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Two-asset variance bridge

A 40/60 allocation with 20%/10% dispersion and correlation 0.3 has variance 0.01288.

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Keep the input record beside the calculation

The hypothetical assets use the same return period and definition. Capital weights are 0.4 and 0.6; standard deviations are 0.2 and 0.1. The assumed correlation is 0.3. No expected return or named investment is supplied.

Convert correlation first

Covariance is 0.3×0.2×0.1=0.006. The two own variance terms are 0.4²×0.2²=0.0064 and 0.6²×0.1²=0.0036. They would be the whole calculation only if covariance were zero.

Include both cross products

Variance reconciliation
TermDecimal variancePercentage points²
A own term0.006464
B own term0.003636
Cross term0.0028828.8
Sum0.01288128.8

Interpret the result

The square root is approximately 0.11349009, or 11.349009%. The 128.8 squared-unit figure is not a percentage volatility. Reversing the square-root and unit conversions reproduces the input variance.

Further references