Explainer, in Risk & Portfolio Construction
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.
3 questions. Published May 10, 2026. By AI Fin Hub Research.
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 textbook benchmark. When edge estimates are uncertain, practitioners typically use quarter-Kelly or less.
Negative f* is not a bet to size down. It is a no-trade signal.
Related terms
Run the numbers next
- Calculators Kelly Criterion Calculator
Size positions with full, half, quarter, or eighth Kelly and stress-test the choice with a drawdown Monte Carlo simulator. Client-side. Private by default.
- Calculators 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.
Questions people ask next
Why don't most traders use full Kelly?
Because Kelly is exact only if p and b are exact. In practice both are estimated from limited history. A 5-percentage-point error on p at full Kelly turns a growth-optimal strategy into one with a 30%+ chance of catastrophic drawdown. Half- or quarter-Kelly absorbs that estimation error at a small cost in expected growth.
Does Kelly apply to non-binary bets?
Yes. The continuous-outcome version maximizes E[log(1 + f·R)] over the bet fraction f, where R is the per-trade return distribution. For a normal-ish return with mean μ and variance σ², f* ≈ μ / σ². The binary form is a clean special case.
What if my win rate changes over time?
Then Kelly's stationarity assumption is violated and full Kelly will overbet during drawdowns. The standard fix is a rolling re-estimate of p and b plus a fractional multiplier — and a hard cap on single-bet size that's independent of the formula.
Sources
- A New Interpretation of Information Rate , Bell System Technical Journal (Kelly, 1956)
Keep the topic connected
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