The Kelly criterion in trading is a formula that works out the fraction of your account to risk on each trade so that, in theory, the account grows as fast as possible over the long run. It needs only your win rate and your average win compared with your average loss. The catch is that those inputs are estimates, and full Kelly punishes any error in them hard.
Quick answer: what is the Kelly criterion in trading?
The Kelly criterion sets the share of capital to risk per trade as f* = p – q/b, where p is the win rate, q is the loss rate and b is the average win divided by the average loss. It assumes your edge is known exactly, so most traders who use it risk only a fraction of the figure, or treat it as a ceiling.
Where the Kelly formula comes from
John Kelly, a scientist at Bell Labs, published the idea in 1956 as a way to size repeated bets with a positive expected return. A CFA Institute article on the Kelly criterion sums up its appeal: it aims for the highest long-term growth, but it needs an estimate of the probabilities of each outcome in advance.
That last point matters more in trading than at a betting table. A coin’s odds are known. A method’s win rate and payoff are only measured from past trades, and they drift as markets change.
The Kelly criterion in trading: the formula
For trades with a fixed stop, where a loss costs 1R (the amount you risk) and an average win pays b times that, the formula is:
f* = p – q/b
- f*: the fraction of the account to risk to the stop, not the size of the position.
- p: the win rate, as a decimal.
- q: the loss rate, which is 1 – p.
- b: the win/loss ratio, average win divided by average loss.
The same thing can be written as (bp – q)/b. A neat cross-check: f* equals your expectancy per trade in R divided by b. If expectancy is zero or negative, Kelly says risk nothing, which is the honest answer for a method without an edge.
Worked example: a 45 percent win rate at 2:1
Example (hypothetical): a trader’s backtest of one rule set shows a 45 percent win rate, with average winners of 2R and average losers of 1R. So p is 0.45, q is 0.55 and b is 2.
Kelly gives 0.45 – (0.55 / 2) = 0.45 – 0.275 = 0.175, or 17.5 percent of the account at risk per trade. Checking it the second way: (2 x 0.45 – 0.55) / 2 = 0.35 / 2 = 0.175. The expectancy route agrees too: (0.45 x 2R) – (0.55 x 1R) = 0.35R, and 0.35 divided by 2 is 0.175.
On a £5,000 account, full Kelly means risking £875 on a single trade. Compare that with the 1 percent, or £50, many risk guides use. The table shows what ten losses in a row would do at each level, which any method with a 55 percent loss rate will meet sooner or later.
| Risk rule | Risk on first trade | Balance after 10 straight losses |
|---|---|---|
| Full Kelly (17.5 percent) | £875 | About £730 |
| Half Kelly (8.75 percent) | £437.50 | About £2,001 |
| Quarter Kelly (4.375 percent) | £218.75 | About £3,197 |
| Fixed 1 percent | £50 | About £4,522 |
Each figure assumes the risk is recalculated from the current balance after every loss. At full Kelly, ten losses leave 0.825 to the power of 10, about 14.6 percent of the account. Recovering from there needs a gain of nearly 585 percent, which is why our guide to handling a trading drawdown starts with keeping losses small.
Why traders use a fraction of Kelly
Full Kelly is the theoretical maximum for growth, not a sensible risk level. There are three practical reasons to cut it down.
Your inputs are estimates
Suppose the true win rate in the example is 40 percent, not 45. Then the correct Kelly figure is 0.40 – 0.60/2 = 0.10, and the trader risking 17.5 percent is betting 1.75 times too much. At a true win rate of one in three, Kelly is zero: there is no edge at all. A sample from a backtest you have not fooled yourself with still carries this uncertainty.
Overbetting hurts more than underbetting
In the simple model, growth falls away on both sides of the Kelly figure, but faster on the high side. For our example, risking 35 percent, twice Kelly, brings the expected long-run growth rate down to roughly zero. Half Kelly, by contrast, keeps about three quarters of the theoretical growth rate with far smaller swings.
Drawdowns are hard to live with
The CFA Institute article notes that most investors will not tolerate the volatility and drawdowns of full Kelly and reduce the allocation. Traders also face real-world costs, gaps and correlated positions that the formula ignores, and the odds of a deep hole are covered in our guide to the risk of ruin in trading.
How we use Kelly in practice
We treat Kelly as an upper boundary and a sanity check, never as a target. Our working order is:
- Measure the edge from a large sample of trades taken by one rule set, after costs.
- Calculate Kelly with a deliberately pessimistic win rate and payoff.
- Compare it with your fixed risk. If Kelly is near zero or negative, the method needs work, not a smaller stake.
- Set your actual risk using the guidance on how much to risk per trade, which for most traders is a small fraction of even quarter Kelly.
- Turn risk into a stake with our guide to calculating position size for forex, CFDs and spread bets.
Leverage changes nothing in the formula but magnifies the damage from getting it wrong. With spread bets and CFDs, a gap through a stop can lose more than the planned amount, which makes a Kelly-sized stake even more dangerous.
Common mistakes
- Using Kelly as position size. f* is the share of the account at risk to the stop, not the notional size of the trade.
- Trusting a short sample. Twenty trades cannot pin down a win rate closely enough for Kelly.
- Ignoring costs. Spread and slippage lower b, and the Kelly figure with it.
- Reading the win rate alone. As win rate vs risk:reward shows, the payoff matters just as much.
- Applying it to each open trade separately. Correlated positions add up to one larger bet.
Frequently asked questions
What is half Kelly?
Half Kelly means risking half the fraction the formula gives. In our example that is 8.75 percent rather than 17.5 percent, which is still far above the risk most retail traders use.
Can the Kelly criterion be negative?
Yes. A negative result means the inputs show a negative expectancy. The formula is telling you not to trade that method at all.
Is Kelly the same as the 1 percent rule?
No. The 1 percent rule is a fixed, conservative risk level chosen for survival. Kelly is a theoretical growth-maximising figure that depends on your measured edge and is usually much larger.
Next steps
Run the formula on your own journal with a pessimistic win rate, then compare the result with your current risk per trade. Our pillar on building a rules-based risk model shows where sizing fits alongside stops and daily limits.
A rules-based risk model is part of our price action trading course, and the basics section is free to start.
This article is for education only and is not financial advice. Trading leveraged products such as CFDs and spread bets carries a high risk of losing money.
