Kelly Criterion
Definition
The Kelly Criterion is a position-sizing formula that maximises long-term geometric growth: f* = (bp − q) / b, where b is the win/loss ratio, p is win probability, and q is loss probability. Full Kelly is mathematically optimal but variance-aggressive; most retail traders use 'fractional Kelly' (1/4 or 1/2 Kelly) to reduce drawdown variance.
Formula
f^* = \frac{bp - q}{b}f* = (b × p − q) / b, where b = win/loss ratio, p = win probability, q = loss probability
In-depth: Kelly Criterion
The Kelly Criterion, developed by Bell Labs physicist John L. Kelly Jr. for analysing signal noise in long-distance telephone calls, was rapidly adopted by Edward Thorp and others for gambling and later trading applications. Kelly proved that betting f* fraction of capital on each opportunity maximises the long-term logarithm of wealth — equivalent to maximising geometric mean growth.
Basic formula (binary outcome): f* = (bp − q) / b Where: - f* = fraction of capital to risk - b = win/loss payoff ratio (avgWin / avgLoss) - p = probability of win - q = 1 − p = probability of loss