Kelly Criterion Calculator

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.