Position sizing and the Kelly criterion

Kelly finds the bet size that grows capital fastest over time. Bet more and growth falls; bet twice Kelly and you go nowhere. Professionals bet a fraction of it, because the edge is never known exactly.

A loss costs the full amount risked. A trade risking $1 to make $2 has a payoff of 2.

Growth by bet size

Full, half and quarter Kelly

SizingPositionGrowthChance of ever losing half

Half Kelly keeps about three quarters of the growth while cutting the chance of a 50% drawdown from about one in two to about one in eight. Drawdown odds use the continuous-time approximation.