The Kelly Criterion

advanced7 min read

The math of optimal bet sizing for growth — and why most pros use a fraction of it.

The Kelly Criterion is a famous formula that answers “how much should I bet?” to maximise long-run growth of capital, given an edge. It’s the mathematically optimal position size for compounding — and understanding why pros use only a fraction of it is the real lesson.

Kelly’s insight: there’s a single, optimal bet size that maximises long-term wealth growth — bet more than it and you take on ruinous risk that lowers growth; bet less and you grow too slowly. Bigger edge → bet more; bigger potential loss → bet less. But here’s the crucial practical truth: **almost no serious investor bets full Kelly — they use a fraction (often quarter- or half-Kelly).* Why? Full Kelly is brutally volatile, producing gut-wrenching drawdowns most humans can’t survive emotionally, and it assumes you know your edge precisely — but in markets your edge is estimated and uncertain, and over-estimating it (easy to do) pushes you past optimal into the ruin zone. Since betting too much is far more dangerous than betting too little (the curve is asymmetric — over-betting destroys you, under-betting just slows you), fractional Kelly buys a huge* reduction in volatility for only a small sacrifice in growth. The deep lesson: even the “optimal” size must be cut down to respect uncertainty and human psychology. Optimal-on-paper is reckless in practice.

What it is — the bet size that maximises long-run capital growth given your edge (more edge → bet more; more risk → bet less).
Asymmetric danger — over-betting past Kelly destroys growth and risks ruin; under-betting merely slows you.
Why fractional — full Kelly is wildly volatile, and real edges are uncertain (over-estimating pushes you into the ruin zone).
The practice — most use quarter/half-Kelly: far less volatility for a small growth sacrifice.

ExampleKelly might say “bet 20% of capital per trade” given your estimated edge. But if your edge estimate is even slightly too optimistic, 20% courts ruin in a losing streak — and the drawdowns are stomach-churning. A half-Kelly 10% (or quarter-Kelly 5%) sacrifices only a little long-run growth while dramatically cutting volatility and the chance of catastrophe — which is why the pros bet fractions.

Key takeawayThe Kelly Criterion gives the bet size that maximises long-run growth (more edge → bet more; more risk → bet less). But over-betting risks ruin while under-betting only slows you, and real edges are uncertain — so pros use fractional Kelly (quarter/half), trading a tiny growth sacrifice for far lower volatility. Even “optimal” must be cut for uncertainty.

FAQs

Should I use the Kelly Criterion to size my trades?

Use its *logic* (size scales with edge and inversely with risk) but apply a *fraction* and combine it with simpler risk rules (like the 1% rule). Full Kelly assumes a precisely-known edge you don’t have and produces drawdowns most can’t endure. Fractional Kelly, or conservative fixed-fractional sizing, captures the benefit while respecting uncertainty and your psychology.