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Define the return combination
Portfolio return is wARA+wBRB for stated weights over one common period. This reference uses fully invested long-only weights with wB=1−wA. The variance identity itself is a second-moment relationship.
Keep the two symmetric cross terms
Expanding the squared deviation yields two identical covariance products. Their sum creates the factor two.
All dispersions and correlation describe compatible returns.
Check the original numbers
Weights 0.4/0.6, dispersions 0.2/0.1 and correlation 0.3 give 0.0064+0.0036+0.00288=0.01288. The square root gives portfolio standard deviation; it is not the sum of weighted standard deviations except in the appropriate perfect-correlation case.
Use a coherent covariance record
For two positive dispersions, correlation must lie from −1 to 1. Larger matrices need broader coherence checks; valid pairwise labels alone do not establish a valid multi-asset variance model.