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I know that the formula for covariance is

But this is for two securities. How do I find the covariance between two portfolios? more specifically between the global minimum variance (GMV) and the mean-variance efficient (MVE) portfolio.

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    $\begingroup$ In general it is $w_1^T \Sigma w_2$ where $\Sigma$ is the covariance matrix and $w_1,w_2$ the weights for the two portfolios. $\endgroup$ – noob2 Jun 13 at 18:40
  • $\begingroup$ @noob2 can you tell me whether the weight matrix is a column matrix or a row matrix? $\endgroup$ – Karmanya GB Jun 13 at 18:45
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    $\begingroup$ $w$ is $n \times 1$ that is a column vector. $\endgroup$ – noob2 Jun 13 at 18:47
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It does not matter whether you measure covariance of two portfolios or two securities, the formula is the same. Simply instead of returns and expected values for securities, put those for portfolios.

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