The Kelly criterion: sizing positions by edge, not feel
The Kelly criterion turns an edge into a position size: stake the fraction f* = (b·p − q)/b of the capital allocated to a strategy, where p is your probability of winning, q is 1 − p, and b is the profit per $1 staked. On an event contract trading at 38¢ that your research says is worth 52¢, that comes to about 22% of the bankroll at full Kelly — aggressive enough to feel wrong, which is why most practitioners trade half Kelly, near 11%. The formula is only ever as good as the probability you put into it.
Quantreno Research · Updated July 26, 2026
The Kelly criterion is a formula for one of trading's hardest questions: how much? Given an edge and the odds on offer, Kelly tells you what fraction of your bankroll to stake so that your capital compounds as fast as mathematically possible — while never deliberately staking the whole bankroll. (That's a property of the model, not a safety guarantee: drawdowns, estimation error, and correlated losses remain very real, as we'll see.) It was published by John Kelly at Bell Labs in 1956, adopted by card counters and then by quantitative investors, and it remains the standard starting point for position-sizing everywhere edges are explicit — prediction markets most of all, because there your edge is literally a probability you can write down.
The formula
For a bet that pays out at odds b (profit per $1 staked), where your probability of winning is p and of losing is q = 1 − p:
The Kelly fraction
f* = (b·p − q) / b
f* is the fraction of bankroll to stake. The numerator (b·p − q) is your edge — expected profit per dollar; the denominator is the odds. No edge (b·p = q) → stake zero. Negative edge → the formula says don't bet, and means it.
A worked prediction-market example
Event contracts make Kelly concrete because the odds come straight from the price. A contract at 38¢ pays $1 if YES: staking 38¢ wins 62¢, so b = 62/38 ≈ 1.63. Say your research puts the true probability at 52%:
Sizing a 38¢ contract you believe is worth 52¢
| Step | Calculation | Result |
|---|---|---|
| Odds b | 0.62 / 0.38 | ≈ 1.63 |
| Edge b·p − q | 1.63 × 0.52 − 0.48 | ≈ 0.368 |
| Full Kelly f* | 0.368 / 1.63 | ≈ 22.5% of bankroll |
| Half Kelly | f* / 2 | ≈ 11% of bankroll |
On a $1,000 budget, full Kelly says ≈ $225 on one contract position — which should feel aggressive. It is: full Kelly assumes your 52% is exactly right. It rarely is, which is why practitioners cut it down.
Why practitioners trade fractional Kelly
Full Kelly is optimal only if your probability estimate is perfect. Overestimate your edge — the single most common failure in all of trading — and full Kelly systematically overbets, and overbetting Kelly doesn't just slow compounding, it can destroy it. The properties that matter:
- Half Kelly keeps ~75% of the growth at half the volatility. In the worked example above the share is 75.6%. Volatility scales with position size, so half the stake means half the swings — a quarter of the variance. The growth curve is flat near the top, so giving up a little theoretical growth buys a lot of smoothness and error tolerance.
- Betting more than full Kelly is strictly worse. Near 2× Kelly, expected log-growth falls back to zero — the exact point depends on the odds (about 1.985× in the example above) — and beyond it goes negative. The penalty for overconfidence is asymmetric — always round down.
- Correlated bets share one Kelly budget. Five positions that all die on the same CPI print are one bet in five costumes; sizing each independently is quiet overbetting.
This is why disciplined desks default to fractional Kelly with a hard per-trade cap. Quantreno sizes exactly this way: half Kelly on the estimated edge, capped per trade, inside a budget you set per strategy — the formula sizes, the caps constrain, and you confirm. To run the same arithmetic on your own numbers, use our Kelly criterion calculator.
Common mistakes
- Garbage in, precise out. Kelly is only as good as p. If your 52% is vibes, the output is vibes with decimals. The formula's real gift is forcing you to write a number down and defend it.
- Ignoring fees and spread. The edge that matters is net: after the exchange fee and after crossing the spread. Thin gross edges routinely go negative net.
- Kelly on the whole portfolio's behalf. Bankroll means the capital allocated to this strategy — not your net worth. Sizing against money you'd never actually risk inflates every stake.
- Re-Kellying losers into the ground. Kelly resizes as bankroll and edge change, but recomputing a stake to "win it back" after a loss with the same stale estimate is just martingale with a bibliography.
Beyond binary bets
The same logic extends to continuous instruments — for a stock or basket, the Kelly-optimal exposure is approximately expected excess return divided by variance, the object portfolio optimizers actually maximize. That is the sizing layer underneath a long/short book, where the same discipline decides how much of the capital any one pair deserves. The intuition survives the generalization: size with the edge, shrink with the uncertainty, and never bet so much that being wrong once takes you out of the game. For where sizing fits in a full workflow — research, thesis, size, review, exit — see how the Quantreno loop works or the desk terminology glossary.
Frequently asked questions
- What is the Kelly criterion formula?
- f* = (b·p − q) / b, where f* is the fraction of the bankroll to stake, p is your probability of winning, q is 1 − p, and b is the profit per $1 staked. The numerator is your edge — expected profit per dollar — and the denominator is the odds. With no edge the formula stakes zero; with a negative edge it says do not bet, and means it. On an event contract the odds come straight from the price: a contract at 38¢ that pays $1 wins 62¢ per 38¢ staked, so b ≈ 1.63.
- What is half Kelly, and why do traders use it?
- Half Kelly is staking half of what the formula says. Full Kelly is optimal only if your probability estimate is exactly right, and overestimating an edge is the most common error in trading, so the halved stake buys tolerance for that error cheaply: on the 38¢-contract example, half Kelly keeps about 76% of full Kelly's expected log-growth while halving the position size, and volatility scales with size. The growth curve is flat near its top, so giving up a little theoretical growth buys a lot of smoothness.
- Can you bet too much using the Kelly criterion?
- Yes, and the penalty is asymmetric. Staking more than full Kelly does not just slow compounding — past a point it destroys it. On the 38¢ contract with a 52% estimate, expected log-growth falls back to zero at about 1.985 times the full-Kelly stake and goes negative beyond it; the exact multiple depends on the odds. Since overestimating your own edge silently produces exactly this overbetting, the practical rule is to round down.
- What counts as your bankroll for a Kelly calculation?
- The capital you have allocated to that strategy — not your net worth, and not money you would never actually risk. Sizing against a larger notional inflates every stake by the same multiple. Correlated positions share one bankroll too: five positions that all resolve on the same CPI print are one bet in five costumes, and sizing each of them independently is quiet overbetting.
More on strategy and sizing
Examples on this page are simplified and assume the stated execution prices, fees, and settlement rules. Displayed market prices may not be executable at the size you want; fees, spreads, partial fills, and rule interpretation can eliminate an apparent edge. Market prices are not guaranteed probabilities.