Portfolio Variance Calculator

Two-asset formula: variance is computed using the direct algebraic formula for two assets: var = w1^2 σ1^2 + w2^2 σ2^2 + 2 w1 w2 ρ12 σ1 σ2.

General method: for N assets the portfolio variance is the quadratic form w' Σ w, where w is the weights column vector and Σ is the covariance matrix. If a covariance matrix is not provided, Σ may be constructed from standard deviations and a correlation matrix by Σ_ij = ρ_ij σ_i σ_j.

Estimation from returns: when historical return series are provided the sample or population covariance matrix is estimated from the returns table. The estimator choice (sample vs population) and the annualization factor materially affect the magnitude of variance and must match how the returns were computed.

Two-asset example: w1=0.6, w2=0.4, σ1=10% (0.10), σ2=20% (0.20), ρ=0.25 → compute using the two-asset formula to get portfolio variance and standard deviation.

Matrix example: paste weights 0.2,0.3,0.5 and provide a 3x3 covariance matrix (rows separated by semicolon). The tool computes w' Σ w directly.

Estimation example: paste daily returns for three assets (rows = days). Select the sample estimator and set annualization_period=252 to obtain annualized variance and standard deviation.