Two-asset portfolio variance

Calculation contract

v_p = w1^2*v1 + 2*w1*w2*c12 + w2^2*v2; sigma_p = sqrt(v_p)

Method and interpretation

The cross term is essential. Adding weighted standalone variances while ignoring covariance changes the model rather than simplifying the same calculation. With default weights 0.6/0.4, the variance is 0.01888; its square root is approximately 0.1374045.

No annualization is hidden in the engine. Annual covariance produces annual volatility; period covariance produces period volatility. Inputs labelled percentages must first be converted to decimals, and covariance scales with the square of that conversion.

Where the reference stops

The matrix summarizes second moments, not tail loss or liquidity. Shorting, derivatives, nonlinear exposure and cash flows are outside this two-asset card. Symmetry and positive semidefiniteness are mathematical admission checks, not evidence that an estimate is economically reliable.

Published synthetic inputs

{
  "weights": [
    0.6,
    0.4
  ],
  "covariance": [
    [
      0.04,
      0.006
    ],
    [
      0.006,
      0.01
    ]
  ]
}

Frozen calculation output

{
  "variance": 0.01888,
  "volatility": 0.13740451229854134
}

Two aligned long-only weights and a same-frequency covariance matrix. No additional annualization is applied.

Verification coverage

• Direct quadratic form, zero weights and perfectly offsetting covariance checked.
• Order consistency, weight sums and PSD bounds validated.

Unit and independent-reference checks test arithmetic and rejection rules, not future investment performance.

Method references

• MOSEK: portfolio variance and allocation constraints

Read the assumptions in context