Position Sizing: The Maths Nobody Teaches
Most traders spend their time on entries. Position size determines survival, and survival is a precondition for everything else.
Two traders take identical signals with identical accuracy. One compounds steadily, the other blows up. The difference is position size, and the mathematics behind it is unforgiving.
The recovery asymmetry
Losses and gains are not symmetric, because they compound against a shrinking base.
- Lose 10% — need 11% to recover
- Lose 25% — need 33%
- Lose 50% — need 100%
- Lose 75% — need 300%
- Lose 90% — need 900%
This is why capital preservation is not conservatism but arithmetic. Deep drawdowns are mathematically difficult to escape regardless of skill.
Fixed fractional sizing
The most widely used approach risks a fixed percentage of the account per trade — commonly 1% or 2%. The position size follows from three inputs:
Position size = (Account × Risk %) ÷ Distance to stop
The consequence is important: a wider stop produces a smaller position, and a tighter stop a larger one. Risk stays constant while position size varies. Most beginners do the reverse, keeping size constant and letting risk float with volatility.
Why 1–2%
Consider a run of losses, which will happen. At 2% risk, ten consecutive losses cost roughly 18% of the account — painful but recoverable. At 10% risk, the same streak costs 65%, which requires a near-tripling to recover from. With a 40% win rate, ten losses in a row is not a tail event; it will occur.
Position sizing is not about maximising the good case. It is about surviving the normal bad case.
Volatility adjustment
A refinement is sizing by volatility — typically using ATR — so that a volatile instrument gets a smaller position than a calm one for the same account risk. This produces more consistent risk across a portfolio than fixed percentage sizing alone.
On the Kelly criterion
Kelly gives the mathematically growth-optimal fraction. In practice it is almost never used at full size, for two reasons: it assumes you know your true edge, which you do not; and it produces drawdowns that are psychologically intolerable even when theoretically optimal. Overestimating your edge with full Kelly leads directly to ruin. Half-Kelly or less is the common compromise.
Educational content only. Not financial advice. Trading involves substantial risk of loss.
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