Risk management
The Kelly Criterion is a mathematical formula that tells you what percentage of your capital to risk on a trade, given your win rate and your average payoff ratio. It was developed by John L. Kelly Jr. at Bell Labs in 1956 and has since been adopted by gamblers, investors, and traders worldwide.
Used correctly, it maximizes long-term growth. Used incorrectly (or with bad inputs), it can blow up your account. Here is how it works and how to apply it responsibly.
f* = (bp − q) / b where:
Suppose your strategy has: win rate 55% (p = 0.55); average win $600; average loss $400; payoff ratio b = 600/400 = 1.5. Then f* = (1.5 × 0.55 − 0.45) / 1.5 = (0.825 − 0.45) / 1.5 = 0.375 / 1.5 = 0.25. The Kelly Criterion says to risk 25% of capital per trade — that is Full Kelly. Most practitioners use a fraction of this number.
Run your own numbers with the Kelly Criterion Calculator.
Full Kelly vs Half Kelly (illustrative).
| Win rate | Payoff ratio | Full Kelly | Half Kelly |
|---|---|---|---|
| 40% | 2.0 | 10.0% | 5.0% |
| 45% | 2.0 | 17.5% | 8.75% |
| 50% | 1.5 | 16.7% | 8.3% |
| 55% | 1.5 | 25.0% | 12.5% |
| 60% | 1.0 | 20.0% | 10.0% |
| 50% | 1.0 | 0.0% | 0.0% |
| 40% | 1.0 | −20.0% | Do not trade |
The last two rows matter: 50% win rate with 1:1 payoff gives Kelly of zero — no edge. 40% with 1:1 gives negative Kelly — expected loss. The formula is telling you not to trade.
Full Kelly maximizes long-term growth mathematically, but it implies extreme volatility. A full Kelly bettor can often see drawdowns of 50% or more — psychologically hard for most people and a breeding ground for panic mistakes.
Half Kelly (risking half the Kelly-recommended amount) cuts long-term growth by only about 25% but roughly halves volatility. That is why many professionals use Half Kelly or Quarter Kelly:
If in doubt, use Half Kelly. You trade a small amount of growth for a far more survivable path.
Kelly assumes you know true win rate and payoff ratio. In reality they are estimates from past data. Overestimating win rate by even a few percent can massively oversize positions — a key reason to use Half Kelly as a safety margin.
Kelly assumes each trade is independent. In real markets, correlated positions (e.g. several tech names) break that assumption — a sector selloff hits them together, which standard Kelly does not model.
Kelly ignores commissions, slippage, margin, and simultaneous positions. Frictions shrink your real edge — another reason to stay conservative.
If the formula gives a negative value, expected value is negative. Do not take the trade. Do not try to work around it.
You can use the Expectancy Calculator to confirm positive expectancy before relying on Kelly sizing.
The 1–2% rule is simpler and safer. Kelly is more optimal in theory but needs accurate inputs and discipline. For many retail traders, fixed percentage is the better default. Kelly shines for systematic traders with large samples and stable statistics.
If you are starting out, use fixed percentage risk. As your track record grows and statistics stabilize, use Kelly as a sanity check on size.
The Kelly Criterion answers “how much should I risk?” with math — but it needs honest inputs and fractional Kelly in practice. Treat it as a guide, not a mandate. With position sizing and drawdown control, it can improve long-term outcomes.
Kelly was built for binary-style bets, but you can adapt it for stocks by defining wins and losses from your stop and target: win rate (p) = share of trades that hit take-profit before stop-loss; average win (W) and loss (L) in dollars or percent from entry; payoff ratio b = W / L.
Example: 2:1 risk-reward and 45% win rate: f* = (2.0 × 0.45 − 0.55) / 2.0 = 17.5% Full Kelly; Half Kelly ≈ 8.75% of portfolio per trade. Many swing traders cap below that and use Kelly as a ceiling check.
With multiple open positions, plain Kelly can overestimate total risk. Two approaches: divide Kelly by number of positions (simple but ignores correlation); or reduce further when positions are correlated (e.g. same sector). Five correlated 2% bets can behave like one 10% bet.
It tells you what fraction of capital to risk based on your edge. Example: 55% wins and 1.5:1 payoff → Full Kelly about 25%, Half Kelly about 12.5%. It aims to grow wealth long-term while limiting ruin risk when inputs are right.
Yes for almost everyone. Full Kelly maximizes growth but causes huge drawdowns. Most pros use Half or Quarter Kelly; growth drops modestly, the ride is smoother.
At least 50, ideally 100+. Fewer trades give unreliable win rate and payoff estimates. Until then, prefer the 1–2% fixed risk rule.
Yes — same math. Crypto is more volatile with fatter tails, so estimates are less stable; prefer Quarter Kelly or lower. Also account for exchange and liquidity risk that Kelly does not model.
Negative Kelly means negative expected value — you lose over time. Do not trade that setup; improve win rate, payoff, or both until Kelly turns positive.
Use the Kelly Criterion Calculator to explore scenarios.
Educational content only. Not investment advice. Trading involves substantial risk of loss.