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Kelly Criterion Calculator
Estimate the full Kelly fraction and a fractional Kelly size from win rate and payoff ratio, or from expected return and variance.
Kelly inputs
Kelly result
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Educational tools for non-US traders · not directed at US persons.
The binary Kelly fraction is f* = W - (1 - W) / R, clamped at zero when the edge is not positive. With a 60% win rate and a 2:1 payoff ratio, f* = 0.6 - 0.4 / 2 = 0.4, or 40%. Half Kelly scales that to 20%.
How it works
What Kelly sizing estimates
The Kelly criterion estimates the fraction of capital that maximizes long-run log growth under the inputs. It is a mathematical sizing model, not a trading recommendation. The result is extremely sensitive to win rate, payoff ratio, expected return and variance.
Binary formula
For a win/loss setup, with win rate W, loss rate q = 1 - W and payoff ratio R:
f* = (R × W - q) / R = W - (1 - W) / R
If the raw value is negative, the tool clamps it to zero. That means the inputs do not justify a long position under the binary Kelly model; it does not mean the model is recommending a short.
Continuous formula
For a continuous return model, this calculator uses:
f* = (mu - risk-free rate) / variance
With mu = 0.10, variance 0.04 and risk-free rate 0, the full Kelly fraction is 0.10 / 0.04 = 2.5. Because that is above 1, the page flags it as a leverage warning while still showing the raw value.
Fractional Kelly
Fractional Kelly multiplies the full Kelly result by a chosen fraction. The default is 0.5, or half Kelly. Institutions commonly use half Kelly or quarter Kelly because full Kelly can become too aggressive when the parameters are overestimated.
Worked example - binary Kelly
With W = 0.60 and R = 2, the formula is 0.60 - 0.40 / 2 = 0.40. Full Kelly is therefore 40%. At half Kelly, the displayed fractional size is 20%.
Common mistakes
- Using full Kelly with noisy inputs. If the win rate or payoff ratio is too optimistic, full Kelly becomes larger than the true Kelly fraction and drawdown or ruin risk can rise sharply.
- Ignoring the zero clamp. When
R × W <= q, the binary formula gives zero after clamping. Do not force a positive size just because the calculator has a field. - Mixing variance and volatility. The continuous formula uses variance, not standard deviation. Passing sigma instead of sigma squared makes the result wrong.
Frequently asked questions
What is the Kelly criterion?
Why does the calculator show zero Kelly?
R × W <= 1 - W, the binary Kelly formula is zero or negative. This tool clamps that to zero instead of treating it as a short signal.