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Use one coherent input record
An original model has capital weights 40% and 60%, same-period standard deviations 20% and 10%, and correlation 0.3. Both weights are nonnegative and sum to one. These are hypothetical inputs, not forecasts for named assets.
Convert correlation to covariance
In decimal-return units, covariance is 0.3×0.2×0.1=0.006. In percentage-point units the same quantity is 60 percentage points squared. Keep the unit representation consistent with the squared standard deviations.
Add the three variance components
| Component | Decimal-return variance |
|---|---|
| Asset A own term | 0.4²×0.2² = 0.0064 |
| Asset B own term | 0.6²×0.1² = 0.0036 |
| Cross term | 2×0.4×0.6×0.006 = 0.00288 |
| Total | 0.01288 |
Take the square root after summing
Model standard deviation is 11.349009%. A weighted mean of asset standard deviations gives 14%, a different quantity except under the relevant perfect-correlation case. The result needs compatible inputs but does not assume a normal return distribution.