Kelly Criterion
The Kelly criterion gives the bet size that maximizes the expected logarithm of bankroll over many independent trades. For a binary bet with win probability p, loss probability q = 1 − p, and win/loss ratio b, the formula is f* = (b·p − q) / b. f* greater than zero means the edge is positive; f* less than or equal to zero means there is no profitable bet to size and the answer is to skip.
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Definition
Kelly criterion
The Kelly criterion gives the bet size that maximizes the expected logarithm of bankroll over many independent trades. For a binary bet with win probability p, loss probability q = 1 − p, and win/loss ratio b, the formula is f* = (b·p − q) / b. f* greater than zero means the edge is positive; f* less than or equal to zero means there is no profitable bet to size and the answer is to skip.
Why it matters
Kelly is the upper bound of rational sizing. Any constant fraction above it is provably worse for both growth and drawdown. Most production systems sit well below it because the inputs (win rate, payoff ratio) are estimated, not known — and small errors at full Kelly produce massive overbetting.
How it works
Estimate p and b from the strategy. Compute f* = (b·p − q) / b. Apply a fractional multiplier (half, quarter, eighth) to absorb estimation error, then clamp by an absolute single-bet cap to handle edge cases like very high win rates with tiny payoffs. Re-estimate p and b as more trades arrive — Kelly assumes a stationary edge, real markets do not provide one.
Example
Crypto vol-breakout strategy
Win rate p
0.55
Win/loss ratio b
1.2
Raw Kelly f*
(1.2·0.55 − 0.45) / 1.2 = 17.5%
Quarter Kelly
0.25 × 17.5% = 4.4%
Full Kelly says bet 17.5% per trade. Quarter Kelly trims to 4.4% — same expected growth ranking, much smaller drawdown tail when p is wrong by a few points.
Key Takeaways
Full Kelly maximizes long-run growth only if p and b are exactly known. They never are.
Half Kelly cuts roughly half the volatility for about three quarters of the growth — the standard practitioner trade.
Negative f* is not a bet to size down. It is a no-trade signal.
Related Terms
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Fractional Kelly Sizer
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Position Sizing under Edge Variance
Bayesian-Kelly bet sizing when your edge is itself uncertain. Compare deterministic Kelly, Bayesian-adjusted, and conservative lower-bound versions.
FAQ
Questions people ask next
The short answers readers usually want after the first pass.
Sources & References
- A New Interpretation of Information Rate — Bell System Technical Journal (Kelly, 1956)
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