ARMFKelly criterion
The Kelly criterion gives the share of capital at which long-term growth is at its maximum. The formula was derived for bets with known probabilities — and in trading they are not known but estimated. Hence the practical consequence: full Kelly is almost never used, but the value itself is useful as an upper bound of sensible risk.
The Kelly formula for trading
f = (win rate × R/R − (1 − win rate)) ÷ R/R
The numerator is that same expectancy in units of risk. Dividing by the ratio converts it into a share of capital. For a system with a win rate of 45 % and a ratio of 1 : 2 you get f = (0.45 × 2 − 0.55) ÷ 2 = 0.175, that is 17.5 % of capital per trade.
| Win rate | R/R | Full Kelly | Half | A quarter |
|---|---|---|---|---|
| 40 % | 1 : 2 | 10.0 % | 5.0 % | 2.5 % |
| 45 % | 1 : 2 | 17.5 % | 8.8 % | 4.4 % |
| 50 % | 1 : 2 | 25.0 % | 12.5 % | 6.3 % |
| 35 % | 1 : 3 | 13.3 % | 6.7 % | 3.3 % |
| 60 % | 1 : 1 | 20.0 % | 10.0 % | 5.0 % |
| 33 % | 1 : 2 | 0.0 % | 0.0 % | 0.0 % |
The last row is telling: at a win rate of 33 % and a ratio of 1 : 2 the formula gives zero — that is exactly a break-even system, and the optimal bet in it is nil. At a win rate below break-even the result is negative, which means «there is nothing to bet».
Why nobody trades full Kelly
The numbers in the first column of the table are from 10 to 25 % of capital per trade. That is ten to twenty times more than the usual risk per trade, and there are three reasons for it, each sufficient on its own.
Kelly requires an exact win rate. A real win rate is an estimate from a sample with an error of a few percentage points, and the formula is sensitive to that error: overestimating the win rate by 5 points pushes the share into the zone where growth turns negative.
the main reasonEven with correct probabilities the path passes through drawdowns of tens of percent. The formula maximises growth, not comfort: it knows nothing about the fact that trading can be abandoned.
the behavioural limitThe formula assumes two outcomes: a win of a fixed size or a loss of the stake. Real trades are closed partially, by a trailing stop, with slippage — the distribution is wider and the optimal share is lower.
the model is simplifiedA property of the growth curve. The function of capital growth by risk share is asymmetric: to the left of the optimum it declines gently, to the right sharply. A bet half the size of Kelly gives about three quarters of the maximum growth, while a bet twice the size gives negative growth. That is why erring on the smaller side is safer.
How the Kelly criterion is used on a forex account
Not as a way to set the risk but as a reference and as a check.
- As an upper bound
- If your usual risk per trade exceeds a quarter of Kelly, it is worth stopping and re-checking the win rate estimate: the formula is already saying the bet is aggressive even with perfect knowledge of the probabilities.
- As an indicator of system quality
- A negative or near-zero Kelly means there is no edge. That is the same conclusion expectancy gives, but in the form of «how much to bet» — sometimes more convincing.
- As an argument against raising the bet after a winning streak
- Kelly depends only on the win rate and the ratio, not on the latest results. A run of wins does not increase the optimal share.
Practical risk values — 0.5–2 % per trade — are usually between a fifth and a twentieth of full Kelly. Such a share barely reduces long-term growth but radically reduces drawdowns and makes the result resilient to an error in the win rate estimate.
What happens to a forex account at different fractions of Kelly
The growth curve is asymmetric, and that is easier to see in a table. The calculation is for a system with a win rate of 45 % and a ratio of 1 : 2, whose full Kelly is 17.5 % of capital.
| Fraction of Kelly | Risk per trade | Growth rate as a share of the maximum | Drawdown from a streak of 8 stops |
|---|---|---|---|
| 10 % | 1.75 % | about 19 % | −13 % |
| 25 % | 4.38 % | about 44 % | −30 % |
| 50 % | 8.75 % | about 75 % | −52 % |
| 100 % | 17.50 % | 100 % | −79 % |
| 200 % | 35.00 % | negative | −97 % |
The growth rate is the share of the maximum logarithmic growth that full Kelly gives. The drawdown is calculated for the streak of eight consecutive losses expected at a win rate of 45 %, with the risk recalculated from current equity.
Note the third row: half Kelly preserves about three quarters of the growth rate while the drawdown is noticeably softer. And the last one: doubling the optimal share gives negative growth — the capital melts away even though the edge in each individual operation stays positive.
Frequently asked questions
What is the Kelly criterion in simple words?
It is a formula that answers the question «what share of capital to bet so that the capital grows fastest over a long distance». It takes into account both the probability of a win and its size relative to the loss.
Why are half or quarter Kelly recommended?
Because of the shape of the growth curve: halving the bet preserves most of the long-term growth but noticeably reduces drawdowns and, above all, protects against an error in the win rate estimate. Exceeding Kelly, on the contrary, reduces growth very quickly.
Can Kelly be applied to forex?
With caveats. The formula assumes a binary outcome and known probabilities, while real trades give a distribution of results and an estimated win rate. That is why the value is used as an upper reference rather than as a working risk figure.
What to do if Kelly gives a negative value?
Do not trade that system. A negative Kelly is a direct consequence of negative expectancy: the optimal bet in such a game is zero, and any positive value only speeds up the loss of capital.
How is Kelly applied to a forex account in practice?
As an upper bound: work out the share from your own win rate and ratio and make sure the working risk does not exceed a quarter of it. At a win rate of 45 % and an R/R of 1 : 2 full Kelly is 17.5 %, a quarter is 4.4 %, and a practical risk of 1 % lies deep in the safe zone.
Why is 1 % taken in practice rather than 4 %?
Because the win rate is estimated from a sample and changes with the market. The buffer is needed not for caution as such but in case the real parameters turn out to be 3–5 percentage points worse than the measured ones.
Does Kelly work with partial closes?
The formula assumes two outcomes of a fixed size, so with partial exits its result becomes an approximation. It can be used as a reference, but not as an exact value.
How does Kelly relate to the drawdown limit?
It does not: the formula maximises the growth rate and knows nothing about the fact that trading can be abandoned. Drawdowns at full Kelly run into tens of percent, so the practical risk is chosen from the acceptable drawdown while Kelly serves as an upper bound.
How does half Kelly differ from the 2 % rule?
In the nature of the number. The 2 % rule is an external reference, the same for every system. Kelly is derived from your own win rate and ratio, so it shows how far your risk is from the mathematical limit.
Does Kelly have to be recalculated after every trade?
No. It is enough to review it together with the rest of the statistics — once a month or every fifty trades. Reacting to the latest results turns the formula into a source of noise.
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