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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. $\endgroup$
    – nbbo2
    Jun 13, 2020 at 18:40
  • $\begingroup$ @noob2 can you tell me whether the weight matrix is a column matrix or a row matrix? $\endgroup$ Jun 13, 2020 at 18:45
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    $\begingroup$ $w$ is $n \times 1$ that is a column vector. $\endgroup$
    – nbbo2
    Jun 13, 2020 at 18:47
  • $\begingroup$ @noob2 I was going through someone's work and i saw them use your formula with both weights bein w1. Can you help me understand what this is? $\endgroup$ Jun 28, 2021 at 6:53
  • $\begingroup$ That's the variance of portfolio 1. $\endgroup$
    – nbbo2
    Jun 28, 2021 at 13:08

1 Answer 1

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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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