growth at full Kelly = r + (μ ÷ σ)² ÷ 2μ is the expected annual return above the risk-free rate r, and σ the annual volatility. μ ÷ σ is the Sharpe ratio, so the best achievable excess growth is half the Sharpe ratio squared.
The calculator reports growth as the median result per trade, eg − 1, which is what a typical account experiences, rather than the average result, which is pulled up by a few lucky sequences.
A worked example
Trades with a set risk. A system wins 45% of the time, and its winners average 2 times its losers. The Kelly fraction is 0.45 − 0.55 ÷ 2 = 17.50%. On a $50,000 account that is $8,750 at risk on every trade, an aggressive figure for most traders. Full Kelly grows the account by a median +2.967% per trade; half Kelly (8.75%) still gives +2.246%, which is 76% of the full-Kelly growth.
A leveraged strategy. A strategy expects 6% a year above cash with 18% volatility. Kelly leverage is 1.85×, growing at 9.56% a year including the 4% risk-free rate, but with 33.3% volatility. Half Kelly at 0.93× grows at 8.17% with half the swings.
Why betting more than Kelly backfires
The growth curve under the first tool rises to a peak at the Kelly fraction and then falls. Past the peak, each extra percent of risk adds less expected gain than it costs in volatility drag, because a loss of x% needs a gain of more than x% to recover.
For the example system, growth returns to zero at a fraction of 35.57%, which is 2.03 times Kelly. Above that, the account shrinks in the long run although each trade still has an edge of $0.35 per dollar risked. In the continuous model the crossing point is exactly twice Kelly: at twice the Kelly leverage, growth falls back to 4.00%, the risk-free rate.
Over-betting is the more dangerous mistake. Betting half of Kelly costs a quarter of the growth; betting twice Kelly costs all of it.
Estimation error and fractional Kelly
The Kelly formula assumes you know p and b. You do not: they come from a finite sample, and they drift as markets change. Kelly is also very sensitive to them. If the example system’s true win rate were 40% rather than 45%, Kelly would be 10.00%, and betting 17.50% would be 1.75 times the true optimum. If it were 50%, Kelly would be 25.00%. Five points either way moves the answer from 10.00% to 25.00%.
Fractional Kelly is the standard response. The trade-off in the continuous model is clean:
| Bet size | Excess growth kept | Volatility | Chance of ever halving |
|---|---|---|---|
| Full Kelly | 100% | 33.3% | 50.0% |
| Half Kelly | 75% | 16.7% | 12.5% |
The chance of ever falling to half your current wealth is 0.5(2/c − 1) for a fraction c of Kelly. At full Kelly it is 50% whatever the strategy, which is why full-Kelly equity curves are hard to live with even when the edge is real.
Kelly in practice for traders
- Kelly sizes the risk, not the position. In the win/loss tool, f is the share of the account lost if the stop is hit. Use the position size calculator to turn that risk into shares or lots.
- Treat Kelly as a ceiling. Many traders risk a quarter of Kelly or less, especially for new strategies with short records.
- Correlated positions share one Kelly budget. Several trades on related markets behave like one larger bet.
- Recalculate as the record grows. A longer record narrows the uncertainty in p and b, and the Kelly fraction with it.
What this calculator does not include
The win/loss model assumes every win is b times the risk and every loss is exactly the risk, with independent trades. The continuous model assumes normally distributed returns, constant volatility and borrowing at the risk-free rate; fat tails and volatility spikes make real drawdowns deeper. Neither model includes trading costs unless your inputs already reflect them. The risk of ruin calculator shows the drawdowns a given risk per trade produces.