The formula
combined risk = √( r₁² + r₂² + 2 · ρ · r₁ · r₂ )
Where ρ is the correlation between the two positions. Three reference points make the whole thing legible:
| Correlation | Two 1% positions combine to |
|---|---|
| ρ = 1.0 (identical) | 2.00% |
| ρ = 0.9 | 1.95% |
| ρ = 0.5 | 1.73% |
| ρ = 0.0 (unrelated) | 1.41% |
| ρ = −1.0 (opposite) | 0.00% |
The naive sum — 2% — is only correct when the positions are the same trade. Independent positions give 1.41%, which is where the diversification benefit lives.
Where the rule quietly breaks
A trader with a strict 1% per-trade rule opens four positions: long EURUSD, long GBPUSD, long AUDUSD, short USDJPY.
Each obeys the rule. Together they are one short-dollar bet in four costumes, with correlations in the 0.7 to 0.9 range. The combined risk is close to 3.8%, not 1% and not 4% — and on the day the dollar moves, all four move together, because that is what correlation means.
No individual trade broke anything. The rule was per-trade, and the risk arrived per-account.
The last row on the calculator makes this concrete: effective number of independent bets. Two positions at ρ = 0.9 come to about 1.05 independent bets. You have the workload of two trades and the diversification of one.
Rough correlations worth knowing
Indicative, and worth checking against current data rather than trusted as constants — correlations move, and they move most in exactly the conditions where it matters:
- Currency pairs sharing a leg: EURUSD and GBPUSD often 0.8–0.9. Anything against the dollar is partly a dollar position.
- Major indices in the same session: frequently above 0.9.
- Large-cap tech names: 0.6–0.8 with each other and with the index.
- Gold and the dollar: typically negative, around −0.4 to −0.6, and unreliable.
The general rule: in a crisis, correlations move towards 1. Diversification is thinnest precisely when it is needed, which is a reason to size for the correlated case rather than the average one.
What this does not model
It handles two positions. Real books have more, and the arithmetic extends through a covariance matrix rather than a single formula.
For practical purposes, group the book into themes — long dollar, long index, long crypto beta — treat each theme as one position, and apply this to the themes. That approximation is crude and far closer to the truth than counting positions.