TL;DR
The Kelly Criterion is the mathematically optimal position sizing formula that maximizes long-run portfolio growth — given your win rate and average win/loss ratio, it calculates exactly what fraction of capital to risk on each trade.
What Is the Kelly Criterion?
The Kelly Criterion is a position sizing formula derived by John L. Kelly Jr. at Bell Labs in 1956, originally for signal transmission theory and later applied to gambling and investment. In trading, it answers the question: given what you know about your strategy’s win rate and average win/loss ratio, what fraction of your capital should you risk on each trade to maximize the long-run growth rate of your account?
The formula produces the theoretically optimal bet size — not the one that maximizes single-trade expected value (that would be 100% of capital), but the one that maximizes the geometric growth of compound returns over many trades. Betting below Kelly is safe but leaves growth on the table; betting above Kelly actually reduces long-run wealth, even though it increases expected value per trade. The Kelly Criterion represents the precise mathematical boundary between these two outcomes.
The elegant insight of Kelly’s work is that variance matters for compound growth in a way that expected value calculations miss. A 100% win rate strategy that bets 100% of capital and occasionally loses still compounds to zero eventually — because a single loss is permanent. Kelly sizing accounts for this: as your edge degrades or your win rate drops, the optimal fraction shrinks toward zero. When edge disappears entirely (win rate at breakeven), Kelly outputs zero — bet nothing.
Key Formula / Numbers
Kelly Fraction = W - (1 - W) / R
Where:
W = Win rate (fraction of trades that are profitable)
R = Win/loss ratio (average win size / average loss size)
1-W = Loss rate
Example:
Win rate = 55% (W = 0.55)
Average win = $150, Average loss = $100
R = 150/100 = 1.5
Kelly = 0.55 - (0.45/1.5) = 0.55 - 0.30 = 0.25 = 25% of capitalKelly fraction in practice:
| Kelly Fraction | Practical Approach |
|---|---|
| Full Kelly | Theoretical maximum growth; extreme volatility |
| Half-Kelly (50%) | Most commonly recommended; good growth, tolerable drawdown |
| Quarter-Kelly (25%) | Conservative; near-optimal Sharpe; low drawdown |
How Quantzee Uses This
Kelly Criterion optimization requires accurate input data — win rate and average win/loss ratio — that can only be reliably generated from non-repainting backtest results. A backtest that uses repainting indicators will overstate win rate and the average win amount, leading to an inflated Kelly fraction and dangerous over-sizing in live trading. Quantzee’s non-repainting signals provide the clean historical data needed to calculate honest Kelly inputs: the win rate and payoff ratio you see in the Strategy Tester are the ones available in real time.
Common Mistakes
- Using full Kelly in live trading: The theoretical full-Kelly fraction often falls between 20–40% of capital — sizes that produce extreme volatility and psychological difficulty. Most professional traders use half-Kelly or quarter-Kelly, which provide most of the growth benefit with far less drawdown variance.
- Estimating Kelly inputs from too-short sample periods: Kelly fraction is highly sensitive to win rate estimates. A win rate estimated from 50 trades has a margin of error of ±7% — which can change the Kelly fraction by 30–50%. Use at minimum 200 trades for reliable Kelly estimation.
- Treating Kelly as static: As market conditions change and strategy performance evolves, Kelly inputs change. Recalculate Kelly periodically using rolling window win rate and payoff data, not just the initial backtest numbers.
Related Terms
FAQ
What does the Kelly Criterion calculate?
The Kelly Criterion calculates the optimal fraction of your capital to risk on each trade to maximize the long-run growth rate of your account — based on your historical win rate and average win/loss ratio.
Why do traders use half-Kelly instead of full Kelly?
Full Kelly is theoretically optimal but produces extreme account volatility — many traders use half-Kelly because it retains roughly 75% of the maximum growth rate while reducing variance and drawdown to psychologically manageable levels.
Can the Kelly Criterion produce a negative fraction?
Yes — when a strategy has a negative expected value (lose more than you make over time), Kelly outputs a negative fraction, meaning you should not trade the strategy at all in its current form.