Risk & Money ManagementKelly FormulaKelly Bet Sizing
Kelly Criterion
A formula giving the fraction of capital to risk per trade that maximises the long-run growth rate, given a known edge.
What Kelly Criterion means
Developed at Bell Labs in 1956 for signal transmission and later adopted by gamblers and investors, the Kelly criterion computes the stake fraction that maximises the expected logarithm of wealth. In its general form the fraction is f = ((b x p) - q) / b, where p is the probability of winning, q is 1 minus p, and b is the net payoff received on a win per unit risked. Betting less than f grows capital more slowly; betting more than f eventually reduces growth and then destroys it.
The mathematics is sound but its assumptions rarely hold in trading. Kelly requires an accurately known and stable probability and payoff, independent repeated bets, and the ability to size continuously without gaps. Real edges are estimated from noisy samples, and overestimating an edge means systematically over-betting, which is far more damaging than under-betting. Even a correctly specified full Kelly stake produces drawdowns exceeding 50 percent as a matter of routine, which is why half-Kelly or quarter-Kelly is the usual practical compromise.
Worked example
A system winning 55 percent of trades at a 1:1 payoff gives f = ((1 x 0.55) - 0.45) / 1 = 0.10, or 10 percent of capital per trade. Most traders apply half Kelly, taking that to 5 percent, and many take considerably less.
Related terms
- ExpectancyThe average profit or loss a system produces per trade given its win rate and its average win and loss sizes.
- Position SizingThe process of choosing how many lots to trade so that a losing trade costs a predetermined amount of capital.
- Risk Per TradeThe share of account equity a trader is prepared to lose on a single position, normally expressed as a percentage.
- Risk of RuinThe probability that an account will lose a defined portion of its capital before reaching a chosen profit objective.
- Win RateThe percentage of closed trades that finish in profit, calculated as winning trades divided by total trades.
Frequently asked questions
What does Kelly Criterion mean in forex trading?
A formula giving the fraction of capital to risk per trade that maximises the long-run growth rate, given a known edge.
How does Kelly Criterion work in practice?
The mathematics is sound but its assumptions rarely hold in trading. Kelly requires an accurately known and stable probability and payoff, independent repeated bets, and the ability to size continuously without gaps. Real edges are estimated from noisy samples, and overestimating an edge means systematically over-betting, which is far more damaging than under-betting. Even a correctly specified full Kelly stake produces drawdowns exceeding 50 percent as a matter of routine, which is why half-Kelly or quarter-Kelly is the usual practical compromise.
What is an example of Kelly Criterion?
A system winning 55 percent of trades at a 1:1 payoff gives f = ((1 x 0.55) - 0.45) / 1 = 0.10, or 10 percent of capital per trade. Most traders apply half Kelly, taking that to 5 percent, and many take considerably less.
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