Fixed-fractional sizing

Definition

Fixed-fractional sizing risks a constant fraction of current account equity on each position: position size = (equity × risk fraction) ÷ per-unit risk (the distance to the stop or the structure’s defined maximum loss). It is the platform’s default sizing rule — simple, self-scaling (size shrinks in drawdowns, grows in gains), and the denominator that makes every strategy’s stop distance meaningful.

How it works / structure

• Formula: units = (E × f) / R, where E = current equity, f = risk fraction (commonly 0.25%-2%), R = per-unit loss at the exit (stop distance × unit value for stopped positions; max loss for defined-risk options; a scenario loss for undefined-risk structures — which is where the rule gets honest or does not, see failure modes).
• Parameters (engine-executable): f, the R definition per strategy type (pinned — stop-based, structure-max, or scenario-based), equity mark convention (closed vs total), and per-position + aggregate caps (risk-max-drawdown-budget links f to the portfolio budget).
• Self-scaling property: consecutive losses shrink E and therefore size — geometric decay toward zero rather than ruin; the anti-martingale shape (contrast: doubling after losses, which concentrates ruin).
• What f implies: a losing streak of n trades costs approximately 1 − (1−f)^n of equity; at f = 1%, twenty straight losses cost ~18% — the arithmetic behind the platform’s default f range.

When it applies

Every position the platform sizes — this is the base rule others modify: volatility targeting scales R’s estimate (risk-volatility-targeting); Kelly reasoning bounds f from above (risk-kelly-criterion); correlation budgets cap the sum across positions (risk-correlation-exposure).

Risk profile & failure modes

• R is a model, not a bound: gaps execute beyond stops (mgmt-stop-loss), undefined-risk structures exceed their scenario loss, and correlated positions share one R event — the rule contains per-trade risk only as well as R is honest.
• f chosen by mood: fractions raised after wins and cut after losses reintroduce the variance the rule exists to remove; f is a ratified parameter, changed by decision, not drift.
• Many-small-positions illusion: twenty positions at 1% each is not 1% risk if they share a factor (port-correlation-budgets owns the aggregation).
• Equity-mark games: sizing off open-profit-inflated equity compounds into the drawdown exactly when marks revert.

Evidence & limits

Fractional sizing’s properties are arithmetic, not empirics — the geometric-decay and streak-cost formulas above are derivations. The theory literature (MacLean-Thorp-Ziemba 2011) covers fractional strategies’ growth/drawdown trade-offs rigorously under known distributions; live distributions are estimated, which is why practical f sits far below growth-optimal values (risk-kelly-criterion). No f value is evidence-blessed; the platform requires f declared and its streak arithmetic acknowledged at ratification.

Falsifiable-thesis examples

Illustrations only, not signals:

• “Strategy S at f = 0.5% will keep its worst 3-month replay drawdown under 10% this year” — falsified by the replay path.
• “Halving f from 1% to 0.5% cuts strategy S’s replay max drawdown by more than a third while keeping over half its return” — falsified by the paired replay.

Cross-references

• The ceiling above it: risk-kelly-criterion; the estimator refinements: risk-volatility-targeting, indicator-atr
• The R definitions: mgmt-stop-loss (stopped), strategy-iron-condor (defined), risk-scenario-analysis (undefined)
• Aggregation: risk-max-drawdown-budget, port-correlation-budgets