What the Kelly criterion is
The Kelly criterion is the fraction of your capital to risk on each bet that makes the account grow fastest over the long run. It was published by John Kelly at Bell Labs in 1956 and taken up by gamblers and investors who noticed that maximising the average result of a bet is not the same as maximising how fast the money compounds.
For a trade that either wins a fixed multiple of what it risks or loses the amount risked, the formula is short:
Kelly fraction = win rate − (loss rate ÷ payoff ratio)
The payoff ratio is the average win divided by the average loss. If the result is zero or negative, the strategy has no edge and Kelly says to risk nothing.
A worked example
Take the figures loaded above: a 55% win rate and winners that average 1.5 times the size of losers. Kelly is 0.55 − 0.45 ÷ 1.5 = 25% of the account per trade. Played over many trades, that compounds the account by about 4.7% per trade on average, the most any fixed fraction can achieve with these odds.
Almost nobody trades at 25% a trade, and for good reason. Half Kelly, 12.5%, keeps about 75% of that growth rate. Quarter Kelly, 6.25%, keeps about 44%. The growth you give up is modest; the drawdowns you avoid are not. At full Kelly, a string of five losses, which a 45% loss rate produces regularly, takes the account down 76%.
Push past full Kelly and growth falls while drawdowns keep rising. At twice Kelly, 50% a trade here, the expected growth rate is already below zero: a strategy with a real edge loses money because it is sized too large.
Why traders use a fraction of Kelly
- The inputs are estimates. Kelly assumes the win rate and payoff are known. A trader’s figures come from a finite sample and drift as markets change. Overestimating the edge pushes you past true Kelly, which is the expensive side to be wrong on.
- Kelly is very sensitive. In the example, a win rate of 50% instead of 55% drops Kelly from 25% to 16.7%. A few points of optimism in the win rate become a much bigger bet.
- Outcomes are not two-valued. Real trades lose more than planned when stops slip or gaps occur, and winners vary in size. Kelly for a simple win-or-lose bet understates the risk of a fat-tailed one.
- Drawdown tolerance is the real limit. Full Kelly maximises growth for someone indifferent to the ride. Most people stop trading a system long before it recovers from a 60% fall.
Kelly as a ceiling, not a target
The useful way to treat Kelly is as an upper bound. Anything above it is pure damage: more risk and less growth. Anything below it trades some growth for a smoother path. For most discretionary traders the risk-per-trade that a drawdown budget allows, typically 0.5% to 2%, sits far below even quarter Kelly, which is a sign the drawdown limit, not Kelly, is the binding constraint. The risk of ruin calculator shows what each risk level means for drawdowns, and the position size calculator turns the percentage into contracts, shares or lots.
Measure the inputs from your own closed trades rather than a backtest’s best case. The expectancy calculator gives the win rate and payoff ratio from a pasted list of results, and tells you whether the sample is large enough to trust.