RISK MANAGEMENT
Kelly Criterion Calculator
The Kelly formula converts your win rate and average win/loss ratio into the bet size that maximizes long-run growth — and this calculator also gives you the fractional sizes traders actually use.
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THE MATH
The growth-optimal fraction
Developed at Bell Labs in 1956, the Kelly criterion answers one question: given an edge, what fraction of your bankroll maximizes the long-run growth rate of your capital?
f* = p − (1 − p) ÷ b · expectancy per $1 = p × b − (1 − p)Here p is your probability of winning and b is your average win divided by your average loss. A 55% win rate with wins 1.5× the size of losses gives f* = 0.55 − 0.45 ÷ 1.5 = 25% of the account per trade. Bet more than f* and volatility eats your growth; bet a lot more and even a winning edge goes broke. Bet less and growth is smoother but slower — half Kelly delivers about 75% of the growth with half the drawdown volatility.
If f* comes out at or below zero, the formula is telling you something more basic: with those numbers you have no positive edge, and the growth-optimal bet is nothing at all.
KELLY CRITERION CALCULATOR
LiveFULL KELLY
25%
of account per trade — see warning below
HALF KELLY
12.5%
the common practical ceiling
Assumes your win rate and payoff ratio are exact and stable — real trading stats are estimates, which is why fractional Kelly exists.
THE WARNING
Nobody should trade full Kelly
The formula is mathematically correct and practically dangerous — the standard result comes with a standard caveat that matters more than the formula.
Full Kelly assumes you know p and b exactly. You don’t — you estimate them from a limited sample of past trades, and Kelly is brutally sensitive to those estimates. Overstate your win rate by five points and “optimal” becomes over-betting, which the math punishes harder than under-betting. Real markets add fat tails, correlated positions, and regime changes the simple formula never sees, and even a true full-Kelly bettor endures drawdowns — a 50% loss of capital is expected eventually — that no trader sits through calmly.
That’s why practitioners treat f* as a ceiling, not a target. Half Kelly and quarter Kelly are the working range, and most professional traders end up at 0.5–2% per trade — fixed-fraction sizing far below their theoretical Kelly. Use the number to check whether your current risk is wildly out of line with your edge, not as an instruction.
WORKED EXAMPLE
55% win rate, 1.5:1 payoff
Your last hundred journaled trades: 55% winners, average win $300, average loss $200.
b is 300 ÷ 200 = 1.5. Full Kelly is 0.55 − 0.45 ÷ 1.5 = 25% of the account per trade — a number that should immediately feel absurd, and is: four consecutive losses at full Kelly would cost roughly 68% of the account, and a 100-trade sample isn’t nearly enough certainty about that 55%. Half Kelly is 12.5%, quarter Kelly 6.25% — still aggressive. The useful readings are the expectancy (+$0.325 per $1 risked, a genuinely strong edge) and the direction: with this edge, risking 1–2% per trade is comfortably inside the safe zone, and there’s no mathematical case for risking 10%.
FAQ
What do the inputs mean exactly?＋
Win rate is the percentage of your trades that close profitable. The win/loss ratio b is your average winning trade divided by your average losing trade (in dollars or R) — not your risk/reward on any single setup. Both should come from a real sample of trades, ideally 50 or more.
Why does the calculator show half and quarter Kelly?＋
Because full Kelly assumes your stats are exact, and they never are. Fractional Kelly trades a little theoretical growth for much smaller drawdowns and protection against estimation error: half Kelly keeps roughly 75% of the growth rate with far gentler swings. Most practitioners who use Kelly at all use a fraction.
My result says no positive edge — what does that mean?＋
With the win rate and payoff ratio you entered, the average trade loses money: p × b − (1 − p) ≤ 0. No position size fixes negative expectancy — smaller bets just lose more slowly. The fix is the strategy (better entries, better exits, lower costs), not the sizing.
Can I apply Kelly directly to my risk-per-trade percentage?＋
Only loosely. The formula models a simple binary bet with fixed odds; real trades have variable outcomes, correlation between positions, and costs. Treat the output as an upper bound and a sanity check on your fixed-fraction risk — if you risk 2% and your quarter Kelly is 6%, you have margin; if you risk 5% and full Kelly is 4%, you are over-betting a possibly imaginary edge.
Where does the Kelly criterion come from?＋
John Kelly derived it at Bell Labs in 1956 as an application of information theory. It was popularized by blackjack and convertible-bond legend Edward Thorp, who used fractional Kelly in both casinos and markets — and who is also on record warning that betting the full amount is a mistake in practice.
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OpenKelly needs honest stats. Your journal has them.
TerraTrade computes your real win rate and average win/loss from imported trades — per setup, per instrument, per session — so the numbers you feed this formula aren't guesses.
Win rate, payoff ratio, and expectancy computed from your actual fills