Kelly Criterion: Optimal Sizing for Known Edges
The Kelly Criterion calculates the mathematically optimal position size for a known edge. But the full Kelly comes with a warning label.
What Is the Kelly Criterion?
Developed by John Kelly Jr. at Bell Labs in 1956, the Kelly Criterion answers: given your strategy's win rate and R:R ratio, what percentage of your capital maximizes long-term geometric growth? It was adopted by Ed Thorp in blackjack and options markets, then by professional traders worldwide.
The Formula
Kelly % = W − [(1 − W) / R]
W = Win rate (decimal) | R = Reward/Risk ratio
Example: 55% win rate, 1.8R average win:
Kelly = 0.55 − [0.45 / 1.8] = 0.55 − 0.25 = 0.30 (30% risk per trade)
The Full Kelly Problem
30% risk per trade is dangerous because real trading involves parameter uncertainty — win rates and R:R fluctuate. Full Kelly with slightly wrong inputs leads to overbetting and severe drawdowns that the math says should not occur but live trading routinely produces.
Half Kelly and Quarter Kelly
- Half Kelly (0.5×): Dramatically reduces volatility while capturing ~75% of theoretical growth. Most common professional application.
- Quarter Kelly (0.25×): Very conservative, minimal volatility, ideal for early-stage live trading when edge confidence is lower.
Kelly as a Strategy Ranking Tool
The most practical retail use of Kelly is not as a precise sizing calculator but as a ranking tool. A strategy with 25% Kelly output has substantially more edge than one with 10% output. This guides relative allocation across strategies — higher Kelly output = higher allocation.
Full Kelly is theoretically optimal and practically dangerous. Use it to rank your strategies and calibrate relative allocation — not as a literal sizing instruction.