Position Sizing and the Risk of Ruin

Two traders can take identical signals and end the year with opposite results. The difference is almost never signal quality — it is sizing.

Drawdown mathematics

Losses compound asymmetrically. Recovering a drawdown requires a larger percentage gain than the loss itself:

Formally, recovery requires $g = \frac{d}{1-d}$ for a drawdown fraction $d$. The curve is gentle until roughly 20% and brutal after 30% — which is why professional risk limits cluster well below that.

Size from invalidation, not conviction

The disciplined formulation makes position size a consequence of the trade's structure:

risk_amount = account_equity × risk_per_trade
position_size = risk_amount ÷ (distance_to_invalidation × value_per_pip)

Two consequences follow immediately. A setup whose invalidation is far away gets a smaller position, not a wider stop. And "high conviction" changes nothing about size unless it changes the invalidation distance — conviction is exactly the input least supported by evidence.

Expectancy and the limits of a good system

Expectancy per trade is:

$$E = (p \times W) - ((1-p) \times L)$$

with $p$ the win rate, $W$ the average win, and $L$ the average loss. A positive $E$ is necessary but not sufficient: a positive-expectancy system sized too aggressively still fails, because the sequence of losses that any real process produces will breach your capacity to keep trading it.

Correlation is hidden concentration

Three long positions in EUR/USD, GBP/USD, and AUD/USD are largely one short-dollar position. Sizing each at "1% risk" can mean 3% on a single macro outcome. Group correlated exposure and size the group.

Practical limits

Common institutional practice — not advice, and not a guarantee:

• Fixed fractional risk per trade, typically well under 2%.
• A daily and weekly loss limit that stops trading when hit.
• A maximum aggregate risk across correlated positions.
• Size reductions during drawdown, not increases.

Key takeaways

• Drawdown recovery is non-linear; protecting the downside dominates.
• Derive size from invalidation distance, never from conviction.
• Correlated positions are one position for risk purposes.