The Kelly criterion: sizing positions by edge, not feel

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:

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%:

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. 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 proposes, the caps constrain, and you approve.

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. 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.