Kelly criterion
Quantitative Finance glossary · Quantitative Finance
Definition
Bet-size fraction maximising expected log-wealth growth: for a single risky asset, f^* = (μ - r)/(σ^2), identical to the Merton fraction with risk-aversion γ = 1. Maximises mathbbE[ln W_T] — equivalently, the geometric mean of wealth — but is brutally aggressive: typical practical drawdowns at full Kelly are unacceptable to most investors, so practitioners use half-Kelly or fractional Kelly. Sensitive to estimation error in μ — overstating μ by 50% has more cost than under-betting by 50% (asymmetric loss in geometric growth).
Kelly criterion in plain English
The Kelly criterion answers a gambler's eternal question: given an edge, how much should I bet? Bet too little and you barely grow; bet too much and one bad streak wipes you out. Kelly finds the sweet spot that maximizes your long-run compounded growth — for an investment it works out to your edge divided by how wildly it swings, f^* = (μ - r)/(σ^2). The catch is that full Kelly is stomach-churningly aggressive, with gut-wrenching temporary losses along the way, so most pros bet half of it or less. It's also dangerously sensitive to overconfidence: overestimating your edge hurts far more than being too cautious, so betting scared is the safer mistake.
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