Kelly Criterion
Quick definition
Kelly Criterion: The Kelly criterion is a formula that calculates the fraction of your account to risk on each trade so the account grows as fast as possible over the long run, given your win rate and the size of your wins relative to your losses. For trading it reads Kelly % = W − (1 − W) ÷ R.
The Kelly criterion is a formula for how much of your account to put at risk on each bet or trade so that the account compounds as fast as possible over many repetitions. John Kelly, a researcher at Bell Labs, published it in 1956 while working on information theory (Kelly, 1956), and Edward Thorp later carried it into blackjack and then the stock market (Kelly criterion, Wikipedia).
For traders it answers a question that position sizing rules usually skip: given the edge you actually have, what is the largest risk that still makes sense? The answer is useful mostly as a ceiling. Almost nobody who understands the Kelly criterion trades at the full size it suggests.
The Kelly Criterion Formula for Trading
The trading version uses two numbers from your record:
Kelly % = W − (1 − W) ÷ R
- W is your win rate, as a decimal.
- R is your average win divided by your average loss, the payoff ratio. If you measure trades in R-multiples, it is simply your average winner in R, since losers average about 1R.
The result is the fraction of the account to risk on each trade, meaning the amount you lose if the trade hits its stop. It is not the size of the position.
A worked example
Take a strategy that wins 40% of the time, with winners averaging 2R and losers 1R. Its expectancy is (0.40 × 2) − (0.60 × 1) = +0.2R per trade, a real edge.
Kelly % = 0.40 − 0.60 ÷ 2 = 0.40 − 0.30 = 0.10
Full Kelly says to risk 10% of the account on every trade. On a $50,000 account that is $5,000 of risk per trade, about ten times what most traders would consider normal.
| Win rate | Payoff ratio | Kelly % (risk per trade) |
|---|---|---|
| 35% | 2.0 | 2.5% |
| 40% | 2.0 | 10% |
| 50% | 1.5 | 16.7% |
| 55% | 1.0 | 10% |
| 60% | 1.0 | 20% |
| 30% | 2.0 | negative (no edge) |
The last row is the formula's most useful output. A negative Kelly percentage means the strategy has a negative expectancy, and no position size will grow the account.
How the Kelly Criterion Maximizes Growth
The formula comes from maximizing the average growth of the account per trade on a compounding basis, which is the same as maximizing the expected logarithm of wealth. Risk too little and the account grows slowly. Risk too much and the losses, which compound against a shrinking balance, start to outweigh the wins.
The curve above is the exact growth rate for the 40% win rate, 2R strategy at every risk level. Three things stand out:
- The peak is flat. Half Kelly, 5% risk, earns 76% of the maximum growth rate with half the risk. Even 2% risk keeps 37% of it.
- The far side is steep. At twice Kelly, 20% risk, the growth rate falls to almost zero. Past that, a strategy with a genuine edge loses money over time purely because of its size.
- Overbetting costs more than underbetting. Risking 5% instead of 10% gives up about a quarter of the growth. Risking 15% gives up the same amount of growth and carries far deeper drawdowns.
The Drawdowns That Come With Full Kelly
Growth rate is only half the story. The same strategy, simulated over 20,000 runs of 1,000 trades each, shows how large the typical worst drawdown gets at each size:
| Risk per trade | Share of max growth | Median worst drawdown | Chance of a 50% drawdown |
|---|---|---|---|
| 1% | 19% | 18% | essentially zero |
| 2% | 37% | 34% | 5% |
| 5% (half Kelly) | 76% | 68% | 98% |
| 10% (full Kelly) | 100% | 93% | 100% |
At full Kelly, the median run loses 93% of its peak equity at some point along the way. That path is mathematically growth-optimal and almost impossible to sit through. It is the same lesson the risk of ruin page draws from the other direction: the size that grows fastest on paper is rarely a size a person can keep trading.
