Quantitative Methods & RiskPosition Sizing & Capital Allocation

Fixed-Fractional Risk & Why Size Is the Strategy

13 min read

An edge you can't survive is not an edge

You can have a genuine positive expectancy and still go broke — if you bet too big and a normal losing streak takes you to zero before the edge plays out. Position sizing is the bridge between a statistical edge and a survivable account. The most common professional approach is fixed-fractional risk: risk a fixed small percentage of current equity on every trade, so that bet size scales down as you lose and up as you grow.

Formula

Fixed-fractional position size

Units = (f · Equity) / (StopDistance · ValuePerUnit)

Heads up

The risk-of-ruin arithmetic

Even a winning strategy carries a risk of ruin that rises sharply with bet size. Risking 10% of equity per trade, an ordinary run of losing trades can cut an account in half; a few such runs and you are mathematically unable to recover. Halving the risk fraction more than halves the probability of a deep drawdown. The smaller bettor with the same edge survives; the larger one is removed from the game before the edge can work.

Risk per trade100/100 %

1/100 %1000/100 %

Risking 1.00% of equity per trade, a string of 69 consecutive full-stop losses would roughly halve the account (compounding the losses). At very small f the account is almost impossible to ruin from a losing streak; as f climbs past a few percent, a statistically ordinary run of losses becomes account-threatening. Survival is governed by f far more than by the edge.

Fixed-fractional sizing

Term

Risking a constant fraction f of current equity on every trade. Position size grows after wins and shrinks after losses, which dampens drawdowns and makes ruin from a losing streak mathematically very unlikely at small f. The trade-off is slower compounding than an aggressive fixed-dollar bet — by design.

position_size.py

python

1def position_units(equity, risk_fraction, stop_distance, value_per_unit):
2    """Size so a stop-out loses exactly risk_fraction of equity."""
3    risk_budget = risk_fraction * equity
4    loss_per_unit = stop_distance * value_per_unit
5    return risk_budget / loss_per_unit
6 
7# $50k account, risk 1%, 50-pip stop, $10/pip per standard lot
8lots = position_units(50_000, 0.01, 50, 10)
9print(f"{lots:.2f} lots")   # 1.00
10# Cut the account to $30k and re-run: size auto-scales to 0.60 lots.

The stop distance and the risk fraction together determine size — never pick a lot size first and back into a stop. Risk budget comes first; size is the consequence.

Tip

Why pros risk so little per trade

Institutional and disciplined retail traders commonly risk 0.25%–1% of equity per position, not because they lack conviction but because survival across thousands of trades demands it. The math is unforgiving: small, consistent risk lets the law of large numbers deliver your edge; large risk lets variance deliver your ruin.

Knowledge check

You have $20,000 and risk 2% per trade with a 40-pip stop on a pair worth $1/pip per micro-lot ($1 per pip per 1,000 units). How large a position does the fixed-fractional rule give?