Position Sizing

The math of how much capital to put on each trade, given an edge.

Key Points

• Kelly is the theoretical maximum, not the practical target — fractional Kelly (0.25x–0.5x) reduces drawdowns by 50%+ at modest cost to long-term growth
• Volatility targeting keeps total portfolio risk constant: position size = (target vol) / (asset vol)
• Risk parity allocates by inverse volatility so each position contributes equal risk; less correlated with benchmark than market-cap weighting
• Anti-Kelly: when you have reason to believe your edge is overstated, halve your calculated Kelly
• Position size should scale down after a drawdown — meta-Kelly or “current equity” sizing prevents compounding losses
• The optimal f (Ralph Vince) generalizes Kelly by maximizing the geometric growth rate, accounting for the full distribution of returns

Strategies

Fractional Kelly with Volatility Targeting

Use 0.25x Kelly scaled by target vol / realized vol. Capped at 5% of capital per position.

Risk Parity Allocation

Allocate inversely to vol, with leverage set by target portfolio vol. Periodic rebalance to maintain parity.

Metrics & Formulas

• Kelly fraction: f* = (p × b − q) / b
• Optimal f (Vince): f* = argmax log(1 + n × f × (b − 1) − n × f × p) over f
• Vol-targeted size: size = (target vol) / (asset vol × price)