Suppose your backtest shows a strategy that wins 55% of the time, and the average winner is one and a half times the average loser. The numbers look good. The question that decides whether you make money with it is a different one: how much of the account should each trade risk? The Kelly criterion is the formula that answers it from the strategy's own statistics.
This guide covers the formula, a worked example, why nobody trades at full Kelly, and how to use it as a ceiling for the position sizing rule in an automated strategy.
What the Kelly criterion is
The Kelly criterion gives the fraction of capital to risk on each bet that maximizes the long-run growth rate of the account. John Kelly derived it at Bell Labs in 1956 for a problem in information theory, and it moved quickly into gambling and then into trading. Unlike a rule of thumb such as "risk 2% per trade", it is derived from the strategy's measured edge: how often it wins and how much it wins relative to how much it loses.
The result is the sizing that grows the account fastest over many trades. That is not the same as the sizing that is safest, which is why the formula is better used as an upper bound than as a target.
The formula
For a strategy with a known win rate and a known ratio of average win to average loss:
f = (p × b − q) / b
- f is the fraction of capital to risk on the trade.
- p is the probability of a win, the strategy's win rate.
- q is the probability of a loss, which is 1 − p.
- b is the payoff ratio: average winning trade divided by average losing trade.
Take the strategy from the opening. The win rate is 0.55, so q is 0.45, and b is 1.5. Then f = (0.55 × 1.5 − 0.45) / 1.5 = 0.25. Full Kelly says risk 25% of the account on every trade. Almost no one does that, for the reasons below.
If the formula comes out at zero or below, the strategy has no edge at the measured win rate and payoff ratio. No position size fixes that.
Why full Kelly is too much
- The inputs are estimates. The backtest's win rate is not the true win rate. A few percentage points of error in p moves the Kelly fraction a long way, and the error is usually in the optimistic direction, because the backtest did not include every cost and every bad fill.
- Trades are not independent. The formula assumes each bet is unrelated to the last. Positions in correlated instruments, or several trades open in the same market regime, behave like one larger bet.
- The drawdowns are brutal. At full Kelly, long losing runs produce drawdowns of half the account or more. Few people keep following a system through that, and a system abandoned in a drawdown never gets its recovery.
Fractional Kelly fixes most of this. Risking half the Kelly fraction gives up a modest share of the growth rate while cutting the swings substantially, because growth falls slowly as you move away from the optimum while variance falls quickly. Half Kelly is a common choice for systematic traders. Quarter Kelly is common when the statistics come from a small sample or the strategy is new.
In the example, half Kelly is 12.5% of equity at risk per trade and quarter Kelly is about 6%. Both are still large by the standards of most risk guidelines, which is the point: Kelly tells you the ceiling, and a fixed cap tells you where you actually sit under it.
Using Kelly in an automated strategy
- Take the inputs from the backtest. Win rate, average win and average loss come straight from the trade list. Profit factor divided by the win-to-loss trade ratio gives the payoff ratio if you only have aggregates.
- Apply a haircut. Shave the backtested win rate before you calculate, since the live rate is almost always lower. Ten to twenty percent off the win rate is a reasonable margin.
- Choose a fraction. Half or quarter Kelly. Compute the per-trade risk percentage.
- Cap it anyway. Put a hard ceiling on per-trade risk and on total exposure that does not move with the Kelly estimate. Many systematic traders cap per-trade risk at a few percent regardless of what the formula allows.
- Recalculate on a schedule. As live trades accumulate, recompute the inputs from the live record, not the backtest. Every fifty to one hundred trades is a sensible cadence. More often than that mostly tracks noise.
Kelly against the alternatives
- Fixed fractional (risk 1% or 2% per trade). Simple and robust. It ignores the strategy's edge, so a strong strategy is undersized and a weak one oversized. Kelly tells you which side of that you are on.
- Fixed dollar amount. Simplest of all, but it does not scale with the account, so risk per trade drifts as equity changes.
- Volatility-based sizing, such as ATR. Sizes the position so a normal move costs a set amount. This handles the instrument's volatility well but says nothing about the strategy's win rate. It combines well with Kelly: Kelly sets how much to risk, ATR sets how big a position that risk buys.
How Horizon fits
Horizon's backtest reports the win rate, profit factor, maximum drawdown and the full trade list for any strategy you describe in plain English, which are the inputs the formula needs. The sizing rule itself is part of the description, for example "risk 1% of equity per trade with a 2x ATR stop", so the position size you chose is tested in the backtest and carried unchanged into paper trading and live deployment.
If the Kelly calculation says the strategy could carry more risk than that, you can raise the rule in the description and rerun the backtest to see what it does to maximum drawdown. For the rest of the risk controls an automated strategy needs, see automated trading risk management.
Frequently asked questions
What fraction of Kelly should I use?
Half Kelly if the statistics come from a large sample and the strategy has a live track record. Quarter Kelly if either is missing. Start low; you can raise it as the live record confirms the inputs.
Can the Kelly fraction be negative?
Yes. A negative result means the strategy loses money on average at the measured win rate and payoff ratio. It should not be traded.
How often should I recalculate?
Every fifty to one hundred trades, or monthly, whichever comes first. Use the live trade record once it is large enough, and keep the backtest numbers only as a cross-check.
Does Kelly work for options?
The principle holds for any strategy with a measurable win rate and payoff ratio. With options the payoff ratio varies with the structure, so compute it from the actual trade outcomes rather than from the theoretical maximum gain and loss.
Size the trade from the strategy's own numbers
Backtest the rules, read the win rate and payoff ratio, set the per-trade risk under the Kelly ceiling and write it into the strategy. Horizon tests and runs the whole thing from a plain-English description, with no code.
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