Dynamic Position Sizing: Fractional Kelly and Volatility Targeting

Fixed fractional sizing ("risk 1% per trade") is a starting point, not a finished rule. It ignores that edge and volatility move. Dynamic sizing scales position size to current conditions — larger when edge is high and vol is low, smaller when the reverse holds.

The Kelly formula

Full Kelly maximizes long-run growth:

f* = (p * b - q) / b

where p is win probability, q = 1 - p, and b is the win/loss ratio. For a strategy with 55% win rate and 1.5 payoff ratio: f* = (0.55 × 1.5 − 0.45) / 1.5 = 0.25 — 25% of capital per bet.

Full Kelly is mathematically optimal for growth and psychologically untradeable: it produces drawdowns of 50%+ with regularity. A 50% drawdown requires a 100% gain to recover; most traders quit before that.

Fractional Kelly

Run a fraction of full Kelly — typically ¼ to ½. The math: half-Kelly captures 75% of the growth rate at 50% of the volatility. Quarter-Kelly captures about 44% of growth at 25% of volatility. The growth sacrifice is small; the drawdown reduction is large.

For the example above, half-Kelly is 12.5% per trade, quarter-Kelly is 6.25%. Most professional strategies run 0.25–0.5 Kelly.

Volatility targeting

Combine Kelly with a volatility target. Scale each position so its contribution to portfolio volatility is constant:

size = target_vol_per_position / asset_vol

If target risk per position is 1% daily and an asset's 20-day realized vol is 2% daily, size it to 50% of the notional you would use at 1% vol. This prevents the high-vol position from dominating the portfolio.

Use EWMA or GARCH vol estimates; a 20-day exponential weighted average tracks regime shifts faster than a simple 60-day window.

Scaling by edge confidence

Edge is not constant. Scale size by a confidence multiplier:

• Backtested, walk-forward validated edge: 1.0× base size
• Live, but edge confirmed over 100+ trades: 1.0×
• New strategy, under 30 live trades: 0.25×
• Strategy in drawdown beyond historical norm: 0.5× until recovered

The anti-martingale rule

Increase size after wins (within Kelly bounds), decrease after losses. This is the opposite of the gambler's instinct to "win it back." Concretely: after a 10% equity drawdown, cut all position sizes by 30% until equity recovers to within 5% of peak. After a 20% drawdown, cut to 50% indefinitely.

Practical implementation

Daily, compute: each strategy's recent vol, its Kelly fraction given recent win rate and payoff, and the volatility-targeted size. Cap the combined portfolio risk at 6% daily. Reallocate weekly, not per trade — per-trade resizing over-trades and increases costs.

Dynamic sizing is the difference between a strategy that compounds and the same strategy that grinds sideways. The edge is in the sizing as much as in the entry.