Why Traders Use Fractional Kelly
Because of those drawdowns and the estimation problem, most traders who use the Kelly criterion at all use a fraction of it: half Kelly, quarter Kelly, or less. A quarter Kelly bet in the example is 2.5% risk per trade.
Fractional Kelly does three jobs:
- It absorbs estimation error. If your edge is smaller than your record suggests, a fraction of Kelly may still be at or below the true Kelly size, rather than on the steep side of the curve.
- It cuts drawdowns far more than it cuts growth. Halving the size roughly halves the swings while keeping most of the growth rate.
- It respects the ruin line you actually have. Few traders can tolerate a 50% drawdown, so the useful question is how large the risk can get before that becomes likely. For most strategies the answer sits well below full Kelly.
A practical way to use it: calculate Kelly from at least a few hundred trades on one setup, treat the result as the absolute ceiling, and then size from your risk per trade rule and your drawdown tolerance, which almost always lands far lower.
Key Takeaways
- The Kelly criterion gives the risk per trade that maximizes long-run compound growth: Kelly % = W − (1 − W) ÷ R.
- A strategy with a 40% win rate and 2R winners has a full Kelly size of 10% risk per trade.
- Growth peaks at full Kelly but falls off sharply above it, and at twice Kelly a profitable strategy barely grows.
- Full Kelly comes with drawdowns that most traders cannot survive, so half Kelly or less is the common practice.
- A negative Kelly result means the strategy has no edge, and no size will fix it.
Common Mistakes
Treating the Kelly percentage as position size. The formula outputs the share of the account you lose at your stop. A 10% Kelly result with a tight stop does not mean a position worth 10% of the account. It means a stop-out costs 10%.
Feeding it a hot streak. A win rate from 30 trades or a single good month will overstate the edge, and Kelly scales size up in proportion. Use a long sample and assume your real numbers are a little worse.
Blending setups. Kelly computed from your whole account mixes good and bad strategies into one average. Calculate it per setup, or the number describes no strategy you actually trade.
Ignoring correlation. Kelly assumes one bet at a time. Several open positions that tend to move together act like one larger bet, so per-trade Kelly sizes on each of them add up to overbetting.
Rounding up. Because overbetting hurts more than underbetting, any uncertainty should push you below the Kelly number, never above it.
How JournalX Tracks the Kelly Criterion Inputs
The Kelly criterion is only as good as the win rate and payoff you feed it, and those come from your journal. JournalX calculates your win rate, average win and average loss in R, and expectancy, and you can filter them by setup, session, or symbol so each strategy gets its own numbers instead of a blended average. With those in hand you can work out a Kelly ceiling per setup, then check your actual risk per trade from your pre-trade plans against it, and see how far below the ceiling you are really trading.
Related terms
Frequently asked questions
What is the Kelly criterion in trading?
The Kelly criterion is a sizing formula that tells you what fraction of your account to risk on each trade to maximize long-run compound growth. It uses two inputs from your trading record, your win rate and the ratio of your average win to your average loss.
What is the Kelly criterion formula?
For trading, Kelly % = W − (1 − W) ÷ R, where W is your win rate and R is your average win divided by your average loss. A strategy that wins 40% of the time with winners twice the size of its losers gives 0.40 − 0.60 ÷ 2 = 0.10, so Kelly says risk 10% of the account per trade.
Why do traders use half Kelly?
Full Kelly produces very deep drawdowns, and it assumes you know your true win rate and payoff, which you never do. Half Kelly cuts the size in half but keeps about three quarters of the growth rate, and it leaves a margin of safety if your real edge turns out smaller than your record suggests.
What does a negative Kelly percentage mean?
A negative Kelly result means the inputs describe a strategy with no edge. The win rate and payoff together produce a negative expectancy, so there is no position size that makes the account grow over time. The answer the formula gives is not to take the trade.
Is the Kelly percentage my position size?
No. In the trading version of the formula, the Kelly percentage is the share of the account you lose if the trade hits its stop, which is your risk per trade. The position size then follows from that risk and the distance to your stop.