Kelly
Kelly
Estimate the optimal position size (Kelly) and its fractions.
Full Kelly
8.3 %
Half Kelly
4.2 %
Quarter Kelly
2.1 %
The Kelly criterion answers one specific question: what fraction of your capital, committed on every trade, would maximise long-term growth if your win rate and your average win/loss ratio stayed constant. This calculator applies the original 1956 formula to two numbers you can read straight out of a trading journal: the percentage of winning trades, and the ratio of average win to average loss.
The result is a percentage of capital. Full Kelly is a theoretical maximum and is famously aggressive: a small estimation error is enough to make it excessive, which is why the tool also shows half Kelly and quarter Kelly, the fractions many practitioners use as more conservative reference points. A negative result means the combination you entered has no statistical edge: the formula then says to risk nothing at all, not simply to risk less.
The formula
f* = W - (1 - W) / R, where W is your win rate expressed between 0 and 1 and R your ratio of average win to average loss. In plain words: your probability of winning, minus your probability of losing divided by how much a win pays relative to what a loss costs. Multiplied by 100, the result is a fraction of capital in percent. With the tool's default values, a 45% win rate and a 1.5 ratio give 0.45 - 0.55/1.5 = 8.3% full Kelly, i.e. 4.2% half Kelly and 2.1% quarter Kelly.
One example, number by number
Say a journal shows 52% winning trades, an average win of 210 and an average loss of 150. The ratio is 210 / 150 = 1.4. The formula takes W = 0.52, so 1 - W = 0.48, and 0.48 / 1.4 = 0.343. That leaves 0.52 - 0.343 = 0.177: full Kelly comes out at 17.7% of capital, half at 8.9%, quarter at 4.4%. Pause on the size of that number: 17.7% of your capital exposed on a single trade. The formula maximizes theoretical long-term growth and knows nothing about nerves or the losing streaks you actually live through, which is exactly why practitioners quote the half and the quarter rather than the full figure.
Computed reference points: three win rates, three ratios
Every value comes from the same function as the calculator above. A negative or zero result means no fraction is optimal: the combination has no edge.
| Win rate | Win/loss ratio | Full Kelly | Half Kelly | Quarter Kelly |
|---|---|---|---|---|
| 40% | 1 | -20.0% | -10.0% | -5.0% |
| 45% | 1 | -10.0% | -5.0% | -2.5% |
| 50% | 1 | 0.0% | 0.0% | 0.0% |
| 40% | 1.5 | 0.0% | 0.0% | 0.0% |
| 45% | 1.5 | 8.3% | 4.2% | 2.1% |
| 50% | 1.5 | 16.7% | 8.3% | 4.2% |
| 40% | 2 | 10.0% | 5.0% | 2.5% |
| 45% | 2 | 17.5% | 8.8% | 4.4% |
| 50% | 2 | 25.0% | 12.5% | 6.3% |
What the number does not tell you
It does not tell you that your two inputs are true: the win rate and the ratio are estimates drawn from a limited history, and the formula is brutally sensitive to them. At a 1.5 ratio, a 40% win rate gives a Kelly of 0.0% and a 50% win rate gives 16.7%: five points of estimation error swing the answer from committing nothing to very large fractions. It does not tell you what the ride feels like either: full Kelly maximizes average growth while accepting deep drawdowns along the way. And it assumes independent trades with stable statistics, which real trading never guarantees.
The classic mistake
Reading full Kelly as a size to aim for. The curve above shows why that is the wrong way round: the error is not symmetric. Staking half the Kelly keeps about 75% of the theoretical growth, staking double brings it back to almost zero, and beyond that every trade erodes capital on average. Erring low costs a little growth; erring high can cancel all of it. Since the formula's inputs are estimates, sitting exactly on the peak amounts to betting that you never err on the high side.
Frequently asked questions
Why divide Kelly by two or four?
Full Kelly assumes you know your true win rate and win/loss ratio exactly, but real figures are estimated from a limited trade history and drift over time. Overestimating your edge makes full Kelly commit too much, and committing too much damages growth faster than committing too little. Halving or quartering the fraction cuts the swings dramatically while keeping most of the theoretical growth, which is why these are the variants quoted in practice.
What does a negative Kelly mean?
It means the win rate and ratio you entered produce no statistical edge: on average, that combination loses money. In that case the formula does not suggest a smaller position, it says the optimal fraction is zero. The calculator deliberately shows the negative value instead of hiding it at zero, so the absence of an edge stays visible.
Does the Kelly criterion apply directly to trading?
The formula was derived for repeated bets with fixed, known odds and independent outcomes. Trading meets none of those conditions perfectly: statistics are estimates, market conditions change, and positions can be correlated. That is why the number is best read as a theoretical ceiling to compare against, not an instruction · this tool describes the calculation and does not recommend any position size.
How many trades does it take to estimate a win rate?
More than you would think. Over 30 trades, an observed win rate easily sits 9 points away from the true one (that is the standard deviation of a proportion measured on 30 draws); over 100 trades, still 5 points. And the formula is highly sensitive to exactly those points: the sensitivity example above fits entirely inside that error margin. A Kelly computed on a short history mostly describes the sample, not yet the strategy.
Why does growth fall back to zero around double the Kelly?
It is a property of the growth curve itself: around the peak it is almost symmetric, so the growth accumulated between zero and the optimal stake is undone roughly between the optimum and its double. With the figure's values (45% win rate, 1.5 ratio, peak at 8.3%), the exact calculation puts zero growth at a 16.8% stake, a hair above double. Beyond that, expected growth is negative: no longer a matter of caution but of arithmetic, staking even more shrinks capital on average.
See also
Monte Carlo
Replay your trading system across hundreds of randomly drawn trade sequences. See the median, best and worst outcomes and how wide the range of paths really is.
Expectancy
Work out your strategy's expectancy from win rate, average win and average loss. See what a trade returned on average, in your currency and in R multiples.
Required win rate
Work out the minimum win rate you need to break even from your average win and average loss. Free, with no sign-up, everything runs inside your browser.