Optimal size, and why you should use less
Kelly Criterion Calculator
The growth-optimal bet fraction, with the half and quarter positions most practitioners actually run.
The Kelly criterion gives the bet fraction that maximises the long-run growth rate of capital: f* = (b·p − q) ÷ b, where p is the win rate, q is 1 − p, and b is the payoff ratio. At a 45% win rate with 2:1 payoff, full Kelly is 17.5% of capital per trade. Almost no one trades that: full Kelly is optimal only when the edge is known exactly, and with an estimated edge it produces drawdowns above 50% as a routine event, which is why half- or quarter-Kelly is the practical setting.
Strategy statistics
From a sample large enough to be meaningful — hundreds of trades, not dozens
2 means the average winner is twice the average loser
Runs entirely in your browser. No inputs are transmitted or stored.
Kelly fractions
- Full Kelly
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- Half Kelly
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- Quarter Kelly
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- Expectancy per unit risked
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- Break-even win rate
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Growth-optimal only if the edge is known exactly. Negative means no edge — do not size at all.
Below this win rate, this payoff ratio loses money
Kelly is extraordinarily sensitive to the win-rate estimate. Overstating win rate by five points can double the recommended fraction, so the honest input is the lower bound of your confidence interval, not the point estimate.
The formula
f* = (b · p − q) ÷ b
p = win rate q = 1 − p
b = payoff ratio (average win ÷ average loss)
Expectancy per unit risked = b · p − q
Break-even win rate = 1 ÷ (b + 1)
Assumes a known, stationary edge and independent outcomes.- 1 Enter the win rate from a sample large enough to be statistically meaningful.
- 2 Enter the payoff ratio: average winning trade divided by average losing trade.
- 3 Read full Kelly, then look at the half and quarter figures — those are the ones to work from.
- 4 Check your win rate against the break-even figure to confirm the edge exists at all.
Why practitioners use a fraction of Kelly
Full Kelly maximises growth for a known edge, and trading edges are never known — they are estimated from a finite sample of a non-stationary process. Half-Kelly gives about 75% of the growth rate with roughly half the volatility and far shallower drawdowns; quarter-Kelly gives up more growth for a curve most people can hold through. Since the strategy that gets abandoned in a drawdown returns nothing at all, the fraction that survives is the one that compounds.
A negative Kelly is the useful answer
When f* comes out negative, the win rate and payoff ratio together have no edge — expectancy is below zero and no position size fixes that. This is the calculator’s most valuable output, because it is testable before capital is committed. Compare your win rate against the break-even figure: at 2:1 payoff you need better than 33.3%, and at 1:1 you need better than 50%.
Related tools and reading
Sources
- A New Interpretation of Information Rate — Bell System Technical Journal (AT&T Bell Laboratories)
- Good and bad properties of the Kelly criterion — L.C. MacLean, E.O. Thorp & W.T. Ziemba, 2010 author preprint (hosted by the UC Berkeley Department of Statistics)
Educational calculator. Outputs describe arithmetic under the assumptions you enter — they are not a forecast, a recommendation, or investment advice. Quantitative trading can lose money.
Frequently asked
Short answers, with the assumptions stated.
What is a realistic Kelly fraction to actually trade?
Most systematic practitioners run between a quarter and a half of full Kelly. The reasoning is not conservatism for its own sake: the inputs are estimates, and Kelly’s optimality guarantee evaporates when they are wrong in the optimistic direction — which is the direction estimation error usually points.
Can I apply Kelly across several strategies at once?
Not by computing it independently for each. Simultaneous positions interact through correlation, and summing individual Kelly fractions overstates total safe exposure — sometimes badly, since correlations rise precisely in the stressed conditions where sizing matters. Treat the single-strategy figure as a ceiling, then scale down for portfolio overlap.
How does Kelly relate to fixed-percentage risk?
They answer different questions. Kelly says what fraction of capital to expose given an edge; fixed-fractional sizing says how to translate a chosen risk budget into an order size. In practice Kelly informs the risk percentage, and the position size calculator turns that percentage into a quantity given the stop distance.
Take the number into a terminal that enforces it
Position caps, drawdown stops, and liquidation distance are limits QANTERION applies while a strategy runs — not figures you re-check by hand.