What the Kelly criterion is
The Kelly criterion is a formula that gives the share of your capital to risk on each bet or trade. It aims to maximise the long-run growth rate of capital. It was built for repeated bets where the odds and the payout are known exactly.
Traders use it to set risk per trade: the share of account equity you would lose if the stop loss is hit. It does not tell you what to trade or when, and it does not create an edge. It only sizes positions for an edge you already have. If that edge is not real, Kelly sizing makes losses bigger.
Leveraged forex and CFD trading can lose money fast. A sizing formula does not change that.
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The Kelly formula for position size
For trades with a fixed win size and a fixed loss size, the formula reads:
Kelly fraction = W − (L ÷ R)
| Term | Meaning |
|---|---|
| W | Win rate: the share of trades that end in profit |
| L | Loss rate: the share of trades that end in loss (all trades that are not wins) |
| R | Payoff ratio: average win divided by average loss |
| Kelly fraction | Share of equity to risk per trade |
How to read the result:
- Positive result: the numbers show a positive edge. The result is the risk per trade that, in theory, grows capital fastest.
- Zero or negative result: the numbers show no edge. Kelly says the correct size is nothing. No position size turns a losing system into a winning one.
The payoff ratio is the same idea as the risk-reward ratio, measured from real results rather than planned targets. The formula is closely linked to trading expectancy and the break-even win rate. If expectancy is not positive, the Kelly fraction is not positive either.
From Kelly fraction to lot size
The Kelly fraction is a share of equity at risk, not a lot size. To turn it into lots:
- Multiply account equity by the Kelly fraction (or by your chosen fraction of it). This gives the money you accept losing on the trade.
- Measure the distance from entry to stop loss in pips or points.
- Divide the money at risk by the loss per lot over that distance.
The position sizing page and the calculators handle this step.
The assumptions behind Kelly
Kelly is exact only when its conditions hold. In trading, most of them hold only roughly.
- Known probabilities. Kelly assumes you know your true win rate and payoff ratio. You only have estimates from a backtest or a trading journal, and small samples can be far from the truth.
- Stable conditions. Kelly assumes the edge stays the same. Markets change, and a strategy that worked in one period may not work in the next.
- Independent trades. Each trade should not affect the next. Correlated positions, such as several pairs that share a currency, act like a single larger bet. See correlation risk.
- Fixed outcomes. The simple formula assumes every win and every loss is the same size. Real trades vary, and gaps or slippage can make a loss larger than the stop. See gap and weekend risk.
- No costs. Spreads, commissions and swaps reduce the edge, so they reduce the correct Kelly fraction.
- Reinvestment and patience. Kelly growth is a long-run property. Over a short series of trades, results can be far from the theory.
The most serious problem is overestimating your edge. Growth falls when you risk more than the true Kelly fraction. Risk far enough above it and expected long-run growth turns negative, even with a real edge. Because estimated edges are usually too optimistic, a "full Kelly" figure from your own data is often already above the true Kelly level.
Why full Kelly is extremely volatile
Even when every assumption holds, full Kelly is a rough ride.
- Deep drawdowns are normal. At full Kelly, large falls from a peak are expected, not rare. See drawdown and maximum drawdown.
- Recovery takes long. A deep drawdown needs a much larger percentage gain to recover. The drawdown recovery calculator shows how the required gain rises as losses deepen.
- Losing streaks hurt more. At high risk per trade, an ordinary run of losses removes a large part of the account. The risk of ruin page covers this in detail.
- Psychology breaks first. Many traders abandon a method in the middle of a deep drawdown, often at the worst moment. See trading psychology.
With leverage, there is a further limit. A high Kelly fraction can push margin use close to stop-out levels. See effective leverage and avoiding margin calls.
Fractional Kelly
Fractional Kelly means risking a set share of the full Kelly figure instead of all of it. Traders do this for two reasons:
- It gives up only a small part of long-run growth, but it cuts drawdowns and the spread of outcomes by much more.
- It leaves a buffer for the case where your edge estimate is too high.
Many traders go further and treat Kelly only as an upper limit. They use a smaller fixed share of equity per trade, set by the drawdown they can live with rather than by the formula. The pages on risk per trade and fixed fractional vs fixed lot compare these approaches.
Comparing Kelly levels in the simulator
500 random runs of the same rules. This is a model of arithmetic, not a forecast: real markets have costs, slippage and streaks the model ignores.
The simulator runs a Monte Carlo model of a fixed-risk strategy. It plays many random sequences of trades with the win rate, payoff ratio and risk per trade you enter, then shows the spread of final results and the drawdowns along the way. It is a model, not a forecast.
A useful test:
- Enter your estimated win rate and payoff ratio.
- Run it with risk per trade set to the full Kelly fraction from the formula above.
- Run it again at a smaller share of full Kelly, then at a still smaller share.
- Compare the median result, the worst paths and the typical maximum drawdown.
- Lower the win rate slightly and repeat, to see what happens if your edge is overestimated.
Read the results as a range of possible paths. The simulator shows how much a sizing choice can swing; it says nothing about what your account will actually do. If the edge you enter is not real, every row of the simulation is wrong. Testing a method on a demo account is a separate step that checks how it works in live market conditions.
For a full framework, see risk management and build a personal risk plan.
Frequent questions
Is the Kelly criterion a way to make profit in trading?
No. Kelly only sizes positions for an edge you already have. It cannot create an edge, and with a wrong estimate it increases losses.
What does a negative Kelly result mean?
Your numbers show no positive edge. The formula's answer is zero size. Changing position size will not fix the system.
Why do traders use fractional Kelly instead of full Kelly?
Full Kelly produces deep drawdowns and is very sensitive to errors in the win rate and payoff ratio. A smaller share of Kelly reduces both problems at the cost of some long-run growth.
Is the Kelly fraction the same as lot size?
No. It is a share of equity at risk per trade. You convert it to lots using your stop-loss distance; see position sizing.
How much trade history do I need to estimate Kelly?
There is no fixed amount, but small samples give unreliable estimates. The fewer trades you have, the more cautious your fraction should be.
Does the simulator predict my results?
No. It is a Monte Carlo model of the inputs you give it. It shows a range of possible outcomes and drawdowns, not a forecast.