Standard Deviation of Portfolio Calculator
Why Two Risky Assets Can Make a Less Risky Portfolio
Combining two volatile assets doesn't necessarily produce a volatile portfolio — it depends heavily on how the two move relative to each other. When assets aren't perfectly correlated, their swings partly cancel out, so a two-asset portfolio's standard deviation is usually lower than a simple weighted average of the individual standard deviations. That's the mathematical basis of diversification.
The Formula
w1 and w2 are the normalized portfolio weights, σ1 and σ2 are each asset's standard deviation, and ρ (rho) is the correlation coefficient between the two assets, ranging from -1 (perfectly opposite) to +1 (perfectly aligned).
Why Correlation Is the Key Variable
- Correlation of +1 — the assets move in lockstep; portfolio risk is simply the weighted average of the two individual risks, with no diversification benefit.
- Correlation of 0 — the assets move independently; combining them already reduces portfolio risk below the weighted average.
- Correlation below 0 — the assets tend to move in opposite directions, which can reduce portfolio risk substantially, sometimes below either individual asset's own volatility.
60/40 Portfolio: 15% and 8% Volatility, by Correlation
| Correlation | Portfolio Std Dev |
|---|---|
| -1.0 (perfectly opposite) | 5.8000% |
| -0.5 | 7.9019% |
| 0.0 (independent) | 9.5520% |
| 0.5 | 10.9563% |
| 1.0 (perfectly aligned) | 12.2000% |
At correlation 1.0, portfolio std dev (12.20%) equals the simple weighted average of 15% and 8% — there's no diversification benefit at perfect correlation.
How to Use This Calculator
- Enter Asset 1 Weight and Asset 2 Weight (as percentages or proportional values).
- Enter Asset 1 Std Deviation and Asset 2 Std Deviation as percentages.
- Enter the Correlation Coefficient between the two assets, from -1 to 1.
- Select Calculate to see the combined portfolio standard deviation.
Related Calculations
Use this result to estimate potential losses with the Value at Risk Calculator, or check single-asset volatility with the Risk Calculator.